SEISMIC PERFORMANCE AND FORENSIC ANALYSIS OF A PRECAST CONCRETE HOLLOW-CORE FLOOR SUPER-ASSEMBLAGE
A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF
MASTER OF ENGINEERING AT THE
UNIVERSITY OF CANTERBURY BY
CAMERON MACPHERSON
UNIVERSITY OF CANTERBURY CHRISTCHURCH, NEW ZEALAND
2005
TABLE OF CONTENTS Abstract………………………………………………………………………………………...vi Acknowledgements…………………………………………………………………………... vii
1
INTRODUCTION………………………………………………………………………...1-1 1.1
Introduction……………………………………………………………………..1-1
1.2
Previous Relevant Research…………………………………………………… 1-3
1.3
Findings from Matthews (2004)………………………………………………...1-4
1.4
2
1.3.1
Origin of the Test Specimen Super-Assemblage……………………. 1-4
1.3.2
Loading System……………………………………………………... 1-5
1.3.3
Major Findings: Beam-to-Floor Slab connection…………………… 1-6
1.3.4
Major Findings: Lateral Frame-to-Floor connection………………... 1-7
1.3.5
Analytical Findings………………………………………………….. 1-8
Findings from Lindsay (2004) ………………………………………………… 1-9 1.4.1
Hollow-core Connection Details……………………………………. 1-9
1.4.2
Major Conclusions and Recommendations………………………... 1-11
1.5
Outline of this Thesis…………………………………………………………. 1-13
1.6
What is new and significant in this Thesis?…………………………………...1-15
1.7
References……………………………………………………………………..1-16
SUB-ASSEMBLAGE EXPERIMENTAL INVESTIGATION…………………………… 2-1 Section Summary………………………………………………………………………..2-1 2.1
Introduction……………………………………………………………………..2-2
2.2
Previous Research Findings and New Zealand Guidelines……………………. 2-3
2.3
Test Specimen Details………………………………………………………... 2-11
2.4
2.3.1
Specimen 1………………………………………………………….2-11
2.3.2
Specimen 2………………………………………………………….2-12
Beam Elongation……………………………………………………………... 2-13 2.4.1
Sub-Assemblage Elongation……………………………………….. 2-15
2.5
Experimental Set-up…………………………………………………………...2-17
2.6
Experimental Results: Specimen 1…………………………………………… 2-20
2.7
Experimental Results: Specimen 2…………………………………………… 2-23
Page i
2.8
3
Strength and Failure Mode Prediction Models……………………………….. 2-28 2.8.1
Moment Capacity…………………………………………………...2-28
2.8.2
Low Cycle Fatigue…………………………………………………. 2-29
2.9
Discussion of Results…………………………………………………………. 2-30
2.10
Conclusions……………………………………………………………………2-32
2.11
References……………………………………………………………………..2-32
SUPER-ASSEMBLAGE EXPERIMENTAL INVESTIGATION………………………… 3-1 Section Summary………………………………………………………………………. 3-1 3.1
Introduction……………………………………………………………………..3-2
3.2
Findings from Previous Research……………………………………………… 3-3
3.3
Super-Assemblage Specimen Design Details and Construction………………. 3-6
3.4
3.5
3.3.1
Hollow-core Seating Details………………………………………… 3-6
3.3.2
Lateral Connection and Diaphragm Reinforcement………………….3-8
3.3.3
Super-Assemblage Construction……………………………………. 3-9
3.3.4
Material Properties………………………………………………….3-11
Experimental Set-up…………………………………………………………...3-12 3.4.1
Instrumentation…………………………………………………….. 3-12
3.4.2
Loading Protocol…………………………………………………... 3-16
Experimental Observations…………………………………………………… 3-17 3.5.1
Phase 1: Longitudinal Loading…………………………………… 3-17
3.5.2
Phase 2: Transverse Loading………………………………………. 3-19
3.5.3
Phase 3: Longitudinal Re-Loading………………………………… 3-20
3.6
Hysteretic Performance and System Strengths……………………………….. 3-23
3.7
Discussion of Results and Effectiveness of Design Changes………………… 3-25 3.7.1
Transverse Beam Torsion………………………………………….. 3-25
3.7.2
Hollow-core-to-Supporting Beam Connection…………………….. 3-29
3.7.3
Supporting Beam Detailing Enhancements………………………... 3-30
3.7.4
Moment Timber Infill Connection and Diaphragm Reinforcing…... 3-31
3.7.5
Displacement Incompatibility……………………………………… 3-32
3.8
Conclusions……………………………………………………………………3-34
3.9
References……………………………………………………………………..3-35
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4
FORENSIC ANALYSIS OF FAILURE AND BEHAVIOUR MODES………………….. 4-1 Section Summary………………………………………………………………………. 4-1 4.1
Introduction……………………………………………………………………..4-2
4.2
Torsional Behaviour of the Transverse Support Beams……………………….. 4-4
4.3
4.4
5
4.2.1
Determination of the Torsional Demand……………………………. 4-9
4.2.2
Transverse Beam Torsional Capacity……………………………… 4-12
Displacement Incompatibility………………………………………………… 4-14 4.3.1
Identified Issues and Previous Findings…………………………… 4-14
4.3.2
Analytical Modelling of Displacement Incompatibility…………… 4-17
4.3.3
Scope for Future Advancements…………………………………… 4-19
Lateral Load Capacity of the System………………………………………….4-20 4.4.1
Bowstring Effect…………………………………………………… 4-21
4.4.2
General System Strength…………………………………………... 4-26
4.4.3
Localised Strengths………………………………………………… 4-28
4.5
Beam Elongation……………………………………………………………... 4-31
4.6
Low Cycle Fatigue of the Reinforcement…………………………………….. 4-33
4.7
Comparisons with Previous Research………………………………………... 4-34 4.7.1
Performance of the Seated Connection……………………………..4-35
4.7.2
Performance of the Perimeter Frame to Hollow-Core Connection... 4-37
4.7.3
Overall Performance Comparisons………………………………… 4-38
4.8
Conclusions……………………………………………………………………4-40
4.9
References……………………………………………………………………..4-41
CONCLUSIONS AND RECOMMENDATIONS………………………………………... 5-1 5.1
Summary……………………………………………………………………….. 5-1
5.2
Conclusions……………………………………………………………………..5-2
5.3
Recommendations for Professional Practice…………………………………... 5-5
5.4
Recommendations for Future Research………………………………………... 5-7
5.5
References………………………………………………………………………5-9
Page iii
APPENDIX A – SUB-ASSEMBLAGE EXPERIMENTS: CONSTRUCTION & RESULTS...A-1 A.1
Construction Details and Photographs………………………………………… A-1
A.2
Material Tests…………………………………………………………………..A-5
A.3
Testing Photographic Log……………………………………………………... A-1 A.3.1
Experiment Set-up and Instrumentation……………………………. A-6
A.3.2
Specimen 1………………………………………………………….. A-7
A.3.3
Specimen 2………………………………………………………….. A-8
A.4
Loading Protocol……………………………………………….......................A-10
A.5
Low Cycle Fatigue Prediction………………………………………………...A-11
A.6
References……………………………………………………………………. A-12
APPENDIX B – SUPER-ASSEMBLAGE CONSTRUCTION PHOTOGRAPHS AND DESIGN DETAILS…………………………………………………………………………………….B-1 B.1
Building Construction Drawings……………………………………………….B-1
B.2
Building Construction Photographic Log……………………………………. B-20
APPENDIX C – SUPER-ASSEMBLAGE TESTING AND PHOTOGRAPHIC LOG……….. C-1 C.1
Material Testing………………………………………………………………...C-1 C.1.1
Reinforcement Testing……………………………………………… C-1
C.1.2
Concrete Testing……………………………………………………. C-3
C.1.3
Hollow-core Properties……………………………………………... C-4
C.2
Instrumentation Photographs………………………………………………….. C-5
C.3
Testing Photographic Log……………………………………………………... C-7
C.4
C.3.1
Phase 1: Longitudinal loading……………………………………….C-7
C.3.2
Phase 2: Transverse loading………………………………………... C-9
C.3.3
Phase 3: Longitudinal re-loading………………………………… C-10
C.3.4
End of Testing……………………………………………………... C-13
Concrete Topping Delamination……………………………………………... C-14
APPENDIX D – ANALYTICAL RESULTS………………………………………………... D-1 D.1
Yield Drift Calculation…………………………………………………………D-1 D.1.1
Beam Contribution………………………………………………….. D-1
D.1.2
Beam Column Joint Contribution…………………………………... D-2
Page iv
D.1.3
Column Contribution……………………………………………….. D-2
D.2
Super-Assemblage Stiffness……………………………………………………D-4
D.3
Torsion Test…………………………………………………………………… D-5
D.4
General Super-Assemblage Performance……………………………………... D-6
D.5
D.6
D.4.1
Central Column Joint Reinforcing Bar Slip………………………… D-6
D.4.2
Hollow-core floor unit pull-off……………………………………... D-8
D.4.3
Beam Column Joint – Rotation Contributions…………………….. D-10
D.4.4
Reinforcement Strain Information…………………………………….D-12
West Transverse Beam Torsion……………………………………………… D-18 D.5.1
Experimental Results……………………………………………… D-18
D.5.2
Calculation of Torsional Demand…………………………………. D-19
D.5.3
Calculation of Torsional Capacity………………………………… D-20
Displacement Incompatibility………………………………………………... D-23 D.6.1
Experimental Results……………………………………………… D-23
D.6.2
Analytical Modelling……………………………………………… D-28
D.7
Beam Elongation……………………………………………………………...D-31
D.8
Low Cycle Fatigue Fracture of Reinforcement……………………………… D-34
D.9
Observed Bowstring Effect…………………………………………………... D-36
D.10
Super-Assemblage Capacity Mechanism Calculations……………………… D-38
D.11
D.10.1
Phase 1 and 3: Longitudinal ……………………………………... D-38
D.10.2
Phase 2: Transverse……………………………………………….. D-40
References……………………………………………………………………. D-46
Page v
ABSTRACT Recent earthquakes and laboratory research has demonstrated the seismic vulnerability of buildings constructed with precast prestressed concrete hollow-core floor systems. However, further investigations have shown that with simple detailing enhancements, significant improvement in the seismic performance of hollow-core floor systems can be expected. The New Zealand Concrete Structures Standard provides two “acceptable solutions” for the connection of hollow-core floor units to concrete supporting beams (Amendments to NZS 3101, 2004). The second of these “acceptable solutions” is currently untested, and the present experimental investigation aims at validating this solution as well as several other new detailing enhancements. Two dimensional sub-assemblage component experiments are conducted utilising a newly developed, more realistic loading configuration. Based on the sub-assemblage research findings, a concrete frame super-assemblage is constructed incorporating a reinforced connection that rigidly ties the floor into the supporting beam and an articulated topping slab cast onto a timber infill solution that bridges between the hollowcore units and parallel longitudinal frame beams. The full-scale structure is cyclically tested in both the longitudinal and transverse directions to inter-storey drifts of ±5%. Visual and instrumental observations from the experiment are presented and discussed. A forensic analysis of the experimental observations is performed. Torsional hinging behaviour that is observed due to a strong floor-to-beam connection and weak support beam is explained and experimentally observed displacements are compared with computational modelling. The lateral load capacity of the super-assemblage is predicted and it is seen that it is necessary to incorporate all sources of strength enhancement. Finally, the results from this present investigation are compared and contrasted with similar previous research investigations and recommendations for the forthcoming revision of the New Zealand Concrete Standard, NZS 3101, are made. The experimental observations demonstrate that with appropriate detailing enhancements there can be significant seismic behaviour improvements whereby a relatively fragile hollow-core flooring system is transformed into a robust frame-floor system where all the damage is transferred into the plastic hinge zones of the supporting moment resisting frame.
Page vi
ACKNOWLEDGEMENTS This research was undertaken in the Department of Civil Engineering, at the University of Canterbury under the supervision of Professor John Mander and Professor Des Bull. I would like to thank John and Des for their support, encouragement, expertise and guidance throughout this research and my university studies. This project would simply not have been possible without the support of many companies and organizations. Financial support has been made for this research by a grant from the EQC Research Foundation. Products and support were provided by the following organisations: University of Canterbury, Firth Industries Ltd, Stresscrete, Pacific Steel and Fletcher Reinforcing, Construction Techniques and McDowels Concrete Accessories. All of this financial and in-kind support is gratefully acknowledged. Jeff Matthews and Renee Lindsay, from whom this research has continued on from, deserve enormous amounts of thanks. Their friendliness, knowledge and experience from their studies have helped me considerably. Jeff and Renee’s high standard of work has also set high qualities for me to aspire to. I would like to thank John Trowsdale for his support throughout my research, and acknowledge his work on the sub-assemblage part of this project. John’s practical expertise and friendliness were invaluable in completing the experiments. I would also like to thank my fellow postgraduate students for their friendship and understanding of postgraduate life. Full credit must go to all of the technical staff of the Civil Engineering Department. I am thankful for everyone’s helpfulness and guidance. I would like to give special thanks to Russel McConchie, Nigel Dixon, Tim Perigo and Richard Newton for the amount of effort they have put into my research and for all of their support and friendliness that made my experimental work so enjoyable. I would also like to thank Dr Stefano Pampanin for his guidance, expertise and encouragement. I have learnt a lot from Stefano throughout my postgraduate studies. Finally, I would like to thank my friends and family for all the love and support and most especially, Ryoko for her guidance, patience and support throughout my time at university.
Page vii
1.
1.1
Section 1 – Introduction
INTRODUCTION
Recently, precast concrete construction has become the conventional form of construction in New Zealand. The ease of construction, rapid erection times and the appeal of the off-site construction and factory-like controls available in the precast, prestressed industry are reasons for its popularity. Since the 1980’s, one of the most common construction types in New Zealand has been the use of precast prestressed hollow-core floor units seated on reinforced concrete moment resisting frames. However, the proliferation of precast concrete construction has preceded research in many areas and there are concerns over the seismic performance of these hollow-core floor systems in New Zealand. The possibility for the loss of seating to occur, lack of composite bond strength with the topping concrete, cracking of the webs of the hollow-core units and the general lack of structural redundancy have been highlighted as main factors that could lead to poor performance and collapse of several precast concrete buildings. Over the last few years, research at the Universities of Auckland and Canterbury has sought to investigate the seismic performance of these precast systems and the level of seismic vulnerability of New Zealand buildings. Recently, research was conducted to fully assess the adequacy of a typical New Zealand designed and built concrete structure with hollow-core floors (Matthews, 2004; Matthews et al, 2003, 2004). A full-scale three-dimensional section of a common New Zealand multi-storey concrete frame building with hollow-core floor units was constructed. Traditionally, research effort has either focused at a structural component level or at investigating lateral load resisting systems, and the effects of floor diaphragms have often been overlooked by the simplification of the rigid diaphragm assumption. The results from the
Page 1-1
Matthews (2004) experiment showed that precast concrete structures in New Zealand may not perform as well as would be hoped and the collapse of floors could be expected. The overall collapse of the floor units during the experiment showed similar traits to some failures observed after the Northridge (1994) earthquake (Norton et al, 1994), and the main concern became the detailing used for the connections of the hollow-core floors to the concrete frame. The investigation into the seismic vulnerability of existing buildings provided several questions requiring immediate answering. In particular, new solutions needed to be obtained for future construction, the retrofit of existing structures with hollow-core floors, as well as further investigations into the problems. The issues surrounding the use of prestressed floors that have stemmed from the Matthews (2004) experiment, previous research and earthquake events, have been recognised in New Zealand Concrete Design Standards. Specific requirements are in place prescribing minimum seat widths and different connection solutions that will address the shortcomings highlighted with traditional construction methods – however it is important to verify design standard details analytically and experimentally. In response to the Matthews (2004) testing a repair was carried out on the concrete superassemblage and second phase testing was undertaken by Lindsay (2004) and Lindsay et al (2004). This experiment investigated improved connection details for the hollow-core floor systems for new construction that have been included in proposed amendments to the New Zealand Concrete Design Standard (NZS 3101, 2004). This thesis follows the research completed by Matthews (2004) and Lindsay (2004). This chapter initially briefly discusses the previous sub-assemblage and super-assemblage research related to hollow-core floor systems. A summary of the Matthews (2004) and Lindsay (2004) experiments is provided, including the origins of the test specimen, the development of the loading system, and a review of the main test findings. The main sections of the thesis are then outlined.
Page 1-2
1.2
PREVIOUS RELEVANT RESEARCH
The performance of hollow-core floor systems has been examined in many experimental programs at a two-dimensional sub-assemblage level. Meija-McMaster and Park (1994), Herlihy et al (1995), Oliver (1998) and Herlihy and Park (2000) have all examined the seat requirements of hollow-core floor units due to beam elongation for a variety of end connection details. Further research by Bull and Matthews (2003) and Liew (2004) have similarly tested various connection details, but introduced the relative rotation between the floor slab and supporting beam as the main cause of damage. A more in-depth summary of previous research is located in Section 2 of this thesis. There have been many super-assemblage research programs relevant to this project involving concrete frame structures with and without floor slabs. Zerbe and Durrani (1989, 1990), Fenwick and Megget (1993), Restrepo (1993), Fenwick et al (1995) and Lau (2002) have conducted tests examining beam elongation and the contribution of floor slabs to the overall performance and strength of lateral load resisting elements. However, due to the respective test set-ups used, beam elongation has been either promoted or restrained and the results were not realistic. Despite sub-assemblage research previously investigating hollowcore seating connections, prior to the Matthews (2004) investigation, a full-scale experiment examining the seismic adequacy of hollow-core floor systems had not been undertaken. The need for these tests is due to three-dimensional effects, such as beam elongation, torsion and displacement incompatibility between the perimeter concrete frames and flooring, which all must be present to ensure realistic performance is represented. The particular issue of displacement incompatibility has been acknowledged as a source of damage (Lau et al, 2002 and Priestley et al, 1999), but little quantitative research has been done to explore the issue.
Page 1-3
1.3
FINDINGS FROM MATTHEWS (2004)
Owing to the widespread use of hollow-core flooring in precast concrete construction, an experimental program was initiated to examine the seismic adequacy of such systems in the New Zealand building stock. A two bay by one bay concrete moment resisting frame performed relatively well whereas the hollow-core flooring system behaved poorly and collapsed at moderate levels of seismic intensity. The following subsections briefly describe the origin and details of the super-assemblage including the seated and lateral connections of the hollow-core floor units, the development of the self-equilibrating load frame and the main observations and analytical results from the experiment.
1.3.1
Origin of the test specimen super-assemblage
The super-assemblage is a one-storey corner segment of a typical multi-storey precast concrete moment resisting frame building built in New Zealand over the last two decades. Figure 1-1 shows a view of a representative structure from which test specimen was derived from. The corner section was chosen to examine the effects of earthquake actions in different directions - longitudinally as well as orthogonal to the span of the flooring system. The bay widths were 6.1m long and the 300 series hollow-core flooring spans over two bays past an intermediate column and is seated on the two end beams. Although this type of construction whereby the double span flooring is present is not the most common form, it was chosen to investigate a worst-case scenario. Buildings of this type have been constructed in Wellington, which is a high seismicity region of New Zealand, whereas the use of double span hollowcore is less frequent in Auckland and other regions of New Zealand. For these reasons, the layout of super-assemblage has been questioned (O’Grady, 2004). As the following descriptions of the findings from the Matthews (2004) test will indicate, the serious
Page 1-4
inadequacies of the hollow-core flooring were centred on the supporting beam-to-slab connection, which is irrespective of the hollow-core span.
Selected portion to be tested
Figure 1-1 Selection portion representing the test super-assemblage (Matthews, 2004)
1.3.2
Loading System
An integral part of the Matthews (2004) experimental program was the development of the loading frames. As a strong wall or strong floor was unavailable to provide reaction support for loading, a self-equilibrating load frame was constructed to load the structural superassemblage. The loading frames were designed and implemented such that under lateral loading, the building deforms in a realistic manner and that the advent of beam elongation is neither restrained nor promoted. The self-equilibrating primary loading frame is shown in Figure 1-2. By controlling the actuators within the loading frame, equal and opposite diagonal loads are applied to the tops and bottoms of the columns ensuring that the system is in equilibrium (no axial forces are induced in the beams) and that axial forces cancel within the system. To ensure that the columns displace parallel to each other as they would in a real building, a secondary load frame (SLF) was used. The frame, as shown in Figure 1-2, acts to keep the columns parallel to each other but also allows beam elongation to occur through a
Page 1-5
reduction of the initial angle of the frame. The design of the loading frames and test specimen allows the super-assemblage to be tested in both longitudinal and transverse directions. For longitudinal loading, additional rams are attached at the base of the back columns to maintain the same column inclinations and ensure that any artificial torsion in the transverse beams does not occur. Secondary loading frame
Secondary loading frames
Ac tua
tua Ac Primary Loading frame
B tor
D
tua Ac
E tor
Ac tu a tor
tor
A
Primary Loading frames
Side Elevation
Front Elevation
Figure 1-2 Self equilibrating and secondary loading frames used by Matthews (2004)
1.3.3
Major Findings: Beam-to-Floor Slab Connection
In compliance with the overlying investigation into the seismic abilities of existing buildings, the test super-assemblage included the floor slab connection with the supporting beam predominantly used in New Zealand construction practice. The seating connection featured a 300 series hollow-core unit seated on a mortar bed on either a 20mm or 40mm seating. The cores at the end of the floor units were plugged with common plastic end bungs to prevent concrete from entering the cores. A 75mm thick topping slab was cast on top of the floor units and conventional Grade 300 starter bar reinforcement was used together with the cold drawn mesh in the topping slab. Initial damage to the supporting beam-to-floor slab connection during testing occurred earlier than expected and the mode of failure was different to what was previously assumed. Originally it was thought that loss of seating occurred due to the floor units sliding off the seat of the supporting beams. However, it became apparent that the Page 1-6
relative rotation between the flooring and beam was the major source of damage. The mortar bed possessed sufficient rigidity to ensure that the floor units could not slide, and the negative moments induced by the relative rotation caused diagonal compressive struts and orthogonal tensile stresses, led to splitting of the unreinforced webs of the hollow-core. Positive moments created large crack openings, and under cyclic loading the connection deteriorated considerably, ultimately causing the entire support at both ends of the structure to be lost. A photograph illustrating the overall failure of the flooring is shown in Figure 1-3, and a diagram of the supporting beam floor slab connection is shown in Figure 1-4(a).
1.3.4
Major Findings: Lateral Frame-to-Floor Connection
Figure 1-4(b) shows the connection used for the Matthews (2004) experiment between the perimeter moment resisting concrete frame and the adjoining parallel hollow-core unit. In addition to the damage incurred by the end connection, the first hollow-core unit adjacent to the perimeter frame showed signs of distress at an early stage of testing. The construction connection inadvertently rigidly tied the floor into the perimeter beams, and under lateral displacements, the flooring was forced to displace in the double curvature pattern of the frame beams. Hollow-core flooring sags by nature and this undesirable deformation caused internal cracking of the webs of the hollow-core unit and the eventual failure of the lower half of the first unit. The displacement incompatibility coupled with the tension forces in the floor diaphragm caused the cold drawn mesh reinforcement within the topping slab to fracture and a large tear to form within the topping concrete along the interface between the first and second hollow-core units spanning parallel to the perimeter frame. This caused the centre column of the front frame to displace outwards, transverse to the plane of loading. The broader ramifications of this can be seen if this outward column movement was applied to
Page 1-7
several floors of a multi-storey structure during an earthquake. Premature buckling of the interior intermediate columns could result in the potential collapse of the structure. This also identifies the necessity to tie the intermediate column into the floor diaphragm, and this was recommended for further research.
Figure 1-3 Overall failure of the floor units in the Matthews (2004) experiment
1.3.5
Analytical Findings
In addition to the experimental investigation conducted by Matthews (2004), significant analytical work was undertaken to complement the observed results. A capacity mechanism analysis was used to calculate the overall strength capacity of the super-assemblage. A method was proposed to determine the contribution of the floor diaphragm to the overall performance. Similarly, a theory was developed by Matthews (2004) and Matthews et al (2004) to predict beam elongation. The method uses rigid body kinematics and a “rainflow counting� technique to predict growth of plastic hinges under increasing rotations. For both beam elongation and the strength capacity prediction models, the comparisons with the experimental results were good. Page 1-8
1.4
FINDINGS FROM LINDSAY (2004)
A continuation of the work done by Matthews (2004) was conducted by Lindsay (2004). This investigation aimed to verify recommended details for the improved performance of future precast concrete construction practice, which is in contrast to Matthews (2004) who investigated past construction techniques (1985-2000) and the resulting problems with seismic performance. Lindsay (2004) repaired and reconstructed the Matthews (2004) fullscale super-assemblage specimen and then retested it under a more rigorous loading regime. Modifications were made to improve the performance of the hollow-core floor system for both the lateral and end seating connections between the frame and hollow-core units, as well as more adequately tying the central column into the floor diaphragm.
1.4.1
Hollow-core Connection Details
As shown in Figure 1-4(c), Lindsay (2004) employed a beam to floor connection detail that used a low-friction bearing strip and a compressible backing board, which replaced the plastic end plugs in the cores at the end of the units. The seating connection detail used during the Matthews (2004) test could be likened to a “semi-rigid” type of connection. The poor behaviour led to further testing of a “pinned” type of connection by Lindsay (2004), whereby the low friction bearing strip allows the floor units to slide horizontally relative to the supporting beam, and the compressible backing board to compress – reducing large compression stresses entering the floor unit. The overall performance was satisfactory, and significant improvements were seen relative to the Matthews (2004) support condition. The connection was able to sustain sizeable relative rotations with overall structural inter-storey drifts reaching +5%. The compressible backing board did not compress as expected which indicates beam elongation effects were causing pull-off of the flooring units off the seating Page 1-9
away from the supporting beam. The low friction bearing strips also did not perform as originally expected, whereupon the rough side of the bearing strip slid on the concrete seat and the low friction side adhered to the floor unit. Significant spalling of the concrete ledge (seat) of the supporting beams later in the experiment reduced the seat width to minimal amounts and further jeopardised the integrity of the support connection. Conventional end-plug
Zone of Grade 430 starters weakness at 300 crs & 665 mesh in 75mm topping
Grade 300 starters at 300 crs & ductile mesh in topping 75mm concrete topping Mortar bed
300 series hollow-core unit
First Second Hollow-core Hollow-core Unit Unit Perimeter beam
20mm seat East end 40mm seat West end
Column face
(a) Matthews (2004) floor-slab connection
(b) Matthews (2004) lateral connection Zone of weakness
5mm Compressible material
Grade 300 starters at 300 crs & ductile mesh in topping
Existing grade 430 starters at 300 crs & ductile mesh in 75mm topping
Low Friction bearing strip
Timber in-fill 750mm
Hollow-core Units Perimeter beam
75mm seat
Column face
(c) Lindsay (2004) floor-slab connection
(d) Lindsay (2004) lateral connection
Figure 1-4 Hollow-core connection details used by Matthews (2004) and Lindsay (2004)
To overcome the issues of the displacement incompatibility that occurs between the perimeter frame and the floor units, a topping slab was cast onto a timber infill that bridged between the hollow-core units and perimeter frame beams. Figure 1-4(d) shows a diagram of the connection. The timber infill was proposed subsequent to the poor behaviour witnessed in the Matthews (2004) experiment to allow more desirable one-way hollow-core action. The thin slab was designed to provide a flexible interface and accommodate the displacement Page 1-10
incompatibility between the floor and perimeter beams. Overall, the infill detail showed a marked improvement (when compared to Matthews (2004). However the ductile mesh used to reinforce the topping slab fractured and a major longitudinal tear formed along the interface between the infill and hollow-core, which interfered with the transfer of inertia and structural interaction forces from the floor to the moment resisting frame. The presence of the drag bar reinforcement tying the centre column into the floor plate ensured that there was no outward translation of the centre column similar to what was observed during the Matthews (2004 experiment.
1.4.2
Major Conclusions and Recommendations
The improved detailing utilised in terms of the seated and lateral hollow-core connection details and adequate tying of the central column into the floor, meant that the superassemblage was able to sustain inter-storey drifts up to +5%, until the low cycle fatigue of the beam longitudinal reinforcement occurred. Although the experiment was success in many areas, it also uncovered other issues that the experiment was unable to address. Some of the detailing alterations made from the Matthews (2004) experiment still required further enhancement and the following recommendations for professional practice and improving design standards were made by Lindsay (2004): 1.
Cold drawn or ductile mesh should not be used and conventional reinforcement should be used in its place for diaphragm topping reinforcement over precast hollow-core units.
2.
In the presence of an infill slab offsetting the flooring from adjacent frame beams, the starter bars used should extend over the infill, across the infill-to-hollow-core floor interface and extend above the first floor slab unit. This will increase the ductility at the infill-floor slab interface and minimise the risk of reinforcement fracture.
Page 1-11
3.
Hollow-core units should not be seated on potential plastic hinge zones of supporting beams. This should be overcome by having an infill slab over the highly deformable hinge region, and hooked longitudinal reinforcement within the supporting beam to concentrate large deformations away from the seated hollow-core units and close to the column face.
4.
A second generation low friction bearing strip should be employed for future use, whereby the floor slab slides horizontally on the strip relative to the supporting beam, and the strip adheres to the concrete seating. A strip featuring longer “teeth� on the rough side will help to minimise spalling by evening out the surface roughness of the seat concrete and help to ensure that the bearing strip will stay on the seat as designed. In addition, transverse reinforcement should be used within the concrete seating of the supporting beams.
Similarly, several recommendations were made by Lindsay (2004) for future research. These include the following: 1.
Due to the large amount of time and resources required to undertake large full-scale super-assemblage tests, more two-dimensional proof-of-concept tests should be performed, similar to those performed by Bull and Matthews (2003) and Liew (2004). Despite the limitations of this method of testing, the comparable performance and failures observed with full-scale three-dimensional experiments mean that subassemblage tests are of great use in order to easily and relatively quickly assess the adequacy of many other types of seated connections. Such tests could allow the generation of a database of results and allow for a wide range of details to be tested including all the different types of precast elements used in New Zealand construction. The effects of beam elongation should also be incorporated into the testing procedure.
Page 1-12
2.
Of a more urgent nature, the second of the two details included in the 2003 Amendment to the New Zealand Concrete Structures Standard (NZS 3101, 2004) needs to be tested as part of a full-scale three-dimensional super-assemblage experiment.
3.
Owing to the inadequacies associated with hollow-core flooring connection details in existing buildings, a retrofit connection solution needs to be developed and tested such that life-safety in existing buildings can be maintained.
Other questions relating to hollow-core seated connection details were raised including; what is the effect of negative seating (a bridged connection detail when the hollow-core units are cut too short)? What is the effect of different beam geometries? What are the effects of placing additional shear reinforcement in the cores of the units? Recommendations were also made for further analytical research. The torsion of the transverse beams needs to be modelled to gain an idea of when full activation of the starter bars occurs. Also analytical modelling of the diaphragm, and in particular, the “bowstring effect� needs to be conducted.
1.5
OUTLINE OF THIS THESIS
This thesis comprises of three main sections. Following this introductory section, Section 2 discusses the testing of two sub-assemblage beam-to-hollow-core specimens. Previous research at a sub-assemblage level is more closely reviewed and the experimental set-up is described. The results are presented and from which the conclusions and recommendations are drawn. Section 3 covers the construction of the moment resisting frame and the modifications made from the original Matthews frame (2004), as well as the final super-assemblage specimen details and hollow-core connection details. The experimental loading regime and instrumentation are outlined. The second part of this section provides visual and instrumental
Page 1-13
observations from the testing, hysteretic performance of the structure and a discussion of the major results. The penultimate section, Section 4, provides a forensic analysis of the experimental observations. Modelling of displacement incompatibility between the lateral load-resisting frame and the first floor slab unit is undertaken and comparisons between the analytical results and experimental observations are made. The lateral system capacity is calculated from the individual components of the system and compared with the experimental results. The bowstring effect of floor slabs is also examined. The beam elongation results from the experiment will be compared to theoretical predictions. Finally, a comparison will be made between this experiment, Matthews (2004) and Lindsay (2004) in terms of the floor seating connection, the lateral connection between the frame and initial hollow-core unit, and the overall system strengths. The final section of this thesis provides a summary and major conclusions from
the
research presented. Recommendations are made for professional practice and future research. Considerable material has also been included at the end of this thesis in the various appendices. This material supplements the information provided in the main sections of the thesis. ƒ
Appendix A consists of additional material from the sub-assemblage experimental investigation and features photographic logs of the construction and testing as well as extra construction details.
ƒ
Appendix B comprises of a construction drawings and a photographic log of the construction of the main super-assemblage structure.
ƒ
Appendix C provides supplementary material to the testing of the super-assemblage. Details and photographs of the test configuration are included as well as a photographic record of the testing.
Page 1-14
ƒ
Appendix D offers additional instrumental results from the testing and calculations to supplement the various theoretical work undertaken throughout this thesis.
1.6
WHAT IS NEW AND SIGNIFICANT IN THIS THESIS?
The investigation presented in this thesis experimentally examines the seismic capabilities of a reinforced hollow-core support connection detail that has been proposed in amendments to the New Zealand Concrete Design Standard (NZS 3101, 2004). To this point, the specific detail has not been tested, and this research describes the performance of the connection detail in a new and improved two-dimensional experiment configuration before more realistic testing in a three-dimensional full-scale structure. A precast concrete super-assemblage specimen has been constructed and incorporates the new detailing enhancements that seek to address the shortcomings of hollow-core floor systems that have been highlighted from previous research. Analytical work has been conducted to aid the understanding of displacement incompatibility between the floor and frame elements of a structure. Non-linear modelling has been undertaken and the results compared with actual values obtained from the experiment. The model has then been extended and examples of the possible applications of the model are discussed. The bowstring effect in floor slabs is examined and a method is introduced to allow for the influence it has on the lateral load capacity of the super-assemblage. The overall findings from this research produce a greater level of understanding of hollow-core floor systems and the three-dimensional interaction between floor slabs and reinforced concrete frames.
Important recommendations are made for both professional
design practice and construction as well as providing ideas for future research. According to the results of the hollow-core connection detailing, direct recommendations are made for the upcoming revised New Zealand Concrete Design Standard. Page 1-15
1.7
REFERENCES
Bull D.K, Matthews J.G, 2003, Proof of Concept Tests for Hollow-core Floor Unit Connections, Precast NZ report, Feb 2003. Fenwick R.C, and Megget L.M, 1993, Elongation and load deflection characteristics of reinforced concrete members containing plastic hinges, Bulletin of NZNSEE, Vol 26, No. 1, March, pp28-41. Fenwick R.C, Davidson B.J, and McBride A, 1995, The influence of slabs on elongation in ductile seismic resistant concrete frames, Proceedings for NZNSEE technical conference, Rotorua, March, pp36-43. Herlihy M.D, Park R and Bull D.K, 1995, Precast Concrete Floor Unit Support and Continuity, Research Report 93/103, Department of Civil Engineering, University of Canterbury, Christchurch, New Zealand. Herlihy M.D, and Park R 2000, Precast concrete floor support and diaphragm action, Research Report 2000/13, Department of Civil Engineering, University of Canterbury, Christchurch, New Zealand. Lau D.B.N, Fenwick R.C and Davidson B.J, 2002, Seismic performance of R/C perimeter frames with slabs containing prestressed units, Proceedings for NZSEE conference, Napier, March, Paper No. 7.2. Lindsay R.A, 2004, Experiments on the seismic performance of hollow-core floor systems in precast concrete building, Masters Thesis, Department of Civil Engineering, University of Canterbury, Christchurch, New Zealand. Lindsay R.A, Mander J.B, and Bull D.K, 2004a, Preliminary results from experiments on hollow-core floor systems in precast concrete buildings, 2004 NZSEE Conference, Rotorua, NZ, Paper 33, 8 pp.
Page 1-16
Lindsay R.A, Mander J.B, and Bull D.K, 2004b, Experiments of the Seismic Performance of Hollow-core Floor Systems in Precast concrete Buildings, 13th World conference on Earthquake Engineering, Vancouver, Canada, CD ROM paper No. 585. Liew H.Y, 2004, Performance of Hollow-core Floor Seating Connection Details, Masters Thesis, Department of Civil Engineering, University of Canterbury, Christchurch, New Zealand. Matthews J.G, 2004, Hollow-core floor slab performance following a severe earthquake, PhD Thesis, Department of Civil Engineering, University of Canterbury, Christchurch, New Zealand. Matthews J.G, Bull D.K, and Mander J.B, 2003a, Background to the Testing of a Precast Concrete Hollowcore Floor Slab Building, 2003, Pacific Conference on Earthquake Engineering, February, Christchurch, NZ, CD ROM paper 170. Matthews J.G, Bull D.K, and Mander J.B, 2003b, Preliminary Experimental Results and Seismic Performance Implications of Precast Floor Systems with Detailing and Load Path Deficiencies, 2003 Pacific Conference on Earthquake Engineering, February, Christchurch, NZ. CD ROM paper 077. Matthews J.G, Mander J.B, Bull D.K, 2004, Prediction of beam elongation in structural concrete members using a rainflow method, 2004 NZSEE Conference, Rotorua, NZ, Paper 27, 8 pp. Meija-McMaster J.C and Park R, 1994, Tests on Special Reinforcement for the End Support of Hollow-core Slabs, PCI Journal, Vol 39, No. 5, pp. 90-105, September-October. NZS3101, 1995, Concrete Structures Standard, NZS3101, Parts 1 & 2, Standards New Zealand, Wellington, New Zealand. NZS3101, 2004, Amendment No. 3 to 1995 Standard (NZS3101), Standards New Zealand, Wellington, New Zealand.
