Design of steel structures for buildings in seismic areas Eurocode 8 Design of steel structures in seismic areas Part 1 1 General rules and rules for buildings
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Design of steel structures for BuilDings in seismic AreAs
eccs eurocoDe Design m A nuA ls
eccs eDitoriAl BoArD
Luís Simões da Silva (ECCS)
António Lamas (Portugal)
Jean-Pierre Jaspart (Belgium)
Reidar Bjorhovde (USA)
Ulrike Kuhlmann (Germany)
Design of steel structures – 2nD eDition
Luís Simões da Silva, Rui Simões and Helena Gervásio
fire Design of steel strcutures – 2nD eDition
Jean-Marc Franssen and Paulo Vila Real
Design of PlAteD structures
Darko Beg, Ulrike Kuhlmann, Laurence Davaine and Benjamin Braun
fAtigue Design of steel AnD comPosite structures
Alain Nussbaumer, Luís Borges and Laurence Davaine
Design of colD-formeD steel structures
Dan Dubina, Viorel Ungureanu and Raffaele Landolfo
Design of Joints in steel AnD comPosite structures
Jean-Pierre Jaspart and Klaus Weynand
Design of steel structures for BuilDings in seismic AreAs
Raffaele Landolfo, Federico Mazzolani, Dan Dubina, Luís Simões da Silva and Mario D’Aniello
ECCS – SCI EUROCODE DESIGN MANUALS
Design of steel structures, uK eDition
Luís Simões da Silva, Rui Simões, Helena Gervásio
Adapted to UK by Graham Couchman
Design of Joints in steel structures, uK eDition
Jean-Pierre Jaspart and Klaus Weynand
Adapted to UK by Graham Couchman and Ana M. Girão Coelho
ECCS EUROCODE DESIGN MANUALS – BRAZILIAN
EDITIONS
DimensionAmento De estruturAs De Aço
Luís Simões da Silva, Rui Simões, Helena Gervásio, Pedro Vellasco, Luciano Lima
Information and ordering details
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Design of steel structures for BuilDings in seismic
AreAs
Eurocode 8: Design of structures for earthquake resistance
Part 1-1 – General rules, seismic actions and rules for buildings
Raffaele Landolfo Federico Mazzolani
Dan Dubina
Luís Simões da Silva
Mario D’Aniello
Design of Steel Structures for Buildings in Seismic Areas
1st Edition, 2017
Published by:
ECCS – European Convention for Constructional Steelwork publications@steelconstruct.com www.steelconstruct.com
Sales: Wilhelm Ernst & Sohn Verlag für Architektur und technische Wissenschaften GmbH & Co. KG, Berlin
All rights reserved. No parts of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior permission of the copyright owner.
ECCS assumes no liability with respect to the use for any application of the material and information contained in this publication.
Copyright © 2017 ECCS – European Convention for Constructional Steelwork
ISBN (ECCS): 978-92-9147-138-6
ISBN (Ernst & Sohn): 978-3-433-03010-3
Legal dep.: 432199/17 Printed in Sersilito, Empresa Gráfica Lda, Maia, Portugal
Photo cover credits: Dan Dubina
v tABle of contents tABle of contents foreworD xiii PrefAce xvii Chapter 1 SEISMIC DESIGN PRINCIPLES IN STRUCTURAL CODES 1 1.1 Introduction 1 1.2 Fundamentals of seismic design 2 1.2.1 Capacity design 2 1.2.2 Seismic design concepts 6 1.3 Codification of seismic design 11 1.3.1 Evolution of seismic design codes 11 1.3.2 New perspectives and trends in seismic codification 19 Chapter 2 EN 1998-1: GENERAL AND MATERIAL INDEPENDENT PARTS 25 2.1 Introduction 25 2.2 Performance requirements and compliance criteria 27 2.2.1 Fundamental requirements 27 2.2.2 Ultimate limit state 32 2.2.3 Damage limitation state 34 2.2.4 Specific measures 35 2.3 Seismic action 36
The fundamentals of the dynamic model 36
Basic representation of the seismic action 40
The seismic action according to EN 1998-1 46 2.3.4 Alternative representations of the seismic action 52 2.3.5 Design spectrum for elastic analysis 54 2.3.6 Combinations of the seismic action with other types of actions 56 2.4 Characteristics of earthquake resistant buildings 58 2.4.1 Basic principles of conceptual design 58 2.4.2 Primary and secondary seismic members 60
