Blast Effects on Buildings, 2nd Edition-D. Cormie

Progressive collapse of structures

Copyright © ICE Publishing, all rights reserved.

To Misuk, Rudi, Leo, Enno, and Lisa


To Misuk, Rudi, Leo, Enno, and Lisa



Uwe Starossek Hamburg University of Technology


Published by Thomas Telford Limited, 40 Marsh Wall, London E14 9TP. www.thomastelford.com

Distributors for Thomas Telford books are USA: ASCE Press, 1801 Alexander Bell Drive, Reston, VA 20191-4400 Australia: DA Books and Journals, 648 Whitehorse Road, Mitcham 3132, Victoria

Also available from Thomas Telford Limited Blast Effects on Buildings , second edition, edited by David Cormie, Geoff C. Mays and Peter D. Smith, ISBN: 978-0-7277-3521-8 Forensic Engineering: From failure to understanding , 4th International Conference on Forensic Engineering, edited by Brian S. Neale, ISBN: 978-0-7277-3613-0 Modern Structural Analysis: Modelling process and guidance , by Iain A. MacLeod, ISBN: 978-0-7277-3279-8

Cover photograph of the partial collapse of the Charles de Gaulle Airport Terminal in 2004 — an example of a structural failure which did not lead to progressive collapse owing to structural segmentation. Image courtesy of AP/Press Association Images. First published 2009 A catalogue record for this book is available from the British Library ISBN: 978-0-7277-3610-9 # Thomas Telford Limited 2009

All rights, including translation, reserved. Except as permitted by the Copyright, Designs and Patents Act 1988, no part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying or otherwise, without the prior written permission of the Publisher, Thomas Telford Limited, 40 Marsh Wall, London E14 9TP. This book is published on the understanding that the author is solely responsible for the statements made and opinions expressed in it and that its publication does not necessarily imply that such statements and/or opinions are or reflect the views or opinions of the publishers. While every effort has been made to ensure that the statements made and the opinions expressed in this publication provide a safe and accurate guide, no liability or responsibility can be accepted in this respect by the authors or publishers.

Typeset by Academic þ Technical, Bristol Printed and bound in Great Britain by Antony Rowe Limited, Chippenham Index created by Indexing Specialists (UK) Ltd, Hove


Contents Preface

ix

1 1.1 1.2 1.3 1.4

Introduction Opening Failure incidents State of research Standards and guidelines

1 1 2 5 7

2 2.1 2.2 2.2.1 2.2.2 2.2.3 2.2.4 2.2.5 2.2.6 2.3 2.4 2.4.1 2.4.2 2.4.3 2.4.4 2.4.5 2.4.6 2.4.7 2.5

Typology of progressive collapse General Types of progressive collapse Pancake-type collapse Zipper-type collapse Domino-type collapse Section-type collapse Instability-type collapse Mixed-type collapse Classes of progressive collapse Collapse-promoting features Dynamic action and force concentration Brittle material behaviour Overstrength and ductile material behaviour Continuity or discontinuity Series or parallel load transfer Spatial orientation, size, and slenderness Structuredness Summary

11 11 12 12 14 16 18 20 23 25 25 25 26 26 27 28 28 29 30

3 3.1 3.2

Current design procedures Inadequacy of current procedures Possible improvements

32 32 34

v


4 4.1 4.2 4.2.1 4.2.2 4.3 4.3.1 4.3.2 4.3.3 4.3.4

Design against progressive collapse General Two definitions Robustness Collapse resistance Design criteria Design requirements Design objectives Design methods Verification procedures

37 37 38 38 39 40 40 42 47 48

5 5.1 5.2 5.2.1 5.2.2 5.2.3 5.3 5.3.1 5.3.2 5.3.3 5.3.4 5.3.5 5.4 5.5

Design methods General Prevent local failure Specific local resistance Non-structural protective measures Discussion and further remarks Assume local failure General Alternative load paths Isolation by segmentation Redundancy versus segmentation Interaction and progressive collapse Local failure: prevent or assume? Prescriptive design rules

52 52 55 55 55 56 58 58 59 62 71 77 80 83

6 6.1 6.2 6.2.1 6.2.2 6.2.3 6.2.4 6.2.5 6.3 6.3.1 6.3.2 6.3.3 6.3.4 6.3.5 6.3.6

Applications General Design of collapse-resistant bridges General Continuous girder bridges Cable-stayed bridges Suspension bridges Arch bridges Design of collapse-resistant high-rise buildings General Specific local resistance Non-structural protective measures Alternative load paths Isolation by segmentation Fire protection, fire fighting, and evacuation

vi


86 86 87 87 88 89 97 99 99 99 100 112 113 114 121

7 7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8

Measures of robustness and collapse resistance General Areas of application Requirements Present approaches Stiffness-based measures of robustness Damage-based measures of robustness Energy-based measures of robustness Summary and future directions

123 123 123 124 125 126 127 130 131

8 8.1 8.2

Conclusions Synopsis Outlook

133 133 137

References

139

Index

147

vii



Preface I became involved with the topic of this book 16 years ago, when, as a practising engineer involved in the design of the Confederation Bridge, Canada, I was charged with the progressive collapse analysis and design of that structure. Apart from a few papers, mostly on the Ronan Point incident, and some references in building codes, little was known about progressive collapse at that time. This was a blessing in disguise, however, because my colleagues and I at J. Muller International, San Diego, were free to develop our views and approaches almost from scratch. I have remained involved with this topic ever since. When entering academia a few years later, I had the time to reflect on the previous project-related work and to develop it further into a more formalised and generally applicable concept. Progressive collapse is arguably the most dramatic and feared form of failure in structural engineering. It usually occurs unexpectedly and causes high losses. Although there has been an awareness for a long time that such failures can occur, this has barely been reflected, until recently, in a professional effort commensurate to the problem. Since the bombing of the Alfred P. Murrah Federal Building in 1995, and even more so since the events of 11 September 2001, research on progressive collapse has clearly intensified. Nevertheless, most publications only focus on particular aspects of the problem, and there is still no generally accepted use of nomenclature and procedures. The standard provisions that exist today lack general applicability. This book attempts to close that gap. Its purpose is to give a plain and comprehensive introduction to the phenomenon of progressive collapse, to offer a consistent and generally applicable set of nomenclature and procedures, to provide guidance to the practicing engineer in both a systematic and pragmatic manner, and to give an outlook on future developments. Because the book is self-contained and requires only a basic understanding of structural analysis and design, it is also ix


