SEI 4 2017

SEI Volume 27 | Number 4 | November 2017 Structural Engineering International

Yavuz Sultan Selim Bridge Turkey

STRUCTURAL ENGINEERING INTERNATIONAL

«I then design the structure down to the last details, since I believe that the quality of a structure hinges largely on these details.»

Volume 27 | Number 4 | November 2017

© Photo Credits: Photo Galery Soletanche Freyssinet / F.Vigouroux - 2017

International Association for Bridge and Structural Engineering (IABSE)

Eugène Freyssinet

IABSE

www.freyssinet.com

Recent Structures and Research Follow us on:

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Structural Engineering International International Association for Bridge and Structural Engineering

Contents Nr. 4/2017 Editorial New and on-going Challenges for Structural Engineers regarding Existing Structures; B. Godart; France

481

Scientific Papers*

Shear configuration, testing setup, pg. 502

Unified Flexural Design Method for Deep and Shallow Beams Using Non-Linear Grid Model; D. Xu, Y. Zhang, F. Xu; China, P. Gauvreau; Canada Robust Optimum Design of Tuned Mass Dampers to Mitigate Pedestrian-Induced Vibrations Using Multi-Objective Genetic Algorithms; J. F. Jiménez-Alonso, A. Sáez; Spain An Innovative Connection System for Cross-Laminated Timber Structures; A. Polastri, I. Giongo, M. Piazza; Italy Experimental Study on the Seismic Behaviour of Mortise–Tenon Joints of the Ancient Timbers; L.-k. Chen; China, USA, S.-c. Li, Y.-t. Wang, Y.-j. Zhao, M. Zhang, X.-y. Song, X.-w. Li; China, T. Wu; USA, L.-z. Jiang; China Suspension Bridge over the Zambezi in Tete—Original Stringer Bronze Bearings versus Recent Modification; J. Fonseca, C. Pinto; Portugal Seismic Behaviour of Irregular Structures; S. Chandra Dutta, P. K. Das, P. Sengupta; India Seismic Performance of Pile-Cap Connections of Prestressed High-Strength Concrete Pile with Different Details; Z. Guo, W. He, X. Bai; China, Y. Frank Chen; USA, China Negative Angle Vertical Rotating Construction Method of Reinforced Concrete Arch Bridge; W. Li, C. Huang, C. Tang; China

482

492 502

512 520 526 546 558

Technical Reports The Pearl Bridge, China, pg. 558

Case Study of the 156 m Simply Supported Steel Truss Railway Bridge; X. Yu, Y. Deng, B. Yan; China Design and Construction of Concrete Simply-Supported Guideway Beam in the Changsha Maglev Line; G. Dai, G. Chen, W. Liu; China, F. Y. Chen; USA, L. Yang; China The Glass Fibre-Reinforced Polymer–Steel Hybrid Footbridge of Saint Mateus Park, Portugal: From Conceptual Design to In Situ Assessment; M. Sá, J. Correia, A. Gomes, N. Silvestre; Portugal

563

569

575

IABSE News View of the New Yellow River Bridge, pg. 564

IABSE Conference Kuala Lumpur 2018 IABSE in Vancouver 2017 Vancouver Symposium: A Great Success!

IABSE Annual Meetings 2017 IABSE Strategy Implementation Technical Activities IABSE Conference Copenhagen 2018 IABSE Calendar of Events

581 583 584 587 588 590 591

*Peer-reviewed papers

Front Cover: Changsha Maglev Line, Changsha.

See article on pg. 570

Structural Engineering International Nr. 4/2017

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Structural Engineering International International Association for Bridge and Structural Engineering SEI: Structural Engineering International (SEI) is the leading journal of structural engineering dealing with all types of structures and materials. Articles are written by practicing engineers and academia from around the world, and reflect the highest standards. All articles are reviewed by the SEI Editorial Board, with collaboration from over 250 experts and 28 correspondents. Scientific papers that have undergone a detailed peer-review by independent experts and demonstrate a significant contribution to the state of structural engineering knowledge are marked by the peer review stamp. To recognise contributions of the highest quality, an Outstanding Paper Award is presented each year. SEI is the quarterly journal of the International Association for Bridge and Structural Engineering (IABSE).

Aims and Scope: Structural Engineering International (SEI) publishes technical reports and scientific papers with a focus on structural engineering, to bridge the gap between professionals and academics. SEI is a journal with a mix of articles ranging from practical to scientific. SEI publishes articles on recent structures, developments in practice and research. Articles in SEI consider all types of structures, bridges, buildings, offshore structures, etc., constructed from all types of building materials: concrete, steel, composites, timber, fibre reinforced polymers, glass, etc. Articles in SEI also deal with the sustainability of structures and a broad range of structural engineering practice from design to construction to maintenance and monitoring, and finally to the re-use or demolition of structures.

SEI Editorial Board Guido Morgenthal, Bauhaus-Universität Weimar, Germany (Chair) Ana Mandic Ivankovic, University of Zagreb, Croatia (Vice Chair) Elsa de Sá Caetano, University of Porto, Portugal Charles-Darwin Annan, Université Laval, Canada Flávio de Souza Barbosa, Federal University of Juiz de Fora, Brazil

Stathis Bousias, University of Patras, Greece Dongzhou Huang, Atkins, United States Adam Lubell, Read Jones Christoffersen, Canada Anastasios Sextos, University of Bristol, United Kingdom Tina Vejrum, COWI, Denmark Takashi Yamaguchi, Osaka City University, Japan

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Structural Engineering International Nr. 4/2017

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24.11.16 16:12

New and on-going Challenges for Structural Engineers regarding Existing Structures

Bruno Godart Deputy-Director of the Materials and Structures Department at IFSTTAR Marne-la-Vallée France

Considering the level of infrastructure development achieved in many developed countries, work conducted in the field of civil engineering will increasingly focus on the maintenance and repair of structures. The maintenance of existing structures will therefore become a significant challenge, whether for infrastructure managers, who will have to improve their management methods, or for companies that will have to carry out works under specific, and sometimes difficult conditions, or for the structural engineers who will have to design and plan innovative solutions. Concerning this last point, we could mention, as an example, the development of the so-called, somewhat caricatured term “stealth work sites”. This term refers to works on sites that will increasingly have to be carried out with the least possible interference to the operation of the structure, and which will require imaginative approaches in order to find solutions adapted to the severe operation constraints of certain road and railway infrastructures, particularly in urban areas.

In addition, accidental actions such as earthquakes, floods and cyclones will pose an increasing number of questions to the structural engineer, both in the design of new structures and in the dimensioning of cost-effective strengthening of existing structures. The considerable destruction that occurred on the islands of StMartin and St Barthelemy during the very recent passage of the IRMA hurricane (95% of the existing building stock was destroyed or damaged) remind us that reinforcement is necessary so that existing structures can withstand exceptional climatic events, the frequency of which is unfortunately likely to increase in the future (a displeasing fact for some climatic skeptics ...). The collapse and destruction of structures should also favor the development of forensic engineering based on all the methods and techniques applied to the investigation in order to analyze and understand the origin of the disasters, and draw lessons from them.

It seems that lessons from failures have not been drawn on sufficiently in the past and one of the solutions consists in significantly reinforcing the teaching of the pathology of structures and forensic engineering at universities and schools, teaching which appears to still be very weak in most countries.

Another challenge awaits the structural engineer in the management of existing structures. This involves the assessment and detailed evaluation of structures with specific material pathologies such as internal swelling of concrete, freeze–thaw damage, corrosion of rebar in reinforced concrete, fatigue of metal or deterioration of wood. Collaboration with material scientists will be essential to move forward on advanced models and numerical calculations that allow for safety, serviceability and durability limit state checks, and facilitate the design of reinforcements adapted to increase the lifespan of structures.

The challenge ahead is therefore to evaluate and maintain our heritage of existing buildings and civil engineering structures, while enhancing and modernizing it to make it safer and more sustainable.

Bruno Godart

Structural Engineering International Nr. 4/2017

Editorial

481

Unified Flexural Design Method for Deep and Shallow Beams Using Non-Linear Grid Model Dong Xu, Prof., Dr.; Yu Zhang, Dr., Department of Bridge Engineering, Tongji University, Shanghai, China; Fangyuan Xu, Dr., Department of Civil Engineering, Zhejiang University Ningbo Institute of Technology, Zhejiang, China; Paul Gauvreau, Prof., Department of Civil Engineering, University of Toronto, Toronto, Canada. Contact: xu_dong@tongji.edu.cn DOI: 10.2749/222137917X14881937844892

Abstract The fundamental design theory of reinforced concrete deep beams is not consistent with that of shallow beams due to non-compliance with the plane section assumption. This paper proposes a grid model that is valid for the flexural capacity prediction and reinforcement design of both shallow and deep beams, which unifies the design process and extends the sectional analysis to deep beams. The grid model is actually based on structural analysis such that stress distribution can be calculated automatically without the plane section assumption. In order to apply sectional design principles, it assumes that design of the critical section is independent of the status of other sections, which means that other sections will remain elastic when the critical section fails. As a result, by inserting the concerned section into the grid model with non-linear material constitutive relationship and failure criteria, the capacity prediction and reinforcement design on that section can be achieved. The axial grid in the grid model guides the design of the flexural reinforcement in two kinds of layouts. Two series of experiments are listed to validate the model. The results of the proposed method are also compared with other wellestablished methods, for example traditional sectional method, layered section approach and strut-and-tie model (STM) method.

Keywords: deep beams; grid model; sectional analysis; flexural capacity; reinforcement design.

Introduction Concrete beams usually can be divided into shallow beams and deep beams. According to ACI 318-11 (2011),1 members are considered to be deep beams when the span to depth ratio is ≤4 or when the shear span ratio is ≤2. Members with span to depth ratio and shear span ratio greater than these values are considered to be shallow beams.

Currently, the two most common flexural design methods of reinforced concrete deep beams are the strut-and-tie model (STM) and semi-empirical sectional analysis method. STM method is actually a kind of structural analysis with an aim to design against the suspected stress paths. The typical arch action in deep beams can be directly reflected. The failure criteria of STM Peer-reviewed by international experts and accepted for publication

by SEI Editorial Board Paper received: August 25, 2016 Paper accepted: April 15, 2017

482

Scientific Paper

include yielding of reinforcing ties, crushing of a strut, anchorage failure of reinforcing ties, and nodal failure. The compression-softening effect is usually employed to check the crushing of a strut. The use of STM for the design of deep beams is allowed by several design standards, including ACI 31811, Eurocode 2, and the AASHTO LRFD Specification.1–3 Semi-empirical sectional analysis method, in which traditional sectional analysis equations commonly used for shallow beams are modified on the basis of experimental results, are allowed by standards such as the China Concrete Structure Design Code (GB5000-2010, 2010).4 STM is based on the lower-bound method of the theory of plasticity, which requires that forces in the model be in equilibrium with the given loads and that the capacity of the members and the nodes be greater than demand.

More than one STM is usually possible for a given structure and loading.

Several design methods based on STM have been proposed so far but still without a recognized standard. Topology5 or grid model approach6 was also

used to get an optimal STM. Reference 7 proposed a modified STM based on the Mohr–Coulomb criterion. Reference 8 proposed a compatibility STM by combining arch action and truss action. However, finding the most suitable model generally requires insight and experience.

On comparing the experimental and analytical results of the ultimate capacity of concrete beams with different spans shown in Fig. 1,9 it can be observed that neither the STM nor the sectional model10 can perfectly predict ultimate capacity for both shallow and deep beams. The lack of consistency between design methods for deep and shallow beams may lead to inconsistencies in detailing of reinforcement, especially for the members in between shallow and deep beams.

This paper proposes a unified grid model that is valid for the analysis and design of both shallow and deep beams, but only flexural strength is discussed on account of the space limitation. The proposed model, based on a non-linear grid, inserts the critical section into the structure to extend sectional analysis method into deep beams. Although it is in fact a structural model, this model provides a similar sectional analysis basis for predicting ultimate capacity and conducting reinforcement design for both deep and shallow beams. By separating components of the stiffness matrix in the grid, the flexural reinforcement design can be obtained by the “substitution” of tensile members in the grid model. Four shallow or deep beam experiments and two flexural reinforcement design cases are listed to validate the model in the last part.

The Proposed Non-Linear Grid Model Grid Model The purpose of the proposed grid model is to provide a unified analysis basis that is valid for both shallow and deep reinforced concrete beams. The grid model is based on structural

Structural Engineering International Nr. 4/2017

typical two dimensional (2D) stress regions, all the stresses at Sections 1-1, 2-2 and 3-3 are crucial to the analysis and thus should be checked. In all cases, agreement between the models is excellent.

700 a

P

P

a 610 mm

b

500

fc′ = 27.2 MPa max.agg. = 19 mm d = 538 mm b = 155 mm As = 2277 mm2 fy = 372 MPa

400

d

Ultimate load, P (KN)

600

610 mm

It should be noted that l0 and h0 are the element lengths of the longitudinal and vertical elements respectively, as shown in Fig. 2b

Strut-snd-tie model (STM)

300 200

Tests

Sectional model

Sectional Analysis Approach Using the Grid Model

100 0 0

2

4 Shear span ratio, a/d

6

Fi g. 1: Predicted and observed ultimate load of a series of reinforced concrete beams

analysis such that stress distribution can be calculated automatically without the plane section assumption. The truss action of shallow beams and arch action of deep beams can also be reflected in the form of stress distributions at sections. A given beam is represented by an orthogonal grid consisting of horizontal and vertical beam elements connected rigidly at their intersection. The horizontal elements are spread across the depth. The vertical elements are spread along the span. Beam elements were chosen to provide consistency with current design standards and to maximize convenience of implementation of the design approach presented later in the paper. An example of the proposed model is shown in Fig. 2.

In its simplest form, that is for elements with linear–elastic material properties, the proposed grid model

(a)

P = 900 kN

can be solved using familiar algorithms for frame analysis. This was done for the example structure and loading case shown in Fig. 2a. Stresses were calculated at Sections 1-1, 2-2, and 3-3 as shown in Fig. 2a using grid models with two different mesh sizes and compared with stresses computed using finite element models (FEMs) composed of solid elements, also for two mesh sizes. The primary characteristics of these models are given in Table 1.

Figure 3 compares normal and shear stresses computed at Sections 1-1 and 2-2. Figure 4 compares the vertical compressive stress (also called “clamping stress”) and horizontal shear stress at Section 3-3. Since deep beams are Element size l0 × h 0

½ K = ½ K N + ½ Kf + ½ KS

ð1Þ

The terms on the right-hand side of Eq. (1) are defined as follows: • [KN] is the stiffness matrix derived by concrete axial rigidity and thus can be called as concrete axial rigidity contribution.

• [Kf] is the stiffness matrix derived by concrete bending shear rigidity and thus can be called as concrete bending shear rigidity contribution.

Grid model 1

Grid model 2

Solid model 1

Solid model 2

0.25 × 0.25

0.4 × 0.4

0.25 × 0.25

0.4 × 0.4

Table 1: Four models for stress comparison (unit: m)

P = 900 kN

(b)

1

nl × l0

2000

2

Based on the good agreement between the grid model and the FEM described above, the grid model was developed further to incorporate the presence of reinforcing steel, cracking in concrete and plastic behaviour in both materials. This refined model is based on a stiffness matrix [K] that is considered to be the sum of three components:

nh × h0

3

2000

3

h0

2 1000

1 1000

2000

2000

l0

Beam element

Fi g. 2: Simply-supported (a) deep beam and the corresponding (b) grid model

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Scientific Paper

483

(a)

(b) 4.0 Grid_1 Grid_2 Solid_1 Solid_2

3.5

4.0 Grid_1 Grid_2 Solid_1 Solid_2

3.5

2.5 2.0 1.5

3.5 3.0 Beam depth (m)

3.0 Beam depth (m)

3.0 Beam depth (m)

(c) 4.0

2.5 2.0 1.5

2.5 2.0 1.5

1.0

1.0

1.0

0.5

0.5

0.5

0.0

0.0

0.0 –2000

–1000

0

1000

2000

–1000

0

1000

2000

3000

4000

–1500

Grid_1 Grid_2 Solid_1 Solid_2

–1000

–500

0

500

F ig . 3: Comparison of normal and shear stresses at Sections 1-1 and 2-2. (a) Normal stresses on Section 1-1 (kPa); (b) normal stresses on Section 2-2 (kPa); (c) shear stresses on Section 2-2 (kPa)

(a) 0

1

(b)

Span (m) 3

2

4

5

6

Span (m) 1000

0

Grid_1 Grid_2 500 Stress value (kPa)

–500 Stress value (kPa)

Solid_1 Solid_2

–1000

–1500

Span (m) 0

1

2

3

4

5

6

0

–500 Grid_1 Grid_2

Solid_1 Solid_2

–2000 –1000

F ig . 4: Comparison of normal and shear stresses at Section 3-3. (a) Normal stresses on Section 3-3 (kPa); (b) shear stresses on Section 3-3 (kPa)

2 EA c 6 l 6 0 6 6 e e e 6 kc = kN + kf = 6 E0 A 6− c 6 l 6 4 0 0

Ec A l 0 0 Ec A l 0 0

3

0 0

0 0 0 0

0 0

0 0 0 0

0 0 0

• [KS] is the stiffness matrix derived by reinforcement axial rigidity and thus can be called as reinforcement contribution. In this paper, the reinforcement contribution accounts for the presence of longitudinal steel.

At the element level, the three components can be written as follows: 484

Scientific Paper

0

60 7 6 6 7 07 6 7 6 0 07 + 6 7 6 6 0 07 7 6 7 6 6 0 05 6 4 0 0

0 0 −

0 0

2

2

0 0 12Ec I 6Ec I l3 l2 6Ec I 4Ec I l2 l 0 0 12Ec I 6Ec I − 3 − 2 l l 6Ec I 2Ec I l2 l

0 0 0 0 0 0

3 0 0 12Ec I 6Ec I 7 − 3 7 l l2 7 6Ec I 2Ec I 7 7 − 2 l l 7 7 0 0 7 7 12Ec I 6Ec I 7 7 − l3 l2 7 5 6Ec I 4Ec I − 2 l l

3 E s As 0 0 − 0 07 6 l 6 7 6 0 0 0 0 07 6 7 6 7 e 6 0 0 0 0 0 07 7 ks = 6 6 E s As 7 Es A s 6− 0 0 0 07 6 7 l l 6 7 6 0 0 0 0 0 07 4 5 0 0 0 0 0 0 E s As l 0

ð3Þ

ð2Þ

where Ec and Es are the elasticity modulus of concrete and reinforcement respectively; A and I are the area and inertia moment of the section; As is the area of reinforcement; l is the length of element.

Based on the principle of small displacee e e ments, the three terms kN , kf and ks can be considered to be independent,

Structural Engineering International Nr. 4/2017

Critical section

(a)

(b)

P P

Concrete bending shear grid

h0

Concrete axial grid

Shared node

Non-linear elements l0

Steel grid

Fi g. 5: Grid model. (a) Glued grid model; (b) critical section in the grid model P

P

Critical section I

Critical section II

P

P

Critical section IV

Critical section III

Fi g. 6: Non-linear analysis at critical sections through the span

(a)

(b)

σs fu

σs fy

fy

O εy εsh

εu

εs

O

εy

εu

εs

Fi g. 7: Stress–strain relation of reinforcing steel. (a) Stress–strain relation of reinforcing steel taken from experiments; (b) bilinear stress–strain model

which means they do not overlap and thus can be separated. On this basis, the overall model can be regarded as made up of three grids “glued” together with equal displacements at

each of the shared nodes, as shown in Fig. 5a.

In the proposed model, it is assumed that in the ultimate state the behaviour

Structural Engineering International Nr. 4/2017

of all elements is linear and elastic except for the elements at one specific section, called the critical section, for which non-linear behaviour is allowed in accordance with the given material stress–strain laws and failure criteria.

The position of the critical section can be either specified in advance or made at all possible sections that resist maximum loads. For example, the flexural capacity of the deep beam in Fig. 5b is calculated on the basis of a critical section defined at mid-span.

The non-linear elements considered in this case are shown in red. Also, the critical section along the span can be selected as shown in Fig. 6; thus the flexural reinforcement can be designed along the whole span. The proposed model embodies important aspects of the sectional approach, which enables a unified basis for the design of reinforcement in both shallow and deep beams, while maintaining the benefits of the grid approach for deep beams demonstrated previously.

The non-linear calculation proceeds iteratively, considering the non-linear material properties of concrete and the change of elements in the grid model. This study is restricted only to normal strength concrete, and constitutive relation of concrete described in Ref. 11, given in Eq. (4), is used for concrete non-linear analysis. The stress–strain relation of reinforcing steel taken from earlier experiments is shown in Fig. 7a, where σ s and εs are the uniaxial stress and strain of reinforcing steel respectively; εy, εsh, εu are the yield strain, strain-hardening point, and ultimate strain; fy, fu are the yield stress and ultimate stress respectively. For the practical analysis of Scientific Paper

485

balanced–reinforced beams, the elastic, perfectly-plastic approximation is reasonable and accurate enough.

Thus, the bilinear stress–strain model is used for reinforcing steel in the study, as shown in Fig. 7b. " 2 # ε ε ð4Þ σ = fc0 2 − ε0 ε0

f1 Eq. (6)

Eq. (5)

ft f2

fc'

F ig . 8: Modified Mohr–Coulomb criterion for tension–compression stress state

where σ and ε are the uniaxial stress and strain of concrete respectively; ε0 is the strain at peak; fc0 is the concrete compressive strength.

Start Input information: structure, load, bound

Similar to application of compressionsoftening effect for checking the crushing of a strut in STM, the failure of concrete at the critical section in the grid model should also consider the interaction of principal stresses in two orthogonal directions. The 2D stress failure of concrete is checked using the modified Mohr–Coulomb In the tension– criterion.12 compression stress state, the failure criterion can be written as follows, and is shown in Fig. 8:

i=0

Load increment Pi =

1 2

i

P0

Establish element stiffness Assemble global stiffness matrix Calculate displacement increment δi

Reestablish element stiffness Calculate element internal force Pi′ ΔP = Pi –Pi′ Remove axial stiffness of the cracking element; Reverse the tensile force

Modified N-R method for displacement increment Δ δi

Δ δi ≤ eps = 1.0E–5 (mm)

NO Reinforced element: Calculate Reinforcement area

YES

Non-linear element reaches concrete tensile strength

YES

Determine flexural reinforcement layout

NO Reinforced element: Modify reinforcement areas

Calculate the principal stresses at the critical section

YES

Modified Mohr–Coulomb Criterion Concrete reaches compressive strength

NO YES

Back to the last stage

i=0 NO

i=i+1

i=i+1

NO Load increment/Initial increment ≤ eps = 1.0E–3

Output

F ig . 9: Flow chart of the grid model for sectional design of a reinforced concrete beam 486

Scientific Paper

kf1 − f2 = fc0

ð5Þ

f1 ≤ ft

ð6Þ

where f1 and f2 are principal tensile and compressive stresses respectively, and fc0 and ft are the concrete compressive and tensile strength; k is a coefficient related to the material internal friction. For concrete, k = 4.

The flow chart shown in Fig. 9 illustrates the sectional design approach based on the proposed grid model. The factored load should be used for the design of reinforcement in the ultimate state, which is parallel with the common practice for reinforced concrete design. In the flowchart, P0 is the factored load. The dotted box in Fig. 9 relates to the design of flexural reinforcement that will be discussed in detail later in this paper. When the axial force in the concrete of the nonlinear elements reaches the tensile strength of the concrete, the concrete axial contribution of the corresponding element is removed for all subsequent steps in the calculation and the original axial force in the element is reversed at the end nodes, in a manner similar to the analytical treatment of removal of a given cable in the modelling of cablestayed bridges. The bending shear stiffness of the concrete remains as the shear stress can be transferred across the flexural vertical cracks.

Structural Engineering International Nr. 4/2017

Flexural reinforcement in single layer

Section division

Axial internal force at critical section

Critical section

Tensile stress zone

Axial internal force at critical section

Critical section

Flexural reinforcement in multiple layers

Given location

Compression zone

(b) Section division

Compression zone

(a)

Fig. 10: Two flexural reinforcement layouts: (a) flexural reinforcement design in given location; (b) flexural reinforcement design in multiple layers

(a)

P

of the concrete axial contribution and the flexural reinforcement contribution thus provides a means of designing flexural reinforcement automatically.

Reinforcement layout T-2 T-1

600

P

2ø20

4ø23

3ø22 2000

2000

(b)

250

Non-linear elements P 6 × 100

5 × 100

P

250

2000

Critical section 20 × 100 20 × 100 60 × 100

20 × 100

250 Longitudinal elements at critical section

Fi g. 11: Series I: flexural analysis of reinforced concrete shallow beams (Units: [mm]). (a) Shallow beam; (b) grid model

Reinforcement layout P (kN)

T-1

T-2

Traditional sectional method

147

145

Layered section approach

149

146

Grid model

147

145

Table 2: Capacity comparison of Series I

Design of Flexural Reinforcement Based on the Grid Model The concrete axial rigidity contribution [KN] and the flexural reinforcement contribution [KS] defined in Eq. (1) are

(b)

P

P

6#8 200

6#8 2240

P #3@150

915

200

305

D6 D5 D4 D3 D2 D1

4#3

4#3 915

12#3

1 915

P

12#3

5 × 150

#3@150

915

1

The model considers two different bases for the design of reinforcing steel: under-reinforced design and balanced design. The two bases differ according to the value of applied load. In the former case, the applied load increases up to the given design load; therefore the yielding of steel occurs before crushing of concrete. In the latter case, the applied load keeps increasing until to the limit where the concrete reaches its compressive strength and the steel yields at the same time; therefore the applied load is usually greater than the given design load. Two kinds of flexural reinforcement layout are also provided, as shown in Fig. 10. The flexural reinforcement in the first layout (Fig. 10a) is specified at given locations, whereas in the second layout (Fig. 10b) it is arranged in the form of multiple layers at those locations where tensile strength of the concrete is reached. The difference in the two types of layout is explained further in the examples described later in this paper.

6#8

165

(a)

linked in the following way: the act of “removing” a concrete element cracked in axial tension increases the tensile force resisted by the corresponding steel element in the grid. The transformation

The axial tensile force in the removed element is transferred to the reinforcement designed at that section. As the load increases, the area of the reinforcement is adjusted in accordance with the axial force in the reinforcement element (to ensure that the reinforcing steel remains elastic) to implement a “design” procedure.

6#8 Sectional division in NLGM

200

915

2240

915

200

305

Fi g. 12: Series II: flexural capacity analysis of reinforced concrete deep beams (Units: [mm]). (a) Beam ACI-I; (b) beam STM-I

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487

Steel, fu (MPa)

Steel, fy (MPa)

Beam

Concrete, fc0 (MPa)

Concrete, ft (MPa)

#3

#8

#3

#8

ACI-I

32

2.15

450

420

720

700

STM-I

32

2.15

450

420

720

700

Table 3: Material properties of the beams of Series II

properties of concrete with a linear strain distribution in multiple strips of concrete and steel at the section. In this example, twenty layers are considered at mid-span. The results of these methods are presented in Table 2. It is obvious that the flexural capacities obtained from the grid model for Series I agree closely with the two common methods.

Tcr=65 kN Steels at the bottom D1

416 409

Steels in multi layers

236 244

re in

co n

–46

fo

0.5 es

ist es

–11.5

R

D3

ist

ed

ed

by

by

D4

cr et e

rc em

en t

D5

R

Longitudinal elements

D6

D2

Series II: Flexural Capacity of Reinforced Concrete Deep Beams

–105

–606 D1 –537 –600

–200

–400

0

200

400

Axial force of the elements on the critical section (kN)

F ig . 13 : Internal forces in longitudinal elements at the mid-span section obtained from the grid model

Grid Model for Capacity Calculation

section. The grid model that was used is shown in Fig. 11b.

In this section, the grid model is used to calculate the capacity of reinforced concrete shallow beams (Series I) and deep beams (Series II). The results are compared with well-established theoretical results and, when available, experimental results.

The results obtained from the grid model are compared with two other common methods for calculating the flexural capacity of reinforced concrete shallow beams. The first is the traditional sectional method which is widely described in textbooks.13 The other is the layered section approach,10 which also considers the material non-linear

Series I: Flexural Capacity of Reinforced Concrete Shallow Beams The reinforced concrete shallow beams of Series I are detailed in Fig. 11a. Two reinforcement arrangements are considered: Beam T-1 has an area of reinforcement As = 1662 mm2 and Beam T-2 has As = 1768 mm2. The concrete compressive strength is fc0 = 23 MPa. The concrete tensile strength is ft = 2.6 MPa. The yield strength of reinforcing steel is fy = 357 MPa. The section at mid-span, where bending moment is the maximum, is taken as the critical

Beam

Pexp (kN)

Pgrid (kN)

ACI-I

1356

1349

STM-I

1134

1217

Sectional method

In Ref. 14, tests for the two reinforced concrete deep beams shown in Fig. 12 were conducted. The material properties are given in Table 3. Beam ACI-I was assigned a roughly equal effectiveness factor of horizontal and vertical web reinforcement according to ACI 318-9915 (Eq. 11-30). Beams STM-I was designed by the STM specified in ACI 318-02.16 The distributed web reinforcement satisfies the required reinforcement in ACI 318-11 A.3.3 (Eq. A-4). It was observed that beams ACI-I and STM-I failed in flexure.

The grid models for these two specimens considered critical sections in the region of pure bending zone. The results obtained from the grid model are compared with the results from the tests, semi-empirical sectional Grid model Reinforcement in D1

Grid model Reinforcement in multiple layers

As (mm2)

1695

1699

1505,P 294 ( As = 1799)

Reinforcement ratio

0.0113

0.0113

0.0120

Concrete compression, Fc (kN)

606

606

653

Reinforcement stress (MPa)

357 (yield)

357 (yield)

357 (yield)

Table 5: Comparison of the flexural reinforcement results for shallow beams Psemi(kN)

Pexp/PsemiPSTM (kN)

Pexp/Pgrid

empirical

Pexp/PSTM

Failure mode

1013

1005

1.01

1.34

1.35

Flexure

948

903

0.93

1.20

1.26

Flexure

0.97

1.27

1.31

empirical

AVG (average) Table 4: Comparison of calculation and test results of Series II 488

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1500

93

960 kN 13 44 kN

kN

26

A 1350

(c)

P = 2840 kN

B

1920 kN Strut

2700

1

Tie

44

kN

960 kN

C

Node

Section division D6 D5 D4 D3 D2 D1

13

1

500

947 kN

1893 kN

4050

P = 2840 kN

6 × 250

(b)

P = 2840 kN

938 kN

(a)

Fi g. 14: Example of deep beam (Units: [mm]). (a) Deep beam; (b) strut-and-tie model; (c) grid model

analysis method specified in China Concrete Structure Design Code (2010), and STM specified in the ACI 318-11, as in Table 4. From the comparison, it can be seen that the grid model gives a reasonably accurate prediction of the failure load while the semi-empirical sectional analysis method and STM are a little conservative.

Grid Model for Flexural Reinforcement Design To illustrate the unified design of flexural reinforcement based on the grid model, shallow beam and deep beam design examples are listed. Two arrangements of reinforcement, as discussed previously, are considered.

The results are compared with traditional design methods.

Flexural Reinforcement Design of Shallow Beams The beams considered in this example are identical to the Series I beams described previously in this paper. A

concentrated load P = 150 kN is applied at the one-third point of the span. The traditional sectional method and the grid model approach are used for the design of the flexural reinforcement. In the grid model, the critical section at mid-span is divided into six longitudinal elements, named D1 to D6, along the depth of the section as shown in Fig. 11b. Two arrangements of reinforcement are considered for the grid model, namely, bars at the bottom layer D1 alone and multiple layers of bars (at those locations where the longitudinal elements reach the concrete tensile strength). The traditional sectional model considers only reinforcement in a single layer D1. Figure 13 shows the distribution of axial force at mid-span section obtained from the grid model for the two reinforcement arrangements. Because the axial tensile force of each longitudinal element resisted by concrete is limited to Tcr = 65 kN, the excess tensile force is expected to be resisted by the flexural reinforcement, the area of which can be determined by A = T/fy. As shown in Table 5, when the reinforcement is

Tcr=255 kN 1887 1710 2046

D5 e co

rc e

nc

m

re t

en

t

–26

by

in

fo

D4

ed R

es

es ist ed

D3

ist

by

re

–68

–310

R

Longitudinal elements

D6

–813 D2 –676

Steels at D1 Steels at D1 and D2 Steels in multi layers

–1074 D1 –1710

–966 –1500 –1000 –500

0

500

1000

1500

2000

Axial force of the elements on the critical section (kN)

Fi g. 15: Internal forces in longitudinal elements at the critical section obtained from the grid model

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provided only at the bottom of the section, the grid model approach agrees closely with the traditional sectional method. If the reinforcement is arranged in multiple layers along the section, the total area of steel required is 5.6% larger than the steel-only in the bottom layer.

Flexural Reinforcement Design of Deep Beams A simply supported deep beam, shown in Fig. 14a, is loaded with a single concentrated load P = 2840 kN at the onethird point of the span. The concrete compressive strength is fc0 = 28 MPa and the concrete tensile strength is ft = 2.04 MPa. The yield strength of the reinforcement is fy = 410 MPa. The STM specified in the ACI 318-02, the semi-empirical sectional analysis method prescribed by Eq. (7) as specified in China Concrete Structure Design Code (2010), and the grid model are used to design the flexural reinforcement.

8 M = f y As z > < z = αd ðh0 − 0:5xÞ ð7Þ > : αd = 0:80 + 0:04 l0 h where z is the internal force arm of the section, x is the height of the compression zone in the section, h is the height of the section, l0 is the clear span of the beam and αd is the modification factor of internal force arm which is related to the span to depth ratio.

The flow of forces in the deep beam according to the STM17 is shown in Fig. 14b. On this basis, flexural reinforcement can be dimensioned to resist the tensile force in Tie AB. Section 1-1 in Fig. 14c was used as the critical section in the grid model and for the sectional method. Non-linear longitudinal elements on the critical section, named D1 to D6, are provided along the depth of the Scientific Paper

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As (mm2) Reinforcement ratio Steel stress (MPa)

ACI 318-02 STM

Chinese code semi-empirical method

Grid model Reinforcement at D1

4683

5951

4171

Grid model Reinforcement at D1 and D2 2619, P 1984 ( As = 4603)

Grid model Reinforcement in multi-layer 2356, P 1649, 755 ( As = 4760)

0.00624

0.00793

0.00556

0.00614

0.00635

410 (yield)

410 (yield)

410 (yield)

410 (yield)

410 (yield)

Table 6: Comparison of the flexural reinforcement results for deep beam

section as shown in Fig. 14c. Three different arrangements of reinforcement were calculated using the grid model: (a) reinforcement provided only in layer D1, (b) reinforcement provided in layers D1 and D2, and (c) reinforcement provided in multiple layers as described previously. In all cases, the axial tensile force resisted by concrete in each longitudinal element is limited to Tcr = 255 kN. The distribution of axial force at the critical section obtained from the grid model is shown in Fig. 15.

Table 6 compares the design of reinforcement obtained from the design methods considered. If the reinforcement is arranged entirely in the bottom layer D1, detailing requirements will not be satisfied. The bars are therefore arranged in two bottom layers. When two layers of steel are provided, there is good agreement between the required area of steel calculated using the STM and the grid model. The area of reinforcement calculated by Eq. (7) is about 20% more than both the STM and the grid model. If the steel is arranged in multiple layers, the total amount of steel is 12% greater than the case with steel provided only in layer D1, and 7.7% greater than the case when steel is provided in layers D1 and D2. The comparison illustrates that the semiempirical sectional analysis method for flexural reinforcement design of deep beams as specified in Chinese Code is conservative, which is similar to the observation in Ref. 18.

Conclusions A grid model was developed for unifying the sectional design approach for shallow and deep beams. The stiffness matrix of the model is composed of three components which reflect the primary elements of behaviour of reinforced concrete beams. By inserting the critical section into the grid model with non-linear material constitutive relationship and failure criteria, 490

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the capacity prediction on that section can be achieved. The design of flexural reinforcement can also be conducted automatically through a suitable transformation of the concrete axial component of stiffness and the flexural reinforcement component of stiffness. The model was validated using two series of reinforced concrete shallow and deep beams. The results were also compared with results predicted by other well-accepted analytical methods.

The conclusions that can be drawn as following: 1. A comparison of the grid model and a FEM using solid elements indicates that the grid model is a valid basis for calculating the structural response of deep beams. The advantage of a grid model based on beam elements is compatibility with current design standards, which will facilitate the design of flexural reinforcement.

2. By modifying the grid model with the addition of a critical section, at which non-linear behaviour is permitted, the model is able to maintain the accuracy of the grid and provide a consistent approach for the full range of shallow and deep beams.

3. The axial component of stiffness and the flexural reinforcement contribution to stiffness in the grid model can be transferred to provide the basis for a unified design of flexural reinforcement. The transformation is obtained by removing axial forces in cracked axial members and increasing the tensile force resisted by the reinforcement by the same amount.

4. The model was validated using two series of beams from the literature.

The comparisons indicate that the grid model approach is valid for reinforced concrete beams, both shallow and deep. The flexural reinforcement design cases indicate that reinforcement dimensioned on the basis of the grid model agrees

well with reinforcement dimensioned on the basis of common sectional methods for shallow beams.

For deep beams, the reinforcement dimensioned using the grid model method is close to that dimensioned using STMs.

References [1] American Concrete Institute. Building Code Requirements for Structural Concrete and Commentary (ACI 318-11) American Concrete Institute: Farmington Hills, MI, 2011.

[2] CEN. Eurocode 2: Design of Concrete Structures: Part 1-1: General rules and rules for buildings European Committee for Standardization: Brussels (Belgium), 2004.

[3] AASHTO Load and Resistance Factor Design. Bridge Design Specifications American Association of State Highway and Transportation Officials: Washington, D.C., 2010.

[4] Ministry of Housing and Urban–Rural of the People’s Republic of China. Code for Design of Concrete Structure (GB 50010-2010) China Architecture & Building Press: Beijing, 2010.

[5] Liang QQ, Uy B, Steven GP. Performancebased optimization for strut–tie modeling of structural concrete. J. Struct. Eng. 2002; 128(6): 815–823.

[6] Yun YM, Kim BH. Two-dimensional grid strut–tie model approach for structural concrete. J. Struct. Eng. 2008; 134(7): 1199–1214.

[7] Tang C, Tan K. Interactive mechanical model for shear strength of deep beams. J. Struct. Eng. 2004; 130(10): 1534–1544.

[8] Scott RM, Mander JB, Bracci JM. Compatibility strut-and-tie modeling: part I—formulation. ACI Struct. J. 2012; 109(5): 635.

[9] Collins MP, Mitchell D. Prestressed Concrete Structures Englewood, CO: Prentice Hall, 1991.

[10] Vecchio FJ, Collins MP. Predicting the response of reinforced concrete beams subjected to shear using modified compression field theory. ACI Struct. J. 1988; 85(3): 258–268.

[11] Hognestad E. Study of combined bending and axial load in reinforced concrete members.

University of Illinois Engineering Experiment Station Bulletin, no. 399, 1951.

[12] Nielsen MP. Limit Analysis and Concrete Plasticity Prentice-Hall: Englewood Cliffs, NJ, 1984.

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[13] Hassoun MN, Al-Manaseer A. Structural Concrete: Theory and Design John Wiley Sons: Hoboken, NJ, 2012.

[14] Aguilar G, Matamoros AB, ParraMontesinos GJ, Ramírez JA, Wight JK. Experimental evaluation of design procedures for shear strength of deep reinforced concrete beams. ACI Struct. J. 2002; 99(4): 539–548.

[15] American Concrete Institute. Building Code Requirements for Structural Concrete and Commentary (ACI 318M-99) American Concrete Institute: Farmington Hills, MI, 1999.

[16] American Concrete Institute. Building Code Requirements for Structural Concrete and Commentary (ACI 318-02) American Concrete Institute: Farmington Hills, MI, 2002.

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[17] Wight JK, Parra-Montesinos GJ. Strutand-tie model for deep beam design. Concr. Int. 2003; 25(5): 63–70.

[18] Lie-Ping Y, Jie M, Yu-Hang W. Application of strut-and-tie model in design of reinforced concrete deep beams. J. Archit. Civil Eng. 2009; 26(2): 81–86.

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Robust Optimum Design of Tuned Mass Dampers to Mitigate Pedestrian-Induced Vibrations Using Multi-Objective Genetic Algorithms Javier Fernando Jiménez-Alonso, Asst. Prof., Department of Building Engineering and Geotechnical Engineering, Universidad de Sevilla, Seville, Spain; Andrés Sáez, Prof., Department of Continuum Mechanics and Structural Analysis, Universidad de Sevilla, Seville, Spain. Contact: jfjimenez@us.es DOI: 10.2749/222137917X14881937844685

Abstract Tuned mass dampers (TMDs) are well-known control devices used widely to mitigate the pedestrian-induced vibrations on footbridges. The main purpose of this study is the robust optimum design of TMDs using multi-objective genetic algorithms in order to control the pedestrian-induced vibrations on footbridges considering the uncertainties associated with their modal properties. The performance of the TMD is improved via the robust optimum design of its modal parameters using multi-objective genetic algorithms. As an example, a benchmark footbridge, modelled by frame and shell elements, is used to assess numerically the performance and accuracy of the proposed method. The pedestrian action is simulated by an equivalent harmonic load. The proposed method is compared with the conventional Den Hartog’s proposal. The results show that this new method is more effective than the conventional proposal and the resulting damping device is more economic due to the smaller value of its design parameters.

Keywords: footbridge; passive structural control; tuned mass dampers; robust design optimization; multi-objective genetic algorithms.

Introduction A tuned mass damper (TMD) is a passive control system formed by mechanical components such as mass, spring and viscous damper. TMD is a vibrating mass that undergoes movements in the opposite direction to the main structure. To achieve these contrary movements, the mass is elastically linked to the structure and tuned for the resonant frequency. The movement of the TMD causes inertial forces that compensate the movements of the structure, reducing in this manner the amplitude of its vibration.

The effect of this device on the structure may be understood as an increase of its structural damping that attenuates the peak of the frequency response function, while the required TMD added mass is only a small fraction of the modal mass of the considered vibration mode.

Peer-reviewed by international experts and accepted for publication

by SEI Editorial Board Paper received: September 1, 2016 Paper accepted: January 24, 2017

492

Scientific Paper

These damping devices have been installed successfully in slender footbridges for controlling vibrations induced by pedestrian action.1–4 Although active vibration control is more effective for control of civil engineering structures,5 its high cost and maintenance requirements favour the practical use of passive control techniques.6 TMDs are widely used to retrofit footbridges experiencing pedestrian-induced vibrations, as these devices can be easily attached to the deck of the structure without any restrictions (Fig. 1a).

The current international standards and guidelines7–9 still recommend the design principles proposed by Den Hartog10 (DH) in order to determine the TMD parameters to control the pedestrian-induced vibrations on footbridges. According to this conventional method, the vibration level of an undamped mechanical system, under a harmonic load, may be reduced if the natural frequency of the implemented damping device is tuned to the natural frequency of the mechanical system.

The practical design of the TMD is based on an initial selection of its mass and an optimum value of its stiffness

and damping parameters in order to minimize the displacement response of the structure. Otherwise, a TMD design, performed according to this method, has to overcome two problems in order to guarantee the TMD performance for its overall life cycle:11 (a) the modification of the natural frequencies of the structure during its overall life cycle12,13 due to the non-linearities of its structural behaviour and the variation of the operational and environmental conditions14,15 and (b) the distance between the TMD mass and the deck must be large enough to avoid the impact between the two elements.

The main consequence of the detuning of the TMDs whose parameters have been designed based on this method (DH) is a reduction of the performance of the damper.1 In order to overcome the first requirement and optimize the TMD parameters, several studies that take into account the uncertainties during the design process of the TMD have been conducted. Rarely these studies focus on controlling the vibrations induced by pedestrians, being more frequently on the works that optimize the TMD parameters to control the response of buildings and bridges under earthquake16–18 and wind actions.19 The initial proposals that treated uncertainty in TMD design assumed that such uncertainty only affects the loads.

Among these works, the following may be cited: Ref. [20] proposed the use of a multi-objective optimization problem in order to obtain the TMD parameters. As an objective function, a weighted sum of the mean value and the standard deviation of the peak response were implemented. Subsequently, Ref. [21] proposed a fuzzy approach in order to simulate the uncertainties. Later Ref. [22] compared the results of a TMD design considering a conventional approach, singleand multi-objective robust design optimization (RDO).

Significant

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(a)

(b) md kd mf

cd

ud ur

p* (t) uf

kf

cf

Fi g. 1: (a) TMD installed under the deck of a footbridge.7 (b) TMD–footbridge interaction model

differences were observed between the conventional and the robust approaches.

Recently, Ref. [23] has proposed a robust optimization approach for the design of a TMD that accounts for uncertainties in the modal parameters of the footbridge. This approach makes use of fuzzy logic to deal with the uncertainties together with a multi-interval approach as a global optimization method.

In this paper, a new approach is presented and assessed in order to improve the performance of the TMD, when employed to reduce the pedestrian-induced vibrations on footbridges during their overall life cycle.

The proposal is based on the principles of metaheuristic optimization,24 that previously have been successfully used to improve the design of TMD devices in buildings under earthquake actions.16,18 Here, we focus on the design of TMDs in order to reduce the pedestrian-induced vibrations in footbridges in the vertical direction.

The main objective of the work is to obtain robust optimum TMD design parameters that guarantee an adequate level of comfort in the footbridge. The variation in the modal properties of the structure due to the modification of the operational and environmental conditions is simulated considering these magnitudes as uncorrelated random variables that follow a normal distribution.12,13 A RDO procedure is performed based on a probabilistic approach. The properties of the probabilistic distribution are used to perform a robust estimation of the optimum TMD parameters. Additionally, a sensitivity study is conducted in order to analyse how the designed TMD parameters vary with the uncertainty level considered by the designer.25 Multi-objective

genetic algorithms are used in the optimization method. The multi-objective global optimization26 (MGO) presents better results than single-objective global optimization22,27 when several criteria must be considered simultaneously. In this new proposal, none of the TMD parameters are preselected, as opposed to the conventional method (DH), where the mass ratio is initially chosen.

The performance of the proposed method is assessed by correlating the TMD parameters obtained by the application of the conventional DH method and the proposed method (MGO) on a benchmark footbridge, reported in the French standard,8 in order to guarantee an adequate comfort level under different pedestrian flows. The TMD parameters are estimated under two approaches, deterministic and stochastic. The idea is first to check the new method under a simplified approach (deterministic approach), where the change of the model properties of the structure is only caused by the pedestrian– structure interaction, and later under a refined approach (robust approach), where the variation of the modal parameters of the footbridge is associated with the modification of its operational and environmental conditions.28 In the deterministic approach, the estimation of the structural change is performed following the rules recommended by the Synpex guidelines.7 In the second approach, a refined version of the changes is considered. In this second approach, the variation of the modal parameters of the structure is estimated considering an uncorrelated probabilistic normal distribution, based on the results observed from the continuous monitoring of two existent footbridges.12,13 Finally, a discussion about the parameters obtained by the

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two methods, and considering the two approaches, is provided. The parameters obtained under the two approaches following the proposed method (MGO) are smaller than the values obtained from the conventional method (DH), which is beneficial for both the footbridge, the force applied by the damper is less, and the TMD, since its cost is also less due to lesser amount of materials needed for its manufacture.

The main contribution of the proposed method is the RDO of the TMD parameters, in order to reduce the walking pedestrian-induced vibrations in the vertical direction and taking into account the uncertainties in the modal parameters of the footbridge. It is assumed that the modal properties of the footbridge are normally distributed uncorrelated random variables, which simplifies the definition of the robust optimization procedure.

The main advantages of the proposed method (MGO) against the conventional method (DH) recommended in current design guidelines7–9 are: (a) better adaptation to the comfort criterion, which allows reducing the magnitude of the TMD parameters and (b) better adaptation to the effects originated by the modification of the operational and environmental conditions.

Furthermore, the proposed method (MGO) also presents some advantages when compared to recent proposals based on fuzzy logic.21,23 First, it is a simpler-to-follow method for design engineers, more accustomed with probabilistic methods rather than fuzzy methods; and second, it allows obtaining directly the TMD parameters according to the confidence level established by the designer.

The paper is organized as follows: In the second section, the equations of motion that governs the TMD– structure interaction model are expressed. Additionally, the assumptions established to model the pedestrian action, based on the proposal of the Synpex guidelines7 are presented.

Next, the TMD design based on the conventional DH proposal is briefly summarized for completeness. In the fourth section, the TMD design based on the use of MGO is explained. Subsequently, the uncertainties associated with the modification of the modal properties of the structure—due to Scientific Paper

493

Response of Structure Equipped with TMD under Walking Load The implementation of the TMD– footbridge interaction model may be performed by the application of the dynamic equilibrium equations29 to a double degree of freedom (d.o.f.) model (Fig. 1b). It is assumed, in this study, that only one vibration mode of the structure needs to be controlled.

The TMD is modelled as a single d.o.f. system characterized by three parameters (mass, damping and stiffness).

Additionally, it is assumed that the damping device is located at the position with the maximum displacement of the considered vibration mode. u f + cf u_ f + cd ðu_ f − u_ d Þ mf :€ + kf u_f + kd ðuf − ud Þ = p* ðt Þ € d + cd ðu_ d − u_ f Þ md u + kd ðud −uf Þ = 0 p* ðt Þ = ϕiT pðt Þ

ð1Þ ð2Þ ð3Þ

where mf is the modal mass of the considered vibration mode of the footbridge (kg), md is the mass of the € f , u_ f ,uf are the acceleraTMD (kg), u tion, velocity and displacement of the considered vibration mode of the € d , u_ d , ud footbridge (m/s2, m/s, m), u are the acceleration, velocity and displacement of the TMD (m/s2, m/s, m), ur = ud − uf is the relative displacement between md and mf (m), cf = 2 mf 2 π ff ζf is the modal damping of the considered vibration mode of the footbridge (Ns/m), kf = mf (2 π ff)2 is the modal stiffness of the considered vibration mode of the footbridge (N/m), ff is the natural frequency of the considered vibration mode of the footbridge (Hz), ζf is the 494

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damping ratio of the considered vibration mode of the footbridge (−), cd = 2 md 2 π fd ζ d is the damping of the TMD (Ns/m), kd = md (2 π fd)2 is the stiffness of the TMD (N/m), fd is the natural frequency of the TMD (Hz), ζd is the damping ratio of the TMD (−), p*(t) is the modal projection of the equivalent pedestrian load (N), ϕiT is the transpose of the considered vibration mode of the footbridge and p(t) is the equivalent pedestrian load (N/m).

Equations (1) and (2) may be reorganized in matrix form to yield: M € u ðt Þ + C u_ ðt Þ + K uðt Þ = Fðt Þ ð4Þ where

mf 0 cf + cd −cd M= C= 0 md − cd cd

* ð5Þ kf + kd −kd p ðt Þ K= F ðt Þ = −kd kd 0 and

€ f ðt Þ u_ f ðt Þ u € ðt Þ = ;u_ ðt Þ = ; u € d ðt Þ u u_ d ðt Þ ð6Þ

u f ðt Þ uðt Þ = ud ðt Þ The proposed system may be integrated in time domain using a β-Newmark method, with parameters β = 1/4 and γ = 1/2, thus ensuring an unconditionally stable system.