2.3.1
2.3.2
2.3.3
2.6
2.7
2.6.1
2.6.2
2.6.3
2.6.4
2.7.1
2.7.2
2.7.3
2.7.4
2.7.5
2.8
3.1
2.11.1
3.2.1
3.2.2
vi
Criteria for structural regularity 61 2.5 Methods of structural seismic analysis 70 2.5.1 Introduction 70 2.5.2 Lateral force method 72 2.5.3 Linear modal response spectrum analysis 75 2.5.4 Nonlinear static pushover analysis 84
Nonlinear time-history dynamic analysis 90
tABle of contents 2.4.3
2.5.5
Structural modelling 94
Introduction 94
Modelling of masses 96
Modelling of damping 98
Modelling of structural mechanical properties 101
Accidental
effects 107
torsional
Accidental
107
eccentricity
109
Accidental torsional effects in the lateral force method of analysis
110
Accidental torsional effects in modal response spectrum analysis
analysis 111
Accidental torsional effects in nonlinear static pushover
Accidental
effects in linear and nonlinear dynamic time history analysis 114
torsional
induced by different components of the seismic action 114
Combination of effects
structural
117
Second
effects in seismic linear elastic analysis 118
121
2.9 Calculation of
displacements
2.10
order
2.11 Design verifications
Safety
121 2.11.2
126
verifications
Damage limitation
129
Chapter 3 EN 1998-1: DESIGN PROVISIONS FOR STEEL STRUCTURES
for steel buildings 129
Design concepts
for steel mechanical properties 133
3.2 Requirements
Strength and
133
ductility
Toughness 135
3.3
3.4 Design criteria and detailing rules for dissipative structural behaviour common to all structural types
3.4.1
3.4.2
rules for cross sections in dissipative members
3.4.3 Design rules for non-dissipative connections
3.4.4
3.4.5
3.5
3.5.1
3.5.2
3.5.3
3.6 Design criteria and detailing rules for concentrically braced frames
3.6.1
3.6.2
3.7
4.4
3.7.1
3.7.2
3.7.3
4.3.1
4.3.2
4.3.3
4.4.1
4.4.2
4.4.3
4.4.5
vii tABle of contents
Structural typologies and behaviour factors 137
Structural types 137 3.3.2 Behaviour factors 141
3.3.1
145
145
Introduction
145
Design
147
148
Design rules and requirements for dissipative connections
148
Design rules and requirements for non-dissipative members
Design criteria and
rules for moment resisting frames 149
detailing
Code requirements for beams 149
Code requirements for columns 152
Code
joints 153
requirements for beam-to-column
158
Code
158
requirements for braces
Code
for
162
requirements
beams and columns
164
Design criteria and detailing rules for eccentrically braced frames
Code
for
links 164
requirements
seismic
Code
links 171
requirements for members not containing seismic
Code
connections
seismic links 172
DESIGN RECOMMENDATIONS FOR DUCTILE DETAILS 173 4.1 Introduction 173
Seismic design
composite steel-concrete
174
Ductile
182
requirements for
of the
Chapter 4
4.2
and detailing of
slabs
4.3
details for moment resisting frames
182
Detailing of beams
Detailing
186
of beam-to-column joints
Detailing
bases 210
of column
215
Ductile details for concentrically braced frames
Introduction 215
Detailing
216
of brace-to-beam/column joints
Detailing
228
230
of brace-to-beam midspan connections
4.4.4 Detailing of brace-to-brace connections
235
Detailing of brace-to-column base connections
tABle of contents
4.4.6 Optimal slope, constructional tolerances and local details for braces
4.5 Ductile details for eccentrically braced frames
4.5.1 Detailing of links
4.5.2 Detailing of link lateral torsional restraints
4.5.3 Detailing of diagonal brace-to-link connections
4.5.4 Detailing of link-to-column connections
Chapter 5
DESIGN ASSISTED BY TESTING
5.1 Introduction
5.2 Design assisted by testing according to EN 1990
5.2.1
5.2.2
5.2.3
5.2.4
overview of EN 1990
of design values
5.3 Testing of seismic components and devices
5.3.1 Introduction
5.3.2 Quasi-static monotonic and cyclic testing
5.3.3 Pseudo-dynamic testing
5.3.4 Dynamic
5.4 Application: experimental qualification of buckling restrained braces
5.4.1 Introduction and scope
5.4.2
5.4.3