Page 1-17
Norton J.A, King A.B, Bull D.K, Chapman H.E, McVerry G.H, Larkin T.J and Spring K.C, 1994, Northridge Earthquake Reconnaissance Report, Bulletin of the NZNSEE, Vol. 27, No. 4, December. O’Grady C.R, 2004, Letters to the Editor, Journal of the New Zealand Structural Engineering Society (SESOC), Vol 17, No. 2, pp 8-9. Oliver S.J, 1998, The Performance of Concrete Topped Precast Hollow-core Flooring Systems Reinforced with and without Dramix Steel Fibres under Simulated Seismic Loading, Masters Thesis, Department of Civil Engineering, University of Canterbury, Christchurch, Canterbury. Priestley M.J, Sritharan S, Conley J.R, Pampanin S, 1999, Preliminary results and conclusions from the PRESSS five-storey precast concrete test building, PCI Journal, Vol. 44, No. 6, November-December, pp 42-57. Restrepo J.I, Park R and Buchanan A, 1993, Seismic behaviour of connections between precast concrete elements, Research Report 93-3, Department of Civil Engineering, University of Canterbury, Christchurch, New Zealand. Zerbe H.E, and Durrani A.J, 1989, Seismic Response of Connections in Two-bay R/C Frame Subassemblies, Journal of Structural Engineering, Vol. 115, No. 11, November, pp 2829-2844. Zerbe H.E, and Durrani A.J, 1990, Seismic Response of Connections in Two-bay R/C Frame Subassemblies with a floor slab, ACI Structural Journal, Vol. 87, July-August, pp 406415.
Page 1-18
2.
Section 2 – Sub-Assemblage Experimental Investigation
SECTION SUMMARY The present research experimentally investigates, by means of a two-dimensional sub-assemblages, two hollow-core-to-support beam seated connections under simulated seismic loads. The support connections are reinforced and rigidly tie the floor into the supporting beam, the first of which has been proposed in Amendment No. 3 to the New Zealand Concrete Standard, (NZS 3101, 2004). A newly developed test set-up is described which incorporates both the relative rotation between the supporting beam and hollow-core floor, and tension in the floor, to represent the elongation of a parallel moment resisting frame, as the sources of damage. The sub-assemblage specimens were tested up to equivalent inter-storey drifts of Âą5.0% and visual and instrumental observations from the experiments are outlined. A simplified analytical study is conducted to better understand the performance and observed failure modes. Results show promising behaviour, and after testing in a concurrent full-scale super-assemblage experiment, recommendations for adoption into the forthcoming revision of the New Zealand Concrete Standard, NZS 3101, are made.
Page 2-1
2.1
INTRODUCTION
Recent earthquake events and research undertaken has raised serious concerns of the seismic performance of hollow-core floor systems. Experiments undertaken by Matthews (2004) at the University of Canterbury have showed that a hollow-core floor diaphragm supported by a ductile moment resisting concrete frame structure performed inadequately under simulated seismic loads. Further experimental research conducted by Lindsay (2004) and Lindsay et al (2004) demonstrated that improved detailing significantly improved the performance of these hollow-core floor systems. Amendments to the New Zealand Concrete Design Standard (NZS 3101, 2004) stipulate two new “acceptable solutions”. The two connections could be characterised as either “pinned” or “rigid.” The former “pinned” connection detail was tested by Lindsay (2004), but the latter remains untested, and is the subject of this research. In this section, the seismic performance of two hollow-core floor unit-to-support beam connections is experimentally investigated. The experiments were conducted in a twodimensional sub-assemblage component test format. The loading set-up was developed from previous sub-assemblage tests (Bull and Matthews, 2004 and Liew, 2004) whereby tensile elongation effects were imposed on the floor-to-beam connection. This was considered necessary to simulate the effect of beam growth that takes place in plastic hinge zones as a result of cyclic loading effects. The two specimens feature rigidly reinforced connection details, one of which is the detail proposed in Amendment No. 3 to NZS 3101:1995 (2004) and the other is a modified detail following similar principles. This section firstly reviews research relevant to these experiments, both at subassemblage and super-assemblage formats and the progression made from this research to the current specifications detailed in the New Zealand Concrete Design Standard. The details of the test specimens and experimental set-up are provided and discussed. The second part of this section outlines the results from the experiments. Page 2-2
2.2
PREVIOUS RESEARCH FINDINGS AND NEW ZEALAND GUIDELINES
There have been several research programs at a sub-assemblage level that have investigated hollow-core support conditions. Meija-McMaster and Park (1994), Herlihy et al (1995), Oliver (1998) and Herlihy and Park (2000) examined seat requirements of hollow-core units due to beam elongation. In each set of experiments, various end connection details were investigated under either a monotonic or a cyclic horizontal load, to simulate the loss of seating (pull-off) effects that occur due to beam elongation. The experiments were primarily undertaken to investigate whether the cast in-situ topping slab and starter bar reinforcement as well as different reinforced core configurations are sufficient to stop the floor units from collapsing when the hollow-core unit was pulled off the seat of the supporting beam. Meija-McMaster and Park (1994) demonstrated that various reinforced connections between the hollow-core floor units and supporting beams, designed to carry the weight of the floor units, performed well when a loss of seating occurred. The use plain round bars also showed that a ductile connection could be achieved due to an early loss of bond strength enabling large plastic elongations to be sustained. A limitation of the use of the beam-to-floor connections used within structures expected to experience large horizontal movements was placed. Herlihy et al (1995) conducted several experiments looking at traditional beam-tofloor connection details used in New Zealand construction. The testing showed that the “hairpin” type of connection (reinforcement hooked at both ends connecting the floor and supporting beam at the bottom of the hollow-core cells) performed adequately but concluded that there was insufficient composite bond strength between the cast-in-place topping and the hollow-core units to maintain a ductile connection when there was no reinforcement crossing the topping to hollow-core interface. The authors raised concern over the performance of the connections within structures under large horizontal movements and proposed an alternative connection detail, the “paperclip” using plain round bars (two layers of reinforcement in the Page 2-3
shape of a paperclip between the hollow cores and supporting beam) that could be used to resist these large displacements. Further research by Herlihy and Park (2000) included a monotonic downward loading to induce tension in the topping and to observe the amount of additional bending moment resistance added by the continuity steel. Oliver (1998) examined the “paperclip” connection in more detail. Similar conclusions were found to suggest that deformed bars traditionally placed in topping slabs are insufficient to resist the effects of beam elongation that occurs in ductile frames. Oliver (1998) concluded that the “paperclip” tie reinforced connection is not suitable in situations where beam elongation is critical, such as the corner regions of a ductile concrete moment resisting frame structure. The use of steel reinforced fibre concrete (SFRC) was also investigated, and it was shown that the increased tensile capacity of the concrete due to the steel fibres meant that higher displacements could be sustained. The aforementioned research has examined the performance of hollow-core flooring under the tension induced in the floor system from beam elongation effects. The failure modes witnessed from these tests were different to the damage observed in the aftermath of the Northridge Earthquake, when a loss of seating failure of hollow-core occurred (Norton et al, 1994) and photographs showing the different failure modes are shown in Figure 2-1. The relative rotation between the hollow-core floor slab units and the supporting beams was not examined and therefore, failure due only to the induced tension is unrealistic. Matthews (2004) tested in a full-scale three-dimensional super-assemblage, the supporting beam-to-hollowcore slab connection details commonly used in New Zealand construction prior to 2001. The connection detail consisted of hollow-core units seated on a mortar bed on a 20mm or 40mm concrete seating. This mortar bed did not allow the floor units to slide horizontally relative to the supporting beam as originally assumed. The cyclic relative rotations between the floor and supporting beams, due to lateral loading of the super-
Page 2-4
assemblage, resulted in diagonal compression stresses from the seating to the topping slab and orthogonal tensile stresses within the unreinforced webs of the hollow-core units. Due to the cyclic loading, these tensile stresses led to cracking and ultimately, the loss of seating failure of the hollow-core units (Figure 2-1(c)). The experimental results showed that the relative rotation between the flooring and supporting beam was the major contributing factor to failure.
(a) Meadows Apartment Building, Northridge Earthquake 1994 (Norton et al, 1994).
(b) Herlihy and Park (2000) failure mode.
(c) Matthews (2004) failure mode.
(d) Liew (2004) Specimen 2 failure mode
Figure 2-1 Comparison of the failure modes observed during previous experiments.
One of the actions taken following the inadequate behaviour of the hollow-core floor system observed during the Matthews (2004) experiment was the formation of a Technical Advisory Group on precast floors (TAG). TAG sought to address the identified problems associated with hollow-core floor systems and proposed new hollow-core support connection solutions for future construction subject to experimental investigations.
Page 2-5
Bull and Matthews (2003) conducted four proof-of-concept sub-assemblage tests that were commissioned by Precast NZ. The testing regime introduced the relative rotation between the floor slab and support beam as the chief failure mode by way of a cyclic vertical load at the end of the 6m long hollow-core units. A diagram of the test set-up is shown in Figure 2-2(d) and the specific details for the test specimens are included in Figure 2-2.
(a) Control Specimen (200 and 300 series)
(c) Paperclip seating connection detail
(b) Flexible seating detail
(d) Test configuration
Figure 2-2 Seating connection details and the test configuration used by Bull and Matthews (2003) Two of the specimens comprised of traditional connection details, one with a 300 series hollow-core unit and the other with a 200 series hollow-core unit, denoted as the “control specimens”. The traditional connection details (for the 200 and 300 series hollow-core units) comprised of the floor unit seated on a mortar bed, core end plugs to prevent concrete from entering the cores, and conventional continuity starter bar reinforcement in the topping slab. The floor-to-beam connection for the 300 series hollow-core unit was identical to the detail used in the Matthews full-scale super-assemblage experiment (Matthews, 2004). The other two specimens were newer connection details, recommended by TAG, and one of which effectively created a “pinned” connection with a compressible backing board and a low Page 2-6
friction bearing strip, and the other was a rigid “paperclip” connection, tying the beam and floor slab together with reinforced cores. The traditional methods behaved poorly with web cracking observed at low inter-storey drifts and full delamination of the hollow-core units from the topping slab. There was also significant displacement of the floor units down the face of the supporting beams at higher drifts. The damage patterns were similar between the 200 series and 300 series hollow-core specimens as well as what was observed in the fullscale three-dimensional Matthews (2004) tests (Figure 2-1(c)). The two newer methods behaved well and were able to sustain high drifts without a loss of seating occurring. As a result of the previous research and the widespread use of precast floors in construction practice, specific details governing the use of precast concrete systems have been implemented within New Zealand design standards. Amendment No. 3 to NZS 3101:1995 (2004) provides two “acceptable solutions” for connecting hollow-core floors into supporting beams, as indicated by Figure 2-3(a) and (b). The first solution is a pinned, simple type of connection, which features the hollow-core unit seated on 75mm seat with a low frictionbearing strip, and has a compressible backing board between the end face of the hollow-core unit and supporting beam. This detail was experimentally tested and validated, firstly by Bull and Matthews (2004) and then in a full-scale super-assemblage experiment (Lindsay, 2004). Significantly improved behaviour was observed (as compared to Matthews (2004)), and the beam-floor connection was able to withstand super-assemblage inter-storey drifts to +5%. The second of these “acceptable solutions” has currently not been tested experimentally. This floor-to-beam connection solution, as shown in Figure 2.3(b) could be classified as a rigid type of connection with reinforcing tying the hollow-core units into the supporting beam. The rigid reinforced detail requires more effort to construct (as compared with the “simple” connection detail tested by Lindsay (2004)) with the need to pre-cut cores and place extra reinforcement.
Page 2-7
(a) Hollow-core with compressible backing on low friction bearing strips.
(b) Hollow-core with 2 – 2 leg R 16 hairpins on low friction bearing strips.
(c) Capacity design actions in hollow-core.
Figure 2-3 Support for hollow-core flooring units: details proposed in Amendment No. 3, NZS 3101:1995 (2004) (Figure C4.3/2).
Page 2-8
However, the rigid connection offers redundancy by being tied into the supporting beams, and because of the chance for hollow-core units to arrive on site short (due to shrinkage, creep or construction tolerances), this type of connection construction can be rendered more suitable. Liew (2004) continued the research from Bull and Matthews (2003) and investigated the relative rotation characteristics of hollow-core seated connections. Two new connection details were investigated as well as a retrofit solution, which are all shown in Figure 2-4. The first detail included a 70mm seating, and each core (4 cores) of the hollow-core unit was reinforced with Grade 500 R16 reinforcement and Grade 500 D12 starter bars (where the “R” and “D” denote plain round and deformed reinforcement respectively). The second specimen was identical to the first specimen, except that there was no seating. This “negative seating” case was to investigate whether units that arrive short to site could be propped and connected to the supporting beam with a strongly reinforced bridging connection. The third specimen used the same traditional detail previously tested by Matthews (2004) and Bull and Matthews (2003) but featured an angle section “catcher” to act as a retrofit measure. The findings from Liew’s (2004) experiments highlighted that over-reinforced beamto-floor connections leads to inferior performance. Incipient failure of Specimen 1 occurred at a drift of –1%, and despite suffering significant damage, Specimen 1 was able to function without collapse up to ±4% drifts. The detail however performed poorly in comparison to the paperclip detail tested under the Bull and Matthews (2004) research program (Figure 2-2(c)), which utilised two D12 (Grade 300) paperclips instead of the four R16 (Grade 500) paperclips. The zero seating specimen performed inadequately and failed under the expected 2% drift design demand. Although the moment capacity of the connection was suitable, the lack of shear resistance from the zero bearing proved to be totally inadequate. The retrofit detail tested did not perform as well as the author would have hoped, with the angle bracket effectively catching the unit, but at the same time restraining the rotation of the floor unit.
Page 2-9
Hurricane "Ductile Mesh"
HD12 starter bars 612
100
43
D24
65
R60
Plastic end plug
4 R16 Paperclips
H/C unit seated on mortar pad 70
(a) Specimen 1: Paperclip detail with 70mm seating HD12 starter bars 100
43
612
65
R60
Hurricane "Ductile Mesh"
Plastic end plug
4 R16 Paperclips
(b) Specimen 2: Paperclip detail with zero seating H R C 66 5 M esh
R 1 2 @ 1 0m m c/c 612
P la stic e nd p lug
16
1 70
150 x150 x12 E .A M cD ow el B ea ring S trip seate d on A ng le S eat A nch or B olt 20
(c) Specimen 3: Retrofit of a grouted seat
Figure 2-4 Test specimens and their dimensions from testing by Liew (2004).
Liew (2004) concluded that it would be interesting to repeat the experiments including the effects of beam elongation. In the early sub-assemblage research performed, only horizontal pull-off loads were used. The sub-assemblage experiments by Bull and Matthews (2003) and Liew (2004) included cyclic vertical loading inducing relative rotations between the hollowcore floor unit and the supporting beams. To this point, no sub-assemblage experimental
Page 2-10
program has investigated the effect of both horizontal tension in the floor and relative rotation between the floor unit and supporting beam. The second hollow-core connection detail stipulated by Amendment No. 3 to NZS 3101:1995 (2004), as shown in Figure 2-3(b), currently has not been experimentally tested. For this reason, this connection detail between the supporting beam and hollow-core is the focus of this experimental study.
2.3
TEST SPECIMEN DETAILS
The two test specimens are described in the following subsection and can be seen in Figure 2-5(a) and (b). Full design and construction details of the specimens are provided in Appendix A.
2.3.1
Specimen 1
The seated connection detail used for this experiment is the second detail proposed by Amendment No. 3 to NZS 3101:1995. The 6m long 300 series hollow-core unit was seated on a 75mm wide seat and a low friction bearing strip. The connection features two of the four hollow cores reinforced and filled with concrete. Starter bars consisted of D12 (Grade 300) reinforcement spaced at 300mm centres. Two cores of the four hollow cores were reinforced with hooked R16 (Grade 300) bars placed close to the bottom of the cores. The topping slab consisted of D12 (Grade 300) reinforcement, which was lapped with the starter bars, and placed at 300mm centres in both directions. It is also worth noting that backing boards were used in place of traditionally used end plugs, to prevent concrete entering the un-filled cores. This is to aid the beam-to-slab interface becoming the critical zone, concentrating the rotational demand at this interface and not into the hollow-core unit.
Page 2-11
D12 Starter Bars (Grade 300)
2*R16 (Grade 300) - 1 per filled core Seat Transverse Reinforcement
Low Friction bearing strip 75mm seat
(a) Code Amendment detail D12 Starter Bars (Grade 500) @ 300mm, continuous as topping reinforcing
4*D12 (Grade 500) - 2 per filled core Seat Transverse Reinforcement
Low Friction bearing strip 75mm seat
(b) Modified seating detail
Figure 2-5 Test specimen details.
2.3.2
Specimen 2
Specimen 2 was based principally on Specimen 1. However the Grade 300E reinforcement was replaced with Grade 500E deformed reinforcement to represent present construction practice in New Zealand. The hollow-core unit is similarly seated on a 75mm seat and a low friction bearing strip, and features two reinforced cores. Starter bar reinforcement consisted of D12 bars placed at 300mm centres above each of the cores. The R16 reinforcement used for Specimen 1 in two of the four cores has been replaced by 2-D12 bars for Specimen 2. The reason for this was to provide equal top and bottom reinforcement (4-D12) and hence equal Page 2-12
positive and negative connection moment capacities. Transverse reinforcement was used within the reinforced cores, with the placement of one leg of R10 reinforcement at 150mm spacings, tied between the starter bar and bottom reinforcement. This was to investigate whether implementation of transverse reinforcement in hollow-core units is an adequate way to overcome situations when overly high shear demands are present, which might be experienced with long spans, bridges or other cases. The reinforcement passing the beam-toslab interface (4-D12 reinforcement top and bottom) has been de-bonded over 150mm with plastic tubing to reduce the risk of reinforcement fracturing and to support the critical section occurring at the beam-slab interface. In addition to this, a thin plastic strip was placed on the top of the starter bars beneath the concrete surface to both act as a crack initiator and further promote rotation at the critical section.
2.4
BEAM ELONGATION
The inelastic rotations experienced by plastic hinges of concrete frame structures under seismic loading cause the phenomenon of beam elongation, whereby the beam grows in length. Beam elongation has been quantified through many research programs over the last decade such as Fenwick et al (1999). Typical values for beam elongation vary from between 2% and 5% of the beam depth, and these estimated values have been used to explain permanent deformations of frame structures as well as a way of assessing precast floor seating widths. Matthews (2004) and Matthews et al (2004) presented a new theory for predicting elongation for structural concrete members. The theorem is based on simple rigid body kinematics and utilises a rainflow counting method to calculate the amount of elongation due to inelastic bending of a plastic hinge in a frame system. Elongation occurs only if plastic
Page 2-13
deformations exceed those of previous peaks. In its essence, the theorem can be given by the expression:
Gi
T u ecr
(2.1)
in which Gi = elongation of the ith hinge; T = rotation of the hinge; and ecr = eccentricity between the centre of gravity of the concrete (c.g.c) for the beam and the centroid of the compression force (instantaneous centre of rotation, I.C.R.). The elongation of a frame (Gel) with ith plastic hinges can be separated into the elastic and inelastic components and can be expressed as:
G el
G eel G pel
T
p
T p T y
ÂŚ e n
cr
(2.2)
i 1
where G eel = unloading recoverable elastic elongation, G pel = non-recoverable plastic elongation, T p = positive plastic rotation, T p = negative plastic rotation, T y = yield rotation of the frame. The growth of the beam lengths occurs as tensile strains within the reinforcement are higher than the accompanying compression strains within the concrete. Under reversing loading, compression yielding does not fully close the flexural cracks caused by the reinforcement which has previously yielded in tension. Figure 2-6(a) illustrates beam elongation by showing the relationship between the hysteretic behaviour and recoverable elastic and non-recoverable plastic components of elongation. The theorem is dependent on the loading, with respect to the plastic rotations and the yield drift and ecr values are a function of the structural and geometrical properties of the structure. The ecr eccentricity value for example is a function of the reinforcement and the presence of topping reinforcement and prestressing strands of adjoining floor slabs. Figure 2-6(b) and (c) show the derivation of the ecr values for a typical concrete frame. For a more in-depth explanation of the development of this model, reference can be made to Matthews (2004). Page 2-14
2.5.1
Sub-Assemblage Elongation
With the beam elongation prediction model proposed by Matthews et al (2004) and further verified by Lindsay (2004), there became a method to introduce beam elongation effects into two-dimensional sub-assemblage tests. A second actuator has been implemented to induce tension forces in the floor through a displacement controlled loading, which was modelled on the beam elongation prediction model. The drift displacement history was controlled by the vertical actuator in a prescribed manner, and as the theorem predicts beam elongation in terms of rotation (of a plastic hinge or frame) under lateral loading, the use of Equation 2.2 allowed beam elongation results to be calculated for each inter-storey drift increment. After accounting for geometry (as the horizontal actuator rotates), an input file was developed listing the target ram displacements for both the vertical and horizontal rams at each increment of drift. The amount of elongation was calculated with reference to the super-assemblage frame used during the Matthews (2004) project as well as the full-scale tests associated with this current research. Beam elongation was calculated as one half of the total frame elongation, or the pull-off displacements which one end support of the hollow-core flooring units would experience. The amount of beam elongation calculated was based on an exterior moment resisting frame and it is accepted that there would be a difference between this value and that experienced by a floor unit that is seated away from the frame due to out-of-plane bending and torsion of the transverse supporting beams. Also, a yield drift rotation, T y , of Âą0.5% was assumed and used for the generation of the beam elongation data for these experiments. It is later verified that although this was a priori assumption, it was a valid approximation.
Page 2-15
Load 3
5
1
Deflection 2 4 T+p
'el Tp-
Unloading recovery
5
4
Unloading recovery
3 Elastic growth
2
1
T y
Ty
Elastic growth
Drift T
(a) Detailed diagram of beam elongation showing the hysteretic relationship and recoverable elastic and non-recoverable plastic components. T Elongation due to negative moment
I.C.R
jD
ecr |0.475D
D
c.g.c ecr |0.425D
jD
Elongation due to positive moment
Instantaneous centre of rotation (I.C.R)
(b) Exterior plastic hinge lever arms for reinforced concrete beams Elongation due to negative moment
I.C.R
T
Prestressing strands c.g.s
ecr |0.225D
jD
ecr |0.275D
D
c.g.c
Elongation due to positive moment
Instantaneous centre of rotation (I.C.R)
(c) Interior plastic hinge lever arms
Figure 2-6 Diagrammatic representation of beam elongation (adapted from Matthews (2004))
Page 2-16
2.5
EXPERIMENTAL SET-UP
The construction of the test specimens, albeit sub-assembly components of a real structure, was conducted in accordance with customary site practice. Figures 2.7(a) and (b) shows a few stages of the construction process. Initially, the support beams were cast to half height using typical reinforcement for a concrete frame beams. The 6m long 300 series hollow-core units were then lowered into place on top of a low friction bearing strip. The top flanges of two of the hollow-core voids were pre-cut 75mm wide and approximately 800mm long to allow for the placement of the connection reinforcement. The connection and topping reinforcement was put in place together with cast in beams to tie down the support beam, and the top half beam, reinforced cores and 75mm topping concrete were cast. Tensile tests were carried out on samples of the reinforcement used in the two tests. For Specimen 1, the average yield strengths were 311 MPa for the D12 reinforcement and 325 MPa for the R16 reinforcement. For Specimen 2, the average yield strength for the D12 (Grade 500) reinforcement was 570 MPa. Standard structural ready mix concrete was used with a specified 30 MPa 28-day strength, 19mm maximum aggregate size and a 100mm slump. Test day compression cylinder test strengths were 41 MPa and 35 MPa for the topping concrete of Specimens 1 and 2 respectively, and 45 MPa for the supporting beams. Further information from the material tests is provided in Appendix A. The configuration of instruments used in the tests is illustrated in Figure 2-7(c). Strain gauges were attached to the starter bar and “hairpin� bar reinforcement to measure the level and amount of propagation of inelastic behaviour into the topping slab and hollow-core unit. Linear potentiometers were used to measure the relative movement of the supporting beam and floor slab as well as the horizontal pull-off and vertical dropping of the hollow-core unit relative to the supporting beam. Inclinometers were used to attain an accurate level of the drift
Page 2-17
imposed on the floor. Purpose-built data acquisition and control programs were employed to track the experimental data and automatically control the two actuators loading the specimen. A new loading rig and set-up was developed to test the two specimens. This loading set-up, through the use of dual displacement controlled actuators, loads the specimen in such a way that both the relative rotation between the floor and supporting beam and induced tension in the floor are integrated. A schematic of the set-up is shown in Figure 2-7(d). In the same way as the Bull and Matthews (2003), and Liew (2004) sub-assemblage tests were undertaken, a vertical actuator was located at the end of the 6m long hollow-core unit. This is able to provide negative and positive moments at the connection of the supporting beam with the hollow-core unit. In addition, a 35kN concrete block is placed at mid-span to generate extra shear force at the connection, which assures an equivalent shear force distribution to the full-scale prototype structure. The development from the previously conducted subassemblage tests (outlined in Section 2.2) is the coupling of the motions of the vertical and horizontal actuators. The horizontal actuator induces a net tension force in the floor slab and mimics the effects of beam elongation that occurs in three-dimensional structures. The displacement controlled loading history of the vertical actuator comprised of 2 complete reversing cycles to inter-storey drift amplitudes of ±0.5%, ±1%, ±2%, ±3%, ±4%, and ±5%. The inter-storey drift used throughout this section refers to the rotation (as a percentage) of the hollow-core floor unit with respect to the supporting beam. Positive drift denotes tension on the bottom of the hollow-core unit and negative drifts imply tensions within the starter bars and topping concrete of the floor unit. It should also be noted that from analysis of the test data, the target drifts and displacements were not always achieved due to the rotation and sliding of the supporting beam relative to the ground. Throughout the results and analysis presented in the following sections, this discrepancy has been accounted for.
Page 2-18
(a) Photograph showing the pre-cutting of the hollow core.
(b) Supporting beam reinforcing and connection detail (Specimen 1).
Starter bar strain gauges Inclinometers (spaced along the floor unit) Hairpin bar strain gauges
Beam-to-floor potentiometers
Floor unit pull-off potentiomenters Floor unit vertical displacement potentiomenters
(c) Instrumentation layout Vertical (drift controlling) Actuator
Reaction Frame
Reaction Frame 35kN Concrete Weight
Support beam and restraints 300 series hollow-core unit
6000mm
Horizontal (beam elongation) Actuator
South (side) elevation
Hollow-core unit Support beam and restraints
West (end) elevation
(d) Experiment set-up: location of the actuators and reaction frame.
Figure 2-7 Test set-up photographs and diagrams
Page 2-19
2.6
EXPERIMENTAL RESULTS: SPECIMEN 1
Figure 2-8 presents photographs of damage observed for the testing of Specimen 1 and further results are displayed in Appendix A. A crack opened at the floor unit-to-supporting beam interface during the ±0.5% cycle and this widened to around 5-6mm during the ±1% cycle peaks. During the ±2% cycles, this continuity crack had opened to around 10mm on the tension side and 5-6mm on the compression side, and following the second cycle to ±2%, the residual opening at this interface was 9-10mm, which signified the amount of beam elongation pulling the floor unit off the seat of the supporting beam. To this point, the only other signs of damage were hairline cracks that opened up at –2% within the topping concrete. However, on the subsequent cycle these cracks closed and did not reopen throughout the remaining testing. The ±3% and ±4% cycles were characterised by the continuing widening of the beam-floor opening, and at the conclusion of the test after a second ±4% cycle, the residual opening was around 25mm. The performance of this specimen is easier to describe by discussing what did not occur during the test. The large crack opening at the beam-floor interface showed that the rotational demand imposed on the floor unit was nil, and no damage of the floor unit was observed. The bearing strip performed its intended purpose of allowing the unit to slide horizontally relative to the supporting beam while staying in place on the concrete seat. The improved performance of the bearing strip also meant that no spalling of the concrete seat of the supporting beam occurred.
Page 2-20
(a) Cracking of topping at –2%.
(b) Beam-to-floor interface crack at the end of testing.
Figure 2-8 Photographs of the testing of Specimen 1.
A collection of the important instrumental results is shown in Figure 2-9 for Specimen 1. The overall hysteretic performance of the specimen is shown by the moment rotation relationship in Figure 2-9(a). The hysteresis shows good energy dissipation of the beam-to-floor connection at the interface and no premature degradation of stiffness or strength to drifts of ±4%. The maximum positive and negative moment capacities occurred at the first cycle to ±0.5% respectively, and the following cycles to ±4% showed a constant level of moment strength. It is noticeable for the negative drift cycles, that there were reductions in strength between the first and second cycle. The theoretical predictions show good agreement, and the derivation of the nominal and overstrength theoretical values are outlined in Section 2.8. The overstrength was determined from material testing for the reinforcement, and was taken to be the ratio of the ultimate tensile stress to the yield tensile stress. Behaviour from the strain gauged reinforcing is presented in Figures 2-9(b) through (e). The notation of the north core and south core refers to the northern most and southern most reinforced cores, or the second and fourth cores. Each of the four graphs for the starter and hairpin show similar trends.
Page 2-21
Moment (kNm)
100 80 60 40 20 0 -5
-4
-3
-2
-1
-20
0
1
2
3
4 Drift (%) 5
-40 Experiment Nominal Capacity 125% Overstrength Capacity
-60 -80 -100
(a) Moment rotation hysteresis performance of Specimen 1. Starter bar 1 4
2 5
3
1 & 4: 2 & 5: 3 & 6: Yield:
6
The drift displacement peak (time) denotes is a count of the half cycles. Appendix A provides a list of the displacement peaks for each count
45
45
40
40
35
35
30
30
strain
strain
Hairpin bar
25 20
25 20
15
15
10
10
5
5 0
0 -5
0
10
20
30
40
-5
0
(b) North core starter bar strains. 45
45
40
40
35
35
30
40
30
30
strain
strain
20
(c) South core starter bar strains.
50
25 20
25 20
15
15
10
10
5
5
0 -5 0
10
Drift displacem ent peak (tim e)
Drift displacem ent peak (tim e)
0 10 20 30 Drift displacem ent peak (tim e)
40
-5
0
10
20
30
Drift displacem ent peak (tim e)
(d) North core hairpin bar strains.
(e) South core hairpin bar strains.
Figure 2-9 Experimental Results for specimen 1: code amendment detail. Page 2-22
40
The strain measured by the strain gauges at the critical section at the beam-floor interface showed distinctly higher strains. This matches the experimental observations whereby the damage and cracking was concentrated at the beam-to-floor interface, and there was minimal amounts of cracking into the topping slab over the hollow-core unit. This indicates that the design objective of concentrating the rotational demand at the critical section was achieved. For the starter bar reinforcement, yielding occurred early – either at –0.5% or during the first cycle to -2% at the floor to beam interface. Whereas yield penetration reached the topping strain gauges 150mm away during the subsequent –2% cycles. Yield penetration however did not progress back into the beam until the final stages of the test. The same trend is shown for the hairpin reinforcement, where the plastic strains were highest at the critical section.
2.7
EXPERIMENTAL RESULTS: SPECIMEN 2
A collection of photographs from the testing of Specimen 2 are presented in Figure 2-10 and extended results are shown in Appendix A. Very little damage occurred during the ±0.5% cycles where there was only cracking at the sides at the end of the floor unit of the beam-slab interface and minor cracking within the topping slab. At –1% the continuity crack along the interface between the floor slab and supporting beam had opened to around 4mm, at +2% it had closed to be a hairline crack and at –2% it was 8-10mm wide. During the second cycle to +2%, spalling of the seat concrete of the supporting beam was observed which progressively worsened throughout the remainder of testing. At the second cycle to –3%, the continuity crack had widened to be 20mm at both the top and bottom of the hollow-core unit (Figure 2-10(b)). On the first cycle to +4%, a loud noise and accompanying drop off in load-carrying capacity was noticed at +3.8% suggesting reinforcement fracture of one of the bottom D12 bars. On the subsequent second cycle to ±4% there were similar fractures at +2.84% and then at –0.9%, -2.2% and -3.3%. Following the ±4% cycles, the spalling had extended over the Page 2-23
whole width of bearing of the floor unit. The bearing strip had become clearly visible as can be seen in Figure 2-10(c), and the seat width had been reduced to approximately 20mm. There was also evidence of the floor unit dropping down the face of the supporting beam. Prior to the Âą4% cycles the damage was moderate and repairable. However, following the first cycle to +4% the damage could be categorised as major and a similarly damaged building could only be entered under extreme caution. At +5% the bearing strip had split, was sliding horizontally off the seat with the hollow-core unit, and the unit had dropped by around 10mm down the face of the supporting beam. The beam-floor crack had opened to widths over 35mm. At +4.8% on the second cycle to +5% the north starter bar fractured and the seated support was lost.
(a) Topping and beam-floor interface cracking at –2%.
(c) Extent of seat concrete spalling.
(b) Beam-floor interface crack at +3% drift.
(d) Failure after a loss of seating (at 4.78% on the second cycle to 5%.
Figure 2-10 Photographs of the testing of Specimen 2
Page 2-24
Figure 2-11 displays the key results derived from the instrumentation from the testing of Specimen 2. The moment rotation behaviour is illustrated in Figure 2.11(a). An additional 20kN concrete weight was added at the midspan for upward loading (unloading from a negative drift peak), and both midspan weights taken off for downward loading (unloading from a positive drift peak to a negative drift peak). The increased bending moment gradient heightened the shear force at the support imparting higher shear demands on the beam-floor connection. In this case the compatibility with the full-scale testing was forsaken in order to more rigorously test the shear reinforcement of the connection detail. The instances of the reinforcement fracture are shown on Figure 2-10(a) by the sudden decrease of load carrying capacity. The overall hysteresis shows good performance up to the first cycle to +4%, but after the first reinforcement fracture (at 3.83% on the first cycle to +4%), there was a significant reduction in stiffness and load carrying capacity of the floor-tobeam connection. There was a distinct reduction of peak moments between the first and second cycles to +4%, largely due to reinforcement fracture at +2.8%, and on the second cycle to –4%, a series of three reinforcing fractures reduced the load carrying capacity appreciably. The capacity of the floor-to-beam connection during the ±5% cycles was minimal as a result of the prior reinforcement fractures, and overall failure occurred when the final starter bar fractured, under a positive drift, and the floor unit lost its seating at +4.78% on the second to +5%. The maximum positive moment capacity of the beam-floor connection occurred at +4%, and the maximum negative moment capacity occurred at –0.5%. This shows that for the positive drift cycles there was a good degree of strain hardening of the bottom reinforcement, which would have occurred prior to the reinforcement fracture. The theoretical predictions overlain on the moment rotation relationship show good agreement with the experimental results.
Page 2-25
Moment (kNm)
100 80 60
First Fracture
40 20
Drift (%)
0 -6
-5
-4
-3
-2
-1
-20 0
1
3
4
5
6
Fracture
-40
Fracture
2
Experiment Nominal Capacity 125% Overstrength Capacity
-60 -80 -100
(a) Moment rotation hysteresis performance of specimen 2. Starter bar 2
1 4
5
3
1 & 4: 2 & 5: 3 & 6: Yield:
6
The drift displacement peak (time) denotes is a count of the half cycles. Appendix A provides a list of the displacement peaks for each count
Hairpin bar
45
45
40
40
35
35 30
strain
25 20 15
25 20 15
10
10
5
5
0 -5 0
10
20
30
40
0 -5
-10
0
10
Drift displacem ent peak (tim e)
(b) North core starter bar strains.
20 30 Drift displacem ent peak (tim e)
40
(c) South core starter bar strains.
40
45
35
40
30
35 30
25
25
strain
strain
strain
30
20
20
15
15
10
10
5
5
0 -5
0
0
10
20
30
Drift displacem ent peak (tim e)
40 -5
(d) North core hairpin bar strains.
0
10 20 30 Drift displacem ent peak (tim e)
(e) South core hairpin bar strains.
Figure 2-11 Experimental Results for specimen 2: modified detail. Page 2-26
40
A comparison between the moment rotation behaviour for Specimen 1 and Specimen 2 shows the relative strengths of the two reinforced connection details. For Specimen 2, the higher positive moment capacity of the floor-to-beam connection and extra mid-span loads under upward loading would have imparted larger compression reaction forces on the seat, and the higher stresses can help to explain the amount of spalling. Figures 2-11(b) and (c) present the strain behaviour of the starter bars, and similarly 2-11(d) and (e) the hairpin reinforcement for the floor-to-beam connection. The behaviour is similar to that observed for Specimen 1, where the starter and hairpin reinforcement show similar trends. Pre-yield compression strains were experienced during the early stages of the test, however, following tensile yielding, the strains never returned below this yield strain value and the reinforcement hysteretic behaviour would have been characterised by a distinct shift into positive tensile strains. Yielding occurred early for the starter bars – during the first cycle to -1%, whereas yield penetration reached the topping concrete strain gauges (150mm from the end of the beam-floor interface) during the ¹2% cycles and 150mm back into the beam later during the ¹3% cycles. Plastic strains either side of the critical section of the hairpin reinforcement were experienced later relative to Specimen 1. To investigate the effects of vertical acceleration during seismic excitation, the testing procedure could have been modified. Vertical accelerations have important implications, and are accommodated for in design standards. Upward accelerations reduce the gravity loads on the flooring, causing a reduction of the bending moment gradient, and extending the demand on the topping reinforcement. The use of the additional concrete weight could have been used oppositely (extra midspan loads for downward loading, and no loads for upward loading). However, the strain relationship exhibited by the starter bar reinforcement shows that maximum demand is placed on the reinforcement at the interface, and the strain reduces further into the topping. The extent of which the strain diminishes away from the supporting
Page 2-27
beam over a greater length was not fully investigated, but it is assumed that either the continuous starter bars, or starter bars lapped with the same type of diaphragm reinforcement, that these effects would be accommodated.