The equivalent vertical acceleration of walking pedestrian load, p(t), is simulated, for the purpose of this study, according to the method proposed by the Synpex guidelines,7 as a distributed harmonic load, that represents the equivalent pedestrian stream: pðt Þ = PG cosð2π fs t Þ n0 ψ=Lf

ð7Þ

where PG cos(2π fs t) is the harmonic load due to a single pedestrian,

PG is the dynamic component of the pedestrian step load (280 N for vertical direction according to the Synpex guidelines),7 fs is the step frequency, which is assumed to be equal to the natural frequency of the footbridge, ff, n0 is the equivalent number of pedestrians on the loaded footbridge (i.e. number of synchronized pedestrians that cause the same response as n arbitrary pedestrians with a normal distributed step frequency on the footbridge). Its value may be determined from (with d being the pedestrian density in persons per unit area, P/m2): n0 =

pffiffiffiffiffiffiffiffi 10:8 p ζ fffiffiffi n d < 1:00P=m2 if 1:85 n d ≥ 1:00P=m2

ð8Þ

ψ is the reduction coefficient to take into account the probability that the footfall frequency approaches the natural frequency under consideration. It may be estimated in the vertical direction for the pedestrians walking on the footbridge (Fig. 2) according to the natural frequency.

Lf is the length bridge (in m).

of

the

foot-

Different design scenarios must be established according to the expected pedestrian traffic (Table 1), the situation and importance of the footbridge.

The comfort level, determined by the owner of the structure, is checked by comparing the maximum acceleration obtained under the different design scenarios against the limit values established in Table 2.7 Finally, the Synpex guidelines7 account for the modification of the modal properties of the structure due to the pedestrian–structure interaction by considering two scenarios: (a) an empty scenario, where the natural frequency of the footbridge is calculated considering the unoccupied deck and

1.00 1st Harmonic Vertical Walking 0.80

ψ (–)

changes in the operational and environmental conditions—are introduced and a RDO procedure is presented in order to incorporate these uncertainties into the TMD design. Next, the numerical validation of the proposed method is presented. For this purpose, a benchmark footbridge, as reported in the French standards,8 is used. A comparison between the parameters of the TMD obtained by considering both methods (DH and MGO) and the two approaches (deterministic and stochastic) is provided. Finally, some concluding remarks are drawn to close the paper.

2nd Harmonic Vertical Walking

0.60 0.40 0.20 0.00 1.00

1.50

2.00

2.50

3.00

3.50

4.00

4.50

Frequency (Hz)

F i g. 2 : Reduction coefficient ψ in vertical direction for walking pedestrians7

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Density, d

Classes TC1

Characteristics

<15 P

Very weak traffic

TC2

<0.20 P/m2

TC3

2

Unrestricted walking, significantly dense traffic

2

Comfortable and free walking

<0.50 P/m

TC4

<1.00 P/m

Uncomfortable situation, obstructed walking

TC5

<1.50 P/m2

Unpleasant walking, very dense traffic

7

Table 1: Traffic classes Level

Degree

Vertical acceleration (m/s2)

CL1

Maximum

CL2

Medium

0.50–1.00

<0.50

CL3

Minimum

1.00–2.50

CL4

Discomfort

>2.50

Table 2: Defined comfort classes with limit acceleration ranges7

(b) a full scenario, where an additional mass of 70 kg for each considered pedestrian is assumed, once the total pedestrian mass exceeds 5% of the modal mass of the unoccupied deck.

Deterministic TMD Design Conventional Design In order to mitigate the vibrations induced by pedestrian flows in footbridges, both the more advanced international codes8 and the Synpex guidelines,7 recommend the use of the conventional DH proposal10 as the method to determine the optimum parameters of a TMD. The method provides the parameters of the TMD that minimize the displacement response of the structure. This procedure may be summarized as follows: 1. Choice of TMD mass, md, based on the mass ratio μ = md/mf.

2. Calculation of the optimum TMD ratios:30 frequency ratio, δopt, and damping ratio, ζopt. δopt = 1=ð1 + μÞ = fd =ff sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 3μ ζopt = 8 ð1 + μÞ

ð9Þ ð10Þ

3. Calculation of the TMD constants: spring and damping constant.

2 kd = md 2 π δopt ff ð11Þ cd = 2 md 2 π δopt ff ζ opt

ð12Þ

In this way, the design consists of selecting iteratively a mass ratio, μ, that reduces the acceleration of the structure under the limit value, alim, according to the established comfort level of the structure (Table 2). Further, the relative displacement, ur, between the TMD and the footbridge must be lower than a limit value (distance between the TMD mass and the deck) established by the TMD manufacturer. In this study, a constrained single-objective optimization procedure is used27 to implement this conventional design method. As objective function, the mass ratio of the TMD is chosen. Two inequality constraints are defined; (a) first, in order to ensure that the maximum acceleration of the footbridge is lower than the limit acceleration (Table 2) and (b) second, the previously mentioned relative displacement requirements. A search domain is established in order to guarantee that the optimum obtained parameter, i.e. the mass ratio of the TMD, is physically meaningful. The optimization problem is solved using genetic algorithms.

Multi-Objective Global Design The conventional method previously described presents as main restriction that only one parameter may be tuned (TMD mass) to mitigate the pedestrian-induced vibrations on footbridges. This limitation can reduce the performance of the TMDs designed according to this method under uncertainty conditions. In order to overcome this subject, an alternative method is proposed in this study. The method, based on the solution of a MGO problem, considers the three TMD parameters as design variables to be tuned during the TMD design.

Traditional optimization methods, based on gradient, have certain difficulties to solve accurately modern engineering optimization problems as they are not able to avoid local minimums. Alternatively, metaheuristic optimization algorithms are used to

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solve structural optimization problems. They have been applied in the design of TMDs for buildings under earthquake action.16,18 Among these metaheuristic optimization algorithms, genetic algorithms are effective search methods used for solving optimization problems that are not adequate for standard optimization algorithms such as those where the objective function is highly non-linear.27 Genetic algorithms use a population (set of points) that evaluates the objective function using several random operators (initialization, reproduction, crossover and mutation).

The objective of this procedure is to investigate the search domain comparatively in order to obtain the optimum solution.27 In the single-objective optimization process, the value of the design variables is found to arrive at the optimum value of a single objective function. On the other hand, in the multi-objective optimization process several objective functions are minimized, offering an optimal set of solutions rather than one optimal value.

Additional conditions must be considered to find the optimal value among the set of solutions.

It is well accepted that genetic algorithms work adequately to solve both single-objective and multi-objective optimization problems.26 In this study, both the single-objective and the multi-objective optimizations are performed using the Optimization Toolbox provided by the software Matlab.31 As mentioned in the previous section, the single-objective optimization is used to find the optimum TMD mass ratios based on DH method. On the other hand, a new proposal, based on multi-objective genetic optimization (MGO), is presented as alternative.

The purpose of the multi-objective optimization problem is to find a design vector x = {x1, x2, …, xm}T, in a search domain (being m the number of design variables), which could optimize k objective functions, f = {f1, f2, …, fk}T, under r inequality and q equality constraints. The multi-objective optimization may be described as: find x, optimize f, subject to

Ai ðxÞ ≤ 0 i = 1, …, r Aeq, j ðxÞ = 0 j = 1, …,q Scientific Paper

ð13Þ

495

where x 2 ℜm is the design variable vector, f 2 ℜk is the objective functions vector, and Ai(x) and Aeq,j(x) are the inequality and equality constraints respectively.

The optimal solutions are called Pareto front. To determine one optimal set in the Pareto front, additional information must be taken into account. For the purpose of this study, the compliance of the comfort level established by the designer is considered.

As a result of the multi-objective optimization process, the global Pareto optimization solutions are obtained, resulting in minimal values of the objective function. However, the solutions reached may be very sensitive to the uncertainties of the parameters of the system. In order to guarantee that the global Pareto front presents solutions less sensitive to the variation of the modal parameters of the system, a robust design approach is considered.18 In the following section, the RDO approach is presented.

Robust TMD Design The modal parameters of the footbridge may vary due to the changes in its operational and environmental conditions, generating uncertainties on the finite element (FE) model used to simulate the behaviour of the structure. The performance of the TMD– footbridge system may be sensitive to such uncertainties1,23 even if the TMD parameters have been adjusted optimally from a deterministic approach.

For a RDO of the TMD parameters, these uncertainties must be taken into account. A stochastic optimization approach is considered, where the uncertain parameters are considered as probabilistic modifications and a stochastic optimal design can be performed in order to obtain the robust TMD parameters.18 In order to simulate this stochastic behaviour, the main procedure used in the robust design method is a Monte Carlo simulation.25 According to this method, random variables are generated assuming predefined probabilistic distributions for the uncertain parameters. The modal parameters of the footbridge are assumed to be random variables that, for the purpose of this study, follow normal probabilistic distributions according to the results provided by researchers regarding the 496

Scientific Paper

modification of the modal properties of two real footbridges due to changes in their operational and environmental conditions.12,13 Several “states” are generated, being a ‘state’, each set of generated modal properties (natural frequencies and associated damping ratios) of the structure. Then, the behaviour of the footbridge is simulated considering each of these randomly generated states. The determination of the robust optimum TMD parameters is performed by the reduction of the number of cases that after the implementation of the TMD, do not meet the considered comfort criteria.25 If X is a random variable, then a possible model for uncertainties in stochastic randomness is the probability density function, fX(x), or the cumulative distribution function, FX(x), where the subscript X refers to the random variable.25 Two statistical moments, known as the mean value (or expected value), denoted by E(X), and the variance, denoted by σ 2(X), respectively are the most important probabilistic parameters for RDO. The main objective of this approach is to minimize the mean value, E(X), and the standard deviation, σ(X), of each random variable simultaneously.18,20,25 For this purpose, the following equations may be defined depending on the number of objective functions that define the optimization problem.

1. For a single-objective optimization problem as an inequality constraint: Ai ðX Þ =

EðX Þ + Δ σ ðX Þ Xα = −1 ≤ 0 Xlim Xlim ð14Þ

2. For a multi-objective optimization problem as an objective function for each random variable: f=

EðX Þ + Δ σ ðX Þ Xα = Xlim Xlim

ð15Þ

where X is a random variable, Ai(X) is an inequality constraint, Δ is a scale factor that modifies the confidence level of the equation, E(X) is the mean value of the random variable X, σ(X) is the standard deviation of the random variable X, Xα is the percentile αth of the probability distribution of the random variable X, Xlim is the considered limit value of the random variable X. The value of the scale factor, Δ, varies in terms of the probabilistic distribution that fits better the considered random

variable and the confidence level required by the designer. However, as it is possible to define the required confidence level in terms of the percentile αth of the probability distribution function, this criterion is used in this study.

Numerical Validation The assessment of the proposed methodology is validated by correlating the dynamic response of a benchmark footbridge, reported in the French standard,8 after the implementation of a TMD whose parameters are designed according to the two previously mentioned methods, conventional and multi-objective global design methods. Additionally, two approaches are considered, a deterministic and a robust TMD design.

In the deterministic approach, the TMD design is performed under the two methods (DH and MGO), considering that the first natural frequency of the footbridge only changes due to the pedestrian–structure interaction15 following the rule established by the Synpex guidelines.7 In the robust approach, it is considered that the modal properties of the footbridge (first natural frequency and its corresponding damping ratio) may vary randomly due to the modification of the operational and environmental conditions.12,13 The TMD design is done ensuring their robustness during the overall life cycle of the structure.

Finally, a comparison of the results obtained by the two methods under the two approaches is provided.

The Benchmark Footbridge (Without TMD): Description and Numerical Assessment of Its Preliminary Dynamic Behaviour The structure considered as benchmark for this study is a footbridge proposed in the French standard8 as an example to explain the methodology proposed by this normative to check the comfort level under pedestrian action. The footbridge is a composite steel–concrete structure configured by a single span of 38.85 m. The longitudinal profile of the structure has a vertical radius of curvature of 450 m. The structure is composed by two lateral Warren trusses with a constant depth of 1.215 m. The lateral distance between trusses is ~2.90 m. The lower chord of both trusses is braced by strut elements. A reinforced concrete slab

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of 0.10 m depth and 2.50 m width rests on the strut elements. For all the chord elements, a rectangular hollow section of 400 × 200 × 12 mm is considered.

For the diagonal and strut elements, another rectangular hollow section of 120 × 120 × 8 mm is considered. The footbridge is pinned at one support and vertically simple supported at the other one (Fig. 3).

order to check the comfort level of the structure, the method proposed by the Synpex guidelines7 is implemented.

In this manner, five load cases are defined under the expected traffic level of the footbridge according to the values proposed by the Synpex guidelines.7 These load cases are characterized by the traffic level (pedestrian density) of the footbridge. The five load cases and their corresponding pedestrian densities are defined in Table 3.

The footbridge is modelled with frame elements, BEAM188 (two nodes per element, 6 d.o.f. in each node), and shell elements, SHELL181 (four nodes per element, 6 d.o.f. in each node), in the FE package ANSYS.32 The mesh consists of 646 frame elements and 540 shell elements (Fig. 3).

The steel and reinforced concrete are simulated as homogenous materials, considering (a) for the steel, a Young’s modulus: Es = 210 GPa, a Poisson’s ratio: υs = 0.30 and density: ρs = 7850 kg/m3; and (b) for the reinforced concrete, a Young’s modulus: Ec = 31 GPa, Poisson’s ratio: υc = 0.20 and density: ρc = 2500 kg/m3. The structural damping ratio of the footbridge is estimated from the values proposed in Ref. [7].

In the design scenario according to the Synpex guidelines7, maximum comfort class, alim = 0.50 m/s2, is required for all the considered load cases. Additionally, the relative displacement between the footbridge and the TMD is limited: ur ≤ ulim = 20 mm.

For each load case, the equivalent walking pedestrian load is determined and applied to the footbridge. The modal parameters of the footbridge are modified by the pedestrian– structure interaction according to the rule established in Ref. [7]. The maximum numerical vertical acceleration of the footbridge is obtained for each load case. In Table 3, the maximum numerical vertical acceleration, amax, and the corresponding comfort level for each load case are shown.

A numerical modal analysis of the footbridge is performed in order to obtain the numerical natural frequencies and vibration modes of the structure. It is verified that the first vertical vibration mode (Fig. 3) is affected by the pedestrian–structure interaction; so in A

400 × 200 × 12 mm

According to these results, the benchmark footbridge does not verify the 120 × 120 × 8 mm 1.215 m

A 38.85 m

R = 450 m

Section A-A 120 × 120 × 8 mm

2.90 m

First vertical vibration mode ff = 2.14 Hz

Fi g. 3: FE model of the benchmark footbridge and its first vertical vibration mode8

comfort level criterion for the considered design scenario. In order to improve its dynamic behaviour, a TMD device is installed at the point of the maximal modal deflection of the first vertical vibration mode. The TMD parameters are obtained considering both the mentioned methods and approaches. Finally, the performance of the TMD parameters designed according to the above conditions is validated.

Deterministic TMD Design for the Benchmark Footbridge As a first approach, the TMD parameters are obtained by the application of the two methods and by considering that the natural frequency of the affected vibration mode of the footbridge only changes due to the modifications of its operational conditions according to the deterministic rule established by the Synpex guidelines.7 First, the TMD parameters are determined by the application of the DH proposal. A constrained single-objective optimization procedure is used for this purpose. The mentioned optimization problem is defined as follows: find μ, optimize f = μ, subject to i i amax −1 ≤ 0 = Ai amax alim

uj ð16Þ r, max −1 ≤ 0 Aj urj , max = ulim i = I, …, V for each load case j = I, …, V i where amax is the maximum vertical acceleration for the considered load case i and urj , max is the maximum relative displacement for the considered load case j.

Genetic algorithms are used in the optimization method.27 The optimization method chosen ensures that the problem solution is not conditioned by the selected starting point of the search. To avoid problems of illconditioning, the search domain is restricted. A search domain for the

d (P/m2)

n (P)

mf (kg)

ff (Hz)

amax (m/s2)

Comfort degree

Comfort level

I

<0.20

15

34 706

2.14

1.05

Minimum

CL3

II

0.20

19

34 706

2.14

1.16

Minimum

CL3

III

0.50

48

37 710

2.05

1.74

Minimum

CL3

Load case

IV

0.80

76

39 500

2.00

2.08

Minimum

CL3

V

1.00

96

40 750

1.97

4.96

Discomfort

CL4

Table 3: Comfort level of the benchmark footbridge

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Both the population size (mass ratio of TMD) and the maximum number of iterations are set to 100. Each individual modifies its value (via the operations of reproduction, crossover and mutation) in order to minimize the value of the objective function.

After the estimation of the optimum mass ratio of the TMD according to this method, the other two parameters (δopt and ζ opt) are established through the application of the Eqs. (9) and (10). Subsequently, the TMD constants (md, cd and kd) are determined from Eqs. (11) and (12).

The TMD parameters designed according to the DH proposal under the deterministic approach are shown in Table 4.

Subsequently, the TMD parameters are obtained through the application of the multi-objective optimization procedure26 under the deterministic approach. The multi-objective optimization problem considered is defined as follows: findfμ, δd , ζd g, optimize f = ff1 , f2 g

I

V = μ, max amax =alim , …, amax =alim ð17Þ where δd = fd/ff is the frequency ratio of the TMD, max( ) is the maximum I V function, amax , …, amax is the maximum vertical acceleration for each considered load case.

Multi-objective genetic algorithms are used in the optimization method.26 As in the previous case, a search domain for the TMD parameters is established: (a) mass ratio of the TMD, μ 2 [0.00 − 0.05], (b) frequency ratio of the TMD, δd 2 [0.85 − 1.00] and (c) damping ratio of the TMD, ζd 2 [0.05 − 0.15].

Both the population size (each individual is a vector that contains the TMD parameters) and the maximum number of iterations are set to 100 again. A Pareto front with 20 individuals is considered. An additional physical constraint is included in order to obtain the deterministic optimum solution among the possible solutions

of the Pareto front. A limit accelerai =alim = 1 i = I, …, V, is tion ratio, amax established in order to determine the deterministic optimum solution. The deterministic optimum solution is established as the member of the Pareto front that minimizes the first component of the multi-objective function, f1, and guarantees that its second component, f2, is lower than 1.

Subsequently, for the deterministic optimum solution, the maximum relative displacement, ur, between the footbridge and the TMD is checked to be lower than 20 mm.

Figure 4 illustrates the Pareto front (blue colour) of the deterministic TMD design based on the multiobjective genetic algorithms procedure. The Pareto front shows the variation of the two components of the multi-objective function. Each axis represents the corresponding component of the multi-objective function. The deterministic optimum solution is shown in magenta colour.

Additionally, the limit acceleration ratio is shown in a discontinuous red line.

The deterministic optimum solution, obtained from the Pareto front, is adopted as the values of the TMD parameters designed according to this method. Thus, the TMD parameters determined, according to the MGO method under the deterministic approach, are shown in Table 4.

Finally, the frequency response function in terms of accelerations ratio, Ha, of the TMD–footbridge system is obtained29 for the two considered design methods (Fig. 5). This function expresses the dynamic response of the system (vertical accelerations) to the walking pedestrian load as a function of the frequency. The function shows the ratio between the dynamic and pseudo-static vertical acceleration.

The mentioned frequency response functions under the worst load case (load case V) are shown in Fig. 5.

The proposed method reduces, under the deterministic approach, the magnitude of the TMD parameters, by around 10% for both the TMD mass and TMD stiffness, and around 5% for the damping (Table 4). This improvement may be justified by two facts: (a) the conventional method focuses on minimizing the displacements while the proposed method focuses on minimizing the accelerations, and (b) the proposed method fits better the performancebased design requirements.

Finally, as it is illustrated by Fig. 5, in spite of the reduction of the TMD parameters provided by the new proposal, the modification of the frequency response functions is almost negligible.

As a consequence of these results, it is clear that the proposed method allows reducing the TMD parameters under a deterministic approach against the conventional method recommended in current design guidelines.7–9

3.0 Limit acceleration ratio 2.5

Deterministic pareto front

2.0 f2 (–)

mass ratio of the TMD is established with μ 2 [0.00 − 0.05].

Deterministic optimum solution

1.5 1.0 0.5 0.0 0.00

0.01

0.02

0.03

0.04

0.05

f1 (–)

F i g. 4 : Diagram of Pareto front of the deterministic TMD design for the considered design scenario

μ (%)

δopt

ζ opt (%)

md (kg)

kd (N/m)

cd (Ns/m)

DH

3.19

0.909

10.12

1110

165826

2747

MGO

2.85

0.907

10.72

989

147114

2586

Method

Table 4: Design of TMD according to the deterministic approach 498

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30

simulated state, ur,max is a vector that contains the maximum vertical relative displacement of the benchmark footbridge for each simulated state, aα is the percentile αth of the probability distribution of the maximum vertical accelerations of the benchmark footbridge, uα is the percentile αth of the probability distribution of the maximum vertical relative displacements of the benchmark footbridge.

wo_TMD w_TMD_DH

25

w_TMD_MGO

Ha (–)

20 15 10 5 0 1.70

1.80

1.90

2.00

2.10

2.20

2.30

2.40

2.50

Frequency (Hz)

Fi g. 5: Frequency response functions (accelerations ratio), Ha, of the deterministic TMD design for the considered design scenario, being wo_TMD, without TMD; w_TMD_DH, with TMD design according to DH and w_TMD_MGO, with TMD design according to MGO

Robust TMD Design for the Benchmark Footbridge As mentioned previously, in this approach, the TMD parameters are determined by the application of the two mentioned methods and by considering that the modal parameters of the benchmark footbridge (first vertical natural frequency and corresponding damping ratio) may vary randomly due to the modification of the operational and environmental conditions.

According to the results reported in the literature12,13 about the analysis of the variation of the modal properties of two real footbridges, it is assumed here that the modal parameters of the benchmark footbridge may vary randomly considering a variation range of 10%. Based on Monte Carlo simulations,25 20 000 possible states are defined considering uncorrelated normal distribution functions. In order to establish the sample size, a convergence analysis is performed. A level of significance of 0.01 and an accuracy of 0.01 m/s2 for the estimation of the maximum vertical acceleration of the structure are considered.25 The TMD parameters must be robust enough to guarantee the mentioned design scenario under the overall simulated states. A RDO is implemented, considering that the maximum vertical acceleration of the Monte Carlo

simulation may be treated as a random variable and by modifying the constraint equation and the objective function respectively for the two design methods. The definition of the maximum vertical acceleration of the structure is done via the considered percentile of the probability distribution of the maximum vertical acceleration of the benchmark footbridge under the overall simulated states.

Additionally, in order to reduce the computational time, each simulated state calculation is assumed with the load case V of the deterministic approach. A sensibility study about the influence of the uncertainty in the estimation of the TMD parameters is performed via the various considered percentiles.

First, the TMD parameters are determined by the application of the DH method and by considering a constrained single-objective optimization procedure defined as follows: find μ, optimize f = μ,subject to aα Aðamax Þ = −1 ≤ 0 ð18Þ alim uα Aður, max Þ = −1 ≤ 0 ulim where amax is a vector that contains the maximum vertical accelerations of the benchmark footbridge for each

The optimization procedure of genetic algorithms is performed considering the same population size and maximum number of iterations as the deterministic approach. The search domain of the mass ratio is increased, μ 2 [0.00 − 0.07], to take into account the unfavourable effect of the uncertainty in the design of the TMD parameters.

The TMD parameters designed according to the DH proposal under the stochastic approach are shown in Table 5.

The results show the robust design parameters for the considered design scenario. Two percentiles (95th and 99th) are considered for the estimation of the maximum vertical acceleration in order to demonstrate how the uncertainty influences the TMD design.

Finally, the TMD parameters are obtained through the application of the MGO method26 under the stochastic approach. The considered multi-objective optimization problem is defined, in this case, as follows: find fμ, δd ,ζ d g, optimize

aα f = ff1 , f2 g = μ, alim

ð19Þ

Multi-objective genetic algorithms are used in the optimization method.26 The following ranges are considered as search domains for the TMD parameters: (a) mass ratio of the TMD, μ 2 [0.00 − 0.07], (b) the frequency ratio of the TMD, δd 2 [0.85 − 1.00] and (c) the damping ratio of the TMD, ζd 2 [0.05 − 0.15]. Subsequently, for the robust optimum solution, the maximum relative displacement, ur, is found to be lower than 20 mm.

Method

αth

μ (%)

δopt

ζ opt (%)

md (kg)

kd (N/m)

cd (Ns/m)

DH

95

5.62

0.946

14.13

1950

316108

7015

99

6.63

0.937

15.27

2301

365886

8861

95

4.05

0.907

6.74

1405

209055

2310

99

5.00

0.902

9.09

1735

255255

3828

MGO

Table 5: Design of TMD according to the stochastic approach

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f2 (–)

4.5

of the TMD–footbridge system is obtained29 for the two design methods by considering two confidence levels (percentiles 95th and 99th). The mentioned frequency response functions are shown in Fig. 7. The same state considered in the deterministic approach is taken into account as reference. Figure 7 illustrates the uncertainty influences of the TMD design.

Limit acceleration ratio

4.0

Robust pareto front 95th

3.5

Robust optimum solution 95th

3.0

Robiust pareto front 99th Robust optimum solution 99th

2.5 2.0 1.5 1.0 0.5 0.0 0.00

0.01

0.02

0.03

0.04

0.05

f1 (–)

F ig . 6: Diagram of Pareto front of the robust TMD design for the considered design scenario and the two considered confidence levels (percentiles 95th and 99th)

(a)

30 wo_TMD

25

w_TMD_DH 95th

Ha (–)

20

w_TMD_DH 99th

15 10 5 0 1.70

1.80

1.90

2.00

2.10

2.20

2.30

2.40

2.50

Frequency (Hz)

(b)

30 wo_TMD

15 10

Conclusions

w_TMD_MGO 95th w_TMD_MGO 99th

20 Ha (–)

On the other hand, the TMD parameters estimated under the stochastic approach are greater than the deterministic approach, indicating the importance of considering the uncertainty in the TMD design. Not considering this approach may lead to a reduction of TMD performance.1 However, further research is recommended to assess experimentally the performance of real TMDs designed according to this proposal.

The results from both approaches show that the proposed method allows reduction of the TMD parameters compared to the conventional method recommended in current design guidelines.7–9

25

5 0 1.70

1.80

1.90

2.00

2.10

2.20

2.30

2.40

2.50

Frequency (Hz)

F ig . 7: Frequency response functions (accelerations ratio), Ha, of the robust TMD design for the considered design scenario and the two considered confidence levels (percentiles 95th and 99th), being wo_TMD, without TMD; w_TMD_DH, with TMD design according to DH and w_TMD_MGO, with TMD design according to MGO (a) DH method and (b) MGO method

Figure 6 illustrates the Pareto front (blue colour) of the robust TMD design based on the multi-objective genetic algorithms procedure for the two considered confidence levels (percentiles 95th and 99th). The robust optimum solution is shown in magenta colour. Additionally, the limit 500

As in the deterministic approach, the proposed method reduces the value of the TMD parameters for the considered design scenario (around 25% for the TMD mass, around 30% for TMD stiffness, and around 50% for the damping). Similarly, Fig. 7 shows that, in spite of the reduction of the TMD parameters obtained by the proposed method, the differences among the frequency response functions are almost negligible within the range of frequencies that characterizes the vertical acceleration of walking pedestrian action.

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acceleration ratio is shown in a discontinuous red line.

The TMD parameters designed according to the MGO method under the stochastic approach are shown in Table 5.

Finally, the frequency response function in terms of acceleration ratio, Ha,

The main purpose of this paper is to determine the robust optimum parameters of a TMD in order to control the dynamic response of footbridges under pedestrian flows considering the uncertainties associated with the modal parameters of the structure. Optimum parameters must achieve minimum physical, practical and economical values. MGO is used to optimize the parameters of a TMD (mass, stiffness and damping). The response of a benchmark footbridge under a pedestrian flow is checked during the optimization process considering only the walking pedestrian action. This action is simulated via an equivalent harmonic load according to the Synpex guidelines. The study was performed

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under two approaches, deterministic and stochastic. In the deterministic approach, the uncertainties about the change of the modal properties of the structure are determined following the rules established by the Synpex guidelines. In the stochastic approach, the natural frequencies and the damping ratios of the footbridge are assumed to vary randomly due to the change in the operational and environmental conditions. A variation range is established by the results reported in the literature about the modification of dynamic behaviour of real footbridges during their life cycle. In order to guarantee the robustness of the TMD parameters, under the stochastic approach, a RDO procedure is implemented.

The performance of the method is assessed comparing the results between the conventional DH method and the proposed MGO method.

Regardless of the approach, the TMD parameters obtained from the proposed method are smaller than the values obtained from the conventional method which is beneficial for both the footbridge, the force applied by the damper is less, and the damping device, because its cost is also less.

Finally, further studies are recommended, both to assess experimentally the performance of real TMDs designed according to this proposal and to establish better the parameters of the probabilistic distribution that govern the modification of the modal parameter of footbridges during their overall life cycle.

Acknowledgements This work was partially funded by the Spanish Ministry for Science under the research project DPI2014-53947-R.

References [1] Caetano E, Cunha A, Magalhães F, Moutinho C. Studies for controlling humaninduced vibration of the Pedro e Inês footbridge, Portugal. Part 2: implementation of tuned mass dampers. Eng. Struct. 2010; 32(4): 1082–1091. https://doi.org/10.1016/j.engstruct.2009.12.033 [2] Casado CM, Diaz IM, de Sebastian J, Poncela AV, Lorenzana A. Implementation of a passive and active vibration control on an inservice footbridge. Struct. Control Health Monit.

2011; 20(1): 70–97. https://doi.org/10.1002/stc.471 [3] Moutinho C, Cunha A, Caetano E. Analysis and control of vibrations in a stress-ribbon footbridge. Struct. Control Health Monit. 2011; 18(6): 619–634. https://doi.org/10.1002/stc.390

[4] Van Nimmen K, Van den Broeck P, Butz C, Lombaert G, De Roeck G. Numerical and experimental evaluation of the vibration serviceability of a lively footbridge with tuned mass damper. In Past, Present and Future.

Footbridge 2014, Debell L, Russel H (eds) Hemming Information Services: London, 2014; 170–171.

[5] Domaneschi M, Martinelli L, Perotti F. Wind and earthquake protection of cablesupported bridges. Proc. Inst. Civil Eng. Bridge Eng. 2016; 189(3): 157–171. https://doi.org/10.

1680/bren.14.00026 [6] Soong TT, Costantinou MC. Passive and Active Control Structural Vibration Control in Civil Engineering. State University of New York at Buffalo, Springer: Springer-Vertag New York, 1994; 160 pp.

[7] Butz CH, Heinemeyer CH, Goldack A, Keil A, Lukic M, Caetano E, Cunha A. Advanced Load Models for Synchronous Pedestrian Excitation and Optimised Design Guidelines for Steel Footbridges (SYNPEX). RFCS-Research Project RFS-CR-03019, 2007.

[8] SETRA/AFGC. Guide méthodologique passerelles piétonnes (Technical Guide Footbridges: Assessment of Vibration Behaviour of Footbridge under Pedestrian Loading), 2006.

[9] Weber F, Feltrin G, Hult O. Guidelines for Structural Control. Structural Engineering Research Laboratory, Swiss Federal Laboratories for Materials Testing and Research: Dubendorf, 2006.

[10] Den Hartog JP. Mechanical Vibrations.

McGraw-Hill: New York, 1947; 464.

[11] Caetano E, Cunha A, Raoul J, Hoorpah W. Footbridge Vibration Design. CRC Press, Taylor and Francis Group: Leiden, 2009; 192.

[12] Hu WH, Caetano E, Cunha A. Structural health monitoring of a stress-ribbon footbridge.

Eng. Struct. 2013; 57: 578–593. https://doi.org/10.

1016/j.engstruct.2012.06.051 [13] Soria JM, Díaz I, García-Palacios J, Ibán N. Vibration monitoring of a steel-plated stress-ribbon footbridge: uncertainties in the modal estimation. J. Bridge Eng. ASCE, 2016; 21(8): C5015002. https://doi.org/10.1061/(ASCE) BE.1943-5592.0000830 [14] Georgakis C, Jorgesen NG. Change in mass and damping on vertically vibrating footbridges due to pedestrians. In Topics in Dynamics of Bridges, Volume 3: Proceedings of the 31st IMAC. The Society for Experimental Mechanics, Inc: Springer-Vertag New York, 2013.

[15] Jiménez-Alonso JF, Sáez A. A direct pedestrian–structure interaction model to characterize the human induced vibrations on slender footbridges. Inform. Constr. 2014; 66(EXTRA-1): m007. https://doi.org/10.3989/ic.13.110 [16] Bekdas G, Nigdeli SM. Estimating optimum parameters of tuned mass dampers using harmony search. Eng. Struct. 2011; 33(9): 2716–2723. https:// doi.org/10.1016/j.engstruct.2011.05.024 [17] Moutinho C. An alternative methodology for designing tuned mass dampers to reduce

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seismic vibrations in building structures. Earthq.

Eng. Struct. Dyn. 2012; 41(14): 2059–2073. https://doi.org/10.1002/eqe.2174 [18] Pourzeynali S, Salimi S, Eimani Kalesar H. Robust multi-objective optimization design of TMD control device to reduce tall building responses against earthquake excitations using genetic algorithms. Sci. Iran. A 2013; 20(2): 207–221. https://doi.org/10.1016/j.scient.2012.11.015 [19] Domaneschi M, Martinelli L, Po E. Control of wind buffeting vibrations in a suspension bridge by TMD: hybridization and robustness issues. Comput. Struct. 2015; 155: 3–17. https:// doi.org/10.1016/j.compstruc.2015.02.031 [20] Zang C, Friswell MI, Mottershead JE. A review of robust optimal design and its application in dynamics. Comput. Struct. 2005; 83: 315–326. https://doi.org/10.1016/j.compstruc.2004.10.007 [21] Marano GC, Cuaranta G. Robust optimum criteria for tuned mass dampers in fuzzy environments. Appl. Soft Comput. 2009; 9(4): 1232–1243. https://doi.org/10.1016/j.asoc.2009.03.010 [22] Marano GC, Greco R, Sgobba S. A comparison between different robust optimum design approaches: application to tuned mass dampers. Probab. Eng. Mech. 2010; 25(1): 108–118. https://doi.org/10.1016/j.probengmech.

2009.08.004 [23] Lievens K, Lombaert G, De Roeck G, Van den Broeck P. Robust design of a TMD for the vibration serviceability of a footbridge.

Eng. Struct. 2016; 123: 408–418. https://doi.org/ 10.1016/j.engstructut.2016.05.028 [24] Nocedal J, Wright SJ. Numerical Optimization. Springer: New York, 1999; 683.

[25] Bucher C. Computational Analysis of Randomness in Structural Mechanics. CRC Press, Taylor & Francis Group: London, 2009.

[26] Kim G, Park Y. An improved updating parameter selection method and finite element model update using multi-objective optimisation technique. Mech. Syst. Signal Process 2004; 18(1): 59–78. https://doi.org/10.1016/S0888-3270 (03)00042-6 [27] Koh Ghee C, Perry MC. Structural Identification and Damage Detection using Genetic Algorithms. CRC Press, Taylor and Francis Group: London, 2010.

[28] Domaneschi M, Martinelli L. Refined optimal passive control of buffeting-induced wind loading of a suspension bridge. Wind Struct.

2014; 18(1): 1–20. https://doi.org/10.12989/was.

2014.18.1.001 [29] Clough RW, Penzien J. Dynamics of Structures. McGraw-Hill Book Company: New York (EEUU), 1993; 634.

[30] Asami T, Nishihara O, Baz AM. Analytical solutions to H∞ and H2 optimization of dynamic vibration absorbers attached to damped linear systems. J. Vibr. Acoust. 2002; 124(2): 284–295. https://doi.org/10.1115/1.1456458 [31] Matlab R2011a. http://www.mathworks.com/ [32] ANSYS Mechanical Release. http://www. ansys.com/

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An Innovative Connection System for Cross-Laminated Timber Structures Andrea Polastri, Researcher, Trees and Timber Institute - National Research Council of Italy (CNR-IVALSA), San Michele all’Adige, Italy; Ivan Giongo, Research Fellow; Maurizio Piazza, Prof., Department of Civil, Environmental and Mechanical Engineering, University of Trento, Trento, Italy. Contact: polastri@ivalsa.cnr.it DOI: 10.2749/222137917X14881937844649

when buildings are subjected to strong seismic events.3

Abstract The paper presents a new connection system for cross-laminated timber (CLT) structures, named X-RAD. This innovative connection system is characterised by the use of a single connector type that is positioned at the corners of the CLT panels. X-RAD is formed by a metal part surrounding a hardwood insert that is fixed to the panels by means of all-threaded screws introduced with double inclination. The peculiar geometry of the connector and the combination of different materials allow the full exploitation of the capacity of the CLT panels while ensuring a ductile response of the connection. Construction modularity, fast assembly/disassembly speed and prefabrication are some of the aspects that can be associated with X-RAD development. The outcomes of an extensive testing campaign on the new connector are also presented in the paper.

Keywords: cross-laminated timber; innovative connections; point-to-point connections; experimental testing; calculation method.

Introduction In the next decade, the availability of new and large building areas in the emerging countries and the requalification/reconstruction of old, abandoned urban areas inside the major European cities will foster the expansion of the timber building industry. Such expansion, however, is really possible only if the following requisites are guaranteed: construction speed, reliable construction time and cost and high-quality standards. The cross-laminated timber (CLT) technology could potentially meet all the requirements listed above as the panels are produced under severe quality control procedures and are characterised by high mechanical performance and machining precision.1 They are manufactured in modern industrial plants and are able to provide the production volume required for the big construction sites mentioned earlier. In addition, the CLT manufacturers frequently supervise and take care of the entire construction process, from the three dimensional (3D) design and optimisation of the panel cutting to the transport and then assembly of the completed structure.

Peer-reviewed by international experts and accepted for publication

by SEI Editorial Board Paper received: May 25, 2016 Paper accepted: December 29, 2016

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The versatile nature of CLT as a structural product has certainly helped the diffusion of CLT buildings. CLT panels, in fact, ensure that the timber structures have a high strength in both loading directions, in-plane or out-of-plane (wall/diaphragm configuration). In addition, when loaded edge-wise, they also offer an extremely stiff response.

Another aspect that has fuelled the use of CLT is its environmental friendliness, being a renewable and recyclable material with excellent insulating qualities.

On the other hand, there are some critical issues that limit the full development of CLT construction technology: problems in handling, difficulty in positioning and assembling and inadequate connection systems.

In the standard CLT assembly system, single panels are usually connected to the foundation and to the floor panels by means of hold-down elements and angle brackets.2 These connectors, originally designed for other construction technologies (e.g. light-timberframe [LTF] wall buildings), have been adopted for CLT structures with little or no modifications. As a result, the building capacity is limited by the strength of those connectors, which also show ultimate deformations not compatible with the CLT panel stiffness (Fig. 1). In addition, those connectors have often proved to be inadequate to transfer the lateral loads

Moreover, all the connectors (screwedin elements included) are fixed on site, with significant time waste and consequent uncertainty due to the hard-toverify quality of an on-site installation.

These drawbacks turn into critical problems when tall buildings are concerned. Attempting to solve them, different research groups have proposed alternative systems for the construction of multi-storey buildings. For example, solutions that involve the use of posttensioned timber frames4,5 or hybrid steel–timber systems6 can be found.

Therefore, in order to comply with the most recent and most advanced standards (especially with regards to seismic hazard) and also to satisfy the needs of an international market that is becoming more and more interested in the CLT technology, it is fundamental to develop new and more efficient connection systems. A tendency to substitute the nailed connections spread all over the wall edges, with all-threaded screws concentrated in few well-defined positions, can be found in some recent works.7,8 Similar to the innovative construction systems/connectors originated from the aforementioned studies, X-RAD was designed to provide a viable solution for some of the most crucial issues related to the CLT technology, such as the handling and the assembly phases. At the same time, the connector characteristics were selected to ensure high performance in terms of stiffness, strength and ductility, as requested by tall CLT buildings.

Analysis of the Connection System Typically Used for CLT Structures Description of the Connectors Typically Used in CLT Structures As mentioned in the section Introduction, the hold-downs and angle brackets that are commonly

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ductile joints. Alternatively, laminated veneer lumber (LVL) strips can be nailed into grooves obtained on the matching edges of adjacent panels.

Fi g. 1: LTF wall (a) and CLT wall (b) schematics. A close-up on connections—holddowns and angle brackets—and some failure modes are reported on the right side of the figure. Supposedly ductile elements are reported in green, while strong elements are represented in red

used in CLT structures for transferring tension and shear forces have been derived directly from the LTF construction technology without major alterations. LTF structures are, by definition, light and therefore, in case of a seismic event, are subjected to smaller actions than CLT structures of comparable size. In addition, the walls of LTF buildings are made by sub-components (the nails, the framing and the sheathing) that, generally, ensure higher energy dissipation than the monolithic CLT walls, thus resulting in reduced seismic actions. Consequently, the standard systems that were originally developed to connect timber frame walls are inadequate to bear the inertial loads generated by the heavier and stiffer CLT panels.

Because of the more severe seismic demand related to CLT structures (compared to traditional LTF structures), shear brackets and hold-downs have grown in size over time, and all the manufacturing companies currently produce oversized versions of their standard connectors, specifically for CLT constructions. Such oversize connectors can usually accommodate an excessively large number of nails/ screws that may induce a premature failure of the connector plate before any nail/screw yielding (Fig. 1b).

Besides, the magnitude of the forces that the oversize connectors transfer to the reinforced concrete (RC) foundation makes the use of chemical/ mechanical anchors quite challenging.

Aspects related to practicality of the on-site assembly often determine that hold-downs and angle brackets are installed only on the internal side of the perimeter walls. This causes an asymmetrical loading condition that is

generally not accounted for when defining the default properties to be adopted in the engineering practice.

Usually, experimental tests are performed in symmetric configuration;9 otherwise, setups are to be designed to avoid rigid out-of-plane deformations and buckling phenomena.10 Simplified Analysis Model and Load Paths in CLT Structures In CLT buildings, the vertical forces are transferred to the foundation via wall panels loaded in-plane. The same panels also withstand the lateral loads due to wind and earthquakes (panels loaded edgewise). Horizontal floor panels work out-of-plane as they are loaded flat-wise by the service loads but also in-plane when diaphragm action is required. Since the early nineties, when CLT started being used as structural product, it became evident that the use of CLT could facilitate a box-like behaviour where all the structural parts (both vertical and horizontal) are connected together and collaborate in defining the global response of the building (Fig. 2a).

The CLT construction system is a platform system, that is, the vertical structural elements are interrupted by the horizontal diaphragms at the floor levels. The floor panels’ role is to connect the wall panels and also distribute the lateral forces to the loadresisting elements (Fig. 2b). Being the panels limited in size by production/ transportation issues, it is necessary to provide adequate panel-to-panel connection in order to obtain sufficient inplane floor stiffness (Fig. 2a). A common solution is to use all-threaded screws inserted in a crossed disposition, which ensures extremely stiff yet non-

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Connection systems in CLT buildings can be grouped into two classes: (a) ductile/dissipative connections, composed by nails, nail plates and laterally loaded screw fasteners, and (b) brittle/non-dissipative connections, made by inclined screws.11 It is not uncommon in CLT structures to observe a mixed use of ductile and brittle connections resulting in an increased complexity that makes it difficult to characterise the building’s global response in terms of strength, stiffness and ductility.

Experimental research on full-scale buildings, such as research projects SOFIE,3 SERIES,12,13 and FPinnovation14, has demonstrated that simplified procedures and two dimensional (2D) finite element (FE) modelling might not be adequate to describe the real response of the structure, especially concerning the fundamental period of vibration. In fact, in addition to the uncertainties ensuing from connections with significantly different performance, the effects of the aforementioned box-like behaviour greatly influence the building response.

Therefore, refined 3D models need to be implemented in order to correctly interpret the experimental results.15,16 A further source of complexity can be found in the edge joints between vertical panels, inevitable because of the panel geometric limitations. Moreover, some producers have focused their production on small-sized panels (panel width <2 m) in order to increase versatility and minimise cuts on the panels. This implies structures with a larger number of vertical edge joints when compared to buildings assembled using wider panels (width >2 m). An increase in the number of vertical joints usually means a reduction of the global stiffness but can also ensure a higher ductility if the connection system (nails or screws) is adequately designed.10,17 On the other hand, it must be remarked that the design practice is typically based on an extremely simplified approach where the timber walls are treated as cantilevers spanning from the foundation level to the roof level, similar to the soft spandrel approach that is often adopted for the assessment of unreinforced masonry buildings (Fig. Scientific Paper

503

Fh

q

Fh,j Vj

Fh,j

Vj

Fh

FHD

Fc

(a)

(d) Fh,j

Fh

q

FHD

FHD Vb

(b)

Vj

Vi Vj

Fc

(c)

Vj

Vj Vi

F1 F2 F3

FHD

(e)

F ig . 2: (a) CLT building box-like behaviour; (b) identification of vertical resisting elements; (c) simplified cantilever approach adopted in the design practice; (d, e) force distribution scheme for calculating the connection elements for a wall subjected to lateral loading (Units: [-])

2b). Such a method obviously does not consider any coupling effect that may be provided by the spandrels or any 3D effect related to the aforementioned box-like behaviour.

Two alternative methods are generally employed to evaluate the rocking capacity and shear strength of the timber walls once the forces on the vertical cantilevers have been determined.

In the first method (Fig. 2d), the wallrocking stability is ensured solely by the hold-down connectors, while the angle brackets are just responsible for the shear capacity and do not provide any vertical constraint. The second method acknowledges that the angle brackets have a non-negligible vertical stiffness and consequently contribute to the wall-rocking behaviour (Fig. 2e).10,18 Concerning deformability, Ref. [19] has reported that evaluating the connector stiffness by using the analytical procedures available in literature usually results in a large overestimation of the actual values. In fact deformability of the connection system can lead to local failure modes and force transfer mechanisms that are quite different from those expected by relying on simplified calculation approaches. Adeis quate connection ductility11 required to ensure force redistribution between the elements that constitute the connection in order to avoid premature failures due to a domino effect.

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It should be added that in earthquakeprone areas, the use of non-linear procedures for the seismic design of timber buildings is not uncommon. In this scenario, large displacements and significant deformation levels are allowed if not desired (large dissipation of energy); consequently, adequate ductility of the connections must be ensured to accommodate such deformations.

It is thus of fundamental importance to provide thorough, reliable data on the performance (both stiffness and strength) of mechanical connections with regards to the elastic phase and the post-elastic phase at different levels of displacement; these aspects are partially addressed by standard codes, such as EN 2689120 and EN 12512.21 A precise tuning of the calculation method and the correct definition of the connection over-strength factors are therefore crucial in order to avoid brittle failures and unforeseen collapse mechanisms.

Description of the New Connection System

metallic envelope with an internal steel plate, an inner core made of hardwood and a set of six all-threaded self-tapping screws VGS 11 × 350 (diameter [mm] × length [mm]) (Fig. 3).22 Unlike single-threaded screws or double-threaded screws,23,24 the insertion of all-threaded screws does not introduce any compression forces, and therefore, no stress is applied to the metal envelope. To complete the system, steel bolts and steel linking plates are used to join together the X-RAD units belonging to adjacent and/or intersecting panels (Fig. 4b and c).

In order to maximise the withdrawal strength, the all-threaded screws are installed at two different angles of inclination, as recommended by Ref. [25] (Fig. 3b). This implies that the XRAD connectors, where the screws are subjected to a combination of shear and tension forces, are stronger and stiffer than the traditional joints where shear is the main action. Therefore, thanks to the crossed disposition of the screw fasteners, the X-RAD system is capable of engaging the full capacity of both the CLT panels and the all-threaded screws.

Description of the New Connector The X-RAD system can be effectively described as a point-to-point mechanical connection system to be placed at the corners of the CLT panels (Fig. 3).

An X-RAD connector is comprised of three main components: an outer

X-RAD Production, Handling and Assembly The X-RAD units are fixed to the plant corners of the panels directly at the production plant where CLT panels are manufactured. Prior to the unit

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2

2

Holes for bolts M16

Inner steel plate

1 110

Transversal bolt M12 Hardwood insert Screw 11 x 350

°

Lateral screws

50°

270 90

90

Lateral screws Central screws

CLT layer

3

Outer metal envelop

Othogonal CLT layer

(a)

(b)

(c)

(d)

Fi g. 3: Schematic description of the connector

(a)

(b)

(c)

Fi g. 4: Production phases: (a) shaping and lifting the CLT panel; (b) X-RAD units jointed by the external linking plates; (c) render of a mock-up structure assembled with the X-RAD system

installation, the panel corners have to be chamfered by using a computer numerical control (CNC) cutting system. Once the panel has been properly shaped, the all-threaded self-tapping screws are inserted into the pre-drilled hardwood element, and the X-RAD unit is definitively joined to the panel.

When all the units are installed, the panel is ready to be lifted (the X-RAD units serve as lifting hooks) and transported to the building site (Fig. 4a).26 At the building site, the pre-assembled CLT wall panels with the X-RAD units already installed at the corners can be lifted directly from the truck and positioned on special steel plates anchored to the foundation. Such plates are fixed to the foundation beams in compliance with the building design, thus favouring the correct positioning of the CLT panels. To secure the panels into their final position, only a few standard steel bolts that connect the anchoring plates to the XRAD units must be inserted. The result of this is that any on-site nailing/ screwing operation is avoided.

Different versions of the linking plates that connect the X-RAD units were developed to allow multi-way

connections (Fig. 4b). Because of the characteristics listed in this chapter, the X-RAD system appears to be particularly suitable for modular pre-fabricated buildings where fast erection speed and optimised construction costs are crucial (social housing). The ease of disassembly and re-assembly makes the X-RAD system a valid choice also for temporary constructions such as fair/exhibition stands or post-disaster/ emergency shelters and reconstruction buildings (housing recovery).

Inevitably, some X-RAD innovative aspects represent a limit, for example, in case of irregular building geometries that are difficult to realise: ad hoc linking plates have to be designed in order to connect non-orthogonal walls.

Analysis of the Innovative Connection System for CLT Structures Relevant Features of the Connection System Design Process The design of X-RAD’s various components was developed to attain the objectives listed in the following list.

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• To exploit the full capacity of allthreaded screws both in tension and compression: the load transfer mechanism that defines the mechanical performance of the X-RAD system is the pull-out/pull-through of the threaded screw shanks. Forces are, in fact, transferred from the CLT panel to the hardwood insert and to the metal components via axially loaded screws.

• To engage the maximum local strength of the CLT panels, screws are inserted in a crossed disposition, which guarantees the involvement of all the panel layers in the resisting mechanism (Fig. 3b).

• To create a connection that is effective in any loading direction: thanks to the peculiar arrangement of screws.

• To provide sufficient ductility to the connection system: the use of the outer metal envelope and the internal steel plate ensures a high deformation capacity that enables adequate force redistribution.

Brittle failure of the hardwood insert is prevented by the confining action offered by both the metal wrapping and the M12 transversal bolts (Fig. 7c).

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Tension α = 90°

2

α = -45°

Analytical Study— At Failure

α = 45° Shear α = 0°

1

50°

50°

90

°

Hardwood insert

CLT panel external layer

Lateral screws Central screws

Lateral screws

(a)

CLT panel ortogonal layer

(b)

F ig . 5: Reference system for X-RAD geometry

Analysis of Sub-Components Screws A characteristic tensile strength of 38 kN is declared by the producer for the all-threaded screws VGS 11 × 350 adopted in the X-RAD system; a mean value equal to 42 kN (Fscr,T) was then assumed in the analytical calculations reported in section Analytical Study— At Failure. Similar values were found via direct experimental testing. According to the Eurocode 527 and the European Technical Approval,22 in order to fully engage such an axial load-carrying capacity, the embedment depth of the screws when inserted in class C24 softwood (the strength class of the boards generally used for CLT panels) should be 295 mm.

The actual embedment depth is 275 mm for the lateral screw fasteners and 290 mm for the central ones. The condition, where the fasteners are driven at odd angles through differently orientated layers of material (Fig. 3a and b), makes the analytical evaluation of the mechanical performance quite challenging. It is worth mentioning that pull-out extraction of the fasteners from the CLT panel was observed in none of the experimental tests performed so far (more than 80 tests).