suitable and, I hope, particularly educational for advanced undergraduate and graduate students. The book is based on a previous contribution to Betonkalender 2008, a yearbook popular among German-speaking structural engineers. Thanks are due to Konrad Bergmeister, the editor who had invited me to contribute, and to Ernst & Sohn Verlag, Berlin, the publisher who has allowed the use of this previously published material. Furthermore, I would like to gratefully mention a few individuals who helped shape my early understanding of the problem, namely Gerard Sauvageot, Jean Muller, Paul Mondorf, Daniel Tassin, and Gamil Tadros. More recently, discussions with Bob Smilowitz, Mohammed Ettouney, Franco Bontempi, and Luisa Giuliani have influenced my views in one way or another, which is also appreciated. Special thanks are extended to Hyun-Moo Koh, my host at Seoul National University. During my sabbatical stay there, the collapse typology presented in this book came into being. Warm thanks are also due to his graduate student Yong-Suk Park for our discussions on bridge collapses. I would like to thank my students at Hamburg University of Technology, most notably Maren Wolff and Marco Haberland, who were involved in some of the studies reported here. Moreover, they have read various parts and versions of the manuscript and helped to improve its clarity and correctness. The latter also applies to my brother Bernd Starossek. Thanks are also due to Deima Aslan and Todd Parry for helping with preliminary translations of some parts of the book, and to Axel Seils for preparing most of the illustrations. Finally, it is a great pleasure to acknowledge my indebtedness to the one person without whom this project would not have been realised. Stuart Alexander encouraged me to submit the proposal for this book to Thomas Telford Ltd, and was instrumental in getting it accepted and bringing it to print. He reviewed the entire manuscript, and not only helped straighten out my English but also made many invaluable and helpful comments on the contents. Any remaining errors or misconceptions are my own. Wholehearted thanks go to my wife Misuk and our children for their patience during the work on this book. Uwe Starossek

x


1 Introduction 1.1

Opening

If there is a pronounced disproportion between a comparatively minor event and the ensuing collapse of a major part or even the whole of a structure, then this is a disproportionate collapse. When the collapse commences with the failure of one or a few structural components and then progresses over successive other components, a fitting label would be progressive collapse. Although the two terms are often used interchangeably, a distinction can be made. The term ‘disproportionate collapse’ is more appropriate in the context of design and performance because a precise definition of ‘disproportionate’ requires the choice of design objectives (see Section 4.2.2). When referring to the physical phenomenon and mechanism of collapse, on the other hand, the term ‘progressive collapse’ is more suitable. Nevertheless, disproportionate collapse mostly occurs in a progressive manner. The main subject of this book, therefore, is progressive disproportionate collapse or, for short, progressive collapse. The nature of the triggering event is irrelevant to the qualitative definition of disproportionate collapse given above as well as to the quantitative definition discussed later. It can be a local action or a local lack of resistance. Thus, the term ‘event’ includes all types of potential triggering circumstances. Since these occur with a low probability or even wholly unexpectedly, they are called accidental circumstances. Traditionally, this term referred more to events like accidents and natural disasters or design and construction flaws. In the light of emerging new threats, however, it nowadays also includes deliberate damage inflicted by explosion and other kinds of malicious action. Different structures are susceptible to progressive collapse to different degrees. Such differences remain unrecognised, though, even in modern verification procedures using partial safety factors. This follows, in particular, from not factoring in the structural response to an initial local 1



failure. Additional considerations are therefore necessary concerning both the initial local failure and the ensuing response of the structure. Such considerations have in the past been made only in isolated cases — such as for embassy buildings or very long bridges, that is, for obviously exposed or susceptible structures — and for the most part at the discretion of the design engineer. Codified procedures did not exist until recently; and those that exist today lack general applicability. The design measures resulting from such considerations can either aim at increasing the level of safety against local failure or at limiting the total damage following local failure. Structures that are insensitive to local failure, which is denoted by a limited extent of total damage, are here termed robust. For preventing disproportionate collapse, as per the definition above, what ultimately is required, however, is not insensitivity to local failure, that is, robustness, but insensitivity to accidental circumstances — a property for which the term collapse resistance is introduced here. Collapse resistance can be achieved through robustness, but also by other means. Robustness and collapse resistance are key terms that will be defined more precisely later (Sections 4.2.1 and 4.2.2). Disregarding a possible susceptibility to progressive collapse in structural design can be associated with such major disasters as the collapses of the Alfred P. Murrah Federal Building (Oklahoma City, 1995) and the twin towers of the World Trade Center (WTC) (New York, 2001), as well as with a large number of less dramatic failures. Hence the potential risk is high. Progressive collapse seems comparable in this regard to earthquakes and other natural disasters. A further common feature shared with earthquakes is the importance of dynamic forces. On the other hand, the problem considered here is clearly differentiated from the problems of seismic engineering by the diversity of the triggering circumstances and the large variety of possible collapse scenarios. In the rest of this introductory chapter, first a few incidents of structural failure are presented where accidental circumstances led to varying degrees of collapse. This is followed by an account of the current states of research and standardisation in the field of progressive collapse. A detailed discussion of the theoretical and practical aspects of this problem is given in Chapters 2 to 8.