2.8
STRENGTH AND FAILURE MODE PREDICTION MODELS
2.8.1
Moment capacity
To assess the strength of the reinforced floor-to supporting beam connections for both specimens, simplified moment equations have been used in order to calculate the positive and negative moment capacities. The structural actions imposed on the connection are shown in Figure 2-3(c) and the moment capacities were calculated from the common reinforced concrete relationship: Mn = Asfy(d-d’)
(2.3)
in which As = the cross sectional area of tension reinforcement, fy = yield stress of tension reinforcement,
d = effective depth to the centre of the tensile reinforcement taken from the
outermost compression fibre, and d’ = depth from the outermost compression fibre to the centre of the compression reinforcement. Actual values for the yield stress and reinforcment and the measured lever arm between the top and bottom reinforcement were used in the calculations. The overstrength moment capacity of the two reinforced floor-to-beam connections was also calculated as 125% of the nominal (yield strength measured from material tests) strength. Table 2-1 presents the values used and the corresponding moment capacities: The moment capacities have been plotted overlaying the experimental moment rotation behaviour and can be seen in Figures 2-9(a) and 2-11(a). It can be seen that there is good agreement with the experimental data for both of the test specimens. The moment rotation relationship for Specimen 1 is illustrated in Figure 2-9(a) where it can be seen that Page 2-28
the maximum positive and negative moments were experienced during the first cycle to ±0.5%. Despite this, the predictions for Specimen 1 showed that the experimental values lay within the 125% overstrength and nominal strength bounds. A similar quality of prediction is evident for Specimen 2, as shown in Figure 2-11(a). Although the first cycle to –0.5% produced the highest negative moment, there was some degree of overstrength or strain hardening that was predicted by the calculated values. From these results, it is evident that the use of an additional 25% strength to represent strain hardening effects is a satisfactory indicator of component overstrength at the floor unit-to-seat connection.
Table 2-1 Nominal moment capacity calculations. As-
(d-d')
MPa
mm 2
mm 2
mm
333 -
402 452
452 452
280 280
f y (D12)
f y (R16)
units
MPa
Specimen 1 Specimen 2
321 570
property
2.8.2
As+
Io 1.25 1.25
M n+
M n-
kNm
kNm
38 72
41 72
Low cycle fatigue
When assessing the ultimate deformation capacity of a structure, low cycle fatigue of reinforcing bars must be considered a likely failure mode, as described by Mander et al (1994). Further investigation by Dutta and Mander (2001) produced a low cycle fatigue theory that enables the plastic rotation life capacity of reinforcement to be calculated. The theory is expressed as follows:
Tp
§ D ·§ L p 0.16¨ ¸¨¨ © D' ¹© D
·§ 1 L p · ¸¸ 2 N f ¸¸¨¨1 ¹© 2 L ¹
0.5
(2.4)
in which Tp = plastic drift; L = lever arm of the cantilever column; D = overall member depth; D’ = distance between outer layers of steel, 2Nf = the number of reversals to the appearance of
the first fatigue crack with which Nf is the effective number of constant amplitude cycles for a
Page 2-29
variable amplitude displacement history and Lp = equivalent plastic hinge length, or the length of reinforcement where plastic strains are expected. Miner’s well-known cycle counting method can be utilised to calculate the equivalent number of equi-amplitude cycles (Nf):
Nf
§ T ¦i ¨¨ T © ref
· ¸ ¸ ¹
2
(2.5)
where T = drift for the ith cycle of loading and Tref = reference drift for an equivalent constant amplitude loading history. A more complete description of this theory and the calculations are present in Appendix A. Using a reference drift of 4% an applied cyclic demand of Nf = 3.8 cycles is calculated. Using Equation 2.4 and an equivalent plastic hinge length of the un-bonded length of reinforcment (150mm), a plastic drift Tp of 0.03 radians was found. Together with an elastic yield rotation of 0.7% that was derived from the experimental observations, the rotational capacity of the reinforcement before fracture is 0.037 radians, or 3.7% as calculated by Equation 2.4. This compares well to the observed first fracture that occurred at +3.83% drift.
2.9
DISCUSSION OF RESULTS
The visual and instrumental observations show that both specimens behaved well. Specimen 1 was able to sustain drifts of ±4% with no major damage to the supporting beam and hollowcore floor slab. Specimen 2 performed well up to the low cycle fatigue fracture of the reinforcement at +3.83% drift, but was still able to withstand further ±4% and ±5% cycles until a loss of seating failure occurred at +4.78% on the second cycle to +5%. The relative rotation damage was concentrated at the critical section at the interface between the
Page 2-30
supporting beam and floor interface for both specimens, and there was very little damage to the hollow-core units and topping concrete away from this critical section. However, there were still some shortcomings observed during the testing of Specimen 2. Large amounts of seat spalling was observed, which minimised the bearing area for the floor unit. During the final stages of testing, the amount of deterioration of the concrete seat meant that the hollowcore floor unit was sliding down the face of the supporting beam. The low friction bearing strip performed well for Specimen 1, but inadequately for Specimen 2, whereby the bearing strip slid horizontally with the hollow-core floor unit relative to the supporting beam. The unbonding of the reinforcement passing the critical section for Specimen 2 also showed an inability to prevent failure of the reinforcement. The maximum moments sustained by Specimen 2 were 70% greater than the maximum moments experienced by Specimen 1, which is to be expected from similarly reinforced connections with Grade 300 and 500E reinforcement. The larger moment capacity would have caused larger vertical reactions to be resisted by the seating concrete of the supporting beam. This can help to explain why the bearing strip performed as intended for Specimen 1, but not for Specimen 2, where the bearing strip slid horizontally with the hollowcore unit relative to the seat of the supporting beam. In turn, the poor performance of the bearing strip would have accelerated the spalling of supporting beam concrete seat. It is difficult to infer at what point a floor-to-beam connection becomes over-reinforced, but the relative damage between the two specimens indicates that the Grade 500E reinforced connection may have been too strong. Also, the plain round R16 bars (used for Specimen 1) appear to be more suitable in high ductility connections under high drift demands than the deformed bars used for Specimen 2.
Page 2-31
2.10 CONCLUSIONS From the experimental investigation presented in this chapter, the following conclusions may be drawn: 1.
The second of two hollow-core support details, as proposed by Amendment No. 3 to NZS 3101:1995: a rigid, reinforced floor-to-beam connection, behaved well, and was able to sustain inter-storey drifts up to Âą4% with little damage occurring to the supporting beam and hollow-core unit.
2.
A new testing procedure that introduced the realistic coupling of relative rotation of the hollow-core and supporting beam and the net tension in the floor slab from beam elongation three-dimensional effects as the main sources of damage was undertaken successfully.
3.
Simple analytical methods were proposed to assess the strength capacity of the hollowcore to supporting beam connections. Similarly low cycle fatigue theory was used to predict the rotation limit leading to reinforcement fracture. Both analyses provided accurate representations when compared with the experimental data.
4.
Evidence of over-reinforcement was observed with the use of Grade 500E reinforcement with increased amounts of damage being observed for Specimen 2. The presence of plain round reinforcement was more capable of resisting high ductility demands than the unbonding of deformed reinforcement, which led to fracturing of the reinforcement.
2.11 REFERENCES Bull D.K, Matthews J.G, 2003, Proof of Concept Tests for Hollow-core Floor Unit Connections, Precast NZ report, Feb 2003.
Dutta A and Mander J.B, 2001, Energy Based Methodology for Ductile Design of Concrete Columns, Journal of Structural Engineering, Vol. 127(12), December, pp 1374-1381. Page 2-32
Fenwick R.C, Davidson B.J, and Lau D, 1999, Strength Enhancement of Beams in Ductile Seismic Resistant Frames due to Prestressed Components in Floor Slabs, Journal of
the New Zealand Structural Engineering Society (SESOC), Vol 12, No. 1, pp 35-40. Herlihy M.D, Park R and Bull D.K, 1995, Precast Concrete Floor Unit Support and Continuity, Research Report 93/103, Department of Civil Engineering, University of
Canterbury, Christchurch, New Zealand. Herlihy M.D and Park R 2000, Precast concrete floor support and diaphragm action, Research Report 2000/13, Department of Civil Engineering, University of Canterbury, Christchurch, New Zealand. Lindsay R.A, 2004, Experiments on the seismic performance of hollow-core floor systems in precast concrete building, Masters Thesis, Department of Civil Engineering,
University of Canterbury, Christchurch, New Zealand. Lindsay R.A, Mander J.B, and Bull D.K, 2004a, Preliminary results from experiments on hollow-core floor systems in precast concrete buildings, 2004 NZSEE Conference,
Rotorua, NZ, Paper 33, 8 pp. Lindsay R.A, Mander J.B, and Bull D.K, 2004b, Experiments of the Seismic Performance of Hollow-core Floor Systems in Precast concrete Buildings, 13th World conference on
Earthquake Engineering, Vancouver, Canada, CD ROM paper No. 585. Liew H.Y, 2004, Performance of Hollow-core Floor Seating Connection Details, Masters Thesis, Department of Civil Engineering, University of Canterbury, Christchurch, New Zealand. Mander J.B, Panthaki F.D, Kasalanati A, 1994, Low Cycle Fatigue Behaviour of Reinforcing Steel, Journal of Materials in Civil Engineering, ASCE, Vol 6(4), November, pp 453-
468.
Page 2-33
Matthews J.G, 2004, Hollow-core floor slab performance following a severe earthquake, PhD Thesis, Department of Civil Engineering, University of Canterbury, Christchurch, New Zealand. Matthews J.G, Mander J.B, Bull D.K, 2004, Prediction of beam elongation in structural concrete members using a rainflow method, 2004 NZSEE Conference, Rotorua, NZ,
Paper 27, 8 pp. Meija-McMaster J.C and Park R, 1994, Tests on Special Reinforcement for the End Support of Hollow-core Slabs, PCI Journal, Vol 39, No. 5, pp. 90-105, September-October.
NZS3101, 1995, Concrete Structures Standard, NZS3101, Parts 1 & 2, Standards New Zealand, Wellington, New Zealand. NZS3101, 2004, Amendment No. 3 to 1995 Standard (NZS3101), Standards New Zealand, Wellington, New Zealand. Norton J.A, King A.B, Bull D.K, Chapman H.E, McVerry G.H, Larkin T.J and Spring K.C, 1994, Northridge Earthquake Reconnaissance Report, Bulletin of the NZNSEE, Vol. 27, No. 4, December. Oliver S.J, 1998, The Performance of Concrete Topped Precast Hollow-core Flooring Systems Reinforced with and without Dramix Steel Fibres under Simulated Seismic Loading, Masters Thesis, Department of Civil Engineering, University of Canterbury,
Christchurch, Canterbury. Trowsdale J.F, 2004, Seismic Performance of Hollow-core Seating Details Specified by Amendment No. 3 to NZS 3101:1995, Research report submitted as part of third
professional year coursework, Department of Civil Engineering, Christchurch, New Zealand.
Page 2-34
3. Section 3 – Super-Assemblage Experimental Investigation
SECTION SUMMARY Recent earthquakes and laboratory research has demonstrated the seismic vulnerability of buildings constructed with precast prestressed concrete hollow-core floor systems. However, follow-up research has shown that with simple detailing enhancements, significant improvement in the seismic performance of hollow-core floor systems can be expected. The present experimental research aims at validating several new detailing enhancements. Based on previous research findings, the present super-assemblage experiment included the following details: (i) a reinforced connection that rigidly ties the floor into the supporting beam, (ii) an articulated topping slab cast onto a timber infill solution that bridges between the hollow-core units and parallel longitudinal frame beams; (iii) a specially detailed plastic hinge zone in the beams that support the floor, that concentrates damage away from the hollow-core units; (iv) Grade 500E reinforcing steel used in the main frame elements; and (v) mild steel deformed bars in the concrete topping in lieu of the customary welded wire mesh. The full-scale structure is cyclically tested in both the longitudinal and transverse directions to inter-storey drifts of Âą5%. Visual and instrumental observations from the experiment are presented and discussed. The experimental observations demonstrate that with appropriate detailing it is possible to avoid undesirable failure modes induced in the hollow-core flooring and to shift all damage into the plastic hinge zones of the supporting moment resisting frame. Recommendations for the forthcoming revision of the New Zealand Concrete Structures Standard, NZS 3101, are made.
Page 3-1
3.1
INTRODUCTION
Research over the last decade at the Universities of Auckland and Canterbury has sought to determine the seismic adequacy of precast buildings with hollow-core flooring systems in New Zealand and to provide better solutions to preserve life safety. One of the major concerns identified from both overseas earthquake events and experimental investigations was the connection of these precast hollow-core units to the surrounding lateral load resisting system. Under earthquake loading that induces significant storey lateral displacements, the potential for the hollow-core units to lose their seating, leading to a possible partial or full collapse of the floor, focused research into the connection of the floor units with the surrounding perimeter beam. The collapse of the hollow-core units during testing by Matthews (2004) and Matthews et al (2003) identified serious flaws for existing precast concrete frame structures with hollow-core flooring structural systems. A continuation of this research (Lindsay, 2004 and Lindsay et al, 2004) demonstrated that enhanced reinforcement details could be implemented into new structures that should result in improved behaviour in a seismic event. This research project is a further continuation of previous work on existing structures (Matthews, 2004, and Matthews et al 2003, 2004) and on new structures (Lindsay, 2004, and Lindsay et al 2004). The popularity and widespread use of precast concrete is recognised in New Zealand design standards where there is specific reference to precast concrete flooring support conditions. Amendment No. 3 to the current New Zealand Concrete Structures Standard NZS 3101:1995 provides two specific “acceptable solution� details for the connection of hollowcore floor units to reinforced concrete frame supporting beams. The second solution specifies a reinforced connection that rigidly ties the floor into the supporting beam, but to this point remains untested in any large-scale three-dimensional experiments. The research reported herein presents an experimental investigation of the effectiveness of this solution and its Page 3-2
adequacy for inclusion into the upcoming revised New Zealand Concrete Code and use in New Zealand construction practice. Following a summary of the findings from previous research, this section initially provides an overview into the experimental set-up. The construction of the test specimen and the modifications made to the concrete moment resisting frame super-assemblage from the previous test programs are discussed. The specific details of this series of experiments are then provided including the hollow-core seating details, the lateral connection between the hollow-core unit and the parallel perimeter beams as well as the diaphragm reinforcement. The set-up of the experiment, including the material properties of the specimen, the instrumentation and the displacement drift controlled loading regime used are then discussed. The second part of this chapter provides the visual and instrumental observations of the testing. The hysteretic behaviour and strengths in terms of load displacement relationships of the system are shown. The results and overall effectiveness of the design changes and new features are discussed and concluding remarks are made.
3.2
FINDINGS FROM PREVIOUS RESEARCH
Owing to the widespread use of hollow-core flooring in precast concrete construction, an experimental program was initiated to examine the seismic adequacy of such systems in the New Zealand building stock (Matthews, 2004; Matthews et al 2003, 2004). A two bay by one bay concrete moment resisting frame was constructed to represent a one-floor corner segment of a typical New Zealand 10-20 storey precast concrete frame building. General results from that program showed that although the concrete frame performed relatively well, the “semirigidly� supported hollow-core flooring system, behaved poorly and collapsed at a relatively low level of seismic intensity. The main source of damage occurred due to the relative rotation between the supporting beams and floor and the expected sliding action of the floor Page 3-3
on the supports provided by the beams did not occur. A snapping action at the hollow-core-tosupport beam connection and in particular within the webs of the hollow-core led to the eventual failure of the floor. Recommendations for future connection details were made to ensure that any inelasticity and relative rotation was centred at the interface between the floor and supporting beam thereby protecting the hollow-core units. The connection between the floor and the frame spanning parallel to the hollow-core units also performed poorly as a result of the displacement incompatibility between the flooring, which is designed to sag and the perimeter beams, which deform in double curvature. The undesirable deformation demands placed on the hollow-core caused internal web cracking, fracturing of the cold drawn mesh that reinforces the diaphragm and ultimately, the failure of the lower half of the first hollow-core unit next to the two bay perimeter beams. Analytical work provided a more accurate means of determining the lateral strength capacity of the structure accounting for the influence of the floor slab contributing to the strength of the frame. A theory was developed to predict beam elongation (Matthews et al, 2004). A “rainflow counting� theory was advanced and validated against the experimental results. This provided a suitable method to calculate required seat widths for precast floor systems. In response to the poor behaviour of the hollow-core flooring during the Matthews (2004) experiment, a Technical Advisory Group on precast floors (TAG) was formed and new and improved seated connection details were recommended. Proof-of-concept sub-assemblage tests were carried out by Bull and Matthews (2003) under sponsorship from Precast NZ Inc. One of the new beam to floor connection details, which featured a low-friction bearing strip with a compressible backing board replacing the plastic bungs in the end cores of the units, performed well and was consequently recommended for firstly full-scale testing, and subsequent inclusion into a revised New Zealand Concrete Structures Standard.
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Lindsay (2004) repaired and reconstructed Matthews (2004) full-scale superassemblage specimen and then retested it. Whereas the Matthews (2004) experiment was retrospective examination of past construction techniques (1985-2000), Lindsay (2004) looked towards developing solutions for improved performance for future precast concrete construction practice. The seating detail included a low friction bearing strip and compressible backing board, and was implemented along with a connection isolating the first hollow-core unit from the perimeter beams by way of a timber infill solution. A more adequate connection was used which tied the central column into the floor plate. These modifications produced significantly improved behaviour, and the super-assemblage withstood up to inter-storey drifts up to +5%. Despite the good performance, the bearing strip was observed to slide on the seat (the ledge cast along the beams that support the precast hollow-core floor), the compressible backing board did not compress and hollow-core units seated on or near the highly deformed plastic hinge zones of the supporting beams showed cracking across the corners of the hollow-core units. The concrete of the seat spalled considerably, and although the hollow-core was relatively undamaged, the units were beginning to slide off the seat and down the face of the supporting beam. The infill detail behaved well and proved to be a suitable flexible link isolating the beams and floor. However premature fracture of the diaphragm ductile mesh produced a longitudinal tear within the topping concrete along the interface between the timber infill and the first hollow-core unit. Other research programs have looked at hollow-core connection detailing at a subassemblage component level. Meija-McMaster and Park (1994), Herlihy et al (1995), Oliver (1998) and Herlihy and Park (2000) tested various reinforced hollow-core to beam connections. Tests were primarily featured pull-off tension loads, to determine the adequacy of reinforcing to be able to carry the weight of the floor if a loss of seating occurs. Among the results, the tests showed that plain round reinforcing could provide suitably ductile behaviour.
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By comparing the aforementioned sub-assemblage component research with the failure modes witnessed during the Matthews (2004) experiment, it was realised that the earlier work was fundamentally flawed in that the rotational component of deformation was not included in the sub-assemblage experiments. Subsequently, testing by Bull and Matthews (2003) and Liew (2004) included a cyclic vertical force into the testing set-up to create cyclic relative rotations between the supporting beam and precast floor slab.
The experiment
conducted by Liew (2004) showed that over-reinforced connections could be detrimental towards performance. By forming a strong, rigid connection between the floor slab and supporting beam, the relative rotational demand concentrated the damage at the relatively weaker regions in the hollow-core floor slab away from the supporting beam. The brittle nature of hollow-core meant that failure occurred at low imposed drift demands. It is therefore important that there is a consideration of the influence of reinforcing the connection between the hollow-core units and the supporting beams.
3.3
SUPER-ASSEMBLAGE SPECIMEN DESIGN DETAILS AND CONSTRUCTION
3.3.1
Hollow-core Seating Details
The seated connection detail used for this experiment is the second “acceptable solution” detail given in Amendment No. 3 to NZS 3101:1995. The connection features two of the four cores within the hollow-core units reinforced and filled with concrete, and is diagrammatically shown in Figure 3-1(c). Deformed 12mm Grade 300 (D12) reinforcing is used at 300mm centres for the starter bars, which is lapped with the same steel as the diaphragm reinforcement. In the two reinforced cores, R16 Grade 300 bars (the “R” denotes plain round bars) were placed close to the bottom of the cores, with both ends hooked to provide sufficient anchorage in the beam and hollow-core.
Page 3-6
Reaction frame
Pinned steel tie beams Unit 4
750x750 columns
Unit 3
300 series hollowcore units
Transverse beams
Unit 2
N W
475x750 transverse beams
Unit 1
E
750 wide timber infill
S
400x750 longitudinal beams
Plan 6100
6100
3500
6100
Double acting roller bearings
Pinned fixed column Side elevation
Front elevation
(a) Details and geometry of the super-assemblage. Starter bars from the longitudinal beams
Column
(extended into first hollowcore unit)
Hollowcore Units
Timber Infill
Transverse Beam Hooked Bar (in addition to the regular reinforcing)
Longitudinal Beam
(b) Design modifications incorporated within the super-assemblage D12 Starter Bars (Grade 300)
Floor Unit
Supporting Beam
Low friction bearing strip
Concrete Seat (ledge)
2*R16 (Grade 300) - 1 per filled core Seat Transverse Reinforcement
10mm
15mm 50mm
Low Friction bearing strip
75mm
75mm seat (west end) 50mm seat (east end)
(c) Hollow-core Seating Connection Detail D12 Starters extending 600mm into the first hollow-core unit (lapped with diaphragm reinforcing)
Hollowcore Units
(d) Close-up view of the seating
75mm Concrete Topping Timber in-fill 750mm
200mm*25mm Timber boards Perimeter beam
(e) Lateral Articulated Infill Slab Connection Detail
Figure 3-1 Super-Assemblage building and hollow-core connection details.
Page 3-7
To prevent concrete entering the two non-filled cores of each hollow-core unit, a backing board was used in place of the more conventional end plug. This was used to ensure that the rotation of the floor units relative to the beam occurs at the critical section at the beam-tofloor interface and that the relatively brittle hollow-core unit did not experience high rotational demands. The backing board substitutes for the conventional use of end plugs, which create a concrete stub part way into the cores, which, under relative rotations, causes prying and splitting forces within the un-reinforced hollow-core webs. The hollow-core unit was seated on a low friction bearing strip and the seat widths are 50mm and 75mm at the east and west ends of the test structure respectively as shown in Figure 3-1(c) and (d). The code Amendment prescribes a 75mm seating, even so, it was decided to investigate the effect of a shorter seat width for cases when hollow-core units arrive on site shortened, due to shrinkage and creep, indicative of real construction practice.
3.3.2
Lateral Connection and Diaphragm Reinforcement
The infill detail used in this experiment stems from the recommendations made by Lindsay (2004) and is shown in Figure 3-1(e). A 75mm concrete topping is cast on a 750mm long by 25mm thick timber plank infill running between the first hollow-core unit and the longitudinal beams. The starter bars from the perimeter beams extend 600mm into the topping above the first hollow-core unit. The longer starter bars and use of conventional reinforcement instead of cold drawn or ductile mesh was used as a means to increase the ductility capacity at the infill-hollow-core interface and mitigate the risk of fracture from occurring, as observed previously (Matthews, 2004; Matthews et al 2003, 2004; Lindsay, 2004; Lindsay et al, 2004). For this experiment, Grade 300 D12 bars (the “D� designates bars with deformations) have been used at 300mm centres in both directions. The use of D12 bars in the topping slab is beneficial because they are the same as the starter bars used, and all lapping is between the
Page 3-8
same type of reinforcement. The current standards as proposed in the amendment to NZS 3101:1995, state that starter bars should extend to the larger of either 20% of the hollow-core span, or the development length (ld) plus an additional 400mm, which in some cases can be a considerable length. In this case, the starter bars and diaphragm bars are the same cross sectional area and spacing, meaning effectively full-length starter bars with no curtailment. The starter and lapped bars were strain gauged to investigate the optimal length that starter bars should be. Also, two XD20 “drag” bars (where the “X” denotes Grade 500 bars), which were successfully implemented into the testing by Lindsay (2004), were cast through the topping over the flooring and the central column to tie back the column to the floor.
3.3.3
Super-Assemblage Construction
The full-scale super-assembly specimen, shown in Figure 3-1(a), was a two-bay by one-bay structure designed as a lower storey corner section of a multi-storey precast concrete moment resisting frame building. The pretensioned flooring system runs parallel to the longitudinal beams (east-west), past the central column, and are seated on the transverse beams. The frame dimensions were identical to the original Matthews (2004) supper-assemblage to maintain the same loading set-up and to be able compare results. The columns were 750mm square in section, spaced at 6.1m centres with an inter-storey height of 3.5m. The longitudinal beams were 750mm deep by 400mm wide, while the transverse seat beams were 750mm deep by 475mm wide. The super-assemblage was constructed in a similar fashion as it would be done on a construction site. A photograph of the frame during construction can be seen in Figure 32. A full set of construction drawings and photographs can be found in Appendix B. The original super-assemblage experiment (Matthews, 2004) was a retrospective look at the structural details of existing buildings, whereas the second experiment (Lindsay, 2004) along with the present investigation are aimed at providing new solutions for future construction. With this in mind, it was decided to use Grade 500E seismic reinforcement Page 3-9
throughout the frame, which is currently the most commonly used grade of steel in New Zealand construction practice. The concrete frame was designed according to NZS 3101:1995, and is in keeping with the original Matthews frame strength and hierarchy of strength. Following weak beam-strong column capacity design principles, the beam plastic hinges were designed to the same strength as the original cases, however, using Grade 500E steel. The beams required 6-XD25 bars, the exterior columns required 12-XD25 bars and the centre column contained 24-XD 25 bars.
Figure 3-2 Photograph showing the precast concrete frame after it has been erected. During previous testing, the hollow-core units seated on the potential plastic hinge zones of the supporting beams suffered damage due to the high deformation occurring in these zones. To avoid such deformation demand on the floor units, a hooked bar was placed within the beam to force the hinge to occur close to the column face as shown in Figure 3-1(b). Another negative feature revealed in the previous experiments was the spalling of the seat concrete. To overcome this, transverse reinforcement was placed within the seat to tie the seat concrete back into the beam, as shown in Figure 3-1(c). A second generation of low friction bearing strip was used which featured longer ‘teeth’ to both increase the friction resistance on the underside of the strip, which is in contact with the ledge of the seat, and to negate the effects of seat surface roughness. Page 3-10
3.3.4
Material Properties
New Zealand manufactured Grade 500E seismic reinforcement was used throughout the super-assemblage, with the exception of the diaphragm and hollow-core-to-frame connection, which used Grade 300 seismic reinforcement. Table 3-1 presents a summary of the tensile test information while a full set of stress strain curves are presented in Appendix C.
Table 3-1 Reinforcing steel tensile test material properties. Tensile Test Strength and Strain Characteristics Location Reinforcing
fy (MPa)
fsu (MPa)
Es (GPa)
Esh (GPa)
Hsh
Hsu
Column & Beam Longitudional Steel
YD25
536
675
214
3.27
0.0015
0.0128
Column & Beam Transverse Steel Support Connection Starter Bars and Diaphragm Drag Bars
YR12 R16 D12 YD20
530 336 307 580
714 469 447 724
190 186 181 246
4.48 3.65 3.82
0.0005 0.0031 0.0029 0.0012
0.0152 0.0200 0.0218 0.0156
Ready mixed concrete with a specified target compression strength of 30MPa, a maximum aggregate size of 19mm and a slump of 120mm was used to cast the precast specimen components. The topping slab was a 30MPa pump mix with a maximum aggregate size of 13mm. Table 3-2 shows the 7-day, 28-day and test day cylinder compressive strengths measured from an average of three 200mm long by 100mm diameter cylinders.
Table 3-2 Concrete compressive strength material properties. Compression Test Strengths (MPa) Location
7 Day
28 Day
Test Day
26.7 21.2 25.1 31.8 31.0 -
37.8 30.1 32.0 -
45.3 41.2 35.2 46.0 40.6 > 60
Precast Frame Units 1 Precast Frame Units 2 Precast Frame Units 3 Splice Half Beams Topping Slab & Half Beams Grout: Column Reinforcing
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3.4
EXPERIMENTAL SET-UP
The testing of the super-assemblage was completed in four Phases: (i) longitudinal loading; (ii) transverse loading, (iii) re-loading in the longitudinal direction, and (iv) re-loading in the transverse direction. For Phase 1 and 3 loading, the set-up shown in Figure 3-3(a) illustrates the location of the secondary load frames and primary load frames, which were attached to the south frame of the super-assemblage. In each bay there were two actuators in opposing diagonal directions: one that is displacement controlled, the other force controlled. Actuators attached to the bottom of the north columns were displacement controlled and used to maintain the same inclinations as the south columns and thereby minimise the torsion in the transverse beams. Figure 3-3(c) shows an elevation of the loading setup for the south centre column. For the previous experiments by Matthews (2004) and Lindsay (2004) this was the setup for the transverse loading only, but this setup remained for the entire duration of testing for this experiment. These actuators, by applying equal and opposite forces were able to keep the centre column at a suitable transverse (north south) inclination during the longitudinal (Phase 1 and 3) loading – again minimising the torsion of the longitudinal beams. During the transverse Phase 2 loading, these actuators ensured that the central column was at the same inclination as the corner columns. The configuration shown in Figure 3-3(b) shows the transverse set-up that was attached to the east and west frames (as shown) to allow loading in the orthogonal transverse direction.
3.4.1
Instrumentation
Due to the size of this test specimen, an extensive array of instrumentation was required to acquire all the experimental data. A custom designed program and data acquisition system developed at the University of Canterbury were used to record and save the data from all of the various types of instruments at each increment of load. Similarly, a control program was Page 3-12
developed, in house, to actively control each of the actuators to load the structure in a displacement-controlled manner. For a full account of the control system and algorithms utilised for the loading, refer to Matthews (2004). Diagrams showing the instrumentation can be seen in Figure 3-4. The load was monitored by load cells that were attached to each of the eight hydraulic actuators used during the experiment. Similarly, rotary potentiometers were able to monitor the actuator displacements. Each leg of the secondary load frames was strain gauged in a full-bridge configuration allowing the load to be monitored and the redistribution of load through the system to be followed. A significant portion of the instrumentation was to measure the displacements of the structure through inclinometers, linear potentiometers and displacement transducers. The drift displacement controlled nature of the experiment was achieved by using inclinometers to measure the inter-storey drift of the structure or inclination of the columns. Sonic displacement transducers were used at the base of the columns to accurately measure the column sliding movement. Linear potentiometers of different sizes were placed at numerous positions of the building to measure any large displacements, such as the flexural, shear and elongation deformations of the plastic hinges, movement of the hollow-core units and relative movement of the timber infill. The floor diaphragm was also extensively instrumented by a grid pattern of ‘Demec’ points, where the distance measured between the points allow strain patterns of the entire floor to be generated. Vertical levelling was undertaken at discrete points on the floor to obtain a contour map of the vertical displacements of the diaphragm as well as provided an absolute measure of the vertical displacement of the whole structure. Finally, starter bar and “hairpin” reinforcement for the support connections, starter bars passing over the infill and the bars tying the central column into the floor were also been strain gauged to monitor the level of load or inelasticity that the reinforcement were subjected to.
Page 3-13
(a) Load frame and hydraulic actuator set-up for Phase I and 3 in-plane. Secondary loading frame
Ac tua tor D E tor a tu Ac Self equilibrating loading frame
(b) West end elevation of the load frame and hydraulic actuator set-up for Phase 2 out-of-plane testing. Hydraulic actuator (Ram H)
Back Steel Tie Frame Columns
Reaction frame
Hydraulic actuator (Ram G)
Reaction frame
Linear bearings
(c) Side Elevation view of the central column load frame and loading set-up.
Figure 3-3 Loading set-up for the three loading Phases. Page 3-14
Strain Gauge Location 300
T
1
3 2
B
1
2
4
Strain Gauge Locations 600
600
600
Timber Infill
5
Hollowcore Units
30mm pots measuring the horizontal pull-off and vertical drop of the floor units relative to the supporting beam Low Friction bearing strip on the 50 or 75mm seat
(a) Hollowcore support potentiometers and strain gauge instrumentation.
50mm pots
Potentiometers measuring the relative vertical displacement between the floor diaphragm and perimeter beams
(b) Timber infill potentiometers (16 sets) and strain gauge instrumentation.
Pots to measure half beam elonation
Displacement Transducers - One in either direction on front columns
Front elevation
Pinned fixed column
Displacement Transducers - One in in-plane direction on back columns
Side elevation
(c) Location of displacement transducers and Inclinometers. Potentiometers (top and bottom) measuring the fixed-end rotation and curvature of the beam plastic hinges
Beam Plastic Hinge Potentiometer instrumentation - measuring hinge shear and flexural deformation
Potentiometers measuring longitudinal beam bar slip through the beam-column joint
Beam-Column Joint Potentiometer instrumentation - measuring joint shear deformation
(d) Location of beam plastic hinge and beam column joint potentiometers.
Figure 3-4 Instrumentation used for the super-assemblage testing.
Page 3-15
3.4.2
Loading Protocol
Experimental loading protocols at the University of Canterbury have commonly been based on cyclic loading at increasing ductilities (Park, 1989). For the Matthews (2004) experimental investigation into the seismic performance of existing structures a new loading pattern was developed. The aim of the displacement loading regime was that it would be indicative of what a similar structure would experience during a real earthquake event. The loading protocol was based on studies into probable drift demands of a range of precast concrete frame buildings subjected to time history analyses under a suite of different earthquake records. For the Lindsay (2004) experiment, the experiment was centred on investigating the seismic behaviour of newly designed or constructed structures. Therefore, a more conservative assessment of the seismic capacity was sought and hence a higher displacement demand was necessary. This experiment also investigates the performance of a new solution, and is utilising the same loading protocol as what was used during the Lindsay (2004) tests offering a direct comparison of the results. The experiment consists of four phases comprising of: (i) longitudinal loading of two completely reversed cycles of ±0.5%, ±1% and ±2%; (ii) transverse loading of two completely reversed cycles of ±0.5%, ±1%, ±2% and ±3%; (iii) longitudinal re-loading of an initial cycle to ±2% followed by two completely reversed cycles of ±3%, ±4% and ±5%; and (iv) transverse re-loading of one complete reversed cycle of ±3%, and then two completely reversed cycles of drift amplitudes of ±4% and ±5%. The Matthews (2004) or Lindsay (2004) experiments did not conduct Phase 4. Therefore, for comparative purposes, only the first three phases of results are reported herein.
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3.5
EXPERIMENTAL OBSERVATIONS
3.5.1
Phase 1: Longitudinal Loading
Phase 1 longitudinal loading included two cycles at increasing drift amplitudes to ±2%. Some photographs of the key damage are shown in Figure 3-5. Throughout the descriptions of the test results, a positive inter-storey drift refers to when the tops of the columns move in an east direction and the bottoms of the columns move west. From the early stages of testing, diagonal torsional cracks appeared at the ends of the transverse beams and continued to extend and widen throughout this phase of testing. Figure 3-5(b) shows early stages of torsion with ‘X’ type cracking. Cracks, propagating diagonally outwards from the longitudinal beams across the infill slab first appeared at +0.25% and continued to extend into the topping concrete of the first hollow-core unit. Figure 3-5(c) shows the tendency of the crack pattern to arch towards the south central column. At +1%, a longitudinal crack was observed between the first and second hollow-core unit, and after the 2% cycles this had extended to be around 6m long. Damage in the plastic hinge zones was largely restricted to one major crack at the beam to column interface, and another significant crack around 300mm from the column. Some instances of spalling of seat cover concrete were evident at +1% and after the 2% cycles, the spalling had not extended but had worsened in a few areas as can be seen in Figure 3-5(d). A single continuity crack formed along the beam to floor interfaces, as shown in Figure 3-5(a), hairline soffit cracks were first noticed underneath the a filled core at the east end of Unit 1 and then a web crack was observed at +2% propagating at 45 degrees from the seat to the topping. Beam elongation was illustrated both with the residual crack openings and by the sliding of the floor units off the supporting beams (which could be seen by the exposure of unpainted soffit of the hollow-core floor units). Results showed that the bearing strips worked as expected. The residual drift after the ±2% cycles was around ±1.1% and the structure had suffered moderate but possibly repairable damage. Page 3-17
(a) Continuity crack forming at the east end at +2%.
(b) Torsional cracking of the North West Transverse Beam at –1%
(c) Cracking over the infill and floor of the west bay (looking towards south centre column) after Phase I testing.
(d) Removed spall concrete at east end and exposure of the bearing strip after Phase I testing.
Figure 3-5 Damage to the test super-assemblage during and after Phase I longitudinal loading.
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3.5.2
Phase 2: Transverse Loading
A selection of photographs showing the behaviour of the test specimen under Phase 2 transverse loading is shown in Figure 3-6 where the convention for postive drift is when the tops of the columns move north and the bottoms of the columns move south. The early stages of testing exhibited little new damage, and behaviour was characterised by the pre-existing cracks (caused by Phase 1 loading) opening wider. In a similar fashion to the longitudinal beams, the rotation experienced by the transverse beams was concentrated at or near the column face rather than being distributed over a conventional plastic hinge zone length. Figure 3-6(a) and (b) show the damage in these zones, where crack widths were approximately 15mm at +3% drift. There was little new damage to the floor and topping slab in general, although elongation of the transverse frames was clearly apparent with large openings between the column and topping slab at the top of the beams under negative moments. At +3% drift, the opening was around 15mm at the top of the transverse beams at the north ends and the topping slab was pulling away from the south corner columns by approximately 25mm at –3%. Vertical deformations of the floor also became apparent with the floors dropping away from the column, which could also be seen from the shear deformation along of the large cracks at the ends of the transverse beams. The large deformations occurring at the northern end of the east transverse beam, due to shear and flexure, resulted in a crack to propagate from the seat through the northernmost filled core of Unit 4 and into the topping slab, as shown in Figure 3-6(c). This damage did not worsen during the rest of the testing. After the completion of the Phase 2 transverse loading to ¹3% the residual drifts were approximately ¹1.6% and the structure had suffered moderate damage but was still in a repairable state.
Page 3-19
(a) Damage to the south end of the west transverse beam at +3%.
(b) Damage to the north end of the west transverse beam at +3%.
(c) Hollowcore web cracking and damage at the north east corner after Phase 2 testing.
Figure 3-6 Notable damage from Phase 2 transverse testing.