In the shear loading configuration, the head of the screws placed on the leeward side of the specimen (see Fig. 6b on the left) tend to be pushedout from the hardwood insert that is

compressed against the CLT surface by the metal envelope. A mean axial capacity in compression of 34.5 kN (Fscr,c) was derived for an embedment depth of 70 mm from a testing campaign performed at the CNR IVALSA Research Institute in 2013.28 Outer Metal Envelope/Internal Steel Plate/Transversal Bolts The steel components in the X-RAD unit, namely the outer metal envelope, the internal plate and the M12 bolts, were designed to meet the requirements described in the following list.

• Limit the stress level in the LVL insert, where the screw distances from the edges do not meet the standard requirements and where brittle failures may arise due to tension perpendicular to the grain.

• Transfer all the stresses (coming from the screws) to the point where the X-RAD connections are fixed to one another.

• Provide ductility to a system otherwise composed by brittle elements.

The metal elements (with thickness ranging from 2.5 mm for the outer metal envelope to 6 mm for the internal plate) are made of DX51D steel that, according to the manufacturer, exhibits an elongation at failure of about 30% and a tensile strength of 360 MPa. Tests carried out at CNRIVALSA gave a yield strength of 348 MPa and an ultimate strength of 429 MPa (mean values).

Analytical failure load, Flim (kN)

Loading configuration

Screw side

Tension α = 90 Shear α = 0 Shear–tension α = +45 Shear–compression α = −45

Analytical formulations to evaluate the capacity of CLT panels provided with the X-RAD connection system were developed for different loading conditions. The analysis approach was based on the static theorem of the plasticity theory, which gives lowerbound estimations (thus on the safe side) of the actual capacity of the connectors. Mean values were adopted for the mechanical input parameters of each component so that a direct comparison of the analytical predictions with the experimental results was possible (Table 1). Four loading configurations were considered, as reported in Fig. 6: tension configuration, perpendicular to the interface surface between the CLT panel and the X-RAD unit; shear configuration parallel to the interface; 45 inclination to the interface for the sheartension; and shear-compression configurations.

The failure mechanisms adopted in the analysis are derived from the equilibrium condition in the four loading directions represented in Fig. 6b.

A direct comparison between analytical predictions and experimental results will be given in Table 1 (details on the test campaign that provided the experimental data will be given in section Test Results).

In the tension configuration, all the screw fasteners are subjected to a tensile force, and the total screwconnection capacity (Flim) can be determined by simply projecting and then summing the reaction forces offered by the screws.

F⊥ = 2Fscr, T + 4Fscr, T sin⁡α = 2Fscr, T + 4Fscr, T , ⊥

The collapse load for the metal components (see section Outer Metal Envelope/Internal Steel Plate/Transversal Bolts) was determined according to the provisions contained in

Mean capacity from tests, Fmean (kN)

Steel side

ð1Þ

Experimental failure mode

212.69

152.12

171.15

Steel side

98.56

130.17

108.95

Screw side

99.71

130.17

128.95

Screw side

173.71

*

185.87

Screw side

*The block-tearing failure mode does not activate for the shear–compression loading configuration.

Table 1: Summary of capacity values calculated for the different failure mechanisms 506

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15 18

F⊥

18 36

D=

Fscr,T

15

F⊥

Fscr,T

24

18

Fscr,T,// Fscr,T,//

F//

Fscr,T

Fscr,C

Fscr,T⊥

Fscr,T

F//

Fscr,T

(a)

(b) F⊥ F⊥

Fext F//

Fext F//

Fjj = Fext cos⁡45

ð3Þ

ð4Þ

(d) (c) Fi g. 6: Force equilibrium for different loading configurations: (a) tension; (b) shear; (c) shear–tension; (d) shear–compression (tensile forces and tension-resisting elements are in red; blue is for compression, and green is for shear) (Units: [-])

compression (struts). The central screws are assumed to remain unloaded. The screw connection capacity is therefore: Fk = 2Fscr, T cos⁡α + 2Fscr, C cos⁡α = 2Fscr, T , k + 2Fscr, C, k

ð5Þ

Fk = F⊥

σ⊥

ð2Þ

The collapse load values calculated for the steel-side failure modes are higher than Fk, which consequently represents the X-RAD connection capacity. This was consistent with the experimental observations (Fig. 8),

In the shear configuration (Fig. 6b), a strut-and-tie mechanism can be identified, where two of the inclined screws are responding in tension (ties), and the other two are working in

The shear–tension configuration consists of a combination of the shear configuration and the tension configuration. As the external force Fext is applied with an angle equal to 45 , the force projection along the parallel (Fk) and perpendicular axis (F⊥), with respect to the X-RAD base, gives: F⊥ = Fext sin⁡45

τfriction

Eurocode 3.29 The actual capacity of the X-RAD connection is the minimum among all the capacities along the resistance path. As shown in Table 1, block tearing of the metal envelope provides the minimum strength values and therefore determines the X-RAD connection capacity in the tension configuration (Fig. 7).

where the failure condition corresponded to the collapse of one of the two tension screws.

The connection capacity is governed by the windward screws that are loaded in tension by both Fk and F⊥ (Fig. 6c). In the shear–compression loading configuration, a friction force (Fμ) originates from the compressive stresses at the steel-to-timber interface (a friction coefficient μ = 0.2 was assumed). As for the shear–tension loading condition, the external load is applied with an angle equal to 45 ; therefore: Fk = F⊥ Fμ = F⊥ μ

ð6Þ

Fk = 2Fscr, T cos⁡α + 2Fscr, C cos⁡α + Fμ

1 2Fscr, T , k + 2Fscr, C, k ! Fk = 1−μ ð7Þ Experimental evidence showed a failure mode similar to that of the shear configuration, with collapse of the screws subjected to tension. Such behaviour was matched by the

150 100

Force (kN)

50

Displacement (mm)

200 40 30 20 10 0

0

0

500

1000 Time (s)

1500

2000

–50

F

–100

Global Local Local

–150 –200 –40

–30

–20

–10

0

10

20

30

40

Displacement (mm)

(a)

(b)

(c)

Fi g. 7: Tension configuration: F–v curve and instrumentation (a), testing setup (b) and failure mode (c)

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200 Displacement (mm)

40

150

Force (kN)

100 50

20 0 –20 –40

0

1000 2000 3000 4000 5000 Time (s)

0

F

–50

Local

–100

Global

–150

Local

–200 –40

–30

–20

–10 0 10 Displacement (mm)

20

30

40

(a)

(b)

(c)

F ig . 8: Shear configuration: F–v curve and instrumentation (a), testing setup (b) and failure mode (c)

analytical calculation, which provided for the steel failure mechanisms higher-capacity values than those calculated for the screw failure mechanism.

version of X-RAD, as reported in section Description of the New Connectors, was finalised based on the experimental outcomes from the prototype campaign.

Experimental Analysis

Main Testing Campaign: Setup and Test Configurations

Preliminary Tests An extended experimental campaign on X-RAD prototypes was performed since 2013 at the Mechanical Testing Laboratory of CNR-IVALSA in San Michele all’Adige (Trento).

The first phase was aimed at maximising the withdrawal capacity of the all-threaded, self-tapping screws that are driven into the hardwood insert, which is wrapped by the outer metal envelope. Different hardwood species and material types (solid wood specimens and veneered specimens) were studied.28 Results obtained from the aforementioned tests lead to the design of the first version of the X-RAD prototype.

Fourteen specimens were tested according to both monotonic and cyclic protocols.28 In 2014, the final

The main experimental campaign was focused on the X-RAD connector as a whole, that is, each specimen consisted of an X-RAD unit, fixed to a 100 mm thick CLT panel (Figs. 7 and 8). To connect the X-RAD unit to the CLT panels, all-threaded self-tapping screws (VGS 11 × 350) were employed, as described in Description of the New Connectors. The connection system was tested in different loading configurations to characterise X-RAD behaviour in the most likely working conditions. Four loading directions were addressed, consistently, with the calculations shown in the Analysis section (Fig. 6).

The tension and shear configurations were subjected to cyclic loading21 as monotonic testing on these configurations had previously been conIncreasing monotonic ducted.30

Shear cyclic tests (15 specimens)

Tension cyclic tests (15 specimens) Fmax (kN)

Fy (kN)

vy (mm)

D

Fmax (kN)

Fy (kN)

loading (displacement controlled at a speed of 0.1 mm/s) was applied to the shear–tension and shear–compression configurations. Five displacement transducers were employed to record both global and local deformations (Figs. 7a and 8a), while the force magnitude introduced by the hydraulic jack was measured by a 250 kN load cell.

Test Results The test results were analysed in accordance with Ref. [21]. As an example, the load–displacement curve and the ideal bilinear curve (red lines) for cyclic test LPM-035 (tension) and LPM-027 (shear) are reported in Figs 7 and 8, respectively.

The outcome in terms of backbone curve for one of the monotonic tests conducted in the same loading configuration is portrayed by the dashed line. Consistent stiffness values were observed for the cyclic test and the monotonic test. Finally the green line in the graph represents the local displacement between the X-RAD unit and the CLT support panel. The green curve stiffness reflects the

Shear–compression monotonic tests (6 specimens)

Shear–tension monotonic tests (6 specimens)

vy (mm)

D

Fmax (kN)

Fy (kN)

vy (mm)

D

Fmax (kN)

Fy (kN)

vy (mm)

D

Min.

163

84

3.1

4.4

89

86

7.6

1.2

119

96

6.06

1.88

169

149

8.92

1.6

Max.

180

121

5.3

8.6

138

133

16.7

3

143

110

12.56

2.74

199

178

11.16

1.9

Mean

171

99

4.3

6.3

108

100

11.7

2

129

103

8.96

2.23

186

165

10.11

1.8

14.6

16.9

18.6

28

9.4

5.7

CoV (%)

2.9

11.6

8.9

10.2

7.1

4.6

24.1

14.2

6.6

7.7

CoV: Coefficient of variation

Table 2: Test results: maximum capacity, yielding point and ductility 508

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stiffness of the load-transfer mechanism provided by the self-tapping screws, regardless of the deformation of the outer metal envelope and transversal bolts. Table 2 summarises the results from the main testing campaign for the diverse loading conditions in terms of maximum capacity (Fmax), yielding point (Fy, vy) and ductility (D).

resisting mechanisms that are engaged also differ (see section Analytical Study—At Failure), and both the elastic and the post-elastic properties of XRAD vary: in the shear configuration, where collapse is determined by the tensile failure of the screws, a mean ductility factor (Dmean = 2.0), significantly smaller than in the tension configuration, was found. With regards to the energy dissipation, the connector response in the shear configuration presented a remarkable sensitivity to the displacement amplitude: mean veq values equal to 19.3 % (first-iteration cycle) and 14.3% (third-iteration cycle) were found for a displacement vmax = 2 × vy; mean νeq values equal to 30.8% (first-iteration cycle) and 15.5% (third-iteration cycle) were found for a displacement vmax = 4 × vy. Such high levels of dissipation are obtained due to the combined effects of local failures inside the hardwood insert, as seen for the tension configuration and of friction phenomena that originated at the X-RAD-toCLT interface, due to the compression force generated by the rotation of the tension-loaded screws at large displacements.

The collapse of the specimens tested in the tension configuration was reached after significant deformation, when the steel plates experienced block-shear failure. It is worth noting that before such an ultimate condition was reached, the M12 transversal bolts and the metallic envelope had undergone considerable plastic deformations. Local failures in the hardwood insert were also observed. The specimens that were tested in the shear, shear–tension and shear– compression configurations exhibited progressive tensile failure of the screws loaded in tension. At the end of the tests, the internal wood insert showed cracks and splitting in the area close to the screws (Fig. 8c).

Table 3 gives an example of the data processing required to identify the post-elastic behaviour of specimens subjected to cyclic loading as recommended by Ref. [21]

Further study certainly needs to be undertaken in order to investigate the X-RAD behaviour with regards to ductility and energy dissipation, especially for loading directions other than those described in Fig. 6.

In the tension configuration, X-RAD showed a significant post-elastic deformation with a mean ductility factor Dmean = 6.8. Significant energy dissipation, expressed in terms of equivalent viscous damping ratios νeq, was observed for all deformation levels, with the mean value of νeq equal to 17.7% for the first-iteration cycles and 10.0% for the third-iteration cycles.

This was ascribed to the steel elements already exceeding the plastic threshold at small displacement amplitudes. If the load direction changes, the load-

CLT Structure Assembled with X-RAD System Description of Structural Behaviour and Load Path In the standard CLT system, the wall panels are connected to one another and fixed to the foundation through hold-downs, angle brackets and screws. The floor panels are inserted

Tension configuration: LPM-035 Ductility level

νeq1 (%)

0.75 × vy

9.11

between the upper edge of vertical wall panels belonging to a storey and the bottom edge of the panels placed on the succeeding storey. Therefore, the horizontal diaphragm panels are subjected to compression perpendicular to the grain, producing possibly large vertical deformation in the case of high-rise buildings. In addition, the interruption of the vertical-wall continuity means that, at each level, the uplifting forces and the horizontal forces have to be transferred from the upper walls to the floor and again to the lower walls by means of a great number of connectors.

The X-RAD connection system allows different wall-to-diaphragm configurations: it is possible to adopt the wellknown platform system (Fig. 9b), or alternatively, the diaphragm panels can be suspended by means of allthreaded screws or hangers to multistorey span wall panels without creating interruptions in the vertical loadcarrying elements (Fig. 9c).

In case of platform system, because the X-RAD units are located at the panel corners only, it is possible to create a slot in the central part of the upper edge of the panels to accommodate the floor panels (fixed by means of screws). This disallows direct contact between the horizontal panels and the upper walls, thus avoiding issues related to loading orthogonal to the fibres. Special linking plates that should enable an alternative fixing solution where the floor panels are connected directly to the corners of the walls (where the X-RAD units are positioned) are currently under development.

Although the X-RAD system was designed to be suitable for sundry building typologies, it finds its optimal use in constructions with a regular plan/vertical geometry, where the

Shear configuration: LPM-027 (+)

νeq3 (%)

Impairment of strength (%)

νeq1+ (%)

4.61

5

Shear configuration: LPM-027 (−)

νeq3+ (%)

Impairment of strength (%)

νeq1− (%)

νeq3− (%)

Impairment of strength (%)

15.71

16.11

3

13.31

13.14

3

1 × vy

9.43

4.75

5

15.94

15.85

3

11.55

11.61

4

2 × vy

15.21

6.24

8

20.89

15.34

13

15.58

11.70

10

4 × vy

18.25

8.11

11

32.01

11.17

59

29.29

6 × vy

15.38

8.21

12

*

*

*

*

–

–

*

*

*Specimens in shear configuration, including specimen LPM 027, failed at a displacement level equal to 4 × vy.

Table 3: Example of test data processed according to Ref. [21]: specimen LPM-035 and LPM-027

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(a)

(b)

(c)

F ig . 9: Load path and primary structural elements in CLT structures assembled with: (a) typical connections; (b) X-RAD connections— platform system; (c) X-RAD connections—cantilever system (continuous vertical walls)

entire façade is supposed to withstand lateral loads as a whole.

The position of the X-RAD connectors (confined to the corners of the wall panels) and the presence of the linking plates (that join connectors belonging to different walls into forming a single node) determine a clear load path if compared with the frequently unclear force exchange existing between panels and fasteners in the standard CLT connection system.

It is worth noting that with the XRAD system, the façade becomes a single structural unit in terms of assembly, mechanical behaviour and, consequently, structural analysis.

Proposal of a Calculation Method for CLT Structures Assembled with XRAD Connection System An extremely simplified analysis method for CLT structures, where the X-RAD system is adopted, is proposed hereafter. A more refined method is currently under review and will be published in the near future.

The forces acting on the X-RAD connectors are determined by considering the building façades as 2D structural systems constituted by quadrilateral elements (CLT panels) joined at their

(a)

corners (Fig. 10a and b). The deformability of the joining steel plates is neglected in this phase.

The plate design complies with the capacity design, which means that the linking plates are stronger than the XRAD connectors forming the connection branches. This assures a reliable global robustness of the structure as the collapse of a connector does not imply the failure of the whole connection, and load forces can find alternative paths.

Once the forces acting on the node are determined (Fig. 10d), the verification of each X-RAD connector can be performed by using the approach presented in section Analytical Study—At Failure. For force directions intermediate to those associated with the capacity values reported in Table 1, linear interpolation can provide reasonable and reliable approximations. The use of a single type of connection, positioned only at the panel corners and whose components have clearly defined mechanical properties, permits the adoption of an extremely simplified design/verification approach.

The interaction between orthogonal walls, generated by X-RAD linking plates, is neglected, and a 2D analysis

(b)

(c)

approach is adopted, consistent with what is typically done in engineering practice. Experimental testing and numerical study on the interaction between orthogonal walls have already been scheduled, the results of which will be published in the near future.

Conclusions An innovative connection system for assembling CLT buildings was developed. The proposed system is a pointto-point mechanical connection system, designed to be fixed to the corners of the CLT panels and intended to be an alternative to the hold-downs and angle brackets. The innovative system is composed of factory-assembled units that are connected to the panels by means of screw fasteners. The screws are installed at two different angles of inclination so as to maximise the withdrawal strength by crossing multiple CLT layers. The units can also be used as a lifting hook for rapid and safe positioning. This will help to improve the safety of the construction process, its quality level and its profitability as well.

According to the proposed system, named X-RAD, the new connections are linked to each other by means of linking metal plates and steel bolts.

(d)

F ig . 10 : Steps of the simplified calculation method: (a) CLT panels and X-RAD units as primary structural elements; (b) consequent structural schematisation; (c) FE implementation; (d) resulting vector forces on the X-RAD units 510

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Several experimental tests were performed on different prototype configurations (monotonic and cyclic tests).

The test outcome led to the definition of the X-RAD final version, which is characterised by strong capacity and high stiffness. The experimental results of the final version of the connector showed that, due to plastic deformation developed under cyclic loading, the adoption of the X-RAD system in seismic-prone areas could ensure adequate performance in terms of ductility and energy dissipation. The simplified analytical approach, adopted for the evaluation of the system capacity, proved to be sufficiently accurate when compared the experimental results. An experimental testing campaign on fullscale walls and wall assemblies, which investigates the response of the system under seismic actions, is currently underway.

Acknowledgements The authors thank Rothoblaas company.

The development of the X-RAD connection system was conducted within the framework of a research project financed by the Autonomous Province of Bolzano (Italy).

References [1] Brandner R, Flatscher G, Ringhofer A, Schickhofer G, Thiel A. Cross laminated timber (CLT): overview and development. Eur. J. Wood Wood Prod. 2016; 74: 331–351. DOI: https://doi.org/10.1007/s00107-015-0999-5 [2] Gagnon S, Pirvu C. CLT Handbook: CrossLaminated Timber FPInnovations: Point-Clare, Canada, 2011.

[3] Ceccotti A, Sandhaas C, Okabe M, Yasumura M, Minowa C, Kawai N. SOFIE project—3D shaking table test on a sevenstorey full-scale cross-laminated timber building. Earthq. Eng. Struct. Dyn. 2013; 42: 2003–2021.

[4] Smith T, Fragiacomo M, Pampanin S, Buchanan AH. Construction time and cost for post-tensioned timber buildings. Proc. Inst. Civil Eng. Constr. Mater. 2009; 162: 141–149.

[5] Wanninger F, Frangi A. Experimental and analytical analysis of a post-tensioned timber frame under horizontal loads. Eng. Struct. 2016; 113: 16–25.

[6] Loss C, Piazza M, Zandonini R. Connections for steel–timber hybrid prefabricated buildings. Part II: innovative modular structures. Constr. Build. Mater. 2015; 122: 796–808.

DOI: https://doi.org/10.1016/j.conbuildmat.2015.

12.001 [7] Nakashima S, Kitamori A, Komatsu K, Que Z, Isoda H. Development and evaluation of CLT shear wall using drift pinned joint.

Proceedings of the 13th World Conference on Timber Engineering WCTE 2014, Quebec City, Canada, 2014.

[8] Kraler A, Kögl J, Maderebner R. SherpaCLT-Connector for cross laminated timber (CLT) elements. Proceedings of the 13th World Conference on Timber Engineering WCTE 2014, Quebec City, Canada, 2014.

[9] Gavric I, Fragiacomo M, Ceccotti A. Cyclic behaviour of typical metal connectors for crosslaminated (CLT) structures. Mater. Struct.

Mater. Constr. 2015; 48: 1841–1857.

[10] Gavric I, Fragiacomo M, Ceccotti A. Cyclic behavior of CLT wall systems: experimental tests and analytical prediction models. ASCE J. Struct. Eng. 2015b; 141(11).

[11] Piazza M, Polastri A, Tomasi R. Ductility of joints in timber structures. Special issue in timber engineering. Proc. Inst. Civil Eng. Struct.

Build. 2011; 164(2): 79–90.

[12] Piazza M, Tomasi R, Grossi P, Costa AC, Candeias PX. Seismic performance of timber buildings: the Series project. Proc. Inst. Civil Eng. Struct. Build. 2015; 168(11): 788–802.

[13] Flatscher G, Schickhofer G. Shaking-table test of a cross-laminated timber structure. Proc.

Inst. Civil Eng. Struct. Build. 2015; 168(11): 878–888.

[14] Popovski M, Gavric I. Performance of a 2-story CLT house subjected to lateral loads. J. Struct. Eng. 2016; 142(4).

[15] Fragiacomo M, Dujic B, Sustersic I. Elastic and ductile design of multi-storey crosslam massive wooden buildings under seismic actions.

Eng. Struct. 2011; 33(11): 3043–3053.

[16] Rinaldin G, Poh’sie GH, Fragiacomo M, Amadio C. Non-linear modelling of the three and seven storey X-lam buildings tested within the SOFIE Project. Proceedings of the 13th World Conference on Timber Engineering WCTE 2014, Quebec City, Canada, 2014.

[17] Pozza L, Scotta R, Trutalli D, Polastri A, Smith I. Experimentally based q-factor estimation of CLT walls. Proc. Inst. Civil Eng. Struct.

Build. 2016; 169: 492–507. DOI: https://doi.org/ 10.1680/jstbu.15.00009 [18] Popovski M, Pei S, van de Lindt JW, Karacabeyli E. Force modification factors for CLT structures for NBCC. RILEM Book Series 2014; 9: 543–553.

[19] Polastri A, Pozza L, Loss C, Smith I. Numerical analyses of high- and medium-rise CLT buildings braced with cores and additional shear walls. Proceedings of the 3rd International Conference on Structures and Architecture:

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Concepts, Applications and Challenges, ICSA 2016, 2016. Structures and Architecture – Cruz (Ed)© 2016 Taylor & Francis Group, London, ISBN 978-1-138-02651-3. pp. 128–136.

[20] European Committee for Standardization. EN 26891 Timber structures—Joints Made with Mechanical Fasteners–General Principles for Determination of Strength and Deformation Characteristics CEN: Brussels, Belgium, 1991.

[21] European Committee for Standardization.

EN 12512, Timber Structures. Test Methods.

Cyclic Testing of Joints Made with Mechanical Fasteners CEN: Brussels, Belgium, 2006.

[22] European Organisation for Technical Assessment. Rotho Blaas Self-Tapping Screws, European Technical Approval ETA-11/0030 EOTA: Charlottenlund, Denmark, 2012.

[23] Giongo I, Piazza M, Tomasi R. Investigation on the self tapping screws capability to induce internal stress in timber elements. Adv. Mat. Res. 2013; 778: 604–611.

[24] Giongo I. Study on timber compression forces induced by self-tapping screw fasteners.

Eur. J. Wood Wood Prod., Holz als Roh- und Werkstoff 07/2015 2015; 74(3): 473–475. DOI: https://doi.org/10.1007/s00107-015-0958-1 [25] Brandner R. Group action of axiallyloaded screws in the narrow face of cross laminated timber. Proceedings of the 14th World Conference on Timber Engineering WCTE 2016, Vienna, Austria, 2016.

[26] Polastri A, Angeli A, Dal RG. A new construction system for CLT structures.

Proceedings of the 13th World Conference on Timber Engineering WCTE 2014, Quebec City, Canada, 2014.

[27] European Committee for Standardization.

EN 1995-1-1:2004+A2:2014. Eurocode 5— Design of Timber Structures, Part 1-1, General— Common Rules and Rules for Buildings CEN: Brussels, Belgium, 2014.

[28] Polastri A, Angeli A. An innovative connection system for CLT structures: experimental–numerical analysis. Proceedings of the 13th World Conference on Timber Engineering WCTE 2014, Quebec City, Canada, 2014.

[29] European Committee for Standardization.

EN 1993-1-8:2005. Eurocode 3—Design of Steel Structures—Part 1-8: Design of Joints CEN: Brussels, Belgium, 2005.

[30] Polastri A, Brandner R, Casagrande D. Experimental analysis of a new connection system for CLT structures. Proceedings of the 3rd International Conference on Structures and Architecture: Concepts, Applications and Challenges, ICSA 2016, 2016. Structures and Architecture – Cruz (Ed) © 2016 Taylor & Francis Group, London, ISBN 978-1-138-02651-3. pp.

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Experimental Study on the Seismic Behaviour of Mortise–Tenon Joints of the Ancient Timbers Ling-kun Chen, College of Civil Science and Engineering, Yangzhou University, Yangzhou, PR China; School of Civil Engineering, Southwest Jiaotong University, Chengdu, PR China; Department of Civil, Structural and Environmental Engineering, University at Buffalo, State University of New York, Buffalo, NY, USA; Sheng-cai Li; Yan-ting Wang; You-jun Zhao; Ming Zhang;

Xing-yu Song, College of Civil Science and Engineering, Yangzhou University, Yangzhou, PR China; Xiao-wei Li, School of Civil Engineering, Southwest Jiaotong University, Chengdu, PR China; Teng Wu, Department of Civil, Structural and Environmental Engineering, University at Buffalo, State University of New York, Buffalo, NY, USA; Li-zhong Jiang, School of Civil Engineering, Central South University, Changsha, PR China. Contact: lingkunchen08@hotmail.com DOI: 10.2749/222137917X14881937844720

Abstract Mortise–tenon joints (MTJs) have been playing a crucial role in traditional timber structures to resist service and earthquake loading. In the present work, an experimental study was carried out to investigate the seismic performance of joints of ancient timber structure. Five types of joints from Fu-Jiu Zhou house, a historical building in Yangzhou city, were selected as the test prototype. All of the members of the test specimens were directly extracted from the aged building and were manufactured according to traditional methods. Based on the cyclic loading tests, efforts have been made to investigate the hysteresis curves, backbone curves and energy dissipation of the MTJs. The test results indicate that the bearing bracket in the tenon can improve pulling-out resistance capacity, rotational stiffness and energy dissipation of MTJs, and reduce the bending capacity. It is suggested that the dovetail MTJ may be one of the best connection configurations for pulling-out resistance and bending capacity.

Keywords: ancient timber structure; mortise–tenon joints; experimental study; pulling-out resistance; seismic performance.

Introduction Ancient architecture showcases the history of ancient Chinese civilization, and has important cultural and historical value. Ancient Chinese buildings are mainly composed of timber structures. The main connection form of a timber structure is the mortise–tenon joint (MTJ), and it is an important feature of timber structure connections without a nail or rivet especially in old timber structures. Under external loads, it suffers from the composite function forces, such as bending moment, shear force and axial force.

For the seismic performance of traditional timber structures, the MTJ is the vital component. For example, in each storey of a Chinese traditional timber frame building, the posts and beams were connected by MTJs in the column rings.1 Therefore, it is of great Peer-reviewed by international experts and accepted for publication

by SEI Editorial Board Paper received: December 3, 2016 Paper accepted: January 17, 2017

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significance for the overall performance of the timber structures to study the performance of MTJs under an earthquake.

In recent years, the seismic events that have occurred in Japan (1995 Kobe and 2004 Niigata-ken Chuetsu), China (2008 Wenchuan) and Italy (2009 L’Aquila, 2012 Emilia-Romagna and 2016 Marche-Lazio-Umbria), countries that are all faced with the preservation of historical and architectural heritage against natural disasters, have clearly shown the high seismic vulnerability of the existing ancient timber structures.

On one hand, researchers have shown renewed interests in various timber joints including MTJs, and advancements in the theoretical and experimental analysis on seismic performance of the MTJs have been seen.2 One study3 attempted to define a fracture criterion under mixed-mode loading (I + II), that is the double cantilever beam test and the end notched flexure tests. Results demonstrated that the fracture linear energetic criterion showed to be adequate to describe the fracture envelop with the exception of

a small presence of mode I. A novel method was presented in Ref. 4 to simulate the behaviour of nailed and screwed timber joints using the finite element (FE) method. It predicted stress and strain distributions in the timber along the screws, which were intractable by both theoretical methods and simplified FE analyses using spring elements at each screw location. A comprehensive study was carried out in Ref. 5 on the flexural behaviour of dovetail MTJs in timber structures. The experimental and numerical results show that the main failure mode of the dovetail joints from the current experiments was the pull-out of the tenon. A method for macro-modelling timber-totimber dowel-type joints under shear loads using FE was presented in Ref. 6, which could be used for predicting hysteretic behaviour in scarce information scenarios where a single monotonic load-slip curve or reference values can be used for calibration purposes.

Another study7 estimated the structural performance of the beam–column joints of Yingxian Wood Pagoda based on the 1 : 3.4 scale test. Results demonstrated that the equivalent viscous damping coefficient of the test model of the beam–column joint is between 0.1 and 0.36 with an average of 0.23, which is higher than that of the beam– column joint of reinforced concrete structures.

On the other hand, a number of researches have also been carried out to investigate the seismic performance of ancient timber structures. One study8 performed the low cyclic reversed loading tests on MTJs in historical timber buildings, and analyzed the semi-rigid characteristics and the change rules of stiffness degradation of typical MTJs in historical timber buildings. By simulating the state of a MTJ with varied stiffness elements, the

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relation between the varied stiffness and the relative flexibility was presented. The behaviours of damaged straight MTJs of ancient timber buildings were studied in Ref. 9, such as the failure characteristics, hysteretic loops and backbone curve, degradation of rigidity and energy dissipation capacity, by low cyclic reversed loading experiments. The results indicate that the hysteretic loops of all joints were Sshaped and the gathering effect became more obvious with the increase in damage degree. Reference 10 carried out a research on the seismic characteristics of four typical MTJs of Chinese southern traditional timber-frame buildings, namely failure modes, hysteresis curves, backbone curves and rotational stiffness. The results provided a theoretical basis for seismic research, protection and maintenance of Chinese southern traditional timber-frame buildings. Static and cyclic lateral load tests were conducted by Ref. 11 on two ancient Korean timber frames under lateral load, in which dovetail joints were used to connect the beams with the columns at the column top. Results indicated that the failure modes of the frames were shear failure or bending failure of mortise branches. A FE analysis and experimental research was performed in Ref. 12 on the historical Dieh–Dou timber building structures under earthquake conditions. Results suggested that an accurate value of the Dieh–Dou joint stiffness is essential to estimate global lateral displacements and capacity performance of the structure under earthquake loading.

resistance is highly dependent on the accurateness of the connection.7 The existing research and current standards mainly pay attention to the modern dowel-type joints and usually provide little guidance to designers regarding traditional joints. Most of current research undertaken is focused on the reinforcement of dowel-type connections. There is little concern about the influence of the bearing bracket in the tenon in carpentry joints. The present experimental research conducted in this study aims to investigate the seismic behaviour of typical MTJs of ancient timber structures based on the cyclic loading test of five types of MTJs. The study analyzes the mechanism of the MTJs used in traditional Chinese timber buildings, and efforts have been made to investigate the failure mode, the hysteretic and envelope curves and the strength and energy dissipation of the MTJ. This study will contribute to the seismic research, preservation, retrofitting and strength enhancement of historical and architectural heritage structures against natural disasters.

Regarding the aged carpentry joints, the timber structural stiffness has significant effects on the whole displacement of the building, while the rotation stiffness depends on the magnitude of vertical load applied to the joint; the translational stiffness is not affected by the external vertical load applied. In addition, the pull-out

As shown in Fig. 1a, the dovetail joint is composed of a pair of dovetail tenon and mortise with an inverted trapezoid cross-section, and the upper side of the trapezoid cross-section is wider than its lower side. The tenon tongue might be pulled out from the mortise hole when under external load. Initially, it is subjected to the

Mechanical Properties of Typical MTJs A mechanical characterization analysis of five typical MTJs used in the Fu-Jiu Zhou house is performed. The dovetail joint is taken as an example, which is in a complex triaxial stress state subjected to external loads.

N′

M1

f

axial force N, which is in equilibrium with the friction force f between the tenon tongue and the mortise hole produced by two sides of tenon, and extrusion force N0 between the tenon tongue and the mortise hole. Second, the tenon tongue is subject to the bending moment M when the rotation of the tenon tongue is restrained by the mortise hole. As shown in Fig. 1b, M can be divided into M1 and M2, where M1 is produced by the extrusion between the top and bottom surfaces of the tenon tongue, and M2 is produced by the extrusion between the side surfaces of the mortise.

As shown in Fig. 1c, shear force acting on the MTJ is in equilibrium with the vertical friction force f between the tenon and the sides of the mortise, and the extrusion force Q between the top surface of the mortise and bottom surface of the tenon. Under external loads, various failure patterns could be developed in the dovetail joint, such as shear failure (as shown in Fig. 2a), bending failure (as shown in Fig. 2b) and pulling-out failure.

Experimental Campaign of Typical MTJs Test Specimens The historical building Fu-Jiu Zhou house in Yangzhou is composed of two brick−concrete structures and a Chinese building, built during the end of the Qing dynasty. The appearance of the brick−concrete building is the

(a)

(b)

F ig . 2: Failure patterns in the dovetail joint. (a) Shear failure; (b) bending failure

Q

M2 f

f

q′ q′

f N′ q′

(a)

(b)

(c)

Fi g. 1: Mechanical property of the dovetail joint. (a) Axial force effect; (b) moment effect; (c) shear force effect

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(a)

(b)

(c)

F ig . 3: Fu-Jiu Zhou house. (a) Gate of the house; (b) post and lintel frame structure of the house; (c) pavilion located at northwest corner of the house

interesting result of influence by Western culture.

The Chinese building of the Fu-Jiu Zhou house is a typical representative of traditional Huizhou-style architecture (Fig. 3).

In the Fu-Jiu Zhou house, the MTJs are mainly dovetail joint , pinned joint and blind pinned joint (blind: not going all the way through). Nonetheless, in order to investigate the influence of the bearing bracket on the seismic response of MTJs, the blind pinned joint with bearing bracket and pinned joint with bearing bracket were investigated in this study. The schematic illustrations of the five types of MTJs considered in this contribution are shown in Fig. 4.

The specimens are made of common fir grown in the southern area of China. The mechanical parameters of

(a)

(d)

the test were strictly carried out in terms of General Requirements for Physical and Mechanical Tests of Wood (GB/1927-1943-91).13 The members used in the specimens were seasoned according to the kiln drying method. The moisture content for kiln drying wood was 10.60%, and the kiln drying density of wood was 0.497 g/cm3. Other material parameters of the wood are reported in Table 1.

which the cross-section of the column is 120 mm (diameter) × 1550 mm (height), and the size of the beam is 70 mm (width) × 110 mm (thickness) × 1100 mm (length).

The dimensions of MTJs are shown schematically in Table 2, where 1 and 2 indicate specimen 1 and specimen 2 for each joint.

Test Setup and Loading Program

In order to study the seismic performance of the aged wood building, the joint prototypes of the test were all selected from the Chinese building of the Fu-Jiu Zhou house, and the test specimens were made following the traditional craft of the Chinese southern timber structure.14 Each joint had two specimens. Ten 1 : 2 reducedscale specimens were constructed, in

The test setup is schematically shown in Fig. 5. To prevent the P-Δ effect on the MTJs during the test, the column was horizontally arranged, and both ends of the column were fixed on the base. To prevent rotation of the column and over-strictly constraining the deformation at the tenon tongue and the mortise hole, a loop was used to strengthen the column, and the position is 300 mm from the column ends.

(b)

(c)

(e)

F ig . 4: Schematic illustration of MTJs. (a) Blind pinned joint; (b) pinned joint; (c) dovetail joint; (d) blind pinned joint with bearing bracket; (e) pinned joint with bearing bracket 514

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fc.0 (MPa)

fc, 90, n (MPa)

fc, 90, t (MPa)

fm (MPa)

ft.0 (MPa)

Em (MPa)

MV

53.76

5.50

2.01

71.72

64.27

11 389.54

SD

3.96

0.28

0.03

3.82

1.82

299.54

Each material parameter of wood is a mean value of four specimens.

MV: mean value.

SD: standard deviation. fc.0: compressive strength parallel to grain. fc, 90, n: compressive strength perpendicular to grain along radial direction. fc, 90, t: compressive strength perpendicular to grain along tangential direction. fm: bending strength parallel to grain along tangential direction. ft.0: tensile strength parallel to grain.

Em: flexure modulus of elasticity.

Table 1: Mechanical parameters of common fir

Type of joints

Configuration

Blind pinned joint

W

H1

H2

L1

L2

Dimension (m)

Cutline Tenon height H1

55

Tenon height H2

110

Tenon length L1

40

Tenon length L2

80

Tenon width W

35

Tenon height H

110

W

W1

W2

H

Dovetail joint

Tenon bottom W1

40

Tenon top W2

50

Tenon length L

40

L

L

Pinned joint

L2

H1

W

H2

L1

W

Tenon height H1

55

Tenon height H2

110

Tenon length L1

60

Tenon length L2

180

Tenon width W L

H

Blind pinned joint with bearing bracket

L H

Pinned joint with bearing bracket

35

Bearing bracket length L

140

Bearing bracket height H

35

Bearing bracket length L

180

Bearing bracket height H

35

Table 2: Dimensions of mortise–tenon joints

The testing apparatus was pinsupported at the bottom end and loaded with a hydraulic jack from the top to maintain the desired axial force. The axial force in the column was 10 kN which accounts for the reduced scale.15 A horizontal load was applied at the beam end. Four displacement transducers (MIRAN), numbered WYJ1, WYJ2, WYJ3 and WYJ4, were employed. WYJ1 and WYJ2 were arranged to measure the

pull-out displacement of the joint, while WYJ3 and WYJ4 for the rotational displacements of the joint, as illustrated in Fig. 5.

The loading process was controlled by the displacement procedure and the specimens were subjected to monotonic loading until the failure of the joint, which typically involved the pull-out of the tenon from the mortise. Loading reversals in push and pull direction

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were symmetric, considering an increment amplitude of 15 mm every time.

The test consisted in two groups of three cycles, each of which were controlled by displacement, three cycles in the range [−15 mm, +15 mm] and three cycles in the range [+30 mm, −30 mm].

Loading time was 1 s for 1 mm of loading displacement.

The overall deformations of the tenon relative to the mortise may be Scientific Paper

515

Pulling-Out Displacement of Joints Hoop Beam 200

WYJ3 WYJ4

Hoop

WYJ1

Support

WYJ2

Hoop

Jack Support

Column

Angle iron

Angle iron

Base

F ig . 5: Schematic of the test setup

where u3 and u4 are the horizontal displacement readings from WYJ3 and WYJ4; l1 is the vertical distance from WYJ3 and WYJ4. u0 = ðu1 + u2 Þ=2

ð2Þ

where u1 and u2 are the vertical displacement readings from WYJ1 and WYJ2.

12.00 8.00 4.00

–50 0 50 Horizontal displacement (mm)

4.0 2.0

30 60 90 Horizontal displacement (mm)

(a) 16.00 Pulling -out value (mm)

120

(b) 220.0

Right pulling-out, 1 Left pulling-out, 1 Right pulling-out, 2 Left pulling-out, 2

12.00

8.00

4.00

1 2

116.0 112.0 8.0 4.0 0.0

–100

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6.0

0

0.00

516

8.0

100

General Observations from the Tests –50 50 0 Horizontal displacement (mm)

100

0

30 60 90 Horizontal displacement (mm)

(c)

120

(d) 16.0

Pulling -out value (mm)

Due to the initial insignificant gaps which always exist between the mortise hole and the tenon tongue, those joints stayed loose. When uploading in experiment, the mortise hole and tenon tongue will squeeze up with each other under the effect of initial horizontal displacement. Therefore, the joints suffer less load and there is a slight noise when squeezing happens. The sound intensified slowly, while the overall response remained steady until the tenon was pulled out.

The rotation angle of MTJs and the deformation increased with the cyclic displacement. Meanwhile one side of the joint (tenon tongue) was

1 2

0.0

–100

ð3Þ

where p is the horizontal load applied at the column tip (measured by a load cell); l2 is the vertical distance between the loading position and the column.

16.00

10.0

0.00

The bending moment exerted on the dovetail joint (M) can be calculated as: M = pl2

Right pulling-out, 1 Left pulling-out, 1 Right pulling-out, 2 Left pulling-out, 2

20.00

Pulling -out value (mm)

ð1Þ

For the case of the same displacement-controlled loading, the pulling-out value of blind pinned joint was the largest among the five types of joints, while the value of the dovetail joint was the smallest (see Fig. 6).

For the blind pinned joint, the pulling-out value was larger than the blind pinned joint with bearing

Pulling -out value (mm)

θ = ðu3 − u4 Þ=l1

squeezed, and the other side (tenon tongue) was pulled out. As a result, the tenon was partly pulled. When the displacement returned to the initial position, the MTJs were entirely pulled out. Finally, cracks occurred at the foot of the mortise, and the foot of mortise was finally broken.

Pulling -out value (mm)

represented by a rotation (θ) and a pulling-out displacement (u0). θ and u0 may be deduced from the relative displacements measured of the column and beam:

As mentioned in the General Observations section, the leaning was associated with the fact that most of the tenon tongue linked with the joint had been pulled out from its position. The pulling-out value of joints indicated the dissipation of energy. To some extent, the larger pulling-out demonstrates the greater energy dissipation.

Figure 4 shows the pulling-out value of left or right side of the joints, and 1 and 2 indicate specimen 1 and specimen 2 for each type of joints, respectively.

1 2

12.0

8.0

4.0

0.0 0

30 60 90 Horizontal displacement (mm)

120

(e) F i g. 6 : Pulling-out value of different types of joints. (a) Blind pinned joint; (b) dovetail joints; (c) pinned joint; (d) blind pinned joint with bearing bracket; (e) pinned joint with bearing bracket

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(a)

(c)

(b) 2.0

3.0

Blind pinned d joint

3.0

Dovetail joint

Pinned joint

–2.0 –4.0

Moment (kN.m)

2.0

0.0

Moment (kN.m)

Moment (kN.m)

2.0

1.0 0.0

1.0 0.0 –1.0 –2.0

–1.0

–3.0

–6.0

–2.0

–0.20 –0.15 –0.10 –0.05 0.00 0.05 Rotation (Rad)

(d)

0.10

–4.0

–0.20 –0.15 –0.10 –0.05 0.00 0.05 Rotation (Rad)

0.20

0.15

0.15

–0.20 –0.15 –0.10 –0.05 0.00 0.05 Rotation (Rad)

0.20

0.10

0.15

0.20

(e)

4.0

4..0

Blind pinned joint with bearing bracket

3.0

Pinned jjoint with bearing bracket b

3..0

2.0

Moment (kN.m)

Moment (kN.m)

0.10

1.0 0.0 –1.0

2..0 1..0 0..0 –1.0 –2.0

–2.0

–3.0 –3.0 –0.20 –0.15 –0.10 –0.05 0.00 0.05 Rotation (Rad)

0.10

0.15

0.20

–0.20 –0.15 –0.10 –0.05 0.00 0.05 Rotation (Rad)

0.10

0.15

0.20

Fig. 7: M–θ hysteretic curve of different types of joints. (a) Blind pinned joint; (b) dovetail joint; (c) pinned joint; (d) blind pinned joint with bearing bracket; (e) pinned joint with bearing bracket

bracket, which demonstrates that the bearing bracket can effectively increase the pulling-out resistance of the blind pinned joint. For the dovetail joint, the tenon was cut to exactly fit the mortise hole. Usually, there exist shoulders as the joint fully enters the mortise hole, and the joint may be pinned or locked into the location.

Traditionally, the pin hole in the tenon is bored a little closer to the shoulder

than in the mortise, and hence the pin pulls the joint together very tightly.16 The pulling-out resistance capability of the dovetail joint is the strongest due to its special configuration. For the pinned joint, the length of pinned joint tongue is greater than the tenon of the blind pinned joint. As a result, the pulling-out resistance of the pinned joint is stronger than that of the blind pinned joint.

M–θ Hysteretic Curve

(a)

(b)

(c)

1 2

4.00

3.0

Moment (kN.m)

Moment (kN.m)

4.0

5.0

2.0 1.0 0.0 –1.0

4.0

1 2

3.00 2.00 1.0 0.0

–0.15

–0.10

–0.05 0.00 0.05 Rotation (Rad)

(d)

0.10

0.15

–3.0 –0.20 –0.15 –0.10 –0.05 0.00 0.05 Rotation (Rad)

0.0 –1.0

–4.0

0.10

0.15

0.20

–0.2

–0.1

–0.1 0.0 00.1 Rotation (Rad)

0.1

0.2 2

(e)

4 4.0

4.00 1 2

3 3.0

Moment (kN.m)

1.0 0 0.0 –1.0

2.00 1.00 0.00

–2.0

–1.0

–3.0

–2.0

–4.0

–0.15

–0.10

1 2

3.00

2 2.0 Moment (kN.m)

1.0

–3.0

–2.0

–3.0

2.0

–2.0

–1.0

–2.0

1 2

3.0 Moment (kN.m)

5.0

The rotation information was measured by the displacement gages, and the M–θ hysteresis curves of the MTJs are shown in Fig. 7. As shown in the figure, the hysteretic loop was of a typical Z-shape for the cyclic tests. Pinching on the hysteretic loops can be seen for any relatively larger displacement, and this

–0.05 0.00 0.05 Rotation (Rad)

0.10

0.15

–3.0

–0.15

–0.10

–0.05

0.00 0.05 Rotation (Rad)

0.10

0.15

Fig. 8: M–θ backbone curve of different types of joints. (a) Blind pinned joint; (b) dovetail joints; (c) pinned joint; (d) blind pinned joint with bearing bracket; (e) pinned joint with bearing bracket

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Scientific Paper

517

indicates the degradation energy dissipation.

of

the

The peak value of the moment of the first cycle was higher than the others for each round, as seen in Fig. 5.

Actually, the first cycle of the each round further develops based on the curve of the previous round loading until the required displacement value is achieved (as shown in Fig. 4a).

The plastic deformation of the joint was basically initiated at the first cycle in every round, and there was little or no plastic deformation in the other cycles. At the same time the corresponding strength and stiffness were reduced. If the displacement of each cycle does not exceed the one of the previous round, the plastic deformation is consistent with those of previous round, and the characteristics of the hysteretic curve remain the same.

In case the displacement of the previous cycle exceeds the one of previous cycle, new plastic deformation will occur. Accordingly, the joint can bear larger moment. The test results show that the peak moment of the pinned joint is the maximum, while the blind pinned joint with bearing bracket is the minimum. Hence, the existing bearing bracket could reduce the moment capacity of the joints.

five types of joints. Generally, the main characteristics of all experimental backbone curves, including the feature points, the shape and the developing leaning of the curve, are consistent. The curves could be approximately divided into three phases in the loading process, namely initial sliding phase, squeezing phase and re-sliding phase. Initially, the tenon and mortise are in gradual contact with each other, and increased with applied loading. Thus, the slope of the backbone curve was small.

With the rotation angle increasing, the tenon and mortise were more tightly contacted, and the plastic deformation occurred. With further increasing of the displacement, the tightened mortise–tenon joints became loose, and the slope of the backbone curve gradually reduced, and the limited capacity of joints was achieved.

The energy dissipation capacity, which is denoted by the effective viscous damping coefficient, is an important index to evaluate the structural seismic-resistance capacity. The effective viscous damping coefficient can be calculated as Eq. (4):17 1 SABC + SCDA ð4Þ 2π SOEB + SODF where E is the energy dissipation factor of a structure; SABC is the area (in mm2) enclosed by the curves of A– B–C; SCDA is the area (in mm2) enclosed by the curves of C–D–A; SOBE is the area (in mm2) enclosed by the polyline of O–B–E and SODF is the area (in mm2) enclosed by the polyline of O–D–F. SABC + SCDA denotes the area surrounded by the hysteretic loop; SOBE + SODF denotes the area E=

p B

Energy Dissipation F

A

Figure 8 shows the envelope curves obtained for the scaled specimens of

As shown in Fig. 9, energy dissipation is measured by the area enclosed by the load–displacement hysteretic loop, and the energy input per cycle equals the damping energy loss per cycle.

The accumulated area of hysteretic loops reflects the amount of energy dissipation. A large hysteretic loop represents a better energy dissipation capacity of the structure.

F i g. 9: Lateral force–displacement hysteretic loop

(a)

(b)

(c)

M–θ Backbone Curve of the Joints

0.13 1 2

0.12

0

1 2

0.16

0 0.13

0.11

1 2

0.14

E

E

E

0 0.12

0.10

0 0.11 0 0.10

0.09

0.12

0.10

0 0.09

0.08 0.00

Δ

E

D

0 0.15 0 0.14

C

0.03

0.06

0.09

0.12

0.08

00.08 0.00

0.15

0.03

0.06

Rotation (Rad)

0.009

0.12

0.00

0.15

0.03

0.06

(d)

(e) 0.150

0.09

0.12

0.15

Rotation (Rad)

Rotation (Rad)

0.114

1 2

1 2 0.112

E

E

0.135

0.110

0.120

0.008

0.105

0.00

0.03

0.06

0.09

0.12

Rotation (Rad)

0.15

0.00

0.03

0.06

0.09 0.12 Rotation (Rad)

0.115

F ig . 10 : Energy dissipation curve of different types of joints. (a) Blind pinned joint; (b) dovetail joints; (c) pinned joint; (d) blind pinned joint with bearing bracket; (e) pinned joint with bearing bracket 518

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surrounded by the straight line DB and displacement coordinate axis.

During initial loading, the rotation was relatively small. Hence, the friction between the mortise hole and the tenon tongue was not obvious due to the initial gap. With the increase of rotation, the friction and squeeze increased because of the tight contact of joints. Finally, the tenon tongue rotated about the mortise hole and was pulled out from the mortise hole.

Meanwhile, the energy dissipation capability reduced. As can be seen from Fig. 10, with the increase of the rotation, the effective viscous damping coefficient eventually stabilized. The effective viscous damping coefficient of the pinned joint with bearing bracket is largest, while the one of the blind pinned joint is smallest.

Conclusions Ten scaled specimens of five types of MTJs of ancient timber structure have been experimentally studied for quasistatic loading. Based on the analyses of test results, the following conclusions can be obtained.

1. Under low reversed cyclic loading, joints substantially suffered from the squeeze and compress in the regions of the tenon tongue and edge of the mortise hole. The tenon pulled out from the mortise hole with increase in displacement.

2. The moment–rotation curve of the five types of joints appears to be of a Z-shape for the cyclic displacement, and could be divided into slip phase, contact extrusion phase and re-slide phase in the loading process. These joints present a significant moment-resisting capacity, and should be considered as a semi-rigid characteristic.

3. Among the five types of joints, dovetail joint has the best performance to resist the pulling-out and is compatible with larger bending capacity, while pinned joint has the best performance to resist bending and energy dissipation. Generally, the use of bearing bracket weakens the bending capacity of the blind tenon and mortise but correspondingly the energy dissipation capacity could be enhanced.

Acknowledgements This paper was supported by the National Natural Science Foundation of China (Grant Nos. 51338001, 51478409), China Postdoctoral Science Foundation (Grant Nos. 2015M581702 and 2016M592695), the Natural Science Foundation of Jiangsu Province, PR China (Grant No. BK20161337), the University Science Research Project of Jiangsu Province, the Financial Aid Scheme for Selecting and Training Project of High-level Talents of the 10th “Top 6 Talent Peak” in Jiangsu Province, PR China (Grant No. 2013-JZ-005). The above grants are gratefully acknowledged.

[1] Chen ZY, Zhu E, Lam F, et al. Structural performance of Dou-Gong brackets of Yingxian Wood Pagoda under vertical load—an experimental study. Eng. Struct. 2014; 80: 274–288.