5.4.4 Test setup and loading protocol for ITT
5.4.5
5.4.6 Fabrication Production Control tests
Chapter 6
MULTI-STOREY BUILDING WITH MOMENT RESISTING FRAMES
6.1 Building description and design assumptions
6.1.2 Normative
6.1.3
viii
236
239
239
241
244
245
247
247
248
Introduction 248
250
General
Testing 252
254
Derivation
262
262
262
275
277
testing
278
278
279
Test specifications
Test
280
specimens
280
281
Results
283
285
285
285
6.1.1 Building description
references 287
288
Materials
6.3
6.2.5
6.3.1
6.5.6
Chapter 7
ix tABle of contents 6.1.4 Actions 289 6.1.5 Pre-design 292
Structural analysis and calculation models 293 6.2.1 General features 293 6.2.2 Modelling assumptions 296 6.2.3 Numerical models and method of analysis 297 6.2.4 Imperfections for global analysis of frames 301
6.2
Frame stability and second order effects 303
Design and verification of structural members 304
Design and verification of beams 304
Design and verification of columns 310 6.3.3 Panel zone of beam-to-column joints 316 6.4 Damage limitation 319 6.5 Pushover analysis and assessment of seismic performance 320 6.5.1 Introduction 320 6.5.2 Modelling assumptions 321 6.5.3 Pushover analysis 328
Transformation to an equivalent SDOF system 331
Evaluation of the seismic demand 333
6.3.2
6.5.4
6.5.5
Evaluation of the structural performance 334
MULTI-STOREY BUILDING WITH CONCENTRICALLY BRACED FRAMES 335 7.1 Building description and design assumptions 335 7.1.1 Building description 335 7.1.2 Normative references 337 7.1.3 Materials 337 7.1.4 Actions 338 7.1.5 Pre-design 340 7.2 Structural analysis and calculation models 342 7.2.1 General features 342 7.2.2 Modelling assumptions 342 7.2.3 Numerical models and method of analysis 344 7.2.4 Imperfections for global analysis of frames 348 7.2.5 Frame stability and second order effects 349
7.3
Chapter 8
8.1
8.2
8.1.1
8.1.2
8.3
8.3.1
8.3.2
8.3.3
8.3.4
Chapter 9
9.2.3
9.3
9.3.1
x
tABle of contents
Design and verification of structural members 350 7.3.1 Design and verification of X-CBFs 350 7.3.2 Design and verification of inverted V-CBFs 357 7.4 Damage limitation 365
MULTI-STOREY BUILDING WITH ECCENTRICALLY BRACED FRAMES 369
Building description and design assumptions 369
Building description 369
Normative references 371
Materials 371
Actions 372
8.1.3
8.1.4
Structural analysis and calculation models 374
General features 374 8.2.2 Modelling assumptions 375 8.2.3 Numerical models and method of analysis 376 8.2.4 Imperfections for global analysis of frames 380 8.2.5 Frame stability and second order effects 380
8.2.1
Design and verification of structural members 381
Design and verification of shear links 381
Design and verification of beam segments outside the link 384
Design and verification of braces 384
Design and verification of columns 385
Damage limitation 388
8.4
CASE STUDIES 391 9.1 Introduction 391
The Bucharest Tower Centre International 393
General description 393 9.2.2 Design considerations 397
9.2
9.2.1
Detailing 421
Construction 422
9.2.4
Single storey Industrial Warehouse in Bucharest 432
General description 432
xi tABle of contents 9.3.2 Design considerations 435 9.4 The Fire Station of Naples 449 9.4.1 General description 449 9.4.2 Design considerations and constructional details 456 9.4.3 The anti-seismic devices 467 REFERENCES 475
foreworD
There are many seismic areas in Europe. As times goes by, regional seismicity is better known and the number of places where earthquake is an action to consider in design increases. Of course, there are substantial differences in earthquake intensity between regions and the concern is much greater in many areas of Italy, for instance, than in most places in Northern Europe. However, even in Northern Europe, for structures for which a greater level of safety is required, like Seveso industrial plants, hospitals and public safety facilities, seismic design can be the most requiring design condition.