3.5.3
Phase 3: Longitudinal Re-Loading
Figure 3-7 shows some key photographs of the Phase 3 longitudinal re-loading of the test specimen. During the initial stages of loading below ±2% no additional significant damage occurred. At +3% drift, several of the infill slab cracks extended over the hollow-core units and small vertical displacements were first noticed (~1mm) at these cracks. A 1m long soffit crack, 1-2mm wide, appeared at the west end of Unit 1 underneath one of the filled cores. However no more damage to the hollow-core or beam seats of the supporting beams was witnessed throughout the remaining testing. Upon loading towards –3% drifts, crushing of the top concrete of the south centre column occurred at –2.4%, which can be seen in Figure 37(d) and was matched by a small load drop off. It was also apparent to see the torsional nature of the transverse beams. Whilst the south frame and columns were inclined the transverse beams appeared to remain near vertical, acting to minimise the relative rotation imposed on the hollow-core-to-beam seating connections. Cracking at the ends of the transverse beams
Page 3-20
showed between 2mm and 5mm of outwards movement and evidence of torsional hinging. It was expected that the transverse beams would rotate rigidly with the corner columns with slight inclination changes towards the midspan due to the eccentric loading of the flooring. At ±4% drifts, significant amounts of concrete had become loose and fallen from the plastic hinge zones at the ends of the south, east and west beams, and several of the reinforcing bars became visible at the bottom of the southwest hinge and top of the southeast hinge of the south beams. Although the structure was still in a stable condition, the damage in some areas became irreparable and major components would need to be replaced for further structural use. The phenomenon of beam elongation was again illustrated on several instances. Figure 37(c) shows the gap opening of around 25mm wide at the southwest column, and Figure 3-7(e) demonstrates by way of the unpainted floor, the amount of sliding of the floor units off the supporting beams. Prior to the first cycle to –4% drift, buckling of the compression bars at the bottom of the southwest beam was observed, as illustrated in Figure 3-7(f) and at the top of the southeast beam. On the accompanying cycles with an opposite bending moment, the bars did not straighten completely in tension. During the final cycle of loading to ±5% drift, at –1.14% and then at –0.36% unloading from –5%, the inside and outside top reinforcing bars respectively at the southeast beam hinge, fractured as shown in Figures 3-7(g) and (h). Although the load-carrying capacity of the structural system was jeopardised, collapse prevention was maintained; all but two reinforcing bars ensured that the frame remained stable and the lack of damage to the hollow-core units and seating support mitigated any major life safety concerns.
Page 3-21
(a) Super-assemblage specimen at +5% interstorey drift.
(b) Damage to southeast plastic hinge at +5% of the south frame.
Direction of movement
(c) Top view: crack opening (~25mm) at between the southwest column and floor topping slab.
(d) Top view: concrete crushing at south centre column.
(e) Evidence of elongation and the floor units sliding on the bearings. (seen as the unpainted soffit, Unit 1 west end)
(f) Longitudinal beam bar buckling (southwest beam bottom, south frame).
(g) Longitudinal beam bar fracture at –1.14% (southeast beam top outside bar)
(h) Longitudinal beam bar fracture at –0.36% (southeast beam top inside bar, south frame).
(i) Infill and floor damage after testing.
Figure 3-7 Damage during and after Phase 3 longitudinal reloading. Page 3-22
3.6
HYSTERETIC PERFORMANCE AND SYSTEM STRENGTHS
Figure 3-8 presents the lateral base shear force displacement (drift) hysteretic performance of the super-assemblage for each of the three loading phases. Figure 3-8(a) shows the behaviour for Phase I loading, where a maximum positive and negative base shear capacities of 1460kN and –1380kN was observed. These maxima both occurred on the first cycle to ±2%, although it must be noted that there was only a small reduction in base shear capacity during the second cycle. The hysteresis loop for Phase 1 loading exhibits a small reduction of stiffness at low inter-storey drifts. This could be explained by the opening and closing of cracks and the general “slop” associated with the pins within the load frames and actuators. Phase 2 conversely shows no premature deterioration of strength or stiffness and that the longitudinal Phase 1 had little effect on the structural behaviour. The maximum positive and maximum negative base shear forces were 755kN and –801kN respectively which both occurred on the first cycle to ±3%. There was no loss is base shear capacity during the second ±3% cycle. The non-symmetrical layout of the super-assemblage, with the tie frame at the north end can help to explain the differences between the positive and negative base shear capacity values. Under negative drift cycles, the south beam starter bars that pass over the infill tying the beam into the floor are activated under negative bending moments. A crack extending along this beaminfill interface opened up during testing to negative drifts, and was 8mm wide near the columns and 1mm wide at midspan of the south beams. Under positive drifts there are no starter bars along the northern edge of the floor to be activated, and hence a slightly smaller base shear capacity is observed.
Page 3-23
Base Shear Force (kN)
W
E
2000 1500 1000 500
Inter-Storey Drift (%) -2.5
-2
0
-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
-500 -1000
W
E
-1500 -2000
S
Base Shear Force (kN)
(a) Hysteresis behaviour for Phase 1 longitudinal loading.
N
1000 800 600 400 200
Inter-Storey Drift (%) -4
0 -2
-3
-1
-200
0
1
2
3
4
-400 S
-600
N
Pre Torsion
-800
Post Torsion
-1000
(b) Hysteresis behaviour for Phase 2 transverse loading.
W
Base Shear Force (kN)
2000
E
1500 1000 500
Inter-Storey Drift (%) 0 -6
-5
-4
-3
-2
-1
0
1
2
3
4
5
-500 -1000
W
E Phase 3
-1500
Phase 1
-2000
(c) Hysteresis behaviour for Phase 3 longitudinal re-loading.
Figure 3-8 Base Shear Force – Inter-storey drift Hysteresis behaviour for the three phases of testing.
Page 3-24
6
The hysteretic performance of the super-assemblage during Phase 3 longitudinal loading is shown in Figure 3-8(c). The maximum positive base shear was 1583kN and the maximum negative base shear force was recorded at –1536kN which both occurred during the first cycle to ±3%. Noticeable reductions in the base shear capacity were observed between the first and second cycles to ±4% and again to ±5% - approximately a 14% decrease in base shear capacity. Sudden drop-offs in load due to crushing of the topping concrete either side of the south central column can be seen in Figure 3-8(c) firstly at –2.4% and at +3.5%. The overlying hysteretic behaviour from Phase 1 shows that the damage from the transverse Phase 2 loading did not have a detrimental effect, and the maximum positive and negative base shear forces were observed during Phase 3 testing. Subsequent longitudinal testing to high drifts would, due to the longitudinal beam reinforcing bars fracturing (on the second cycle, unloading from –5%), result in a reduction in the base shear capacity of the structure.
3.7
DISCUSSION OF RESULTS AND EFFECTIVENESS OF DESIGN CHANGES
3.7.1
Transverse Beam Torsion
Perhaps the most significant feature of the present experiment was the extent of torsional twisting evident, under longitudinal loading, of the two transverse floor-supporting beams. Five inclinometers were installed on the western transverse beam to gauge the amount of torsion experienced. Figure 3-9(a) presents the torsion, in terms of percentage drift as a function of time for Phase 1 and Phase 3 loading, and the true extent of the relative torsional twist that occurred in the plastic hinge zones at the ends of the transverse beams is illustrated in Figure 3-9(b). It can be seen that during early stages of testing, the rotation of the beam followed that of the corner columns - rigid rotation which would be expected. In the latter stages of Phase 1 the beam rotation was similar to the columns for positive drifts but less for negative drifts. This can be explained by the eccentric loading of the flooring units rotating Page 3-25
the beam in a positive direction, and torsional moments generated by the moment resisting beam-floor connection reinforcement, as the torsional stiffness of the beam progressively degrades. During testing, cracking was observed on the transverse beam hinges at early stages and at -1%, ‘X’ type torsion cracks were evident. The torsion behaviour for Phase 3 loading, seen in Figure 3-9(a) showed interesting results and that the transverse Phase 3 loading had had a marked effect. The results illustrate that the beams remained essentially upright throughout the test. There is an apparent tendency towards positive drifts accounting for the eccentric floor support. For example, at the first cycle to +4% the beam was at an average +1% inclination, and the first cycle to –4%, the beam remained at around +0.1%. All five of the inclinometers show similar behaviour. This indicates that the torsion occurred at the ends of the beams in the plastic hinge zones. Similar behaviour and damage was observed at the eastern end of the super-assemblage. Appendix D shows the location of the five west beam inclinometers. The presence of torsional hinges had important effects on the behaviour of the structure. The first issue is that the torsion could reduce the strength of the flexural hinges placing increased demand on the reinforcement and concrete. This could possibly jeopardise the integrity of the structure. However, no major detrimental behaviour was observed. The positive implications of the torsional hinging was that the relative rotation between the flooring units and supporting beam, which is the primary cause of damage to the supporting beam-to-floor connection, was effectively small and can help explain the improved performance of the seated connection and lack of damage as compared to the floor tested by Matthews (2004). The torsional behaviour is quite different to what was observed during the previous experiments
conducted
by
Matthews
(2004)
and
Lindsay
(2004).
Figure
3-10
diagrammatically illustrates the difference in behaviour between the experiments. It was
Page 3-26
expected that in a similar way to the previous tests, the torsion would be distributed over the length of the beam rather than at torsional hinges at the beam ends. The current experiment featured a lower amount of reinforcement (6XD25: U = 0.98% compared with 12D24: U = 1.8% of the earlier experiments) passing into the column, resulting in a reduced torsional stiffness. However, the most likely cause of the torsional hinging is the effect of the reinforcement connecting the supporting beam and hollow-core units. The rigid floor-to-beam connection acted to keep the beam more upright, imposing an opposing torsional force as the column and beam rotates. The floor-to-beam connection detail used in the Lindsay (2004) experiment was in effect a ‘pinned’ connection, and this lack of fixity of the connection detail would mean that the additional torsion applied to the supporting beam would not be present.
Torsion Rotation (%)
A more detailed examination of the torsional behaviour observed is provided in Section 4. 6 5 4 3 2 1 0 -1 -2 -3 -4 -5 -6
Phase 3 loading
Phase 1 loading
SW Column Inclination Inclinometer 2 Inclinometer 4
Inclinometer 1 Inclinometer 3 Inclinometer 5
An gle of Twist (rad/m)
(a) West beam inclination during Phase 1 and 3 loading. 6 5 4 3 2 1 0 -1 -2 -3 -4 -5 -6 -7 -8
Phase 3 loading
Phase 1 loading
(b) Torsional twist of the south hinge of the west transverse beam (radians/metre in plastic hinge zone)
Figure 3-9 Torsion rotational behaviour of the western transverse beam.
Page 3-27
Large rotation at the end of the beam
South-West Column
Small rotation at the centre of the beam
Torsion distributed over length of beam Eccentric weight of floor units
(a) Behaviour observed during Matthews (2004) and Lindsay (2004) experiments (adapted from Matthews (2004))
Large rotation at the end of the beam
South-West Column
South-West Column
3D effects of beam elongation front frame elongates and pulls beam ends away from floor, but out-of-plane bending and strong floor-beam connections means small openings at beam centre
N
Torsion distributed over short length of the beam ends Small rotation at the centre of the beam
(b) Behaviour observed during the current experiment, under positive drift (left) and negative drift (right)
(c) Damage and evidence of torsional hinging (northwest connection).
(d) Torsion of the east transverse beam at +5%.
(e) Torsion of the east transverse beam at –5%.
Figure 3-10 Torsional behaviour and damage of the transverse beams. Page 3-28
3.7.2
Hollow-core-to-Supporting Beam Connection
Beam torsion played a significant role in the performance of the super-assemblage. While torsion individually may be considered a sign of adverse behaviour, it had a beneficial effect on mitigating the damage within the hollow-core-to-supporting beam connection. Figure 3-9 shows the difference between the rotation of the columns and the west transverse supporting beam. The low rotations measured by the inclinometers indicated that the transverse beams were remaining close to vertical, and the hollow-core floor slabs horizontal. Therefore, the relative rotations between the floor slab and supporting beam was minimal. The connection detail performed admirably and the super-assemblage structure was able to sustain inter-storey drifts up to Âą5% with damage restricted to the support beam alone and not the floor. At the conclusion of testing, there was minor diagonal web cracking at the eastern end, both at the south and north sides of Units 1 and 4 respectively. A camera that could be placed into four of the hollow cores showed that there was no observable internal cracking of those particular cores. Soffit cracking was observed under several of the filled reinforced cores at both ends of the structure. However these cracks appear to have had little effect on the performance. The single crack that formed along the support beam-to-floor interfaces on the topping concrete and lack of any other cracking in the adjacent floor confirmed the objective to concentrate the relative rotation on this plane and restrict the rotational demand on the floor units. The bearing strip was also adequate and allowed the floor units to slide relative to the supporting beam whilst staying on the seat. At the Âą4% peaks, around 16mm of pull off was recorded and could be seen underneath the structure, while the bearing strip on the seat remained in place. The improved friction resistance and better grip associated with the newer generation of bearing strip seems to have improved the performance of the bearing strip. The minimal amount of seat spalling was also a positive feature of the experiment. It is difficult to pinpoint the exact reasons why there was little
Page 3-29
spalling, but aside from the torsion of the supporting beams reducing the amount of rotation experienced by the supporting beams, the bearing strips evened out the surface irregularities of the seat concrete and the presence of transverse reinforcing tying the seat concrete back into beam would have helped. The performance of the seated connection detail showed very similar performance characteristics to the same connection detail tested under two dimensional sub-assemblage conditions outlined in Section 2. The close similarity of observed performance between the two-dimensional and three-dimensional experiments, illustrates the usefulness of twodimensional tests that are much easier to undertake in terms of time, cost and resources. It must also be noted that there was no discernible difference in the behaviour between the 50mm and 75mm seating ends of the structure. Minor spalling amounted for a loss of the 50mm seat, however this was confined to a small area of around 300mm wide. Although good behaviour of both ends shows that the connection detail can be utilised over smaller than code specified seat widths (75mm), short seat widths should not be specified. The experiment was undertaken in a controlled situation where the seating details were constructed as designed and the seat widths were measured. Specification of a minimum of 75mm seat accounts for the likely maximum drifts while maintaining a minimum bearing width for the construction tolerances and shrinkage and creep of the hollow-core units that occur, and specification should adhere to minimum seat widths of 75mm or more. Furthermore, the laboratory investigation was not a real time dynamic test such that neither vertical accelerations nor higher mode effects were applied. This further underlines the need to maintain 75mm bearing widths.
3.7.3
Supporting Beam Detailing Enhancements
To overcome some of the deficiencies observed during the Matthews (2004) and Lindsay (2004) experiments, detailing improvements including a hooked bar in the transverse Page 3-30
supporting beams, to promote column face hinging (see Figure 3-1), and seat transverse reinforcing were implemented. The minor damage that occurred within the hollow-core units at the southern corners of the structure point to the added hooked bar performing as designed – restricting the plastic hinge to the column face. The hinging itself was confined to a small area, approximately within half the beam depth from the column face for all of the plastic hinges within the structure, so it is difficult to say that the hooked bar was solely responsible. However, the unit seated on the northeastern corner plastic hinge did experience web cracking, which can be seen in Figure 3-6(c), which further supports the contention that it is preferable to seat hollow-core floor units away from areas of high deformation within supporting beams, and isolation infill-type details should be used over plastic hinge zones. The presence of the second generation bearing strip possibly contributed to a reduction of stress concentrations along the seat, thereby reducing the spalling (as compared to Lindsay (2004)).
3.7.4
Timber Infill Connection and Diaphragm Reinforcing
The inclusion of the timber infill connection isolating the longitudinal beams from the floor system performed moderately well during Lindsay’s (2004) experiment. However, that experiment demonstrated the disadvantage of using relatively brittle welded wire mesh. In the present experiment the provision for longer starter bars and use of conventional reinforcement (instead of ductile mesh) proved to be successful. The crack pattern extended through the first floor unit and across the second floor unit indicating that the longer starter bars were more suitable and able to distribute the loads over a larger area. The use of conventional reinforcement within the diaphragm also proved to be successful. Longer starter bars throughout the topping concrete ensured that no major cracks appeared and therefore the diaphragm reinforcement was not highly strained therefore avoiding failure.
Page 3-31
3.7.5
Displacement Incompatibility
Figure 3-11 presents the displacement incompatibilities between the perimeter longitudinal beams and the first hollow-core floor unit at peak drift amplitudes under Phase 1 and 3 loading. The displacements are plotted along the length of the structure from the west end to the east end and were derived from levelling carried out on the floor. The results shown indicate the amount of relative vertical displacements between the floor units (Unit 1) and south frame beams. Figure 3-11(a) shows the vertical displacements for Phase 1 loading. It can be seen that there was a relatively symmetrical relationship between the positive and negative drifts. The maximum incompatibility was approximately -10.5mm at +2% drift on the west side of the south centre column meaning that the floor had dropped relative to the beam. Figure 3-11(c) illustrates a similar trend but distinct shift in the negative direction indicates how much the floor dropped following transverse loading. The damage incurred by the transverse beam hinges was associated with a shearing displacement that lowered the beam and flooring together. The effect of the transverse loading is also shown in Figure 3-11(b) where the Âą2% cycle peak incompatibilities are compared for both loading phases. The crossover point that occurred close to the centre of the structure (6100mm) shows the floors had dropped approximately 8mm. The maximum incompatibility evident shows a 33mm drop of the floor relative to the beam at +4% drift. This corresponds to a 4.4% slope over the infill in a north south sense. Due to the lack of observed damage or tearing of the topping concrete, it can be deduced that such slopes could be accommodated by the infill topping concrete and starter bars. Further displacement incompatibility results from the experiment, and accompanying computer modelling and analysis is located in Section 4.
Page 3-32
10 Position along fram e (m m ) 5 Displacement (mm)
0 -5
0
2000
4000
6000
8000
10000
12000
-10 -15 Phase 1: 1% Phase 1: -1% Phase 1: 2% Phase 1: -2%
-20 -25 -30 -35
(a) Relative vertical displacement incompatibilities during Phase 1 loading (displacement of the floor with respect to the longitudinal beams). 10 5 Pos ition along fram e (m m ) Displacement (mm)
0 -5
0
2000
4000
6000
8000
12000
10000
-10 -15 -20
Phase 3: 2% Phase 3: -2% Phase 1: 2% Phase 1: -2%
-25 -30 -35
(b) Comparison of the Âą2% cycle displacement incompatibilities between Phase 1 and Phase 3. 10 5 Position along fram e (m m )
Displacement (mm)
0 -5
0
2000
4000
6000
8000
10000
12000
-10 -15
Phase 3: 2% Phase 3: -2% Phase 3: 3% Phase 3: -3% Phase 3: 4% Phase 3: -4%
-20 -25 -30 -35
(c) Relative vertical displacement incompatibilities during Phase 3 loading (displacement of the floor with respect to the longitudinal beams).
Figure 3-11 Vertical displacement incompatibilities between the floor and longitudinal beams during Phase 3 loading. (Note a negative displacement means that the floor has dropped relative to the beams)
Page 3-33
3.8
CONCLUSIONS
From the experimental investigation that has been presented in this section, the following conclusions are made: 1.
A two-bay by one-bay reinforced concrete precast frame with one-way hollow-core flooring
super-assembly
was
designed
and
constructed
in
accordance
with
NZS3101:1995 and included the Amendment No. 3 rigid connection hollow-core seating detail. The specimen performed well up to inter-storey drifts of Âą5% when the longitudinal reinforcing bars in the beam fractured due to low cycle fatigue. The floor system sustained only minor damage, which in no way impaired life safety. The onset of damage in the plastic hinge zones and hollow-core-to-supporting beam connections occurred at +1% and irreparable damage to the plastic hinges zones of the south beams occurred at +4% during longitudinal re-loading. 2.
The rigid floor-to-supporting beam connection behaved well up to structural inter-storey drifts of Âą5%, where damage to the hollow-core units and seated support was minimal. Previously, the details investigated herein were untested, and for that reason Amendment No. 3 to the current New Zealand Structures Standard NZS 3101:1995 limited interstorey drifts of this class of construction to 1.2%. In light of the good performance, this restriction should be removed.
3.
The articulated timber infill slab connecting the lateral load resisting system longitudinal beams with the floor slab performed well with no major cracking and tearing experienced. The use of longer starter bars and conventional reinforcement in place of the cold drawn and ductile mesh ensured that any displacement incompatibility was accommodated and diaphragm action was maintained. The performance also verifies the details proposed by Amendment No. 3 to NZS3101:1995.
Page 3-34
4.
Three-dimensional effects of torsional hinging have arisen throughout the course of this investigation. A rigid beam-to-floor connection acted to keep the floor horizontal and beams upright forcing torsion of the transverse beams to occur over a limited zone in the plastic hinges at the ends of the transverse beams under high drift rotations of the superassemblage. More research and analysis of torsion within precast concrete structures is required.
5.
Precast concrete moment resisting frames designed and constructed with Grade 500E reinforcement can be expected to perform well under substantial seismic displacements. Plastic hinge zones appear to be less than half the depth of the beam long, and most rotation is centred at large cracks at the beam-column interface. More research needs to be carried out utilising various reinforcement ratios and investigating the buckling and low cycle fatigue characteristics of Grade 500E reinforcement within three-dimensional concrete frames.
3.9
REFERENCES
Bull D.K, Matthews J.G, 2003, Proof of Concept Tests for Hollow-core Floor Unit Connections, Precast NZ report, Feb 2003. Herlihy M.D, Park R and Bull D.K, 1995, Precast Concrete Floor Unit Support and Continuity, Research Report 93/103, Department of Civil Engineering, University of Canterbury, Christchurch, New Zealand. Herlihy M.D and Park R 2000, Precast concrete floor support and diaphragm action, Research Report 2000/13, Department of Civil Engineering, University of Canterbury, Christchurch, New Zealand.
Page 3-35
Liew H.Y, 2004, Performance of Hollow-core Floor Seating Connection Details, Masters Thesis, Department of Civil Engineering, University of Canterbury, Christchurch, New Zealand. Lindsay R.A, 2004, Experiments on the seismic performance of hollow-core floor systems in precast concrete building, Masters Thesis, Department of Civil Engineering, University of Canterbury, Christchurch, New Zealand. Lindsay R.A, Mander J.B, and Bull D.K, 2004a, Preliminary results from experiments on hollow-core floor systems in precast concrete buildings, 2004 NZSEE Conference, Rotorua, NZ, Paper 33, 8 pp. Lindsay R.A, Mander J.B, and Bull D.K, 2004b, Experiments of the Seismic Performance of Hollow-core Floor Systems in Precast concrete Buildings, 13th World conference on Earthquake Engineering, Vancouver, Canada, CD ROM paper No. 585. Matthews J.G, 2004, Hollow-core floor slab performance following a severe earthquake, PhD Thesis, Department of Civil Engineering, University of Canterbury, Christchurch, New Zealand. Matthews J.G, Bull D.K, and Mander J.B, 2003a, Background to the Testing of a Precast Concrete Hollowcore Floor Slab Building, 2003, Pacific Conference on Earthquake Engineering, February, Christchurch, NZ, CD ROM paper 170. Matthews J.G, Bull D.K, and Mander J.B, 2003b, Preliminary Experimental Results and Seismic Performance Implications of Precast Floor Systems with Detailing and Load Path Deficiencies, 2003 Pacific Conference on Earthquake Engineering, February, Christchurch, NZ. CD ROM paper 077. Matthews J.G, Mander J.B, Bull D.K, 2004, Prediction of beam elongation in structural concrete members using a rainflow method, 2004 NZSEE Conference, Rotorua, NZ, Paper 27, 8 pp.
Page 3-36
Meija-McMaster J.C and Park R, 1994, Tests on Special Reinforcement for the End Support of Hollow-core Slabs, PCI Journal, Vol 39, No. 5, pp. 90-105, September-October. NZS3101, 1995, Concrete Structures Standard, NZS3101, Parts 1 & 2, Standards New Zealand, Wellington, New Zealand. NZS3101, 2004, Amendment No. 3 to 1995 Standard (NZS3101), Standards New Zealand, Wellington, New Zealand. Oliver S.J, 1998, The Performance of Concrete Topped Precast Hollow-core Flooring Systems Reinforced with and without Dramix Steel Fibres under Simulated Seismic Loading, Masters Thesis, Department of Civil Engineering, University of Canterbury, Christchurch, Canterbury. Park R, 1989, Evaluation of ductility of structures and structural assemblages from laboratory testing, Bulletin of the New Zealand National Society for Earthquake Engineering, Vol.22, No. 3, September, pp 155-166.
Page 3-37
4. Section 4 – Forensic Analysis of Failure and Behaviour Modes
SECTION SUMMARY Present experimental research has sought to verify new detailing requirements for the use of hollow-core flooring in precast concrete structures. A full-scale two bay-by-one bay concrete frame structure with hollow-core flooring is cyclically tested to increasing lateral displacements in both the longitudinal and transverse directions. This chapter provides a forensic analysis of the present research experimental observations. Torsional hinging behaviour that is observed due to a strong hollow-core floor connection with a weak supporting beam is explained. A comparison is made between the calculated torsional capacity and torsion demands. The state-of-the-art understanding of beam-to-floor displacement incompatibility is also discussed. Experimentally observed displacement incompatibilities are compared with those determined computationally. Examples of the potential of modelling for future research and construction are provided. The overall base shear capacity of the structure is predicted and is shown to agree well with experimental results. To achieve this calculation, it is demonstrated that it is necessary to embody all sources of strength enhancement, including a so-called “bowstring� effect whereby compressive forces are transferred into beams running parallel and adjacent to the prestressed concrete floor units. Finally, the present research is compared and contrasted with previous similar experimental investigations. It is concluded that through subtle detailing enhancements there can be improvements in seismic performance whereby a relatively fragile hollow-core flooring system is transformed into a robust frame-floor system where all the principal sources of damage are developed into the ductile frame.
Page 4-1
4.1
INTRODUCTION
Over the previous two decades, prestressed concrete hollow-core flooring systems have become one of the preferred forms of precast construction in New Zealand. This research described herein seeks to explain certain key experimental observations made in a lateral loading test conducted on a two-bay by one-bay full-scale precast concrete super-assemblage, which is shown in Figure 4-1. Reaction frame
Pinned steel tie beams Unit 4
750x750 columns
Unit 3
300 series hollowcore units
Transverse beams
Unit 2
W
E
750 wide timber infill
Plan
400x750 longitudinal beams
6100
6100
6100
3500
S
475x750 transverse beams
Unit 1
N
Double acting roller bearings
Pinned fixed column Side elevation
Front elevation
(a) Super-assemblage details.
(b) View of the floor of the super-assemblage.
(c) Load frame set-up.
Figure 4-1 Super-assemblage test specimen details.
Page 4-2
The experiment is the third super-assemblage examination on precast concrete structures. The first of these was conducted by Matthews (2004) on existing buildings with pre-2001 construction details. Matthews’s work discovered that existing hollow-core flooring details performed unsatisfactorily and can be expected to behave poorly in a design basis earthquake (10% probability of occurrence in 50 years). As an upshot of the work by Matthews (2004), Amendment No. 3 was fast-tracked into the New Zealand Concrete Design Standard (NZS 3101, 2004). In Amendment No. 3, two “acceptable solutions” are given for detailing hollowcore-to-supporting beam connections. The first of these was tested by Lindsay (2004). This current research has investigated the viability of the second “acceptable solution.” Where past research has focused on lateral load resisting systems overlooking the effect of floor diaphragms, the interaction between the two became a principal focus for these investigations. One significant finding in the current strong floor-to-weak support beam experiment was the extent of the plastic torsional response of the supporting beams. This section seeks to provide a forensic analysis of these experimental results. Several other failure mode aspects of the super-assemblage specimen are also examined in an analytical fashion. The performance of the floor diaphragm is assessed with particular emphasis on displacement incompatibility between the hollow-core flooring and the adjoining parallel perimeter concrete frame. Previous experimental findings and analytical work on displacement incompatibility is summarised and the experimental results are compared with results from computer modelling. New design solutions to combat the problems associated with displacement incompatibility and reducing floor slab damage and the potential benefits for furthering this work are also outlined. The lateral force-deformation capacity of the structural system is assessed using a theoretical pushover analysis. Comparisons of the theoretical and experimental lateral forcedeformation capacity results are provided and reasons for the discrepancies are explained.
Page 4-3
Additional results obtained from the experiment are compared with existing theoretical relationships where the beam elongation values are evaluated against the “rainflow� analysis methodology proposed by Matthew et al (2004). Throughout this section, the current experiment is compared and contrasted with respect to the preceding two investigations (Matthews, 2004 and Lindsay, 2004) as a means to complete the overall investigation into the seismic adequacy of hollow-core flooring supported by concrete frame structures.
4.2 TORSIONAL BEHAVIOUR OF THE TRANSVERSE SUPPORT BEAMS The behaviour of the transverse beams from observations of the experiment demonstrated interesting torsional behaviour. Figure 4-2 presents the torsional behaviour of the west beam observed during the experiment. Figure 4-2(c) shows the amount of torsional twist that occurred within the south hinge of the west transverse beam. The rotations were measured from inclinometers spaced evenly along the west transverse beam, which can be seen in Appendix D. The results show that torsional hinges formed at the ends of the beams and that the middle of the beam remained vertical and the flooring horizontal for most of the testing. The comparison between Phase 1 and Phase 3 shows that there was a large increase in the torsional twisting at the ends of the transverse beam following Phase 2 transverse loading. During Phase 2, the ends of the transverse beams formed flexural plastic hinges, and as a result of the damage caused due to the high flexure and shear actions, the torsional stiffness of the ends of the transverse beams was significantly reduced. This sub-section examines the experimentally observed torsional behaviour from Phase 1 and 3 longitudinal loading and compares the observations with calculated torsional demands and capacities. The torsional behaviour of the transverse beam was not measured or analysed during Phase 2 transverse loading, but it is explained that the damage sustained by the transverse beams during transverse loading has a significant impact on the torsional behaviour during Phase 3. Page 4-4
Large rotation at the end of the beam
South-West Column
South-West Column
3D effects of beam elongation front frame elongates and pulls beam ends away from floor, but out-of-plane bending and strong floor-beam connections means small openings at beam centre
N
Torsion distributed over short length of the beam ends Small rotation at the centre of the beam
6 5 4 3 2 1 0 -1 -2 -3 -4 -5 -6
Phase 1 Loading
SW Column Inclination Inclinometer 2 Inclinometer 4
Phase 3 Loading
Inclinometer 1 Inclinometer 3 Inclinometer 5
(b) West beam inclination during Phase 1 and 3 loading. Angle of Twist (rad/m)
Torsion Rotation (%)
(a) Schematic representation of the torsional behaviour
6 5 4 3 2 1 0 -1 -2 -3 -4 -5 -6 -7 -8
Phase 1 Loading
Phase 3 Loading
(c) Torsional twist of the south hinge of the west transverse beam (radians/metre in plastic hinge zone)
Figure 4-2 Observed torsional behaviour of the west transverse beam
Page 4-5
Figure 4-3(a) shows an idealised diagram of the hypothesised relationship between the torsional strength (torsion moment) and torsional twist. In a similar way to the calculation of the shear capacity of a reinforced concrete beam section, the torsional strength comprises of strength contributions from the concrete, Tc, and the reinforcement, Ts. The ultimate torsional moment strength, Tu, is a sum of the concrete and reinforcement contributions and is shown as the upper bound torsional moment strength in Figure 4-3(a). Torsion Strength
Monotonic torsion capacity: Tu = Tc + Ts
Ultimate Torsion Strength, Tu = T c + Ts
Tc Cyclic torsion capacity: Tu = Ts
GKc r Torsional Demand Cracking Torsion = Tc GK
Reduced torsion capacity flexure, shear and cyclic interaction
OTc
Stiff pre-cracking response
Phase 1 response: initial stiff precracking response and small torsional twist rotations
Phase 3 response: “soft� postcracking response due to damage during Phase 2 transverse loading, large torsional twist rotations
Ts
Torsion Twist
O = load path dependent parameter (O<1) that depends on the degree of previous loading and flexure-shear-torsion interaction
(a) Schematic relationship between the torsion force and torsional twisting South-West Column
Torsional Capacity of the beams resisting the torsion at the beam ends
North-West Column
Reinforced Connection under positive moments
Torsional Demand from the eccentric floor loading and reinforced connection moment
Reinforced Connection under negative moments
(b) Schematic illustration of torsional the demand and capacity.
Figure 4-3 Idealised torsional behaviour of the west transverse beam
Page 4-6
The derivation of the torsional capacity of reinforced concrete sections is complex, and it is difficult when considering interaction with flexure and shear actions and pre- and postcracking behaviour. Significant work has been undertaken by Hsu (1993) and Mitchell and Collins (1991), particularly with prestressed structures, and Park and Paulay (1975) for reinforced concrete structures. These sources provide examples for the calculation of torsional demands and capacities for concrete structural elements and several aspects of this work have been reflected in the New Zealand Concrete Structures Standard, NZS 3101: 1995. For compatibility torsion, which is the case in this experiment, a reduction of the torsional moment can occur due to the redistribution of internal forces when cracking first occurs. NZS 3101:1995 provides an equation for calculating the cracking torsional moment for a section, and is the same as the formulation given by Mitchell and Collins (1991). The cracking torsion, or maximum design torsional moment can be calculated by:
Tc
I
f c' § Acp2 ¨ 3 ¨© p cp
· ¸ ¸ ¹
(4.1)
where Tc = design torsional moment force at section at the ultimate limit state; or cracking torsion; I = strength reduction factor; f’c = concrete compressive strength; Acp = area enclosed by the outside perimeter of the concrete cross-section; and pcp = outside perimeter of the concrete cross section. After diagonal cracking has occurred, a truss mechanism of vertical transverse reinforcement ties and diagonal concrete compression struts form, and the contribution to the torsional resistance from the reinforcement can be calculated. Park and Paulay (1975) provide an expression for the reinforcement contribution to torsion capacity as a function of the transverse and longitudinal reinforcement, which is shown as Equation 4.2. The equivalent design expression for the nominal torsional strength from NZS 3101:1995 relates to the
Page 4-7
amount of transverse reinforcing and stems from the work presented by Park and Paulay (1975).
Ts
2 A0
At f y Al f ly s
P0
(4.2)
where Ao = area enclosed by the connecting lines between the centres of the longitudinal reinforcement; At = area of a transverse reinforcement stirrup leg; fy = yield strength of the transverse reinforcement; s = transverse reinforcement spacing; Al = total area of the longitudinal reinforcement; fly = yield strength of the longitudinal reinforcement; and Po = perimeter formed by area Ao. Prior to torsional cracking occurring or the torsional strength given by the concrete being exceeded, the response is stiff and defined by the pre-cracking stiffness, GK. After cracking occurs, the torsional stiffness is significantly reduced. As is shown in Figure 4-3, the effect of cyclic loading has a large effect on the torsional stiffness whereby the concrete torsional strength contribution diminishes, and the ultimate torsional strength becomes Ts, the torsional capacity of the reinforcement. To calculate the torsional twists corresponding to the cracking and ultimate torsion moments, relationships from Mitchell and Collins (1991) and Park and Paulay (1975) for the torsional stiffness were used. For the initial stiffness, the section is represented by an equivalent thin walled tube or hollow section with the same overall dimensions and is a function of the section geometry. The post-cracking torsion stiffness is governed by the deformation of the reinforcing. The pre-cracking stiffness was calculated using: GK
G
4 A02 t po
(4.3)
where GK = the pre-cracking torsional stiffness; G = the shear modulus; A0 = area enclosed by the centreline of the thin walled tube with thickness, t; and po = perimeter of the area. The equivalent wall thickness can be found by using: Page 4-8
t
3 Acp 4 p cp
(4.4)
Where Acp = area enclosed by the outside perimeter of the concrete cross section, pcp = perimeter of the area Acp. To find the post-cracking stiffness, GKcr, a ratio of the post-cracking stiffness to precracking stiffness was calculated using methods included in Park and Paulay (1975). This method uses the aspect ratio of the section, and a modified reinforcement ratio expression. For the present experiment, the postulated relationship between torsional strength and torsional twisting incorporates a distinct reduction of the torsional strength due to flexure, shear and cyclic interaction. The reduced torsion capacity represents the damage that occurred from Phase 2 transverse loading, whereby high shear forces and bending moments were present and flexural plastic hinging occurred. The concrete contribution to the overall torsional strength is rapidly diminished, and the torsion demands are sustained by the reinforcement. Featured in Figure 4-3(a) is a representation of the torsional demand. Using the intersection of the torsional demand and idealised torsion-twist capacity values, an estimation of the expected torsional twists can be found. The following sub-sections describe the calculation of the torsional strength and stiffness parameters as well as the torsional demands such that the relationship (Figure 4-3(a)) can be quantitatively examined.
4.2.1 Determination of the torsional demand
The torsion due to eccentrically supported flooring systems on beams can be easily calculated. However, the added torsional demand that can be caused by a moment resisting reinforced connection between floors and supporting beams, under relative rotations between the slabs and beams, is less well understood. Concern has been raised in New Zealand as to the “unacceptable� torsion that would be generated by seating hollow-core units using a compressible backing board and low-friction bearing strip on an external supporting beam Page 4-9
(O’Grady, 2004). This connection detail was experimentally tested in the Lindsay (2004) experiment, and only minor effects of torsion were observed. The degree of twist did not raise any issues over the performance of the floor. Elliot et al (1998) discussed the effects of eccentrically loaded external beams for both the isolation type floor-to-beam connection (compressible backing board) and a reinforced floor-to-beam connection, such as the connection presented in this research. Elliot et al (1998) states:
“If the beam is tied into the floor slab through the normal arrangement of continuity tie bars concreted into some of the opened cores in the floor slab, the torsional stress is virtually eliminated. There are two reasons for this: (1) a reaction force R generated in the floor plate will prevent the top of the beam from experiencing inward deflections and (2) the eccentricity of the load is reduced because of an extended bearing at the end of the cast-in-place infill.�
This statement is fundamentally flawed when lateral displacement conditions are considered. The relative rotations between the floor and supporting beam induce moments in the floor to beam connection and these moments generate significant torsion demands at the ends of the beams. The assumption that the floor remains rigidly connected to the supporting beam, and rotates with the beam is false. Previous experiments (Matthews, 2004 and Lindsay, 2004) as well as the current experiment, have shown that under lateral displacements when the supporting beam rotates, the floor slab stays predominantly horizontal. This relative rotation between the floor and supporting beam induces a force couple within the reinforcement connecting the floor and beams. Figure 4-4 shows the falsely claimed behaviour and the observed behaviour of the reinforced beam-floor connections. The induced moments caused by the relative rotations impose torsion on the beam, as shown in Figure 4-3(b) and Figure 4-4(b). Therefore, the statement made by Elliot et al (1998) that torsionally stresses are virtually eliminated by using a reinforced composite beam-to-floor connection is incorrect.