1.2

Failure incidents

Naturally, structural failure provides the strongest impetus for investigating the present problem. Accounts and investigations of incidents 2


Introduction

of failure can also be an important basis for research. Corresponding publications are relatively scarce, however, and often lack the detail required for scientific utilisation. Wearne1 portrays a number of failure incidents of recent years, ranging from Ronan Point (a high-rise building in London, 1968) to the Sampoong Superstore (a department store in Seoul, Korea, 1995). The courses of failure described are characterised by sensitivity to local failure, and can mostly be identified as progressive collapses. The triggering events include design and construction flaws (Sampoong Superstore), accidental gas explosion (Ronan Point), bomb attack, and a multitude of other circumstances. An abundance of failure cases of bridges, buildings, and other structures is described in detail and discussed by Scheer,2 occasionally referring to lack of structural robustness as a concurring cause of collapse. Again, the triggering events are manifold. The Viadotto Cannavino, a four-span continuous girder bridge in Italy, partially collapsed during construction in 1972.3 The triggering event was a formwork failure. The ensuing collapse was facilitated by a lack of structural robustness, at least at that particular stage of construction. Another progressive collapse occurred during the construction of the Haeng-Ju Grand Bridge, a continuous prestressed concrete girder bridge in Seoul, Korea, in 1992. Presumably after the failure of a temporary pier in the main span — the triggering event and the exact location of the initial failure have not yet been officially determined — the collapse progressed through the adjacent ten spans, and an 800 m section of bridge was lost.2 4 In both cases, the continuous prestressing tendons in the superstructure of the bridge played a specific and disastrous role. When the Haeng-Ju Grand Bridge collapsed, most tendons resisted the enormous stresses caused by the rupture of the encasing concrete and the failure and fall of structural components.4 The high degree of strength or toughness of the material, coupled with the continuity of the tendons over the length of the bridge, worked against the robustness of the structure. A chain reaction ensued where the forces transmitted by the tendons led to the collapse of all 11 continuous spans between transition joints. Remarkably, it did not progress further into the other spans. A classification of the type of collapse is attempted in Section 2.2.6. A different course of events developed during a failure incident affecting the Tasman Bridge near Hobart, Australia, in 1975.2 5 6 Due to the impact of a 7200 t ore carrier, two piers of the bridge were destroyed, and three spans of deck supported by them collapsed. The ;

;

;

3



other 19 spans remained intact. The bridge deck was made of precast prestressed concrete beams. The absence of collapse progression and thus the robustness of that bridge are apparently related to the discontinuity of prestressing tendons between adjacent spans. Interestingly, preventing progressive collapse was an original design intent. Hence even though the deck slab was continuous over the supports, the longitudinal concrete reinforcing bars in the slab were interrupted there and locally spliced with light reinforcement of limited well-defined yield stress. Furthermore, the diaphragms over the supports were split in half and the splitted parts were connected by keyed joints — a measure that allowed the transfer of compression and shear but not of tension.6 These observations on the occurrence and non-occurrence of progressive collapse of bridges hint at the possible effectiveness of structural fuses and segmentation — design approaches that are studied further in Sections 2.4.3 and 5.3.3. The collapse of the I-35W Mississippi River Bridge in Minneapolis in 2007, on the other hand, has been ascribed partly to the lack of alternative paths for load transfer.7 Alternative load paths, if present, are activated when forces that were carried by failing structural components are redistributed into the structure. Because they require continuity, this case indicates that structural robustness can increase with the degree of continuity. This contrasts with the conclusions reached in the previous cases. The resolution of this apparent paradox requires a quantification of robustness — as will be made later in Section 4.2.1. Prendergast8 reports on the partial collapse of the Alfred P. Murrah Federal Building in Oklahoma City in April 1995. It was triggered by the detonation of a truck bomb outside the building. The high degree of destruction, and the large number of casualties, are attributed to insufficient structural redundancy, that is, to a lack of alternative paths. Every second exterior column was indirectly supported by a continuous transfer girder at the second floor instead of extending to the foundation. In the corresponding Federal Emergency Management Agency report9 and in Ref. 10, this and other particularities of design and weakness of the structure are exposed, and recommendations for structural design are derived from them. Among other provisions, concrete reinforcement continuity is recommended to prevent the fall of failed floor slabs. In the light of some of the other failure incidents described above, an undifferentiated and overall increase in continuity does not automatically enhance the robustness and collapse resistance of a structure and, in certain cases, can even be harmful. This recommendation, 4


Introduction

therefore, deserves further examination (see Sections 5.3.4, 5.3.5, and 5.5). In terms of tragedy and loss, the above-mentioned incidents are far exceeded by the collapse on 11 September 2001 of the twin towers of the WTC. The impacts of the aircrafts and the subsequent fires led to local damage. The ensuing loss in vertical load-carrying capacity extended, however, over the complete cross-section of each tower. The upper part of the structure started to fall. Its collision with the lower part caused large impact forces, which resulted in the complete loss of vertical load-carrying capacity in the area of impact. Failure progressed in the same manner, and led to total collapse.1116 The mechanism of collapse is further described in Section 2.2.1 in connection with a classification of the type of collapse. The progressive collapse of the neighbouring WTC Building 7 was triggered by the fires that followed the impact of debris from the collapse of the north tower (WTC 1). The sequence of collapse seems to have been more complex in that the failure progressed in both the horizontal and vertical directions and involved various mechanisms of collapse.17

1.3

State of research

Progressive collapse has, time and again, been a topic of research and, on a few occasions, the focus of conferences.18 19 The publications address specific aspects of the phenomenon or its occurrence in particular kinds of structures.2025 Further contributions consider specific actions that can trigger a progressive collapse, such as fire26 or impact and blast loading.27 28 Yokel et al.29 examine the design of the US embassy building in Moscow in terms of susceptibility to progressive collapse. They compare analysis methods, consider alternative load paths, and recommend measures to increase the collapse resistance. Other project-related papers centre on the design of the 12.9 km-long Confederation Bridge, Canada,3034 discussing the possibility of a collapse progressing over many spans of the bridge and the corresponding design countermeasures. The publications mentioned so far deal with specific projects or particular kinds of structures under specific triggering actions. They are independent of each other and do not lay the groundwork for a comprehensive theory of progressive collapse. The approaches, results, and recommendations vary from case to case. A comprehensive account of the phenomenon of progressive collapse and the derivation of general rules for design and verification have rarely ;