Designing for earthquake has original features in comparison with design for classical loading like gravity, wind or snow. The reference event for Ultimate Limit State seismic design is rare enough for an allowance to permanent deformations and structural damages, as long as people’s life is not endangered. This means that plastic deformations are allowed at ULS, so that the design target becomes a global plastic mechanism. To be safe, the latter requires many precautions, on global proportions of structures and on local detailing. The seismic design concepts are completely original in comparison to static design. Of course, designing for a totally elastic behaviour even under the strongest earthquake remains possible but, outside of low seismicity areas, this option is generally left aside because of its cost.
This book is developed with a constant reference to Eurocode 8 or EN 19981:2004; it follows the organization of that code and provides detailed explanations in support of its rather dry expression. Of course, there are many other seismic design codes, but it must be stressed that there is nowadays a strong common thinking on the principles and the application rules in seismic design so that this book is also a support for the understanding of other continents codes.
Chapter 1 explains the principles of seismic design and their evolution throughout time, in particular the meaning, goals and conditions set forward by capacity design of structures and their components, a fundamental aspect of seismic design.
xiii foreworD
Chapter 2 explains the general aspects of seismic design: seismic actions, design parameters related to the shape of buildings, models for the analysis, safety verifications. Methods of analysis are explained in an exhaustive way: theoretical background, justifications of limits and factors introduced by the code, interest and drawbacks of each method, together with occasionally some tricks to facilitate model making and combination of load cases.
Chapter 3 focuses on design provisions specific to steel structures: ductility classes, requirements on steel material, structural typologies and design conditions related to each of them; an original insight on design for reparability is also included.
Chapter 4 provides an overview about the best practice to implement the requirements and design rules for ductile details, particularly for connections in moment resisting frames (MRF), concentrically braced frames (CBF) and eccentrically braced frames (EBF), and for other structural components like diaphragms.
Chapter 5 describes the guidance provided for design assisted by testing by EN 1990 and the specific rules for tests, a necessary tool for evaluating the performance characteristics of structural typologies and components in the plastic field and in cyclic/dynamic conditions.
Chapter 6 illustrates and discusses the design steps and verifications required by EN 1998-1 for a multi-storey Moment Resisting Frame.
Chapter 7 and 8 do the same respectively for buildings with CBF’s and EBF’s.
Chapter 9 presents three very different examples of real buildings erected in high seismicity regions: one tall building, one industrial hall and one design using base isolation. These examples are complete in the sense that they show the total design, where seismic aspects are only one part of the problem. These examples are concrete, because they illustrate practical difficulties of the real world with materials, execution, positioning…
The concepts, design procedures and detailing in seismic design may seem complex. This publication explains the background behind the rules, which
xiv foreworD
clarify their objectives. Details on the design of the different building typologies are given, with reference to international practice and to recent research results. Finally, design examples and real case studies set out the design process in a logical manner, giving practical and helpful advice.
This book will serve the structural engineering community in expanding the understanding and application of seismic design rules, and, in that way, constitute a precious tool for our societies safety.