Page 4-10
(a) Erroneous claimed behaviour of the reinforced seated floor slab connection (Elliot et al 1998)
(b) Observed behaviour of the reinforced seated floor slab connection
Figure 4-4 The torsional demand from reinforced hollow-core to floor slab connections
In addition to the torsion moment generated by the reinforced floor-beam connection, the effects of beam elongation also cause torsional demands. The growth of the perimeter frame beams, parallel to the floor span, exert tension forces into the flooring, which acts to pull the floor slabs off the seating of the supporting beams. This means that the reaction force, R, generated in the floor plate is not present, and the tension force from beam elongation further adds to the torsional demand. The torsional demands calculated for this experiment were derived from the results from two-dimensional sub-assemblage testing (discussed in Section 2). The moment capacity of the floor-to-beam connection (for one hollow-core unit) was observed from the experimental results and good comparisons were found between the calculated positive and negative moment capacity values. This moment capacity was used to find the torsional moment demand imposed on the transverse beams, as is shown in Figure 4-4(b). Accounting for the moment generated by the connection between the supporting beam and four hollowcore units, an applied torsional moment at the beam ends of 79kNm was calculated (same for both positive and negative moments). For the compressible backing board connection (Lindsay, 2004), the eccentric loading of the hollow-core flooring on the concrete seat of the supporting beams does result in torsion under static conditions. Under lateral loading, the moment induced by the section under relative rotations was minimal as it was observed that the compressible backing board did not actually compress and a force couple could not be Page 4-11
achieved. A torsional moment demand from the eccentric floor loading of 20kNm at each end of the transverse beams was calculated, although it must be noted that this is a lower bound value as live loading was not included in the testing.
4.2.2
Transverse beam torsional capacity
For Phase 1 and 3, the amount of bending moment and shear force acting at the ends of the transverse beams would have been small, as determined from the static loading of the floor slabs. Therefore, the following calculations of the torsional capacity of the concrete transverse beam do not include flexure and shear actions, as they are sufficiently small to negate. Under different circumstances, for example a 45 degree earthquake whereby the longitudinal and transverse directions are simultaneously loaded, then the torsion would have to be considered together with flexure and shear. Using the equations and methods presented, the torsional strength and stiffness values for the transverse beams were calculated. The cracking torsion moment was calculated to be 77kNm and the torsion contribution from the reinforcement was found to be 200kNm. Using the stiffness formulation presented in Equations 4.3 and 4.4, the pre-cracking stiffness was 95500kNm2 and from methods presented in Park and Paulay (1975), the post-cracking stiffness was found to be 4% of the pre-cracked stiffness (3800kNm2). Using these calculated torsional strength and stiffness values, the torsion-twist relationship was generated (Figure 4-5). This offers a quantitative form of the idealised torsion-twist relationship shown in Figure 4-3(a). The representation of the torsional demand and capacity shown in Figure 4-5, can be used to explain the amount of torsional twisting that occurred within the plastic hinge regions of the west transverse beams (Figure 4-2(b)). The intersection between the demand for the current experiment and capacity curves for Phase 1 indicates that there would be a torsional
Page 4-12
rotation of around 0.0064 radians (0.64%). This is approximately true for the experimental discrepancies seen during the later stages of Phase 1, where at the first and second cycles to –1%, the difference between the rotation of the column and the supporting beam adjacent to the plastic hinges was around 0.7%. At the first and second cycle peaks to -2% drift, the torsional twist at the ends of the west transverse beam was around 1%. The reduced stiffness for Phase 3 longitudinal re-loading indicates that significantly higher torsional twisting occurred. The intersection point between the capacity and demand for Phase 3 shows that torsional drifts of around 0.021 radians (2.1%) could be expected. During the later stages of the experiment, the ends of the beams were experiencing rotations of over 4%. The calculated value of 2.1% underestimates the amount of torsional twisting of the torsional hinges. However, the suggested representation still provides a relatively good approximation of the large rotations that can occur due to torsion.
Torsion Moment (kNm)
300 250 200 150 100
Phase I Phase III Current Experiment Demand Lindsay (2004) Experiment Demand
50 0 0
0.01
0.02
0.03 0.04 Torsional Twist (rads/m)
0.05
0.06
0.07
Figure 4-5 Representation of the calculated torsional strengths and demands
The difficulty in accurately assessing torsion quantitatively means that it is difficult to confidently predict torsional performance. Uncertainties arise due to the difference between various methods in calculating the torsional capacity of section as well as the assessment of the torsional demand on the supporting beams. However, the calculations provided a reasonably accurate insight into the amount of torsional rotations of the supporting beam
Page 4-13
plastic hinge zones that can occur. However, the fact that the simple calculations produce estimates of torsional rotation that are less than what was shown by the actual experimental results, means that torsion of floor supporting beams needs to be considered seriously.
4.3
DISPLACEMENT INCOMPATIBILITY
4.3.1
Identified Issues and Previous Findings
The occurrence of vertical displacement differences between flooring systems and lateral load resisting frame systems has been accepted as a source of damage for floor diaphragms. However, little analytical and experimental work has been done to assess the incompatibility. The displacement incompatibility arises due to the different deformation patterns of the flooring and frame elements, and is schematically shown in Figure 4-6. Under lateral loading, the frame beams deform in double curvature, whereas flooring systems, that span parallel to the frame, are most commonly designed to act as though simply supported. In cases where the flooring is adequately tied into the beams and is forced to deform in an undesirable double curvature pattern, the floor slab is prone to damage and effective load paths and transfer of inertia forces are jeopardised. Displacement incompatibility between the frame and h/c unit
Hollow-core unit sags and deforms in single curvature
Displacement incompatibility between the frame and h/c unit
Frame deforms in double curvature
Figure 4-6 Illustration of the causes of displacement incompatibility (Matthews, 2004)
In previous experiments, damage due to displacement incompatibility has been reported. Lau’s (2002) experiments observed damage between the perimeter beams and floor and concluded that the vertical movement of the floor relative to the beams has the potential to cause failure of the slab. Displacement incompatibility was evident due to damage that Page 4-14
occurred during the hollow-core super-assemblage experiment conducted by Matthews (2004). A strong connection between the first hollow-core unit and adjoining perimeter beams (Figure 4-7(a)) forced the floor to deform in double curvature and these deformations could not be sustained by the webs of the hollow-core unit adjacent to the perimeter beams. Ultimately the localised over-stressing resulted in the collapse of the bottom half of the first hollow-core unit beside the main frame. The adverse deformations also resulted in fracturing of the cold drawn mesh reinforcing the topping slab and caused an ‘unzipping’ tear longitudinally between the first and second floor units which can be seen in Figure 4-7(c). This tear was first noticed when cracking was observed adjacent to the centre column at 0.75% inter-storey drift, and by 1.95% all of the cold drawn mesh crossing this crack had fractured. Zone of Grade 430 starters weakness at 300 crs & 665 mesh in 75mm topping
75mm topping slab
First Second Hollow-core Hollow-core Unit Unit Perimeter beam
First Hollow-core Unit
Zone of weakness
750mm timber infill Perimeter beam Column face
Column face
(a) Lateral connection used in the Matthews (2004) experiment
(b) Lateral connection used in the Lindsay (2004) experiment
(c) ‘Tearing’ damage observed during Matthews (2004) testing
(d) Infill floor damage witnessed during the Lindsay (2004) experiment
Figure 4-7 Lateral perimeter beam floor unit connection details and damage. Page 4-15
The Lindsay (2004) experiment investigated future construction details addressing the problems observed during the Matthews (2004) test. The lateral connection between the perimeter beams and initial hollow-core floor unit consisted of a topping slab cast over a timber plank infill 750mm wide, as shown in Figure 4-7(b). This was intended to be a flexible link isolating the two structural systems to accommodate the vertical displacement incompatibilities while still being able to transfer inertia forces from the floor to the frame. Figure 4-7(d) shows the damage incurred by the infill slab during the testing. The solution was able to satisfactorily withstand the displacement incompatibility and damage to the flooring was minimised. However the premature termination of the starter bars at the interface between the infill and first hollow-core unit created a zone of weakness where tearing was observed and the ductile mesh reinforcing the topping slab fractured.
The testing of precast seismic structural systems in the PRESSS research program (Priestley et al 1999) included connection solutions designed to overcome the problems associated with displacement incompatibility. The welded ‘X’ plate connectors, such as those shown in Figure 4-8, connected the double tee flooring to the perimeter frame at discrete points on the lower levels of the structure. The ‘X’ plate connectors were designed by capacity design principals to act as an energy dissipating device, and limit the amount of inertia forces transferred to the perimeter moment resisting frame.
Figure 4-8 Welded X-plate connecting device Page 4-16
4.3.2
Analytical modelling of displacement incompatibility
The analysis involved the construction of an analytical model in the inelastic time history program Ruaumoko (Carr, 2002), utilising a plasticity concentrated approach. A twodimensional model was set up to model the longitudinal lateral loading of the front frame, and consisted of members representing the frame and floor elements and springs connecting the floor to the frame. Different spring members were used to model the level of fixity of the end support conditions, and along the frame between the frame and flooring. The model was calibrated by assessing the base shear capacity of the system and comparing it to the experimental values. Figure 4-9 shows the displacement incompatibility between the longitudinal perimeter beams and the adjacent parallel hollow-core unit from the experiment and modelling for both the Lindsay (2004) and current experiments. The lateral spring properties modelling the infill connection were kept the same, but the end spring properties were altered to model the pinned type seating connection for Lindsay (2004) and the rigid connection in the present experiment. The results show promising correlation between the experiment and analytical model. The overall deformation trends are matched although the model slightly underestimates the amount of incompatibility that occurs. After gaining satisfactory comparisons with the experiment, changes to various parameters of the model allowed other areas of interest to be investigated. Sensitivity analyses were performed examining the effect of: different end support conditions, different lateral connection details, different bay lengths and numbers of bays and different flooring types. The effects of the different parameters was seen by examining both the displacement incompatibility patterns as well as the overall system base shear capacities, and the results from these analyses are presented in Appendix D.
Page 4-17
Displacement Incompatibility (mm)
12 10 8 6 4
Position along fram e (m m )
2 0 -2 0
2000
4000
6000
8000
10000
12000
-4 Experiment 1% Model 1% Experiment 2% Model 2%
-6 -8 -10 -12
(a) Observed and modelled displacement incompatibility from Lindsay (2004) Displacement Incompatibility (mm)
12 10 8 6 4 2
Position along fram e (m m )
0 -2 0
2000
4000
6000
8000
10000
12000
-4 Experiment 1% Model 1% Experiment 2% Model 2%
-6 -8 -10 -12
(b) Observed and modelled displacement incompatibility from the current experiment
Figure 4-9 Observed and modelled displacement incompatibility
From the sensitivity analyses, it was seen that the end connection detail, through the stiffness of the end spring, had a large influence on system strength capacity and displacement incompatibility values. The base shear capacity for the system was 25% higher for the rigid connection than the pinned and semi-pinned connections. This is matched to a certain extent by the higher ultimate base shear capacity of the current experimental structure than the equivalent Lindsay (2004) base shear capacity. For the rigid end conditions, the maximum displacement incompatibility occurred on both sides adjacent to the central column, as the floor unit deformed in single curvature due to the fixity at the ends. For the pinned end
Page 4-18
conditions, which allowed the floor to simply sag, displacement incompatibility peaks were seen close to the supports as well as either side of the central column, and the displacement incompatibility values were generally higher than for the fixed end case. The computational modelling conducted has more recently been extended by work completed at the University of Canterbury through several research projects. Taylor (2004) used results from sensitivity analyses of the controlling parameters, to find the points of minimum displacement incompatibility. For each of the influencing parameters, a list of the non-dimensional lengths at which displacement incompatibilities are a minimum have been made to be able to form the basis for the location of connectors. This work preceded work by McKenzie (2004), who investigated the importance of higher mode inertia forces and if energy dissipating discrete connectors were able to reduce the demand imposed on lateral load resisting systems. Jensen (2004) analysed the diaphragm action due to the effects of different locations and numbers of floor-frame connectors. More favourable conditions were seen for several connectors as the inertial forces could be distributed over a wider area, however the location of the connectors is an important parameter considering the displacement incompatibility issues discussed.
4.3.3
Scope for future advancements
A recent change in direction in earthquake engineering structural research into the development of post-tensioned rocking frame and wall solutions involved with damage avoidance design principles has required accompanying attention to floor systems. In particular, research has focused into isolating the floor and lateral load resisting elements to limit damage, while still maintaining a connection capable of transferring inertia and structural interaction forces from the floor to the lateral load resisting system. Work has been done testing various mechanical connectors and devices that can join floor and frame
Page 4-19
members, and one such connector is shown in Figure 4-8. Connectors that possess energy dissipation qualities, which are able to limit the inertia forces being transferred to a perimeter lateral load resisting frame, which in turn restricts damage, have previously been developed and tested. Naito et al (2004) modelled connectors for double tee floors and found that connectors designed according to capacity design principals performed in a ductile and desirable manner. The welded ‘X’ plate type connectors used in the PRESSS program, as shown in Figure 4-8, use shear forces to produce a flexural response, which increases the ductility and significantly improves performance (Priestley et al, 1999). Despite this previous research, similar work investigating the viability of systems involving these connectors has been minimal in New Zealand and research should look to develop systems tailored for New Zealand construction practice. The timber infill solution has proven to be a successful way to overcome the displacement incompatibility issue. However, in other building situations, the timber infill may be undesirable, and a flat-soffit option with flooring butted up against the perimeter frame may be required. In these cases, discrete connectors that allow vertical displacement but are fixed horizontally – transferring inertia and structural interaction forces and dissipating energy, would be required.
4.4 LATERAL LOAD CAPACITY OF THE SYSTEM
This section discusses the calculation of the lateral load capacity of the super-assemblage and the comparisons of the predicted strengths with the actual behaviour. The lateral load capacity of the system was found by incorporating all sources of strength enhancement, including the starter bar and beam-to-floor slab reinforcement, diaphragm reinforcement and the influence of the floor slab through the “bowstring effect”. Full calculations of the lateral load capacity values are provided in Appendix D.
Page 4-20
4.4.1
Bowstring Effect
The bowstring effect occurs as a three-dimensional consequence of beam elongation. The floor system provides restraint due to the growth of the concrete frames. This restraint causes large compression forces in the frame beams, which significantly increases the moment capacity of the frame. Tensile forces are induced in the flooring, which are transferred to the frame beams in a compression arching manner, which explains the name the “bowstring effect�, where the tension in the floor acts as the string, and the compression arch represents the bow. Fenwick et al (1999) demonstrated that the presence of floor slabs parallel to perimeter frame beams can cause a significant increase in the negative moment capacity of the beams. The bowstring effect is further explained by Bull (2003) and was observed during experiments conducted by Matthews (2004) and Lindsay (2004). The bowstring effect was also graphically evident during the present experiment. Cracking within the topping slab over the timber infill and hollow-core floor units near the east and west ends of the structure, arched inwards towards the south centre column. The crack distribution followed the same compression arching pattern of the bowstring effect as shown by Figure 4-10. centroid of compression arch
compression struts
end connection reinforcement
eccentricity (e) 2e
uniformly distributed load due to diaphragm reinforcement and drag bars
centroid of tension tie
N Figure 4-10 Bowstring effect present in the floor slab
Page 4-21
Figure 4-10 shows the location of the compression arch and the centroid of the tension tie in the floor. The depth of the compression arch, the eccentricity, is the distance between the centroid of the tension tie in the floor, and the centroid of the compression force at the inside edge of the south perimeter beams. The tie force is a combination of the capacity of the reinforcement at the hollow-core to support beam connection as well as friction of the floor. This resultant tie force acts at a distance of the eccentricity and is a combination of the attributing tension forces from the end connection reinforcement over a width of two times the eccentricity. The tie force can be found from the following: T
2eAs f y s
2PWle
(4.5)
where e = midspan eccentricity of the tie force with respect to the centroid of the compression strut (2e is the width that contributes to the combined tie force); T = combined tie force; l = overall span of arch (the length of the structure for this case); As = end connection reinforcement area (starter bars and hairpin bars);
fy = end connection reinforcement yield
strength; s = end connection reinforcement spacing; P = coefficient of friction for the bearing strip; and W = weight of the hollow-core. By equilibrium, the tension force in the floor slab is transferred to the perimeter beams by diagonal compression struts. These diagonal struts follow the observed crack pattern in the arching pattern demonstrated in Figure 4-10. The eccentricity can be found by considering the diaphragm reinforcement orthogonal to the tie force. The moment generated by the force couple between the floor slab and perimeter beams can be equated with the moment generated by the distributed load given by diaphragm reinforcement orthogonal to the tie force, w. The compression arch is equivalent to the moment from the uniformly distributed load given by the diaphragm reinforcement, which is in the shape of a parabola (as is the case for simply supported beams under distributed loads). The mechanism can be expressed as follows when considering equilibrium: Page 4-22
Te
wl 2 Pl 8 4
(4.6)
Where the first and second parts of (the right hand side of) Equation 4.6 respectively represent the uniform distribution of slab topping reinforcement along the entire floor span, and the drag bars anchored into the central column. Equation 4.6 can be expanded to give: Te
Asd f yd l 2 8s sd
Ast f yt l 4
(4.7)
where Asd = area of one bar of the diaphragm reinforcement; fyd = yield strength of the diaphragm reinforcement; ssd = spacing of the diaphragm reinforcement; and Ast = area of one drag bar; fyt = yield strength of the drag bar reinforcement This formulation provides an admissible mechanism from which the eccentricity can be found (by combining Equations 4.5 and 4.6), and therefore the combined tie force and by equilibrium, the compression axial force induced in the south perimeter beams can be calculated. This solution provides an upper bound method as it assumes that the reinforcement at the end supports of the hollow-core floor slabs, and diaphragm reinforcement orthogonal to the floor span are yielding. Using these equations, and the measured material properties of the reinforcement, an eccentricity of 2.5m was found. From strain gauge information of the drag bars tying the interior column into the floor plate, it was observed that the reinforcement was yielding, and the inclusion for this reinforcement in the mechanism analysis (Equation 4.6) was verified (see Appendix D for strain information for the drag bar reinforcement). The calculated value of the depth of the compression arch or eccentricity lies over the middle of the second hollowcore unit. The location of the calculated tie force and depth of the compression arch matches well with the cracking pattern witnessed throughout testing as is shown by 4-11(a) whereby a schematic of the bowstring effect is superimposed on a photo of the floor. During testing, a longitudinal crack over 7m long formed at the interface between the first and second hollowPage 4-23
core units, close to the calculated centroid of the tie force, which indicates that the calculated eccentricity for the mechanism is supported by the observed behaviour. Using the calculated eccentricity value, a combined tension force distributed over 5m, of 1254kN was found. By equilibrium, this tension force is resisted by a compression force of the same magnitude, which, in this case is experienced by the central column (at the top of the arch). Figure 4-11(b) shows the internal and external actions for the plastic hinges adjoining the south centre column. The compression force, N, which is transferred through the topping slab into the perimeter beams, has a significant effect the strength of the plastic hinges of the southeast and southwest beams framing into the central column. Compression Arching between the floor diaphragm and perimeter beams
Compression Arching following the observed crack pattern
N
N
2 * Eccentricity = 2e
Eccentricity = e
T Centroid of the tension tie in the floor diaphragm
(a) Observed bowstring effect South Centre Column
N D
(d-d')
M
(d')
N
T C S +CC C S +CC
M
-
(d-d')
T
South East Beam
South West Beam
M = (A sfy (d-d'))+(N(d))
Axial force from the bowstring effect, acting at the level of the topping slab
+
M = A sfy (d-d')
(b) Moment strength enhancement due to the bowstring effect
Figure 4-11 The influence of the bowstring effect
Page 4-24
As it is displayed in Figure 4-11(b) the negative moment capacity of the plastic hinges framing into the south centre column are increased by the axial compression force which is shown to act at the level of the topping slab. The moment contribution from both of the plastic hinges framing into the interior column can be found by the following: M beams
( As As ) f y (d d ' ) Nd
(4.8)
In which As+ = area of tension reinforcement; As- = area of compression reinforcement; fy = yield strength of tension reinforcement; d = the distance from the extreme compression fibre to the centroid of the tension reinforcement; d’ = the distance from the extreme compression fibre to the centre of the compression block; and N = the axial compression force due to the bowstring effect. Using the moment capacity Equation 4.8, the total moment from both of the southeast and southwest beams hinges (joining the south centre column) experienced by the column is 1859kNm. This is compared to 1004kNm when the bowstring effect in the floor slabs is not included. The compression axial forces due to the bowstring effect in this case have been represented at the height of the topping slab although it is acknowledged that the distribution of the compression axial forces is more complex than what has been described. The inclusion of the bowstring effect has been done by way of a simplistic mechanism approach, although it is acknowledged that it is an upper bound method. Due to this, a significant increase of the strengths of the perimeter beam plastic hinges was noted due to the compression axial force. The following sub-sections include the bowstring effect into calculations of the total superassemblage lateral load capacity and compare these predictions with the experimental results.
Page 4-25
4.4.2
General System Strength
An important part of finding the capacity of the structure is assessing the negative moment capacity enhancement provided by tension reinforcement within the topping slab. Matthews (2004) provided a method of calculating the activated slab width and accompanying strength from the starter bar reinforcement. This method was based on the experimental findings from the Matthews (2004) experiment and is a function of the specific structure. It provided an accurate means of calculating the lateral load capacity of the system. Comparisons were made with the equivalent methods prescribed in New Zealand Concrete Structures Standard (NZS 3101:1995) and the American Concrete Code (ACI 318-02) and it was found that these methods significantly underestimated the amount of strength contribution from the activated tension flange. Undervaluing the amount of moment capacity enhancement creates the potential of an undesirable strong beam-weak column mechanism forming, and it is therefore important that the slab and diaphragm reinforcement is accounted for correctly. The method used by Matthews (2004) characterises the progressive activation of starter bars according to increasing lateral displacement. Two distinct points are required to define the width of slab activation: the onset of yielding, and full plasticity. These points were found by examining the crack widths crossing the interface where starter bar or diaphragm reinforcement is present. The torsional stiffness of the beam is important in determining the rate of activation of the starter bar reinforcement. For beams of relatively low torsional stiffness, the starter bars in the middle of the beam will be activated much later from those at the end. In this experiment, it was observed that the beams formed torsional hinges at the ends, and can be classified as having low torsional stiffness. However, a sizeable crack formed in the topping concrete at the beam-to-floor interface and it was determined that the initial yield point and point of full plastification were similar to that assumed by Matthews (2004).
Page 4-26
For this experiment, the slab width at the first yield point was found to be the width of the timber infill (0.75m), which incorporates three starter bars or longitudinal diaphragm bars, and full plasticity was reached at 2% drift with an activated slab width of 3.05m, approximately half the width of the bay. This effective slab width is the same as what was used by Matthews (2004) and Lindsay (2004) and Figure 4-12 shows the contributing slab widths. Activated tension flange
Activated tension flange Beam + starters
Beam + starters
JD
Centre of the compression force
Centre of the compression force
(a) First Yield
(b) Full Plastification
Figure 4-12 Activated slab width for negative moment enhancement.
The overall strength of the system observed from the experiment is shown in Figure 4-13 for both the longitudinal and transverse loading phases. The theoretical pushover curves are superimposed to assess the validity of the theoretical calculations. This predicted strength capacity incorporates the nominal and overstrength strengths of the beams, starter bar contributions during the progression from yielding to full plasticity, the effect of the end support beam-to-floor slab connection reinforcement and the axial compression forces induced by the bowstring effect. As it can be seen by examining Figure 4-13(a) for both Phase 1 and 3 loading, the correlation is satisfactory. The overstrength capacity strengths (assumed as 125% and 140% of the nominal strengths) have been plotted as upper bound values and actual strength of the system lies between the two overstrength predictions. It can be seen that the later cycles are well predicted; the Âą3% and Âą4% cycle peaks or maximum strengths are slightly underestimated by the nominal theoretical values but well matched by the 40% overstrength prediction.
Page 4-27
The base shear capacity for the transverse loading phase is shown by Figure 4-13(b). The accompanying theoretical pushover curve shows good agreement with the experimental results. For positive drifts, the experimental results experimental values fall in between the upper bound overstrength capacity values and the lower bound nominal strengths. The negative drift predictions conversely, are higher than the actual results. This could signify that there was less starter bar reinforcement activated than what was assumed during calculating the pushover curve. The experimental values graphed are for before and after a torsion test that was conducted mid-way through Phase 2 loading. It is discussed further in Appendix D, but it can be seen that the torsion test undertaken did not cause a reduction in the load carrying capacity of the system. It should also be noted that a yield inter-storey drift of Âą0.64% was used for the yield strengths. As the hysteretic behaviour indicates, this theoretical yield drift compares well with the observed experimental yielding point and elastic stiffness. A more in depth assessment of the super-assemblage stiffness as well as details of the calculation of the yield drift are located in Appendix D.
4.4.2
Localised Strengths
The individual or combined plastic hinge strengths are shown by the moment rotation relationships in Figure 4-14. The plastic hinges of the south frame for longitudinal loading are shown in Figure 4-13(a) for both the southeast and southwest hinges, and the combination of the centre hinges framing into the centre column. The general agreement is good with the later cycle peaks lying between the nominal and overstrength estimates. The comparison between the observed experimental behaviour theoretical predictions for the central column is good, which indicates that the method, albeit an upper bound approach, used to quantify the added moment due to the bowstring effect is sufficiently accurate.
Page 4-28
Base Shear Force (kN)
1800 1600 1400 1200 1000 800 600 400 200
Inter-Storey Drift (%)
0 -6
-5
-4
-3
-2
-1
-200
0
1
2
3
4
5
6
-400 -600 -800 Experiment Phase 3
-1000
Experiment Phase 1 -1200
Nominal Prediction
-1400
25% Overstrength Prediction
-1600
40% Overstrength Prediction
-1800
(a) Phase 1 and 3 Longitudinal loading: Experimental base shear capacity and theoretical pushover curve. Base Shear Force (kN)
1200
900
600
300
Inter-Storey Drift (%) 0 -4
-3
-2
-1
0
1
2
3
-300
-600
Experiment (pre-torsion) Experiment (post-torsion)
-900
Nominal Prediction 25% Overstrength Prediction
-1200
(b) Phase 2 Transverse loading: Experimental base shear capacity and theoretical pushover curve.
Figure 4-13 Base shear capacity: experimental and theoretical relationships.
Page 4-29
4
800 600 400 200
-6
-5
-4
-3
-2
-1 0 -200
2500 2000 1500 1000 500
R o t a t io n ( %)
0 1
2
3
4
5
-6
6
-5
-4
-3
Moment (kNm)
1000
R o t a t io n ( %)
3000
Moment (kNm)
Moment (kNm)
1200
R o t a t io n ( %)
0 -2
-1 0 -500
1
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5
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-5
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Phase 1
-1500
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Nominal Strength
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1000 800 600 400 200 0
-2
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-1 0 -200
1
2
Phase 1 Phase 3
5
6
Phase 3
-800
Nominal Strengt h
-1000
25%Overstrengt h
25%Overstrength
-3000
Southwest hinge, south beams
4
Phase 1
-600
Nominal Strengt h 25%Overst rengt h
-2500
-1200
3
-400
-1200
South centre hinges
Southeast hinge, south beams
1200
1000
1000
Moment (kNm)
Moment (kNm)
(a) Phase 1 Longitudinal loading: plastic hinge strengths 1200
800 600
800 600
400
400
200 Rotation (%) -4
-3
200 Rotation (%)
0 -2
-1 -200 0
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0 -1 -200 0
-400 Pre-Torsion Post-Torsion
-600 -800
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1200
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1000
Moment (kNm)
Moment (kNm)
North hinge, East transverse beam
800 600
-1 -200 0 -400 -600 -800 -1000
600
200
Rotation (%)
0 -2
800
400
200 -3
25% Overstrength
-1200
400
-4
4
Nominal Strength
-1000
North hinge, West transverse beam
Rotation (%)
3
Post-Torsion
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2
Pre-Torsion
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Nominal Strength 25% Overstrength
-1000
1
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Pre-Torsion Post-Torsion Nominal Strength 25% Overstrength
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-600
Post-Torsion
-800
Nominal Strength
-1000
4
25% Overstrength
-1200
-1200
South hinge, West transverse beam
South hinge, East transverse beam
(b) Phase 2 Transverse loading: Individual hinge strengths.
Figure 4-14 Individual hinge strengths: experimental and theoretical pushover relationships.
Experimental and theoretical comparisons for the transverse loading are provided in Figure 4-14(b). It is shown that the theoretical strength model represents the actual behaviour well. The positive moment capacities for each of the hinges are matched well by the overstrength moment predictions. However, there is a slight over-prediction of the negative moment Page 4-30
capacities for the southeast and southwest hinges of the transverse beams. The nominal moment capacity values provide a more suitable match in this case. This overestimation could mean that the amount of activated slab contributing is less than what was specified; half of the longitudinal south bays at full plasticity.
4.5 BEAM ELONGATION One of the significant outcomes from the Matthews (2004) experiment was the development of a rational mechanics based theory to predict beam elongation. A rainflow counting method was been employed to account for the growth of plastic hinges in a frame system under inelastic rotations. The theory is briefly explained in Section 2 of this thesis, but further information is provided by Matthews (2004). The calculations made for the theoretical predictions of beam elongation are tabulated in Appendix D. Figure 4-15(a) and (b) displays the observed and theoretical beam elongation results for Phase 1 and 3 longitudinal loading. The elongation values represented are for the total frame and a consideration of the pull-off demands imposed on the floor seating connections require the values shown to be halved. As it is illustrated, the observed and predicted results agree well, especially during Phase 1. The theoretical elongations slightly underestimate the actual values up until the first cycle to –4% during Phase 3, after which the experimental values level off and even decrease. The elongation predictions of the final loading cycles to ¹5% are not reached due to instrumental errors, but despite this, the agreement is satisfactory up until the ¹4% cycles. After Phase 1 loading, the permanent elongation was 32mm, from which the elongation continued to grow during Phase 3 re-loading and at the end of testing, the permanent elongation was 72mm.
Page 4-31
Figure 4-15(c) shows the frame beam elongation results obtained from the Phase 2 transverse loading. The predicted values display elongation for the outside transverse frames and are displayed by Figure 4-14(d). The beam elongation theory once again predicts the actual behaviour well. The actual results are marginally lower than the predicted values, however the difference is small. At +4% the predicted beam elongation was 30mm and the recorded experiment elongations were 29mm and 30mm for the west and east bays
120
Elongation (mm)
120 100
T heor y
100
80
80
60
60
40
40
Phase 1
20
Elongation (mm)
respectively.
20
Phase 3 0
0
-6
-5
-4
-3
-2 -1 0 1 2 Inter-storey Drift (%)
3
4
5
6
-5
-4
-3
-2 -1 0 1 2 Inter-storey Drift (%)
35 30 25
-2
-1
5
6
T heor y
25
15
15
10
10 5
West Bay 0
0 -3
4
30
20
East Bay
-4
35
20
5
3
(b) Phase 1 and 3 longitudinal theoretical beam elongation Elongation (mm)
Elongation (mm)
(a) Phase 1 and 3 longitudinal experimental beam elongation
-6
0
1
2
3
4
-4
-3
-2
-1
0
1
2
3
Inter-storey Drift (%)
Inter-storey Drift (%)
(c) Phase 2 transverse experimental beam elongation
(d) Phase 2 transverse theoretical beam elongation
Figure 4-15 Experimental and theoretical beam elongation results.
Page 4-32
4
4.6 LOW CYCLE FATIGUE OF THE REINFORCEMENT The fracture of the reinforcement observed during the later stages of the experiment can be predicted by low cycle fatigue theory. The fracture of the longitudinal reinforcement during the Lindsay (2004) experiment was able to be predicted to a satisfactory level of accuracy. Low cycle fatigue is also addressed in Section 2 for the sub-assemblage tests. The low cycle fatigue theory enables the plastic rotation life capacity of the reinforcement to be calculated and is expressed as follows (Dutta and Mander, 2001):
Tp
§ D ¡§ L p 0.16¨ ¸¨¨ Š D' šŠ D
¡§ 1 L p ¡ ¸¸¨¨1 ¸¸ 2 N f 2 L šŠ š
0.5
(4.9)
where Tp = plastic drift; L = lever arm of the cantilever column; D = overall member depth; D’ = distance between outer layers of steel; 2Nf = the number of reversals to the appearance of the first fatigue crack with which Nf is the effective number of constant amplitude cycles for a variable amplitude displacement history; and Lp = equivalent plastic hinge length, which is given by: Lp
0.08 L 4400H y d b
(4.10)
in which Hy = the yield strain and db = the diameter of longitudinal reinforcement. Miner’s well-known linear damage accumulation theory can be utilised to calculate the equivalent number of equi-amplitude cycles (Nf):
Nf
§ T Œi ¨¨ T Š ref
¡ ¸ ¸ š
2
(4.11)
where T = drift for the ith cycle of loading and Tref = reference drift for an equivalent constant amplitude loading history. Using a reference drift of 5% an applied cyclic demand of Nf = 4.5 cycles is calculated for the experiment. This signifies that 4.5 equivalent cycles of 5% drift caused the low cycle fatigue fracture of the reinforcement. By re-arranging Equation 4.9, the
Page 4-33
theoretical equivalent number of equi-amplitude cycles can be found. Using a reference drift of 0.05 radians, a yield drift of 0.0064 radians and a equivalent plastic hinge length of 511mm, an equivalent number of 3.6 cycles to 5% was calculated This underestimates the first fracture, which occurred after 4.5 cycles. Given that conventional wisdom considers that any result that falls within Âą25% of the predicted value is satisfactory, it is evident that the experiment (NF-Expt = 4.5) and theory (NF-Theory = 3.6) match to a satisfactory level.
4.7 COMPARISONS WITH PREVIOUS RESEARCH The research presented in this thesis report follows work that has identified the seismic inadequacies of precast hollow-core floor systems and investigated solutions to address the identified problems. With the results and understanding gained from each of the three superassemblage experiments and associated two-dimensional sub-assemblage investigations, the nuances of hollow-core behaviour have become clearer. There has been a progression of design solutions and correspondingly better performance. This experiment, as it was aimed to do, has answered many questions and proven the recommendations given by previous researchers. This sub-section briefly assesses aspects of this experiment in relation to the investigations by Matthews (2004) and Lindsay (2004) as a way to conclude this particular line of hollow-core research. Figure 4-16 shows the lateral load demand imparted on the structure during each of the three super-assemblage experiments as well as the timing of significant failure events. As it can be seen, the cyclic demand for the Lindsay (2004) and current investigations of new construction details, was more onerous than the original Matthews (2004) experiment, which examined of existing buildings. The location of failure events also signify improved performance throughout the three experiments, with the later two experiments being able to sustain much higher drift amplitudes and number of cycles. Page 4-34
5 4 3 2 1 0 -1 -2 -3 -4 -5
Inter-storey Drift (%)
Initial Mesh Fracture
Inter-storey Drift (%)
Inter-storey Drift (%)
5 4 3 2 1 0 -1 -2 -3 -4 -5
5 4 3 2 1 0 -1 -2 -3 -4 -5
Partial Collapse
Total Collapse
5 4 3 2 1 0 -1 -2 -3 -4 -5
Inter-storey Drift (%)
5 4 3 2 1 0 -1 -2 -3 -4 -5
Inter-storey Drift (%)
Inter-storey Drift (%)
(a) Loading protocol used for the Matthews (2004) experiment 5 4 3 2 1 0 -1 -2 -3 -4 -5
Initial Mesh Fracture
Low cycle fatigue of main beam bars
5 4 3 2 1 0 -1 -2 -3 -4 -5
Inter-storey Drift (%)
5 4 3 2 1 0 -1 -2 -3 -4 -5
Inter-storey Drift (%)
Inter-storey Drift (%)
(b) Loading protocol used for the Lindsay (2004) experiment 5 4 3 2 1 0 -1 -2 -3 -4 -5
Low cycle fatigue of main beam bars
(c) Loading protocol used for the current experiment
Figure 4-16 Loading cycles imposed and observed failures for the current and previous experiments.