;

5



been attempted. Leyendecker and Ellingwood35 suggest that progressive collapse should be prevented either by providing alternative paths or by increasing the local resistance of the key elements of the structure (specific local resistance). Gross and McGuire36 also compare design methods for avoiding progressive collapse. They recommend verification of the strength of a structure after notionally removing selected elements, and thus also embrace the engineer-like deterministic approach of providing alternative paths. Examples of possible detailing solutions for the design of so-called insensitive structures are given by KerskenBradley.37 Ideas for enhancing robustness — applying this term not only to strength but also to serviceability and durability — are presented by ¨tzl.38 First efforts towards probabilistic verification procedures in line Po with reliability theory are made in Refs 39—42. Progressive collapses mostly involve dynamic effects induced by local failure and failure progression. Such effects are not yet considered in the papers mentioned in this paragraph. Since the events of 11 September 2001, research into progressive collapse has been intensified and more closely coordinated.4346 The intention to address all open questions, to define objectives for research and codification, and to develop a collective research programme becomes clear in the Multihazard Mitigation Council report43 that contains the contributions of a workshop held in 2002. In contrast to earlier publications, a number of aspects are now emphasised: the necessity of establishing performance expectations as part of the design criteria; a differentiation of requirements on collapse resistance and accuracy of verification procedures depending on significance and exposure of the structure (tiered approach); a distinction between prescriptive design rules (indirect design) that can be implemented quickly — such as the requirement of continuity of reinforcement — and more elaborate methods that are based on design criteria and structural analysis (direct design, performance-based design). The need to verify and improve the analysis tools is also pointed out. As for verification, analytical comparisons with full model tests, with structures that did not collapse despite serious damage, and with controlled demolition of structures are suggested. The present state of research is reflected in three special editions of relevant professional journals. Articles concerning explosive blast loading and the corresponding local and global failure mechanisms can be found in a 2005 issue of the Journal of Structural Engineering .47 The focus is on that particular triggering action and on the analytical or experimental determination of the structural response. The article 6


Introduction

by Hayes et al.48 pursues the question of whether a design that meets seismic requirements at the same time provides a higher resistance to explosion-triggered progressive collapse. An overview of current problems and methods of resolution is given by a 2006 issue of the Journal of Performance of Constructed Facilities.49 Strategies for analysis and verification as well as design methods are investigated, partly in connection with case studies. The problem of impact loading caused by separated and falling structural components now attracts more attention.50 51 Controlled demolition experts also have their say.52 Even though their goal is the opposite of preventing collapse, they provide some interesting insights into the structural behaviour under extreme actions and impact loading. Only one out of 12 papers argues for an application of the probabilistic theory of reliability, albeit without addressing the problems identified in Chapter 3 of this book. A workshop organised by the Joint Committee on Structural Safety and the Building Research Establishment in 200546 focused on the robustness of structures with regard to progressive collapse; selected contributions appeared in revised form in a 2006 issue of Structural Engineering International.53 While some of these articles are concerned with particular kinds of structures and specific actions, others5458 strive for a fundamental understanding of progressive collapse. One way into the problem is to examine the robustness of a structure or its complementary property, called vulnerability. Various definitions of robustness and vulnerability are suggested, and how these properties could be quantified and computed is investigated. These approaches are discussed further in Chapter 7. ;

1.4

Standards and guidelines

The requirement of structural resistance to progressive collapse is not yet incorporated in structural design codes in a consistent and effective manner. The CEB-FIP Model Code 199059 states in its very first paragraph: ‘1.1.1 General requirements: Structures should with appropriate degrees of reliability, during their construction and whole intended lifetime, perform adequately and more particularly: (a) withstand all actions and environmental influences, liable to occur, (b) withstand accidental circumstances without damage disproportionate to the original events (this is called the insensitivity requirement).’ Requirement (b) calls for collapse resistance in the qualitative sense as introduced in Section 1.1. Thus, the problem at hand is openly and 7



correctly addressed, although in quite general terms. The practical impossibility of completely precluding damage from accidental circumstances is accepted here. It is required, however, that such damage is limited. Further rules for design and verification are not specified. The implementation of these requirements in a particular construction project is up to the discretion and capability of the design engineer and the consent of the owner. Eurocode EN 199060 does not, apparently, go much further by stressing that the failure of one structural component shall not lead to the collapse of the entire structure. Nevertheless, this requirement now calls for robustness, instead of collapse resistance, in the qualitative sense as introduced in Section 1.1. It is in line with the American Society of Civil Engineers (ASCE) 7-02 guideline61 that states: ‘buildings and structural systems shall possess general structural integrity, which is the quality of being able to sustain local damage with the structure as a whole remaining stable and not being damaged to an extent disproportionate to the original local damage’. The term ‘general structural integrity’ thus defined corresponds to robustness as understood here. Such a qualitative requirement has also been included in the German DIN 1055-100 standard. 62 Structural integrity is also called for in the American Association of State and Highway Transportation Officials specifications,63 together with the recommendation to consider ‘the use of continuity and redundancy to provide one or more alternate load paths’ and ‘external protection systems to minimise the effects of reasonably conceived severe loads’ (see Section 1.1.2 of Ref. 63). More precise rules for design and verification have been specified to date only for particular kinds of structures such as buildings and cablestayed bridges. For design of the latter, the Post-Tensioning Institute recommendations64 state that the loss of any one cable shall not lead to ‘structural instability’. For the verification of such conditions, it is recommended that cable loss should be assumed to occur suddenly so that an impulsive dynamic loading is produced. Similar recommendations are made in guidelines issued by the International Federation for Structural Concrete.65 Concerning more precise code rules for building design, the British standards have a long tradition that started with the Ronan Point incident. Moore66 gives a survey of their historical and current development, focusing on accidental actions. The most recent British provisions can be found in Approved Document A.67 Buildings are classified according to the consequences of a collapse. The design requirements and applicable design methods differ for the various classes. They 8