[2] Chen Z, & Zhu E. A review on structural mechanics of Chinese ancient wood structures.

Adv. Mech. 2012; 42(5): 644–654 (in Chinese).

[3] de Moura MFSF, Oliveira JMQ, Morais JJL, & Dourado N. Mixed-mode (I + II) fracture characterization of wood bonded joints. Construct. Build. Mater. 2011; 25(4): 1956–1962.

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[6] Lacourt PA, Crisafulli FJ, & Mirasso AE. Finite element modelling of hysteresis, degradation and failure of dowel type timber joints.

Eng. Struct. 2016; 123: 89–96.

[7] Chen Z, Zhu E, Pan J, et al. Energydissipation performance of typical beam– column joints in Yingxian Wood Pagoda: experimental study. J. Perform. Constr. Facil.

2015; 30(3): 04015028.

[8] Yao K, Zhao HT, & Hong-Peng GE. Experimental studies on the characteristic of mortise–tenon joint in historic timber buildings.

Eng. Mech. 2006; 23(10): 168–173 (in Chinese).

[9] Xie Q, Zheng P, Xiang W, et al. Experimental study on seismic behaviour of mortise tenon joints of ancient architectures. J. Build. Struct.

2014; 35(11): 143–150(in Chinese).

[10] Chun Q, Yue Z, Pan JW, et al. Experimental study on seismic characteristics of typical mortise tenon joints of Chinese southern traditional timber frame buildings. Sci. China Technol. Sci. 2011; 54(9): 2404–2411.

[11] Seo JM, & Choi IK. Static and cyclic behaviour of wooden frames with tenon joints under lateral load. J. Struct. Eng. 1999; 125(3): 344–349.

[12] D’Ayala DF, & Tsai PH. Seismic vulnerability of historic Dieh–Dou timber structures in Taiwan. Eng. Struct. 2008; 30(8): 2101–2113.

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263–269.

[5] Chen CC, Qiu HX, & Lu Y. Flexural behaviour of timber dovetail mortise–tenon joints. Construct. Build. Mater. 2016; 112: 366–377.

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[13] GB/(1927–1943)-91. Physical and Mechanical Tests of Wood China Technical Committee for Standardization of Timber: Beijing, 1991 (in Chinese).

[14] Ma BJ. Chinese ancient wooden construction technology Science press: Beijing, 1991 (in Chinese).

[15] Wang T. Static analysis of ancient timber structures Cultural Relics Press: Beijing, 1992 (in Chinese).

[16] Branco JM, & Descamps T. Analysis and strengthening of carpentry joints. Construct.

Build. Mater. 2015; 97: 34–47.

[17] Clough RW, & Penzien J. Dynamics of Structures, 3rd edn. McGraw-Hill: New York, NY, USA, 1995.

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Suspension Bridge over the Zambezi in Tete—Original Stringer Bronze Bearings versus Recent Modification João Fonseca, Prof., Dr.-Ing; Clemente Pinto, Prof., Departmento de Engenharia Civil e Arquitectura, Universidade da Beira Interior, Covilhã, Portugal. Contact: jfonseca@ubi.pt DOI: 10.2749/222137917X14881937844766

Abstract This paper addresses the role of the bearings under the stringers of the suspension bridge over the Zambezi River in Tete (Mozambique). The original bronze solution is compared with a recent modification using neoprene. It is proved that the higher stiffness of the original bearings is more efficient than the neoprene flexibility. A similar behavior can be observed in most stone structures and the conclusions may be generalized. The paper falls within the scope of recent research at the University of Beira Interior, aiming to develop concepts for new prestressed stone structures, using the force paths approach. It was motivated by a controversy over a recent structural rehabilitation of the Tete Bridge. The fundamental issue is related to the rotation of the suspended cross-beams. The original solution proves to be adequate because it is based on metallic plates in the contact zones between the cross-beams and the stringers. Replacing stiff components by flexible neoprene elements changes the fundamental characteristics of the original solution and reduces the capacity to generate rotational equilibrium under traffic loads within the range of small displacements.

Keywords: suspension bridge; bearings; bronze; stiffness; rehabilitation.

Introduction The Samora Machel Bridge (Fig. 1) over the Zambezi River in Tete (Mozambique) is a five span cable-truss bridge that has been in service since 1972 and can be considered a masterpiece of 20th century structural engineering based on certain aspects of the original design.1,2 The conceptual design follows the development of suspension bridges after the collapse of the Tacoma Narrows Bridge in 19403,4 and the construction of the San Marcos Bridge in El Salvador, 1952.5,6 One of the main features of the structural system is the high stiffness of the cable truss, as compared to the stiffening girders of typical suspension bridges. In the Tete Bridge, the deck structural system is innovative, based on independent concrete modules, partially prefabricated, without significant contribution to the overall stiffness.

With the Tete suspenders arrangement and deck system, the actions on the truss are statically determinate, whereas in the continuous deck of Peer-reviewed by international experts and accepted for publication

by SEI Editorial Board Paper received: December 8, 2016 Paper accepted: January 29, 2017

520

Scientific Paper

San Marcos there was some uncertainty in the distribution of internal forces and in the interaction between the cables and the concrete.

The present paper contains an analysis and discussion about the support system of prefabricated stringers on the crossbeams and was motivated by some controversy about a recent structural rehabilitation process.7 One of the fundamental issues is related to the rotation possibility of the suspended cross-beams, following recent research work in the University of Beira Interior.8–13 The paper aims to highlight the advantages of the original bronze bearings solution when compared with the recently implemented “stabilizing system”7 and taking into account the need for rehabilitation of another similar bridge in Mozambique, over the Save River. Another task of this paper is obtaining recognition for the original designer for his innovative solution and the disclosure of less-known aspects of his works that marked the history of the Portuguese structural engineering.

Stringer Support System Original Solution The prestressed concrete bridge deck modules are composed by grids of

nine longitudinal and four transversal prefabricated beams and by an in situ concreted top slab. Each module has a span of 10 m and is supported by cross-beams that are suspended by inclined hangers (Fig. 2a and b).

The deck modules are independent of each other, separated by expansion joints, supported on thin metallic plates over the cross-beams (Fig. 2c), working in simple and direct contact. The reduced height of the bearings (10 mm) and their metallic nature contribute to the stiffness of the connection, reducing the relative rotations between the stringer and the cross-beam. Additionally, the small height of the bearing plates enables the stringer to lean against the edge of the crossbeam, creating an automatic blocking system of excessive relative rotations, which could accidentally occur due to damage of the inclined hangers.

Recent Rehabilitation Solution The rehabilitation project7 modified the original solution, replacing the metallic bearing plates by flexible neoprene bearings and introducing inclined steel stabilizing bars (Fig. 3) in all stringers.

The task of the inclined struts was the reduction of rotations and elimination of “lack of stability” of the suspended cross-beams under the action of unbalanced traffic loads. As excessive rotations were not recorded after the construction of the bridge and appeared only after the damage of some suspension hangers or replacement of the bronze bearings by neoprene, the stability view is not agreed upon.

Rotational Equilibrium of the Cross-Beam Original Solution Because each pair of inclined suspension hangers crosses at one point, a question may arise about the balance of moments around a transversal axis that passes through that point. The equilibrium of moments of symmetrical forces applied on the stringers is assured because the couple of forces

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Fi g. 1: Side view of three-dimensional digital model of the bridge structure (L = 90 + 3 × 180 + 90 = 720 m)

3

3

(a)

(b)

2

2

5

1

(c) 1 – Cross-beam; 2 – Stringer; 4

4

3 – Hanger;

10

4 – Bronze plates 2 × (160 × 200 × 5); 5 – Expansion joint.

2

110 160

80 80 160 110 1

2

Fi g. 2: Suspended cross-beam supporting the stringers; (a) perspective of a cross-beam; (b) lateral view with stringers; (c) detail of two adjacent stringers supported by a cross-beam through metallic bearing bronze plates (dimensions in mm)

Fi g. 3: Lateral view of the stabilizing system (adapted from Ref. 7)

on the left side balances the couple of forces on the right side (Fig. 4a). Furthermore, the system is also efficient for asymmetric loads, because the changes in bearing forces are accompanied by respective changes in the lever arms and thus the rotational balance is assured.

The scheme of Fig. 4b describes the original concept1 for the equilibrium of the cross-beam under the action of asymmetric loads applied on the stringers. When the beam on the left side supports only permanent loads “g” and the beam on the right side supports permanent and traffic loads “g + q” the two resultant forces in the bearings change their position to the left side, increasing the lever arm of

the smaller reaction under the left stringer and decreasing the lever arm of the higher reaction under the right stringer. The closed force polygon indicates the equilibrium of the four forces applied on the cross-beam by the stringers and the hangers.

The capability of the reaction on the side without traffic loads to produce an increasing equilibrant moment results from the change of its application point, thus increasing the respective lever-arm. A minimal rotation of the cross-beam reduces automatically the lever-arm of the larger reaction.

When the supports of the stringers on the cross-beam are made of relatively stiff metallic plates, the balancing

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condition is found automatically by the structure itself without requiring large rotations, in a short transition period.10 The rotation of the cross-beam will only become significant when the reactions concentrate close to the points A and C, which can only happen under the action of significantly more severe traffic loads than those allowed on the bridge. In the example in Fig. 4, the traffic load corresponds to a vehicle of 120 t on the right side of the cross-beam.

The static system originally adopted becomes unstable when, under excessive asymmetric loading, a mechanism of hinges is formed (Fig. 5a). However, that situation will only arise if the transfer of loads from the stringers Scientific Paper

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(b)

A

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160

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C

Dry joints between brittle stone blocks have a relatively stiff behavior and require careful cutting to avoid damage due to high localized stresses. The use of mortar in such joints brings flexibility together with lower exigency on stoneworking and larger tolerable imperfections that do not provoke concentrated stresses. The low average stresses in conventional stone joints are usually compatible with the relatively low strength of mortar and stone.

D

1100 kN

“g + q”

500 kN

500 kN

“g”

500 kN

(a)

220

A

B

100

C

D

However, there is a practical limit for the decrease in stiffness of the mortar in the joints. With flexible filling material, it is difficult to get rotational equilibrium under asymmetric loading. As an example (Fig. 6), masonry arch bridges need joints stiff enough to withstand asymmetric traffic loads. Too flexible joints would not be adequate because of excessive deformations under asymmetric loads. The more flexible the joints are, the lower the load capacity.

F ig . 4: Equilibrium under symmetric/asymmetric vertical loads: (a) dead load; (b) dead + live load (dimensions in mm)

to the cross-beam concentrates on single “points”, on both sides. Until such a limiting state is reached, the system behavior is stable and even statically indeterminate (Fig. 5b).

provoke horizontal shear forces at the bearings, which did not exist in the original solution and which cause wear of the bearings as well as expansion joints.

Modified Solution

Joints in Stone Structures

The introduction of flexible bearings reduces the possibility of changing the position of the resultant forces, which for various loading stages remain close to the center of the neoprene plates (Fig. 5c). The equilibrium under the action of asymmetric loads would imply higher rotation of the cross-beam, which was reduced after installation of the bottom inclined bar (Fig. 3).

The behavior of this type of connection is analogous to that of the joints without tensile strength of stone ashlar or masonry arches, where the local rotational equilibrium is ensured by a specific distribution of the compression normal stresses (eccentric position of the resultant of the axial compressions).

The inclined bar, under tensile or compressive forces depending on whether the traffic loads are on the right or left side of the cross-beam, introduces new horizontal forces that must be transferred by the neoprene bearings. Due to the bar now introduced, the vertical traffic loads

(a)

Joints between stones have been successfully used since centuries for arches and vaults. The role of the joint stiffness, probably mastered by ancient designers and by the designer of the Tete Bridge, is rarely covered in modern engineering schools.

Recent research in the University of Beira Interior attempts to bridge that knowledge gap.8

(b)

In the original design, bronze was used specifically for all stringer bearings while neoprene was applied in the lateral supports of the deck against the piers.

In normal conditions (e.g. without damage in the suspension hangers), the stresses under the bronze bearings were below the concrete strength, even under heavy loading, as for example the equipment for the construction of Cahora Bassa hydroelectric power plant, which had to be transported through the Tete Bridge.

Numerical Analysis Finite Element Model Aiming to prove the correctness of the equilibrium hypothesis for the cross-beams under the action of asymmetric loads, numerical analysis of two-dimensional finite element models was performed (Fig. 7), taking into account geometric nonlinearity, using an updated Lagrangian formulation.14 The contact between the metallic bearing plates was modeled using slide lines, involving master and slave algorithms and Coulomb’s friction law. The

(c)

F ig . 5: Static systems for the bearing plates: (a) unstable mechanism; (b) statically indeterminate structure; (c) the strengthened structure 522

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the right side, the location of the reaction changes significantly, gradually approaching the axis of the cross-beam.

The critical limit occurs when the stress distribution on both sides concentrates on single points and the system loses stability (for live loads of vehicles heavier than 150 t).

q

q,max/g

g

E1 E2

E2/E1

Fi g. 6: Increase of an arch load capacity with the joint stiffness

With relatively stiff metallic plates (Fig. 2c) and increasing live loads applied on

Prestressed longitudinal beams g = 100 kN/m

After the quick initial change of the reaction location under the left stringer, the increase of traffic loads causes less significant changes in the stress distribution on the left side. However, on

10.00

Q = 1000 kN

250 kN

Normal Stresses Acting on the Metallic Plate Bearings

250 kN

The unbalanced limit state (see Fig. 7 for detail) was determined by increasing the live load until loss of equilibrium. For bearing plates with E = 100 GPa, a critical unbalanced live load of about 2000 kN was obtained, which corresponds to a reaction of 1500 kN in the right bearing plate. In further analyses, the bearing plates were modeled with decreasing stiffness assumptions. Finally, the inclined steel stabilizing bar was introduced (Fig. 3).

The stress diagrams for the different load levels show that the resultant reaction on the left side (without traffic loads) moves to the left, increasing the distance to the cross-beam midpoint. This behavior quickly creates a larger lever arm and a bigger equilibrating moment, which occurs even for low levels of traffic loads. The “quick” change of the location of the reaction of the left stringer causes the moment provided by dead load alone to increase to a maximum, balancing the moment of the reaction of the right stringer, whose lever arm decreases as the load increases.

250 kN

The loading corresponds to uniformly distributed loads “g” on the two stringers and a 100 t truck, modeled by four concentrated loads “Q/4” applied on the right stringer (Fig. 7).

the right stringer (Fig. 7), the diagrams of contact normal stresses on the bearings were calculated (Fig. 8). Three load cases were considered, with live load factors F = 0.0 (only permanent loads), F = 1.0 (100 t vehicle) and F = 1.5 (150 t vehicle, not allowed over the bridge).

250 kN

analysis was performed for various values of bearing plate stiffness. The stringers’ prestress was approximately accounted for by centering the reactions due to permanent loads in the middle of the metallic bearing plates.

g = 100 kN/m

10.00

If the concrete of the cross-beam plasticizes under the plates, the required rotation to equilibrium would be greater. However, that does not seem probable because the maximum value of the calculated stresses is in the elastic range, about 50% of the concrete strength in compression.

Normal Stresses on the Neoprene Bearings Due to their flexibility, the neoprene bearings do not allow for an efficient behavior in the change of location of the reactions, as in the case with metallic plates. The change of location of the forces resultant under the left stringer, without traffic loads, requires significant deformation of the flexible neoprene pad, associated with a higher rotation of the suspended cross-beam. Figure 9 shows a comparison of the behavior of the metallic (Fig. 9a) and neoprene (Fig. 9b) solutions in terms of location of the reaction resultants, under the action of a 100 t vehicle on the right stringer. The effect of the stabilizing bar is also shown in Fig. 9c.

Despite the reduction of contact stresses, the neoprene solution does not bring any advantage, since the stresses under the original bronze plates were below the concrete strength. The main problem is the excessive rotation of the cross-beam, which is aggravated by the neoprene solution, due to the location of the reactions and the low distortion stiffness of the bearings.

The values of the neoprene elasticity modulus (E) and thickness (t) influence the results. As these details applied for the Tete Bridge were unknown, approximate values of E = 25 MPa and t = 20 mm were assumed in the conducted analysis.

Rotations of the Suspended Cross-Beams

Fi g. 7: Finite element model of a cross-beam supporting two stringers, under asymmetric loading. Detail of the deformed model under traffic load F × Q = 2000 kN, corresponding to the unbalanced state

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The rotation of the suspended crossbeams under the action of asymmetric loads, obtained from the finite element model calculations, can be plotted as a function of the above defined live load factor F (Fig. 10). The Scientific Paper

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Left side without live loads

necessary for heavier traffic vehicles or for longer stringer spans. The system is robust even with narrow plates because there is a reserve of resistance to rotation instability when the cross-beam edge touches the lower face of the left stringer and the rotation is automatically blocked.

Right side with traffic loads

160

160

F=0 500 kN

500 kN F = 1,0

Conclusions

1000 kN

A rare type of cable-truss bridge structure, opened since 1972, is discussed, highlighting unique little-divulged aspects that were technical advances in comparison to previous structures, namely the special type of bronze bearings originally used between stringers and cross-beams.

500 kN F = 1,5

1250 kN

500 kN

F ig . 8: Distribution of normal stresses on the metallic bearing plates for increasing traffic loads on the right stringer (F=Truck load [kN] /1000) (dimensions in mm)

leftmost curve (metallic bearings) shows very low rotations up to F values close to 2.0 (corresponding to the theoretical limit of the unbalanced situation) and a rotation of less than 0.002 rad for 100 t vehicles. The right-hand curve number 2 in the graph corresponds to the neoprene bearings solution, giving rotations larger than 0.080 rad for F = 1.0. The middle curve number 3 corresponds to the model with the stabilizing bar, which effectively reduces the rotations resulting from the introduction of neoprene bearings, but does not reach the efficiency of the original solution

with metallic plates. For values of F = 0.4, corresponding to the 40 t load test vehicle,7 the calculated rotations are about 0.005 rad.

The choice of bronze for the original bearing plates appears to be purposely selected to control and limit the cross-beam rotations under asymmetric service live loads.

Parameter studies were also performed to quantify the stabilizing effect of the width of the metallic bearing plates. The critical instability load increases with the width of the plates. Wider metallic plates would be

Left side without live loads

160 F = 1,0

(a)

Excessive rotations were not recorded after the construction of the bridge.

The original system is stable even for asymmetric loads, provided that the traffic loads do not exceed critical values that could lead to the formation of a mechanism (Fig. 5a). Any stabilizing system to reduce the rotation of the cross-beam with the original metallic bearings, under the design loads, is considered unnecessary.

1000 kN 500 kN (b) 500 kN

1000 kN

(c)

500 kN

1000 kN

F ig . 9: Comparison between the stiff and flexible bearings in terms of normal stress distribution for a 100 t vehicle. (a) Original solution; (b) solution with neoprene and (c) solution with “stabilizing” bar (dimensions in mm) 524

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The original bearings of the stringers on the cross-beams were specifically made of bronze and not of neoprene, which was used laterally between the deck and the bridge piers. It is likely that this ingenious solution had resulted from previous experience on stone pillars and arches in which joints have no tensile strength.

A detailed numerical analysis confirmed the efficiency of the original solution as compared with the modified solution. Significant rotation of the cross-beams in the ingenious original solution, with the formation of an unstable mechanism, is possible only under the action of much heavier vehicles than those allowed on the bridge.

Right side with live loads (100 t)

160

The stiffness of a joint between two rigid bodies is essential to achieve the rotational equilibrium in the domain of small displacements. In the analyzed problem, equilibrium depends more on joints stiffness than on the resistance of the respective material. From this perspective, the treated problem is similar to the equilibrium of a stone arch under asymmetric loads.

The replacement of stiff bronze bearings by flexible neoprene is inappropriate because it modifies a fundamental

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2

Live load factor ( × 4 × 250 kN)

1

3

1.5

1

Original solution

2

Solution with neoprene

3

Solution with “stabilizing” bar

1

2

0.5

0 0

10

20

30

40

50

60

70

80

Rotation (×10–3 rad)

Fi g. 10: Rotation of the suspended cross-beam for increasing traffic loads on one stringer (Units: [rad, kN])

characteristic of the structure, eliminating the possibility of a quick change of position of the reactions, thereby reducing the capacity to generate rotational equilibrium with small cross-beam rotations and thus reducing the maximum allowable traffic loads.

It is possible that significant cross-beam rotations have occurred in the past, due to damage in the inclined suspension hangers. Such breakdowns can cause rotations not only under the action of traffic loads but also permanently. The automatic blocking of those rotations can be related to the damages of the concrete upper edge of the cross-beam.7 The repair of the hangers would automatically lead to the stabilization of the system.

unfavorable consequences in all expansion joints because it causes the transfer of horizontal forces through the neoprene bearings, closing and opening the expansion joints in every passage of the traffic loads.

Moreover, increasing the clear height between cross-beams and stringers, with thick neoprene bearings instead of thin metallic plates, reduces the possibility of automatic blockage of the rotations caused by damage or failure of an inclined suspension hanger, reducing the robustness of the original design.

Summarizing the above conclusions, the original design1 represents an optimal solution for the support of the stringers on the cross-beams, in the Tete Bridge.

The strengthening solution with inclined bars,7 connecting the stringers to the cross-beams, seems to partially solve the excessive rotations due to the introduction of neoprene bearings.

However, the efficiency of that stabilizing system depends on horizontal forces in the bearings, which equilibrate the force transfer through the inclined bar. For this reason, due to the low distortion stiffness of the neoprene bearings, the inclined bars seem to be relatively inefficient.

[2] Campos e Matos ME. Etude expérimentale d’un nouveau type de pont suspendu. Paper presented at IABSE 1968. Proceedings of the 8th IABSE Congress, New York, September 9–14, 1968. IABSE: Zürich, 1968; 813–825.

The introduction of the inclined bars in all stringers seems to have

[3] Gasparini D. The prestressing of structures: a historical review. Paper presented at ICCH

References [1] Cardoso E. Design of the Bridge over the Zambezi River (in Portuguese) Lisboa: Arquivo do Ministério do Ultramar, Instituto Português de Apoio ao Desenvolvimento IPAD, 1964.

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2006. Proceedings of the Second International Congress on Construction History, Queens’ College, Cambridge University, March 29–April 2, 2006. vol. 2, Construction History Society: Ascot, 2006; 1221–1232.

[4] Gasparini D, Charles C. Sunderland and the diffusion of prestressing technologies in the Americas. Paper presented at ICCH 2009.

Proceedings of the Third International Congress on Construction History, Brandenburg University of Technology Cottbus, Germany, May 20–24, 2009. vol. 2, NEUNPLUS1: Berlin, 2009; 655–662.

[5] Birdsall B, et al. San Marcos Bridge. Civil Eng. ASCE 1954: September 40–52.

[6] Birdsall B. Cable-stiffened suspension bridge updated. Eng. News Record 1953: May 32–39.

[7] Reis A, Baptista C. Rehabilitation of the suspension bridge over Zambezi River in Mozambique. Struct. Eng. Int. 2013; 23(1): 89–93.

[8] Pinto C, Fonseca J. Mechanical behaviour of high strength granite for new prestressed stone structures. Int. J. Rock Mech. Min. Sci. 2013; 60: 452–460.

[9] Fonseca J. The loadpath—a way to understand the quality of structures. J. Int. Assoc.

Shell Spat. Struct. 1997; 38(2): 129–135.

[10] Pinto C. Contribution to the design of new structures with high strength granite (in Portuguese). PhD Thesis in Civil Engineering, University of Beira Interior, Covilhã, Portugal, 2015.

[11] Fonseca J, Pinto C. Samora Machel Bridge over the Zambezi River in Tete Mozambique— study on rotation of the suspended cross-beams and on the deck structural bearings—original solution versus recent intervention (in Portuguese). Technical Internal Report TETE_NT01, University of Beira Interior, Covilhã, Portugal, 2013 (Unpublished).

[12] Nazaré M. Studies of the Edgar Cardoso design for the bridges over the rivers Save, Limpopo and Zambezi, with current methodologies (in Portuguese). MSc Thesis in Civil Engineering, University of Beira Interior, Covilhã, Portugal, 2011.

[13] Ferraz F. Bridge over the Zambezi River in Mozambique—expansion of the Edgar Cardoso Solution for a 360 m span (in Portuguese). MSc Thesis in Civil Engineering, University of Beira Interior, Covilhã, Portugal, 2013.

[14] LUSAS Finite Element Analysis Limited.

Modeller Reference Manual. Version 15.2, Issue 1. Surrey, UK, 2016.

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Seismic Behaviour of Irregular Structures Sekhar Chandra Dutta, Dr, Prof.; Pranab Kumar Das, Research Scholar; Piyali Sengupta, Dr, Asst. Prof., Department of Civil Engineering, Indian Institute of Technology (ISM), Dhanbad, Jharkhand, India. Contact: scdind2000@gmail.com. dutta.sc. civ@ismdhanbad.ac.in DOI: 10.2749/222137917X14881938989765

Abstract Vertically irregular buildings are frequently constructed across the globe for functional as well as aesthetic considerations. However, post-earthquake reconnaissance survey reports revealed high seismic vulnerability of buildings with vertical irregularities. Consequently, it is crucial to explore the reason behind their high seismic vulnerability in order to improve their performance during impending earthquakes. Considering the scarcity of relevant research in this regard in the existing literature, a humble effort is undertaken to comprehend the seismic behaviour of irregular structures. Several case studies comprising different configurations of irregular structures are chosen for performing response spectral as well as non-linear time history analyses. The results of the analysis indicate that the irregular structures may have lesser base shear owing to lesser mass as compared to a similar reference regular structural system.

However, there is ample chance of higher stress concentration as well as higher ductility demand in the members around the irregularity. This phenomenon may trigger early damage of these members, leading to early damage propagation culminating into progressive collapse of the entire or a major part of the structure. Member strength enhancement in the vicinity of vertical irregularity may improve the overall seismic performance of the irregular structures.

Keywords: vertically irregular structure; base shear; ductility demand; equivalent infill brick panel; soil–interaction; member force.

Introduction With the rapid growth of urbanisation occurring across the entire world, irregular buildings are quite frequently built in almost every country, including India. Such irregular buildings generally exhibit higher vulnerability under earthquake loading and thus require a thorough assessment to ensure their safety during seismic events. Irregularities of buildings can be broadly classified into two major groups, namely plan irregularity and vertical irregularity. Vertical irregularity may be further categorised into two subgroups, namely irregularity due to vertical distribution of mass and irregularity due to vertical distribution of stiffness. Photos of two vertically irregular buildings and the schematic diagram of the elevation of the corresponding structural frames are shown in Fig. 1.

Peer-reviewed by international experts and accepted for publication

by SEI Editorial Board Paper received: August 25, 2016 Paper accepted: March 19, 2017

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The seismic performance of buildings with vertical irregularity is the primary focus of this research. Seismic vulnerability assessment of vertically irregular buildings is of the utmost significance for potential risk assessment during impending earthquakes, pre-earthquake emergency disaster response planning and post-earthquake seismic retrofit selection and retrofit prioritisation.1–6 Seismic performance of a building depends on numerous factors such as adequate lateral strength, stiffness, ductility, regularity and the extent of simplicity in its configuration. During an earthquake, geometrically regular-shaped buildings with uniformly distributed mass and stiffness perform relatively well compared to the vertically irregular buildings. Poor performance of vertically irregular buildings, as observed during past earthquakes, can be attributed to their irregularity in the vertical distribution of mass and stiffness. Stress concentration occurs at the elements in the vicinity of the geometrical irregularity due to abrupt changes in mass and stiffness along the height, resulting in high localised ductility demand. Thus, the elements surrounding the abrupt geometrical change maytrigger local damage, which

eventually propagates to the progressive collapse of the entire building or major parts of it.7,8 In reality, almost all the buildings across the world contain irregularities to some extent due to functional or architectural purposes. From the viewpoint of seismic safety, the fundamental period of the structure, base shear and, most importantly, stress concentration and ductility demand in localised regions of a structure play a very crucial role in the seismic vulnerability of the irregular structures.

In this context, this paper aims to explore the reason behind the high seismic vulnerability of the irregular structures in order to improve their seismic resistance and to ensure enhanced seismic safety in case of earthquakes in future. Furthermore, the extent of stress concentration and ductility demand in the elements surrounding the irregular locations of the structure is also studied. Since most of the seismic codes provide prohibitive guidelines, an extensive seismic performance evaluation of several buildings with vertical irregularities may enable the engineering community to propose refined guidelines and design methodologies in order to ensure the seismic safety of such structures.

Provisions of Various Codes for Vertically Irregular Structures There was no provision for vertically irregular structures in the 1984 version of Indian Seismic Code IS 1893.9 However, the revised version (2002) of the IS 189310 has provided some discussion about the same. Different types of irregularities are defined and incorporated in Table 5 of IS 1893 (Part-1): 2002,10 as follows.

1. (a) Stiffness irregularity—soft storey: A soft storey is one in which the lateral stiffness is less than 70% of that in the storey above or less than 80% of the average lateral stiffness of the three storeys above. (b) Stiffness irregularity—extreme

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(a)

(b)

(c)

(d)

Fi g. 1: Real types of irregular buildings and configurations of Indian Seismic Code. (a) Vertically irregular building at Kathmandu, Nepal; (b) idealised form of vertical irregularity; (c) vertically irregular building at Kathmandu, Nepal; and (d) idealised form of vertical irregularity

2.

3.

4.

5.

soft storey: An extreme soft storey is one in which the lateral stiffness is less than 60% of that in the storey above or less than 70% of the average stiffness of the three storeys above. Buildings on stilts are examples of this category.

Mass irregularity: Mass irregularity occurs where the seismic weight of any storey is more than 200% of that of its adjacent storeys. The irregularity need not be considered in case of roofs.

Vertical geometric irregularity: Vertical geometric irregularity is considered to exist where the horizontal dimension of the lateral force-resisting system in any storey is more than 150% of that in its adjacent storey.

In-plane discontinuity in vertical elements resisting lateral force: In-plane discontinuity in vertical elements occurs when an in-plane offset of the lateral force-resisting elements is greater than the length of those elements.

Discontinuity in capacity—weak storey: A weak storey is one in which the lateral strength of the storey is less than 80% of that in the storey above. The lateral strength of the

(a)

Figure 2 presents five different types of vertical geometric irregularities categorised by IS 1893 (Part-1): 2002.10 The Eurocode11 recommends few design guidelines for setback buildings. In a gradual setback preserving axial symmetry, the setback at any floor would not be greater than 20% of the previous plan dimension in the direction of the setback, as explained in Fig. 3a and c. A single setback lower than 15% of the total height of the main structural system would not be greater than 50% of the previous plan dimension, as illustrated in Fig. 3d. If the setback does not preserve symmetry, each face of the setbacks at all storeys would not be greater than 30% of the plan dimension at the ground floor above the foundation or above the rigid basement top. Subsequently, it can be perceived well that the individual setbacks would not be greater than 10% of the previous plan dimension, as shown in Fig. 3b.

(b) L

A

(c) L

A

A

A

Federal Emergency Management Agency FEMA 450, Part 1: 200312 included provisions for some typical irregular buildings.

Additionally, FEMA 356: 200013 incorporated regulations for the irregular structures with out-of-plane discontinuity and severe weak storey irregularity. However, the variation of provisions in different codes and the prohibitive nature of the provisions clearly indicate the necessity of a general consensus to ensure safe seismic performance of such irregular buildings. A detailed study on the seismic behaviour of irregular structures may enlighten the engineering community with the possible mechanisms of initiation of failure. Furthermore, the extent of stress concentration in the elements surrounding the location of the irregularity due to excessive local deformation may also be enumerated.

storey is the total strength of all seismic force-resisting elements sharing the storey shear in the considered direction.

Existing Research on the Seismic Behaviour of Irregular Structures Numerous research works have been conducted on the seismic vulnerability assessment of the regular structures.

However, there is still a dearth of

(d)

(e)

L

L2

L2

A

L1

L1

Shear Wall

A/L > 0.10

A/L > 0.15

A/L > 0.25

L2 > 1.5L1

L2 > 1.5L1

Fi g. 2: Different types of elevation for vertical irregularities10

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(a)

(b)

(c)

L

L1

(d) L3

L1

L2

L

L3

L1

L

L1

L2

H H

0.15H

0.15H L1–L2 L1

≤ 0.2

L–L2 L

≤ 0.3;

L1–L2 L1

≤ 0.1

L1+L3

≤ 0.2 L (Set back occurs above 0.I5H)

L1+L3

≤ 0.5 L (Set back occurs below 0.15H)

F ig . 3: Elevational criteria for irregular buildings11

sufficient research studies to elucidate the possible mechanics involved in irregular structures under earthquake loading. In general, analytical methods are the most common approach in seismic performance evaluation of structures as analytical methods utilise a detailed vulnerability assessment algorithm to allow straightforward calibration with the structures as well as the hazard characteristics. However, the difference between the real structure and its model highly influences the reliability of the results. Consequently, the application of various analytical methods may be limited by the modelling capabilities and the computational effort.

Seismic analysis of structures can be broadly classified into two categories: (a) pseudo static analysis and (b) dynamic analysis. The fundamental period for the vertically irregular buildings is observed to be lesser than their regular counterparts.14 Several approaches are proposed by many researchers to evaluate the fundamental period of vertically irregular buildings, mostly in the form of empirical expressions. In this context, it may be appropriate to present the expressions obtained by a few of researchers for calculating the fundamental periods of the irregular buildings.

Indian Seismic Code IS 1893 (Part-1): 200210 incorporates a formula (Eq. (1)) for calculating the fundamental periods of regular buildings. To calculate the fundamental period of a vertically irregular structure, an empirical expression (Eq. (2)) was proposed15 by modifying the IS 1893 (Part-1): 200210 formula (Eq. (1)), as presented below: Ta = 0:075 h0:75

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ð1Þ

T = 0:075 h0:75 × k

ð2Þ

where k = TTref =

Fundamental period of irregular building Fundamental period of same type of regular building

= ½1− 2ð1 − ηÞ ð2η −1Þ ; for 0:6 ≤ η ≤ 1:0

Here, η = regularity index = Γ1Γ, 1ref; Γ1 = first mode participation factor for the irregular building frame; Γ1,ref = first mode participation factor for the similar regular building frame without vertical steps; h = overall building height (in “m”); and T = fundamental period of irregular building (in “s”).

A modified empirical expression for obtaining the fundamental period of irregular buildings was suggested,16 as mentioned in Eq. (3).

T = λ0 0:075 h0:75

ð3Þ

where period of irregular building λ0 = TTri = Fundamental Fundamental period of regular building

Here, h = overall building height (in m) and T = fundamental period of irregular building (in s).

A qualitative review was conducted by the researchers17 to summarise existing research on the seismic response of vertically irregular buildings. Excerpts from the research suggested that there is ample chance of increase in seismic demand of buildings comprising heightwise irregular distribution of mass, stiffness and strength. Furthermore, the buildings containing the combined stiffness, mass and strength irregularities have a higher seismic demand. Another research18 concluded that the regular buildings are safer in seismic zones II, III, IV and V with respect to their irregular counterparts. It was deduced from the study19 that the seismic zones

may play a very important role in regulating the seismic vulnerability of vertically irregular structures. Additionally, it was observed that the lateral load-carrying capacity of buildings decreases with an increase in the vertical irregularities of the building. Two other studies20,21 focussed on the seismic response of the irregular buildings on sloping ground in hilly areas and found that these buildings experienced higher displacement and base shear compared to the buildings resting on plain ground. Buildings resting on sloping ground are more susceptible to seismic excitations as the shorter column attracts more forces and undergoes early damage during earthquakes.

Mass-irregular and stiffness-irregular buildings face higher storey shear and displacement compared to similar regular buildings.22 After conducting the response spectrum analysis (RSA) on different types of vertically irregular buildings, it was concluded14 that the storey drift increases proportionally with the vertical irregularities of the buildings.

Based on the incremental dynamic analysis results of several buildings,23 it was understood that the dynamic performance of buildings would be affected if their lateral load-resisting properties were not uniformly distributed.

Another study24 explained the different methods for increasing lateral load capacities of soft storey buildings.

High-rise, vertically irregular buildings are observed as being more vulnerable to ground excitation25 as plasticity and damage generally initiate at the locations of the irregularities. Another study26 discussed the accuracy of modal pushover analysis to evaluate the seismic performance of high-rise, irregular buildings. A recent study27 following the Gorkha earthquake in

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Nepal on 25 April 2015 also underlines the vulnerability of the irregular structures. Furthermore, the importance of considering torsional irregularity and higher mode effects in seismic response analyses were highlighted by some researchers.28–30 Non-linear analysis is stated to be essential for performancebased design and collapse prevention of the irregular structures.31–33 Another research34 was conducted on the seismic performance of setback buildings retrofitted with damped braces, incorporating the higher mode effect. Additionally, the behaviour of buildings with torsional irregularity was studied35 using the time history analysis method to examine the effect of eccentricity of the buildings, with regard to seismic excitation, on their seismic performance.

The study presented in this section summarises the empirical expressions for the estimation of the fundamental period of vertically irregular buildings.

Furthermore, the seismic vulnerability of various irregular buildings is briefly demonstrated. However, a detailed study to understand the basic mechanism of irregular buildings under seismic loading is still missing in the literature. Although most of the existing research emphasised the additional vulnerability of the irregular buildings, the location of stress concentration— that is, the zone of initiation of yielding and damage—was not clearly indicated. The location of stress concentration or high ductility demand may give an idea about the failure path of the irregular buildings when subjected to seismic loading. Considering the scarcity of the relevant research in this context in the existing literature, a humble effort is

undertaken to comprehend the seismic behaviour of the irregular structures.

In the first part of the present study, a response spectrum method is employed for the three-dimensional models of vertically irregular buildings to understand their basic response under free vibration analyses. The fundamental periods of the irregular buildings can be accumulated from the results of the analysis to compare the performance of the empirical expressions. The comparison study may enlighten the engineering community about the suitable empirical expression to estimate the fundamental period of irregular structures. In the second part, several case studies comprising different configurations of irregular structures are chosen to perform response spectral as well as non-linear time history analyses. The nature and contribution of various modes may be able to explain the vulnerability of the irregular buildings. Stress concentration and higher ductility demand in the members around the location of irregularity may trigger early local damage, leading to early damage propagation and culminating into progressive collapse of the entire or a major part of the structure. Member strength enhancement in the vicinity of irregularity may improve the overall seismic performance of the irregular structures.

and storey height are chosen for seismic analyses. A symmetrical five-storey building with four bays in each direction is considered a reference symmetrical building, denoted by “R”. The height and bay length of each storey are considered to be 3 and 4 m, respectively. Detailed geometry of the regular frame, along with the cross-sectional details of a typical column and a typical beam, is shown in Fig. 4. A ‘strong column weak beam’ philosophy is utilised for the design of the regular and irregular buildings.

Configurations of Regular and Irregular Buildings In order to understand the effect of irregularities on seismic performance, a five-storey regular frame and a set of irregular frames with similar bay length

(a)

Seismic response of the regular frame is chosen as a reference to compare the response of their irregular counterparts. These irregular counterparts are derived from the regular building frame (R) to encompass various possible types of irregularities, as shown in Fig. 5. The bay length, storey height and cross-sectional properties of irregular frames are similar to the regular frame, as shown in Fig. 4. The crosssectional dimensions and material properties of the beam, column and slabs are shown in Table 1. Dead load and live load applied at the roof levels and floor levels of the regular and irregular Reinforced Concrete (RC) frames are enumerated in Table 2. In this study, the Takeda hysteresis model is utilised to incorporate the non-linearities while modelling the regular and irregular buildings.

Free Vibration and Spectral Analyses of Regular and Irregular Buildings The regular and irregular buildings shown in Figs. 4 and 5, respectively,

(b) 3m

500 mm

3m 3m

25 mm

40 mm

250 mm 40 mm

15 m

25 mm

3m 500 mm

3m

4m

8 mm diameter stirrup

4m

350 mm

8 mm diameter stirrup

4m 4m 4m

4m

16 m

4m4m

4 nos. 25 mm diameter bar at intermediate positions

16 m 4 nos. 28 mm diameter bar at corner positions

1 no. 20 mm diameter bar at intermediate positions 4 nos. 25 mm diameter bar at corner positions

Fi g. 4: Layout and cross-sectional details of a vertically regular (R) RC frame. (a) Layout of vertically regular RC frame building; (b) reinforcement details of a typical column (left); and a typical beam (right)

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529

Irregular Frame 1 (IR1)

Irregular Frame 2 (IR2)

Irregular Frame 3 (IR3)

Irregular Frame 4 (IR4)

Irregular Frame 5 (IR5)

Irregular Frame 6 (IR6)

Irregular Frame 7 (IR7)

Irregular Frame 8 (IR8)

Irregular Frame 9 (IR9)

Irregular Frame 10 (IR10)

Irregular Frame 11 (IR11)

Irregular Frame 12 (IR12)

F ig . 5: Layouts of several irregular (IR) RC frames. (a) Irregular frame 1 (IR1); (b) irregular frame 2 (IR2); (c) irregular frame 3 (IR3); (d) irregular frame 4 (IR4); (e) irregular frame 5 (IR5); (f ) irregular frame 6 (IR6); (g) irregular frame 7 (IR7); (h) irregular frame 8 (IR8); (i) irregular frame 9 (IR9); (j) irregular frame 10 (IR10); (k) irregular frame 11 (IR11); and (l) irregular frame 12 (IR12) Structural elements

Dimensions

Column

500 mm × 500 mm

Beam

350 mm × 250 mm

Slab

125 mm thickness

Materials M25 concrete, Fe 415 for main reinforcement and Fe 250 for transverse reinforcement

Table 1: Cross-sectional dimensions and material properties of RC frame structures Level

Dead load (kN/m2)

Live load (kN/m2)

Roof level

10

1.5

Floor level

12

3

Table 2: Dead load and live load on RC frame structures 530

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are subjected to free vibration analyses to determine the fundamental period and initial three natural frequencies. Then, the same buildings are subjected to complete quadratic combination (CQC) analysis to compute the stresses in the critical members. The mode shapes of the regular and irregular buildings are compared to identify the most deformed members visible from the mode shapes of irregular structures and the stresses developed in them. This method enables the identification of the physical reason of excessive deformation due to stress concentration. Such a stress concentration may initiate local failure that may gradually propagate, culminating into partial or complete structural collapse. In particular, such a proportion cannot be firmly ascertained if the deformation and stress distribution of similar elements of reference symmetric structure are not compared. If the deformations in the mode shapes as well as distribution of forces or stress quantities are much lesser in the similar element of the regular structure, it may be clearly understood that the irregularity contributes to the excessive deformations, forces and stresses. Such an investigation will help in pointing out the vulnerable members of irregular structures and help in arriving at guidelines to protect them. The initial three mode shapes of regular and irregular frame structures, along with their modal participation factors (PF) and the effective masses (mk), are shown in Table 3. The effective mass (mk) as a ratio of modal mass (Mk) and total seismic mass (W) in percentage is computed using Indian Seismic Code IS 1893 Part 1 (2002).10 The first three mode shapes of the irregular buildings and the regular building are presented in a schematic diagram in Table 3 to provide an idea about the deformation pattern in each of three mode shapes. To make the modelling more realistic, the masonry partition walls are modelled as equivalent compressive diagonal struts only.

Furthermore, the periods of low-rise buildings (which are generally stiff in nature) may also be considerably lengthened by soil flexibility. For accuracy of the results, effects such as those described in following section are considered. Generally, the first mode shapes of irregular buildings have primarily lateral and torsional deformation. In the second mode shapes of irregular buildings, the amounts of

Structural Engineering International Nr. 4/2017

Types of building

Regular (R)

Irregular (IR1)

Irregular (IR2)

Irregular (IR3)

Irregular (IR4)

First mode shape

Second mode shape

Third mode shape

Natural Period: 0.572 seconds PF (X): 39.22; PF (Z): 39.33 mk: 78.88%

PF (X): 39.33; PF (Z): 39.22 mk: 79.34%

PF (X): 0.00; PF (Z): 0.00 mk: 80.29%

Natural Period: 0.570 seconds PF (X): 0.00; PF (Z): 63.15 mk: 74.08%

PF (X): 70.71; PF (Z): 0.00 mk: 70.64%

PF (X): 0.00; PF (Z): 0.00 mk: 70.41%

Natural Period: 0.541 seconds PF (X): 0.00; PF (Z): 61.78 mk: 75.34%

PF (X): 73.42; PF (Z): 0.00 mk: 73.62%

PF (X): 0.00; PF (Z): 7.61 mk: 73.73%

Natural Period: 0.534 seconds PF (X): 0.00; PF (Z): 57.61 mk: 73.34%

PF (X): 71.17; PF (Z): 0.00 mk: 71.09%

PF (X): 0.00; PF (Z): 5.46 mk: 70.93%

Natural Period: 0.520 seconds PF (X): 0.00; PF (Z): 50.62 mk: 71.79%

PF (X): 66.68; PF (Z): 0.00 mk: 66.70%

PF (X): 0.00; PF (Z): 3.47 mk: 66.28%

Tab l e 3: Regular and vertically irregular RC frame buildings with their initial three mode shapes

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Types of building

Irregular (IR5)

Irregular (IR6)

Irregular (IR7)

Irregular (IR8)

Irregular (IR9)

First mode shape

Second mode shape

Third mode shape

Natural Period: 0.798 seconds PF (X): 79.39; PF (Z): 0.17 mk: 80.48%

PF (X): 0.17; PF (Z): 20.58 mk: 83.98%

PF (X): 0.06; PF (Z): 63.56 mk: 84.89%

Natural Period: 0.592 seconds PF (X): 0.00; PF (Z): 68.44 mk: 69.86%

PF (X): 69.98; PF (Z): 0.00 mk: 69.67%

PF (X): 0.06; PF (Z): 3.47 mk: 71.80%

Natural Period: 0.570 seconds PF (X): 0.00; PF (Z): 61.29 mk: 76.51%

PF (X): 73.47; PF (Z): 0.00 mk: 73.36%

PF (X): 0.00; PF (Z): 3.44 mk: 73.07%

Natural Period: 0.501 seconds PF (X): 0.00; PF (Z): 55.63 mk: 70.56%

PF (X): 70.71; PF (Z): 0.00 mk: 70.16%

PF (X): 0.00; PF (Z): 0.00 mk: 72.64%

Natural Period: 0.566 seconds PF (X): 33.18; PF (Z): 33.18 mk: 77.00%

PF (X): 38.21; PF (Z): 38.21 mk: 78.34%

PF (X): 6.03; PF (Z): 6.03 mk: 78.44%

T abl e 3: Continued

532

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Structural Engineering International Nr. 4/2017

Types of building

Irregular (IR10)

Irregular (IR11)

Irregular (IR12)

First mode shape

Second mode shape

Third mode shape

Natural Period: 0.560 seconds PF (X): 26.66; PF (Z): 32.98 mk: 72.03%

PF (X): 39.44; PF (Z): 33.04 mk: 75.94%

PF (X): 8.86; PF (Z): 8.55 mk: 75.54%

Natural Period: 0.559 seconds PF (X): 26.71; PF (Z): 32.97 mk: 69.6%

PF (X): 39.26; PF (Z): 32.95 mk: 73.77%

PF (X): 8.60; PF (Z): 8.28 mk: 72.44%

Natural Period: 0.565 seconds PF (X): 0.21; PF (Z): 73.89 mk: 61.52%

PF (X): 74.23; PF (Z): 0.25 mk: 83.21%

PF (X): 0.58; PF (Z): 0.58 mk: 80.25%

Table 3: Continued

(a)

(b)

The portion of brick wall effectively behaving as a compressive strut

Brick infill

Deformed shape of a single panel

(c)

Equivalent compression only diagonal strut

Lateral load a rinf

a rinf

hinf

hcol

θ

Fi g. 6: (a) Reinforced frame building with masonry infill; (b) different configuration of a typical panel of brick infill; and (c) schematic diagram of equivalent compression only diagonal strut36

Structural Engineering International Nr. 4/2017

torsional deformation are increased.

However, in the case of the third mode shape of the irregular buildings, generally, a further domination of torsional displacements, as well as other local deformations, is observed. These may play a very important role in regulating the seismic response. On the other hand, first and second mode shapes of regular buildings have shown purely lateral displacements, and the third mode shape represented the torsional deformation. Further, torsional displacements are dominated specially at the location where the irregularities exist for irregular structures. In fact, this issue will be more clearly understood if the mode shapes of irregular building frames, for example IR9, IR10, IR11 and IR12, are studied. It may be noticed that the members near the sudden geometrical change, which causes irregularity, may suffer larger deformation, particularly in second and Scientific Paper

533

Lateral stiffness of columns (Kframe) Mass of building Translational spring with stiffness Kx

Rocking spring with stiffness Kθ Square footing of length (L) = width (B)

Torsional spring with stiffness Kf

F ig . 7: Idealised model of a structure with translational, torsional and rocking springs to incorporate SSI due to lateral vibration of building

third modes dominated by the torsional deformations. The modal participation factors PF (X) and PF (Z) of the regular and irregular buildings in the X and Z directions, respectively, are presented in Table 3, along with the effective masses (mk) for the initial three modes. The second and third modes together may have a considerable influence on overall building response, as revealed from their PF and effective masses (mk). So, the vulnerability of irregular structures may be attributed to the early failure of individual highly deformed/stressed elements at the point of sudden geometrical change.

Modelling Effect of Masonry Infill and Soil Flexibility Reinforced concrete frames with nonreinforced masonry infill walls are one

Building type

of the most common types of construction throughout the world. A masonry wall can withstand considerable compressive stress but almost no tensile stress. When subjected to lateral loads, especially seismic loads, the masonry infill provides additional stiffness arising from the compressive strut effect, as explained in Fig. 6.

Due to the lateral deformation of a typical rectangular panel caused by the seismic load, the panel tends to take the shape of a parallelogram (Fig. 6b), causing elongation of one diagonal and shortening of the other.

The shortened diagonal will carry a compressive load and behave like a compressive strut in the equivalent sense.

Till date, several researchers have proposed different modelling techniques to capture the realistic behaviour

Stiffness of equivalent spring with inclusion of equivalent diagonal struts and SSI (Kxeqv)

Stiffness of frame (Kframe)

Stiffness of translational spring (Kx)

Stiffness of rocking spring (Kθ)

R1

0.281 × 106

0.289 × 106

17.349 × 106

8251.792 × 106

IR1

0.216 × 10

0.221 × 10

17.349 × 10

6

8251.792 × 106

IR2

0.202 × 106

0.207 × 106

17.349 × 106

8251.792 × 106

IR3

0.191 × 106

0.196 × 106

17.349 × 106

8251.792 × 106

IR4

0.172 × 10

0.175 × 10

17.349 × 10

6

8251.792 × 106

IR5

0.292 × 106

0.302 × 106

17.349 × 106

8251.792 × 106

IR6

0.259 × 106

0.267 × 106

17.349 × 106

8251.792 × 106

IR7

0.224 × 106

0.229 × 106

17.349 × 106

8251.792 × 106

IR8

0.189 × 10

0.192 × 10

17.349 × 10

6

8251.792 × 106

IR9

0.201 × 106

0.215 × 106

17.349 × 106

8251.792 × 106

IR10

0.245 × 106

0.250 × 106

17.349 × 106

8251.792 × 106

IR11

0.243 × 106

0.249 × 106

17.349 × 106

8251.792 × 106

IR12

0.251 × 106

0.258 × 106

17.349 × 106

8251.792 × 106

6

6

6

6

6

6

Table 4: Numerical values of stiffness (kN/m) of various equivalent springs of regular and irregular buildings 534

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of the masonry infill panels of RC frames in the form of an equivalent diagonal strut model, multiple strut model and equivalent bi-diagonal compression strut model.36–44 However, in the present research, an equivalent compression-only diagonal strut model, as shown in Fig. 6, is adopted. During dynamic analysis, between each of the two lateral directions of the diagonal struts, only the equivalent diagonal strut in compression becomes effective. From the literature, dimensions of the compressive strut can be obtained for application in the computational model. Out of the few guidelines available regarding the dimensions rinf, a, hinf of the equivalent diagonal compressive strut shown in Fig. 6c, the formula (Eq. (4)) as provided in FEMA37 is used in the current study. a = 0:175ðλ1 hcol Þ − 0:4 rinf

ð4Þ

where λ1 = [(Emtinf sin 2θ)/(4EfeIcol hinf)]0.25; a is the width of equivalent strut; hcol is the column height between the centre lines of beams; Em is the expected modulus of elasticity of infill; tinf is the thickness of infill panel and equivalent strut; hinf is the height of the infill panel; θ is the angle whose tangent is the aspect ratio of infill (height to length); Efe is the expected modulus of elasticity of frame material; Icol is the moment of inertia of column; and rinf is the diagonal length of infill panel. In this research, hcol = 3000 mm; Em = 14 000 MPa; tinf = 250 mm; θ = 37 ; Efe = 25 000 MPa; Icol = 520833 × 104 mm4; hinf = 2650 mm; rinf = 4390 mm; and a = 500 mm are considered to represent a realistic condition.45,46 Thus, the regular building (R) and irregular buildings (IR1–IR12) are equipped with an equivalent diagonal compressive strut to incorporate the effect of masonry infill in their fundamental period.