4.7.1
Performance of the Seated Connection
Figure 4-17 shows a schematic representation of the behaviour of the hollow-core-to-support beam seated connections for each of the three tests. The seated connection used for the Matthews (2004) experiment was originally assumed to slide on the concrete seating ledge relative to the supporting beam. However, the rigidity of the mortar bed seating surface did not allow the floor unit to slide, and under cyclic loading, the relative rotations between the supporting beam and floor slab resulted in large cracks forming in webs of the hollow-core unit. This eventually caused a loss of seating failure of the hollow-core flooring. The floorbeam connection tested by Lindsay (2004), as a result of the previous poor performance, was
Page 4-35
a “pinned� type connection, which featured the hollow-core flooring seated on a low friction bearing strip to allow sliding and a compression backing board. This detail behaved well, although spalling of the concrete ledge concrete and sliding of the low friction bearing strip relative to the supporting beam occurred late in the experiment. The beam-to-floor connection used in this current experiment rigidly tied the floor into the beam, possessing a degree of redundancy not offered by the Lindsay (2004) detail. Improved performance under relative rotation was observed due to the promotion of a critical section at the beam-slab interface at which the rotation was concentrated. The low friction bearing strip performed well and allowed the flooring to slide relative to the supporting beam under the effects of beam elongation, and after the completion of testing, the hollow-core floor units had suffered very little damage. Compressible material does not compress Column
Snapping action
Unit slides Assumed to slide
Actual behaviour
(a) Matthews (2004) seated connection behaviour. Rotation centred at critical section
(b) Lindsay (2004) seated connection behaviour.
Hollow-core units remain undamaged
Moment resisted by connection reinforcing force couple Unit sliding on low friction bearing strip
(c) Current experiment seated connection behaviour.
Figure 4-17 Observed behaviour of the floor-to-beam under relative rotation.
Page 4-36
The successive experiments have seen dramatic improvements of the seated connection performance details. The problems associated with the inadequate behaviour of “existing� building details has been remedied in terms of future construction and the seismic adequacy of the two latter supporting connection details that have been added to the New Zealand Concrete Code Amendment NZS 3101:2004 have been experimentally verified.
4.7.2
Performance of the Perimeter Beam to Hollow-Core Connection
The lateral hollow-core connection throughout the current and previous experiments has been one of the primary sources of examination and details from the previous tests are shown in Figure 4-7. A leading source of damage witnessed during the Matthews (2004) test occurred due to deformation incompatibilities between the perimeter frame and adjoining hollow-core floor units. The discussion of displacement incompatibility outlines the identified issues and reasons for the damage. As a solution to these issues, a timber infill solution that allows the perimeter beams and flooring to displace freely individually was proposed and tested by Lindsay (2004) and a dramatic improvement was noted. However, the termination of the starter bar reinforcement prior to the infill-to-floor interface placed high demands on the ductile mesh reinforcement in the topping slab which fractured at relatively early stages and a resulting large tear within the topping concrete. To overcome the deficiencies from this solution, a similar timber infill detail was tested again during the current experiment, incorporating longer starter bars and conventional reinforcing in place of the ductile mesh used to reinforce the diaphragm. These enhancements resulted in improved performance whereby the longer starter bars distributed stresses over a larger area and there was no major cracking or tearing ensuring that inertia and structural interaction loads from the flooring are able to be transferred to the perimeter frame.
Page 4-37
4.7.3
Overall performance comparisons
Comparisons between the base shear hysteretic behaviour of the three experiments, shown in Figure 4-18, are able to show the relative overall strengths and stiffnesses of the systems and energy dissipation characteristics. However, the overall performance of the structure cannot be determined from the hystereses relationship as it is dominated by the performance of the reinforced concrete frame. Upon examining Figure 4-18, the major improvements made by the current and Lindsay (2004) experiments are clouded by the similar performances of the perimeter concrete frames. Despite this, it can be seen that similar performance of the perimeter concrete frames can be achieved by repairing existing concrete frames (Lindsay, 2004) and by achieving equivalent strengths using Grade 500E reinforcing. In addition to the design changes made following the Matthews (2004) test to the end and lateral hollow-core connection and the corresponding improved performance, there are also several other aspects of the test structure behaviour to consider. There was little or no damage to the southern end corners of the hollow-core units signifying the hooked bar, utilised in the transverse beams to reduce the risk of relocated plastic hinging from occurring, performed as desired. Other small modifications made from the Lindsay (2004) such as a second generation bearing strip and seat concrete transverse reinforcing also proved to be worthwhile. Interestingly, the pattern of damage within the plastic hinges for the current experiment was different than the Matthews (2004) and Lindsay (2004) experiments. Significant cracks, one at the beam-column interface and another 100-200mm away from the column, formed and progressively opened throughout tests. This contrasts with the previous experiments and expected behaviour of distributed cracking over a conventional plastic hinge zone length.
Page 4-38
1200
Base Shear Force (kN)
Base Shear Force (kN)
1600
1200
800
-4
-3
-2
-1
300
Inter-Storey Drift (%)
0 -5
600
400
Inter-Storey Drift (%) -6
900
0 0
1
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3
4
5
6
-4
-3
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-1
0
-400
-300
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-600
1
2
3
4
3
4
Phase 1 -1200
-900
Phase 3
-1600
-1200
(a) Phase 1 and 3 Longitudional loading (Matthews, 2004)
(b) Phase 2 Transverse loading (Matthews, 2004) 1200
Base Shear Force (kN)
Base Shear Force (kN)
1600
1200
800
400
Inter-Storey Drift (%)
900
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Inter-Storey Drift (%)
0
0 -6
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Phase 1
1
2
-900
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Phase 3 -1200
-1600
(c) Phase 1 and 3 Longitudional loading (Lindsay, 2004)
(d) Phase 2 Transverse loading (Lindsay, 2004) 1200
Base Shear Force (kN)
Base Shear Force (kN)
1600
1200
800
400
Inter-Storey Drift (%) -5
-4
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Inter-Storey Drift (%)
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900
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1
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-400
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Phase 1
1
2
3
4
-900
-1200
Phase 3 -1200
-1600
(e) Phase 1 and 3 Longitudional loading (Current Experiment)
(f) Phase 2 Transverse loading (Current Experiment)
Figure 4-18 Comparative hysteretic behaviour for Matthews (2004), Lindsay (2004) and the current experiment. Page 4-39
4.8 CONCLUSIONS
The results and discussion provided in this section provide a forensic analysis that enabled an overview of the super-assemblage performance to be conducted. From the results presented herein, the following concluding remarks can be made: 1.
Due to the added torque created by the rigidly reinforced floor-to-beam connection, torsional hinging was observed to occur at the ends of the transverse beams. The use of standard torsional strength and stiffness calculations, to make an assessment of the torsional performance of the beam sections, was explained. It was seen that the flexural plastic hinging of the ends of the transverse beams under Phase 2 transverse loading was largely the reason for the deterioration of the concrete contribution to the torsional strength, Tc, and hence led to large torsional twists on the softened cracked beam sections during Phase 3 loading. It is recommended that future research should further address the complexities of torsional behaviour when combined with concurrent shear and flexural actions that are expected to occur under realistic bi-lateral seismic repsonse.
2.
The construction details altered and improved from the Lindsay (2004) experiment that features an articulated topping slab cast over a timber infill demonstrated that it substantial displacement incompatibilities between the hollow-core flooring and perimeter frame can be sustained. Analytical modelling of the displacement incompatibility showed good agreement with the experimental results. It was also shown that extensions of this model could provide a useful tool for analysing and predicting the performance of different structures as well as possible future solutions.
3.
The strength of the super-assemblage was able to be predicted and good correlation was seen between the theoretical pushover curve and the experimental base shear force hysteretic behaviour. The method for accounting for the progressive activation of starter bars with increasing lateral displacement of the structure matched the actual strength Page 4-40
increase from the initial onset of yielding and the assumed point of full plastification. The contribution to the lateral load capacity of the front frame due to the restraint imparted by the floor slab, the “bowstring effect”, was quantified and seen to be significant. The observed crack patterns in the floor slab support the concept of a socalled “bowstring effect”. This effect induced a substantial axial thrust force in the perimeter beams which in turn increases the moment demand on the interior column. 4.
A summary of the preceding Matthews (2004) and Lindsay (2004) experiments and current investigation with respect to the comparative overall structural performance was made. It was seen that there has been distinct improvements through the successive experiments and larger displacement demands can now be maintained without significant damage. Several other detailing changes implemented such as conventional reinforcing in place of mesh, special detailing of the transverse beam, improved bearing strip and reinforcing of the concrete seat all enhanced the overall performance of the structure.
4.9 REFERENCES
ACI 318-02, Building Code Requirements for Structural Concrete and Commentary, American Concrete Institute, Farmington Hills, USA. Bull D.K, 2003, Understanding the Complexities of Designing Diaphragms in Buildings with Earthquakes, Symposium to Celebrate the Lifetime Contributions of Professors
Emeriti Tom Paulay and Bob Park, Christchurch, pp 93-113. Carr A.J, 2003, Ruaumoko 2D User Manual, Computer Program Library, Department of Civil Engineering, University of Canterbury, Christchurch, New Zealand. Dutta A and Mander J.B, 2001, Energy Based Methodology for Ductile Design of Concrete Columns, Journal of Structural Engineering, Vol. 127(12), December, pp 1374-1381. Page 4-41
Elliot K.S, Davies G, Gorgun H, Adlparvar M.R, 1998, The Stability of Precast Concrete Skeletal Structures, PCI Journal, March-April, pp 42-60.
Fenwick R.C, Davidson B.J, and Lau D, 1999, Strength Enhancement of Beams in Ductile Seismic Resistant Frames due to Prestressed Components in Floor Slabs, Journal of
the New Zealand Structural Engineering Society (SESOC), Vol 12, No. 1, pp 35-40. Hsu T.T.C, 1993, Unified Theory of Reinforced Concrete, CRC Press, Boca Raton, USA. Jensen J, 2004, Diaphragm Action Issues in a Jointed Precast Concrete System, Research report submitted as part of third professional year coursework, Department of Civil Engineering, Christchurch, New Zealand. Lau D.B.N, Fenwick R.C and Davidson B.J, 2002, Seismic performance of R/C perimeter frames with slabs containing prestressed units, Proceedings for NZSEE conference,
Napier, March, Paper No. 7.2. Lindsay R.A, 2004, Experiments on the seismic performance of hollow-core floor systems in precast concrete building, Masters Thesis, Department of Civil Engineering,
University of Canterbury, Christchurch, New Zealand. Matthews J.G, 2004, Hollow-core floor slab performance following a severe earthquake, PhD Thesis, Department of Civil Engineering, University of Canterbury, Christchurch, New Zealand. Matthews J.G, Mander J.B, Bull D.K, 2004, Prediction of beam elongation in structural concrete members using a rainflow method, 2004 NZSEE Conference, Rotorua, NZ,
Paper 27, 8 pp. McKenzie R, 2004, Feasibility Study and Optimum Location of Discrete Floor-Frame Connectors in a Precast Concrete System, Research report submitted as part of third
professional year coursework, Department of Civil Engineering, Christchurch, New Zealand.
Page 4-42
Mitchell M.P and Collins D, 1991, Prestressed Concrete Structures, Prentice Hall, Englewood Cliffs, N.J, USA. NZS3101, 1995, Concrete Structures Standard, NZS3101, Parts 1 & 2, Standards New Zealand, Wellington, New Zealand. NZS3101, 2003, Draft Amendment No. 3 to 1995 Standard (NZS3101), Standards New Zealand, Wellington, New Zealand. Naito C.J and Cao L, 2004, Precast Diaphragm Panel Joint Connector Performance, 13th World Conference on Earthquake Engineering [Proceedings], Vancouver, Canada, Aug. 2004, Paper 2722. O’Grady C.R, 2004, Letters to the Editor, Journal of the New Zealand Structural Engineering Society (SESOC), Vol 17, No. 2, pp 8-9. Park R and Paulay T, 1975, Reinforced Concrete Structures, J. Wiley and Sons Inc, New York. Paulay T and Preistley M.J.N, 1992, Seismic Design of Reinforced Concrete and Masonry Buildings, J. Wiley and Sons Inc, New York.
Priestley M.J, Sritharan S, Conley J.R, Pampanin S, 1999, Preliminary results and conclusions from the PRESSS five-storey precast concrete test building, PCI Journal,
Vol. 44, No. 6, November-December, pp 42-57. Taylor L, 2004, Vertical Displacement Incompatibility between Floor Slabs and Seismic Resisting Systems, Research report submitted as part of third professional year
coursework, Department of Civil Engineering, Christchurch, New Zealand. Trowsdale J.F, 2004, Seismic Performance of Hollow-core Seating Details Specified by Amendment No. 3 to NZS 3101:1995, Research report submitted as part of third
professional year coursework, Department of Civil Engineering, Christchurch, New Zealand.
Page 4-43
5.
5.1
Section 5 – Conclusions and Recommendations
SUMMARY
The research presented in this thesis continued work done by Matthews (2004) and Lindsay (2004) into examining the seismic performance of precast concrete structures with hollowcore flooring. The complete failure of the hollow-core flooring observed during the investigation by Matthews (2004) showed that existing structures using hollow-core flooring systems pose a serious risk under seismic events. Continuing research by Lindsay (2004) showed that with simple detailing enhancements, significant improvement in the seismic performance of hollow-core floor systems can be expected. The present experimental research aimed at validating several new detailing enhancements. Initially, two hollowcore-to-support beam seated connections were tested under simulated seismic loads at a two-dimensional sub-assemblage level. The support connections were reinforced and rigidly tied the floor into the supporting beam, the first of which has been proposed in Amendment No. 3 to the New Zealand Concrete Standard (NZS 3101, 2004). A newly developed test set-up was described which incorporated both the relative rotation between the supporting beam and hollow-core floor, and tension in the floor representing the elongation of a parallel moment resisting frame, as the sources of damage. The subassemblage test specimens were tested up to relative rotations of Âą5.0% and visual and instrumental observations from the experiments were outlined. The main investigation of this thesis involved the testing of a full-scale two bay-byone bay concrete frame super-assemblage. The super-assemblage was constructed and several new detailing improvements recommended from previous research were implemented as well as the recently proposed, but untested, hollow-core connections with the concrete frame (NZS 3101, 2004). The full-scale structure was cyclically tested in both the longitudinal and Page 5-1
transverse directions to inter-storey drifts of Âą5%. Visual and instrumental observations from the experiment were presented and discussed. The third major section of this thesis provided a forensic analytical overview of the experimental observations. The torsion behaviour of the transverse beams was discussed and analysed using simple calculations. Displacement incompatibility was also described and results from the experiment were compared with analytical modelling results. The potential uses of extending the model were also described. A theoretical pushover curve was generated predicting the strength of the super-assemblage, and the contribution to the strength of the moment resisting frame of the floor slab, through the bowstring effect, was quantified. Finally, as a way of completing the current line of experimental research, the present investigation was compared and contrasted with previous research conducted by Matthews (2004) and Lindsay (2004). The comparative performances showed that through improved understanding of hollow-core performance and accompanying detailing enhancements there have been significant advancements.
5.2
CONCLUSIONS
From the research presented in this thesis, the following conclusions can be drawn:
1.
The three-dimensional testing of a full-scale two bay-by one-bay concrete moment resisting frame structure incorporating prestressed hollow-core flooring, as designed to New Zealand Concrete Design Standards (NZS 3101:1995 and amendments) performed well under simulated seismic loads. The super-assemblage structure was able to sustain lateral inter-storey drifts up to Âą5% when the longitudinal reinforcement in the beam fractured due to low cycle fatigue. The floor system sustained only minor damage, and life safety was not endangered at any stage during testing. Page 5-2
2.
The reinforced connection between the hollow-core floor slab and supporting beams performed well up to inter-storey drifts of Âą5% and at the conclusion of testing, the damage suffered by the hollow-core floor units was minimal. Desirable action, where the relative rotations between the floor and supporting beam were concentrated at the beamslab interface was achieved. A second generation low friction bearing strip ensured that the hollow-core floor slabs slid horizontally relative to the supporting beam and helped to mitigate spalling of the concrete ledge.
3.
The timber infill connection utilised between the lateral load resisting frame and adjoining hollow-core spanning parallel to the frame performed well during the experiment. This connection detail allowed the flooring and frame elements to deform freely. At the same time, the integrity of the connection, in terms of the capability of transferring inertial forces from the floor to the frame, was maintained. The good performance of the timber infill detail supports its inclusion into New Zealand Concrete Design Standards. The displacement incompatibility between the floor and frame was measured during the experiment and correlations between these results and analytical modelling were good.
4.
The lateral load capacity of the super-assemblage was able to be predicted with satisfactory agreement observed with the experimental results. Although it was seen that the moment resisting frame dominated the overall super-assemblage strength, the contribution of the floor slab was noticeable. Compression forces induced in the longitudinal frame beams due to the bowstring effect were quantified and the progressive activation of starter bars within the transverse beams was accounted for in calculations of the negative moment capacities of the frame beams.
Page 5-3
5.
As a result of the rigidly reinforced connection between the transverse supporting beams and floor slabs, torsional hinging at the ends of the transverse beams was observed. The strong floor-to-beam connection caused the floor to remain horizontal and the supporting beams to stay essentially upright throughout the cyclic lateral loading of the superassemblage in the longitudinal direction, and this placed large torsional demands on the ends of the transverse beams. It was seen that the flexural hinging of the transverse beams during transverse loading caused deterioration of the ends of the transverse beams, which accelerated the effects of torsion observed under longitudinal re-loading.
6.
Sub-assemblage two-dimensional proof of concept testing conducted preceding the fullscale super-assemblage test was seen to provide an accurate representation of the threedimensional test. A new testing procedure was developed to include the dual sources of damage of the relative rotation between the supporting beam and slab, and tension forces in the floor. Although the limitations of the two-dimensional form of test were acknowledged, the ability to achieve useful and realistic results for less time and resource constraints make this format of testing a valuable method of investigation floorto-beam connections.
7.
This overall experimental investigation has shown that a correct level of reinforcement between the floor slab and supporting beam can lead to good performance. However, consideration of previous sub-assemblage research, and the relative performance of each of the sub-assemblage component specimens tested during this current research indicate that over-reinforced beam-to-floor connections can cause inferior performance. It is therefore imperative that a correct level of reinforcement, such as the reinforcement used for the beam-to-floor slab connection in the current super-assemblage, is used.
Page 5-4
5.3
RECOMMENDATIONS FOR PROFESSIONAL PRACTICE
One of the main objectives of this research was to validate previously unproven and untested details proposed in amendments to the New Zealand Concrete Design Standard (NZS 3101, 2004). Recommendations from previous research (Matthews, 2004 and Lindsay, 2004) have also been incorporated to enhance the seismic performance. The following recommendations have been made for improving professional practice and design standards:
1.
Subject to the good performance of the reinforced connection detail used between the hollow-core floor slabs and supporting beams, it is recommended that this detail is fully adopted by New Zealand Concrete Design Standards. Figure 5-1 shows a diagram of the connection detail. Also it can be recommended that the current 1.2% drift design limit imposed on this class of construction be lifted. D12 Starter Bars (Grade 300) (300mm spacing)
900mm (3*hollowcore depth) D12 Bars @ 300mm each way as topping reinforcing 600mm Lap
300 Series Hollow-core 2*R16 (Grade 300) - 1 per filled core Seat Transverse Reinforcement
Low Friction bearing strip 75mm seat (minimum)
Note: Alternate (every second) cores filled and reinforced
Figure 5-1 Recommended hollow-core to supporting beam connection detail.
2.
For cases when an infill slab is used to connect an exterior concrete frame and parallel spanning precast floor, the detail presented in Figure 5-2 should be used. The starter bars from the perimeter beams should extend a minimum distance of 600mm into the first floor unit.
Page 5-5
75mm Concrete Topping D12 Starters extending 600mm Timber in-fill into the first hollow-core unit 750mm (lapped with diaphragm reinforcing)
Hollowcore Units
200mm*25mm Timber boards Perimeter beam
Figure 5-2 Hollow-core connection detail with a parallel load resisting frame
3.
Conventional reinforcement should be used in place of customary cold drawn or ductile mesh in diaphragm topping slabs. Grade 300 D10 or D12 reinforcement (the ‘D’ indicates deformed reinforcement) placed at 300mm centres provide sufficient ductility, decrease the risk of reinforcment fracture and are compatible with conventionally used Grade 300 D12 starter bar reinforcement.
4.
Low friction bearing strips should be used for the seating of hollow-core floor units. These allow horizontal sliding of the floor units relative to the supporting beam and help distribute stresses reducing the chance of concrete spalling from the supporting ledge. Figure 5-3 shows the layout that the seating of precast units should adhere to. Floor Unit
Supporting Beam
Low friction bearing strip
Concrete Seat (ledge)
10mm
15mm 50mm 75mm
Figure 5-3 Precast concrete floor seating requirements (close-up view)
Page 5-6
5.
Hollow-core units should not be seated on potential plastic hinge zones of supporting beams. Infill slabs should be used over these regions and additional hooked reinforcement should be cast in the transverse beams, such as is shown in Figure 5-4, to force plastic hinging of the supporting beams to occur away from the seated hollow-core floor units. Starter bars from the longitudinal beams
Column
(extended into first hollowcore unit)
Hollowcore Units
Timber Infill
Transverse Beam Hooked Bar (in addition to the regular reinforcing)
Longitudinal Beam
Figure 5-4 Recommended floor supporting beam detailing
5.4
RECOMMENDATIONS FOR FUTURE RESEARCH
Although this research has addressed several issues that have arisen from previous research findings, there are still many issues that require research attention. The following lists some areas that need research consideration:
1.
Despite the limitations, the effectiveness and ease of conducting proof of concept subassemblage tests relative to full-scale super-assemblage experiments mean that several other beam-to-floor connections should be investigated. Research should strive towards testing all floor-to-beam connections that have been used in New Zealand construction, including other floor types. This research would be able to highlight vulnerabilities possessed by other forms of construction and help direct further investigations.
Page 5-7
2.
The research conducted in this thesis as well as Lindsay (2004) has successfully provided validated design solutions for future construction. However the shortcomings of hollow-core flooring observed during the Matthews (2004) testing indicate that many existing buildings would be damaged in a seismic event. Future research should look to find suitable economical and practical retrofit measures for existing structures.
3.
As the timber infill detail has been proven as a suitable detail to connect lateral frames with parallel spanning precast floors, future research should seek to develop a “flat soffit” option where the flooring is directly adjacent to the perimeter frame. Research has previously been conducted on such connections, however more specific investigations need to be undertaken focusing on New Zealand construction conditions. The use of discrete floor-to-frame connectors that are able to allow vertical displacements but dissipate energy and transfer inertial loads is one example of a possible connection solution. A suitable “flat soffit” detail would offer designers another option should an infill detail be architecturally undesirable.
4.
As the Matthews (2004) and Lindsay (2004) experiments have shown, hollow-core floor units are susceptible to damage when seated on plastic hinge zones of their supporting beams. Future research should seek to develop advanced seating materials that allow both the horizontal sliding of the floor units relative to the supporting beams and deformations of the supporting beams to be accommodated. Such solutions as rubber bearings should be investigated in more depth.
Page 5-8
In addition to the experimental research recommended, there is also the need for analytical work in order to better predict and assess the behaviour of hollow-core structures. Ideally, all experimental research should be coupled with parallel analytical work so that experimental work can be better explained and understood as well as to offer a useful tool for researchers and designers. More specifically, areas of analytical research should develop what has been touched on in this thesis. Modelling of torsion, the contribution of strength from the floor slabs in terms of the bowstring effect and displacement incompatibility all need to be extended.
5.5
REFERENCES
Lindsay R.A, 2004, Experiments on the seismic performance of hollow-core floor systems in precast concrete building, Masters Thesis, Department of Civil Engineering, University of Canterbury, Christchurch, New Zealand. Matthews J.G, 2004, Hollow-core floor slab performance following a severe earthquake, PhD Thesis, Department of Civil Engineering, University of Canterbury, Christchurch, New Zealand. NZS3101, 1995, Concrete Structures Standard, NZS3101, Parts 1 & 2, Standards New Zealand, Wellington, New Zealand. NZS3101, 2004, Amendment No. 3 to 1995 Standard (NZS3101), Standards New Zealand, Wellington, New Zealand.
Page 5-9
Appendix A – Sub-Assemblage Experiments: Construction & Results
A.1
CONSTRUCTION DETAILS AND PHOTOGRAPHS Full size test
SFD based on 12m span prototype
35kN
SFD based on 6m span
SFD due to additional mass (Pt load = 35KN)
Combined SFD for SW + Pt load
Matching the shears at the beam connection
Comparison between the SFD for both the 12m unit and the 6m unit with an additional mass Reaction provided by vertical actuator
(a) Schematic view of the link with the super-assemblage Reaction Frame
Reaction Frame Vertical (drift controlling) Actuator
35kN Concrete Weight
Support beam and restraints Hollow-core unit
300 series hollow-core unit
6000mm
Horizontal (beam elongation) Actuator
South (side) elevation
Support beam and restraints
West (end) elevation
(b) Test loading set-up
Figure A-1 Test set-up and loading configuration.
Page A-1
(a) Supporting beam details Floor Unit
D12 Starter Bars (Grade 300) (300mm spacing)
Supporting Beam
Low friction bearing strip
Concrete Seat (ledge)
2*R16 (Grade 300) - 1 per filled core Seat Transverse Reinforcement
Low Friction bearing strip 75mm seat (minimum)
10mm
15mm 50mm
Note: Alternate (every second) cores filled and reinforced
75mm
(b) Specimen 1 beam-to-slab connection details D12 Starter Bars (Grade 500) @ 300mm, continuous as topping reinforcing
4*D12 (Grade 500) - 2 per filled core Seat Transverse Reinforcement
Low Friction bearing strip 75mm seat
(c) Specimen 2 beam-to-slab connection details
Figure A.2 Sub-assemblage Specimen design details
Page A-2
(a) Placement of the low friction bearing strip on the concrete seat.
(b) Cutting of the hollow-core cells.
(c) Supporting beam cast in restraints.
(d) Formwork prior to concrete casting.
(e) End view of the loading connections.
(f) Top view after concrete casting.
Figure A-3 Specimen 1 construction photographs
Page A-3
(a) De-bonding of the reinforcing.
(b) View of the supporting beam reinforcement and anchorage of the starter and hairpin bars.
(c) Top view of the reinforcement in supporting beam and topping slab prior to concrete casting.
(d) Reinforcement details for the connection with the loading actuators at the end of the hollow-core unit.
(e) Top view of the test specimen before testing.
Figure A-4 Specimen 2 construction photographs
Page A-4
A.2
MATERIAL TESTS
Tensile tests were conducted to determine the yield and ultimate strengths of the provided concrete. A summary of the tensile test results are shown in Table A-1, a photograph showing reinforcement test coupons are shown in Figure A-5 and stress strain relationships from the tensile tests are shown in Figure A-6. Readymix concrete was used for the casting of the sub-assemblage elements. Standard 30MPa structural concrete mixes were specified with a 120mm slump and 19mm aggregate. Table A-1 also includes the measured compression strengths ascertained by compression tests. Table A-1 Material test properties Concrete Compression Test Strengths (MPa) Location 7 Day Supporting Beams Specimen 1 Topping Concrete Specimen 2 Topping Concrete Reinforcement Tensile Test Strengths Location Supporting Beams Specimen 1: Starters Specimen 1: Hairpins Specimen 2: Starters & Hairpins
28 Day
Test Day
26.7 21.2 25.1
37.8 30.1 32.0
45.3 41.2 35.2
Reinforcing
fy (MPa)
fu (MPa)
XD25 D12 R16 XD12
536 311 325 570
675 450 469 709
Figure A-5 Reinforcement test samples
Page A-5
500
450
450
400
400
350
350
Stress (MPa)
Stress (MPa)
500
300 250 200 150
300 250 200 150
100
100
50
50
0
0 0
0.05
0.1
0.15 Strain
0.2
0.25
0.3
0
0.1
0.15 Strain
0.2
0.25
(b) Specimen 1: R16 reinforcement.
800
800
700
700
600
600 500
500
400
400
300
300 200
200
100
100 0
0 0
0.05
0
0.15
0.1
0.05
Strain
(c) Specimen 2: XD12 reinforcement.
0.1 Strain
0.15
TESTING PHOTOGRAPHIC LOG
A.3.1 Experiment Set-up and Instrumentation
(a) Supporting beam instrumentation
0.2
(d) XD25 Supporting beam reinforcement.
Figure A-6 Reinforcement test properties
A.3
0.3
Stress (MPa)
Stress (MPa)
(a) Specimen 1: D12 reinforcement.
0.05
(b) Actuator set-up
(c) Actuator set-up
Figure A-7 Instrumentation and loading set-up. Page A-6
A.3.2 Specimen 1
(a) Continuity crack at the beam-slab interface at –0.5%.
(b) Vertical crack between the slab and beam at +0.5%.
(c) Top view of the interface crack at +1%.
(d) Topping cracks at –2%.
(e) Widening of the beam-slab interface crack and exposure of the starter bars.
(f) Interface crack at –3%.
(g) Damage at the end of testing.
Figure A-8 Specimen 1 testing photographs Page A-7
A.3.3 Specimen 2
(a) Continuity crack at the beam-slab interface at –1%.
(b) Vertical crack between the slab and beam at -2%.
(c) Vertical crack between the slab and beam at +3%.
(d) Initial signs of concrete seat spalling during the ±3% cycles.
(e) Widening of the beam-slab interface crack at +4%.
(e) Large opening of the beam-slab interface crack at -5% drift.
(f) Progression of spalling observed during the ±4% cycles.
(g) Deterioration of the seat and exposure of the bearing strip.
Figure A-9 Specimen 2 testing photographs Page A-8
(a) Vertical dropping of the hollow-core floor slab during the Âą5% cycles.
(b) Hollow-core unit sliding off and down the damaged seat concrete.
(c) Damage to the topping concrete and extent of vertical dropping during the Âą5% cycles.
(d) Failure of the test specimen with a loss of seating occurring.
Figure A-10 Specimen 2 photographs during the later stages of testing.
Page A-9
A.4
LOADING PROTOCOL
The following table provides a list of the loading input files for the sub-assemblage testing. For each increment of vertical drift displacement, the calculated elongation is shown, and the actual actuator target displacements were listed. Figure A-11 shows the interaction between the vertical and horizontal actuators. Horizontal Ram Displacement
Half Cycle
Drift Amplitude
Drift Amplitude
Elongation
Vertical Ram Displacement
Count
%
rads
mm
mm
mm
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41
0 0.5 0 -0.5 0 0.5 0 -0.5 0 1 0 -1 0 1 0 -1 0 2 0 -2 0 2 0 -2 0 3 0 -3 0 3 0 -3 0 4 0 -4 0 4 0 -4 0
0 0.005 0 -0.005 0 0.005 0 -0.005 0 0.01 0 -0.01 0 0.01 0 -0.01 0 0.02 0 -0.02 0 0.02 0 -0.02 0 0.03 0 -0.03 0 0.03 0 -0.03 0 0.04 0 -0.04 0 0.04 0 -0.04 0
0.00 2.63 0.00 2.63 0.00 2.63 0.00 2.63 0.00 5.25 2.63 7.88 5.25 7.88 5.25 7.88 5.25 13.13 10.50 18.38 0.00 18.38 15.75 18.38 15.75 23.63 21.00 28.88 26.25 28.88 26.25 28.88 26.25 34.07 31.51 39.32 36.76 36.76 39.37 36.76 39.37
0.0 -28.5 0.0 28.5 0.0 -28.5 0.0 28.5 0.0 -57.0 0.0 57.0 0.0 -57.0 0.0 57.0 0.0 -114.0 0.0 114.0 0.0 -114.0 0.0 114.0 0.0 171.0 0.0 -171.0 0.0 171.0 0.0 -171.0 0.0 228.0 0.0 -228.0 0.0 228.0 0.0 -228.0 0.0
0.0 -1.9 0.0 -2.8 0.0 -1.9 0.0 -2.8 0.0 -3.2 -2.6 -7.5 -5.2 -5.8 -5.2 -7.5 -5.2 -6.7 -10.5 -15.3 0.0 -11.9 -15.7 -15.3 -15.7 -10.3 -21.0 -20.6 -26.2 -15.5 -26.2 -20.6 -26.2 -11.5 -31.5 -23.5 -36.8 -36.8 -16.7 -36.7 -23.6
Page A-10
300
Vertical Ram Displacement Control (mm)
200
100
0 -40
-35
-30
-25
-20
-15
-10
-5
0
-100
-200
-300 Horizontal Ram Displacement Control (mm)
Figure A-11 Input loading file interaction between the horizontal and vertical actuators. (Note that negative displacements denotes retraction of the actuator)
A.5
LOW CYCLE FATIGUE PREDICTION
A low cycle fatigue theory proposed by Dutta and Mander (2001), enables the plastic rotation life capacity of reinforcement to be calculated. The theory is expressed as follows:
Tp
§ D ·§ L p 0.16¨ ¸¨¨ © D' ¹© D
·§ 1 L p · ¸¸ 2 N f ¸¸¨¨1 2 L ¹ ¹©
0.5
(A.1)
where Tp = plastic drift; L = lever arm of the cantilever column; D = overall member depth; D’ = distance between outer layers of steel, 2Nf = the number of reversals to the appearance of the first fatigue crack with which Nf is the effective number of constant amplitude cycles for a variable amplitude displacement history and Lp = equivalent plastic hinge length. Miner’s well-known cycle counting method can be utilised to calculate the equivalent number of equi-amplitude cycles (Nf):
Page A-11
§ T ¦i ¨¨ T © ref
Nf
· ¸ ¸ ¹
2
(A.2)
Where T = drift for the ith cycle of loading and Tref = reference drift for an equivalent constant amplitude loading history. The following calculations show how the solution was obtained for this case: T D= D' = Lp = L= Tref = Ty =
T
Ty T p
375 280 150 6000 4 0.7
mm mm mm mm % %
2
ncycles 0.5 1 2 3 4
2 2 2 2 2 6
(T/Tref) 0.03125 0.125 0.5 1.125 2 3.7813
§ 375 ·§ 150 ·§ 1 150 · 0.5 0.007 0.16¨ ¸ 2 u 3.78
¸¨1 ¸¨ © 280 ¹© 375 ¹© 2 6000 ¹
0.037 rads
This compares well with the experimental observations, where the first fracture occurred at 3.83%.
A.6
REFERENCES
Dutta A and Mander J.B, 2001, Energy Based Methodology for Ductile Design of Concrete Columns, Journal of Structural Engineering, Vol. 127(12), December, pp 1374-1381.
Page A-12
Appendix B – Super-Assemblage Construction Photographs and Design Details
B.1
BUILDING CONSTRUCTION DRAWINGS
The following pages display the construction drawings of the super-assemblage frame structure: B-2
South-West Beam-Column Joint and Beams Precast Unit Plan
B-3
South-West Beam-Column Joint and Beams Precast Unit Elevation
B-4
South-East Beam-Column Joint and Beams Precast Unit Plan
B-5
South-East Beam-Column Joint and Beams Precast Unit Elevation
B-6
North-West Beam-Column Joint and Beams Precast Unit Plan and Elevation
B-7
North-East Beam-Column Joint and Beams Precast Unit Plan and Elevation
B-8
South-Centre Beam-Column Joint and Beams Precast Unit Plan and Elevation
B-9
Beam Cross Sections
B-10
South-East and South-West Column Top Segments
B-11
South-East and South-West Column Bottom Segments
B-12
North-East and North-West Column Top Segments
B-13
North-East and North-West Column Bottom Segments
B-14
South-Centre Column Top Segment
B-15
South-Centre Column Bottom Segment
B-16
Longitudinal Beams Lap Splice Details
B-17
Transverse Beams Lap Splice Details
B-18
Lap Splice Beam Cross Sections
B-19
Back Tie Frame Details
Page B-1
Page B-2
Department of Civil Engineering University of Canterbury Christchurch, New Zealand
Precast Unit Details SW Unit Plan
Drawn: CJM Date: 27/11/03 Revision: A Scale: 1:25
PU1
Drawing No.
Page B-3
Department of Civil Engineering University of Canterbury Christchurch, New Zealand
Precast Unit Details SW Unit Elevations
Drawn: CJM Date: 27/11/03 Revision: A Scale: 1:25
PU2
Drawing No.
Page B-4
Department of Civil Engineering University of Canterbury Christchurch, New Zealand
Precast Unit Details SE Unit Plan
Drawn: CJM Date: 27/11/03 Revision: A Scale: 1:25
PU3
Drawing No.
Page B-5
Department of Civil Engineering University of Canterbury Christchurch, New Zealand
Precast Unit Details SE Unit Elevations
Drawn: CJM Date: 27/11/03 Revision: A Scale: 1:25
PU4
Drawing No.
Page B-6
Department of Civil Engineering University of Canterbury Christchurch, New Zealand
Precast Unit Details NW Unit Plan & Elevation
Drawn: CJM Date: 27/11/03 Revision: A Scale: 1:25
PU5
Drawing No.
Page B-7
Department of Civil Engineering University of Canterbury Christchurch, New Zealand
Precast Unit Details NE Unit Plan & Elevation
Drawn: CJM Date: 27/11/03 Revision: A Scale: 1:25
PU6
Drawing No.
Page B-8
Department of Civil Engineering University of Canterbury Christchurch, New Zealand
Precast Unit Details SC Unit Plan & Elevation
Drawn: CJM Date: 27/11/03 Revision: A Scale: 1:25
PU7
Drawing No.
Page B-9
Department of Civil Engineering University of Canterbury Christchurch, New Zealand
Precast Unit Details Beam Cross Section Details
Drawn: CJM Date: 27/11/03 Revision: A Scale: 1:20
PU8
Drawing No.
Page B-10
Department of Civil Engineering University of Canterbury Christchurch, New Zealand
Precast Unit Details SE & SW Column Tops
Drawn: CJM Date: 27/11/03 Revision: A Scale: 1:25
PU9
Drawing No.
Page B-11
Department of Civil Engineering University of Canterbury Christchurch, New Zealand
Precast Unit Details SE & SW Column Bottoms
Drawn: CJM Date: 27/11/03 Revision: A Scale: 1:25
PU10
Drawing No.
Page B-12
Department of Civil Engineering University of Canterbury Christchurch, New Zealand
Precast Unit Details NE & NW Column Tops
Drawn: CJM Date: 27/11/03 Revision: A Scale: 1:25
PU11
Drawing No.
Page B-13
Department of Civil Engineering University of Canterbury Christchurch, New Zealand
Precast Unit Details NE & NW Column Bottoms
Drawn: CJM Date: 27/11/03 Revision: A Scale: 1:25
PU12
Drawing No.