Introduction

consist of prescriptive design rules (ties), provision of alternative paths, and application of a specified accidental design loading to key elements to increase their local resistance. These methods are further detailed in BS 595068 for the design of steelwork in buildings and in BS 811069 for the design of concrete structures, respectively. Eurocode EN 1991-1-770 specifies design actions and describes methods of computation for selected accidental circumstances like internal explosions and vehicle impact. Annex A of that standard strongly resembles Approved Document A.67 Its applicability is likewise limited to buildings and stadia. Annex B provides guidance for performing a risk assessment, as it is required for the design of buildings of the highest consequences class. A detailed comparison between Eurocode EN 1991-1-7 and the current UK standards with respect to provisions on accidental actions and progressive collapse can be found in a Department for Communities and Local Government guide.71 Building design guidelines in the USA and Canada are critically assessed by Dusenberry and Juneja.72 Even when progressive collapse or the need for robustness is mentioned — in particular in the Canadian code,73 the ASCE 7-02 guideline,61 and the American Concrete Institute Committee 318 requirements74 — it is done so without providing much practical guidance. Precise and binding design rules, where given, are of a prescriptive nature and limited to the detailing of concrete reinforcement and connections. The design objectives are not quantified, and applicable design methods and verification procedures are not specified. Nevertheless, arguably the most detailed rules for designing collapse-resistant buildings, although not for the private sector, have been codified and are in use in the USA. In the General Services Administration guidelines for federal office buildings75 and in the United Facilities Criteria for Department of Defense projects,76 requirements are defined and provisions for design and verification are made. The latter includes prescriptive design rules and performance-based design based on structural analysis. Efforts are currently under way to revise both guidelines and to combine them into a single document that applies to all building projects of the US federal government and armed forces.77 The National Institute of Standards and Technology (NIST) issued the report Best Practices for Reducing the Potential for Progressive Collapse in Buildings.78 This document reviews progressive collapse provisions in various national design codes, but is not intended as a design code itself. It is directed towards owners and practising engineers. Practical means 9



for reducing the likelihood of progressive collapse of buildings are presented and design methods for enhancing the resistance to progressive collapse are reviewed. Based on the NIST investigation of the WTC disaster,12 17 changes are being incorporated in the 2009 editions of the International Building Code79 and the International Fire Code.80 These changes focus on fire protection, fire fighting, and evacuation, and not on structural design. New design guidelines for private sector buildings in the USA are being prepared by the Progressive Collapse Standards and Guidance Committee that was formed by the Structural Engineering Institute of the ASCE. Meanwhile, a so-called PreStandard Prospectus81 has been presented that delineates the intended scope and the basic approach of the new guidelines, the publication of which is expected in 2010. 82 The PreStandard Prospectus refers to an article55 by the author when distinguishing between robustness and collapse resistance, although a somewhat different use is made of these terms than set forth in Ref. 55 and in this book. ;

10


2 Typology of progressive collapse 2.1

General

Progressive collapse of structures is typically characterised by a disproportion between a small triggering event and the resulting collapse of a major part or even the whole of the structure. Although the disproportion between cause and effect is a defining and common feature, there are various differing mechanisms of collapse that produce such an outcome. The amenability to conceptual, theoretical, and computational treatment can vary accordingly. Collapse-promoting features, possible or preferable countermeasures, and the suitability of indices for quantifying robustness and collapse resistance will likewise depend on the mechanism of collapse. Finally, different kinds of structures are susceptible to different mechanisms of collapse. It is thus useful to distinguish and describe the different types of progressive collapse and to attempt a classification on that basis.83 In the subsequent sections, six different types of collapse and, at a higher level of abstraction, four classes of collapse are identified. The characteristic features of each category are described and compared, and a terminology is suggested. As an example of how the basis offered here can be applied and used for further study, collapse-promoting features and possible countermeasures are discussed with respect to the various types of collapse. Some insight into possible design methods follows from this discussion. Furthermore, the description of the types of collapse gives hints to a number of analogies that should be pursued further. The term propagating action used in the subsequent discussion refers to the action that in the course of a progressive collapse results from the failure of one structural component and leads to the failure of one or more further structural components. Collapse-promoting features can be deduced, in particular, from an examination of the propagating action. They are material related or inherent to the structural system. Some hitherto little-noticed features can be extracted in this way. 11



2.2

Types of progressive collapse

2.2.1 Pancake-type collapse This type is exemplified by the collapse of the World Trade Center (WTC) towers. The impacts of the aircrafts and the subsequent fires led to damage and resulted in local failures in the areas of aircraft impact. The ensuing loss in vertical load-carrying capacity was limited to a few storeys but extended over the entire cross-section of each tower. The upper part of the structure started to fall and to accumulate kinetic energy. The subsequent collision with the lower part, which was still intact, caused large impact forces that were far beyond both the design and actual reserve capacities of the structure. This structural impact thus again led to the loss of vertical load-carrying capacity over the entire cross-section of the tower in the area of impact. Failure progressed in the same manner and led to total collapse.11—16 (Dissenting explanations were suggested84,85 but have not found general acceptance.) The term suggested for this type of collapse originates from the appearance after collapse of buildings smaller than the WTC towers (Fig. 2.1). Their potential energy is smaller, and hence less destruction occurs when compared with the WTC towers. The floor slabs of these buildings thus pile on top of each other, resembling a stack of pancakes. The mechanism of a pancake-type collapse exhibits the following features:

Fig. 2.1 Pancake-type collapse of a ten-storey building triggered by an earthquake (Islamabad, 2005)

12


Typology of progressive collapse .