André Plumier
Honorary Professor, University of Liege
xv foreworD
PrefAce
This manual aims to provide its readers with the background and the explanation of the main aspects dealing with the seismic design of steel structures in Europe. Therefore, the book focuses on EN 1998-1 (usually named part 1 of Eurocode 8 or EC8-1) that is the Eurocode providing design rules and requirements for seismic design of building structures. After 10 years from its final issue, both the recent scientific findings and the design experience carried out in Europe highlight some criticisms. In the light of such considerations, this book complements the explanation of the EC8-1 provisions with the recent research findings, the requirements of renowned and updated international seismic codes (e.g. North American codes and design guidelines) as well as the design experience of the Authors. Although the manual is oriented to EC8-1, the book aims to clarify the scientific outcomes, the engineering and technological aspects rather than sticking to an aseptic explanation of each clause of the EC8-1. Indeed, as shown in Chapter 4, the proper detailing of steel structures is crucial to guarantee adequate ductility of seismic resistant structures and the current codes does not give exhaustive guidelines to design ductile details since it only provides the fundamental principles. In addition, the practice of earthquake engineering significantly varies between European regions, reflecting the different layouts of each national seismic code as well as the level of knowledge and confidence with steel structures of each country. With this regard, a large number of European engineers believe that steel structures can withstand severe earthquakes without requiring special details and specifications as conversely compulsory for other structural materials like reinforced concrete and masonry. This belief direct results from the mechanical features of the structural steel, which is a high performance material, being stronger than concrete but lighter (if comparing the weight of structural members) and also very ductile and capable of dissipating large amounts of energy through yielding when subjected to cyclic inelastic deformations. However, although the material behaviour is important, the ductility of steel alone is not enough to guarantee ductile structural response. Indeed, as demonstrated by severe past earthquakes (e.g. Northridge 1994,
xvii PrefAce
PrefAce
Kobe 1995 and Christchurch 2011) there are several aspects ensuring good seismic behaviour of steel structures, which are related to (i) the conceptual design of the structure, (ii) the overall sizing of the member, (iii) the local detailing and (iv) proper technological requirements as well as ensuring that the structures are actually constructed as designed.
Therefore, this book primarily attempts to clarify all these issues (from Chapter 1 to 4) for European practising engineers, working in consultancy firms and construction companies. In addition, the examples of real buildings (see Chapter 9) are an added value, highlighting practical and real difficulties related to both design and execution.
This design manual is also meant as a recommended textbook for several existing courses given by the Structural Sections of Civil Engineering and Architectural Engineering Departments. In particular, this manual is oriented to advanced students (i.e. those attending MSc programmes) thanks to the presence of various calculation examples (see Chapter 6, 7 and 8) that simplify and speed up the understanding and the learning of seismic design of EC8 compliant steel structures. In addition, research students (i.e. those attending PhD programmes) can find useful insights for their experimental research activities by reading Chapter 5, which provides some guidance and discussion on how performing experimental tests of structural typologies and components in cyclic pseudo-static and dynamic conditions.
The Authors
Raffaele Landolfo
Federico Mazzolani
Dan Dubina
Luís Simões da Silva
Mario D’Aniello
xviii
Chapter 1
SeiSmic DeSign PrinciPleS in Structural coDeS
1.1 INTRODUCTION
Earthquake Engineering is the branch of engineering aiming at mitigating risks induced by earthquakes with two objectives: i) to predict the consequences of strong earthquakes on urban areas and civil infrastructures; ii) to design, build and maintain structures that are able to withstand earthquakes in compliance with building codes.
Researchers and experts working within emergency management organizations (e.g. the civil protection) actively work on the first issue. On the contrary, structural designers focus their attention and efforts on the second objective. With this regard, it should be noted that the seismic design philosophy substantially differs from the design approaches conventionally adopted for other types of actions, raising difficulties to structural engineers less confident with seismic engineering. Indeed, broadly speaking, for quasi-static loads (e.g. dead and live loads, wind, snow, etc.) the structure should behave mostly elastically without any damage until the maximum loads are reached, while in case of seismic design it is generally accepted that structures can experience damage because they should perform in the plastic range for seismic events. The philosophy of structural seismic design establishes the performance levels that properly engineered structures should satisfy for different seismic intensities, which can be summarized as follows:
1
prevent near collapse or serious damage in rare major ground shaking events, which are called in the following Ultimate Limit State seismic action or ULS seismic action prevent structural damage and minimize non-structural damage in occasional moderate ground shaking events; prevent damage of non-structural components (such as building partitions, envelopes, facilities) in frequent minor ground shaking events.
Hence, the most meaningful performance indexes for seismic resistant structures are the amount of acceptable damage and the repair costs. Owing to the unforeseeable nature of seismic actions, it is clear that damage control is very difficult to be quantified by code provisions, especially because it is related to acceptable levels of risk. The challenge for efficient design of seismic resistant structures is to achieve a good balance between the seismic demand (namely the effect that earthquakes impose on structures) and the structural capacity (namely the ability to resist seismic induced effects without failure). However, the quantification of different types of damage (structural and nonstructural) associated to the reference earthquake intensity (e.g. frequent/minor, occasional/moderate, and rare/major) and the definition of relevant operational design criteria are still open issues that need clarification and further studies.