Furthermore, the effect of soil structure interaction (SSI) is taken into account in the analyses of the regular (R) and irregular buildings (IR1–IR12) to obtain a more realistic seismic response. On the basis of the concept and procedure put forward in the existing literature,47–56 a similar study was conducted to incorporate the SSI effect.

The effects of soil flexibility along the horizontal rotation were introduced through the addition of a torsional spring with stiffness Kf. The effects of soil flexibilities in the lateral and rocking movements are incorporated by a

Structural Engineering International Nr. 4/2017

“T” by Indian Seismic Code10 (s)

“T” by Eurocode11 (s)

“T” by FEMA12 (s)

“T” by FE analysis without considering the effect of masonry infill and SSI (s)

T= 0.075h0.75 × k (s)15

T= λ0 0.075h0.75 (s)16

“T” (s) by considering the effects of equivalent diagonal strut and SSI

Nature of fundamental mode shape

Regular building (R)

0.572

0.572

0.533

0.618

0.572

0.637

0.480

Purely lateral displacement

Irregular building (IR1)

0.572

0.572

0.533

0.570

0.436

0.570

0.518

Lateral and torsional displacement

Irregular building (IR2)

0.572

0.572

0.533

0.541

0.432

0.543

0.535

Lateral and torsional displacement

Irregular building (IR3)

0.572

0.572

0.533

0.534

0.429

0.539

0.540

Lateral and torsional displacement

Irregular building (IR4)

0.572

0.572

0.533

0.520

0.454

0.535

0.560

Lateral and torsional displacement

Irregular building (IR5)

0.572

0.572

0.533

0.798

0.589

0.972

0.507

Lateral and torsional displacement

Irregular building (IR6)

0.572

0.572

0.533

0.592

0.463

0.587

0.503

Lateral and torsional displacement

Irregular building (IR7)

0.572

0.572

0.533

0.570

0.431

0.570

0.516

Lateral and torsional displacement

Irregular building (IR8)

0.572

0.572

0.533

0.501

0.432

0.541

0.568

Lateral and torsional displacement

Irregular building (IR9)

0.572

0.572

0.533

0.566

0.447

0.410

0.542

Lateral and torsional displacement

Irregular building (IR10)

0.572

0.572

0.533

0.560

0.429

0.559

0.502

Lateral and torsional displacement

Irregular building (IR11)

0.572

0.572

0.533

0.559

0.570

0.558

0.504

Lateral and torsional displacement

Irregular building (IR12)

0.572

0.572

0.533

0.565

0.514

0.565

0.496

Lateral and torsional displacement

Types of building

Table 5: Comparison of fundamental periods (in s) of regular and vertically irregular RC frame buildings obtained through various sources with and without incorporating the effect of masonry infill and SSI

translational spring and a rocking spring, respectively. The mathematical expression of equivalent soil flexibility (Kxeqv) in terms of frame stiffness Kframe, translational spring stiffness Kx and rocking spring stiffness Kθ is presented in Eq. (5).57 The effect of SSI in an idealised model of a structure is modelled by adding translational, rocking and torsional springs, as shown in Fig. 7.

1 Kxeqv

=

1 Kframe

+

1 L2 + K x Kθ

ð5Þ

8GR3

0 0 where Kx = ð8GR 2−νÞ and Kθ = 3ð2− νÞ; Kf = K0 (R0). J (L/B); 2 R0 = 2B:π2L = radius of equivalent circular foundation; K0 (R0) = corresponding stiffness of equivalent circular

Structural Engineering International Nr. 4/2017

foundation; J (L/B) = correlation factor; G = shear modulus of soil medium; ν = Poisson ratio of soil medium; and L and B are length and width of rectangular foundation, respectively.

The stiffness of an equivalent spring incorporating equivalent diagonal struts and SSI (Kxeqv), stiffness of frame (Kframe), stiffness of translational spring (Kx) and stiffness Scientific Paper

535

13% higher than the fundamental periods of the same buildings without incorporating the effects of equivalent diagonal strut and SSI. On the other hand, the fundamental periods of vertically irregular buildings IR1–IR2, IR6– IR7 and IR9–IR12 are 1 to 15% lower when the effects of equivalent diagonal strut and SSI are considered. Vertically irregular building IR5 shows a decrease of 36% in the fundamental period when the effects of equivalent diagonal strut and SSI are incorporated.

s Coefficient of spectral acceleration ga

3.0 Type III (soft soil)

2.5

Type II (medium soil)

2.0

Type I (rock or hard soil)

1.5 1.0 0.5 0.0 0.0

0.5

1.0

1.5

2.0 2.5 Period (s)

3.0

3.5

4.0

F ig . 8: Response spectra for rock and soil sites for 5% damping10

rocking spring (Kθ) are summarised in Table 4.

The fundamental periods of regular and vertically irregular buildings obtained from finite element (FE) analysis with and without taking into account the effect of masonry infill and soil flexibility, along with the same outcomes obtained from different code provisions and exiting research guidelines, are presented in Table 5.

Table 5 demonstrates that the fundamental periods of vertically irregular buildings (except IR5) are lower than the fundamental period of the reference regular building (R). The reason may be understood if we consider an example of typical response spectra, which is provided in Indian Seismic Code IS 1893 Part 1 (2002),10 as shown in Fig. 8. This figure implies that with a decrease in the fundamental period, an increase in Sa/g occurs,

which may create a possibility of increase in base shear. However, base shear depends on both spectral acceleration Sa/g and mass. Irregular buildings have less mass compared to their regular counterpart. Therefore, it is very difficult to predict whether the irregularity in buildings will cause an increase in base shear or not. This issue is further investigated by computing the base shear of regular and irregular buildings in the following section.

It can be noticed that the fundamental period of the regular building with inclusion of the equivalent diagonal strut and SSI is 22% lower than the fundamental period of the same building without incorporating the equivalent diagonal strut and SSI. However, the fundamental periods of vertically irregular buildings IR3, IR4 and IR8 with inclusion of the effects of equivalent diagonal strut and SSI are 1 to

Types of building

Base shear (kN) SRSS

CQC

Regular building (R)

626.90

886.67

Irregular building (IR1)

709.75

709.98

Irregular building (IR2)

718.89

730.73

Irregular building (IR3)

699.91

700.73

Irregular building (IR4)

643.12

646.50

Irregular building (IR5)

891.93

894.49

Irregular building (IR6)

887.34

887.90

Irregular building (IR7)

781.03

781.55

Irregular building (IR8)

812.49

816.17

Irregular building (IR9)

552.52

792.03

Irregular building (IR10)

525.01

749.99

Irregular building (IR11)

518.56

739.45

Irregular building (IR12)

666.97

761.90

Table 6: Base shears of regular and vertically irregular RC frame buildings by SRSS and CQC method 536

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Variations in Base Shear in Regular and Vertically Irregular Buildings Base shear of a building depends on both spectral acceleration Sa/g and mass. Irregular buildings have less mass compared to their regular counterparts. However, the fundamental periods of vertically irregular buildings are mostly lower than the fundamental periods of the reference regular buildings. This may result in an increase of Sa/g. Thus, it is very difficult to predict whether the irregularity in buildings will cause an increase in the base shear or not. Therefore, from the response spectrum analyses of the regular (R) and vertically irregular buildings (IR1–IR12) along X direction, base shears of the buildings are calculated using the CQC method and square root of the sum of the square (SRSS) method. The base shears of regular and vertically irregular buildings computed using the CQC method and SRSS method are summarised in Table 6.

Table 6 reveals that the base shears calculated using the SRSS method for vertically irregular buildings IR5–IR6 are approximately 42% higher than the base shears calculated for the regular (R) frame. Similarly, the base shears calculated using the SRSS method for IR7–IR8 are approximately 25 to 30% higher than the base shears calculated for the regular (R) frame. The base shears calculated using the SRSS method for IR1–IR3 are approximately 12 to 15% higher than the base shears calculated for the regular (R) frame.

The base shears calculated using the SRSS method for IR4 and IR12 are approximately 3 to 6% higher than the base shears calculated for the regular (R) frame. The base shears calculated using the SRSS method for IR9–IR11 are approximately 12 to 17% lower than the base shears calculated for the

Structural Engineering International Nr. 4/2017

Building Type

Increased Moment of Members

4 3

5

1 2

Members

6

6

115

5

115

4

121

3

143

2

143

1

144 % of Increase in moment of members

Irregular building (IR1)

9

4

8

127

3

7

127

7

6

2 1

9

8

Members

6 5

120

154

5

167

4

167

3

167

2

168

1 Irregular building (IR2)

2 3 1 6

8 7

9

Members

5

4

168 % of Increase in moment of members

9

164

8

164

7

164

6

167

5

167

4

168

3

168

2

168

1

174 % of Increase in moment of members

Irregular building (IR3)

Tab l e 7: Moments on identified members of vertically irregular buildings

regular (R) frame. On the other hand, the base shears calculated using the CQC method for IR1–IR4 and IR7– IR12 are approximately 8 to 30% lower than the base shears calculated for the regular (R) frame. The base shears calculated using the CQC method for IR5–IR6 are marginally higher than the base shears calculated for the regular (R) frame. Therefore, this clearly shows that irregularity does not necessarily cause a considerable increase in base shear. Thus, the possibility of excessive vulnerability of such buildings may only arise due to excessive force or moment generated in some of the members as predicted earlier. This

issue is investigated in the following section.

Moment Increase in Various Members Due to Irregularities High seismic vulnerability of the irregular buildings may be attributed to the increased bending moment of the members located in the vicinity of abrupt geometrical change. Consequently, bending moments of beams and columns in the regular (R) building and irregular buildings (IR1–IR12) are calculated using RSA based on Indian Seismic Code IS 1893

Structural Engineering International Nr. 4/2017

Part 1 (2002).10 Then, bending moments of beams and columns of irregular buildings are compared to those of the similar members in the regular building. Table 7 presents the increases in bending moment of the critical members of the irregular buildings. The members of an irregular building which experience increased bending moment when compared with the similar members of a regular building are considered the critical members and are marked by bold lines and numbered for ease of identification. The percentages of increase in bending moment of the critical members of irregular buildings Scientific Paper

537

Building Type

Increased Moment of Members

2 1

8

7

9

Members

3

5 4 6

9

123

8

123

7

123

6

161

5

161

4

161

3

168

2

168

1

169 % of Increase in moment of members

Irregular building (IR4)

9 6

5 2

9

8

8

112

7

113

6

114

5

115

4

117

3

120

2

122

1

4

7

Members

3

105

1

% of Increase in moment of members

Irregular building (IR5)

6

2 3 6

5

4 1

Members

5

110 115

4

120

3

120

2

120

1 Irregular building (IR6)

132

127 % of Increase in moment of members

T abl e 7: Continued

with respect to their regular counterparts are presented in Table 7 in the form of a bar diagram.

Table 7 depicts the percentage of increase in moment of the critical members of the irregular buildings (IR1â&#x20AC;&#x201C;IR12) with respect to the similar members in the regular (R) building. In the irregular building IR1, a 115 to 144% increase in moment is observed due to irregularity, with a maximum increase (144%) in moment in the vertical member 1. In the irregular frame IR2, a 120 to 168% increase in moment 538

ScientiďŹ c Paper

is observed, with a maximum increase (168%) in bending moment in the vertical members 1 and 2. Additionally, members 3, 4 and 5 in irregular frame IR2 have 167% increases in moment with respect to their regular counterparts. In the irregular frame IR3, a 164 to 174% increase in moment can be observed in the critical members, with a maximum increase (174%) in moment in the vertical member 1. In the irregular frame IR4, a 123 to 169% increase in moment can be observed in the critical members, with respect to

their regular counterparts. Vertical member 1 of irregular frame IR4 experiences a maximum increase (169%) in moment. By examining the amount of increase in moments in the critical members of the irregular buildings IR1â&#x20AC;&#x201C;IR4, it can be clearly perceived that, with an increase in irregularities, a considerable increase in the moments can be obtained in a higher number of members.

Irregular building IR5 has symmetrical irregularities on both sides of the building, and thus, all the members of

Structural Engineering International Nr. 4/2017

Building Type

Increased Moment of Members

3 1

6

4 Members

2 5 7

8

8

126

7

126

6

131

5

131

4

137

3

171

2

171

1

171 % of Increase in moment of members

Irregular building (IR7)

3 1 5 4 6

Members

2

6

111

5

111

4

112

3

115

2

115

1

115 % of Increase in moment of members

Irregular building (IR8)

9

1

3

4 2 8

5

Members

7 6

9

126

8

130

7

130

6

131

5

131

4

166

3

166

2

167

1

167 % of Increase in moment of members

Irregular building (IR9)

Tab l e 7: Continued

the over-hanged portion experience a 105 to 132% increase in moment compared to the regular building. Furthermore, other members of the building also face some increase in moment compared to the regular building. In the irregular frame IR6, a 110 to 127% increase in moment can be observed in the marked members with respect to their regular counterparts. Additionally, irregular building IR6 is found to be in a more stable condition compared to the irregular building IR5. In the irregular building IR7, a 126 to 171% increase in moment can be observed in critical

members, with a maximum increase (171%) in moment observed in the vertical members 1, 2 and 3. In the irregular frame IR8, a 111 to 115% increase in moment is found in critical members with respect to their regular counterparts.

Irregular buildings IR9â&#x20AC;&#x201C;IR12 contain irregularities in both directions. In the irregular building IR9, a 126 to 167% increase in moment can be observed in critical members, with a maximum increase in moment observed in the vertical members 1, 2, 3 and 4. In the

Structural Engineering International Nr. 4/2017

irregular frame IR10, a 130 to 171% increase in moment can be observed in the critical members, with a maximum increase (171%) in moment observed in the vertical member 1. Vertical members 2 to 5 face a 166 to 167% increase in moment due to irregularities in the building. Irregular building IR11 experiences a 102 to 167% increase in moments in the critical members, with a maximum increase (166â&#x20AC;&#x201C;167%) in the vertical members 1, 2 and 3. In the irregular building IR12, a 116 to 167% increase in moment can be observed in the ScientiďŹ c Paper

539

Building Type

5

Increased Moment of Members

2

4 3

1

6

9 Members

7 8

9

130

8

130

7

132

6

138

5

166

4

166

3

167

2

167

1

171

Irregular building (IR10)

% of Increase in moment of members

9 2 1 4 Members

7

3 5 8 6

9

102

8

102

7

104

6 5 4

115 123 134

3

166

2

167

1

167 % of Increase in moment of members

Irregular building (IR11) 2

3

1

4 8 6

7

9

Members

5

9

116

8

116

7

130

6

130

5

132

4

135

3

135

2

136

1

167 % of Increase in moment of members

Irregular building (IR12)

Table 7: Continued

critical members, with a maximum increase (167%) in moment observed in the vertical member 1.

By inspecting the amount of increase in moment in irregular buildings, a common feature is observed: maximum increase in moment occurs at the location of abrupt change in width, introducing irregularities in the frames. Hence, the irregularities in the buildings cause stress concentration in the vicinity of abrupt geometrical changes. The members located near the sudden geometrical change due to the irregularity of the building exhibit a higher deformation 540

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in the second and third modes, experiencing higher moment. This phenomenon triggers early local failure in the overstressed critical elements, leading to damage propagation and culminating into partial and complete collapse of the building. Consequently, it can be observed that the domination of deformation in the second, third or even higher modes appears to be the physical cause of higher seismic vulnerability in irregular buildings. In the following section, the seismic ductility demand of the critical members of irregular buildings is determined using non-linear time history analyses.

Non-linear Time History Analyses of Regular and Irregular Buildings Seismic ductility demand of the critical members of the irregular buildings can be investigated by performing non-linear time history analyses. Seismic displacement ductility demand of a structural member is the ratio of maximum displacement occurring at the end of seismic time history and the displacement corresponding to the yield level of the structure. In this regard, the regular frame and irregular frames IR3

Structural Engineering International Nr. 4/2017

No.

Year

Earthquake

Magnitude (Mw)

1

1994 Northridge

6.7

2

1971 San Fernando

3

1979 Imperial Valley

Mechanism

Station

Peak Ground Acceleration (PGA) (g)

Peak Ground Velocity (PGV) (cm/s)

Peak Ground Displacement (PGD) (cm)

Thrust

Saturn Street School

0.43

43.52

23.04

6.6

Thrust

Castaic, Old Ridge Route

0.27

25.90

4.87

6.5

Strike Slip

Calexico

0.27

42.49

36.12

Table 8: Ground motion summary

and IR11 were chosen for conducting the dynamic analysis. Three far fault ground motions (GM), which are

selected for the time history analyses, are summarised in Table 8. The effects of masonry infill and soil flexibilities

Building Type

Seismic Ductility Demand of Members 9

2

Ground Motion 1

3 5 1 6

8 7

9

Member Numbers

8

4

are not incorporated in the analyses.

The regular frame and irregular frames IR3 and IR11 are subjected to three

7 6 5 4

R=4

3

R=2

2

R=1

1 0

2

9

Irregular building (IR3)

7 6 5 4 R=4

3

R=2

2

R=1

1 0

2

9

4 6 8 Seismic Ductility Demand

10

Ground Motion 3

8 Member Numbers

10

Ground Motion 2

8 Member Numbers

4 6 8 Seismic Ductility Demand

7 6 5 4 R=4

3

R=2

2

R=1

1 0

2

4 6 8 Seismic Ductility Demand

10

Tab l e 9: Seismic ductility demand of critical members of vertically irregular buildings for response reduction factor R = 1, 2 and 4

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541

Building Type

Seismic Ductility Demand of Members 9 8 Member Numbers

9 2 1 4 3 7

5

Ground Motion 1

7 6 5 4

R=4

3

R=2

2

8

R=1

1

6

0

2

4 6 8 Seismic Ductility Demand

10

9 8 Member Numbers

Irregular building (IR11)

Ground Motion 2

7 6 5 4

R=4

3

R=2

2

R=1

1 0

2

4 6 8 Seismic Ductility Demand

10

9 Member Numbers

8

Ground Motion 3

7 6 5 4

R=4

3

R=2

2

R=1

1 0

2

4 6 8 Seismic Ductility Demand

10

Table 9: Continued

GM time histories with response reduction factors (R) 1, 2 and 4 by assigning adequate strength to the members as derived from the strength demand to remain elastic, that is, at R = 1. Thereafter, the seismic ductility demand of the critical members of IR3 and IR11, as marked in Table 7 , is estimated.

Table 9 presents the ductility demand of the critical members near abrupt stiffness change as identiďŹ ed from the elastic analysis presented in the previous section.

Table 9 demonstrates that the seismic ductility demand of irregular frame 542

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IR3 is 1.6 to 2.1 for response reduction factor R = 1, 3.1 to 4.2 for response reduction factor R = 2 and 6.1 to 7.2 for response reduction factor R = 4.

Similarly, the seismic ductility demand of irregular frame IR11 is 1.3 to 1.8 for response reduction factor R = 1, 2.7 to 4.3 for response reduction factor R = 2 and 5.3 to 8.6 for response reduction factor R = 4. Enhanced displacement ductility demand of the members can also be attributed to the high seismic vulnerability of the irregular buildings due to localised concentration of deformation at places near the change of abrupt stiffness.

Unreinforced Brick Masonry Structures Seismic vulnerability of irregular unreinforced brick masonry (URM) structures is investigated in this section.

A regular building made of URM was considered in the literature.46,58,59 For this study, in-plane stiffness and out-ofplane stiffness were calculated from the basic consideration of bending and shear in a rectangular plate by Eq. (6).

The wall situated in the longitudinal direction of the lateral force is designated as the in-plane wall, while the wall situated in the perpendicular

Structural Engineering International Nr. 4/2017

URM

IRURM1

literature.48 For each storey, the stiffness of the in-plane wall and out-ofplane wall is considered to be springs connected in a parallel series. The equivalent storey stiffness is determined by considering each storey connected in series. This idealization of inter-storey as well as intra-storey walls is based on the basic concept of mechanics, as explained in Fig. 10.59 The lateral stiffness of each wall can be expressed as Kwall as shown in Eq. (6). The equivalent soil stiffness Ksoil is provided in Eq. (7).

IRURM2

Fi g. 9: Regular and irregular buildings made of URM

(a)

Out-of-plane wall

Kwall =

Kout-of-plane

In-plane wall Lateral load

1 fð11H 3 Þ=ð60Em I Þg + fð2αH Þ=ð3Gm AÞg

Lateral load Kin-plane

ð6Þ

Actual building Idealized condition

where H is the height of wall; I is the moment of inertia of wall; A is the area of wall, α is the shape factor; and Em and Gm are modulus of elasticity and shear modulus of brick masonry, respectively.

Ksoil = ½2GL0 =ð2 −νÞ 2 + 2:50χ 0:85

(b) Lateral load 1st storey

K1st

Lateral load

KGr

Ground storey

– ½0:2=ð0:75 − νÞGL0 1 − ðB0 =L0 Þ

Fi g. 10: Representation for carry-out equivalent stiffness. (a) Parallel spring connection for in-plane wall and out-of-plane wall; (b) series spring connection for multistorey building59

direction of the lateral force is termed the out-of-plane wall. The equivalent stiffness due to the effect of soil flexibility is calculated by Eq. (7) using the formula from the literature.46 In the present study, an effort is undertaken to calculate the natural periods of URM buildings. A regular (URM) masonry building and two irregular

Building type

(IRURM-1, IRURM-2) masonry buildings are considered, as shown in Fig. 9.

Storey height and bay dimension of the URM buildings are the same as the dimensions of reinforced concreteframe buildings shown in Fig. 4.

SSI is incorporated into the computational model in the form of equivalent soil springs, as suggested in the

Equivalent spring stiffness for ground storey (KGr)

ð7Þ

where χ = (Ab/4L0 2); Ab = area of foundation; ν = Poisson ratio of soil; G = shear modulus of soil; and L0 and B0 are half-length and half-width of the foundation, respectively.

For analysing the regular and irregular masonry buildings, the masonry walls are modelled as in-plane plate elements, with material properties of masonry obtained from the literature.46,58 Numerical values of equivalent storey-wise

Equivalent spring stiffness for first storey (K1st)

In-plane stiffness (Kinplane)

Out-of-plane stiffness (Kout-of-plane)

In-plane stiffness (Kinplane)

Out-of-plane stiffness (Kout-of-plane)

URM

1 690 140.845

12 614.646

1 690 140.845

12 614.646

IRURM1

1 690 140.845

12 614.646

845 070.422

8409.764

IRURM2

1 690 140.845

12 614.646

563 380.282

4204.882

Table 10: Equivalent in-plane and out-of-plane spring stiffness (kN/m) of unreinforced masonry regular and irregular buildings “T” by Indian Seismic Code9

“T” by FEMA11

“T” by Eurocode12

“T” by FEA

“T” by computational method with SSI

URM

0.190

0.187

0.192

0.190

0.185

IRURM-1

0.190

0.187

0.192

0.190

0.182

IRURM-2

0.190

0.187

0.192

0.190

0.193

Type of building

Table 11: Fundamental periods of regular and irregular URM buildings

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in-plane and out-of-plane springs are provided in Table 10. The fundamental periods of the initial three modes of the regular and irregular masonry buildings, inclusive of the effects of SSI, are determined by Dunkerley’s method.59 Fundamental periods determined by the computational method as well as by using the formulae specified by various codes are shown in Table 11.

forces/stress concentration and ductility demand at the locations of abrupt change in width or height cause early localised damage, resulting in progressive damage propagation and partial or complete collapse of the structures.

The moment in critical members of irregular buildings may increase to 170% with respect to their regular counterparts.

In the following equation, foundation length (L) = 10 m; half length (L0 ) = 5 m; foundation width (B) = 10 m; half width (B0 ) = 5 m; area of foundation (Ab) = 10 × 10 = 100 m2

2 χ = Ab =4 L0 = ð10 × 10Þ=ð4 × 52Þ = 1

Ksoil = ½2GL0 =ð2 −νÞ 2 + 2:50χ 0:85

Similarly, the seismic ductility demand of critical members of irregular buildings may increase to 2.2 for response reduction factor 1, 4.3 for response reduction factor 2 and 8.6 for response reduction factor 4. This observation may be utilised to ensure better seismic performance of irregular buildings by providing greater strength and stiffness to the vulnerable members located near the abrupt geometrical change.

− ½0:2=ð0:75 −νÞGL0 1 − ðB0 =L0 Þ = 4 218 750 kN=m A trend of results similar to that obtained for RC frames is observed for masonry buildings. The walls where sudden change of width takes place exhibit about 20 to 90% more shear for URMIR-1 and 30 to 110% more shear for URMIR-2 compared to the reference regular walls because of high torsional deformation of the structure in the second and third modes. However, the fundamental lateral periods of masonry buildings do not vary much, as observed for irregular RC buildings. The detailed results for regular and irregular masonry buildings are not presented for the sake of brevity.

Summary and Conclusions The present study is an effort to explore the reason and extent of high seismic vulnerability of various irregular buildings. A large variety of setback RC buildings are studied and compared with their regular counterparts.

Effects of masonry infills are accounted for by employing equivalent compressive diagonal struts. SSI is incorporated by adding equivalent soil springs based on the existing literature.

The study provides valuable insights into the vulnerability of irregular buildings. It has been realised that the variations of lateral periods and base shears are not the causes of high seismic vulnerability of the irregular buildings. From the response spectral analysis and non-linear time history analysis, a conclusion has been made that the sudden increases in member 544

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This study as a whole is a humble attempt to identify the reason of high seismic vulnerability of irregular reinforced concrete and masonry buildings with the intention of enhancing their seismic performance during impending earthquake events. This study may further facilitate the building of irregular structures that go beyond the protective provisions of various seismic codes.

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[52] Johnson JJ, Chang C-Y. State of the art review of seismic input and soil–structure interaction. In Appendix E in A Methodology for Assessment of Nuclear Power Plant Seismic Margin (Rev. 1), EERI NP-6041-SL Electric Power Research Institute: Palo Alto, 1991.

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Seismic Performance of Pile-Cap Connections of Prestressed High-Strength Concrete Pile with Different Details Zhaosheng Guo, PhD Candidate; Wubin He, Dr, Assoc. Prof.; Xiaohong Bai, Dr, Prof., College of Architecture and Civil Engineering, Taiyuan University of Technology, Taiyuan, China; Y. Frank Chen, Dr, Prof., College of Architecture and Civil Engineering, Taiyuan University of Technology, Taiyuan, China; Department of Civil Engineering, The Pennsylvania State University, Middletown, PA, USA. Contact: bxhong@tyut.edu.cn DOI: 10.2749/222137917X14881937845963

Abstract This study investigated analytically and experimentally the pile-cap connection of a full-scale prestressed high-strength concrete pile considering three different connection details: the common connection (specimen CT-1), a strengthened connection (specimen CT-2) and an internal T-shape steel connection (specimen CT-3). Specifically, the failure modes, hysteretic performance, ductility and bearing capacity were studied. The test results show that the three connections experience different failure patterns. Specimen CT-1 was severely damaged primarily at the pile-cap connection due to the rupture of anchor plates and the formation of a plastic hinge, but no damage to the pile was observed. This connection consists of a relatively large node angle and behaves like a hinge, resulting in poor energy dissipation due to small moment resistance. Specimens CT-2 and CT-3 were damaged at lesser degree and in more sparse areas. These two types of connections have smaller node angles and behave as a rigid joint with greater moment resistance, leading to a higher energy dissipation. Bond slippage failure of anchor bars was not observed in the cap, and the anchor bar length was found to meet the design requirements.

A non-linear finite element model (FEM) was established to analyse the mechanical properties of the three connections using ABAQUS. The moment– displacement curves obtained from the numerical analyses compare well with the experimental results. The degree of effects of influencing parameters on the behaviour of the connections was evaluated using the FEM. Keywords: PHC pile; pile cap; seismic performance; bearing capacity; ductility.

Introduction Prestressed high-strength concrete pile (PHC pile) is a precast concrete pile wrapped within a round steel tube, as shown in Fig. 1. It is produced using the prestressed technology and a centrifugal shaping method. Presently, PHC piles are used extensively in building and bridge constructions in China.

Earthquake damage surveys reveal that building and bridge substructures suffer serious damage in strong earthquakes, especially in the vicinity of pile-concrete cap connections.1,2 The available relevant research indicates that considerable loads from the superstructure are transferred progressively Peer-reviewed by international experts and accepted for publication

by SEI Editorial Board Paper received: May 17, 2016 Paper accepted: April 3, 2017

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to the substructure, pile cap, piles and soil. Moreover, maximum bending moments, shear forces and axial forces usually occur at the connection between the pile and the concrete cap. There are some characteristics under which the pile heads would be separated from the cap or contribute to a bending failure in the upper part of the pile body due to the formation of plastic hinges.

Inadequate connections will lead to a poor structural performance. Consequently, severe damage will be caused by a small or moderate earthquake, which would require a costly repair.

The likelihood of structural collapse with loss of life will undoubtedly be increased during a strong earthquake.

To prevent such damage or failure from happening, a considerable amount of moment and shear should be transferred through the pile cap. Existing pile-cap connections are generally inadequate to develop the full moment

capacity at connections. The issues on the moment and shear transfer mechanisms and the strength deterioration under cyclic loading remain to be further understood.

The seismic behaviour of pile-cap connections influences the structural performance. Since the 1980s, researchers have begun to pay attention to the seismic performance of these connections with different details. In Ref. [3], eight different connection details where the piles were embedded in cast-in-place (CIP) reinforced concrete caps were proposed. In Ref. [4], the researchers conducted a series of cyclic tests on prestressed concrete pile-cap connections in New Zealand and studied the strength and ductility of the pile-cap connection details. The results of the research show that well-detailed prestressed concrete piles and pile-cap connections are capable of undergoing large inelastic deformations without significant loss in strength when subjected to severe seismic loading. Some large-scale tests to investigate the behaviour of column-footing connections were carried out, and the assessment and retrofit measures were developed. The results show that the existing pile-cap connections constructed based on pre-1972 design practices generally have inadequate details to develop the full column moment capacity at the connections.5 Reference [6] tested three standard Caltrans piles with various pile-cap connection details, including concrete-encased steel pipe piles and precast concrete piles, under fully reversed, varying axial loads (compression and tension) and increasing cyclic lateral loads. In Ref. [7], the capacity of square pile-cap connections was investigated, where the precast prestressed pile was embedded by 0.46 m in the CIP concrete cap without using any reinforcement at the connection, in which the

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simple, yet rational, analytical approach to describe the non-linear behaviour of shallow embedment pile to deck connections under cyclic loading.

Reference [14] presented an improved connection for prestressed concrete piles along with a design procedure.

Reference [15] reported the experimental and analytical results of six pile-cap connections with different details.

Fi g. 1: Prestressed high-strength concrete piles

so-called “plain embedment” recommended by Ref. [3] was adopted and the cross-section of the pile was 0.46 m × 0.46 m. They stated that this embedment alone was adequate to transmit a moment greater than the flexural capacity of the precast pile.

Experiments on prestressed concrete piles3 and steel pipe piles8 have shown that the steel reinforcement inserted into the cap can provide a fixed pilecap connection. Reference [8] also tested a concrete-filled pipe pile with the pile embedment of 0.13 m (0.2 pile diameter). This specimen represents a typical pinned pile-cap connection with no flexural reinforcement. Reference [9] studied experimentally and analytically three full-scale precast prestressed concrete pile-CIP concrete cap subassemblies having the typical details used in bridges in seismic regions.

Researchers in Japan had conducted the study of PHC pile-cap connections as these connections could be damaged by earthquakes. Reference [10] proposed a simplified pile-cap connection for precast concrete piles opposite to the usual connection. The pile head was embedded in the cap by 100 mm without using an anchor bar, and plain concrete was filled in the top steel pipe by 600 mm (1D). Their test results showed that the degree of restraint against rotation of the simplified connection was about 0.7 times that of the usual connection under a stationary axial load condition. Reference [11] proposed an improved simplified connection. The pile head was embedded in the cap by 100 mm with a tapered clearance around the pile head. The test results indicated that the improved simplified connection could reduce the bending moment at the pile head. Reference [12] proposed a method to improve the performance of semi-rigid connections at pile heads by reducing the stress level there, thus decreasing the cost of foundation construction. Reference [13] presented a

In conclusion, the varied details in the pile-concrete cap connections lead to different degrees of restraint against the rotation and capacity of the connection. This paper focuses on the details of the pile-concrete cap connections adopted in engineering practices in China. At present, the common practice for building foundations in China is to embed the PHC pile approximately 50–100 mm in the reinforced concrete cap, with the bottom reinforcing bars caged around the pile.

In high seismic intensity areas, current Chinese design codes require a further increase in the resistance of pilecap connections to withstand a high seismic load. According to the regulations of pretensioned concrete piles,16 when the PHC pile is subjected to smaller lateral forces, a usual shallow connection as shown in Fig. 2a can be used. Yet, an inadequate connection performance will lead to poor structural performance. When the PHC pile is subjected to larger lateral forces, based on the usual connection, the section at the pile head needs to be reinforced to form a strengthened ring connection (Fig. 2b). In addition, the third full-scale PHC pile-cap connection was tested, consisting of a novel connection detail using a Tshape steel in addition to the abovementioned two different connection details. The T-shape steel was applied to the pile-cap connection known as a “stiff joint” (Fig. 2c). Compared with the strengthened ring connection detail, it should be noted that this new connection detail reduces the complexity of the structural construction, because of no interference between the T-shape steel and the steel reinforcement in the cap during construction and it also reduces the amount of reinforcement in the core and strengthening ring. As a result, the pouring of concrete becomes much easier.

This creative connection detail has been authorized by the China National

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Patent Office (no. ZL201410096750.3).

However, the issues regarding the transfer of moment or shear and the occurrence of strength deterioration under cyclic loading remain not fully understood for this type of connections.

There is no effective design calculation method available, nor any published experimental data to describe these connections under cyclic moments and axial loads.

In this paper, three PHC pile-cap connections were tested to evaluate their seismic performance at Taiyuan University of Technology, China.

They were designed based on the current design standards and engineering practices, and different pile-cap connections details were considered. This paper first presents a summary of the test results of the three full-scale PHC pile-cap connections under simulated seismic loading and constant vertical load. The capacity and failure characteristics of the connection are the focus of this study. The validity and reliability of the connection details are verified. The present study gives a better understanding on the performance of a pile-cap connection under cyclic loading, yet simple enough to be used in practice for predicting the behaviour of such connections under lateral loading conditions.

Experimental Program Test Specimen Preparation Three PHC pile-cap connections with different details were tested to evaluate their seismic performance. They were designed based on the current design standards and engineering practices, in which different pile headto-cap connections were considered.

All three test specimens were made of PHC pile which was fabricated with centrifugation, steam and autoclave curing at the factory. The concrete compressive strength of the PHC piles was 82.2 MPa, an average value measured from six test cubes of 150 × 150 × 150 mm3. The diameter of the PHC pile was 400 mm, which was the largest feasible pile as determined by the loading equipment space. The pipe pile was 95 mm in thickness, 2.8 m in length and embedded in a 50 mm thick cap. Seven 10.7 mm diameter prestressed bars with an applied prestress of 994 MPa (that is 70% gross ultimate tensile strength) were used. The stirrup spacing and diameter were 45 and 4 mm, respectively. The cross-sectional Scientific Paper

547

(a)

(b)

Vertical load direction

Lateral load direction

Lateral load direction

PHC pile

Strengthen ring Core concrete

A

D12@200 D12@150

D

A

b

a

Pile cap 900

900

B

d

Pile cap DI2@150

C

Anchor bar

D12@150 Anchor bar

1500

(c)

1500

Vertical load direction

Lateral load direction

Steel jacket

3700

2800

PHC pile

3100

Core concrete C

B

D

A

Longitudinal limb

T-type steel part

Stiffening rib

Pile cap

D12@150

Horizontal limb

140

900

d=300

D12@150

Anchor bar

430 140 430 B = 1000 T-type steel part

1500

F ig . 2: Details of the three test specimens. (a) Common connection detail; (b) strengthened connection detail; (c) internal T-shape steel connection detail (Units: mm)

area of the PHC pile is 910.27 cm2, the ratio of longitudinal reinforcement is 0.69%, the effective prestress design value (σce) is 5.87 MPa, the design value of pile bending bearing capacity is 88.0 kN m and the design value of pile axial compression capacity is 2288 kN. The calculated bending moment at the cracks is 70 kN m. The concrete pile cap section was designed to be large enough to permit the complete transfer of pile shears and moments to the concrete cap. At the same time, the size of the cap was minimized to avoid an excessive specimen weight. Each pile cap was reinforced with 12 mm diameter reinforcing steel at the top and bottom of the cap and 548

Scientific Paper

the test experience from CT-1, an additional strengthened ring of 800 mm (outer diameter, OD) × 400 mm (inner diameter, ID) × 200 mm (thickness) was added, as shown in Fig. 2b. Eleven 12 mm ; normal steel bars were used in conjunction with 8 mm stirrups spaced at 50 mm. The longitudinal pile reinforcement was embedded in the cap by 500 mm.

B8@50

50

DI2@150

c

200

50

D

Core concrete

200

B 3700

C

800

2800

Steel jacket

2000

Steel jacket

PHC pile

3700

Vertical load direction

14 mm diameter reinforcing steel spaced at 150 mm of the pile cap.

For the connection with the common detail (specimen CT-1), the PHC pile was embedded in a 1.5 × 0.8 × 0.9 m3 CIP concrete cap by 50 mm. The top end of each bent anchor bar (75 bent × 620 mm long) was welded to a square steel plate (50 × 120 × 16 mm3), where the square plate was welded to the anchor plate, embedding the entire assembly in the cap to form the connection, as shown in Fig. 2a.

For the connection with the strengthened detail (specimen CT-2), the PHC pipe pile was embedded in a 1.5 × 1.0 × 0.9 m3 CIP concrete cap. Based on

The PHC pile in both specimens CT-1 and CT-2 was filled with CIP concrete. The concrete core was reinforced with four 10 mm bars and the circular stirrups of 6.0 mm spaced at 100 mm. For the connection with the internal T-shape steel detail (specimen CT-3), similar to specimen CT-1, the entire assembly, including PHC pile, square plates and bent anchor bars, was embedded in a 1.5 × 0.8 × 0.9 m3 CIP concrete cap by 50 mm, Fig. 2c. The T-shape steel was cast in the PHC pile with the detailed dimensions as shown in Fig. 2c. Note that the PHC pile was filled with plain concrete with no other internal reinforcement.

Table 1 lists the reinforcement and steel used for the three specimens which were manufactured at the structural laboratory of Taiyuan University of Technology, China, as shown in Fig. 3. Figure 3a–c shows the connection details for specimens CT-1, CT-2 and CT-3, respectively. Figure 3d and e shows the precasting and casting pieces, respectively. The concrete provided by a commercial supplier was redesigned using a specialty concrete, which was cast into the hollow section of the pile, the strengthened part and the cap. The specimens were cured for a minimum of 28 days prior to testing. The average compressive strength for the concrete cap, strengthened part and core is 42.5 MPa, as measured from the 150 × 150 × 150 mm3 test cube. The corresponding modulus of elasticity for those components is 3.25 × 104 N/mm2. The modulus of elasticity for the pile is slightly higher at 3.8 × 104 N/mm2.

The yield strength (fy) and tensile strength (fu) of reinforcement and steel are also listed in Table 1.

Test Set-up and Instrumentation The typical test set-up is shown in Fig. 4. The PHC pile-cap assembly was anchored to a strong floor for testing in an inverted position for the

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Specification (mm)

fy (MPa)

fu (MPa)

Es (MPa)

Prestressed bar

10.7

1322

1501

2.06 × 105

Stirrup of pile

4

511

625

2.06 × 105

Anchor bar

20

365

538

2.06 × 105

Reinforcement of cap

12

359

524

2.06 × 105

Steel part

14#

286

492

2.06 × 105

Longitudinal bars in filler

10

345

519

2.06 × 105

6

315

478

2.06 × 105

12

351

510

2.06 × 105

8

309

498

2.06 × 105

Reinforcement or steel

IMP system, as were the lateral force data of the hydraulic jacks used.

Loading Program

convenience of testing, and each of the three specimens was tested under a reversed cyclic lateral load and constant axial load. Lateral load was applied to the PHC pile using an actuator with 1000 kN capacity and a push/pull stroke of 500 mm. The actuator was connected to a steel jacket placed around the pile to transfer the forces of the actuator to the pile without damaging the pile. The vertical load was applied with a 1000 kN hydraulic jack.

To monitor the lateral displacements of the pile, four displacement sensors with a range of 100 mm were placed at a spacing of 424 mm. Slippage of the cap was monitored using two 50 mm range displacement sensors installed on the two sides of the cap along the loading plane. A pasting strain gauge was used to monitor the strains of the pile concrete, anchor bars, T-shape steel, longitudinal bars and stirrups. The displacement and strain data were measured by an

Each pile-cap assembly was tested under a reversed cyclic lateral load and a constant axial load of 228.8 kN (0.1Agfc) using a hydraulic jack without causing a secondary moment effect on the pile. The axial load was kept constant throughout the test using a regulated hydraulic power supply. The reversed cyclic lateral loads were applied at a distance of 2.8 m from the soffit of the pile cap.

Then, the lateral load actuator was connected to the test specimen after applying the full axial load. A reverse cyclic lateral load was applied in terms of load and displacement controls, as shown in Fig. 5. One cycle was applied for each elastic lateral load.

At each level of ductility displacement (Δy), three full cycles of reverse lateral loading were applied with a time interval of 15 min. The testing was conducted until either the specimen failed due to large deformation or the lateral load resistance of the specimen was down to 85% of the lateral bearing capacity.

(a)

(b)

(c)

Stirrup in filler Longitudinal bars in strengthening ring Stirrup in strengthening ring

Table 1: Material properties of reinforcement or steel

(d)

(e)

Fi g. 3: Fabrication of test specimens. (a) The common connection (specimen CT-1); (b) strengthened connection (specimen CT-2); (c) internal T-shape steel connection (specimen CT-3); (d) the precasting pieces; (e) the casting pieces

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During the test loading process, cracks first appeared at the pipe pilecap junction, then gradually extended and crossed each other on the top cap surface. At the end of the test, the cracks propagated radially from the pile with a length of 100–300 mm (see Fig. 6a). Concrete at the top surface of the cap was peeled. A horizontal crack of 5–10 mm was observed on the side of the cap, located within the thickness of the protective layer in the steel bar, as shown in as Fig. 6b.

Reaction beam Sliding support

Reaction wall

Hydraulic jack LVDT–1

Load cell

LVDT–2

Hydraulic actuator PHC pipe pile

LVDT–3

The testing was conducted until either the specimen failed due to large deformation or the lateral load resistance of the specimen was down to 85% of the lateral bearing capacity.

At the end of the experiment, the lateral bearing capacity of specimen CT2 and specimen CT-3 had greatly reduced; also, an obvious damage was observed in the specimens.

LVDT–4

Threaded rod

Cap LVDT–5

F ig . 4: Typical test set-up Load (kN)

Displacement (mm)

2 Δy Py

Py

1.5 Δy 1 Δy

Cycles number

1 Δy 1.5 Δy 2 Δy

F ig . 5: Load program

According to the results of PHC pilecap connection testing, the various connection details at the pile-cap display very different failure patterns, described as follows.

For specimen CT-1, throughout the experiment, there was no crack on the surface of PHC pile. Crack damage was observed only at the top surface of the cap. The damage of this connection occurred in the critical regions of the cap rather than in the pile.

(a)

(b)

Test Observations

For specimen CT-2, there were numerous cracks appearing on the surfaces of the PHC pile and strengthened ring. During the test loading process, various cracks occurred at different stages including: (1) circumferential cracks on the PHC pile, (2) bond cracks at the PHC pile-cap junction, (3) radial cracks on the strengthened ring, (4) splitting cracks on the side of strengthened ring and (5) diagonal cracks on the side of the strengthened ring, as shown in Fig. 7 When the pile top displacement was 10 mm, the corresponding load was approximately 75% of the ultimate load. Circumferential bond cracks appeared first at the PHC pile-cap junction, followed by a radial crack at the top of the strengthened ring and a circumferential crack in the pile. During the test process, the circumferential crack in the pile and the radial crack at the top of the strengthened (c)

Rupture Crack

F ig . 6: Typical failure mode of specimen CT-1. (a) Cracks on the surface of the cap; (b) the crack at the side of the cap; (c) the rupture of weld seam of square steel plate 550

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(a)

(b)

Fi g. 7: Typical failure mode of specimen CT-2. (a) Cracks in the strengthened ring and PHC pile; (b) cracks on the top of the strengthened ring

ring gradually extended. The cracks on the top surface of the strengthened ring gradually extended to the edge of the ring, expanded downwards and became splitting and diagonal cracks of different lengths along the side of the strengthened ring. The splitting cracks divided the strengthened ring into several blocks. When the lateral load reached its final value, the displacement increased to 65 mm. When the lateral load value was reduced to 121 kN, the separation between the PHC pile and the strengthened ring increased rapidly, indicating that a damage at the connection had occurred.

For specimen CT-3, the distribution of cracks is shown in Fig. 8. When the lateral load was 50 kN (57% of the ultimate load), a circumferential bond crack at the PHC pile-cap junction and a horizontal fracture in the pile were observed. The cracks continued to develop with loading. When the lateral load reached 75.3 kN, the existing cracks revealed bifurcation and circumferential cracks developed at the upper quarter of the pile below the cap. The maximum crack width was about 3–4 mm. With an increase in PHC pile displacement, a new crack (a)

was observed on the top surface of cap, at a distance from the PHC pile. This fact demonstrates that the T-shape steel inserted in the concrete cap has a tendency to pull away, decreasing the capacity of the cap and leading to joint failure.

The final failure mode for the three specimens can be detected without much difficulty. The bending resistance of specimen CT-1 depends on the capacity of the anchoring reinforcement. Moreover, the bending resistance of the pile was developed.

In comparison, the piles and caps in specimens CT-2 and CT-3 show cracking with all the cracks appearing and developing almost simultaneously.

This demonstrates that these two types of connection details have adequate development to the bending capacity of PHC pile and thus can avoid a premature fracture failure at the connection.

Test Results and Discussion Hysteretic Response Figure 9 shows the pile end moment versus lateral deflection responses of (b)

Fi g. 8: Cracks in the cap and pile of specimen CT-2. (a) Front elevation; (b) side elevation

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the three specimens. Specimen CT-1 exhibits damage because of the rupture of steel and the spalling of concrete cap. From Fig. 9a, the seismic performance of pile is determined by the hysteretic response of the connection. The hysteresis curve for specimen CT-1 is relatively steep and not a full one. The horizontal displacement is about 20 mm, and the bearing capacity reaches the extreme value; after unloading, the slope of the curve sharply drops, suggesting a significant capacity loss and poor ductility. At the initial loading stage, specimen CT1 is still under elastic state with certain initial stiffness. The stiffness of specimen CT-1 begins to decline when the gap between the pile and the pile cap appears. As the pile head into the cap is very shallow, the joint part between the pile and pile cap is prone to stress concentration under the action of bending moment, leading to the pressure side concrete being crushed and kicked stripping of the tensile side concrete layer. Once the surface of concrete pile caps faces brittle failure, the internal force of anchoring reinforcement increases instantly, which leads to anchoring reinforcement yielding and connecting plate weld tearing. The slope of the curve decreases rapidly, the hysteretic curve takes on a Z shape, and poor performance is suggested. Eventually, the hysteresis curve of specimen CT-1 expression is steep and not a full one.

Figure 9b and c shows that specimens CT-2 and CT-3 have better hysteretic behaviour than specimen CT-1, Moreover, the ultimate displacements of specimens CT-2 and CT-3 are about 2–3 times that of specimen CT-1. This may be attributed in part to the better deforming ability of the connection, which offers greater ductility in the PHC pile-cap connection preventing the failure of the prestressed bars in the pile. The hysteretic curve of specimen CT-2 is of an arch shape and is relatively full, indicating a better ability to absorb seismic energy. As a result, the stiffness of the member is enhanced and the bearing capacity is increased greatly. For specimen CT-3, the combination of the pile and pile cap is strengthened by using T-shaped steel.

Before cracking, the initial stiffness of the specimen CT-3 is greater than that of the specimen CT-1; with the loading process, the surface of pile caps and pipe pile body cracks gradually at roughly the same time. Brittle cracking is not observed, and the specimen’s Scientific Paper

551

–200

Displacement (mm)

0

20

Experiment data ABAQUS model

80 10 0 12 0

–1

20

–2

0

–4

–8 0

Displacement (mm)

0

–400 0

–400 0

–300

80

60

40

20

0

0 –2

0

0

–4

–6

–8

0

–400

Experiment data ABAQUS model

–300

–6

Experiment data ABAQUS model

–300

0 –4 0 –2 0

–200

–200

0 –100

60

–100

100

40

0

0

–100

100

20

0

80

100

Specimen CT-3

200 Moment (kN m)

200 Moment (kN m)

Moment (kN m)

200

300 Specimen CT-2

60

Specimen CT-1

400

–6

300

–8

300

(c)

00

400

–1

(b) 400

40

(a)

Displacement (mm)

F ig . 9: Hysteretic moment–displacement response for the specimens. (a) Common connection detail; (b) strengthened connection detail; (c) internal T-type steel connection detail

rigidity gradually declines relatively slowly, the curve slope reveals a slowdown and the limit displacement is rather large in the hysteretic curve, but the stiffness degradation is not obvious.

The hysteretic curve of specimen CT-3 is of an S shape and relatively full. The ductility of the specimen is greatly improved as shown in the graph.

Strain of the Anchor Bars Limited by the length of this paper, only strain of the anchor bars is discussed here. Figure 10 shows the strains of anchor bars versus the displacements of specimens. The data were measured based on the first cycle of each displacement level. The strain gauges were installed at the base of each anchor bar (see Fig. 2).

According to the properties of

4000

Steel strain (με)

(b)

6000 Speicment CT-1 A B C D

2000

0

–2000 –30

–10

0

10

20

–80

–40

(d) Speicment CT-2

300

40

800

Speicment CT-2

600

A B C D

Steel strain (με)

Steel strain (με)

400

0

80

120

Displacement (mm)

500

200 100 0 –100 –80

A B C D

Speicment CT-3 500

Displacement (mm)

(c)

400

A B C D

200 0 –200

–60

–40

–20

0

20

Displacement (mm)

40

60

80

–400 –80

–60

–40

–20

0

20

40

60

Displacement (mm)

F ig . 10 : Anchor bar strain–displacement for specimens. (a) Anchor bar of pile at CT-1; (b) anchor bar of pile at CT-3; (c) anchor bar of pile at CT-2; (d) anchor bar of strengthened ring at CT-2 552

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Table 2 shows the comparison of the performance measures of the three specimens in terms of ultimate moment and ductility, where the data represent the average values along the push and pull directions. As indicated in Table 2, a better rotation capacity results in a greater displacement ductility and ultimate moment.