.

. .

.

.

initial failure of vertical load-bearing elements (i.e. elements that are vertically aligned and carry vertical loads) separation of structural components and their fall in vertical rigid-body motion transformation of gravitational potential energy into kinetic energy impact of separated and falling components on the remaining structure failure of other vertical load-bearing elements due to the axial compression forces that result from the impact loading failure progression in the vertical direction.

Characteristic features are, in particular, the separation of structural components (including non-load-bearing elements), the release of gravitational energy, and the occurrence of impact forces. Depending on the size of the falling components and the height of fall, the gravitational potential energy released during the fall can far exceed the elastic potential energy (strain energy) stored in the structure. If that energy is reintroduced into the structure in a subsequent impact, large internal forces ensue. Due to the dynamic nature of impact, they tend to concentrate in the load-bearing elements directly affected by the impact. (Otherwise, the progressing failure fronts observed in the WTC towers would be difficult to explain.) The failure progresses when these forces cause the impacted elements to fail as well. Their actual failure can be associated with any local failure mode, including instability (buckling). The propagating action is the vertical impact force. Another feature of interest is that the principal forces in the failing elements (before the onset of collapse), the propagating action, and the direction of failure progression are all vertical and thus parallel. Furthermore, the structural system is characterised by series primary load transfer. The principal forces, the propagating action, and the direction of failure progression being parallel to each other is related to the primary load transfer being serial. An alternative mode of pancake-type collapse, in which only the floors or the cantilever floors of a building fail in a vertical failure progression, is described in Section 6.3.2.3. Some important features of such a collapse deviate from the description given above. Separation of components can be partial instead of complete. Their fall does not need to occur in a purely vertical rigid-body motion but can also be associated with rotation. Furthermore, element failure is due to bending or shear instead of axial compression and the failing elements are not 13



linked through collective series load transfer. Such a collapse, although limited to a building corner, occurred during the Ronan Point incident (see Fig. 5.18). This alternative mode of pancake-type collapse exhibits some features of the domino-type collapse described in Section 2.2.3. More detailed discussion is left for future work.

2.2.2 Zipper-type collapse For the design of cable-stayed bridges, the Post-Tensioning Institute recommendations64 require that the loss of any one cable shall not lead to structural instability. To prevent such an outcome, it is recommended that loss-of-cable load cases be included in the structural analysis. This requirement is intended, among other things, to prevent a zipper-type collapse triggered by the initial failure of a single cable and progressing due to the resulting overloading and failure of adjacent cables (see Section 6.2.3 for further discussion). Such a failure progression, albeit in a suspension bridge, can be observed in the footage of the collapse of the original Tacoma Narrows Bridge in 1940. After the first hangers snapped due to excessive windinduced distortions of the bridge girder,86 the entire girder peeled off from the hangers and suspension cables, and fell (Fig. 2.2).

Fig. 2.2 Zipper-type collapse of the Tacoma Narrows Bridge, triggered by windinduced vibrations (Washington, 1940)

14


Typology of progressive collapse

A similar mechanism of collapse can be envisaged in anchored retaining walls, where progressive collapse could be initiated by the failure of one or a few anchors.87 The UK Standing Committee on Structural Safety has drawn attention to a number of collapses of heavy acoustic ceilings in cinemas and other buildings that seem to correspond to zipper-type collapses triggered by the failure of one or a few inadequate fixings to the supporting structure.88 In the examples just given, zipper-type collapse is related to the initial failure of tension elements. This, however, is not a necessary condition. Before identifying further possible cases, some characteristics of this type of progressive collapse will be specified. The mechanism of a zipper-type collapse exhibits the following features: . .

.

.

.

. .

initial failure of one or a few load-bearing elements redistribution of the forces carried by these elements into the remaining structure impulsive dynamic loading due to the suddenness of the initial failure and redistribution of forces dynamic response of the remaining structure to that impulsive dynamic loading concentration of forces in load-bearing elements that are similar in type and function to and adjacent to or in the vicinity of the initially failing elements due to the combined static and dynamic structural response to that failure overloading and failure of those elements failure progression in a direction transverse to the principal forces in the failing elements.

Characteristic features are, in particular, the redistribution of forces into alternative load paths, the impulsive loading due to sudden element failure, and the concentration of static and dynamic forces in the next elements to fail. The propagating action resulting from the failure of an element is the negative of the sectional forces in that element prior to failure acting as step impulsive loadings on the faces of the ruptured cross-section (or possibly at the ends of the failing element in the case of buckling). Impact forces, on the other hand, do not typically occur — in contrast to the pancake-type collapse discussed previously. Another interesting difference is that now the principal forces in the failing elements (before the onset of collapse) and the propagating action on the one hand and the direction of failure progression on the other are not parallel but more or less orthogonal. This corresponds 15



to the structural system being characterised by rather parallel instead of series primary load transfer. Failure progression occurs when the alternative paths, which in principle can form, and in reality do tend to form, in such a system, become overloaded and fail. Other cases exhibiting the features listed above can be envisaged: a cable net or membrane structure that unzips following the occurrence of local damage; a continuous girder in which one span fails in bending leading to overloading and failure in bending of adjacent spans; or a continuous girder supported by slender columns in which one column fails leading to overloading and failure of adjacent columns. Also for zipper-type collapse, element failure can be associated with any local failure mode, including instability (buckling).

2.2.3 Domino-type collapse A row of dominoes collapses in a fascinating chain reaction when one piece falls at the push of a finger. The mechanism behind this type of collapse is as follows: . .

. .

.

.