This chapter describes and discusses the concept of capacity design in the light of existing seismic codes, illustrating the evolution of seismic design principles throughout time, and explains the criteria that form the basis of EN 1998-1:2004 (CEN, 2004a), henceforth denoted as EC8-1.
1.2 FUNDAMENTALS OF SEISMIC DESIGN
1.2.1
Capacity design
It is generally acknowledged that structural safety depends on the ductility that the structural system can provide against the design loads. Indeed, ductility represents the capacity of a mechanical system (e.g. a beam, a structure, etc.) to deform in the plastic domain without substantially reducing its bearing capacity. In seismic design of structures it is generally not economical or possible to ensure that all the elements of the structure behave in a ductile manner.
SeiSmic DeSign PrinciPleS in Structural coDeS 2
1.
Inevitably, a dissipative (ductile) structure comprises both dissipative (ductile) elements and non-dissipative (brittle) ones. In order to achieve a dissipative (ductile) design for the whole structure, the failure of the brittle elements must be prevented. This may be done by prioritizing structural elements strength, which will lead to the prior yielding of ductile structural elements, preventing the failure of brittle structural elements. This principle is known as ”capacity design”. Capacity design may be explained by considering the chain model, introduced by Paulay and Priestley (1992) and depicted in Figure 1.1a, whereby the chain represents a structural system made of both ductile elements (e.g. the ring “1”) and brittle zones (e.g. the ring “i”).
According to non-seismic design procedures for quasi-static loads (hereinafter referred to as “direct design”), the design force is the same for all elements belonging to the chain, because the applied force is equal for all rings, being a system in series. Hence, the design resistance Fy,i is the same for all elements. Under this assumption, the yield resistance of the ductile chain F y,1 is equal or even slightly larger than Fy,i.
Figure 1.1 – Ductility of a chain with brittle and ductile rings
FunDamentalS oF SeiSmic DeSign 3
! "#$ %&$' ! ! !#$ ! %&"#( ! !#( F F "#$%&' ()*+,#-./ "#$%&0#1 (23#,,-./ (( ! ) 45.36--3.789$7.: ;"<==>? ! ! ! "#$ %&$' ! ! !#$ ! %& ! !#( "#$%&'
"#$%&0#1
(( ! ) 45.36--3.789$7.: @AB=<>? ! !#$ "#( (*$( ! )+$' ! ! "#$ ! "#$ ! "#$ ! !"# $% ! !"& ! !"# '% ! !"& !CD! !#$ Fy,1 Fy,i "#$%&' ()*+,#-./ "#$%&0#1 (23#,,-./ ! ! Ring 1 (ductile) Overall response: BRITTLE Fy ! "#$ %&$' ! ! !#$ ! %& ! !#( "#$%&' ()*+,#-./ "#$%&0#1 (23#,,-./ (( ! ) 45.36--3.789$7.: @AB=<>? ! !#$ "#( (*$( ! )+$' ! Fu,
! "#$ ! "#$ ! !"# '% ! !"& !CD! !#$
Fy,
δy δu,1 = 10δy δy = δu,i Σi (δy ) ! "#$ %&$' ! ! !#$ ! %&"#( ! !#( "#$%&' ()*+,#-./ "#$%&0#1
! ! "#$%&' ()*+,#-./ "#$%&0#1
45.36--3.789$7.: ;"<==>? ! ! Fy,
Overall
DUCTILE Fy,1 ! "#$ Fu,1 Fu,1 ! !"# $% ! !"& Σi (δy ) Ring 1
δy δy = δ* δu,i Fy,i F*=Fy,1 Fy,1 < Fy,i Σi-1 (δy ) + 10δy δu,1= 10δy
a) b) c)
()*+,#-./
(23#,,-./
1
Ring ‘i’ (brittle)
1 ≥ Fy,i
(23#,,-./
(23#,,-./
1
response:
(ductile)
Ring ‘i’ (brittle)
Ring 1 (ductile) Ring ‘i’ (brittle)
1.2
As shown in Figure 1.1b, with the direct design approach the system cannot develop strength larger than F y and the ultimate elongation of the chain is given as
According to capacity design principles, in order to improve the ductility of the chain, some rings should be designed with ductile behaviour and lower strength, as is the case of ring “1” in Figure 1.1c. The remaining rings “i” that are brittle should be designed to provide a resistance Fy,i larger than the maximum resistance F u,1 exhibited by the ring “1” beyond yielding. The ductile ring “1” behaves as a sacrificial element, i.e. a ductile fuse, which filters the external actions and limits the transfer of forces into the brittle elements. Hence, the maximum force that the chain can sustain is equal to the maximum resistance F u,1 of the ductile ring “1”. It is interesting to observe that the beneficial improvement of the capacity design methodology is the increase of displacement capacity, given as follows:
Comparing equations (1.1) and (1.2), it can be easily recognized that the collapse displacement of the chain is significantly larger than that obtained by adopting the direct design approach.