Figure 11 describes the definitions of yield displacement and displacement ductility, where Δy is the yield displacement that is determined according to the energy method and Δu is the displacement when the lateral load attains ultimate bearing capacity.

Material Properties and Constitutive Models

1000

–500 –120

30

Ductility

Finite Element Analysis

0

–20

Therefore, the anchor bars in specimens CT-2 may be shortened or even removed practically.

2000 1500

Steel strain (με)

(a)

reinforcing steel (Table 1), one can determine that the reinforcement of anchor bars yields at 1766 με. The strain of each anchor bar in specimen CT-1 is relatively large and much greater than the yield value, resulting in yielding for all anchor bars embedded in the pile (Fig. 10a). For specimen CT-2, the maximum strain of the anchor bars at the pile is less than 460 με, but it is higher (about 680 με) for the bars at the strengthened ring. Yielding did not occur in both cases (Fig. 10c and d). Meanwhile, the maximum strains in the anchor bars in specimen CT-3 are about 1700 με, smaller than that of CT-1, but greater than that of CT-2 (Fig. 10b). It can be seen from the test results that the anchor bars do not slip in the cap, which proved that the anchor embedment length is sufficient.

80

A finite element model (FEM) was developed using ABAQUS to simulate the pile-cap connections under a reversed cyclic lateral load and constant axial load. In this study, the elastic hardening model was used to describe the stress–strain relationship of prestressed steel bars and stirrups in piles, as shown in Fig. 12a and described by Eq. (1). The elastic– plastic model, as shown in Fig. 12b and Eq. (2), was used to describe the stress–strain relationship of common reinforcement including anchor bars, cap reinforcement, structural steel, longitudinal bars in fillers and strengthening rings, and stirrups in fillers and strengthening rings.

σ ≤ fy Es ε

ð1Þ σ= fy + Es 0 ε− εy σ > fy

Structural Engineering International Nr. 4/2017

Specimen

CT-1

CT-2

CT-3

Ultimate moment (kN m)

148.3

301.7

214.2

Yield displacement (mm) Ultimate displacement (mm) Ductility (μ)

8.25

12.72

14.85

25.25

54.65

81.40

3.07

4.31

5.48

Table 2: Performance of ductility

σ=

Es ε fy

σ < fy σ ≥ fy

ð2Þ

where σ is the stress, ε is the strain, fy is the yield strength, εy is the yield strain and Es is the elastic modulus. Es and Poisson’s ratio vs were taken as 2.06 × 105 MPa and 0.3, respectively.

17

was The stress–strain relationship widely used to represent the concrete in China. Equations (3)–(6) present the compressive stress–strain relationship, where σ is the stress at strain ε,fc is the axial compressive strength, εc is the peak strain at stress fc, αa and αd are constants.

2 ε + ð3 − 2αa Þ εεc σ = fc αa εc

ε 3 + ðαa − 2Þ ε ≤ εc εc fc ε

:

ε > εc

αd ðε −εc Þ2 + ε

ð3Þ

pffiffiffiffi εc = 700 + 172 fc × 10 −6

ð4Þ

αa = 2:4 − 0:0125fc

ð5Þ

αd = 0:157fc 0:785 −0:905

ð6Þ

The tensile stress–strain relationship can be described by Eqs. (7)–(9): 8 6

ε > ε > 1:2 −0:2 ε ≤ εt f > εt < t εt ð7Þ α= > ft ε > > ε > εt : αt εt − 0:7 ðε −εt Þ1:7 + ε

εt = 65ft 0:54 × 10 − 6

ð8Þ

αt = 0:312ft

ð9Þ

B

2

Figure 13 shows the stress–strain analytical relationship of concrete.

Finite Element Mesh and Boundary Conditions In this paper, three-dimensional (3D) numerical models were established to represent the PHC pile-cap connection specimens. The 3D hexahedral solid element (C3D8) in ABAQUS was chosen to represent the concrete and T-shape steel. And 2-node linear 3D truss element (T3D2) available in ABAQUS was chosen to represent steel bar. The loads, boundary conditions and load conditions were defined using the load function module of ABAQUS. Using the “Embedded Region” command in ABAQUS, the T-shape steel element was embedded in the concrete element, and the displacement of the T-type steel element was determined by the nodal displacement of the concrete element without considering the bond slip between the two elements. The “hard contact” of ABAQUS was used to solve the contact problem between the surfaces of the PHC pile and strengthened ring. The deformation coordination of concrete elements was realized by setting the contact property of friction. The Coulomb friction model was used to

Envelope curve (average of both directions)

Lateral load Pmax

where ft is the axial tensile strength, εt is the peak strain at stress ft that can be calculated by Eq. (8) and αt is a constant estimated by Eq. (9).

(a)

σ = EαΔT

ð10Þ

Numerical Results The load–deformation curves (i.e.

P–Δ curves) under monotonic loading are compared with the experimental results, as shown in Fig. 9. Comparisons of the ultimate strengths of the connections are shown in Table 3.

The FEA results are in fairly good agreement with the experimental ones in terms of strength and stiffness. As depicted in Fig. 9b, the initial stiffness of specimen CT-2 obtained from the

(b) σ

C

simulate the cap and pile shear force transfer, in which the friction coefficient was assumed to be 0.3. In this study, the typical element size of 0.05 m was used.

To simulate the experiments numerically, the same loading procedures and constraints as the experiments were used in the finite element analysis (FEA). The numerical models were loaded in two steps. The axial load was applied to the column first, followed by the lateral load applied at the top of the pile. Trial calculations were made to determine the appropriate discretization mesh size for computational convergence. The boundary conditions and finite element (FE) mesh of the FEA models are shown in Fig. 14. In this study, the initial prestress was applied by the cooling method provided by ABAQUS program. When the heat transfer effect is not considered, the temperature load can be applied on the prestressed steel bars in piles. The thermal expansion coefficient (α) is defined in prestressed steel bars’ material properties, and then, the temperature (ΔT) is input to the program. According to the relationship between stress and temperature variation of prestressed steel bars shown in Eq. (10), the stress of prestressed steel bars is applied. α and ΔT were taken as 1.2 × 10−5 and 351.1 , respectively.

σ ES′

Py

A

D

Δy = (Δy++Δy–)/2

SOAE = SABC

Δu = (Δu++Δu–)/2

ES

ES

Pmax = (P++P–)/2

E μ=

Δu Δy Lateral displacement

0

fy

fy

Δy

Δu

Δ

Fi g. 11: Displacement ductility parameters

εy

ε

εy

ε

Fi g. 12: The stress–strain relationship of steel. (a) The elastic hardening model; (b) the elastic plastic model

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σ

Pile Core

Vertical load

T-type steel part

fc Cap Horizontal load

0.5fc Anchor bar

Strengthen ring

εt εcu

εc

0

ε Cap

ft

F i g. 1 4: Typical finite element mesh

F ig . 13 : The stress–strain analytical relationship of concrete

FEM is lower than the corresponding test result. The main reason is that the surfaces of the PHC pile and strengthened ring were used in the “hard contact” of ABAQUS to solve the contact problem, in which the friction coefficient was assumed to be 0.3.

This is not consistent with the actual initial state of the specimen. In the initial stage of loading, the interface between the PHC pile and the strengthened ring is good. However, with the loading process, the gap between the pile and strengthened ring gradually formed and expanded up to a maximum value of about 210 mm. The initial stiffness of the specimen was larger before the appearance of the gap, and it decreases obviously after the gap appearance.

The stress distributions of the three specimens at ultimate state are respectively shown in Figs. 15, 16 and 17. It can be seen from Fig. 15 that the maximum stress intensity appears at the connection between the PHC pipe pile and the concrete cap. The location of higher stress in the cap matches with that of cracking and crushing, that is the top of the cap. In addition to the end of pipe pile Specimen

Loading direction

CT-1 CT-2 CT-3

embedded in the cap, the stress in other regions of the pipe pile is smaller.

According to Fig. 16 and compared to specimen CT-1, the stresses in CT-2 are more distributed. The stresses in the pile’s anchor bar and the strengthened ring’s anchor bars are relatively small. The maximum tension stress of the cap is as high as 5.37 MPa, which leads to the cracking of the cap surface. Figure 17 shows that the maximum tensile stress appearing in the Tshape steel is about 345 MPa. The Tshape steel is yield. Figure 17c shows that the stress distribution of the cap is in accordance with the concrete crack at the top of the cap. The maximum tension stress of the cap and the pile is as high as 5.24 and 5.81 MPa, which leads to the cracking of the cap and the pile surface. It can be seen from Figs. 15c and 17c that the stress of specimen CT-1 is higher than that of specimen CT-3, but the stress distribution of specimen CT-3 is wider.

Parametric Analyses In order to investigate the effects of system parameters on the behaviour of the connections, numerical analyses were conducted based on the FEMs

Pu,FEM (kN)

Pu,e (kN)

Pu,FEM/Pu,e

+

59

57

1.04

−

−59

−56

1.05

+

118

121

0.98

−

−118

−117

1.01

+

87

91

0.96

−

−87

−78

1.11

Average

1.025

Standard

0.054

Note: Pu,FEM and Pu,e are the ultimate strength from finite element prediction and tests, respectively.

Table 3: Comparison of experimental and numerical results under monotonic loading 554

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for the three specimens under monotonic loading. The embedment depth of pile to cap, outer diameter of the strengthened ring and the size of Tshape steel were varied in the FEMs, and their effects were evaluated and are summarized below.

Embedment Depth (DE) of Pile in Specimen CT-1 The analysis results show that there are three major factors affecting the resistance and node rotation: the first factor is the resistance on the lateral surface of the pile provided by the concrete cap, including the passive resistance on the compression side of pile and the positive resistance on the tension side of pile; the second factor is the resistance between the pile end plate and the cap; and the third factor is the resistance provided by the anchor bar. Consequently, the embedment depth of the pile affects the bearing capacity at the node directly.

The following values for the embedment length, DE were calculated: 50, 100, 150, 200, 250 and 300 mm. A comparison of the numerical results for different DE values of embedment length is shown in Fig. 18a. With increasing DE, the pile to cap connection is altered from hinged joint to partially fixed to fixed joint. The first factor increases gradually with the increase of DE, while the third factor decreases gradually with the increase of DE. The stress in the anchor bars decreases with the increase of DE. It is larger near the pile end, but becomes smaller away from the pile end. As a result, the length of anchor bars can be shortened or even eliminated with the increase of DE. When DE increases from 150 to 200 mm, it can be seen from specimen CT-1 that the strength and stiffness are significantly influenced. While for DE > 200 mm, the capacity of specimen CT-1 is

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(a)

(b)

S, S22 (Avg: 75%)

(c)

S, Mises (Avg: 75%)

+2.674e+06 –7.718e+06 –4.218e+06 –7.664e+06 –1.111e+07 –1.456e+07 –1.800e+07 –2.145e+07 –2.489e+07 –2.834e+07 –3.179e+07 –3.523e+07 –5.868e+07

S, S11 (Avg: 75%)

+9.833e+08 +9.090e+08 +8.347e+08 +7.605e+08 +6.862e+08 +6.119e+08 +5.376e+08 +4.633e+08 +3.891e+08 +3.148e+08 +2.455e+08 +1.662e+08 +9.194e+07

+5.271e+06 –7.284e+05 –2.728e+06 –4.727e+06 –6.327e+06 –8.226e+06 –1.013e+07 –2.202e+07 –3.392e+07 –4.082e+07 –4.572e+07 –5.062e+07 –5.392e+07

Fi g. 15: Numerical stress distribution of CT-1 specimen. (a) Pile; (b) reinforcement in pile; (c) cap (Units: Pa)

not increased significantly. Accordingly, the displacement at the loading point decreases for DE increasing from 150 to 200 mm, and becomes stable when DE > 200 mm. Therefore, the optimal DE value for specimen CT-1 is 200 mm, namely half of the external diameter of PHC pile.

ODs of Strengthened Ring at Specimen CT-2 A comparison of numerical results for different ODs of the strengthened ring at pile to cap is shown in Fig. 18b. It is seen that the strength and stiffness are significantly influenced by the ODs. However, for larger ODs, the capacity of the connection depends on the capacity of the pile.

When the OD of the strengthened ring is over 600 mm, the capacity of (a)

specimen CT-2 remains unaffected.

Therefore, for specimen CT-2, the optimal OD of the strengthened ring is 600 mm.

The Size of T-shape Steel in Specimen CT-3 The size of T-shape steel is mainly determined by the embedment depth d of horizontal limb and the length B of horizontal limb (see Fig. 2c). Various sizes of T-shape steel were obtained by the FEM representing specimen CT-3, including d = 150, 300, 450 and 600 mm and B = 200, 400, 600, 800 and 1000 mm. As shown in the numerical results, with the increase of d value, stress concentration basically appears at the interface of pipe pile and cap.

There is a trend that the stress contour curve for the vertical limb is gradually

(b)

S, S22 (Avg: 75%) +4,609e+06 –2,795e+06 –8,198e+06 –1,360e+07 –1,900e+07 –2,441e+07 –2,981e+07 –3,521e+07 –4,062e+07 –4,602e+07 –5,142e+07 –5,683e+07 –6,223e+07

expanded, while the stress contour curve for the horizontal limb is gradually reduced. The performance of pipe pile-cap connection is weakened. A comparison of the numerical results for d values is shown in Fig. 19a, in which d = 300 mm is deemed the best. As shown in the numerical results, with the shortening of B value, the range of stress contour curve on the cap is gradually reduced; in other words, the limitation of the cap is gradually weakened. The results as shown Fig. 19b indicate that the optimal length of the horizontal limb is 600 mm.

Summary and Conclusions Based on the experimental and nonlinear FE results, the following observations and conclusions are made:

(c)

S, Mises (Avg: 75%) +1,169e+09 +1,072e+09 +9,742e+08 +8,768e+08 +7,794e+08 +6,819e+08 +5,845e+08 +4,871e+08 +3,897e+08 +2,923e+08 +1,948e+08 +9,742e+07 +2,401e–03

S, Max, Principal (Abs) (Avg: 75%) +5,366e+06 +2,258e+04 –2,321e+06 –4,665e+06 –7,009e+06 –9,353e+06 –1,170e+07 –1,404e+07 –1,638e+07 –1,873e+07 –2,107e+07 –2,342e+07 –2,576e+07

Fi g. 16: Numerical stress distribution of CT-2 specimen. (a) Pile; (b) reinforcement bars in specimen; (c) cap and strengthened ring (Units: Pa)

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(a)

(b)

S, S22 (Avg: 75%)

(c)

S, Mises (Avg: 75%)

+5,806e+06 +5,612e+05 –1,883e+06 –4,328e+06 –6,772e+06 –9,217e+06 –1,166e+07 –1,411e+07 –1,655e+07 –2,899e+07 –3,144e+07 –4,388e+07 –4,633e+07

S, S11 (Avg: 75%)

+3,450e+08 +3,164e+08 +2,877e+08 +2,591e+08 +2,304e+08 +2,018e+08 +1,732e+08 +1,445e+08 +1,159e+08 +8,724e+07 +5,860e+07 +2,996e+07 +1,324e+06

+5,240e+06 –6,091e+05 –2,358e+06 –4,108e+06 –5,857e+06 –7,606e+06 –9,355e+06 –1,110e+07 –1,285e+07 –1,860e+07 –2,635e+07 –3,810e+07 –4,985e+07

F ig . 17 : Numerical stress distribution of CT-3 specimen. (a) Pile; (b) T-type steel part; (c) cap (Units: Pa)

• The general failure mode of all test specimens is by flexure. All three types of connections appear to be damaged significantly. Specimen CT-1 (with the common connection details) loses the bearing capacity due to the yielding of anchor bars and the cracking and spalling of the cap. Specimen CT-2 (with the strengthened ring) is damaged because of the cracks in the strengthened rings and PHC pile.

Specimen CT-3 (with the special internal T-shape steel) is damaged because of the cracks in the cap and PHC pile.

• The analysis of anchor bar strains indicates that the anchor bars do not slip in the cap and the anchorage length is sufficient. The strain at the measuring point of specimen CT-1 is more than 1766 με which is beyond the rebar’s yield point. The maximum strain of the anchor bar

(a)

(b)

300

350 300 Moment (kN m)

Moment (kN m)

250 200 150 H = 50 mm H = 100 mm H = 150 mm H = 200 mm H = 250 mm H = 300 mm

100 50 0 0

30 20 Displacement(mm)

10

40

250 200 D = 500 mm D = 550 mm D = 600 mm D = 700 mm D = 800 mm D = 900 mm

150 100 50 0

50

0

10

20

30 40 50 Displacement(mm)

60

70

F ig . 18 : Comparison of numerical results for different design parameters of specimens CT-1 and CT-2. (a) Embedment depth (DE) of pile in specimen CT-1; (b) outer diameter of strengthened ring for specimen CT-2

(a)

(b)

250

200 Moment (kN m)

Moment (kN m)

200

150 d = 150 mm d = 300 mm d = 450 mm d = 600 mm

100

50

0

250

150 B = 200 mm B = 400 mm B = 600 mm B = 800 mm B = 100 mm

100

50

0

10

20

30

40

Displacement (mm)

50

60

70

0

0

10

20

30

40

50

60

Displacement (mm)

F ig . 19 : Comparison of numerical results for different design parameters of specimen CT-3. (a) The embedment depth d of the horizontal limb; (b) the length B of the horizontal limb 556

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in the pile of specimen CT-2 is less than 460 με and it is less than 680 με for the anchor bar in the strengthened ring not yielding in both cases. The strains of the anchor bars in specimen CT-3 are relatively small with the maximum value approaching the yielding point.

• The bearing capacity and stiffness are very different among the different connection details. The hysteretic behaviour is similar between the specimens CT-3 and CT-2. Specimen CT-1 is the worst in terms of seismic resistance. The rotation capacity of specimens CT-2 and CT-3 is greater than that of specimen CT-1 due to the plastic hinge formed in the connection zone and the better bearing capacity and hysteretic behaviour. As a result, connection details CT-3 and CT-2 can withstand a stronger earthquake. In addition, connection detail CT-3 has less construction interference.

• The load–displacement curves derived based on the FEA are in good agreement with the experimental results. The failure modes predicted by the FEA are similar to those from the tests. The developed FEM is deemed reliable and can be used to reliably predict the load– deformation relationship.

• The parametric analysis results show that the strength and stiffness of specimen CT-1 are significantly influenced by the embedment depth of the pile. The optimal DE value for specimen CT-1 is 200 mm, namely half of the external diameter of PHC pile. The parametric analysis results of specimen CT-2 indicate that the optimal

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outside diameter for the strengthened ring is 600 mm. The analytical results of specimen CT-3 show that the optimal embedment depth d is 300 mm and the optimal length B is 600 mm for the horizontal limb.

Acknowledgements The authors would like to acknowledge the National Natural Science Foundation of China for its support to this study under grant no. 51408395.

References [1] Nagai K. Damage to concrete piles in buildings. Cement Concr. Compos. 1997; 19(3): 259–279.

[2] Karkee MB, Kishida H. Investigations on a new building with pile foundation damaged by the Hyogoken–Nambu (Kobe) earthquake.

Struct. Des. Tall Build. 1997; 6(4): 311–332.

[5] Xiao Y, Priestley MJN, Seible F. Experimental evaluation of a typical bridge column footing designed to current Caltrans standards.

Structural Systems Research Project, Rep. No. SSRP-95/08, University of California at San Diego, San Diego, 1995.

[6] Silva PF. Experimental and analytical models to predict the response of pile to pile cap connections under simulated seismic loads. PhD dissertation, University of California, San Diego, California, 1998.

[7] Harries KA, Petrou MF. Behavior of precast, prestressed concrete pile to cast-in-place pile cap connections. PCI J. 2001; 46(4): 82–93.

[8] Silva PF, Seible F, Priestley MJN. Influence of strand development length in formation of plastic hinges in prestressed piles. PCI J. 2001; 46(3): 76–89.

[9] Xiao Y. Experimental studies on precast prestressed concrete pile to CIP concrete pilecap connections. PCI J. 2003; 48(6): 82–91.

[3] Sheppard DA. Seismic design of prestressed concrete piling. PCI J. 1983; 28(2): 20–51.

[10] Katsunori W, Shinichiro A, Noboru M, Kazuki A, Koushirou N. Mechanical characteristics of simplified connection of pile head for precast concrete pile. J. Struct. Constr. Eng. 2003; 570: 85–91.

[4] Joen PH, Park R. Simulated seismic load tests on prestressed concrete piles and pile-pile cap connections. PCI J. 1990; 35(6): 42–61.

[11] Kazuki A, Hiroshi S, Tsutomu K. Mechanical characteristics of pile head joint with improved simplified connection method for

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precast concrete piles. J. Struct. Constr. Eng. 2006; 607: 125–132.

[12] Sstoshi S, Katsumi K, Hideaki Y, Koichi K, Toshiki M, Yoshito U. Study on mechanical behavior of semi-rigid connection on pile head for precast concrete piles using unbonded anchors. J. Struct. Constr. Eng. 2007; 620: 81–86.

[13] Caiza-Sánchez P, Andrawes B, La Fave J. Analytical modeling and damage assessment of shallow embedment pile-deck connections. Adv. Struct. Eng. 2012; 15(10): 1673–1687.

[14] Lehman DE, Roeder C, Stringer SJ, Jellin A. Seismic performance of improved pile-to-wharf deck connections. PCI J. 2013; 58(3): 62–80.

[15] Wang T, Yang Z, Zhao H, Wang W. Seismic performance of prestressed high strength concrete pile to pile cap connections. Adv. Struct. Eng. 2015; 17(9): 1329–1342.

[16] China Institute of Building Standard Design & Research. China Building Standard Design Drawing: Prestressed High Strength Concrete Piles (10G409) China Planning Press: Beijing, 2010.

[17] Guo ZH. The Strength and Constitutive Relations of Concrete: Theory and Application China Building Industry Press: Beijing, 2003.

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Negative Angle Vertical Rotating Construction Method of Reinforced Concrete Arch Bridge Wenwu Li, Civil Eng., Bridge Department, Hunan Provincial Transport Planning, Changsha, China; Cailiang Huang; Chunyan Tang, Civil Eng., Dalian University of Technology, Dalian, China. Contact: scopylee@163.com DOI: 10.2749/222137917X14881937844847

Abstract The construction method is a key technical factor to determine whether a concrete arch bridge design is reasonable and applicable. In most mountain areas of western China, a new construction method is being applied in concrete arch bridge construction in order to meet the challenge of severe construction condition, inconvenient transportation and high construction expenses. Pearl Bridge is the ďŹ rst to adopt the negative angle vertical rotating construction method in China. This paper takes Pearl Bridge as an example to introduce the construction process of this new method and discusses its key procedure and constructional details.

Keywords: reinforced concrete arch bridge; bridge construction; negative angle vertical rotating construction; vertical casting; vertical rotation hinges.

Introduction In most mountain areas of West China, considering the visual effects and economic indicators, concrete arch bridge is widely constructed to cross rivers and valleys (reviewed, e.g. in Ref. 1). Pearl Bridge (Fig. 1), a deck reinforced arch bridge, is situated in Wuchuan County of Guizhou Province, crossing the V-shaped valley of Yanggang River between Wuchuan and Pengshui. Vertical cliffs ďŹ&#x201A;ank the bridge on both sides. The construction site is limited to a narrow area, and poor transportation facilities bring extra difďŹ culties. Initially, bridge engineers planned to use common methods like cable erection and arch centring to build the bridge, but they found it was impossible. Due to the geographical features of the bridge site, construction condition and costs, they ďŹ nally changed to adopt the rarely used negative angle vertical rotating method. It separates the apex of the arch rib into two parts, and pours vertically at its own side, taking advantage of the physical features of the bridge site. Taking the arch spring as rotating hinge, each of the arch rib halves are rotated downwards into the designed position, and ďŹ nally form a complete arch.

Cable hoisting construction, cast-inplace falsework supported construction and cast-in-place cantilever construction are traditional concrete arch construction methods. Compared with above methods, negative angle vertical rotating construction has the following characteristics. â&#x20AC;˘ Less construction area is required, which is more environment friendly and overcomes the shortcomings of narrow construction space. â&#x20AC;˘ No bridging and hoisting equipments are required, which overcomes the disadvantages of inconvenient mountain transportation. â&#x20AC;˘ The arch-rotating system reduces cost by avoiding use of falsework and machinery in the valley. â&#x20AC;˘ Climbing formwork construction improves pouring quality.

Pearl Bridge is the ďŹ rst to use this construction method in China. Germany and Japan were the ďŹ rst to apply this method to build concrete arch bridges.2,3 This paper takes the construction of Pearl Bridge as an example to fully illustrate the negative angle vertical rotating method.

General Description

span ratio is 1/7 and width is 10 m. The water level to bridge deck height is 112 m (Fig. 2a).

The arch rib of the bridge was originally designed to use a three-cell box (Fig. 2b) with a width of 10 m, and then the complete design for the arch-rib section was upgraded when it was subsequently decided to use the negative angle vertical rotating construction method. The original whole box was changed into two single boxes (Fig. 2c) which were united by diaphragms. Width of a single arch rib was 3.867 m. The two arch ribs were rotated and closed during the construction process, thus greatly decreasing the rotating weight and minimising the construction difďŹ culties.

The General Processes of Negative Angle Vertical Rotating Construction of the Pearl Bridge Figure 3 shows construction procedure of Pearl Bridge: ďŹ rst, the rotating hinges were set at arch springing and poured vertically to the arch rib by taking advantage of the rocks beside the arch rib. Second, rotating construction of the arch rib was realised by a buckle cable set at the back of the bridge and a pulling cable set at the opposite bank.

Third, the arch ribs were closed after rotating into place. Finally, another arch rib was constructed, and diaphragms, bridge deck and piers were constructed once the two arch ribs were closed.

Rotating weight was 610 t and the theoretical rotating angle was 71.75 .

This article analysed the vertical pouring, rotation, closure process and other key construction processes in the following sections; however construction process of the bridge deck and piers is not mentioned as they are the same as the common construction methods of a concrete arch bridge.

General Information of the Pearl Bridge Peer-reviewed by international experts and accepted for publication

by SEI Editorial Board Paper received: March 11, 2016 Paper accepted: April 23, 2017

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The Negative Angle Rotating The Pearl Bridge is situated at a typically Construction Method mountainous area in a V-shaped valley and has a span of 120 m. The arch axis is in the form of an inverted catenary; arch-axis coefďŹ cient m = 1.756, riseâ&#x20AC;&#x201C;

Vertical Pouring for the Arch Rib A rotating hinge was set before vertical pouring. As a rock of 20 m height

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In the ďŹ rst phase, the referred rotation was from 0 to 15.93 . At the beginning of the rotation, gravity centre of the arch rib was more on the bridge deck, and rotation of the arch rib was achieved by tensioning the pulling cable on the opposite bank. Gravity centre of the arch rib was transferred to the other side of the rotating hinge when the arch rib was rotated to 3.58 .

Theoretically, the arch rib could rotate by its own dead weight and release the buckle cable, but since there was a large tensile stress on the upper edge of the arch rib during rotation, the pulling cable would adjust its cable tension to improve the arch rib stress.

In order to reduce risk and facilitate construction, the buckle cable and the pulling cable should be conducted alternately, and a detailed theoretical calculation should be conducted to determine the tension of the pulling cable and the buckle cable during each construction procedure.

Fi g. 1: The Pearl Bridge

was present behind the arch springing, an arch rib of 18 m was constructed by stand pouring supported by the rock, and the arch rib was ďŹ xed to the rock by cable and bolt. This was done to avoid accidents caused by dead weight, wind load and earthquake.

The remaining portion of the arch rib was constructed by hydraulic climbing formwork. From economy and safety perspective, the arch rib was divided into 15 segments and poured respectively (Fig. 4); the top surface of the diaphragm worked as the interface. In order to ďŹ x the formwork conveniently, the longest pouring length was 4 m and tilt angle was 18 . (a)

In order to maintain the accuracy of pouring, the engineers arrived at an accurate calculation of coordinates for the arch rib axis. During construction, the largest deviations found in the onsite checking of the four semi-arches after pouring vertically and horizontally were respectively 17 and 16 mm.

Rotating Construction of the Arch Rib The rotating construction of the arch rib was the most crucial to the entire construction of the bridge (Fig. 5), which took place in two phases.

R = 4000 m T = 20 m E = 0.05 m

Wuchuan

In the second phase the referred rotation was from 15.93 to the position where the arch ribs closed. As the pulling cable was dismissed, the arch rib could rotate under the work of its own dead weight and the releasing of the buckle cable; the bottom edge of the arch rib was under great stress when the arch rib was rotated to 20.90 . Additional bars were needed to reduce the stress as the

Pengshui

135.2 3.6

12.50 3.6

16 Ă&#x2014; 8

588.000

0.5%

Bridge deck

-0.5%

588.000

9/2

9/2

1.75

Bridge deck

Pier 19.252

566.975

564.748

564.748

L0 = 120

0.7

2.1

Pier

1.133

4

19.252

F0 = 17.143

0.8

4

588.288

1.75

3.867 10/2

0.7

2.1

Bridge axial

3.867 10/2

Water level 476.300

(c)

3.465

3.07

3.465

0.3

10

3.867

0.25

0.3

1.133

Diaphrgam 0.25

0.25

0.25

2.1

10

2.1

(b)

Diaphragm

0.3

2.266

0.3

3.867

Fi g. 2: The arrangement of the Pearl Bridge (Units: m). (a) Bridge layout; (b) original design section for arch rib; (c) modiďŹ ed section for arch rib

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(a) Cable saddle

Climbing–forwork Framing cast–in–situ Tension–stand for pulling cable

Tension–stand for buckle cable Hinge

(b) Buckle cable

Buckle cable

upstream were rotated first; after closure of these two, the remaining arch ribs downstream were rotated. It took 28, 19, 20 and 26 h respectively to complete all the rotations. Horizontal alignment tolerance of the arch ribs which was vital to the success of the closure was 21 mm for the arch ribs upstream and 8 mm for arch ribs downstream.

Closure Construction of the Arch Rib

Pulling cable

Bar Hinge

Buckle cable

(c) Pulling cable

Bar Hinge

(d) Closure

Dismantle buckle cable

Dismantle bar Reinforcing arch springing

(e) Bridge deck

Diaphragm

Pier

F ig . 3: Vertical rotation construction procedure. (a) Vertical pouring construction; (b) one side arch rib rotating construction; (c) the other side arch rib rotating construction; (d) arch rib closure construction; (e) spandrel structure construction

arch rib was rotated further in the subsequent process.

During construction of the Pearl Bridge, the solutions adopted were:

Buckle cable force was greatly affected by the dead weight of the arch rib during rotation; if the actual weight of the arch rib differed greatly with its theoretical weight, the actual buckle cable force would differ greatly with its theoretical force as well. The difference could lead to misjudgment of the appropriate time to release the pull cable and tension bar; thus the concrete could crack due to excessive stress.

• Reduce actual and theoretical weight difference of the arch rib.

• Measure buckle cable force, pulling cable force and spatial position of the arch rib many times at the beginning of rotation to calculate the actual weight of the arch rib, and modify the calculation model accordingly.

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During the vertical rotating process of the Pearl Bridge, two arch ribs

Closure of the arch ribs proceeded after they were rotated downward to the designed position. Many construction difficulties were involved, and one of them was the construction sequence including crown closure, changing twohinged arch into fixed-hinged arch, and removing the buckle cable and bar.

Reasonable construction sequence should be adopted based on theoretical calculation. The main procedures were as following.

• Closure of stiff skeleton (Fig. 6): Stiff skeleton was made of steel truss embedded in the closure segment.

Before the concrete achieved sufficient strength, the interaction of the stiff skeleton, buckle cable and bar allowed the arch to resist the wind load, dead load of the closure segment and temperature action.

• Pouring concrete of closure segment: Micro-expanded early-strength concrete was poured into the closure segment in order to compensate the shrinkage and creep during concrete curing.

• Removing the buckle cable and bar: After the concrete achieved sufficient strength, the buckle cable and bar were removed alternately.

Following this proper procedure, no cracks and tensile stress appeared.

• Pouring concrete of arch springing: Structural system transformation was completed by using microexpanded early-strength concrete to fix the hinges of the arch rib.

Diaphragms and piers were poured once all the arch ribs were closed.

Finally, bridge decks were built from the abutment to mid-span.

Design of the Key Structure Structural form and mechanical behaviour of the key structural measures of the negative angle vertical rotating construction method are different from other construction methods; the design of the key

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Fi g. 4: Vertical casting construction

structural measures such as vertical rotating hinges, buckle cable and pulling cable should ensure its reliability and economy.

Vertical Rotation Hinges Fabrication and assembly of vertical rotation hinges were vital to the successful closure of the arch ribs, which could not be laterally adjusted during the vertical rotation construction of the Pearl Bridge. The vertical rotation hinges, bearing the entire vertical load during the rotation process, must be strong enough to bear the exterior load and pass the load equally to the arch ribs and the base. The maximum bearing compression force of the vertical rotation hinges was about 9177 kN. Hinges were of the contact-type as the normal pin-type would fail to bear such a large pressure (Fig. 7).The 4 m long axis of the hinges was made of concrete filled steel pipe (ϕ800 × 20 mm). C50 (cube strength) concrete was poured

F i g. 5: Arch rib rotation construction

into a 20 mm thick embedded arch steel board which was grouped as the axis base. Radius of the arch board was 801 mm. Welded steel pipe filled with concrete was fixed to the hinge axis and anchored at the arch rib. Surface of the pipe was welded to the V-shaped steel bar to strengthen the anchorage.

The maximum compressive stress of the concrete of the axis base was 11.8 MPa while the maximum contact stress of the arch steel board was 23.9 MPa. Buckle Cable Buckle cable, consisted of 22 steel strands with ϕ15.2, and was the main bearing member during the rotation of the arch rib. One end was fixed to the top of the arch rib and the other end was anchored to the base of the buckle cable which was controlled by four sets of synchronous hydraulic jacks. Tension force and cable length of the jacks were both controlled by

computer. Only a few steel strands were used at the beginning of rotation as the cable force was small; cable force was increased as the rotation went further, and more steel strands were added to meet the force needs.

Quantity of strands was increased three times during the whole rotation of the Pearl Bridge. First, it was increased to 20 from 10, secondly from 22 to 44, finally the quantity was increased to 88 from 44. The minimum buckle cable force was 260 kN and the maximum was 7709 kN during the whole rotation. The minimum tension of a single steel strand was 26 kN and the maximum was 88 kN. Length of the buckle cable and the vertical angle changed constantly during rotation of the arch rib. Since the anchorage angle of the jack was fixed, a cable saddle was set to make the buckle cable move freely. The steering cable of the Pearl Bridge was made of pulley block. Nine groups of pulley blocks were set on an arc with a radius of 4 m, and each pulley block comprised several small pulley blocks with 20 mm depth and 20 mm width V-shaped groove. With the V-shaped groove, each steel strand could be moved freely on its own, and adjusted individually so as to not mix up with others (Fig. 8).

Pulling Cable

Fi g. 6: Closure segment construction

Structural Engineering International Nr. 4/2017

Pulling cable was not only the drive source for the arch rib at the beginning of the rotation but was also a safeguard measure to arch rib safety.

The pulling cable of the Pearl Bridge was made of a bundle of 10ϕ15.2 steel strands. One end was anchored at the diaphragm of the arch rib, and the other end was fixed to a special tensile Scientific Paper

561

g axis Startin

valleys and mountainous areas where pre-casting facilities and construction site extent are limited. As a bridge construction technology, it is suitable not only for rotating construction of steel concrete arch bridges but also for steel bridges and steelâ&#x20AC;&#x201C;concrete bridges. Climbing formwork and continuous jacks system are adapted in the development trend of bridge construction technology. With the widespread use and maturity of these technologies, construction cost will be largely reduced in the civil engineering industry.

71.

75°

xis

ga

Steel pipe

Hinge base

in ion

t

si Po

Stop

Concrete

References

F ig . 7: Vertical rotation hinge

[1] Yao C-R, Li Y-L, Liang D, Wang X-J. Structural type selection for long span bridges in mountainous region. Bridge Constr. 2012; 6: 81â&#x20AC;&#x201C;86.

[2] Liu J-P, Zhou K, Kunihiko N. Vertical rotating construction Kambara Valley Bridge.

World Bridges 2003; 3: 1â&#x20AC;&#x201C;4.

[3] Cheng F, Zhang Q-F, Wang J-Q. Current development and prospecting of construction techniques for bridge rotation erection in China. Railw. Stand. Des. 2011; 6: 67â&#x20AC;&#x201C;71.

SEI Data Block Owner: Wuchuan Bureau of Communications

F ig . 8: Buckle cable and cable saddle

platform on the opposite bank. The pulling cable was tensioned by a 2000 kN jack and removed once the arch rib was rotated to 15.93 .The largest cable tension was 1222 kN while the smallest was 200 kN. Bars The positive moment of the arch rib increased as the rotation went downward. Every arch rib was supplied with three sets of 6Ď&#x2022;15.2 steel strands as bars, and the bars were anchored

562

ScientiďŹ c Paper

at the diaphragm near the crown and arch springing. Tension of each steel strand was 800 kN. One bar was tensioned while the arch rib was rotated to 20.9 , and the other two bars were tensioned when the arch rib was rotated further to 31.1 .

Conclusion The negative angle vertical rotating construction method surpasses other methods of bridge construction in

Designer: Design Institute of Civil Engineering & Architecture of Dalian University of Technology and Guizhou Provincial Bridge Engineering General Corporation Contractor: Guizhou Provincial Bridge Engineering General Corporation Steel (t) Concrete (m3) Construction cost (USD million)

458 5288 0.32

Service date

January 2010

Structural Engineering International Nr. 4/2017

Case Study of the 156 m Simply Supported Steel Truss Railway Bridge Xiangdong Yu, Assoc. Prof., Dr, Civil Eng.; Yongle Deng, Graduate Student; Bin Yan, Assoc. Prof. Dr, School of Civil Engineering, Central South University, Changsha, China. Contact: binyan@csu.edu.cn DOI: 10.2749/222137917X14881937844603

Abstract Simply supported steel truss bridge has been widely used in the construction of railway lines over the past decades in China due to its light weight, simple structure and convenient construction. This bridge type was used for the New Yellow River Bridge in the Huang-Han-Hou railway line. The span of the New Yellow River Bridge is 156 m and it is presently the longest span simply supported steel truss railway bridge in China. The objective of this paper is to highlight the case features of this simply supported steel truss bridge. The structural components, structural dimensions and design criteria are introduced; results of modal analysis are explored. In addition, key issues associated with structural design are analyzed including disconnections in stringers, longitudinal force in track and seismic response induced by track–bridge interaction. Finally, a brief account of the construction method comparison and incremental launching method are given.

Keywords: simply supported steel truss bridge; structural design; modal analysis; track–bridge interaction; seismic response; incremental launching method.

Introduction The New Yellow River Bridge is located near Yumenkou station of Huang-Han-Hou (HHH) railway line which is an important energy transport route connecting central Shaanxi Province and south of Shanxi Province in China. At least 130 km of the distance was shortened when the HHH railway line was completed in January 2015. The HHH railway line is required to span over the Yellow River that has a width of up to 100 m.

The clearance requirement is also strict as large transport ships need to pass under the bridge. Therefore, the simply supported steel truss bridge was chosen for the main span. The constructed New Yellow River Bridge 558

Technical Report

F i g. 1 : View of the New Yellow River Bridge

is the longest span simply supported steel truss railway bridge in China, spanning the Yellow River which is the second longest river in China (Fig. 1).

Design Criteria The design train speed on the HHH line is 160 km/h. The live load model proposed by the International Union of Railways (UIC) is widely adopted

by European countries, while the live load used in this bridge design is based on ZK (Chinese Passenger Transport) live loads from China codes. This load includes a standard live load (80% of the UIC live load and a special live load, Fig. 2).1 The design life of the New Yellow River Bridge is 100 years and the seismic peak ground acceleration is 0.3 g in the local area.

Structural Design The simply supported steel truss bridge is designed with 156 m span; triangular

truss without vertical bars is adopted in the main truss to economize consumption of steel. The height of the bridge is 17 m and the width is 8.6 m. There are three types of members in the main truss which are named as upper chord, lower chord and diagonal and they are combined with gusset plates by high-strength bolts (Figs. 3 and 4).

The panel length of the lower chords is 14.1 m in the side and 14.2 m in the middle part, similarly 14.15 and 14.2 m are designed as the panel lengths in the upper chords. Two stringers are arranged under the steel rails and the center distance is 2.0 m.

There are some disconnections in the stringers which are designed to improve the mechanical performance of the structure, but during the construction period, some temporary connections were set up to bind the stringers and floor beams for construction convenience to be removed during the last construction phase.

Floor beams are arranged between the two stringers to constitute a common structural system to bear the

4 × 200kN

4 × 200kN

64kN/m

64kN/m

0.8m 1.6m

1.6m

1.6m 0.8m

Standard

1.6m

1.6m

1.6m

Special

F i g. 2 : ZK live load model adopted in China

Structural Engineering International Nr. 4/2017

Upper chord 14 150

e

17 000

a

8 × 14 200

7050

14 150

d b

c

Panel joint A

14 100

9 × 14 200 156 000

14 100 Diagonal

Lower chord

Fi g. 3: Elevation of primary truss (Units: [mm])

The cross-sections of the truss members are divided into box-sections and H-shaped sections in different sizes as shown in Fig. 7. The main scheme of this design is that the dead weight of the bridge would be reduced while the requirements of the forces are met. Regarding structural materials, Q370qE (yield strength is 370 MPa) is chosen for the main truss; the other members including stringers, floor beams, bracing systems are made of Q345qE (yield strength is 345 MPa).

The bridge deck is set up on the stringers and is comprised of reactive powder concrete which has compressive strength of 160 MPa, tensile strength of 18 MPa and elastic modulus of 48 GPa.

Modal Analysis The vibration modes of the simply supported steel truss bridge are very complex, including vertical bending, lateral bending and torsion (Table 1).

The first order mode is lateral bending and the second order mode is a vertical one. The main span of the steel truss bridge is 156 m, and the width is 8.6 m, which results in a small width–span ratio of 1/18. Generally, bridge that has small width–span ratio has a weak lateral stiffness; so the first order mode is the lateral bending vibration mode. Besides, the natural frequencies of the first three vibration modes are close, and the vibration is characteristic of large and complex structures.

Special Considerations during Design Disconnections in the Stringers The stringer and the floor beam usually generate axial force when the main truss is deformed under the

Track–Bridge Interaction The continuously welded rail (CWR) can improve the safety and stability of the train on the rail, and lengthen the service life of the track. But at the same time, due to the continuity of the rail, the deformation of the track itself is subject to constraints, which leads to relative displacement as well as longitudinal force between the track and the bridge.

100

0

In this study, a FEA Finite Element Analysis beam–rail–pier integrative model of the 156 m simply supported steel truss bridge was selected; the beam elements were adopted to

0

Diagonal

100

loads transmitted from the concrete bridge deck. Bracing members are designed to avoid instability of the structure caused by lateral loads; they are welded at the gusset plates and the welds polished smoothly after welding (Fig. 5). A portal frame is established inside the bridge in order to improve the structural torsion resistance (Fig. 6).

effect of vertical load and this type of force will arise with increase in bridge span. Bridge performance is analyzed under the conditions of whether there are disconnections in the stringers. As shown in Table 2, with disconnections in the stringers, the deflection value of the main truss is increased by 2.7%, the maximum compression stress of the floor beam is reduced by 54.5% and the maximum compression stress of the stringer is reduced by 65.8%.

However, with no disconnections in stringers, the maximum compression stress of the floor beam exceeds the allowable compression stress range.

Thus it can be seen that considerable disconnections in the stringers can reduce the stress of the floor beams as well as stringers and benefit the structures greatly.

Diagonal

800

800 00

2×1

100

100

2

100

2×1 00 1

00 1 00

2×1 00 100

Bolted connections

3×

100

50

50

100

00 01 × 10

3×

100

0 505

505 0

3×

100 50

50

3×

100

Gusset plate Lower chord 50

4 × 100

5050

4 × 100

5 × 100 100 100

100 100 50

50

5 × 100

5 × 100

1400

5 × 100

.1

1000

50

50

50

116

4 × 100

50

5050

3 166

4 × 100

3.1

Lower chord 50

1400

7050

20

1300

1200

1200

1280

20

1000

Fi g. 4: Drawing of panel joint A (Units: [mm])

Structural Engineering International Nr. 4/2017

Technical Report

559

Bracing system

Breaking joint of stringer

Breaking joint of stringer

8600

Stringer

1000

9 Ă&#x2014; 14 200

14 100

14 100 1000

Floor beam

F ig . 5: Drawing of lower lateral bracing (Units: [mm])

simulate the bridge and nonlinear spring elements were used to simulate the trackâ&#x20AC;&#x201C;bridge connections.2 In order to simulate boundary conditions, six concrete continuous beams, and ten concrete simply supported beams besides the simply supported steel truss bridge were also simulated under the railway track (Fig. 8).

7000

8600

Portal frame

9300

Main truss

Track Railway ballast 1:

5

1:

1.7

Stringer

1000

2800

1.7

5

Drain hole

2000

2800

1000

F ig . 6: Elevation of main truss (Units: [mm])

The longitudinal forces of the track include expansion force, bending force and braking force. In order to obtain the expansion force in the track, a trackâ&#x20AC;&#x201C;bridge temperature mode was proposed such that the simply supported steel truss bridge temperature changed by 25 C when the concrete temperature changed by 15 C. Because of the long thermal span of the bridge, several track expansion devices were arranged in the track at the positions of #12 and #13 piers. When calculating the bending force, the ZK live load is simpliďŹ ed as three types of most disadvantage cases (Fig. 9). As for the braking force, 0.164 was taken as the Floor beam

Upper and lower chord

Lateral bracing

Stringer

braking force ratio and the driving direction was assumed to be from left to right to ensure the braking force is equal but opposite.3 As illustrated in Fig. 10, the maximum compression stress of the track caused by these longitudinal forces is the expansion force, which appears at the mid-span of the simply supported steel truss bridge, arrived at forces of 55.8 MPa. The maximum stress caused by bending force was also relatively larger; up to 40.9 MPa appeared at the position of the disconnections in the stringers due to the relatively weak longitudinal stiffness. The maximum braking force that appeared at the ďŹ xed bearings of the simply supported steel truss bridge was 15.3 MPa. The maximum relative displacement between the track and the bridge was 2.96 mm and appeared at the movable bearing of the simply supported steel truss bridge. This indicated that the predicted responses satisďŹ ed the requirement of UIC code. In addition, peak values of track stress and deformation occurred at the position of the disconnections in the stringers.

Comparative studies on key design parameters revealed that if there were no track expansion devices arranged on the track, the longitudinal force in the track would exceed the design strength, so it was extremely necessary to arrange the track expansion devices in a logical position.

400

312

398

398

2020

1500

1400

Diagonal

420

Seismic Response 360

Sway bracing

Vertical bending

0.982

Torsional bending

1.318

Traveling Wave Effect

368

800

0.575

800

Lateral bending

According to provision in Ref. 4, the standard response spectrum was introduced into the SIMQKE_GR software developed to generate artiďŹ cial wave, and the response spectrum corresponding to the artiďŹ cial wave was consistent with the standard response spectrum; 0.3 g was assumed as the seismic peak ground acceleration.

1000

1000

1000

480

560

400

F ig . 7: Cross-sections of the truss members (Units: [mm]) Types

Natural frequency (Hz)

Modes of vibration

Table 1: The ďŹ rst three order modes and their characteristics

Max. deďŹ&#x201A;ection (mm)

Max. compressed stress in ďŹ&#x201A;oor beam (MPa)

Max. compressed stress in stringer (MPa)

Unbroken

298.1

438.5

73.4

Broken

306.4

199.7

25.1

Conditions in stringer

Table 2: DeďŹ&#x201A;ection and stress under different conditions in the stringers 560

Technical Report

The seismic response of the trackâ&#x20AC;&#x201C; bridge system under the traveling wave effect was analyzed by largemass method.5 The results are listed in Table 3 and Fig. 11. Compared with uniform excitation, the maximum longitudinal deformation of the track at the movable bearing of the simply supported steel truss bridge increased by 3.6 times under the action of traveling wave effect (the apparent wave velocity is 200 m/s); at the track stress

Structural Engineering International Nr. 4/2017

Upper chord Lower chord

Track beam element

Nonlinear spring element Rigid arm

Embankment

Embankment

Fixed bearing Movable bearing

Abutment 1#

5# 2#

3#

6#

9#

7#

4#

17#

10# 11#

200

3 × 32

2 × 24

14#

13#

12#

40+4 × 64+40

16#

15#

8# 32

156

24

32

24

32

200

X=0

Fi g. 8: Nonlinear model for track–bridge interaction (Units: [m])

Construction Comparison of Construction Methods (a)

In order to span over the Yellow River, three types of construction methods were proposed on the basis of the field environment. The first option is cantilever erection method.

Temporary piers will be constructed on both banks of the Yellow River and sufficient quantity of temporary piers is required to support three panel joints of the simply supported steel truss bridge.

(b)

(c) Fi g. 9: Load cases for bending force calculation Braking force 60

Bending force Expansion force

Track stress (MPa)

40

20

0

–20

–40

–60 –600

–400

–200

0

200

400

600

Mileage (m)

F i g. 10: Track stresses under different longitudinal forces (envelope) Position

Load case

Fixed support

Uniform excitation

2.4

Traveling wave effect

6.3

Uniform excitation

8.5

Uniform excitation

39.0

Movable support

Max. deformation (mm)

Table 3: Longitudinal deformation of the track under different cases

at the position of #4 pier increased by 6.9 times. Due to the arrangement of track expansion devices in the track on both sides of the simply supported steel truss bridge, the track stress near the simply supported steel truss bridge increased 2.3% under the traveling wave effect. A comparative study

between different apparent wave velocities indicated that with the increasing of the apparent wave velocity, the maximum track stress decreased. When the apparent wave velocity reached 2000 m/s, the maximal track stress tended to reach the value under uniform excitation.

Structural Engineering International Nr. 4/2017

The walking crane method is adopted to assemble the truss members symmetrically until the middle span is completed (Fig. 12a). The second option is the Fishing Method, which proposes that the incremental launching method can be used in the construction of the bridge with stayed cables arranged on the piers on the opposite side of the Yellow River.

The steel guide beam is a temporary bent frame. With the process of incremental launching, the force and anchoring position of the stay cables are adjusted until the construction is completed (Fig. 12b). The third option consists of an incremental launching method with guide beam arranged in front of the bridge and temporary piers established in the river (Fig. 12c). Comparing the three types of construction methods, the first option requires an extended construction period as at least six groups of temporary piers are needed to be constructed in the river. The construction process is likely to be difficult and time-consuming if the depth of water in the Yellow River is considered.

Second option needs to control the stay cable force accurately in the process of incremental launching, and the long span of the cantilever steel guide beam will increase the risk of construction. As for the third option, the Technical Report

561

the steel guide beam. Meanwhile, the assembly work of next stage was carried out in the temporary platform until the bridge was assembled completely and launched at the right place. Lastly, the bridge was moved 13 m to the bridge site in the upstream direction on the transverse beams (Fig. 13). With the placing of the beam on the support and transformation of the bridge system, the erection of simply supported steel truss bridge was completed.