Page B-14
Department of Civil Engineering University of Canterbury Christchurch, New Zealand
Precast Unit Details SC Column Top
Drawn: CJM Date: 27/11/03 Revision: A Scale: 1:25
PU13
Drawing No.
Page B-15
Department of Civil Engineering University of Canterbury Christchurch, New Zealand
Precast Unit Details SC Column Bottom
Drawn: CJM Date: 27/11/03 Revision: A Scale: 1:25
PU14
Drawing No.
Page B-16
Department of Civil Engineering University of Canterbury Christchurch, New Zealand
In-Situ Beam Lap Splice Details Longitudional Beams (Beams 1 & 3)
Drawn: CJM Date: 27/11/03 Revision: A Scale: 1:25
BS1
Drawing No.
Page B-17
Department of Civil Engineering University of Canterbury Christchurch, New Zealand
In-Situ Beam Lap Splice Details Transverse Beams (Beams 2 & 4)
Drawn: CJM Date: 27/11/03 Revision: A Scale: 1:25
BS2
Drawing No.
Page B-18
Department of Civil Engineering University of Canterbury Christchurch, New Zealand
Beam Lap Splice Cross Section Details
Drawn: CJM Date: 27/11/03 Revision: A Scale: 1:20
BS3
Drawing No.
Page B-19
Department of Civil Engineering University of Canterbury Christchurch, New Zealand
Back Frame Tie Beam Details
Drawn: CJM Date: 01/03/04 Revision: A Scale: 1:50
BF1
Drawing No.
B.2
BUILDING CONSTRUCTION PHOTOGRAPHIC LOG
(a) North-west column base reinforcement cage
(b) Column bases prior to casting
(c) Mid-span splice of east transverse beam
(c) South east beam column joint reinforcement
(d) Presence of ducting to allow connections of the load frame brackets
(e) Pouring of the column bases
(f) Extrusion of the hollow-core units
Figure B-1 Construction of the precast components.
Page B-20
(a) Lowering of the south-east precast unit
(b) Use of a mobile crane for erecting the precast frame
(c) Moving the north-west precast unit into place
(d) The frame in place
(e) Arrival of the hollow-core floor units
(f) Floor units in place
Figure B-2 Erecting of the precast units and placement of the hollow-core floor units.
Page B-21
(a) Grouting of the column reinforcement ducting and dry packing the precast interface
(c) Placement of the low friction bearing strip on the concrete seat
(b) View of the starter bar reinforcement and backing board coverage of the un-filled cores
(d) The supporting beam reinforcement
(e) Topping reinforcement over the timber infill
(e) View of the central column darg bar reinforcement
(f) Diaphragm topping concrete
Figure B-3 Reinforcement detailing of the supporting beams and topping slab.
Page B-22
(a) Concrete pumping
(b) Pouring of the concrete topping
(c) Vibration of the poured concrete
(d) Manual floating and levelling of the topping concrete
(e) Kelly float finishing of the topping concrete
(f) Curing of the topping concrete
Figure B-4 Pouring of the topping slab.
Page B-23
(a) Laboratory before super-assemblage construction
(b) Laboratory after super-assemblage construction
(c) Completed and painted super-assemblage structure
(d) Back reaction frame and tie beam set-up
Figure B-5 Before and after super-assemblage photographs
Page B-24
Appendix C – Super-Assemblage Testing and Photographic Log
C.1
MATERIAL TESTING
C.1.1 Reinforcement Testing
New Zealand manufactured reinforcement was used for this experimental project. Table C-1 presents the reinforcing properties obtained from the tensile testing carried out using the Avery testing machine in the Department of Civil Engineering Laboratory. Figure C-1 shows the stress strain relationships obtained from the tensile tests.
Table C-1 Reinforcement tensile test properties. Tensile Test Strength and Strain Characteristics Location Reinforcing
fy (MPa)
fsu (MPa)
Es (GPa)
Esh (GPa)
Hsh
Hsu
Column & Beam Longitudional Steel
YD25
536
675
214
3.27
0.0015
0.0128
Column & Beam Transverse Steel Support Connection Starter Bars and Diaphragm Drag Bars
YR12 R16 D12 YD20
530 336 307 580
714 469 447 724
190 186 181 246
4.48 3.65 3.82
0.0005 0.0031 0.0029 0.0012
0.0152 0.0200 0.0218 0.0156
Page C-1
500
450
450
400
400
350
350 Stress (MPa)
Stress (MPa)
500
300 250 200
300 250 200
150
150
100
100
50
50 0
0 0
0.05
0.1
0.15 Strain
0.2
0.25
0
0.3
(a) D12 starter and topping reinforcement
0.1
0.15 Strain
0.2
0.25
0.3
(b) R16 hairpin reinforcement
800
800
700
700
600
600 Stress (MPa)
500 400 300
500 400 300
200
200
100
100
0
0 0
0.05
0.1 Strain
0.15
0.2
0
(c) XD20 drag bar reinforcement
0.05
0.1 Strain
700 600 500 400 300 200 100 0 0
0.05
0.15
(d) XR12 transverse reinforcement
800
Stress (MPa)
Stress (MPa)
0.05
0.1 Strain
0.15
0.2
(e) XD25 beam and column reinforcement Figure C-1 Reinforcement stress strain tensile test results
Page C-2
0.2
C.1.2 Concrete Testing
Standard ready mix concrete was supplied for this project. The mixes were specified with a 30MPa 28-day compressive strength, 19mm maximum aggregate size and 100mm slump. For the topping slab pour, a pump mix was used with a specified 28-day compression strength of 30MPa and 13mm maximum aggregate size. Compression tests were undertaken at 7-day, 28day and the initial day of testing. Table C-2 shows a summary of the compression test data and Figure C-2 shows a photograph of preparation of the concrete cylinders. Table C-2 Concrete compression strengths. Compression Test Strengths (MPa) Location Precast Frame Units 1 Precast Frame Units 2 Precast Frame Units 3 Splice Half Beams Topping Slab & Half Beams Grout: Column Reinforcing
7 Day
28 Day
Test Day
26.7 21.2 25.1 31.8 31.0 -
37.8 30.1 32.0 -
45.3 41.2 35.2 46.0 40.6 > 60
Figure C-2 Preparation of concrete test cylinders.
Page C-3
C.1.3 Hollow-core Properties
Hollow-core concrete units are cast on long casting bed in a single pour and cut to length following curing and hardening of the concrete. Prestressing strands are tensioned prior to an extrusion machine travelling along the casting bed extruding the hollow-core units using ‘zero-slump’ concrete. Several different types of hollow-core units are available which vary in depth, with 200, 300 and 400mm depths available, and number of prestressing strands. A cross section of a typical unit is shown in Figure C-3 and common hollow-core properties are presented in Table C-3.
Figure C-3 Typical 300 series hollow-core unit cross-section.
Table C-3 Section properties of a 300 series hollow-core unit. Hollow-core Section Properties
Section 300 Dycore / Partek
2
Area (m ) 0.1606
4
I (m )
yb (mm) 153
Self Weight (kPa) 28-day f'c (MPa) -3
2.04*10
Page C-4
3.5
42
C.2
INSTRUMENTATION PHOTOGRAPHS
(a) Inclinometers to measure the column drift rotations.
(b) Potentiometers under the timber infill.
(c) Vertical levelling of the floor surface.
(d) Inclinometer and potentiometer instrumentation of the west transverse beam.
(e) Potentiometers measuring floor pull-off.
(f) Sonic transducers measuring the lateral (north-south and east-west) displacements of the columns.
(g) Actuator at base of north west column with load-cell and rotary potentiometer.
Figure C-4 Instrumentation photographs Page C-5
(a) Instrumentation of the south-west longitudinal beam and beam column joint.
(b) Instrumentation of the south-centre beam column joint.
(c) View of the computers used for controlling the experiment and data acquisition.
(d) Data logging and controller boxes.
(e) Load frame set-up for longitudinal loading.
(f) Load frame set-up for transverse loading.
Figure C-5 Instrumentation and load-frame photographs
Page C-6
C.3
TESTING PHOTOGRAPHIC LOG
C.3.1 Phase 1: Longitudinal loading
(a) Cracking of the infill slab at +0.5%
(b) Cracking of the transverse beam (north east end) at +0.5%
(c) Diagonal cracking within the south centre beam column joint at –0.5%
(d) Continuity crack looking towards the north west column at –0.5%
(e) Cracking over the infill slab at –1%
(f) Continuity crack at the west end at –1%
(g) Diagonal torsion cracks, north west corner at –1%
Figure C-6 Phase 1: Damage during the early stages
Page C-7
(a) Cracks extending over the timber infill slab (south west bay) at +2%
(b) Hollow-core cracking at the south east corner at +2%
(c) Web crack forming at south east corner unit at +2%
(d) First instance of spalling noticed on east transverse beam at -2%
(e) Continuity crack along the beam-slab interface at the eastern end at +2%
(f) Crack opening at the south east column at +2%
(g) Longitudinal topping crack between 1st and 2nd hollow-core unit
Figure C-7 Phase 1: Damage during the later stages
Page C-8
C.3.2 Phase 2: Transverse loading
(a) Spalling and exposure of the bearing strip of the east transverse beam at +1%
(b) 13mm crack opening at the north east column at +2%
(c) Large crack at the beam-column interface of the south east corner at +2%
(d) Top view of the damage at the north east corner of the structure at 3%
(e) Damage to the south west transverse hinge at +3%
(f) Damage close to the column face at the north east transverse beam end (+3%)
(g) South east column inclination at –3%
Figure C-8 Phase 2 Transverse loading damage Page C-9
C.3.3 Phase 3: Longitudinal re-loading
(a) Distribution of topping cracking over the south east bay at –2%
(b) Large crack opening at the south east column at +3%
(c) View of the damage to the south east south frame hinge at +3%
(d) Exposure of the reinforcement and vertical dropping of the west transverse beam (north end) at +3%
(e) Hollow-core soffit cracking at the east end at +3%
(f) Damage due to torsional hinging at +3% (south east)
(g) Torsional hinging looking towards the north east column
Figure C-9 Phase 3: Damage during the early stages
Page C-10
(a) Crushing at the top west side of the south centre column at –3%
(b) Torsional behaviour of the east transverse beam at –3%
(c) Interface cracking of the south east hinge of the south beam at +4%
(d) West transverse beam remaining upright at +4%
(e) Damage of the north east hinge (east beam) at +4%
(f) Damage of the north west hinge (west beam) at +4%
(g) Buckling of the bottom reinforcement of the south west beam west hinge at –4%
(h) Top view of the damage at the south west corner of the floor at –4%
Figure C-10 Phase 3: Damage during the middle stages Page C-11
(a) Damage to the north east hinge and evidence of the beam dropping at –4%
(b) Hollow-core soffit cracking, 2nd unit, west end at –4%
(c) Different rotations of the east beam and columns due to torsion at +5%
(d) The plastic hinges (from west to east and left to right) of the south frame at +5% drift
(e) Evidence of hollow-core pull-off (unpainted soffit) at +5%
(f) Increasing buckling of the reinforcement of the south west beam hinge at –5%
Figure C-11 Phase 3: Damage during the later stages Page C-12
C.3.4 End of Testing
(a) Fracture of the top, outside bar of the south east hinge of the south beams
(b) Fracture of the inside and outside top bars of the south east hinge of the south beams
(c) Cracking over the timber infill of the south east bay at the conclusion of testing
(d) Cracking over the timber infill of the south west bay at the conclusion of testing
Figure C-12 Notable damage following the conclusion of testing.
Page C-13
C.4 CONCRETE TOPPING DELAMINATION The occurrence of the concrete topping slab (75mm thick) delaminating from the hollow-core floor units was recorded throughout testing. A hammer was used to find hollow sounding areas indicative of delamination. As Figure C-12 shows, delamination was initially noticed at the ¹2% peaks during Phase 1, and area of delamination gradually increased throughout the remainder of testing. Delamination extended along the length of the building at the infill-toUnit 1 interface, along the beam-to-floor slab interfaces at the ends, and in the southern corners – at the ends of Unit 1.
Unit 4
Unit 3
Unit 2 Unit 1
Timber Infill
Key
(note that the delamination is cumulative)
After +2%, Phase 1 After -2%, Phase 1 After Phase 2 After Phase 3
Figure C-13 Topping slab delamination pattern
Page C-14
Appendix D – Analytical Results
D.1
YIELD DRIFT CALCULATION
It is difficult to accurately determine the experimental yield drift, as there is no clear change in stiffness of the super-assemblage, and it was seen that yielding occurred between around 0.5% drift and 0.7% drift. A yield value of 0.5% drift was used for the formulation of beam elongation results. The following calculations show the contributions of the beam, column and beam-column joint towards the calculated yield drift rotation. The calculations follow the same steps as used by Matthews (2004) and Lindsay (2004).
D.1.1 Beam Contribution The following relationship from Priestley and Kowalsky (2000) was utilised to calculate the contribution from the beam. The yield moment was derived from simple mechanics and actual material test results;
I yb
1.70
Hy hb
6.06 u 10 6
(D-1)
where: Iyb = yield curvature of the beam, Hy = yield strain of the beam longitudinal reinforcement and hb = height of the beam. Knowing the nominal moment capacity of the beam and the previously calculated yield curvature of the beam, the effective stiffness can be determined; EI eff
M yb
I yb
498 u 10 6 6.06 u 10 6
8.22 u 1013 ( Nmm 2 )
(D-2)
where: (,eff = effective flexural stiffness and 0yb = nominal yield moment capacity of the beam section. Using moment area theorem, the deflection of the beam can be found from the following relationship:
Page D-1
Gb
M yb L2b 12 EI eff
498 u 10 6 u 5350 2 12 u 8.22 u 1013
14.45mm
(D-3)
where: Gb = displacement of the beam at its point of inflection and Lb = distance between the beam hinges. Finally, using the height of the column (Lc) this displacement can be converted to an overall column displacement (Gbc);
G cb
Gb
L2c 0.5 u Lb
16.58mm
(D-4)
D.1.2 Beam-Column Joint Contribution To calculate the contribution to the yield drift from the beam column joint, an expression derived by Matthews (2004) was used;
Jj
38.5
As f y § (d d ' ) L · ¨1 ¸ BH Ec ¨© H Lb ¸¹
0.00136rads
(D-5)
where: Jj = joint distortion, % = width of the column, H = height of the column, (d-d’) = internal lever arm of the beam and L = centreline distance between beam inflection points. Using this calculated rotation, the contribution of the joint can be found in terms of the column displacement (G jc) to be 4.76mm.
D.1.3 Column Contribution The contribution from the column can be calculated following a similar method used for the beam. The yield curvature for the column can be determined from the following (Priestly and Kowalsky, 2000):
I yc
2.12
Hy hc
7.56 u 10 6
Page D-2
(D-6)
where: Iyc = yield curvature of the column, Hy = yield strain of the column longitudinal reinforcement and hc = width of the column. The effective stiffness can be found using the nominal moment capacity of the column, 0yc, and is shown by the following equation: EI eff
M yc
I yc
892 u 10 6 7.56 u 10 6
1.18 u 1014 ( Nmm 2 )
(D-7)
From this, the column contribution can be found from:
Gc
M c l c2 3EI eff
223 u 10 6 u (1750 375) 2 3 u 1.18 u 1014
1.2mm
(D-8)
where: 0c = the column moment at the beam face at yielding of the beam (223kNm) and lc = distance between the beam hinges. Thus, with all three constituent contributing sources calculated the overall yield drift can be found from the following:
G
G cb G cj G c
16.58 4.76 1.2
22.54mm
(D-9)
This displacement corresponds to an inter-storey drift of 0.64%.
This calculated value shows good resemblance with the experimental yielding point. It is likely that the experimental value is higher due to a small amount of cracking of the specimen prior to testing as well as the cracking that occurred between the precast construction element interfaces which occurred early in the test. The cracking would influence the effective stiffness of the section, and the larger overall displacements of the super-assemblage due to these cracks would result in the yield drift being higher than predicted.
Page D-3
D.2
SUPER-ASSEMBLAGE STIFFNESS
The initial elastic stiffness of the super-assemblage was calculated using the initial results for each of the three loading phases, and is shown in Figure D-1. It can be seen that the initial stiffness of structure during Phase 1 loading was 62MN/m (Figure D-1(a)). Figure D-2(b) shows that the initial stiffness for Phase 2 loading was 34.7MN/m, which is a 44% reduction of the stiffness exhibited at the start of testing. The cracking of the transverse beams, a large degree due to torsion reducing the stiffness during Phase 1 loading, can explain this. Cracking of the floor diaphragm over the timber infill also would reduce the stiffness for the transverse loading. The stiffness from the early cycles during Phase 3 was 17.5MN/m (Figure D-1(c)). This is only 28% of the Phase 1 stiffness and is due to the damage accrued from Phase 1 and Phase 2 loading. The damage of the ends of the transverse beams consequently led to torsional hinging of these beams, and due to this, the stiffness was significantly reduced. The widening of the cracks around the north and south corner columns, and continuity crack between the floor and beams along the east and west bays would reduce the overall superassemblage stiffness and decrease the stiffening influence of the floor.
1000
500
0
-10
0
10
-500
-1000
600
1500
400
1000 500
-1500
(a) Phase 1
20-30
-20
Inter-Storey Drift (mm)
0 -10 0 -200 -400 -600
10
20
30-100
0
-50
0
50
-500
Base Shear Force (kN)
-20
2000
200 Inter-Storey Drift (mm)
Base Shear Force (kN)
Inter-Storey Drift (mm)
800
-800
(b) Phase 2
Figure D-1 Stiffness of the super-assemblage.
Page D-4
-1000 -1500
Base Shear Force (kN)
1500
-2000
(c) Phase 3
100
D.3
TORSION TEST
A torsion test was undertaken during Phase 2 transverse loading to attempt to determine the torsional stiffness of the super-assemblage. The test involved displacing the east and west bays in opposing directions as shown in Figure D-2. For example, positive drifts denote a positive translation of the east bay (tops of the columns displace north) and negative translation of the west bay (tops of the columns displace south) and vice versa for the negative cycle. One reversing cycle to ±0.5% was undertaken, and Figure D-3 shows the corresponding base shear. This was completed after the second cycle to ±2%, and a following third cycle to ±2% was undertaken to see if there was any degradation of stiffness due to the torsion test.
North
Direction of movement
Direction of movement
East
West
South
Figure D-2 Illustration of the torsion test. 300
S
East Bay
Base Shear Force (kN)
West Bay N
S
N
200 100 Inter-storey Drift (%)
0 -0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0.5
-100 East Bay
-200
West Bay -300
Figure D-3 Base shear results from the torsion test.
Page D-5
0.6
As Figure D-3 shows, the structure had a higher stiffness in positive drift direction, when the respective tops of the columns translated northwards, than the negative direction. For example, for the east bay, the stiffness values obtained from the experimental data for the positive and negative drift cycles were 15.26MN/m and 10.56MN/m respectively, and similar behaviour was observed for the west bay. The negative drift cycles correspond to negative moments of the south east and west hinges, and due to the already highly cracked infill slab section which under negative moments would be in tension, would require less force to reach the target displacements. This can explain the lower stiffnesses observed during the negative drift cycles. During the torsion tests, there was also little noticeable damage to the southern longitudinal beams and after the resumption of the normal testing regime, there was no noticeable degradation due to the torsion tests.
D.4
GENERAL SUPER-ASSEMBLAGE PERFORMANCE
D.4.1 Central Column Joint Reinforcing Bar Slip The slipping of the longitudinal top and bottom beam reinforcement passing through the south central beam column joint was monitored throughout the test by two potentiometers attached to the reinforcement. Figure D-4 shows the bar slip experimental results for both Phase 1 and 3 longitudinal loading. Figure D-4(a) shows that there was up to 1.9mm of bar slippage during Phase 1 and during Phase 3 more slipping occurred with a maximum bar slip of 3.82mm being recorded (Figure D-4(b)). The degradation of bond that would allow this bar slippage would denote a reduction of the stiffness of the super-assemblage during low drift displacements, which was observed to a small degree. The New Zealand Concrete Design Standard (NZS 3101:1995) provide design equations to limit the maximum reinforcing size
Page D-6
passing through a beam column joint, which is based on ensuring that sufficient bond is maintained. These equations are as follows:
f c' db d 3.3D f hc Do f y
(D.10)
where db = the diameter of bar passing through the joint, hc = height of the column section,
Df = factor to allow for one or two way framing, f’c = compression strength of the concrete, Do = overstrength factor for the beam reinforcement, and fy = yield strength of the reinforcement. Application of this formula gives a maximum bar diameter of 23.5mm, lower than the actual XD25 reinforcement used. Although this seems to be an oversight of the design process, it is a smaller bar diameter than commonly used in large concrete frames and the New Zealand Concrete Code offers another form of the equation:
§ D tD p db d 6¨¨ hc © Ds
f c' · ¸¸D f ¹ Do f y
(D.11)
where Dt = factor for the amount of fresh concrete cast below the reinforcement, Dp = factor to allow for the beneficial effects of axial compression forces, and Ds = factor for severe bond conditions. In this case, these factors are all 1, and the maximum allowable reinforcement diameter becomes 42mm, and thus the 25mm bars used are suitable, from a design point of
4
4
3
3
2
2
1
1
Scan N umb er
0 0
1000
2000
3000
4000
-1 -2 -3
Top Bottom
-4
5000
Slip (mm)
Slip (mm)
view, despite the amount of slippage observed.
Scan N umb er
0 0
1000
2000
3000
4000
5000
-1 -2 -3
Top Bottom
-4
(a) Longitudinal bar slip during Phase 1
(b) Longitudinal bar slip during Phase 3
Figure D-4 Longitudinal beam bar slippage through the central beam column joint Page D-7
6000
D.4.2 Hollow-core Floor Unit Pull-off Sprung loaded potentiometers were installed underneath each of the hollow-core units to measure the horizontal sliding displacements of the floor units relative to the supporting beam. Figure D-5 shows the relationship between the horizontal pull-off movements and inter-storey drift. Not surprisingly, and analogous to the beam elongation theoretical predictions, the amount of pull-off increases with increasing inter-storey drift amplitudes and is higher for the second cycles. For Phase 1, both the east and west bays showed similar behaviour, and maximum pull-offs of 12mm and 11.4mm were seen at the second cycle to – 2% and +2% for the east and west bays respectively. Displacement (mm)
14 12 10 8 6 4
East
2
West
Drift (%) -2.5
-2
0 -1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
(a) Horizontal hollow-core unit pull-off for Phase 1 loading. 14 12 10 8 Displacement (mm)
6 4 2 Drift (%)
East West
0 -4
-3
-2
-1
0
1
2
3
(b) Horizontal hollow-core unit pull-off for Phase 3 loading.
Figure D-5 Horizontal hollow-core unit pull-off
Page D-8
4
16
14 Unit 1East Unit 2 East Unit 3 East
12 10 8 6 4
10 8
4 2
Scan N umb er
0
Scan N umb er
0 0
1000
2000
3000
4000
0
(a) East beam pull-off: Phase 1 12
12
10
10
8 6 4 Unit 1 East Unit 2 East Unit 3 East
2
1000
2000
3000
4000
(b) West beam pull-off: Phase 1
Displacement (mm)
Displacement (mm)
\
6
2
8 6 4 Unit 1 West Unit 2 West Unit 3 West Unit 4 West
2 Scan N umb er
0
Scan N umb er
0 0
1000
2000
3000
4000
5000
0
(c) East beam pull-off: Phase 2 18
18
16
16
14
14
12 10 8 6 Unit 1 East Unit 2 East Unit 3 East
4 2
1000
2000
3000
4000
5000
(d) West beam pull-off: Phase 2
Displacement (mm)
Displacement (mm)
Unit 1West Unit 2 West Unit 3 West Unit 4 West
12 Displacement (mm)
Displacement (mm)
14
12 10 8 6 Unit 1 West Unit 2 West Unit 3 West Unit 4 West
4 2
Scan N umb er
0
Scan N umb er
0 0
2000
4000
6000
8000
(d) East beam pull-off: Phase 3
0
2000
4000
6000
8000
(e) West beam pull-off: Phase 3
Figure D-6 Horizontal hollow-core pull-off displacements.
Figure D-6 shows the horizontal pull-off displacement measured underneath all of the hollowcore units, related to time, for each of the three loading phases. The fluctuations show the effect of the cyclic loading, and for Phase 1, the large increases of the pull-off displacement Page D-9
signify new inter-storey drifts being experienced. The pull-off was seen to be minimal for Phase 2, and the slight increase of the pull-off, of less than 1mm, can be explained by torsional behaviour of the transverse beams. The Phase 3 pull-off relationships indicate a decreased rate of pull-off, as compared with Phase 1 where the Phase 3 contributed a further 4mm to the already 12mm from Phase 1, and the overall maximum pull-off experienced was approximately 16mm for both bays.
D.4.3 Beam Column Joints and Plastic Hinge Rotation Contributions Figure D-7 shows a schematic view of the instrumentation used for the beam plastic hinge and beam-column joint regions. It was hoped that the set-up used would be able to measure the relative contributions towards the overall rotation, which would equate to the column inclination. Potentiometers were arranged in such a fashion that joint shear, hinge shear, hinge flexure, shearing at the beam-column interface and fixed end rotation could be monitored. Figure D-8 shows the relative components contributing towards the overall lateral displacement of the structure for Phase 1 and Phase 2 loading.
175mm
Beam-Column Joint Potentiometer instrumentation - measuring joint shear deformation
Potentiometers (top and bottom) measuring the fixed-end rotation and curvature of the beam plastic hinges
700mm
100mm 75mm
600mm
500mm
500mm
600mm
100mm
500mm
500mm 600mm 300mm
300mm
Beam Plastic Hinge Potentiometer instrumentation - measuring hinge shear and flexural deformation
195mm
Figure D-7 Close-up representation of the beam-column joint and hinge instrumentation
Page D-10
0.02 0.015 0.01 0.005
Rotation Contribution (rads)
0.025
Closure Error
Inter-storey Drift (rads) 0 -0.025
-0.02
-0.015
-0.01
-0.005 0 -0.005
0.005
0.01
0.015
0.02
0.025
Fixed End Rotation
-0.01
Hinge Flexure Hinge Shear
-0.015
Closure Error
Joint Shear Column Inclination
-0.02
Total
-0.025
0.025 0.02 0.015 0.01 0.005 Inter-storey Drift (rads)
Rotation Contribution (rads)
(a) Contributions towards lateral displacement during longitudinal Phase 1 loading
Closure Error
0 -0.025
-0.02
-0.015
-0.01
-0.005 0 -0.005
0.005
0.01
0.015
0.02
0.025
Fixed End Rotation
-0.01 -0.015
Closure Error
-0.02
Hinge Flexure Hinge Shear Joint Shear Column Inclination Total
-0.025
(b) Contributions towards lateral displacement during transverse Phase 2 loading
Figure D-8 Components that contribute to the overall lateral displacement of the superassemblage
By comparing the total rotations with the column inclination in the relationships shown in Figure D-8, it can be seen that the instrumentation was able to measure the overall lateral displacements to a satisfactory level. The closure error indicates the discrepancy, and for the transverse loading as seen in Figure D-8(b), the instrumentation slightly over-predicts the amount of lateral displacement of the structure. In terms of the individual components, the Page D-11
fixed end rotation, measured between the column and beam at the top and bottom appeared to dominate the rotation contributions. For Phase 2, almost all the lateral displacement occurs from fixed end rotation with a smaller amount due to plastic hinge flexure. This matches well with the experimental observations whereby damage to the plastic hinges was predominantly a large crack at the beam-column interface. As it was expected, there were minimal contributions from the beam hinge and beam column joint shearing displacements.
D.4.4 Reinforcement Strain Information At several locations within the super-assemblage topping and floor-to-beam connections, the reinforcement was strain gauged to be able to monitor the demands imposed on the reinforcement. One main reason was to monitor the strain development along the length of the starter bars at the end connections to give an idea as to the possible required length of the starter bars. This meant that strain gauges were attached at several points up to 2.1m from the supporting beams. Figure D-9 shows the locations of the strain gauges present within the structure. Figures D-10 and D-11 provide the strain results for the end connection reinforcing (starter bars, lapped diaphragm steel and the hairpin bars) for the east and west ends during Phase 1. Figure D-12 shows the results, for Phase 1 and 2, of the southern beam starter bars that were cast in the infill topping slab and were embedded half way into the southernmost hollow-core unit. Two starter bars were strain gauged, one 1m either side of the central column, approximately where the maximum displacement incompatibility between the floor and beams was expected. Also, the “drag� bars that were cast into the south central column and lapped with reinforcement running across the width of the building, were strain gauged at various points as shown in Figure D-9. Figure D-13 shows the results obtained from the drag bars for Phase 1 and 2 loading.
Page D-12
North
Unit 4
West Tie Bar
Unit 3
Unit 4
East Tie Bar
Unit 3 East
West Unit 2
Unit 2
Unit 1 East Infill Starter
Unit 1 West Infill Starter South
(a) Plan view of the location of the strain gauges Starter bars and diaphragm reinforcement 600
300
3 2
1
1
600
600
4
5
2 300
Hairpin reinforcement
(b) End connection reinforcement strain gauge locations 375mm
300mm
375mm
4
3
2
1
(c) Strain gauging of the starter bars passing over the timber infill
Figure D-9 Strain gauge instrumentation layout
Page D-13
45
12 Interface 300mm 900mm 1500mm 2100mm Yield Strain
strain (%)
8
35 30
6 4
25 20 15 10
2
5
Scan Num ber
0 0
1000
2000
3000
4000
5000
0
1000
2000
3000
4000
5000
-5
(a) Starter bar strain data for Unit 4
(b) Starter bar strain data for Unit 3
12
18 Interface 900mm 2100mm
10
300mm 1500mm Yield Strain
Interface 300mm 900mm 1500mm 2100mm Yield Strain
16 14
8
12
strain (%)
strain (%)
Scan N umb er
0
-2
10
6 4 2
8 6 4 2
Scan Num ber
0 0
1000
2000
3000
4000
5000
Scan Num ber
0 0
-2
1000
2000
3000
4000
5000
-2
(c) Starter bar strain data for Unit 2
(d) Starter bar strain data for Unit 1
45
45
40
40
35
35 30
Unit 4 Interface Unit 4 300mm Unit 3 Interface Unit 3 300mm Yield
25 20 15
strain (%)
30
strain (%)
Interface 300mm 900mm 1500mm 2100mm Yield Strain
40
strain (%)
10
Unit 2 Interface Unit 2 300mm Unit 1 Interface Unit 1 300mm Yield
25 20 15 10
10 5
Scan Num ber
5
Scan Num ber
0
0 0
1000
2000
3000
4000
5000
-5
(e) Hairpin bar strain data, Units 3 & 4
0
1000
2000
3000
4000
-5
(f) Hairpin bar strain data, Units 1 & 2
Figure D-10 Strain data for the west slab-beam connection reinforcement during Phase 1
Page D-14
5000
45
45
Interface 300mm 900mm 1500mm 2100mm Yield Strain
35
strain (%)
30
Interface 300mm 900mm 1500mm 2100mm Yield Strain
40 35 30
strain (%)
40
25 20 15
25 20 15 10
10 5
5
Scan N umb er
Scan N umb er
0
0 0
1000
2000
3000
4000
0
5000
-5
(a) Starter bar strain data for Unit 4
2000
3000
5000
45
Interface 300mm 900mm 1500mm 2100mm Yield Strain
40
2
35
Interface 300mm 900mm 1500mm 2100mm Yield Strain
30
strain (%)
1.5
1
0.5
25 20 15 10 5
Scan N umb er
Scan Num ber
0 0
1000
2000
3000
4000
5000
0 0
1000
2000
3000
4000
5000
-5
-0.5
(c) Starter bar strain data for Unit 2
(d) Starter bar strain data for Unit 1
45
45
40
40 Unit 4 Interface Unit 4 300mm Unit 3 Interface Unit 3 300mm Yield
30 25
Unit 2 Interface Unit 2 300mm Unit 1 Interface Unit 1 300mm Yield
35 30
strain (%)
35
strain (%)
4000
(b) Starter bar strain data for Unit 3
2.5
strain (%)
1000
-5
20 15 10
25 20 15 10
5
Scan Num ber
0 0
1000
2000
3000
4000
5000
5
Scan Num ber
0 0
-5
1000
2000
3000
4000
5000
-5
(e) Hairpin bar strain data, Units 3 & 4
(f) Hairpin bar strain data, Units 1 & 2
Figure D-11 Strain data for the east slab-beam connection reinforcement during Phase 1
Page D-15
25
30 Beam/Infill Mid-Infill Infill/Unit 1 Unit 1 Yield Strain
25
15
strain (%)
strain (%)
20
Beam/Infill Mid-Infill Infill/Unit 1 Unit 1 Yield Strain
20
15 10
10
5
5 Scan Num ber
0 0
1000
2000
3000
4000
0
-5
1000
2000
3000
4000
5000
-5
(a) Strain data for the south west starter bar (1m west of south central column) during Phase 1 longitudinal loading
(b) Strain data for the south east starter bar (1m east of south central column) during Phase 1 longitudinal loading 15
30 Beam/Infill Mid-Infill Infill/Unit 1 Unit 1 Yield Strain
10
5
0 0
1000
2000
3000
Beam/Infill Mid-Infill Infill/Unit 1 Unit 1 Yield Strain
10
strain
20
strain
Scan Num ber
0
5000
4000
5000
6000
7000
8000
Scan Num ber
0 0
2000
3000
4000
5000
6000
7000
8000
Scan Num ber
-10
-5
-20
-10
-30
-15
(c) Strain data for the south west starter bar (1m west of south central column) during Phase 2 transverse loading
1000
(d) Strain data for the south east starter bar (1m east of south central column) during Phase 2 transverse loading
Figure D-12 Strain data for the starter bars passing over the timber infill
As Figures D-10 and D-11 show, significantly higher strains were experienced at the beam-tofloor slab interface than in the topping slab, where the strains diminished rapidly. Similar results were observed for each of the floor units and at both the east and west ends. These results confirm the both the desired and observed results whereby all of the rotational demand was centred at the support beam-to-floor interface. The lack of strain penetration would signify low stresses which was matched by a lack of cracking within the topping away from the supporting beam. The results for the hairpin bars were less reliable due to malfunctioning
Page D-16
strain gauges, although it can be seen that there was higher strains at the beam-floor interface than further into the hollow-core units. Figure D-12(a) and (b) shows that the maximum strains experienced by the south beam starter bars occurred at the interface between the infill slab and hollow-core floor Unit 1. This can be explained by the vertical deformations caused by the relative displacement differences between the floor slab and southern beams and the resultant vertical angle at this interface. Figure D-13 shows there was a small degree of strain penetration along the “drag” bars tying the central column into the floor. Higher strain demand was experienced at the south centre column. Due to the fact that the southern beam starter bars were also anchored into the flooring, and that no fracture or tear occurred, the demand on the tie bars was minimal. 6
4 South Centre Column Infill/Unit 1 Unit 1/Unit 2 Unit 2/Unit 3 Yield Strain
3.5
4
2.5
strain (%)
strain (%)
3
South Centre Column Infill/Unit 1 Unit 1/Unit 2 Unit 2/Unit 3 Yield Strain
5
2 1.5
3 2
1
1
0.5
Scan Num ber
0
Scan Num ber
0
0 0
1000
2000
3000
4000
5000
1000
2000
3000
4000
5000
-1
-0.5
(a) Strain data for the west ‘drag’ bar during Phase 1 longitudinal loading
(b) Strain data for the east ‘drag’ bar during Phase 1 longitudinal loading 8
6 South Centre Column Infill/Unit 1 Unit 1/Unit 2 Unit 2/Unit 3 Yield Strain
5 4
South Centre Column Infill/Unit 1 Unit 1/Unit 2 Unit 2/Unit 3 Yield Strain
6 4
strain
strain
3 2 1
2 0 0
0
-1
1000
2000
3000
4000
5000
6000
7000
8000
Scan Num ber
0 1000
2000
3000
4000
5000
6000
7000
8000
-2
Scan Num ber -4
-2 -6
-3
(c) Strain data for the west ‘drag’ during Phase 2 transverse loading
(d) Strain data for the east ‘drag’ during Phase 2 transverse loading
Figure D-13 Strain data for the drag bars tying in the south centre column Page D-17
D.5
WEST TRANSVERSE BEAM TORSION
D.5.1 Experimental Results Five inclinometers measuring rotation in the longitudinal direction were spaced along the west transverse beam at constant intervals as shown in Figure D-14. Figure D-15 shows the relative torsion rotations between the column and beam for Phase 3, and Figure D-16 provides the west beam torsion results for Phase 1 and 3.
Angle of Twist (rad/m)
Figure D-14 Torsion inclinometers attached to the west transverse beam
6 5 4 3 2 1 0 -1 -2 -3 -4 -5 -6 -7 -8
Phase 1 Loading
Phase 3 Loading
Figure D-15 Torsional twist of the south hinge of the west transverse beam (radians/metre in plastic hinge zone)
Page D-18
2.5 Jo int
2
Torsion Drift (%)
1 1.5
3
1
4
0.5 S c a n N um be r
0 -0.5 0
500
1000
1500
2000
2500
3000
3500
4000
4500
-1 -1.5 -2 -2.5
(a) West beam torsion during Phase 1 6 Jo int 1 2 3 4 5
Torsion Drift (%)
4
2
S c a n N um be r
0 0
1000
2000
3000
4000
5000
6000
7000
8000
-2
-4
-6
(b) West beam torsion during Phase 3
Figure D-16 Observed torsion of the west beam
D.5.2 Calculation of Torsional Demand For the present experiment, the torsional demand was caused by the moment from the connection reinforcement between the supporting beam and floor slabs, which occurs under lateral loading of the structure. The strength of this connection was found during the subassemblage tests undertaken as part of this research, where calculated moment strengths matched the experimental values well. The positive and negative moment capacity values were 38kNm and 40kNm respectively for each hollow-core unit. Accounting for the 1.2m hollow-core unit widths, the torsional moment per metre length of beam is 32kNm/m and 33kNm/m for the positive and negative rotations, which then corresponds to an applied torsion at the beam ends of 79kNm approximated for both positive and negative rotations. Page D-19
For the connection detail tested by Lindsay (2004), the presence of the compressible backing board meant that there was effectively zero moment resistance. Therefore, the torsional demands arose due to the eccentric loading of the floor. The weight of hollow-core flooring was taken to be 3.5kPa, the weight of the topping concrete 24kNm-3 and the eccentricity from the centre of the beam to the centre of the seat was 238mm. This caused a torsional moment demand of 20kNm at each end of the transverse beams.