.

initial overturning of one element (i.e. of one domino) fall of that element in an angular rigid-body motion around a bottom edge transformation of gravitational potential energy into kinetic energy lateral impact of the upper edge of the overturning element on the side face of an adjacent similar element the horizontal pushing force transmitted by that impact is of both static and dynamic origin because it results from both the tilting and the motion of the impacting element overturning of the adjacent element due to the horizontal pushing force from the impacting element failure progression in the overturning direction.

The occurrence and the importance of impact forces suggest a relationship with the pancake-type collapse. On the other hand, the principal forces in the failing elements — which are generally gravityinduced — are now orthogonal to the direction of failure progression, and the elements constitute a parallel load transfer system (at least before the onset of collapse) — two properties that are also shared by the zipper-type collapse (although in that case they hold for the system after the onset of collapse as well). It thus appears reasonable to distinguish the domino-type collapse from the previously discussed types. 16



A characteristic and distinguishing feature is the overturning of individual elements. Another peculiarity is related to the propagating action, which here is the horizontal pushing force that leads to the overturning of the next element. The principal forces in the failing elements (before the onset of collapse) are vertical. Thus, in contrast to the previously described types of collapse, the principal forces and the propagating action are not parallel. A domino-type collapse thus exploits a particular weakness of the structure towards forces that do not act in the direction of the principal forces. Any group of individual structures that are susceptible to overturning and are placed in a repetitive horizontal arrangement, similar to a row of dominoes, could collapse in such a manner. Susceptibility to overturning implies a certain degree of slenderness of the individual structures and a lack of bracing. Such conditions could occur, for instance, in a row of temporary scaffolding towers or in multi-span bridges if the pier height exceeds the span length. Another case exhibiting most of the features listed above is the progressive collapse of the towers of overhead transmission lines, which have occasionally occurred in a number of countries, sometimes ¨nster, on an extremely large scale.89 In such an incident near Mu Germany, in 2005, more than 50 towers were affected. To include such cases of collapse in the domino-type category, two amendments are necessary to the above list of features. First, it is conceded that the lateral impact of an element onto an adjacent element can also be indirect, that is, mediated by other, different elements. For the case just mentioned, the mediating element is the transmission line that connects the individual towers. A corollary to this is that the propagating action does not need to be a pushing force but can also be a pulling force. Second, the failure does not necessarily need to progress in the direction of overturning. Given that the overturning of towers can also occur in a direction transverse to the transmission line, the direction of overturning and the propagating action can either be aligned with or orthogonal to the transmission line and the direction of failure progression. The list of features characterising a domino-type collapse is thus amended as follows: .

.

initial overturning of one element, which can be an individual structure fall of that element in an angular rigid-body motion around a bottom edge 17


Progressive collapse of structures . .

.

.

.

transformation of gravitational potential energy into kinetic energy abrupt deceleration of the motion of the element through sudden activation, possibly effected by mediating elements, of discrete other elements, which can be individual structures the horizontal force induced by that event is of both static and dynamic origin because it results from both the tilting and the motion of the decelerated element overturning of the suddenly activated other elements due to the horizontal force from the decelerated element failure progression in the horizontal direction.

It is noted that this list of features also covers more general cases where the consecutively affected elements or structures are neither similar nor aligned. When the individual elements or structures are anchored to the ground, overturning and failure progression requires the failure of the anchorages. Having said that, an overturning element does not need to be a complete individual structure that turns around a bottom edge at foundation level. The described failure mechanism is also present when — after local structural failure above foundation level — the upper part of an individual structure turns around a plastic hinge at the level of local failure. This was apparently the case in the above-mentioned progressive collapse of overhead transmission line towers in Germany (Fig. 2.3). Essentially unrestrained overturning motion and subsequent deceleration are important features of domino-type collapse as they enable a substantial amount of gravitational energy to be transformed into kinetic energy and that energy to be subsequently reintroduced into the structure. From the list of features given above, another distinguishing peculiarity follows that deserves attention. The horizontal force identified as the propagating action acts exclusively on discrete elements and not on a continuous structure as in the previously discussed types of collapse. This could mean a larger concentration of that force on the one hand and a better predictability of the structural response on the other.

2.2.4 Section-type collapse Consider a beam under a bending moment or a bar under axial tension. When a part of the cross-section is cut, the internal forces transmitted 18



Fig. 2.3 Domino-type collapse of overhead transmission line towers triggered by ice accretion (Germany, 2005). (Source: picture-alliance/dpa/dpaweb. Photo graph: Franz-Peter Tschauner, # dpa)

until then by that part are redistributed into the remaining crosssection. The corresponding increase in stress at some locations can cause the rupture of further parts of the cross-section. In the same manner, failure can progress throughout the entire cross-section. While this kind of failure is usually not called progressive collapse but brittle fracture or fast fracture, it is useful to include it in this description of types of collapse in order to reveal similarities and to exploit analogies that might exist. When compared with the previously discussed types, a section-type collapse exhibits certain similarities to a zipper-type collapse. Indeed, the same list of features applies provided the terms ‘part of cross-section’ and ‘remaining cross-section’ are substituted for the terms ‘element’ and ‘remaining structure’, respectively. The cross-section assumes the role of the structure. The main differences are that the cross-section of a beam or tie rod is unstructured, continuously contiguous, and comparatively homogeneous, whereas a structure, for instance a cable-stayed bridge, is generally structured consisting of discrete elements that are interconnected in various ways and have different properties. Even so, the 19