Uniform excitation Traveling wave effect (200 m/s)

300

Traveling wave effect (500 m/s) Traveling wave effect (1000 m/s) Traveling wave effect (2000 m/s)

Track stress (MPa)

200

100

0

–100

–200

Conclusions

–300 –600

–400

–200

0

200

400

600

With the increasing expansion of railway line network in China, it is inevitable that the new lines will need to cross the various wide rivers. This study introduces the design and construction of the New Yellow River Bridge, the longest span simply supported steel truss railway bridge in China. The incremental launching

Mileage (m)

F ig . 11 : Track stresses under traveling wave effect (envelop)

construction difficulty is relatively reduced with adoption of steel guide beam and temporary piers, and the construction process control becomes easier and reliable. Therefore, the third option was chosen for the construction.

as an assembly platform. The members were assembled in the porary platform by sections pushed ahead on the slide track

truss temand after

Construction Procedures The construction procedures can be divided into three steps. Step one was the construction of temporary piers in the Yellow River, which were 13 m away from the new bridge site at the downstream side. This work had to be finished in the dry season of the Yellow River, which is from April to June. Next, the temporary bent frames were built on the river banks

(a)

(b)

F i g. 1 3: Images of construction sites: (a) steel guide beam; (b) construction of temporary pier

Hoisting machine

Hoisting machine Steel truss

Steel truss

Stayed cables

Bent frame

Bent frame Temporary piers

Steel guide beam

156 m Simply-supported truss bridge

Bent frame 132 Temporary piers

357.24 248.24

(a)

(b) 156 m Simply supported truss bridge 64m Steel guide beam

Slide-track Temporary bent frame

398.31

398.31

Temporary Piers 382.51 ¦Õ1.5 m

¦Õ1.5 m

¦Õ1.5 m ¦Õ=2.0 m

8.6

8 × 9 = 72

9.2

32

64

12

80

16

(c) F ig . 12 : Arrangement plan of the construction methods: (a) first option; (b) second option; (c) third option 562

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Structural Engineering International Nr. 4/2017

method for simply supported steel truss bridge proved to be a safe and reliable technique to cross the wide river as it can shorten the construction period effectively and ensure the quality of installation. Future requirements for long-span railway bridges across wide rivers can consider the design and construction of the New Yellow River Bridge as a guideline.

Acknowledgements The authors would like to thank the National Natural Science Foundational of China (Project 51608542) for the financial support.

The authors also express their gratitude to Yun Liu, Central South University, and Wang Zhao, the Monash University, for improving the language and for their constructive comments on this study, respectively.

References [1] Yan B, Dai G, Hu N. Recent development of design and construction of short span highspeed railway bridges in China. J. Eng. Struct.

2015; 100: 707–717.

[2] Yu X, Sha S, Yan B. Track–bridge interaction of long-span simply supported steel truss bridge in mixed passenger and freight railway.

J. Hunan Univ. 2014; 41(6): 106–111 (in Chinese).

[3] Liu W, Dai G, He X. Sensitive factors research for track–bridge interaction of longspan X-style steel-box arch bridge on highspeed railway. J. Cent. South Univ. 2013; 20(11): 3314–3323.

[4] Yan B, Dai G. Seismic pounding and protection measures of simply-supported beams considering interaction between continuously welded rail and bridge. J. Struct. Eng. Int. 2013; 23(1): 61–67.

[5] Junmei H. Pushing construction technology for the 156 m simply supported steel truss

Structural Engineering International Nr. 4/2017

girder of New Yellow River Bridge. J. Railw.

Constr. Technol. 2014; (5): 64–67 (in Chinese).

SEI Data Block Owner: Huang-Han-Hou Passenger Dedicated Railway Co. Ltd. Structural design: China Railway First Survey and Design Group Co. Ltd. Main contractor: China Railway Engineering Consulting Group Co. Ltd Total steel for 2101.1 truss (t) Total estimated cost (USD million) Service date

586

October 23, 2015

Technical Report

563

Case Study of the 156 m Simply Supported Steel Truss Railway Bridge Xiangdong Yu, Assoc. Prof., Dr, Civil Eng.; Yongle Deng, Graduate Student; Bin Yan, Assoc. Prof. Dr, School of Civil Engineering, Central South University, Changsha, China. Contact: binyan@csu.edu.cn DOI: 10.2749/222137917X14881937844603

Abstract Simply supported steel truss bridge has been widely used in the construction of railway lines over the past decades in China due to its light weight, simple structure and convenient construction. This bridge type was used for the New Yellow River Bridge in the Huang-Han-Hou railway line. The span of the New Yellow River Bridge is 156 m and it is presently the longest span simply supported steel truss railway bridge in China. The objective of this paper is to highlight the case features of this simply supported steel truss bridge. The structural components, structural dimensions and design criteria are introduced; results of modal analysis are explored. In addition, key issues associated with structural design are analyzed including disconnections in stringers, longitudinal force in track and seismic response induced by track–bridge interaction. Finally, a brief account of the construction method comparison and incremental launching method are given.

Keywords: simply supported steel truss bridge; structural design; modal analysis; track–bridge interaction; seismic response; incremental launching method.

Introduction The New Yellow River Bridge is located near Yumenkou station of Huang-Han-Hou (HHH) railway line which is an important energy transport route connecting central Shaanxi Province and south of Shanxi Province in China. At least 130 km of the distance was shortened when the HHH railway line was completed in January 2015. The HHH railway line is required to span over the Yellow River that has a width of up to 100 m.

The clearance requirement is also strict as large transport ships need to pass under the bridge. Therefore, the simply supported steel truss bridge was chosen for the main span. The constructed New Yellow River Bridge

Fi g. 1: View of the New Yellow River Bridge

is the longest span simply supported steel truss railway bridge in China, spanning the Yellow River which is the second longest river in China (Fig. 1).

Design Criteria The design train speed on the HHH line is 160 km/h. The live load model proposed by the International Union of Railways (UIC) is widely adopted

by European countries, while the live load used in this bridge design is based on ZK (Chinese Passenger Transport) live loads from China codes. This load includes a standard live load (80% of the UIC live load and a special live load, Fig. 2).1 The design life of the New Yellow River Bridge is 100 years and the seismic peak ground acceleration is 0.3 g in the local area.

Structural Design The simply supported steel truss bridge is designed with 156 m span; triangular

truss without vertical bars is adopted in the main truss to economize consumption of steel. The height of the bridge is 17 m and the width is 8.6 m. There are three types of members in the main truss which are named as upper chord, lower chord and diagonal and they are combined with gusset plates by high-strength bolts (Figs. 3 and 4).

The panel length of the lower chords is 14.1 m in the side and 14.2 m in the middle part, similarly 14.15 and 14.2 m are designed as the panel lengths in the upper chords. Two stringers are arranged under the steel rails and the center distance is 2.0 m.

There are some disconnections in the stringers which are designed to improve the mechanical performance of the structure, but during the construction period, some temporary connections were set up to bind the stringers and floor beams for construction convenience to be removed during the last construction phase.

Floor beams are arranged between the two stringers to constitute a common structural system to bear the

4 × 200kN

4 × 200kN

64kN/m

64kN/m

0.8m 1.6m

1.6m

1.6m 0.8m

Standard

1.6m

1.6m

1.6m

Special

Fi g. 2: ZK live load model adopted in China

Structural Engineering International Nr. 4/2017

Technical Report

563

Upper chord 14 150

e

17 000

a

8 × 14 200

7050

14 150

d b

c

Panel joint A

14 100

9 × 14 200 156 000

14 100 Diagonal

Lower chord

F ig . 3: Elevation of primary truss (Units: [mm])

The cross-sections of the truss members are divided into box-sections and H-shaped sections in different sizes as shown in Fig. 7. The main scheme of this design is that the dead weight of the bridge would be reduced while the requirements of the forces are met. Regarding structural materials, Q370qE (yield strength is 370 MPa) is chosen for the main truss; the other members including stringers, floor beams, bracing systems are made of Q345qE (yield strength is 345 MPa).

The bridge deck is set up on the stringers and is comprised of reactive powder concrete which has compressive strength of 160 MPa, tensile strength of 18 MPa and elastic modulus of 48 GPa.

Modal Analysis The vibration modes of the simply supported steel truss bridge are very complex, including vertical bending, lateral bending and torsion (Table 1).

The first order mode is lateral bending and the second order mode is a vertical one. The main span of the steel truss bridge is 156 m, and the width is 8.6 m, which results in a small width–span ratio of 1/18. Generally, bridge that has small width–span ratio has a weak lateral stiffness; so the first order mode is the lateral bending vibration mode. Besides, the natural frequencies of the first three vibration modes are close, and the vibration is characteristic of large and complex structures.

Special Considerations during Design Disconnections in the Stringers The stringer and the floor beam usually generate axial force when the main truss is deformed under the

Track–Bridge Interaction The continuously welded rail (CWR) can improve the safety and stability of the train on the rail, and lengthen the service life of the track. But at the same time, due to the continuity of the rail, the deformation of the track itself is subject to constraints, which leads to relative displacement as well as longitudinal force between the track and the bridge.

100

0

In this study, a FEA Finite Element Analysis beam–rail–pier integrative model of the 156 m simply supported steel truss bridge was selected; the beam elements were adopted to

0

Diagonal

100

loads transmitted from the concrete bridge deck. Bracing members are designed to avoid instability of the structure caused by lateral loads; they are welded at the gusset plates and the welds polished smoothly after welding (Fig. 5). A portal frame is established inside the bridge in order to improve the structural torsion resistance (Fig. 6).

effect of vertical load and this type of force will arise with increase in bridge span. Bridge performance is analyzed under the conditions of whether there are disconnections in the stringers. As shown in Table 2, with disconnections in the stringers, the deflection value of the main truss is increased by 2.7%, the maximum compression stress of the floor beam is reduced by 54.5% and the maximum compression stress of the stringer is reduced by 65.8%.

However, with no disconnections in stringers, the maximum compression stress of the floor beam exceeds the allowable compression stress range.

Thus it can be seen that considerable disconnections in the stringers can reduce the stress of the floor beams as well as stringers and benefit the structures greatly.

Diagonal

800

800 00

2×1

100

2 100

100

2×1 00 1

00 1 00

2×1 00 100

Bolted connections

3×

100

50

50

100

00 01 × 10

3×

100

0 505

505 0

3×

100 50

50

3×

100

Gusset plate Lower chord 50

4 × 100

5050

4 × 100

5 × 100 100 100

100 100 50

50

5 × 100

5 × 100

1400

5 × 100

.1

1000

50

50

50

116

4 × 100

50

5050

3 166

4 × 100

3.1

Lower chord 50

1400

7050

20

1300

1200

1200

1280

20

1000

F ig . 4: Drawing of panel joint A (Units: [mm]) 564

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Structural Engineering International Nr. 4/2017

Bracing system

Breaking joint of stringer

Breaking joint of stringer

8600

Stringer

1000

9 Ă&#x2014; 14 200

14 100

14 100 1000

Floor beam

Fi g. 5: Drawing of lower lateral bracing (Units: [mm])

simulate the bridge and nonlinear spring elements were used to simulate the trackâ&#x20AC;&#x201C;bridge connections.2 In order to simulate boundary conditions, six concrete continuous beams, and ten concrete simply supported beams besides the simply supported steel truss bridge were also simulated under the railway track (Fig. 8).

7000

8600

Portal frame

9300

Main truss

Track Railway ballast 1:

5

1:

1.7

Stringer

1000

2800

1.7 5

Drain hole

2000

2800

1000

Fi g. 6: Elevation of main truss (Units: [mm])

The longitudinal forces of the track include expansion force, bending force and braking force. In order to obtain the expansion force in the track, a trackâ&#x20AC;&#x201C;bridge temperature mode was proposed such that the simply supported steel truss bridge temperature changed by 25 C when the concrete temperature changed by 15 C. Because of the long thermal span of the bridge, several track expansion devices were arranged in the track at the positions of #12 and #13 piers. When calculating the bending force, the ZK live load is simpliďŹ ed as three types of most disadvantage cases (Fig. 9). As for the braking force, 0.164 was taken as the Floor beam

Upper and lower chord

Lateral bracing

Stringer

braking force ratio and the driving direction was assumed to be from left to right to ensure the braking force is equal but opposite.3 As illustrated in Fig. 10, the maximum compression stress of the track caused by these longitudinal forces is the expansion force, which appears at the mid-span of the simply supported steel truss bridge, arrived at forces of 55.8 MPa. The maximum stress caused by bending force was also relatively larger; up to 40.9 MPa appeared at the position of the disconnections in the stringers due to the relatively weak longitudinal stiffness. The maximum braking force that appeared at the ďŹ xed bearings of the simply supported steel truss bridge was 15.3 MPa. The maximum relative displacement between the track and the bridge was 2.96 mm and appeared at the movable bearing of the simply supported steel truss bridge. This indicated that the predicted responses satisďŹ ed the requirement of UIC code. In addition, peak values of track stress and deformation occurred at the position of the disconnections in the stringers.

Comparative studies on key design parameters revealed that if there were no track expansion devices arranged on the track, the longitudinal force in the track would exceed the design strength, so it was extremely necessary to arrange the track expansion devices in a logical position.

400

312

398

398

2020

1500

1400

Diagonal

420

Seismic Response 360

Sway bracing

Vertical bending

0.982

Torsional bending

1.318

Traveling Wave Effect

368

800

0.575

800

Lateral bending

According to provision in Ref. 4, the standard response spectrum was introduced into the SIMQKE_GR software developed to generate artiďŹ cial wave, and the response spectrum corresponding to the artiďŹ cial wave was consistent with the standard response spectrum; 0.3 g was assumed as the seismic peak ground acceleration.

1000

1000

1000

480

560

400

Fi g. 7: Cross-sections of the truss members (Units: [mm]) Types

Natural frequency (Hz)

Modes of vibration

Table 1: The ďŹ rst three order modes and their characteristics

Max. deďŹ&#x201A;ection (mm)

Max. compressed stress in ďŹ&#x201A;oor beam (MPa)

Max. compressed stress in stringer (MPa)

Unbroken

298.1

438.5

73.4

Broken

306.4

199.7

25.1

Conditions in stringer

Table 2: DeďŹ&#x201A;ection and stress under different conditions in the stringers

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The seismic response of the trackâ&#x20AC;&#x201C; bridge system under the traveling wave effect was analyzed by largemass method.5 The results are listed in Table 3 and Fig. 11. Compared with uniform excitation, the maximum longitudinal deformation of the track at the movable bearing of the simply supported steel truss bridge increased by 3.6 times under the action of traveling wave effect (the apparent wave velocity is 200 m/s); at the track stress Technical Report

565

Upper chord Lower chord

Track beam element

Nonlinear spring element Rigid arm

Embankment

Embankment

Fixed bearing Movable bearing

Abutment 1#

5# 2#

3#

6#

9#

7#

4#

17#

10# 11#

200

3 × 32

2 × 24

14#

13#

12#

40+4 × 64+40

16#

15#

8# 32

156

24

32

24

32

200

X=0

F ig . 8: Nonlinear model for track–bridge interaction (Units: [m])

Construction Comparison of Construction Methods (a)

In order to span over the Yellow River, three types of construction methods were proposed on the basis of the field environment. The first option is cantilever erection method.

Temporary piers will be constructed on both banks of the Yellow River and sufficient quantity of temporary piers is required to support three panel joints of the simply supported steel truss bridge.

(b)

(c) F ig . 9: Load cases for bending force calculation Braking force 60

Bending force Expansion force

Track stress (MPa)

40

20

0

–20

–40

–60 –600

–400

–200

0

200

400

600

Mileage (m)

Fi g. 10: Track stresses under different longitudinal forces (envelope) Position

Load case

Fixed support

Uniform excitation

2.4

Traveling wave effect

6.3

Uniform excitation

8.5

Uniform excitation

39.0

Movable support

Max. deformation (mm)

Table 3: Longitudinal deformation of the track under different cases

at the position of #4 pier increased by 6.9 times. Due to the arrangement of track expansion devices in the track on both sides of the simply supported steel truss bridge, the track stress near the simply supported steel truss bridge increased 2.3% under the traveling wave effect. A comparative study 566

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between different apparent wave velocities indicated that with the increasing of the apparent wave velocity, the maximum track stress decreased. When the apparent wave velocity reached 2000 m/s, the maximal track stress tended to reach the value under uniform excitation.

The walking crane method is adopted to assemble the truss members symmetrically until the middle span is completed (Fig. 12a). The second option is the Fishing Method, which proposes that the incremental launching method can be used in the construction of the bridge with stayed cables arranged on the piers on the opposite side of the Yellow River.

The steel guide beam is a temporary bent frame. With the process of incremental launching, the force and anchoring position of the stay cables are adjusted until the construction is completed (Fig. 12b). The third option consists of an incremental launching method with guide beam arranged in front of the bridge and temporary piers established in the river (Fig. 12c). Comparing the three types of construction methods, the first option requires an extended construction period as at least six groups of temporary piers are needed to be constructed in the river. The construction process is likely to be difficult and time-consuming if the depth of water in the Yellow River is considered.

Second option needs to control the stay cable force accurately in the process of incremental launching, and the long span of the cantilever steel guide beam will increase the risk of construction. As for the third option, the

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the steel guide beam. Meanwhile, the assembly work of next stage was carried out in the temporary platform until the bridge was assembled completely and launched at the right place. Lastly, the bridge was moved 13 m to the bridge site in the upstream direction on the transverse beams (Fig. 13). With the placing of the beam on the support and transformation of the bridge system, the erection of simply supported steel truss bridge was completed.

Uniform excitation Traveling wave effect (200 m/s)

300

Traveling wave effect (500 m/s) Traveling wave effect (1000 m/s) Traveling wave effect (2000 m/s)

Track stress (MPa)

200

100

0

–100

–200

Conclusions

–300 –600

–400

–200

0

200

400

600

With the increasing expansion of railway line network in China, it is inevitable that the new lines will need to cross the various wide rivers. This study introduces the design and construction of the New Yellow River Bridge, the longest span simply supported steel truss railway bridge in China. The incremental launching

Mileage (m)

Fi g. 11: Track stresses under traveling wave effect (envelop)

construction difficulty is relatively reduced with adoption of steel guide beam and temporary piers, and the construction process control becomes easier and reliable. Therefore, the third option was chosen for the construction.

as an assembly platform. The members were assembled in the porary platform by sections pushed ahead on the slide track

truss temand after

Construction Procedures The construction procedures can be divided into three steps. Step one was the construction of temporary piers in the Yellow River, which were 13 m away from the new bridge site at the downstream side. This work had to be finished in the dry season of the Yellow River, which is from April to June. Next, the temporary bent frames were built on the river banks

(a)

(b)

Fi g. 13: Images of construction sites: (a) steel guide beam; (b) construction of temporary pier

Hoisting machine

Hoisting machine Steel truss

Steel truss

Stayed cables

Bent frame

Bent frame Temporary piers

Steel guide beam

156 m Simply-supported truss bridge

Bent frame 132 Temporary piers

357.24 248.24

(a)

(b) 156 m Simply supported truss bridge 64m Steel guide beam

Slide-track Temporary bent frame

398.31

398.31

Temporary Piers 382.51 ¦Õ1.5 m

¦Õ1.5 m

¦Õ1.5 m ¦Õ=2.0 m

8.6

8 × 9 = 72

9.2

32

64

12

80

16

(c) Fi g. 12: Arrangement plan of the construction methods: (a) first option; (b) second option; (c) third option

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method for simply supported steel truss bridge proved to be a safe and reliable technique to cross the wide river as it can shorten the construction period effectively and ensure the quality of installation. Future requirements for long-span railway bridges across wide rivers can consider the design and construction of the New Yellow River Bridge as a guideline.

Acknowledgements The authors would like to thank the National Natural Science Foundational of China (Project 51608542) for the financial support.

The authors also express their gratitude to Yun Liu, Central South University, and Wang Zhao, the Monash University, for improving the language and for their constructive comments on this study, respectively.

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girder of New Yellow River Bridge. J. Railw.

Constr. Technol. 2014; (5): 64–67 (in Chinese).

References [1] Yan B, Dai G, Hu N. Recent development of design and construction of short span highspeed railway bridges in China. J. Eng. Struct.

2015; 100: 707–717.

[2] Yu X, Sha S, Yan B. Track–bridge interaction of long-span simply supported steel truss bridge in mixed passenger and freight railway.

J. Hunan Univ. 2014; 41(6): 106–111 (in Chinese).

[3] Liu W, Dai G, He X. Sensitive factors research for track–bridge interaction of longspan X-style steel-box arch bridge on highspeed railway. J. Cent. South Univ. 2013; 20(11): 3314–3323.

[4] Yan B, Dai G. Seismic pounding and protection measures of simply-supported beams considering interaction between continuously welded rail and bridge. J. Struct. Eng. Int. 2013; 23(1): 61–67.

[5] Junmei H. Pushing construction technology for the 156 m simply supported steel truss

SEI Data Block Owner: Huang-Han-Hou Passenger Dedicated Railway Co. Ltd. Structural design: China Railway First Survey and Design Group Co. Ltd. Main contractor: China Railway Engineering Consulting Group Co. Ltd Total steel for 2101.1 truss (t) Total estimated cost (USD million) Service date

586

October 23, 2015

Structural Engineering International Nr. 4/2017

Negative Angle Vertical Rotating Construction Method of Reinforced Concrete Arch Bridge Wenwu Li, Civil Eng., Bridge Department, Hunan Provincial Transport Planning, Changsha, China; Cailiang Huang; Chunyan Tang, Civil Eng., Dalian University of Technology, Dalian, China. Contact: scopylee@163.com DOI: 10.2749/222137917X14881937844847

Abstract The construction method is a key technical factor to determine whether a concrete arch bridge design is reasonable and applicable. In most mountain areas of western China, a new construction method is being applied in concrete arch bridge construction in order to meet the challenge of severe construction condition, inconvenient transportation and high construction expenses.

Pearl Bridge is the first to adopt the negative angle vertical rotating construction method in China. This paper takes Pearl Bridge as an example to introduce the construction process of this new method and discusses its key procedure and constructional details.

Keywords: reinforced concrete arch bridge; bridge construction; negative angle vertical rotating construction; vertical casting; vertical rotation hinges.

Introduction In most mountain areas of West China, considering the visual effects and economic indicators, concrete arch bridge is widely constructed to cross rivers and valleys (reviewed, e.g. in Ref. 1). Pearl Bridge (Fig. 1), a deck reinforced arch bridge, is situated in Wuchuan County of Guizhou Province, crossing the V-shaped valley of Yanggang River between Wuchuan and Pengshui. Vertical cliffs flank the bridge on both sides. The construction site is limited to a narrow area, and poor transportation facilities bring extra difficulties. Initially, bridge engineers planned to use common methods like cable erection and arch centring to build the bridge, but they found it was impossible. Due to the geographical features of the bridge site, construction condition and costs, they finally changed to adopt the rarely used negative angle vertical rotating method. It separates the apex of the arch rib into two parts, and pours vertically at its own side, taking advantage of the physical features of the bridge site. Taking the 564

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F i g. 1 : The Pearl Bridge

arch spring as rotating hinge, each of the arch rib halves are rotated downwards into the designed position, and finally form a complete arch.

General Description

Cable hoisting construction, cast-inplace falsework supported construction and cast-in-place cantilever construction are traditional concrete arch construction methods. Compared with above methods, negative angle vertical rotating construction has the following characteristics.

The Pearl Bridge is situated at a typically mountainous area in a V-shaped valley and has a span of 120 m. The arch axis is in the form of an inverted catenary; arch-axis coefficient m = 1.756, rise– span ratio is 1/7 and width is 10 m. The water level to bridge deck height is 112 m (Fig. 2a).

• Less construction area is required, which is more environment friendly and overcomes the shortcomings of narrow construction space.

• No bridging and hoisting equipments are required, which overcomes the disadvantages of inconvenient mountain transportation.

• The arch-rotating system reduces cost by avoiding use of falsework and machinery in the valley.

• Climbing formwork construction improves pouring quality.

The arch rib of the bridge was originally designed to use a three-cell box (Fig. 2b) with a width of 10 m, and then the complete design for the arch-rib section was upgraded when it was subsequently decided to use the negative angle vertical rotating construction method. The original whole box was changed into two single boxes (Fig. 2c) which were united by diaphragms. Width of a single arch rib was 3.867 m. The two arch ribs were rotated and closed during the construction process, thus greatly decreasing the rotating weight and minimising the construction difficulties.

Pearl Bridge is the first to use this construction method in China. Germany and Japan were the first to apply this method to build concrete arch bridges.2,3 This paper takes the construction of Pearl Bridge as an example to fully illustrate the negative angle vertical rotating method.

General Information of the Pearl Bridge

The General Processes of Negative Angle Vertical Rotating Construction of the Pearl Bridge Figure 3 shows construction procedure of Pearl Bridge: first, the rotating hinges were set at arch springing and poured

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(a)

R = 4000 m T = 20 m E = 0.05 m

Wuchuan

Pengshui

135.2 3.6

12.50 3.6

16 Ă&#x2014; 8

588.000

0.5%

Bridge deck

-0.5%

588.000

9/2

9/2

1.75

Bridge deck

Pier 19.252

566.975

564.748

564.748

L0 = 120

0.7

2.1

Pier

1.133

4

19.252

F0 = 17.143

0.8

4

588.288

1.75

3.867 10/2

0.7

2.1

Bridge axial

3.867 10/2

Water level 476.300

(c)

3.465

3.07

0.3

10

3.465

3.867

0.25

0.3

1.133

Diaphrgam 0.25

0.25

0.25

2.1

10

2.1

(b)

Diaphragm

0.3

2.266

0.3

3.867

Fi g. 2: The arrangement of the Pearl Bridge (Units: m). (a) Bridge layout; (b) original design section for arch rib; (c) modiďŹ ed section for arch rib

vertically to the arch rib by taking advantage of the rocks beside the arch rib. Second, rotating construction of the arch rib was realised by a buckle cable set at the back of the bridge and a pulling cable set at the opposite bank.

Third, the arch ribs were closed after rotating into place. Finally, another arch rib was constructed, and diaphragms, bridge deck and piers were constructed once the two arch ribs were closed.

Rotating weight was 610 t and the theoretical rotating angle was 71.75 .

This article analysed the vertical pouring, rotation, closure process and other key construction processes in the following sections; however construction process of the bridge deck and piers is not mentioned as they are the same as the common construction methods of a concrete arch bridge.

The Negative Angle Rotating Construction Method Vertical Pouring for the Arch Rib A rotating hinge was set before vertical pouring. As a rock of 20 m height was present behind the arch springing, an arch rib of 18 m was constructed by stand pouring supported by the rock, and the arch rib was ďŹ xed to the rock by cable and bolt. This was done to avoid accidents caused by dead weight, wind load and earthquake.

The remaining portion of the arch rib

was constructed by hydraulic climbing formwork. From economy and safety perspective, the arch rib was divided into 15 segments and poured respectively (Fig. 4); the top surface of the diaphragm worked as the interface. In order to ďŹ x the formwork conveniently, the longest pouring length was 4 m and tilt angle was 18 .

In order to maintain the accuracy of pouring, the engineers arrived at an accurate calculation of coordinates for the arch rib axis. During construction, the largest deviations found in the onsite checking of the four semi-arches after pouring vertically and horizontally were respectively 17 and 16 mm.

Rotating Construction of the Arch Rib The rotating construction of the arch rib was the most crucial to the entire construction of the bridge (Fig. 5), which took place in two phases.

In the ďŹ rst phase, the referred rotation was from 0 to 15.93 . At the beginning of the rotation, gravity centre of the arch rib was more on the bridge deck, and rotation of the arch rib was achieved by tensioning the pulling cable on the opposite bank. Gravity centre of the arch rib was transferred to the other side of the rotating hinge when the arch rib was rotated to 3.58 .

Theoretically, the arch rib could rotate by its own dead weight and release the

Structural Engineering International Nr. 4/2017

buckle cable, but since there was a large tensile stress on the upper edge of the arch rib during rotation, the pulling cable would adjust its cable tension to improve the arch rib stress.

In order to reduce risk and facilitate construction, the buckle cable and the pulling cable should be conducted alternately, and a detailed theoretical calculation should be conducted to determine the tension of the pulling cable and the buckle cable during each construction procedure.

In the second phase the referred rotation was from 15.93 to the position where the arch ribs closed. As the pulling cable was dismissed, the arch rib could rotate under the work of its own dead weight and the releasing of the buckle cable; the bottom edge of the arch rib was under great stress when the arch rib was rotated to 20.90 . Additional bars were needed to reduce the stress as the arch rib was rotated further in the subsequent process.

Buckle cable force was greatly affected by the dead weight of the arch rib during rotation; if the actual weight of the arch rib differed greatly with its theoretical weight, the actual buckle cable force would differ greatly with its theoretical force as well. The difference could lead to misjudgment of the appropriate time to release the pull cable and tension bar; thus the concrete Technical Report

565

Closure Construction of the Arch Rib

(a) Cable saddle

Climbing–forwork Framing cast–in–situ Tension–stand for pulling cable

Tension–stand for buckle cable Hinge

(b) Buckle cable

Buckle cable

Pulling cable

Bar Hinge

Buckle cable

(c) Pulling cable

Bar Hinge

(d) Closure

Dismantle buckle cable

Dismantle bar Reinforcing arch springing

(e)

Closure of the arch ribs proceeded after they were rotated downward to the designed position. Many construction difficulties were involved, and one of them was the construction sequence including crown closure, changing twohinged arch into fixed-hinged arch, and removing the buckle cable and bar.

Reasonable construction sequence should be adopted based on theoretical calculation. The main procedures were as following.

• Closure of stiff skeleton (Fig. 6): Stiff skeleton was made of steel truss embedded in the closure segment.

Before the concrete achieved sufficient strength, the interaction of the stiff skeleton, buckle cable and bar allowed the arch to resist the wind load, dead load of the closure segment and temperature action.

• Pouring concrete of closure segment: Micro-expanded early-strength concrete was poured into the closure segment in order to compensate the shrinkage and creep during concrete curing.

• Removing the buckle cable and bar: After the concrete achieved sufficient strength, the buckle cable and bar were removed alternately.

Following this proper procedure, no cracks and tensile stress appeared.

• Pouring concrete of arch springing: Structural system transformation was completed by using microexpanded early-strength concrete to fix the hinges of the arch rib.

Bridge deck

Diaphragm

Diaphragms and piers were poured once all the arch ribs were closed.

Finally, bridge decks were built from the abutment to mid-span.

Pier

F ig . 3: Vertical rotation construction procedure. (a) Vertical pouring construction; (b) one side arch rib rotating construction; (c) the other side arch rib rotating construction; (d) arch rib closure construction; (e) spandrel structure construction

could crack due to excessive stress.

During construction of the Pearl Bridge, the solutions adopted were: • Reduce actual and theoretical weight difference of the arch rib.

• Measure buckle cable force, pulling cable force and spatial position of the arch rib many times at the beginning of rotation to calculate the actual weight of the arch rib, and modify the calculation model accordingly.

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During the vertical rotating process of the Pearl Bridge, two arch ribs upstream were rotated first; after closure of these two, the remaining arch ribs downstream were rotated. It took 28, 19, 20 and 26 h respectively to complete all the rotations. Horizontal alignment tolerance of the arch ribs which was vital to the success of the closure was 21 mm for the arch ribs upstream and 8 mm for arch ribs downstream.

Design of the Key Structure Structural form and mechanical behaviour of the key structural measures of the negative angle vertical rotating construction method are different from other construction methods; the design of the key structural measures such as vertical rotating hinges, buckle cable and pulling cable should ensure its reliability and economy.

Vertical Rotation Hinges Fabrication and assembly of vertical rotation hinges were vital to the successful closure of the arch ribs, which could not be laterally adjusted during

Structural Engineering International Nr. 4/2017

Fi g. 4: Vertical casting construction

the vertical rotation construction of the Pearl Bridge. The vertical rotation hinges, bearing the entire vertical load during the rotation process, must be strong enough to bear the exterior load and pass the load equally to the arch ribs and the base. The maximum bearing compression force of the vertical rotation hinges was about 9177 kN. Hinges were of the contact-type as the normal pin-type would fail to bear such a large pressure (Fig. 7).The 4 m long axis of the hinges was made of concrete ďŹ lled steel pipe (Ď&#x2022;800 Ă&#x2014; 20 mm). C50 (cube strength) concrete was poured into a 20 mm thick embedded arch steel board which was grouped as the axis base. Radius of the arch board was 801 mm. Welded steel pipe ďŹ lled with concrete was ďŹ xed to the hinge axis and anchored at the arch rib. Surface of the pipe was welded to the V-shaped steel bar to strengthen the anchorage.

The maximum compressive stress of the concrete of the axis base was 11.8 MPa while the maximum contact

F i g. 5: Arch rib rotation construction

stress of the arch steel board was 23.9 MPa. Buckle Cable Buckle cable, consisted of 22 steel strands with Ď&#x2022;15.2, and was the main bearing member during the rotation of the arch rib. One end was ďŹ xed to the top of the arch rib and the other end was anchored to the base of the buckle cable which was controlled by four sets of synchronous hydraulic jacks. Tension force and cable length of the jacks were both controlled by computer. Only a few steel strands were used at the beginning of rotation as the cable force was small; cable force was increased as the rotation went further, and more steel strands were added to meet the force needs.

Quantity of strands was increased three times during the whole rotation of the Pearl Bridge. First, it was increased to 20 from 10, secondly from 22 to 44, ďŹ nally the quantity was

increased to 88 from 44. The minimum buckle cable force was 260 kN and the maximum was 7709 kN during the whole rotation. The minimum tension of a single steel strand was 26 kN and the maximum was 88 kN. Length of the buckle cable and the vertical angle changed constantly during rotation of the arch rib. Since the anchorage angle of the jack was ďŹ xed, a cable saddle was set to make the buckle cable move freely. The steering cable of the Pearl Bridge was made of pulley block. Nine groups of pulley blocks were set on an arc with a radius of 4 m, and each pulley block comprised several small pulley blocks with 20 mm depth and 20 mm width V-shaped groove. With the V-shaped groove, each steel strand could be moved freely on its own, and adjusted individually so as to not mix up with others (Fig. 8).

Pulling Cable Pulling cable was not only the drive source for the arch rib at the beginning of the rotation but was also a safeguard measure to arch rib safety.

The pulling cable of the Pearl Bridge was made of a bundle of 10Ď&#x2022;15.2 steel strands. One end was anchored at the diaphragm of the arch rib, and the other end was ďŹ xed to a special tensile platform on the opposite bank. The pulling cable was tensioned by a 2000 kN jack and removed once the arch rib was rotated to 15.93 .The largest cable tension was 1222 kN while the smallest was 200 kN. Bars

Fi g. 6: Closure segment construction

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The positive moment of the arch rib increased as the rotation went downward. Every arch rib was supplied Technical Report

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g axis Startin

not only for rotating construction of steel concrete arch bridges but also for steel bridges and steelâ&#x20AC;&#x201C;concrete bridges. Climbing formwork and continuous jacks system are adapted in the development trend of bridge construction technology. With the widespread use and maturity of these technologies, construction cost will be largely reduced in the civil engineering industry.

71.

75°

xis

ga

t

si Po

Steel pipe

Hinge base

in ion

Stop

References

Concrete

[1] Yao C-R, Li Y-L, Liang D, Wang X-J. Structural type selection for long span bridges in mountainous region. Bridge Constr. 2012; 6: 81â&#x20AC;&#x201C;86.

F ig . 7: Vertical rotation hinge

[2] Liu J-P, Zhou K, Kunihiko N. Vertical rotating construction Kambara Valley Bridge.

World Bridges 2003; 3: 1â&#x20AC;&#x201C;4.

[3] Cheng F, Zhang Q-F, Wang J-Q. Current development and prospecting of construction techniques for bridge rotation erection in China. Railw. Stand. Des. 2011; 6: 67â&#x20AC;&#x201C;71.

SEI Data Block Owner: Wuchuan Bureau of Communications Designer: Design Institute of Civil Engineering & Architecture of Dalian University of Technology and Guizhou Provincial Bridge Engineering General Corporation F ig . 8: Buckle cable and cable saddle

with three sets of 6Ď&#x2022;15.2 steel strands as bars, and the bars were anchored at the diaphragm near the crown and arch springing. Tension of each steel strand was 800 kN. One bar was tensioned while the arch rib was rotated to 20.9 , and the other two bars were tensioned when the arch rib was rotated further to 31.1 .

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Technical Report

Contractor: Guizhou Provincial Bridge Engineering General Corporation

Conclusion The negative angle vertical rotating construction method surpasses other methods of bridge construction in valleys and mountainous areas where pre-casting facilities and construction site extent are limited. As a bridge construction technology, it is suitable

Steel (t) Concrete (m3) Construction cost (USD million)

458 5288 0.32

Service date

January 2010

Structural Engineering International Nr. 4/2017

Design and Construction of Concrete Simply-Supported Guideway Beam in the Changsha Maglev Line, China Gonglian Dai, Prof., Dr., Civil Eng.; Guorong Chen, PhD Student; Wenshuo Liu, Lecturer, Post Doctorate, School of Civil Engineering, Central South University, Changsha, China; Y. Frank Chen, Prof., Dr., School of Civil Engineering, East China Jiaotong University, Nanchang, China; Department of Civil Engineering, Penn State Harrisburg, Middletown, USA; Linghao Yang, MS Student, School of Civil Engineering, Central South University, Changsha, China. Contact: chengr93@163.com DOI: 10.2749/222137917X14881938991005

Abstract Changsha Maglev line is a low-speed magnetic levitation (Maglev) line for which traffic was opened in late December 2015. The simply-supported guideway beams (SGBs) of this maglev line adopted a rectangular cross-section. Cross beams were used to connect the SGBs for the first time in this bridge. In this paper, relevant design specifications, geometry of the guideway beam and the accelerated construction method are described. The performance of the SGBs was analyzed numerically and verified by a full-scale field test. The new form of the SGBs is found to perform well and to be costefficient.

Keywords: maglev; concrete simplysupported guideway beam; design specification; accelerated construction; numerical analysis; full-scale test.

Introduction A new transportation system can lead to a rapid social and economic development. In the past few decades, several innovative transportation systems including magnetic levitation (maglev) were introduced. There are two kinds of maglev trains: high-speed maglev (HSM) and low-speed maglev (LSM). A HSM train is suitable for long-distance travels, while a LSM train is more suitable for urban transportation.1,3,4 Comparing with subways and light rail systems (Table 1),5,6 the LSM line has the following advantages: (a) it is environmental friendly as it emits less noise and

Fi g . 1: General view of the Changsha Maglev line

consumes less energy; (b) it occupies less land space as it can travel along routes with smaller curve radius and steeper grades (Figs. 1 and 2) . Furthermore, it has better acceleration and deceleration processes, higher travel safety and lower implementation and maintenance costs than traditional railways. These features allow LSM to be a viable option for urban traffic transportation.

A LSM system is comprised of three parts: substructure, guideways and the train. A technical literature review on various maglev guideways was published in 2011.2 However, practical methodology for the design of a maglev guideway beam has not been publicly reported yet. Therefore, this paper attempts to fill this gap by presenting the relevant design specifications, geometrical properties and mechanical

Design speed (km/h)

Minimum curve radius at design speed (m)

Largest climb grade (‰)

Noise at 30 m (dB)

Changsha LSM

100

500

41

~0

35

Light rail

100

700

30

<70

30–45

Subway

100

700

30

~0

100

Table 1: Comparison of LSM, light rail and subway systems

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Cost (million USD/km)

performance of the Changsha Maglev guideway beam.

The Changsha Maglev line is located in the city of Changsha, China. Its total length is 18.55 km. The purpose of building this line is to provide a rapid transportation system between the city’s high-speed railway station and city’s international airport. The design service life is 100 years and the design speed is 100 km/h. It has two parallel guideways offering two-way traffic. In all, 942 pieces of precast concrete simply-supported guideway beams were used, which constitute 60% of the maglev guideways. Further discussion on the guideways follows.

Design Requirement and Load Models Requirements The maglev train has high demands by way of stability and smoothness of the guideways. In the Changsha line, the gap between the bogies and guide rail had to be maintained within 8 mm.

Any guideway irregularity would affect the safety and comfortability of the line. The related design requirements are summarized in Table 2.7 Technical Report

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F ig . 2: Features of the Changsha Maglev line

Content

Design requirement

Number of line

2

( ); and g the gravitational acceleration (m/s2).

Design requirement

Content Distance between lines

4.4 m

Vertical deflection limit

L/4600

Deflection limit due to temperature gradient

L/7600

Lateral deflection limit

L/4000

Beam end rotation limit

1‰

Deflection limit due to creep

5 mm

Natural frequency of guideway

no > 90/L

According to calculations, the minimum ϕ (on the convex curve) is −0.6 m/s2 and the maximum ϕ (on the concave curve) is +1.15 m/s2.

Transverse Live Load

Table 2: Design requirements

Vertical Live Load According to the design document provided by the maglev train manufacturer, the Changsha Maglev train is 48 m long, consisting of three 15 m long carriages.

Each carriage has five 2.8 m long bogies. Thus, when the train is suspended, each bogie would exert 2.8 m distributed load to the guideways. The static live-load patterns of Changsha Maglev are indicated in Table 3.7 Besides the static live load, the dynamic amplification factor, ϕ, should be taken

into account when calculating the live load. ϕ is determined by ϕ = 1:15 × ðΔaz + gÞ=g

ð1Þ

v2 sin⁡αcos2 β Rh

v2 cos⁡α− g + g⁢cos⁡β + −Rv

The centrifugal force of the LSM line is considerable as the curve radius is small. When rounding the curve, the centrifugal force acts above the guideway at the center of gravity of vehicle and it is calculated by: Fc = Fs ×

v2 127Rh

ð3Þ

ð2Þ

where Fc is the centrifugal force; Fs the static train load; v the design velocity (km/h); and Rh the radius of horizontal curve (m).

where v is the design velocity (m/s); Rh the radius of horizontal curve (m); Rv the radius of vertical curve (m); α the cross slope ( ); β the longitudinal slope

Another transverse force is caused by the oriented magnets on the straight line. This force equals 20% of Fs and acts as a horizontal distributed force toward the guideways.

Δaz =

Maglev train outline (single car shown): 25.8 kN/m

Full load levitating state when the cars are running:

2720

Full load standing state when the cars are in platform:

35 kN

25.8 kN/m

80 35 kN

2160

2720 35 kN

640

25.8 kN/m

80

2720

35 kN 35 kN

2160

640

25.8 kN/m

2160

2720

80 35 kN

35 kN

640

25.8 kN/m

80

2720

35 kN 35 kN

2160

640

35 kN

2160

Table 3: Static live-load patterns of Changsha Maglev line 570

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24940

2100

600

300 Middle cross beam

End cross beam

520

F-shape rail

5900

2N4 2N3 2N2 2N1

300

Diaphragm

Front view of ½ guideway beam

Cutaway view of ½ guideway beam

Fi g. 3: Front view and cutaway view (Units: [mm])

Guideway beam

1300

24940 Guideway beam 1

F i g. 6: Maglev track (Units: [mm])

Diaphragm End cross beam

5700

1300

3100

Middle cross beam

Diaphragm

Guideway beam 2

Fi g. 4: Plan view of the guideway beam (Units: [mm]) Tendon number

N1

N2

N3 1860

Elasticity modulus (GPa)

1.95 × 10

Corresponding tension stress (MPa)

1270

Stands diameter (mm)

15.20

N4

2

Beam Length(m) 20

4

4

4

4

22

5

4

4

5

23

5

5

5

5

25

7

5

5

7

Table 4: Information of prestressing tendons

Imposed Load The breaking force equals 15% of Fs; the wind velocity in Changsha area is 26 m/s, the temperature variation is 20 C and the seismic acceleration is 0.05 g.

Design and Construction Simply-Supported Guideway Beam Simply-supported prestressed precast concrete beams account for 60% of the guideway beams in this line. They were

fabricated in four different spans: 20, 22, 23 and 25 m. In order to simplify the construction, all simply-supported beams adopted the same rectangular section.

The front view and plan view of a 25 m guideway beam are shown in Figs. 3 and 4. The rectangular section is 2.1 m high and 1.3 m wide at the top and 1.4 m at the bottom. The top slab thickness is 240 mm uniformly and the floor slab thickness is 300 to 500 mm and the web thickness is 260 to 360 mm, varying from midspan to beam end, as shown in Fig. 5.

C50 concrete (fc = 23 MPa), HRB400

1300

240 350 360

1200

Middle cross beam End cross beam

Prestressing tendon

1400

1400 ½ Section in mid-span

360 2100

1200

80 300

The maglev tracks are placed above the guideway beams. The maglev

50

260 350

2100

Track

1200

260 Prestressing tendon

The two simply-supported guideways are connected by cross beams. The guideway system consists of four cross beams for 20 and 22 m spans and five cross beams for 23 and 25 m spans. The cross beams are made of precast reinforced concrete beams. The top of the cross beams is placed at 900 mm below the top of guideway beams. The end cross beams are 1.2 m high and 0.6 m wide, while the intermediate cross beams are 0.8 m high and 0.3 m wide.

All cross beams are tied with the diaphragms inside the guideway beams to reduce the shear force in the web of a guideway beam. The thickness of each beam-end diaphragm is 1.0 m, while it is 0.3 m for an intermediate diaphragm.

The addition of cross beams increases the vertical and lateral stiffnesses of both guideways, making them carry the loads together. Furthermore, the cross beams provide the support and space for the emergency channel.

1300 Cast-in-place joint

240

Diaphragm

(fyk = 400 MPa) and HRB300 (fyk = 300 MPa) reinforcement were used in the beams. Four pairs of post-tensioning prestressing tendons were set in each beam. The arrangement of the prestressing tendons is shown in Fig. 3. Other details of prestressing tendons are indicated in Table 4.

Cross Beam

Ultimate strength (MPa)

Amount of stands in tendon (m)

860 Steel sleeper Rubber plate Concrete support

Prestressing tendons

6050

1590

½ Section at beam end

Fi g. 5: Cross-section of the guideway beam (Units: [mm])

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F i g. 7: Emergency channel Technical Report

571

for maintenance and placement of electric cables. The emergency channel is connected to the cross beams also by high-strength bolts.

Rebar splices Cross beams

Construction of Cast-in-Place Joint

Guideway beam Step 1

Reinforcement of CCJs Step 2

Step 3

F ig . 8: Brief description of the construction of CCJs

connected together by high-strength bolts. The tracks are not made continuous so that they can be manufactured in the factory and installed onto the guideway beams, piece by piece. The gap between two adjacent segments of tracks is 20 mm. The design of the tracks is deemed practical and qualifies as an accelerated construction.

Emergency Channel F ig . 9: View of the prefabricated guideway beams Φ 28 mm Rebar

An emergency channel (Fig. 7) is provided between the two guideways, which is 3.2 m high and 1.1 m wide and consisting of two floors. The upper floor is intended for emergency rescue, while the lower floor is used

The guideways are a composite system consisting of two guideway beams and four to five cross beams (Figs. 3, 4 and 5). If the whole guideway system were fabricated in a workshop, difficulties associated with manufacturing, transportation, storing and installation would be encountered. Therefore, the construction solution adopted in this project was prefabricating each part of the guideways separately in a workshop and assembling them together by using the cast-in-place concrete joints (CCJs) after exerting them to the piers. A brief description of this construction method is shown in Fig. 8. The accelerated construction of the joints proceeded in this manner: 1. While fabricating the guideway beams, the rebar splices were embedded in the web of the beam.

One end of the rebar splices was connected with the internal reinforcement in the beams, while the other end was exposed outside of the webs (Fig. 8).

Φ 12 mm Rebar

Guideway 1

F ig . 10 : View of the prefabricated cross beam Emergency channel

Guideway 2 350 mm

F i g. 1 2: Finite element model for the 25 m guideways under live load Cast-in-place Concrete Joint Cross beam

Guideway 1

F ig . 11 : View of the concrete joints

track system differs from the traditional one. It consists of guide rails, steel sleepers, rubber tie plates, concrete supports and guideway beam (Fig. 6). The guide rail has an F-shape appearance and thus is referred to as F-shape rail. The F-shape rail, steel sleepers and guideway beams are 572

Technical Report

Deflection (mm)

0

Guideway 2

–1

–2

–3 0

4

8

12

16

20

24

Distance from beam end (m)

F i g . 1 3 : Deflections of the 25 m guideways under live load

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Reaction beam Self-balance system

Hydraulic jack

Pressure sensor Strain gauge Displacement meter

Fi g. 14: Test setup for 25 m guideway beam

Load (kN)

1500

1000

ω2 ω1 + ω2

ð4Þ

where γ is the LSF; ω1 the deflection of guideway 1; ω2 the deflection of guideway 2.

Live load

500

Full-Scale Test

0 0

2

4

6

8

10

12

Displacement (mm)

Fig. 15: Deflection versus load at mid-span 497kN 969kN 1180kN 1371kN 1625kN 1801kN 1974kN 2296kN 2591kN

2050

Section height (mm)

γ=

In the FE model, the joints are modeled as rigid connections and the live load is assumed to act on guideway 2. The calculated deflections of the 25 m guideways under the live load are shown in Fig. 13. According to the results, the LSF of the guideways is computed to be 0.665. This means that when the live load is placed on one guideway, the other guideway will carry 33.5% of the load.

The second time loading The third time loading The fourth time loading

2000

element (FE) analysis for the load sharing factor (LSF) of a 25 m guideway beam was performed (Fig. 12).

The LSF is defined as:

1500

1000

500

100 –250 –200 –150 –100 –50

0 50 Strain (µε)

100

150

200

250

Fi g. 16: Section load versus strain at mid-span

2. When the concrete of the guideway beams reached standard strength, some reinforcement of the CCJs were screwed into the web of the guideway beams through the rebar splices Fig. 9.

3. After the guideway beams and cross beams were exerted to the piers, the reinforcement of the CCJs were welded together and concrete was poured to fabricate the CCJs, as shown in Figs. 10 and 11.

The use of CCJs has been proven to make the prefabrication, trans-

portation and installation of the guideways much faster and more convenient.

Analysis and Experiment Load Sharing Factor As mentioned above, one important function of the cross beams is increasing the vertical and lateral stiffnesses of both guideways by making them carry the loads together, especially for the live load.

A three-dimensional (3D) finite

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In order to evaluate the actual performance of the guideway beams, a fullscale test of a 25 m beam was conducted on site (Fig. 14). The beam was manufactured at a maglev guideway factory and thus the quality was preserved. The testing system is shown in Fig. 14. The results show that under the live load, the mid-span deflection is 5.19 mm which meets the deflection requirement of L/4600 (or 5.28 mm) and no cracks appear under this working condition. The cracking load and the decompression load of the beam are 2300 and 1600 kN, respectively, both larger than the calculated respective values of 1800 and 1260 kN. The test beam end rotation is 0.649‰ which is below the limiting value of 1‰.The load– displacement graphs are shown in Figs. 15 and 16. The testing data show that the guideway beams are in the elastic state under live load and have a good margin of safety reserved.

Conclusions The Changsha Maglev line, which is fast, quiet, and elegant, has been under operation for more than a year.

The design specifications and the accelerated construction of guideway beams and cross beams are shown to be practical and reliable. The FE analysis and full-scale test indicate that the innovative guideways with rectangular section and cross beams meet the design requirements and have a good margin of safety reserved. The Technical Report

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cross

beams improve the stiffness and load capacity of the guideways.

Acknowledgements The authors would like to thank the National Natural Science Foundation of China (Project 51378503 and Project U13342023), Project of Science and Technology Research and Development Program of China Railway Corporation (Project 2015G001-K) and the Fundamental Research Funds for the Central Universities of Central South University (2017zzts151) for their financial support.

References [1] Zakeri JA, Yaghoubi H. Surveying advantages of magnetically levitated trains over high-speed railway trains. J. Transp. Dev. 2008; 12: 44–53.

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Technical Report

[2] Yaghoubi H, Ziari H. Development of a maglev vehicle/guideway system interaction model and comparison of the guideway structural analysis with railway bridge structures. J. Transp. Eng. 2011; 137(2): 140–154. https://doi.org/10.1061/_ ASCE_TE.1943-5436.0000197 [3] Hoopengardner R, Keever, D. FTA LowSpeed Urban Maglev Research Program LessonLearned. Report No. FTA-DC-26-7260-2009.01.

Federal Transit Administration, USA, 2009.

[4] Hoopengardner R, Thompson M. FTA Low-Speed Urban Maglev Research Program: Updated Lessons Learned. Federal Transit Administration, USA, 2012.

[5] China Railway Corporation. GB50157-2013 Code for Design of Metro China Building Industry Press: Beijing, 2013 (in Chinese).

[6] Ministry of Housing and Urban-Rural.