This trivial example allows to understand that the brittle elements represent protected zones that must be designed to resist larger forces than those supported by the ductile elements. Those larger forces do not directly depend on the external applied loads but they are obtained from the maximum capacity of the connected ductile elements. However, it should be emphasized that the external forces are used to design the dissipative elements, which establish the threshold of structural strength.
Concerning the practical application to building structures, this methodology leads the structural designers to work on two different schemes for the same structure, as follows:
1) elastic behaviour with the calculation of the relevant internal forces FEd to design the dissipative elements. Hence, following an elastic analysis, the ductile structural elements should satisfy the following check:
SeiSmic DeSign PrinciPleS in Structural coDeS 4
∑ δδ δ == 5 uy i y (1.1)
∑ δδ δδ δδ =+ =+ = 10 41014 uy i yy yy 1 (1.2)
1.
In addition to strength, the ductile elements must possess a ductility corresponding to the chosen ductility class. The ductility is provided by using appropriate structural details and different materials and specific design principles for specific types of structures; 2) inelastic response with design of non-dissipative (i.e. brittle) elements on the basis of the plastic strength of the connected dissipative parts. Hence, in order to prevent their failure, brittle elements must be sized so that they present an over strength with respect to the capacity of the ductile elements, as follows:
where Ω is a coefficient (> 1.0) that takes into account different aspects that may lead to ductile elements strengths larger than the design ones (strain hardening phenomena, material strength larger than the nominal values, etc.).
This twofold approach is the basic characteristic of capacity design and represents the main distinctive difference with respect to direct design for quasistatic actions. The example shown in Figure 1.1 also allows understanding that the common belief of non-seismic designers, which consider that the excess of strength is always beneficial and safe, may dramatically impair the non-linear response of a structure either by overdesigning the fuse elements or, with more serious consequences, by inaccurate quality control of the material properties that results in larger strength for the dissipative elements (e.g. a steel element conceived as fuse with grade S355 is supplied with higher grade as S460). The consequence of such events is clear, namely the failure of the system because the hierarchy of resistance is not complied with.
In case of steel structures the best way to dissipate energy is to exploit the tensile capacity of the material, which can be obtained by enforcing plasticity into specific zones called plastic hinges that can involve either flexural, tensile or shear mechanisms depending on the type of adopted structural scheme (e.g. moment resisting frame, concentrically or eccentrically braced frame), while preserving the rest of the structure from damage.
FunDamentalS oF SeiSmic DeSign 5 ≥ FF ductile RdEd , (1.3)
Fbrittle ,Rd ≥ΩFductile ,Rd
(1.4)
1.2
1.2.2 Seismic design concepts
Two substantially different concepts can be used to design structures located in seismic areas, which correspond to two different structural behaviours:
Concept (a): low-dissipative (and/or non-dissipative) behaviour;
Concept (b): dissipative behaviour.
The difference between dissipative and non-dissipative behaviours is dictated by both the ductility and energy dissipation capacity that the structure can provide. The ductility represents the capacity to deform in the plastic domain without substantially reducing its bearing capacity. However, there are other properties that significantly influence the seismic performance, namely the displacement and dissipative capacity. These properties are not synonyms, but all of them contribute towards a satisfactory seismic behaviour. Some examples may be helpful to clarify the differences between ductility, displacement and dissipative capacity.