D.5.3 Calculation of Torsional Capacity For compatibility torsion, as is the case in this experiment, a reduction of the torsional moment can occur due to the redistribution of internal forces when cracking first occurs. An expression from the New Zealand Concrete Code, NZS 3101:1995, was used for calculating the cracking torsional moment of the beam section, and is the same as the formulation given by Mitchell and Collins (1991). The cracking torsion, or maximum design torsional moment can hence be calculated by:
T
*
f c' § Acp2 ¨ I 3 ¨© p cp
· ¸ ¸ ¹
(D.12)
in which T* = design torsional moment force at section at the ultimate limit state, or cracking torsion, I = strength reduction factor (which is omitted in this case for analysis), f’c = concrete compressive strength, Acp = area enclosed by the outside perimeter of the concrete crosssection, and pcp = outside perimeter of the concrete cross section. Knowing that the overall concrete cross-section was 400mm wide by 750mm deep, and concrete compressive strengths obtained from material tests were 35MPa, the torsional cracking moment was 77.2kNm. In this case, the strength reduction factor was omitted, as this is an analysis of a given section, not design.
Page D-20
After diagonal cracking has occurred, a truss mechanism of vertical transverse reinforcing ties and diagonal concrete compression struts forms, and the contribution to the torsional resistance from the reinforcement can be calculated. Park and Paulay (1975), provides an expression for the steel contribution to resisting torsion as a function of the transverse and longitudinal reinforcement, which is shown as Equation D.13. The equivalent design expression for the nominal torsional strength from NZS 3101:2004 relates to the amount of transverse reinforcing and stems from information provided by Park and Paulay (1975). Ts
2 A0
At f y Al f ly s
P0
(D.13)
in which Ao = area enclosed by the connecting lines between the centres of the longitudinal reinforcement, At = area of a transverse reinforcing stirrup leg, fy = yield strength of the transverse reinforcing, s = transverse reinforcing spacing Al = total area of the longitudinal reinforcement, fly = yield strength of the longitudinal reinforcing, and Po = perimeter formed by area Ao. Here, the interior cross section dimensions of the beam between the centre-lines of the longitudinal reinforcing are 286mm wide and 582mm deep. The stirrup sets used were XR12 with an leg area of 113mm2 and the longitudinal reinforcement comprised of 3 XD25 bars top and bottom with a total area of 2946mm2. The stirrup sets were spaced at 150mm and the yield strengths obtained from material tests for the transverse and longitudinal reinforcing were 530MPa and 536MPa respectively. This produced a torsional steel contribution, Ts, of 200kNm. To calculate the torsional twists corresponding to the cracking and ultimate torsion moments, relationships from Mitchell and Collins (1991) and Park and Paulay (1975) for the torsional stiffness were used. In this simplified approach, the section is represented by an
Page D-21
equivalent thin walled tube or hollow section with the same overall dimensions. The precracking stiffness was a function of the section geometry and the post-cracking torsion stiffness is governed by the deformation of the reinforcing. The pre-cracking stiffness was calculated using: GK
G
4 A02 t po
(D.14)
Where GK = the pre-cracking torsional stiffness, G = the shear modulus, A0 = area enclosed by the centreline of the thin walled tube with thickness, t, and po = perimeter of the area. The equivalent wall thickness can be found by using: t
3 Acp
(D.15)
4 p cp
Where Acp = area enclosed by the outside perimeter of the concrete cross section, pcp = perimeter of the area Acp. Utilisation of Equations D.14 and D.15 produce the following result: GK
2 §3 ¡ 4 u 196904 § 3 u (750 u 400) ¡ ¸¸ u ¨¨ ¨ 4730 35 ¸ 1908 4 u 2 ( 750 400 ) Š7 š Š š
95531kNm 2
A ratio of the post-cracking stiffness to pre-cracking stiffness was calculated using methods included in Park and Paulay (1975). Using the aspect ratio of the section, and a modified reinforcing ratio expression, the post-cracking stiffness was found to be 4% of the pre-cracked stiffness (3821kNm2). It is difficult to accurately assess the post cracking torsional stiffness of a concrete section, and the effect of flexural plastic hinging during Phase 2 loading would have had a large effect. The deteriorated state of the concrete within the plastic hinge zone and cyclic loading with which the reinforcing had been subjected to, means that the postcracking stiffness is probably over-estimated. From the calculated values for the torsional strengths and stiffnesses, the corresponding twist rotations can be found. The twist rotations were multiplied by the length Page D-22
of the plastic hinge zone to produce rotations in terms of radians. Considering the torsion demands and capacity values calculated, Figure D-17 could be generated. The contrast between the initial stiff pre-cracked response and the post-cracked response can be seen in Figure D-17. Following Phase 2, the ends of the transverse beams were badly damaged. Thus, the post-cracked response starts from zero torsional twist in Figure 5-17 and as there is no concrete contribution due to the state of damage, the ultimate strength is that of the steel only, as calculated by Equation D.13. The intersection of the torsional demand values gives an idea as to the torsional twist that would occur, and the trends, more so than the specific values, are representative of the actual behaviour.
Torsion Moment (kNm)
300 250 200 150 100
Phase I Phase III Current Experiment Demand Lindsay (2004) Experiment Demand
50 0 0
0.01
0.02
0.03 0.04 Torsional Twist (rads/m)
0.05
0.06
0.07
Figure D-17 Representation of the calculated torsional strengths and demands
D.6
DISPLACEMENT INCOMPATIBILITY
D.6.1 Experimental Results The relative displacements between the south longitudinal beams and the southernmost hollow-core unit were measured throughout testing by an array of potentiometers placed underneath the timber infill topping slab. In addition to this, levelling was undertaken at the first cycle peak inter-storey drifts during testing, and this was able to give both the relative displacements, but also a fixed datum to indicate the vertical displacements with relation to the ground. The following Figures D-18, D-19 and D-20 show the displaced shapes for the Page D-23
south beams, the first hollow-core unit (Unit 1) and the relative displacement incompatibility between the floor and beams. A negative displacement incompatibility equates to the flooring being lower than the beams. 12 Beam 1% Beam -1% Beam 2% Beam -2%
Vertical Displacement (mm)
10 8 6 4 2 0 0
-2
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
11000
12000
-4 -6 -8 -10 Distance along structure (m m )
(a) Vertical displacement profile of the south beams 6 Slab 1% Slab -1% Slab 2% Slab -2%
Vertical Displacement (mm)
4
2 0 0
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
11000
12000
-2
-4 -6 Distance along structure (m m )
(b) Vertical displacement profile of hollow-core unit 1 10 1% -1% 2% -2%
Vertical Displacement (mm)
8 6 4 2 0 0
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
11000
12000
-2 -4 -6 -8 -10 -12 Distance along structure (m m )
(c) Vertical displacement incompatibility between the perimeter beams and floor
Figure D-18 Displacement of the south beams and floor slab during Phase 1 Page D-24
4 Beam 1% Beam -1% Beam 2% Beam -2% Beam 3% Beam -3%
Vertical Displacement (mm)
3 2 1 0 0
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
11000
12000
-1 -2 -3 -4 -5 -6 -7 Distance along structure (m m )
(a) Vertical displacement profile of the south beams 10 Slab 1% Slab -1% Slab 2% Slab -2% Slab 3% Slab -3%
Vertical Displacement (mm)
5 0 0
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
11000
12000
-5 -10
-15 -20 Distance along structure (m m )
(b) Vertical displacement profile of hollow-core unit 1
Vertical Displacement (mm)
10 1% -1% 2% -2% 3%
5
0 0
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
11000
12000
-5
-10
-15 Distance along structure (m m )
(c) Vertical displacement incompatibility between the perimeter beams and floor
Figure D-19 Displacement of the south beams and floor slab during Phase 2
Page D-25
20 Beam 2% Beam -2% Beam 3% Beam -3% Beam 4% Beam -4%
Vertical Displacement (mm)
15 10 5 0 0
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
11000
12000
-5 -10 -15 -20 Distance along structure (m m )
(a) Vertical displacement profile of the south beams Distance along structure (m m )
0
Vertical Displacement (mm)
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
11000
12000
-5
-10
-15 Slab 2% Slab -2% Slab 3% Slab -3% Slab 4% Slab -4%
-20
-25
(b) Vertical displacement profile of hollow-core unit 1 Distance along structure (m m )
5 0 Vertical Displacement (mm)
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
11000
12000
-5 -10 -15 -20 2% -2% 3% -3% 4% -4%
-25 -30 -35
(c) Vertical displacement incompatibility between the perimeter beams and floor
Figure D-20 Displacement of the south beams and floor slab during Phase 3
Page D-26
The displacement profiles for the beam and floor slab for Phase 1 loading show expected results. The beams deform in double curvature, and the floor slab in single curvature over the total span of the building. Figure D-18(c) shows the displacement incompatibility between the beams and floor, where the maximum relative displacement was 10mm when the flooring was lower than the frame beams. Reasonably symmetric behaviour was observed between the positive and negative cycles, and the maximum displacement incompatibility was seen to occur around 1m either side of the central column (6100mm). Similarly, the results from Phase 2 (Figure D-19) were expected. The displacement incompatibility relationship shows that the flooring was a maximum of 5mm higher than the beams during negative drifts when the transverse beams at the south end were inclining upwards, and during the positive drift cycles, the flooring was a maximum of 14mm lower than the frame beams. The results for Phase 3 as seen in Figure D-20 show interesting results. The deformed shape of the beams at various drift amplitudes shows an expected curvature pattern, but the displacement of the floors shows a distinct drop of over 16mm. During the experiment, it was observed that the transverse beams began to drop during Phase 2 loading. Most of the rotation within the plastic hinges at the end of the transverse beams was centred at the beam-column interfaces where a significant crack had formed. During the later stages of Phase 2, it was noticed that the beams were dropping and a vertical dislocation was occurring at these large end cracks. This is displayed by the vertical displacement results whereupon comparing Phase 1 and 3 (Figure 5-18(b) and 5-20(b)) the amount of the dropping of the floor units is noticed. Despite this, and as Figure 5-20(c) shows, the same trends of displacement incompatibility were seen, but the vertical dropping meant that the floor remained predominantly lower than the southern beams. At the floorings units highest point, the floor was 1mm higher than the beams, and at its lowest, 33mm below the beams. The maximum incompatibility results were seen to occur at approximately 1m either side of the central column.
Page D-27
D.6.2 Analytical Modelling The analysis involved the construction of an analytical model in the inelastic time history program Ruaumoko (Carr, 2003), utilising a plasticity concentrated approach. A twodimensional model was been set up to model the longitudinal lateral loading of the front frame, and consists of members representing the frame and floor elements and springs connecting the floor to the frame. Different spring members were used to model the level of fixity of the end support conditions, and along the frame between the frame and flooring. Sensitivity analyses were performed examining the effect of various parameters; different end support conditions, different lateral connection details, different bay lengths and numbers of bays and different flooring types. The effects of the different parameters were seen by examining both the displacement incompatibility patterns as well as the overall system base shear capacities. From the sensitivity analyses, it was seen that the end connection detail, through the stiffness of the end springs, had a large influence on system strength capacity and displacement incompatibility values. This is shown by Figure D-21, and is matched to a degree by the higher ultimate base shear capacity of the current experimental structure than the equivalent Lindsay (2004) base shear capacity. 3500 3000 FIXED
k=9.9x108
Base shear (kN)
2500 k=1x108 2000 k=1x107 1500 PINNED
k=0,1,1000,100000
1000 500 0 0.0
1.0
2.0
3.0
Inclination (%)
Figure D-21 Modelling the effect of the end connection detail on the base shear capacity
Page D-28
Modifying the side spring characteristics was done by altering the spring stiffnesses or the yield point representing the point at which cracking or tearing would occur. Adjusting the stiffness was seen to have a large effect on the displacement compatibility trends, with the obvious increased deformations for softer springs. The more stiff the springs also corresponded to an increase in the strength capacity of the system due to the greater ability to transfer the floor inertia forces to the frame. Figure D-22 shows the effect on the base shear capacity of the structure for various side connection detail stiffness values. 3500 RIGID 3000
8
k=1x10 k=1x107
2500 Base shear (kN)
k=9.9x108
k=0,1,1000 &100000 "SOFT"
2000 1500 1000 500 0 0.0
1.0
2.0
3.0
Inclination (%)
Figure D-22 Modelling the effect of the side connection detail on the base shear capacity
Different bay lengths, using 4m, 6m and 8m showed no major effect on the displacement trends. Altering the floor system types for 200, 300 and 400 series hollow-core was done by changing the member stiffness to 0.35EI, 1EI and 2.2EI respectively. This was seen to have a significant effect with the most severe displacement incompatibility values observed for the stiff 400 series floor. This can be explained by the fact that the more flexible 200 and 300 series flooring is able to deform with the beams in a double curvature manner (within the model, but not in reality), whereas the stiff nature of the 400 series means the floor deforms in a single curvature way.
Page D-29
Figure D-23 shows the displacement incompatibility results from the experimental tests and modelling for both the Lindsay (2004) and current experiments. The lateral spring properties modelling the infill connection were kept the same, but the end spring properties were altered to model the pinned type seating connection for Lindsay (2004) and the rigid connection in the present experiment. The results show promising resemblance between the experiment and analytical model. The overall deformation trends are matched although the model slightly underestimates the amount of incompatibility that occurs. For the rigid end conditions, the maximum displacement incompatibility occurred on both sides adjacent to the central column, as the floor unit deformed in single curvature due to the fixity at the ends. For the pinned end conditions, which allowed the floor to simply sag, displacement incompatibility peaks were seen close to the supports as well as either side of the central column, and the displacement incompatibility values were generally higher than for the fixed end case. 10 8 6 Displacement (mm)
4 Position along fram e (m m )
2 0 -2 0
2000
4000
6000
8000
10000
12000
-4 -6
Experiment 1% Model 1% Experiment 2% Model 2%
-8 -10 -12
(a) Observed and modelled displacement incompatibility from Lindsay (2004) 10 8
Displacement (mm)
6 4 2 Position along fram e (m m )
0 -2 0
2000
4000
6000
8000
10000
12000
-4 -6
Experiment 1% Model 1% Experiment 2% Model 2%
-8 -10 -12
(b) Observed and modelled displacement incompatibility from the current experiment
Figure D-23 Observed and modelled displacement incompatibility Page D-30
D.7
BEAM ELONGATION
The phenomenon of beam elongation is explained in Sections 2 and 3 of this thesis. Matthews et al (2004) developed a “rainflow-counting� method to predict the amount of elongation that occurs. The assumption of the eccentricity values, ecr, is a key part of the theoretical predictions, and the same values used by Matthews (2004) and later by Lindsay (2004) were used in these calculations. The following Figures D-24, D-25 and D-26 plot the observed beam elongation results as well as the predicted response for the three loading phases of the experiment. 14
14
Elongation (mm)
Elongation (mm)
12 10 8 6 Experiment
4
Theo ry
2
Experiment
12
Theo ry
10 8 6
7
4 2
0 -3
-2
0
-1 0 1 Int e r- S t o re y D rif t ( %)
2
3
-3
(a) South west plastic hinge elongation
-2
-1
0
Elongation (mm)
Elongation (mm)
12 10 8 6 4
Experiment
2
Theo ry
0 -2
-1
0
1
2
Theo ry -3
3
(c) South centre east hinge elongation
-2
-1 0 1 Int e r- S t o re y D rif t ( %)
2
(d) South east hinge elongation 45 40 35 30 25 20 15
Experiment
10
Theory -2.5
-2
5 -1.5
-1
3
20 18 16 14 12 10 8 6 4 2 0
Experiment
Int e r- S t o re y D rif t ( %)
Elongation (mm)
-3
2
(b) South centre west hinge elongation
14
7
1
Inter-Storey Drift (%)
0 -0.5 0 0.5 Inter-Storey Drift (%)
1
1.5
(e) Total frame elongation
Figure D-24 Beam elongation results for Phase 1 Page D-31
2
2.5
3
Experiment Theo ry
-4
-3
-2
Elongation (mm)
Elongation (mm)
20 18 16 14 12 10 8 6 4 2 0
-1 0 1 Inter-Storey Drift (%)
2
3
4
Experiment Theo ry
-4
-3
-2
Elongation (mm)
Elongation (mm)
-1 0 1 Int e r- S t o re y D rif t ( %)
2
3
4
-4
(c) South east hinge elongation
-1
0
1
2
Experiment Theo ry
-3
-2
-1 0 1 Inter-Storey Drift (%)
2
35 30 25 20 15 10 Phase II East Bay Phase II West Bay Theory
5 0 -4
-3
-2
-1
0 Inter-storey Drift (%)
1
2
3
4
(e) Total elongation (east and west bays) 120 100 80
Elongation (mm)
Figure D-25 Beam elongation results for Phase 2
60 40 Phase I Phase III Theory
20
-6
-5
-4
-3
3
4
3
4
20 18 16 14 12 10 8 6 4 2 0
(d) North east hinge elongation Elongation (mm)
-4
-2
(b) North west hinge elongation
20 18 16 14 12 10 8 6 4 2 0
Theo ry
-3
Int e r- S t o re y D rif t ( %)
(a) South west plastic hinge elongation
Experiment
20 18 16 14 12 10 8 6 4 2 0
-2
0 -1 0 1 Inter-storey Drift (%)
2
3
4
Figure D-26 Total Beam elongation for Phase 1 and 3
Page D-32
5
6
Theoretical Predictions: Longitudinal Loading Yield Drift 0.5 % 0.005 rad
ecr: External Hinges Distance 0.425D = 0.475D =
(mm) 318.75 356.25
ecr*Ty
(mm) 168.75 206.25
ecr*Ty
1.59375 1.78125
ecr: Internal Hinges Distance 0.225D = 0.275D =
Drift
0.84375 1.03125
Plastic Hinge of South Frame
(%) 0 0.5 0 -0.5 0 1 0 -1 0 1 2 0 -1 -2 0 2 3 0 -2 -3 0 3 4 0 -3 -4 0 4 5 0 -4 -5 0
(rads) 0 0.005 0 -0.005 0 0.01 0 -0.01 0 0.01 0.02 0 -0.01 -0.02 0 0.02 0.03 0 -0.02 -0.03 0 0.03 0.04 0 -0.03 -0.04 0 0.04 0.05 0 -0.04 -0.05 0
Bay
SE
SCE
SCW
SW
0 1.59375 0 1.78125 0 3.1875 1.59375 4.96875 3.1875 4.78125 7.96875 6.375 8.15625 11.71875 9.9375 11.53125 14.71875 13.125 14.90625 18.46875 16.6875 18.28125 21.46875 19.875 21.65625 25.21875 23.4375 25.03125 28.21875 26.625 28.40625 31.96875 30.1875
0 1.03125 0 0.84375 0 2.0625 1.03125 2.90625 2.0625 3.09375 5.15625 4.125 4.96875 6.65625 5.8125 6.84375 8.90625 7.875 8.71875 10.40625 9.5625 10.59375 12.65625 11.625 12.46875 14.15625 13.3125 14.34375 16.40625 15.375 16.21875 17.90625 17.0625
0 0.84375 0 1.03125 0 1.6875 0.84375 2.71875 1.6875 2.53125 4.21875 3.375 4.40625 6.46875 5.4375 6.28125 7.96875 7.125 8.15625 10.21875 9.1875 10.03125 11.71875 10.875 11.90625 13.96875 12.9375 13.78125 15.46875 14.625 15.65625 17.71875 16.6875
0 1.78125 0 1.59375 0 3.5625 1.78125 5.15625 3.5625 5.34375 8.90625 7.125 8.71875 11.90625 10.3125 12.09375 15.65625 13.875 15.46875 18.65625 17.0625 18.84375 22.40625 20.625 22.21875 25.40625 23.8125 25.59375 29.15625 27.375 28.96875 32.15625 30.5625
Page D-33
East 0 2.625 0 2.625 0 5.25 2.625 7.875 5.25 7.875 13.125 10.5 13.125 18.375 15.75 18.375 23.625 21 23.625 28.875 26.25 28.875 34.125 31.5 34.125 39.375 36.75 39.375 44.625 42 44.625 49.875 47.25
Total Elongation West 0 2.625 0 2.625 0 5.25 2.625 7.875 5.25 7.875 13.125 10.5 13.125 18.375 15.75 18.375 23.625 21 23.625 28.875 26.25 28.875 34.125 31.5 34.125 39.375 36.75 39.375 44.625 42 44.625 49.875 47.25
(mm) 0 5.25 0 5.25 0 10.5 5.25 15.75 10.5 15.75 26.25 21 26.25 36.75 31.5 36.75 47.25 42 47.25 57.75 52.5 57.75 68.25 63 68.25 78.75 73.5 78.75 89.25 84 89.25 99.75 94.5
Theoretical Predictions: Transverse Loading Yield Drift 0.5 % 0.005 rad
ecr: External Hinges Distance 0.425D = 0.475D =
Drift
ecr*Ty 1.59375 1.78125
Plastic Hinges
(%)
D.8
(mm) 318.75 356.25
(rads)
North
South
East/West Bay Total (mm)
0 0.5
0 0.005
0 1.59375
0 1.78125
0 3.375
0 -0.5
0 -0.005
0 1.78125
0 1.59375
0 3.375
0 1 0 -1 0 1 2 0 -1 -2 0 2 3 0 -2 -3 0
0 0.01 0 -0.01 0 0.01 0.02 0 -0.01 -0.02 0 0.02 0.03 0 -0.02 -0.03 0
0 3.1875 1.59375 4.96875 3.1875 4.78125 7.96875 6.375 8.15625 11.71875 9.9375 11.53125 14.71875 13.125 14.90625 18.46875 16.6875
0 3.5625 1.78125 5.15625 3.5625 5.34375 8.90625 7.125 8.71875 11.90625 10.3125 12.09375 15.65625 13.875 15.46875 18.65625 17.0625
0 6.75 3.375 10.125 6.75 10.125 16.875 13.5 16.875 23.625 20.25 23.625 30.375 27 30.375 37.125 33.75
LOW CYCLE FATIGUE FRACTURE OF REINFORCEMENT
A low cycle fatigue theory proposed by Dutta and Mander (2001) enables the plastic rotation life capacity of reinforcement to be calculated. The theory has been outlined in Section 2 and Appendix A to predict the fracture of the reinforcement in the sub-assemblage experiments, and Section 4 to assess the fracture of longitudinal reinforcement of the main beams during the super-assemblage experiment. The following calculations outline the derivation of the theoretical fatigue limits of the reinforcement, for longitudinal loading.
Page D-34
The equivalent number of equi-amplitude cycles to the reference drift (5%) experienced during the experiment is calculated as the following: Tref= Nmax=
5 5.12 q
ncycles 0.5 1 2 3 4 5
3 2 3 2 2 2 6
(T/Tref)2 0.03 0.08 0.48 0.72 1.28 1.9 4.49
This calculation shows that the reinforcement withstood 4.5 equivalent cycles (NF-Expt) to 5% during the experiment before fracture occurred. By re-arranging the low cycle fatigue equation from Dutta and Mander (2001), the theoretical equivalent number of 5% cycles, NF-Theory, that the reinforcement will be able to sustain prior to fracture can be found from the following:
N F Theory
N F Theory
ª § D ·§ L p ·§ 1 L p ·¸ º » « 0.16¨ ¸¨¨ ¸¸¨¨1 © D' ¹© D ¹© 2 L ¸¹ » 1« » T T y 2« » « »¼ «¬
2
ª § 750 ·§ 511 ·§ 1 511 · º 0.16¨ ¸¨ ¸¨1 ¸» « 1 636 750 ¹© 2 2675 ¹ » © ¹ © « 2« 0.05 0.0064 » » « ¼ ¬
(D-16)
2
3.6
Therefore, the theoretical number of cycles at an amplitude of 5% required to cause low cycle fatigue fracture of the reinforcement is 3.6.
Page D-35
D.9
OBSERVED BOWSTRING EFFECT
To account for the presence of the floor slab in calculating the overall strength of the structure, simple calculations were used to quantify the bowstring effect. Beam elongation is restrained due to the presence of the floor slab, and this restraint induces large compression forces within the longitudinal beams. To calculate this compression force, a simplified approach is used which calculates the eccentricity or depth of the compression arch. From this, the magnitude of the tension force can be found which is a function of the capacity of the reinforcement of the hollow-core end connections, the friction of the hollow-core seating and the amount of diaphragm steel orthogonal to the tension tie. The calculation is as follows: wl 2 Pl 8 4
Te
(D.16)
where e = midspan eccentricity of the tie force with respect to the centroid of the compression strut, T = combined tie force, l = overall span of arch, P = the tension force provided by the drag bar reinforcement and w = uniformly distributed load given by the diaphragm reinforcing orthogonal to the tension tie. As the tie force, T, is a function of the tension reinforcement capacity at the ends of the floor, it can be represented as: 2eAs f y
T
s
2 PWle
(D.17)
where As = end connection reinforcing area (starter bars and hairpin bars), fy = end connection reinforcing yield strength, s = end connection reinforcing spacing, P = coefficient of friction for the bearing strip and W = weight of the hollow-core. The uniformly distributed load given by the diaphragm reinforcing orthogonal to the tension tie, w, can be found by: w
Asd f yd s sd
(D.18)
where Asd = area of the diaphragm steel, fyd = yield strength of the diaphragm reinforcing and ssd = spacing of the diaphragm reinforcing. Page D-36
Using this formulation, and the measured material properties of the reinforcement, an eccentricity of 2.5m was found. This matches well with the cracking pattern witnessed throughout testing. The eccentricity value allowed a tension force of 1254kN to be calculated. By equilibrium, this tension force is resisted by a compression force of the same magnitude, and this compression force has a significant effect on the capacity of the system and notably the strength of the beam hinges joining the central column. The compression axial force was taken to act at the level of the topping slab and further simplified to occur at the top extreme fibre. Therefore, the moment capacity of both of the hinges was found to be:
M beams +
( As As ) f y (d d ' ) Nd
(D-19)
-
In which As = area of tension reinforcement; As = area of compression reinforcement; fy = yield strength of tension reinforcement; d = the distance from the extreme compression fibre to the centroid of the tension reinforcement; d’ = the distance from the extreme compression fibre to the centre of the compression block; and N = the axial compression force due to the bowstring effect. Using this formulation, the moment demand on the interior column, as found by the sum of the two hinges framing into the south centre column, was found to be 1859kNm. This is equivalent to the nominal moment capacity (1004kNm) when the bowstring effect is omitted.
Page D-37
D.10 SUPER-ASSEMBLAGE CAPACITY MECHANISM CALCULATIONS The capacity mechanisms used to calculate the theoretical pushover curves for both the longitudinal and transverse loading directions, is outlined in this sub-section. The theoretical curve is defined by two points: the onset of yielding and the point of full plastification. Yielding was assumed to occur at Âą0.64% as calculated in Section D.1. Plastification was assumed to occur at Âą2% in keeping with the work done by Matthews (2004) and the observed crack widths during this experiment. The contributions to the overall strength are from the nominal moment strengths of the beams and for negative moment capacities, additional strength is derived from activation of the starter bars or end connection reinforcement and diaphragm reinforcement. The bowstring effect, described in section D.8 is also recognised.
D.10.1 Phase 1 and 3: Longitudinal
For the external hinges of the structure, in this case for longitudinal loading, the southeast and southwest hinges, the negative moment capacity is enhanced by the activation of starter bars from the transverse beams. These starter bars are progressively activated with increasing lateral drift. For the yield point, the contributing slab width was taken as the width of the infill topping slab. At the point of full plastification, the width of activated slab was taken to be 3.05m, or approximately half the span of the transverse beams. At 2% drift the width of the crack between the beam and slab over the full length of the transverse beam, was over 5mm signifying that the bars were yielding and contributing to the strength of the system. The moment capacity values calculated were extrapolated to the column centreline in order to calculate the overall system base shear, and for this, the plastic hinges were assumed to form at 0.5D (375mm) from the column face.
Page D-38
Initial Yield Southeast and Southwest hinges: M+ = 502kNm
(at column centreline)
663kNm
M- = 502kNm + 3 infill starters = 570kNm
(at column centreline)
752kNm
(at column centreline)
663kNm
South central hinges: (accounting for axial compression force due to bowstring effect) M+ = 502kNm M- = 1357kNm
1791kNm
(at column centreline)
Full Plastification Southeast and Southwest hinges: M+ = 502kNm
(at column centreline)
663kNm
M- = 502kNm + 11 infill starters = 707kNm
(at column centreline)
933kNm
(0.8jd used to allow for the hairpin reinforcement in compression reducing the internal lever arm)
South central hinges: M+ = 502kNm
663kNm
(at column centreline)
M- = 1357kNm + 3 diaphragm bars = 1425kNm
(at column centreline)
1881kNm
Also, as the base shear capacity of the entire building is being predicted, the negative moment contribution from the top bars at the northern ends of the transverse beams need to be taken into account. Overall Summary and Base Shear Calculation:
Positive Drift
ÂŚM
Hinge:
NW
SW
SC
SE
NE
6M
Yield
-
663
2453
752
-
3868
1105kN
Plastification
-
663
2543
953
191
4350
1243kN
Yield
-
-752
-2453
-663
-
-3868
-1105kN
-191
-953
-2543
-663
-
-4350
-1243kN
Negative Drift Plastification
Page D-39
Vb
hc
As the experimental results were zeroed at the commencement of testing, the experimental results do not show the residual or natural moments of the structure. During construction, all of the beams were propped during the placement of the floors and the casting of the topping concrete. Upon removal of these supports, the eccentric weight of the floor would have caused the east and west columns to incline inwards (tops of the columns move towards the centre of the building, and the bases of the columns move outwards), and thus cause positive moments within the southeast and southwest hinge zones. This artificially shifted the hystereses off the true zero moment. By way of a simple elastic analysis using the gross section properties of the structure, this initial moment was calculated as 120kNm, and the hysteretic plots for both the southeast and southwest hinges in the longitudinal direction have been shifted by this amount. Figure D-27 shows the comparisons between the predicted and actual strengths. An upper bound solution was also provided based on 25% overstrength.
D.10.2 Phase 2: Transverse
A similar method of analysis was used to calculate the capacity of the super-assemblage in the transverse direction. In this case, the strengths of the transverse beam hinges and the starter bars from the south longitudinal beams were the contributing sources of strength. Due to the presence of the steel tie frame along the northern edge of the structure, no starter bars were present to enhance the negative moment capacity of the northern hinges, and hence slightly non-symmetrical behaviour is present. The amount of starter bars activated within the longitudinal beams was taken to be the same as in the longitudinal loading direction; at initial yield, 1m was the contributing slab width, and at full plastification, the slab width was half the bay width, or 3m.
Page D-40
Initial Yield Southeast and Southwest hinges: M+ = 466kNm
(at column centreline)
531kNm
M- = 466kNm + 3 infill starters = 532kNm
(at column centreline)
607kNm
M+ = 466kNm
(at column centreline)
531kNm
M- = 466kNm
(at column centreline)
531kNm
Northeast and Northwest hinges:
Full Plastification Southeast and Southwest hinges: M+ = 466kNm
(at column centreline)
531kNm
M- = 466kNm + 9 infill starters = 663kNm
(at column centreline)
756kNm
M+ = 466kNm
(at column centreline)
531kNm
M- = 466kNm
(at column centreline)
531kNm
Northeast and Northwest hinges:
Overall Summary and Base Shear Calculation:
Positive Drift
ÂŚM
Hinge:
NW
SW
SE
NE
6M
Yield
531
531
531
531
2124
607kN
Plastification
531
615
531
531
2124
607kN
Yield
-531
-607
-607
-531
-2276
-650kN
-531
-756
-756
-531
-2968
-848kN
Negative Drift Plastification
Vb
hc
These strength predictions for Phase 2 along with Phase 1 and 3 longitudinal loading are shown in the following Figures. Section 4 of this thesis discusses the results and explains the comparisons between the actual and theoretical strengths, whether the comparisons are good or otherwise. Page D-41
Base Shear Force (kN)
1800 1600 1400 1200 1000 800 600 400 200
Inter-Storey Drift (%)
0 -6
-5
-4
-3
-2
-1
-200
0
1
2
3
4
5
6
-400 -600 -800 Experiment Phase 3
-1000
Experiment Phase 1 -1200
Nominal Prediction
-1400
25% Overstrength Prediction
-1600
40% Overstrength Prediction
-1800
(a) Phase 1 and 3 Longitudinal loading: Experimental base shear capacity and theoretical pushover curve. Base Shear Force (kN)
1200
900
600
300
Inter-Storey Drift (%) 0 -4
-3
-2
-1
0
1
2
3
-300
-600
Experiment (pre-torsion) Experiment (post-torsion)
-900
Nominal Prediction 25% Overstrength Prediction
-1200
(b) Phase 2 Transverse loading: Experimental base shear capacity and theoretical pushover curve.
Figure D-27 Base shear capacity: experimental and theoretical relationships.
Page D-42
4
Moment (kNm)
1200
-1
-200 0
R o t a t io n ( %) -6
-5
1000 800 600 400 200 0
-4
-3
-2
1
2
3
4
5
-400
Phase 1
-600
Phase 3 Nominal Strength
-800 -1000
6
25% Overstrength
-1200
Moment (kNm)
(a) Moment rotation behaviour for the southwest hinge of the south frame
R o t a t io n ( %) -6
-5
3000 2500 2000 1500 1000 500 0
-4
-3
-2
-1
-500 0
1
2
3
-1000
4
5
6
Phase 1 Phase 3 Nominal Strength 25% Overstrength
-1500 -2000 -2500 -3000
Moment (kNm)
(b) Moment rotation behaviour for the two centre hinges of the south frame framing into the south centre column
R o t a t io n ( %) -6
-5
1200 1000 800 600 400 200 0
-4
-3
-2
-1
-200 0
1
2
3
4
5
-400
Phase 1
-600
Phase 3
-800
Nominal Strength
-1000
6
25% Overstrength
-1200
(c) Moment rotation behaviour for the southeast hinge of the south frame
Figure D-28 Phase 1 and 3 Moment rotation behaviour: experimental and theoretical relationships.
Page D-43
Moment (kNm)
800 600 400 200
Rotation (%) -4
-3
0 -2
-1
0
1
2
3
4
-200 -400
Pre-Torsion Post-Torsion
-600
Nominal Strength 25% Overstrength
-800
Moment (kNm)
(a) Moment rotation behaviour for the north hinge of the west frame 1200 1000 800 600 400 200
Rotation (%) -4
-3
0 -2
-1
-200 0
1
2
3
4
-400 -600 -800 -1000
Pre-Torsion Post-Torsion Nominal Strength 25% Overstrength
-1200
(b) Moment rotation behaviour for the south hinge of the west frame
Figure D-30 Phase 2 Moment rotation behaviour: experimental and theoretical relationships for the west frame.
Page D-44
Moment (kNm)
800 600 400 200
Rotation (%) -4
-3
0 -2
-1
0
1
2
3
4
-200 Pre-Torsion
-400
Post-Torsion Nominal Strength
-600
25% Overstrength -800
(a) Moment rotation behaviour for the north hinge of the east frame
Moment (kNm)
1000 800 600 400 200
Rotation (%) -4
-3
0 -2
-1
-200
0
-400 -600 -800
1
2
3
Pre-Torsion Post-Torsion Nominal Strength 25% Overstrength
-1000
(b) Moment rotation behaviour for the south hinge of the east frame
Figure D-30 Phase 2 Moment rotation behaviour: experimental and theoretical relationships for the east frame.
Page D-45
4
D.11 REFERENCES Carr A.J, 2003, Ruaumoko 2D User Manual, Computer Program Library, Department of Civil Engineering, University of Canterbury, Christchurch, New Zealand. Dutta A and Mander J.B, 2001, Energy Based Methodology for Ductile Design of Concrete Columns, Journal of Structural Engineering, Vol. 127(12), December, pp 1374-1381. Lindsay R.A, 2004, Experiments on the seismic performance of hollow-core floor systems in precast concrete building, Masters Thesis, Department of Civil Engineering, University of Canterbury, Christchurch, New Zealand. Matthews J.G, 2004, Hollow-core floor slab performance following a severe earthquake, PhD Thesis, Department of Civil Engineering, University of Canterbury, Christchurch, New Zealand. Matthews J.G, Mander J.B, Bull D.K, 2004, Prediction of beam elongation in structural concrete members using a rainflow method, 2004 NZSEE Conference, Rotorua, NZ, Paper 27, 8 pp. Mitchell M.P and Collins D, 1991, Prestressed Concrete Structures, Prentice Hall, Englewood Cliffs, N.J, USA. NZS3101, 1995, Concrete Structures Standard, NZS3101, Parts 1 & 2, Standards New Zealand, Wellington, New Zealand. NZS3101, 2003, Draft Amendment No. 3 to 1995 Standard (NZS3101), Standards New Zealand, Wellington, New Zealand. Park R and Paulay T, 1975, Reinforced Concrete Structures, J. Wiley and Sons Inc, New York. Priestley M.J.N and Kowalsky M.J, 2000, Direct Displacement Based Design of Concrete Buildings, Bulletin of the New Zealand Society for Earthquake Engineering, December, Vol. 33, No.4, pp 421-444. Page D-46