GB14892-2006 Noise Limit and Measurement for Train of Urban Rail Transit Standards Press of China: Beijing, 2006 (in Chinese).

[7] CRS Survey and D Group. Changsha Maglev Design Construction Drawing. China, 2014 (in Chinese).

SEI Data Block Owner: Changsha Metro Group Co., Ltd. Structural design: China Railway SIYUAN Survey and Design Group Co., Ltd. Main contractor: China Railway 23th Construction Bureau, Ltd. Concrete (m3): Steel (t): Total estimated cost (USD millions): Service date:

130 938 30 893 642 December 2015

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The Glass Fibre-Reinforced Polymer–Steel Hybrid Footbridge of Saint Mateus Park, Portugal: From Conceptual Design to In Situ Assessment Mário Sá, PhD, Civil Eng.; João Correia, Full Prof.; Augusto Gomes, Assoc. Prof., Instituto Superior Técnico, CERIS / DECivil – Department of Civil Engineering and Architecturey, Lisboa, Portugal; Nuno Silvestre, Assoc. Prof., Instituto Superior Técnico, IDMEC - Department of Mechanical Engineering, Lisboa, Portugal. Contact: mario.sa@tecnico.ulisboa.pt DOI: 10.2749/222137917X14881937845206

Abstract In the last two decades, the construction of pedestrian and road bridges using glass fibre reinforced polymers (GFRP) combined with traditional materials has notably increased. The potential of such hybrid structural systems stems from their ability to best exploit the mechanical properties of each constituent material. Pultruded multicellular deck panels have proved to offer innovation and competitiveness to the most recent hybrid panelto-girder systems. The high strengthto-density ratio of the decks’ crosssections, the low maintenance costs, the corrosion resistance together with the reduced installation times are particularly advantageous for footbridge applications. It was in this context that a GFRP-steel hybrid design was proposed for the construction of a pedestrian access to the St. Mateus Park in the city centre of Viseu, in Portugal.

This recently opened footbridge is a 13.3 m span and 2.5 m wide simply supported low-rise arch, comprising HEB steel profiles and a pultruded GFRP slab composed by 75 mm thick multicellular deck panels with full interaction between elements (studs fastened and epoxy adhesivelybonded). The footbridge design was developed with support of full-scale tests on deck panels and using current analytical and numerical tools, which have proven to be sufficiently accurate for this particular structural system. The lightness/slenderness and harmonious landscape integration over the St. Mateus Market contributed to the wide acceptance of the hybrid footbridge by both the Municipal Authorities and the population in general.

Keywords: hybrid footbridge; GFRPsteel structure; pultruded composite; multicellular deck panel; analysis models; construction; load test.

Introduction In recent years, glass fibre-reinforced polymer (GFRP) pultruded members have been increasingly used in structural applications of vehicular and pedestrian bridges, in both new construction and for rehabilitation.1 In particular, multi-cellular bridge deck systems have proven to offer innovative and competitive solutions, not only in terms of construction and structural features but also in terms of aesthetical aspects, due to the slender shapes of the typical cross-sections, high strength-toweight ratio, corrosion resistance and low maintenance costs.1,2 Moreover, the new joining techniques that have been developed also play an important role in the assembly operations of the deck panels3 as well as in their connection to supporting girders (steel/concrete), with significant improvements of the construction quality and reductions of the installation times.

All these aspects were critical for the acceptance of the GFRP–steel hybrid solution that was proposed to the Municipality of Viseu for the construction of a complementary pedestrian access to St. Mateus Park over the Pavia river (Fig. 1). Currently, this park is a cultural and lively urbanite space where the oldest market of the Iberian Peninsula is held during the months of August and September. In addition to quick installation requirements and minimal interference with the adjacent pedestrian zone, the river crossing and the urban/landscape integrations were also taken into account with regard to the architectural and structural design projects. The footbridge described in this paper establishes an infrastructural connection between two important centralities of Viseu, St. Mateus Park and Serpa Pinto Street, in-between two urban streets with a distance of about 200 m between them, thereby

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enhancing the crossing flow capacity of that park.

Concept and Structural Description The St. Mateus footbridge is a simply supported structure spanning 13.3 m, comprising two HEB 280 profiles 1.5 m apart and connected to a 75 mm thick pultruded GFRP slab composed of 19 multi-cellular deck panels (45 kgf each). The deck’s cross-section includes seven thinwalled cells (90 × 75 × 4 mm) with a length of 2.5 m in the pultrusion direction, covering the total width of the bridge deck. The deck is assembled by snap-fitting using asymmetrical interlocks along both edges of the panels, allowing for the easy installation of adjacent panels simply through vertical sliding movements (Fig. 2a). The basic structural concept of the hybrid superstructure lies in the structural contribution of the GFRP deck panels transversely oriented to the main bridge axis (Fig. 2b).

The steel girders have a total length of 13.6 m and are supported on steel pins, one fixed and the other sliding in order to avoid the stresses imposed by the action of thermal variations. At the support and third-span sections, four steel crossbeams (IPE.140) transversely connect the girders’ web, stabilizing the cross-section against torsional– distortional effects. The structure exhibits a low-rise camber (arch radius of 114 m) corresponding to a deviation of 203 mm. The metallic structure is made of hot-rolled S275-JR steel, with anticorrosion protection paint; all its joints are welded, forming a single structural steel part, characterized by a reddish hue aiming to highlight it from the surrounding urban environment.

The high longitudinal load-carrying capacity of the deck panel ensures the Technical Report

575

interaction exists on the cellular core of the decks; hence, it needs to be taken into account, namely, to reduce their in-plane mechanical properties.

F ig . 1: GFRP–steel hybrid footbridge of St. Mateus Park, Viseu

(a)

(b)

F i g. 2 : Virtual three-dimensional modeling: (a) deck assembly by snap-fitting and (b) hybrid footbridge

The architectural form chosen for the guard rails comprises various joined steel elements that follow the arched bridge in a ribbed shape without “touching” the composite deck. They are connected to the girder webs in sections that are stiffened internally by steel plates. The slope of the guard rails reduces the bridge’s free width by about 0.35 m. Being connected to the girders, they influence the structural performance of the footbridge, namely, the dynamic response, as their dead weight represents 13% of the entire bridge deck. It is also worth highlighting the slenderness and lightness of the final footbridge solution (4.6 t): the total height and distributed density are around 360 mm and 340 kg/m, respectively, with only 25% of the weight corresponding to the deck panels. A traditional pedestrian bridge solution (concrete/steel) is estimated to have weighed four to five times more than this hybrid structure.

Analysis and Design Methods transverse transmission of the loads to the main girders through both mechanical and adhesive joints. The former connection is used only at the joining panel-to-panel sections (snapfitting) by means of steel fasteners with no special requirements, whereas the latter corresponds to a 3 mm thick epoxy adhesive layer. Despite the

weaker load-carrying transmission of the deck panel in the longitudinal bridge direction, the panel-to-girder connection level provides a full interaction at the GFRP–steel interface.

The GFRP slab, subjected to longitudinal compression, behaves as part of the top chord of the main H-girders,1 although partial in-plane shear

(a)

(c)

(b)

(e)

(d)

F ig . 3: Full-size tests: (a) longitudinal bending, (b) transverse bending, (c) in-plane shear/ compression, (d) push-out and (e) longitudinal bending creep 576

Technical Report

To assess the safety of serviceability and ultimate limit states (SLS/ULS), static analysis and design of the footbridge was performed based on linear beam models and by considering the Eurocode (EC) principles, among other recommendations.4,5 However, given the specificity of the present innovative technology and the lack of consensual methods of analysis and design guidelines for these specific GFRP solutions, the static design was assisted by a comprehensive experimental campaign, as suggested in EC0. Besides extensive mechanical characterization tests on the GFRP laminated material, several short- and long-term full-scale tests were performed on the deck and its joining forms (panel-to-panel and panel-togirder connections), as seen in Fig. 3.

Table 1 summarizes the most relevant full-section mechanical properties obtained in terms of stiffness and strength.

To fulfil the SLS and ULS static design requirements, a live load of 5 kN/m2 was used to check the individual deck and the hybrid girders.

Taking into account the longitudinal responses of the deck assessed from the bending tests, a high deflection

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Loading/Property

E-modulus G-modulus Elastic stress Ultimate stress

Longitudinal bending

31.4 GPa

2.8 GPa

–

122 MPa

Transverse bending

10.3 GPa

–

2.8 MPa

3.6 MPa

In-plane

Compression

12.0 GPa

–

–

17 MPa

Shear

69 kPa

–

1.6 MPa

50 kPa

Flexural creep coefficient (50 years)

0.70

1.90

–

Push-out (per 3 mm hybrid interface)

K = 161 kN/mm

Fu = 50 kN

Table 1: Full-section structural properties of the deck panel

ratio of L/1340, including shear deformation and creep effects, was evaluated for the transverse span of the bridge, with the maximum stresses in GFRP at such SLS being very low.

Regarding the main axis of the footbridge, the maximum deflection and stress levels of the composite girders at SLS and ULS, respectively, were calculated based on the experimental in-plane/transverse properties of the panels. For this purpose, a static elastic method based on the design approach of EC5 was used assuming full composite action at the GFRP–

steel interface and partial shear interaction between the upper and the lower deck flanges, considering the flexibility of the web–flange joints of the deck (Fig. 4).

The design of the steel girders was governed mainly by the dynamic response of the footbridge (discussed below). The midspan deflection of the characteristic load combination was L/240. Due to the relatively low transverse in-plane stiffness and strength of the GFRP deck, the contribution of the pultruded slab to the equivalent beff

75 mm 3 mm

Upper flange panel (A1, E1, I1)

The footbridge design was also supported by three-dimensional numerical models developed with the finite element (FE) package SAP2000 using (1) shell (deck and girders), (2) joint rigid link (interface) and (3) frame (guard rails) FEs. The orthotropic deck walls were modelled according to the material characterization tests.

All analyses were linear-elastic. First, static analyses were performed aiming to assess the accuracy of the analytical methods used to calculate the deformations and maximum stresses of the footbridge components at SLS/ULS. The differences between analytical and numerical predictions were quite low for both limit states, up to 2%. It seems fair to claim that both design tools demonstrate good applicability, also corroborated by the good s1 (max)

e1 (max)

h1 GFRP deck

flexural properties of the hybrid girders was limited. For instance, the equivalent flexural stiffness and the elastic resistance increased by only 10 and 5%, respectively. For the present span, those ratios are not too different (≈2%) from those considering the actual in-plane shear flexibility of the cellular deck panel.

beff/n

Steel girder

358 mm

280 mm

–

h2

Bottom flange panel + HEB profile (A2, E2, I2)

e

Neutral axis z2

–

s

7 mm

+

+

z s2 (max)

e2 (max)

Fi g. 4: Stress and strain distributions in the midspan cross-section of the hybrid girder with partial shear interaction at SLS

1st mode Vertical bending f1 = 4.50 Hz

2nd mode Torsion f2 = 4.91 Hz

3rd mode Lateral bending f3 = 10.15 Hz

Fi g. 5: Modal identification by FE modeling

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Technical Report

577

(b)

×10–3 720

5

3 pedestrians walking slowly synchronized

600

Acceleration (m/s2)

480

Maximum acceleration (m/s2)

(a)

360 240 120 0 –120 –240

4 Exceptional comfort limit

3

2 Damping ratios 0.5% 2.0%

1

–360

1.0% 3.0%

0 5

10

15

20

25

30

35

40

45

50

0

0.5

1.0

1.5

2.0

Pedestraian density (P/m2)

Time (s)

F ig . 6: Accelerations evaluated from (a) the FE model and (b) analytically

agreement between those results and the experimental results obtained from the static load test.

Particular attention was given to the dynamic behaviour of the footbridge due to its overall slenderness/lightness together with the very specific characteristics of the deck’s pultruded

material, that is, deformable and with low damping2 (herein considered 0.5%). In addition, the behaviour of the footbridge under large pedestrian groups or even crowds needed to be analyzed due to the vicinity to the St. Mateus Market. Moreover, the first two natural frequencies of the footbridge were in the critical range for

(a)

(b)

F ig . 7: (a) Installation of the metallic structure using the mobile crane and (b) sliding pin support

(a)

(b)

vertical vibrations (less than 5.0 Hz, Fig. 5), thus requiring a thorough dynamic assessment. In fact, preliminary FE dynamic analyses of more flexible bridge solutions (with shorter HEB profiles), although fulfilling ULS and deformability SLS requirements (L/200 criterion),4 proved that human comfort criteria6 governs the design of this footbridge.

By applying load-time functions (1–3 pedestrians) to the FE model of the footbridge, the acceleration peaks were generally lower than 0.7 m/s2 (Fig. 6a), thus attesting its ability to ensure acceptable vibration levels under individual pedestrian actions.

However, their analytical (1-d.o.f. oscillator) assessment under resonance conditions showed excessive acceleration levels (>2.5 m/s2) for higher pedestrian densities according to the crowd models suggested in particularly SETRA guidelines,6 (c)

F ig . 8: Deck assembly: (a) application of adhesive, (b) fastening of threaded studs and (c) tightening of nuts 578

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Fi g. 9: Static load test

above 0.5 pedestrian/m2 and with damping below 1% (Fig. 6b). These estimates included the influence of the mass increase due to the pedestrians (increase limited to 30% of modal mass) and the guard rails (13% mass vs. 1% stiffness increases) on the reduction of the (critical) fundamental frequency.

Despite the general acceptance of those design guidelines for conventional footbridges (with traditional materials), in this case, they somehow seem to excessively overestimate the vibration levels by human-induced forces due to crowds; this is possibly due to excessive pedestrian density and/or synchronization effect for the bridge/span in question. In addition, such guidance procedures rely on modal parameters—namely, on damping, which is yet to be accurately determined for GFRP—and has great importance for the prediction/evaluation of the dynamic behaviour of footbridges.

Construction and Installation The construction of the footbridge involved some preliminary work for a 1 month period, most of which involved foundation work (reinforced concrete abutments) and exterior improvements (access ramps). The bridge deck was partially manufactured in a factory (80 km from the construction site), namely, the steel supporting structure whose components (crossbeams, internal plates and guard rails) were all welded to the two main girders previously arched by calendering. The metallic structure was then transported to the site inside a road trailer. In situ, a mobile crane helped position it above the river dikes, and subsequently, the top pin connections were inserted in their corresponding bases, which had been previously attached to the abutments using steel-threaded rods anchored to the concrete (Fig. 7).

Fi g . 10: St. Mateus footbridge illuminated at dusk

The assembly operations of the panels were carried out in the following sequence: (1) applying an epoxy adhesive layer over the top flanges of both main girders (cleaned and unpainted), (2) placing a panel over the girders and interlocking (snap-fit) to the previously connected panel, (3) drilling small holes in the other “free” end of the panel, (4) fixing threaded studs across the holes using a powder-actuated fastening tool, (5) tightening stainless steel nuts in the fasteners and (6) spreading epoxy adhesive along the snap-fit edge (Fig. 8). The use of such a mechanical fastening system did not demand strict control of drilling positions. Only 1.5 days were needed to install the entire bridge deck, which highlights an easy and fast construction process.

Lastly, the final elevation of the assembled bridge deck was still set in the supporting systems and a nonslip polymeric coating was applied over the deck’s surface. Architectural steel plates closed the footbridge at their ends without touching the handrails, and other constructive/finishing details were completed, namely, the lighting system (Figs. 1,10).

In Situ Static Load Test Before opening the footbridge to the public, a static load test was performed, in which the footbridge was subjected to uniformly distributed loading (Fig. 9). This test aimed to evaluate the global serviceability response of the hybrid structure under a load of 3.2 kN/m2 applied over a 2.5 × 7.8 m2 surface (corresponding to 55% of EC1 characteristic live load), materialized by a total of 183 cement bags (6405 kgf, each

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weighing 35 kgf ). Displacement transducers were placed underneath the girders to measure the midspan deflections.

The footbridge displayed an almost perfectly linear behaviour up to a deflection of L/390. For the maximum applied load, very similar deflections were measured in both girders, indicating that no relevant torsional deformations occurred. The corresponding deflections predicted (analytical: 30.8 mm and numerical: 30.5 mm), by considering partial shear interaction in the deck panels, slightly underestimated (≈8% lower) the experimental data, suggesting a slightly higher flexibility of the deck’s assembled cellular core . In any case, this experiment showed very reasonable accuracy of the prediction elastic models (1D/3D) used at the design analysis of the footbridge deck.

Conclusion In this paper, the development of the first GFRP–steel hybrid footbridge in Portugal (St. Mateus Park, Viseu) was described with regard to the following features: concept, analysis methods, construction and load testing. The bridge structure comprises a 13.3 m span low-rise arch with full interaction (mechanical and adhesive bonding) between multi-cellular GFRP deck panels and two steel H-girders. The study and design of the footbridge was performed with experimental support and using current modelling analytical and numerical tools that have proven to be accurate enough. The chosen panelto-panel (snap-fitting) and panel-togirder (fastening studs) connection systems showed great potential, allowing for an effective, easy and rapid installation. The lightness/slenderness of the Technical Report

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footbridge and its harmonious landscape integration over the St. Mateus market contributed to its acceptance by the municipal authorities as well as by the general citizens. Despite the excessive vibrations estimated based on available human-induced force models for crowd situations, and although large pedestrian groups seasonally cross the footbridge, no relevant vibration effects were reported since its opening (2 years ago) (Fig. 10).

Acknowledgements The authors thank CERIS and FCT for funding this investigation. The ďŹ rst author also gratefully acknowledges the ďŹ nancial support provided by FCT through the doctoral scholarship n SFRH/BD/42798/2007. This work was also supported by FCT, through IDMEC, under LAETA, project UID/EMS/50022/2013.

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References

SEI Data Block

[1] Keller T. Use of Fibre Reinforced Polymers in Bridge Construction, vol. 7 IABSE: Zurich, 2003.

[2] SĂĄ MF. Analysis of Pultruded GFRP Multicellular Decks Panelsâ&#x20AC;&#x201D;Application to Pedestrian Bridges. PhD Thesis, IST, University of Lisbon, Portugal, 2015 (in Portuguese).

[3] Park SZ, Lee SW, Hong KJ. Current and future applications of glass-ďŹ bre reinforced polymer decks in Korea. Struct. Eng. Int. 2010; 20(4): 405â&#x20AC;&#x201C;408.

[4] SIA 160. Effects of Loads on Structures.

Swiss National Standards, 1989.

[5] National Research Council of Italy. Guide for the Design and Construction of Structures Made of FRP Pultruded Elements. Advisory Committee on Technical Recommendations for Construction, CNR: Roma, 2008.

[6] SĂ&#x2030;TRA (Service dâ&#x20AC;&#x2122;Ă&#x2030;tudes Techniques des Routes et Autoroutes). Footbridgesâ&#x20AC;&#x201D;Assessment of Vibrational Behaviour of Footbridges under Pedestrian Loading. Technical Guide, 2006.

Owner: Urban Rehabilitation Society â&#x20AC;&#x201C; Municipality of Viseu, Portugal Contractor: VILDA â&#x20AC;&#x201C; Construção Civil, SA, Portugal Structural design: TĂŠcnico Lisboa â&#x20AC;&#x201C; DECivil, Dr. MĂĄrio Figueiredo SĂĄ Steel (kg) GFRP (kg) GFRP (kg/m2) Estimated cost (EUR thousand) Service date

3470 880 26 40 September 2013

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IABSE News IABSE Conference Kuala Lumpur 2018 becoming ever more ambitious, especially in the developing world, where they become showcases for nascent economies.

Engineering Innovations for Rapid Urbanization As the world becomes increasingly urbanized, technical innovation is paramount where urban constraints continually challenge designers.

Towards Achieving a Low Carbon Footprint The importance of achieving a low carbon footprint is already recognized in developed economies, however, are the same considerations being given in the developing world?

Night view of Kuala Lumpur with the Petronas Towers

Introduction

Keynote Speakers

The challenges facing engineering practices in the developing world is the core theme of the IABSE Conference Kuala Lumpur 2018. The huge growth in urban development, fuelled by dramatic economic development and fundamental changes to socio-economic structures and norms across the developing world, has left society and the required infrastructures with enormous challenges. As structural and civil engineers we are at the forefront of overcoming these obstacles and shaping the world that will evolve over the next century.

David A Nethercot Emeritus Professor of Civil Engineering, Imperial College London, UK

The IABSE Conference “Engineering the Developing World” will be held from April 25–27, 2018, IABSE Committee meetings will precede the event. The Scientific Committee, chaired by David Collings, is in the midst of receiving full papers for review, and is preparing the programme with the support of the Organising Committee, chaired by Paul Mullins. Authors who still wish to submit an abstract can do so via: www.iabse.org/kualalumpur2018.

Mike Schlaich Professor, Chair of Conceptual and Structural Design at the Technische Universität Berlin, Managing Director at Schlaich Bergermann Partner Datuk Ir Hj Ismail Bin Md Salleh Director General, Malaysian Highway Authority Congzhen Xiao Deputy Chief Engineer, China Academy of Building Research Dato’ Dr. Ismail Mohamed Taib Former Managing Director of Jambatan Kedua Sdn Bhd Ming Thein Commercial and industrial photographer

Themes and Topics Large-Scale Infrastructure Projects Regional and international bridge, tunnelling and structural projects are

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Harmonizing New and Old The integration of new with old is a challenge which requires sensitive consideration, especially in developing nations where often the gulf between the two can almost seem eternal.

The Future of Aesthetic Design Is there a future for aesthetics in design where cost increasingly becomes the only driving factor? This is an important question in rapidly developing economies, where it is oft left behind.

Young Engineers Programme Any author of a paper published at the Conference who is born after 1984 and who personally presents his paper at the Conference, will be considered for the Young Engineers Outstanding Contribution Award. An exclusive Young Engineers networking reception will be held on Tuesday, April 24, 2018, immediately prior to the Ice Breaker party which will open to all delegates at 20:00 hrs.

Technical Tours IABSE Malaysia will offer complimentary technical tours to the following sites. Places are limited and on a first come first served basis.

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IABSE News Venue and Accommodation

KVMRT SSP Line

KVMRT SSP Line Tunnelling Works Wednesday 25 April 2018, 13:30–17:00 The KVMRT SSP line will serve a corridor with a population of around 2 million stretching from Sungai Buloh to Putrajaya. It closely follows the KVMRT SBK line which opened earlier this year. The proposed alignment is 52.2 km of which 13.5 km is underground and to be constructed by tunnel boring machine. A total of 37 stations, 11 of them underground, will be built.

Construction is already well under way on the project. The tour will take delegates deep beneath the city centre to see the progress at the time of the conference.

The five-star Double Tree at Hilton will host the event. It is located in the very heart of the city, rising high from within the city centre. Here you will find the city’s best shopping malls, dining, entertainment and nightlife and the world famous Petronas Twin Towers close by. It is conveniently accessible to and from the international airport and adjacent to the Ampang Park Light Rail Transit.

Kuala Lumpur offers a wide variety of very affordable accommodation to meet any budget. Five star luxury to one star can all be conveniently booked in close proximity to the Conference venue.

Double Tree at Hilton which houses the conference facilities offers superior rooms with breakfast inclusive of all local and government tax at Ringgit Malaysia 400 (approx. EUR 80) a night.

FRIM Canopy Walk; Batik Painting & KL City Open Air Bus Tour; Jungle Trek; Tribal Experiences and Masak Masak Cooking Course; Old City Walking Tour; and Royal Selangor Pewter Tour.

Sponsorship/Exhibition Ranging from the Principle “Naming Partner” to the IABSE Conference Kuala Lumpur 2018 through Premium, Junior and Inventory Specific categories, there is a sponsor package to ensure all individual partner aspirations and budgets. A commercial exhibition will be held at the conference venue and will ensure multiple delegate interaction with exhibitors.

Potential sponsors and exhibitors should contact: pael@integer-asia.com or niggeler@iabse.org.

More Information: www.iabse.org/kualalumpur2018

KVLRT Line 3 Casting Yard Thursday 26 April 2018, 13:30–17:00 The proposed alignment is 37.7 km, which comprises 26 stations, 35 km U-shape viaduct and 2 km underground section, will run between the districts of Bandar Utama and Johan Setia to the west of Kuala Lumpur.

The full span precast U-shape viaduct system is the first to be used in Malaysia, with standard span length of 30 m.

The tour will explore the full span precasting method being implemented.

Merdeka PNB 118 Friday April 27, 2018, 08:30–12:00 Also presently under construction is Merdeka PNB 118, formerly known as KL118 or Warisan Merdeka. This is a 118 storey, 630 m mega tall skyscraper currently under construction in Kuala Lumpur, Malaysia. When completed in 2019, the tower will be the tallest building in Malaysia and the third tallest in the world. It will consist of 400 000 m2 of residential, hotel and commercial space. It will comfortably exceed the height of the 88 storey Petronas Twin Towers, the once tallest building in the world, and is only a short walk from the conference venue.

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100 MYR = approx. 20 EUR

Registration Registration for the Conference is now open, and can be accessed through www.iabse.org/kualalumpur2018. Several registration categories are available, Early Bird rates are offered until January 15, 2018.

Accompanying Persons The following programmes will be provided free of charge for Accompanying Persons at the following times:

Old town walking tour

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IABSE News IABSE in Vancouver 2017

Professor Maria Anna Polak

Over 800 structural engineering professionals descended on Vancouver this past September for the annual IABSE Symposium. A large and diverse gathering, the paper topics addressed innovations in design, construction, policy rules, design oriented research and theoretical research, and included papers that addressed issues of safety, aesthetics, materials and environment.

The symposium offered over 450 papers, which were presented in a variety of session formats. As well as the traditional format of presentations followed by questions, many sessions took up the IABSE mandate of promoting active participation and allotted extra time at the end of their session for an extended discussion of the topic at hand. Poster sessions started with short presentations, another effective innovation. The “Pecha–Kucha” format of fast “open topic” talks provided an entertaining addition to the program. This variety of formats made the symposium attractive and interactive. As well, there was ample opportunity for the conversations to continue outside the meeting rooms, over coffee at the break, at the ice-breaker, at a social networking evening and at the Gala dinner. The response of the participants was extremely positive. Everybody enjoyed the conference format, the fantastic venue and the many attractions that Vancouver has to offer.

The message of the symposium was “Engineering the Future”. Whereas it is the role of all engineers to look into

the future, for structural engineers it means ensuring the safety of new infrastructure, while at the same time promoting innovation, all with an eye to the aesthetics of what we build.

However, the future also includes the future of existing structures and the symposium also had sessions that addressed the very real challenges of structural monitoring, preservation and rehabilitation of existing and historic structures.

The future is also about the younger generations, the future engineers.

IABSE has always taken a very active role in promoting young engineers, and the Young Engineers program at the Vancouver symposium included a very successful networking evening for the young, and the young-at-heart.

In addition, there were awards for the best papers by young engineers, intended to support the new generation of researchers, which were selected under the leadership of Michael Bartlett.

This vibrant exchange of ideas that was so evident throughout the symposium was particularly gratifying for me. As the Chair of the Scientific Committee of the Vancouver Symposium, I worked closely with the lead group: Peter Taylor, Evan Bentz, Adam Lubell, Scott Walbridge and Colin Van Niejenhuis to construct a program that would energize our attendees, and encourage the kind of interdisciplinary conversations that happened. We decided to mix, in each session, research, design and case studies papers to promote interactions of practicing engineers and researchers. We are pleased that it was a success.

This is what makes the IABSE symposia so valuable. The Vancouver meeting attracted structural engineers from all over the world and gave them a much-needed forum in which to exchange ideas and to talk. Practitioners, researchers and policymakers were all there. This diversity makes IABSE a unique opportunity for the cross-pollination of ideas and the IABSE conferences and symposia are

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recognized internationally as the most important forums for such interactions.

This also creates a responsibility on the IABSE’s part to continue in this role as a facilitator of these conversations, and to constantly reinvent the way the organization works to ensure it continues. It is important to remain focused on the values that all this effort can bring to the profession. These values go beyond the papers published in the symposium proceedings. They include promoting structural engineering as a profession, encouraging innovations in design and construction materials, addressing the most pressing research directions, and showcasing bridges and other achievements in built infrastructure. It is during conferences like the IABSE Vancouver Symposium, combined with the pre-conference workshops and meetings, that IABSE reinforces its role as the vehicle that brings together its members so that they can meet in person and have an opportunity to present what they do professionally. This is where we make ourselves visible, as professionals who directly influence built environment. This is, after all, the built environment in which we all live; we pass by bus stops, drive on highways and bridges, work and spend our days in and around variety of buildings that we have designed and built. Our work shapes the world we live in, in a very tangible way.

When I reflect back on this “journey” of chairing the Scientific Committee of the IABSE Symposium in Vancouver, I am even more convinced that this was, and is, an important and useful task, as well as a personally rewarding experience for me. IABSE will go forward strengthened by the experiences at the Vancouver Symposium and continue in its role of promoting us, structural engineers, as creators of the environment in which we spend most of our time: the built environment.

Professor Maria Anna Polak University of Waterloo, Canada Chair, Scientific Committee IABSE Vancouver 2017

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IABSE News Vancouver Symposium: A Great Success!

Peter Taylor, Honorary Chair OC

Two days before the symposium, Vancouver presented itself under a sunny sky, inspiring great spirit for the upcoming event. The much awaited IABSE Symposium was ready to take off, with more than 800 delegates, from 40 countries.

Practitioners, researchers and policymakers including 200 young engineers, had come to Vancouver to actively discuss practical topics related to the structural engineering of buildings, bridges and other civil infrastructure. The 39th IABSE Symposium ‘Engineering the Future’ held from September 21-23, 2017, was exciting and very well prepared by the Organising Committee co-chaired by Katrin Habel and Adam Lubell, and the Scientific Committee chaired by Maria Anna Polak.

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The pre-conference days gave a foretaste of the spirit of great engagement and participation which continued during the symposium. Already before the big event, in parallel to the IABSE Annual Meetings, the wellattended pre-conference workshops were conducted: ‘Bridge Dynamic Response By Design’ (for Young Engineers), and three quite unique workshops on Seismic, Forensic and Timber Engineering. A lot of positive feedback was received from the participants who appreciated the enriching experience, and also the free distribution of SEI issues topically related to two of the workshops. On Wednesday evening before the Symposium, the Icebreaker was hosted by SEABC and the Canadian Group of IABSE. It brought together annual meeting delegates, workshop and conference participants who enjoyed exchanges over drinks and snacks in a relaxed atmosphere.

Next day at the Opening Ceremony Katrin Habel welcomed all participants to the Symposium. This was followed by a First Nations Greeting by Dennis Thomas, and a greeting by Jerry Dobrovolny, City Engineer of the City of Vancouver. Peter Taylor, Honorary OC Chair, gave a talk on ‘Canada on the Move’. Fernando Branco, President of IABSE, concluded the welcomes and the symposium was launched with the first keynote of Ronald Eguchi, President and CEO of ImageCat, inc.

Over three days, 450 papers were presented in 62 technical sessions, 2 poster sessions with short presentations, and 10 special sessions by technical organisations and commissions of IABSE. They were presented in various formats by an impressive roster of keynote presenters, panelists, and industry stakeholders representing design, research, construction, and socio-economic and political aspects of structural engineering.

Participants visibly enjoyed the different formats of the symposium, as they engaged in discussion at the end of the sessions. Lively discussions continued during coffee breaks in the Foyer and over seated lunch. In addition, the symposium app, not only provided all information needed, but also allowed participants to contact each other and to join conversation online in social media.

Keynote Speakers Ronald Eguchi, USA Measuring , Monitoring and Evaluating Community Resilience using Remote Technologies Gian Michele Calvi, Italy Sesimic Assessment and Rational Renovation of the Seismic Assessment and Rational Renovation of the Structural Heritage Peter Irwin, Canada Developments in the Wind Engineering of Tall Buildings

Icebreaker Party

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IABSE News

Discussion at session

At the Opening Ceremony

Yaojun Ge, China Challenge and Innovation of Long Span Bridges in China and over the World.

The Vancouver Symposium was a great success, the opinion of a participant is believed to be overall shared by many who attended and enjoyed the event “The IABSE Symposium in Vancouver provided a high quality professional environment for the international structural engineering community to meet, discuss, and learn. The pre-conference workshops, keynote speakers, and diverse presentations were excellent.

The conference had a strong international and local participation including many young engineers. IABSE proved itself as a true international organisation for all the structural engineers around the globe. IABSE rotating conferences, at least twice a year, from one corner of the Globe to another bonds the structural engineers worldwide as one international community with diverse

Pecha Kucha session

participation and presents excellent opportunity to advance and learn. Many thanks to IABSE Vancouver and all the hard working members of the Organising Committee, well done.”

Social Events On Thursday afternoon, after the last technical sessions ended a ‘Pecha–

Congratulating the Outstanting Structure Award Winners

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Kucha’ session was held, like in former years this was well attended, great fun and entertaining. Then the IABSE Awards were presented and later in the evening the awardees dinner was hosted by the President at a close-by waterfront restaurant. The conference delegates continued the evening at ‘Rogue Kitchen & Waterfront Station’ for a ‘Networking Social’ were young and old colleagues had the opportunity to mingle. On Friday evening, the Gala Dinner was held at the beautifully situated Vancouver Convention Centre West. Magnificent views over Burrad Inlet and the Northshore mountains were admired from the terrace over drinks and talks before being seated.

Later on, conference delegates and accompanying persons joined the After Party, which attracted many young and young-at-heart to the dance floor.

Apero before dinner at the Convention Centre IABSE News

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IABSE News couver Harbour was organised. Tour guest enjoyed a delicious meal complimented by lively story-telling and a stunning scenery. Many of the city’s important bridges were visited, such as the Ironworker’s Memorial Crossing, the Lion’s Gate Suspension Bridge, art deco Burrard Bridge, Granville street truss bridge, as well as the Cambie Street concrete bridge.

Participants at the coffee break

Viewing the Patullo and the Fraser River swing bridge

Closing Ceremony On Saturday, after Peter Irwin had given his keynote ‘Developments in the Wind Engineering of Tall Buildings’, the symposium came to its end.

At the well attended Closing Ceremony, conclusions on the symposium were drawn by the Organisers. Then Michael Bartlett presented the awards for the best contributions made by young engineers: Colin van Niejenhuis,

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Canada, for his paper “Experimental and analytical studies on the benefits of stainless steel rebar use in cracked concrete structures” and to Travis Thonstad, USA, for his paper “Pretensioned, Rocking Bridge Columns for Accelerated Construction and Enhanced Seismic Performance”. The Symposium was concluded with a speech by Fernando Branco and presentations for the next IABSE conferences 2018 in Kuala Lumpur and Nantes.

Symposium Report The Symposium Report will be available for purchase at www.iabse.org/ onlineshop.

Technical Tours After the Symposium many delegates participated in one of the three technical tours offered over the weekend.

On Saturday, a dinner cruise with sightseeing of the magnificent Van-

On Sunday, the tour ‘Bridges on the Fraser River’ was conducted on an authentic paddle-wheeler, cruising the Alex Fraser, the Pattullo; the SkyTrain Sky Bridge, The Port Mann and the Golden Ears bridges. Engineers involved in the design of the modern bridges were on tour and at hand providing technical background and sharing anecdotes from the design and construction challenges that were encountered. Lahja Rydberg Forssbeck, Sweden, who joined the tour shared:” It was interesting to learn on how public transportation is planned in Canada. The tour on Fraser River gave the opportunity to experience bridges of various kinds. The design and construction of three different cable stay bridges were very well presented by Peter Taylor (Thank you Peter!). The guide on the paddle boat presented to us the history and development of the life around the Fraser River. It was really interesting to hear how life and society needs have changed over the years and to realise important skills are at any time.”

An finally, those who had the opportunity stayed longer to join the Whistler Sea-to-Sky Adventure two-days tour from Sunday to Monday, exploring recent engineering projects and the incredible scenery along the Seato-Sky highway on rout to Whistler.

This tour was also accompanied by local designers sharing their insight on these structures.

Visit the Photo gallery at: www.iabse.org /Vancouver2017

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IABSE News IABSE Annual Meetings 2017 The Permanent Committee

The Annual Meetings of IABSE were held prior to the year’s Symposium, from September 19–20, 2017, at the Westin Bayshore Hotel and Conference Centre in Vancouver. Around 130 committee members and accompanying persons from around the world attended. The following meetings were held: Permanent Committee, Administrative Committee, Executive Committee, IABSE Strategy, Technical Committee, Working Commissions, Working Groups, SEI Editorial Board, SEI Correspondents, Bulletin Editorial Board, E-Learning Board, Chairs National Groups, Scientific Committees for Conferences, OStrA Committee, YEP Board, and the Foundation Council.

The PermC approved the annual statement of accounts for 2016 and the budget for 2018. The annual accounts for 2016 closed with total net revenues of CHF 904,561 (Swiss Francs) and an excess of revenues of CHF 79,372. The Association funds amount to CHF 175,521 as of December 31, 2016. For the year 2018 a budget with total net revenues of CHF 867,000 and an excess of revenues of CHF 23,800 were approved.

The PermC approved the revision of the By-Laws. The main change is due to the re-organisation of the Technical Committee which aims to streamline the technical activities of the association allowing flexibility for experts even outside structural engineering profession to contribute to the technical activities of IABSE. The following article on p.588, “IABSE Strategy Implementation Technical Activities”

by Christian Cremona, elaborates the the changes in detail.

elected the new Chair of the Technical Committee, Daia Zwicky, Switzerland, and re-elected the internal auditors Olivier Burdet and Kristian Schellenberg and substitute auditor Marion Rauch. The external auditor BDO was re-appointed.

The Royal Rowing Club, Vancouver

Social Events On Tuesday evening Fernando Branco, President of IABSE, welcomed delegates and accompanying persons for a reception at the Vancou-

Executive Committee At its meeting the Executive Committee (ExC) appointed Andrew J. Martin, Denmark, as the Vice-Chair of the Technical Committee. Elections and finances and other topics to be presented at the Permanent Committee (PermC) meeting were discussed. The decision was taken to outsource the production and distribution of SEI, to reduce costs and to increase visibility of the Association through the network of a commercial publisher.

The Executive Committee

From left to right, the new Vice Presidents: Ch. Cremona, C. Mendez-Galindo, S. Nakamura, L. Sun

Elections The PermC re-elected Vice Presidents Joseph Tortorella, USA, and YunMoo Koh, South Korea, for their second term (Nov. 1, 2017 until Oct. 31, 2021). Four new Vice-Presidents were elected for their first term: Christian Cremona, France; Carlos Mendez-Galindo, Mexico; Shunichi Nakamura, Japan; and Limin Sun, China. IABSE thanks the following Vice Presidents for completing their 2nd term and for their dedicated services rendered: Yaojun Ge, China; Julio Timerman, Brazil; and Akira Wada, Japan. The PermC furthermore

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ver Royal Rowing Club, well located at the waterfront in Stanley Park, where the wonderful view of the skyline of Vancouver City could be enjoyed. On Wednesday evening the Annual Meetings were rounded off at the Icebreaker party at the Westin Bayshore Hotel hosted by the Structural Engineers Association of British Columbia (SEABC) and the Canadian Group of IABSE. Here delegates from both the Annual Meetings and those registered for the symposium the had the opportunity to meet and enjoy the evening with live music.

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IABSE News IABSE Strategy Implementation Technical Activities • Structure production through Task Groups • Give Commissions a role of a forum • Establish an organisation based on structural engineering concerns • Re-connect Commissions and Groups.

are attached to Commissions. Their creation is free but is subject to several guidelines. Task Groups can be initiated

by Commissions, following an event, or by the interest of a group of persons.

Educational Activities

Objectives for Technical Activities Christian Cremona, France

This September, in Vancouver, the Permanent Committee has approved the modification of the IABSE By-Laws that reformats the organisation of the IABSE technical activities. This change is part of the new IABSE strategy implementation that was introduced 3 years ago during the Geneva Annual Meetings.

The objectives of IABSE are to promote at an international level the development of structural engineering through its various technical, societal, economic, aesthetic and environmental issues. These objectives shall be achieved by fostering a strong relationship between research and practice, by disseminating know-how through publications, international congresses and symposia, by producing recommendations, and by networking the structural engineering community.

Vision The vision for technical activities relies on the ambition to organise the production of technical activities around Task Groups and the steering around Commissions and Boards.

Task Groups and Commissions will respectively replace current Working Groups and Working Commissions.

The Technical Committee will play a role of binder between all Commissions and Boards to provide coherence and quality.

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Technical activities constitute the backbone of the IABSE vision and contribute to the association’s visibility. Promoting exchange of knowledge and practice of structural engineering worldwide requires to: • Organise conferences by itself or in collaboration with other organisations • Publish reports, periodicals and guidelines • Identify research and development needs • Initiate or/and support Commissions and Groups.

There are basically five types of technical activities: • • • • •

Educational activities consist of promoting dissemination through training and learning tasks. For this purpose a Training Board is set up and is intended to develop a Forum for the exchange of knowledge and experience in Structural Engineering through the IABSE website. In this respect, the Training Board supports all other committees of the Association and in particular promotes the exchange of knowledge and the advancement of structural engineering in the service of the profession and society. For this purpose, it organises e-learning, training activities, or any type of activities that will help to disseminate technical activities among students, lecturers and practitioners.

Publications Activities

Know-how activities Educational activities Publication activities Event activities Award activities.

Publications activities aim at checking the quality of the different IABSE publications. For this purpose two boards are set up: • SEI Editorial Board • IABSE Bulletin Editorial Board.

Know-how Activities Know-how activities consist of promoting cooperation and understanding among all those concerned with structural engineering. For this purpose, these activities are endorsed by Commissions and Task Groups.

Commissions (C) are intended to organise activities within their scope of expertise and to be a forum place.

They monitor the work done by Task Groups that are attached to them.

They also promote new Task Groups, disband inactive Task Groups. They report their activities and the activities of the attached Task Groups to the Technical Committee.

Task Groups (TG) are intended to produce deliverables (recommendations, special publication, workshop etc.) within a limited period of time. They

The SEI Editorial Board is responsible for the selection of technical contributions for the Association’s journal Structural Engineering International (SEI). It is seconded in this task by external reviewers who review articles submitted for publication in SEI and SEI Correspondents who contribute to SEI by providing information about interesting projects in their region.

The IABSE Bulletin Editorial Board takes care of all different types of publications, except for the journal SEI: • Case studies that can be specifically on design, rehabilitation, forensic among others • Monographs and guidelines • Technical reports that can include research publications.

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IABSE News Chair

Commission 1 Ch. + VC Core Members (6) TG Chairs

Commission 2 Ch. + VC Core Members (6) TG Chairs

Commission n Ch. + VC Core Members (6) TG Chairs

Vice Chair

Core Members (4)

TG1.1 Ch.+ VC + Members

TG1.n Ch. + VC + Members

TG2.1 Ch. + VC + Members

TG2.n Ch. + VC + Members

TGn.1 Ch. + VC + Members

TGn.2 Ch. + VC + Members

Technical Committee

Commission Chairs (6) SEI Edit. Board Chair

SEI Edit. Board Ch. + VC + Members

Bulletin Edit. Board Chair

Bulletin Edit. Board Ch. + VC + Members

Training Board Chair

Training Board Ch. + VC Core Members (4) E-learning Board Ch.

OPAC Chair

OPAC Ch. + VC + Members

OStrAC Chair

OStrAC Ch. + VC + Members

National Groups, or the Commission itself. Core Members are elected for a maximum of 4 times 2 years making the maximum term for all, 8 years.

Nominations for Task Group Chairs are made by IABSE Members, National Groups, or the Commission itself. Task Group Chairs are appointed by the Commission for a maximum of 4 years, but can be reappointed according to the Task Group rules.

Task Groups

E-learning Board Ch. + VC + Members

Ch. = Chair VC = Vice Chair TG = Task Group TG VC and Members

(IABSE Membership is not required.)

Organigram

Event Activities

Organisation

Event activities consist of supporting Scientific Committees of conferences organised by the Association. A Scientific Committee (SC) is established for each Congress and Symposium and set up by the Technical Committee. The SC is responsible for the selection of sub-themes, the type of publications, the choice of sessions, the selection of speakers and papers accepted for presentation and publication and the management of the sessions. A SC is dissolved upon completion of its tasks, which includes the submission of a follow-up report by the Chair of the Scientific Committee.

Technical Committee

The Technical Committee is also in charge to provide advice to the Executive Committee for co-sponsoring events.

The term for Chair and Vice-Chair is 4 years with no extension.

The Technical Committee consists of 4 Core Members, Commission Chairs, Board Chairs, plus Chair and Vice-Chair Chair of the Technical Committee is elected by the Permanent Committee.

The TC Vice Chair is appointed by the Executive Committee.

The four Core Members are nominated by the National Groups. They can be elected for a maximum of four times 2 years making the maximum term for all, 8 years. Elections for Core Members will be held every 2 years.

Commissions’ or Boards’ Chairs are ex-officio members.

Award Activities The Technical Committee sets up an Outstanding Paper Award Committee for selecting the two best papers published in the preceding year’s issues of the SEI journal under the categories Scientific Paper and Technical Report.

The Technical Committee sets up an Outstanding Structure Award Committee for selecting, in different regions of the world, some of the most remarkable and innovative structures completed in the year preceding the nomination.

Any new award created by the Executive Committee will be managed by the Technical Committee.

Commissions The Commissions consist of 6 Core Members, the Task Group Chairs plus Chair and Vice-Chair. Commissions are long term structures and encompass a broad range of topics.

Nominations for Chair and Vice-Chair can be made by the Commission itself or the Technical Committee. Elections for Chair and Vice-Chair will be held every 2 years and they are elected by the Technical Committee.

Nominations for Core Members can be made by IABSE Members,

Structural Engineering International Nr. 4/2017

Task Groups are not restricted in terms of number of members. Members can be non-IABSE Members, but the Chair and Vice-Chair are IABSE Members.

No election process is implemented for Task Groups.

TGs must not exceed a 4 years term and terms of references must be clarified in terms of achievements. After 4 years, extension will be approved by the Commission and the TC. A Task Group is endorsed by one or several commissions, depending on the targeted task.

Other Bodies The Outstanding Paper Award Committee is established every year by the Technical Committee in their Autumn Meeting. Each Commission and Task Group has the obligation to nominate one of its members (only IABSE Members for Task Group). The Chair will, preferably, be one of the Chairs of the Commissions or Task Groups.

The Outstanding Structure Award Committee is established by the Technical Committee in their Autumn Meeting. National Groups, Commissions and Boards can nominate one of its members. Election is made every 2 years. The Chair is appointed by the Technical Committee for a 4-year term with no re-election.

The E-learning, IABSE Bulletin and SEI Editorial Boards consist of a nonfixed number of members. Nominations for membership (IABSE Members only) are only made by these boards and can be made on a yearly basis. All nominations have to be approved by the Technical Committee every year. Members can be re-elected for a maximum of three times 2 years making the maximum term for all, IABSE News

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IABSE News 6 years. The Chairs of these bodies are appointed by the Technical Committee for a 4-year term with no re-election.

Implementation The new Technical Committee organisation will be set-up for the next IABSE meetings in Spring 2018. For this purpose, Champions have been appointed for each Commission to deliver their terms of reference. A first

draft of these terms of reference has been discussed during the last Technical Committee meeting in Vancouver and will be finalised for March 2018 in order to be endorsed by the Executive Committee no later than Spring 2018.

The new organisation does not affect the work of former Working Groups that are automatically transferred into Task Groups. The former Working Commissions require more attention and will be

transformed into Task Groups according to the activities they have currently carried out. Each Champion of the new Commissions and each Chair of former Working Commissions are in charge to secure this transfer process.

Christian Cremona Chair Technical Committee (Nov.1, 2013–Oct.31, 2017)

IABSE Conference Copenhagen 2018 ‘Engineering the Past to Meet the Needs of the Future’ Invitation and Call for Abstracts IABSE invites you to share your experience in operation and maintenance of bridges and other civil structures during a 2 day conference near Copenhagen, Denmark, during June 25–27, 2018.

As management of bridges and other civil engineering structures involves significant expenditures, at a time where public resources are constrained, it requires engineers, researchers and public and private agencies to choose solutions that are efficient in terms of reliability, availability, safety, health, economy and environmental aspects. It is therefore important to ensure that the latest advances in technologies and experiences are shared to ensure we meet the needs of the future.

experiences within the topics of operation and maintenance of bridges and other civil engineering structures.

who personally present their papers at the Symposium, will be considered for a best Young Engineers paper award.

Scientific Programme The Scientific Programme will include Plenary Sessions, Concurrent Technical Sessions and Poster Sessions, inviting submissions under the following themes and topics: • Management • Inspection and Maintenance • Safety.

Authors are invited to submit a short abstract (max. 300 words) of their paper by 20 November 2017, to www.iabse.org/Copenhagen2018.

Technical Visits As part of the conference, participants and their accompanying persons will be able to attend technical excursions covering a Bridge Tour in Copenhagen harbour and a site visit to the Fjord Link Frederikssund high bridge, a balanced-cantilever segmental bridge under construction.

The objective of the conference is to provide a forum for owners, operators, designers, researchers, contractors and suppliers to meet, discuss and exchange ideas and

Young Engineers Programme

More Information

All participants born in or after 1984 will benefit from a reduction in their registration fee. Young engineers,

Visit www.iabse.org/Copenhagen2018 for more information and details on the event.

Great Belt Bridge

Little Belt Bridge

Inspection

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IABSE News

Structural Engineering International Nr. 4/2017

IABSE News Calendar of Events 2018 April 25–27, Kuala Lumpur, Malaysia, IABSE Conference ‘Engineering the Developing World’ *2018 June 20–22 Madrid, Spain ‘IV International Conference on Structural Engineering Education Without Borders’ 2018 June 25–27 Copenhagen, Denmark IABSE Conference ‘Engineering The Past to Meet the Needs of the Future’ *2018 September 5–7 Yogakarta, Indonesia SCESCM 2018, ‘International Conference on Sustainable Civil

Engineering Structures and Construction Materials’ 2018 September 19–21 Nantes, France 40th IABSE Symposium ‘Tomorrow’s Megastructures’ Annual Meetings precede the Symposium *2018 October 28–31 Ghent, Belgium IALCCE 2018 ‘The Sixth International Symposium on Life-Cycle Civil Engineering’ *2018 November 24–28 Cairo, Egypt GeoMEast 2018 ‘International Congress and Exhibition’ ‘Sustainable Infrastructures: Structural Integrity’

Structural Engineering International Nr. 4/2017

2019 March 27–29 Guimarâes, Portugal IABSE Conference ‘Towards a Resilient Built Environment Risk and Asset Management’ 2019 July 24–26 Lisbon, Portugal ICSA 2019 ‘The 4th International Conference on Structures and Architecture’ 2019 September 4–6 New York City , USA IABSE Congress ‘The Evolving Metropolis’ Annual Meetings precede the Symposium *co-sponsored or supported by IABSE

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A matter of confidence.

Stressing of stay cables PAUL supplies s Prestressing installations incl. planning work s Anchor grips s Prestressing machinery (single-/multi-stressing jacks) s Strand pushing and cutting equipment s Automatic prestressing machines for railway sleepers s Prestressing equipment for bridge construction (prestressing cables and stay cables)

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www.paul.eu

Paul at YouTube stressing-channel.paul.eu

Max-Paul-Str. 1 88525 DĂźrmentingen Germany +49 (0) 73 71 / 5 00 - 0 +49 (0) 73 71 / 5 00 - 111 spannbeton@paul.eu

SEI Volume 27 | Number 4 | November 2017 Structural Engineering International

Yavuz Sultan Selim Bridge Turkey

STRUCTURAL ENGINEERING INTERNATIONAL

«I then design the structure down to the last details, since I believe that the quality of a structure hinges largely on these details.»

Volume 27 | Number 4 | November 2017

© Photo Credits: Photo Galery Soletanche Freyssinet / F.Vigouroux - 2017

International Association for Bridge and Structural Engineering (IABSE)

Eugène Freyssinet

IABSE

www.freyssinet.com

Recent Structures and Research Follow us on:

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