Figure 1.2 shows the load-deflection response curves of two different frames subjected to monotonically increasing horizontal loads. The maximum strength F y of the frame corresponds to the yield strength and/ or stability limit load, and the deformation capacity δ u corresponds to the sudden decrease of the strength that can be caused by the rupture of steel material, global and/or local buckling of steel members and/or crushing of concrete. Even though the strength of both frames is identical, the one with the response curve shown in Figure l.2a represents a ductile behaviour, which is substantially different from that of Figure 1.2b that corresponds to a brittle performance. Indeed, the first structure is characterized by a larger ductility μ = δ u / δ y and also a larger displacement capacity δ u , which is the capacity of the structural system to experience large ultimate displacements. Also, the amount of energy absorbed by the frame shown in Figure 1.2a before it reaches the limit deformation δ u is larger than that of the frame shown in Figure l.2b. In light of the remarks in section 1.2.1, the response of the frame shown in Figure l.2a is more efficient for an earthquake resisting structure. 1.
SeiSmic DeSign PrinciPleS in Structural coDeS 6
Figure 1.2 – Ductility of frames: a) high and b) poor displacement capacity
However, adequate seismic behaviour also depends on the shape of the cyclic response of both the structure and the dissipative zones. With this regard, Figure 1.3 shows two examples of hysteresis loops of frames under repeated horizontal load, having the same monotonic response and displacement capacity δ u. In these cases, in addition to the effects indicated above, the shape of the hysteresis loops also depends on the number of loading cycles, since deformation phenomena associated with fatigue caused by the repeated loading may have some effect on it. The frame shown in Figure 1.3a dissipates larger energy before failure than the one in Figure 1.3b, thus providing a better seismic performance, the energy being the area within a loop. Hence, dissipative capacity can be defined as the ability to dissipate energy by means of stable and compact hysteretic loops.
Ductile and dissipative structures are very convenient because they avoid brittle phenomena and lead to less expensive constructions. In order to exploit the ductility, ductile structures are generally designed to resist seismic forces substantially smaller than those needed to obtain an elastic response
FunDamentalS oF SeiSmic DeSign 7 Fy Fy θlocal θlocal > θglobal δy δy δu θglobal δu a) b)
1.2
under seismic action corresponding to the Ultimate Limit State (ULS). However, plastic deformations imposed by the seismic action must not exceed the deformation capacity of the structure in the plastic domain, in order to prevent excessive damage that may compromise the stability against gravity loads and/or make unfeasible a subsequent refurbishment. Thus, the minimum strength F y of the structure against lateral forces that is needed to avoid excessive damage is directly related to the structure’s deformation capacity in the plastic domain. For the ULS seismic action, different strength/ductility combinations can be determined that satisfy the design demands.
1.3 – Dissipative capacity of frames: a) high and b) poor energy absorption
The fundamental relationship between the strength of the structure to lateral forces ( F y) and the displacement demand ( δ Ed) imposed to the structure by a given level of the seismic action is presented in Figure 1.4a.
SeiSmic DeSign PrinciPleS in Structural coDeS 8
Fy δu δy a) b) Fy δu δy
Figure
1.
For the same the same displacement capacity, the lower is the strength of the structure to lateral forces ( F y), the higher is the ductility demand ( μEd,i = δ Ed / δ y,i) imposed to the structure. Thus, the more ductile and dissipative structures may be designed to lower lateral forces that can be determined by scaling the elastic forces by the so-called behaviour factor q, which strictly depends on the structural system (see Figure 1.4b).
1.4 – Strength vs. displacement demand relationship
Modern codes like EC8-1 give the possibility to choose different ductility levels for a structure, providing different ductility classes. It is understandable that choosing a ductility class instead of another has direct consequences on the design process. In case of EC8-1 there are at least two major features. The first is the value of the design seismic load, which is obtained by scaling the elastic design forces by a behaviour factor q (see Figure 1.4b). The structures
FunDamentalS oF SeiSmic DeSign 9
Fy,3 Fy,2 Fy,1 Fel elastic response inelastic response δy,3 δu,3 δu,2 δu,1 δy,1 δy,2 δEd μ3,Ed μ2,Ed μ1,Ed a) b) Fel elastic
seismic
elastic
design
seismic
capacity FEd
q δy δEd δu
response
force
domain
seismic force inelastic domain
demand system
= Fel /
Figure
1.2