similarities might be close enough to apply by analogy the procedures for treating section failure and brittle fracture, and, in particular, the methods of fracture mechanics, to the zipper-type collapse. According to the premises of linear-elastic fracture mechanics, the stresses near a crack tip tend to infinity as the distance from the crack tip approaches zero. In a structure that consists of discrete elements, the distance between the elements consecutively engulfed by the failure front, for instance the cables of a cable-stayed bridge, is non-zero. Nevertheless, in the latter case there is also a force concentration in the elements that neighbour a failing element. This effect is partly dynamic, which should be taken into account when adopting methods of fracture mechanics. The cross-section could also be a fillet or butt weld transmitting tensile stresses perpendicular to the weld, and the same statements apply. A somewhat different situation arises in a fillet weld in longitudinal shear. In this case, the tendency to unzip is amplified by the stress concentrations at the weld ends that already appear before the onset of failure. The same applies to a lap splice of concrete reinforcing bars. In both cases, the failure progresses in the directions of the principal force and the propagating action, contrary to a zipper-type collapse and the other kinds of section-type collapse discussed above. Based on a postulated analogy between progressive collapse and fast fracture, a verification procedure and a measure of robustness were suggested by Smith56 (see also Section 7.7). Mechanisms of collapse in buildings are studied based on evaluating and balancing the various kinds of energy released and transformed during collapse. The effect of separated and falling components that impact the remaining structure is not considered, though, which might be attributed to fundamental difficulties of the theory as presented. Thus, its application to buildings — that is, structures that arguably are more susceptible to pancake-type collapse — might not be as meaningful. As established above, the analogy between progressive collapse and fast fracture is more applicable to structures prone to zipper-type collapse, such as, for instance, cable-supported bridges, cable nets, or membrane structures.

2.2.5 Instability-type collapse Failure of structures due to instability is characterised by small perturbations (imperfections, lateral loading) leading to large deformations or collapse. Structures are designed such that stability failure will not normally occur. This is typically achieved by providing additional 20



structural components that brace or stiffen the structure. When the discussion is limited to static stability failure under conventional loading, the braced or stiffened parts of the structure are load-bearing elements in compression, and the stability failure is called buckling. Preventing stability failure by bracing, on the other hand, means that the failure of a bracing element due to some small triggering event can make a structure unstable and result in collapse. This applies, for instance, to truss or frame structures in which bracing is used to stabilise compression bars or compressed parts of cross-sections. Another example is the initial failure of a plate stiffener that can lead to local instability and the failure of the affected plate, and possibly to global collapse. All these cases potentially exhibit a typical characteristic of progressive collapse, namely a small triggering event resulting in disproportionate collapse. The mechanism of an instability-type collapse exhibits the following features: .

. .

.

initial failure of bracing or stiffening elements that have been stabilising load-bearing elements (of the structure or of crosssections) in compression instability of the elements in compression that cease to be stabilised sudden stability failure of these destabilised compressed elements due to small perturbations immediate collapse or failure progression.

If the element first affected by destabilisation is one of a few primary load-bearing elements, say the corner leg of a truss tower, complete collapse can ensue immediately without a progressive failure of consecutively affected further elements. According to the distinction made in Section 1.1, such an incident would be a disproportionate but not at the same time a progressive collapse — in contrast to the other types of collapse discussed in the previous sections. On the other hand, the stability failure of the element first affected by destabilisation can also set in motion the progressive stability failure of consecutively affected further elements. This would be the case in a continuous girder where the spans fail consecutively due to buckling of the compression chord of the girder (lateral torsional buckling). In this example, however, the subsequently affected elements fail due to overloading as a result of a redistribution of forces — not because of the discontinuance of stabilising elements. Such a failure progression exhibits the features of a zipper-type collapse, discussed above, and should be categorised as such. 21



In order to specify a progressive instability-type collapse, the last item of the above list should be replaced by the following two features (to be appended to the penultimate item in the list): .

.

failure — caused by the stability failure of these destabilised compressed elements — failure of bracing or stiffening elements of other load-bearing elements in compression failure progression in the same repetitive manner.

Failure progression in the course of an instability-type collapse entails progressive destabilisation. The destabilisation can progress consecutively or even continuously. An example of the latter is propagating buckles that can develop in deep-water pipelines and, once initiated, can propagate over great lengths of pipe. A progressive destabilisation occurs when the failure of destabilised elements leads to the failure of stabilising elements. Though not a necessary condition, this can be the case when load-bearing elements are at the same time stabilising elements. In a deep-water pipeline, the load-bearing and stabilising functions are both performed by the cylindrical shell that forms the pipe. Characteristic features of an instability-type collapse are compression in stabilised elements, failure of stabilising elements, and subsequent stability failure of the compressed elements thus destabilised. The importance of compression loading and stability failure for this type of collapse is rooted in the transformation of gravitational potential energy into elastic potential energy (strain energy) that occurs during the deformation of the destabilised elements in compression. Dynamic action can play a greater or lesser role. The collapse of a truss tower after the buckling of a corner leg can be explained by considering only static forces. An appropriate modelling of propagating buckles in deep-water pipelines, in contrast, requires the inclusion of dynamic forces.90 Likewise, the feature of a failure progression over multiple consecutively affected elements can be present or absent, as was discussed above. The presence of this feature indicates a progressive instabilitytype collapse. A propagating action, by definition, arises only in the course of a progressive collapse. It is therefore absent in an instabilitytype collapse without failure progression, such as in the immediate collapse of a truss tower after the buckling of a corner leg. In an instability-type collapse with failure progression, such as in propagating buckles, the propagating action is predominantly a destabilisation and less a force. In both cases, though, the compression loading that causes the failure of destabilised elements is mainly a static force 22



that already acts before the onset of collapse and does not propagate. It is not a force that changes immediately before or during the course of collapse. This peculiarity is another defining and common feature of instability-type collapse. Furthermore, if there is a propagating action that is not predominantly a destabilisation, the type of collapse is different even if the first or subsequently affected elements fail due to instability. The notion of instability includes the concept of disproportion between perturbations, which are small, and structural response, which is large. This resembles the disproportion between a small triggering event and the resulting widespread collapse of a structure that characterises disproportionate and progressive collapse. This similarity of concepts opens up an interesting line of thought. Just as instability-type collapse is introduced here as one of several types of progressive collapse, progressive collapse could conversely be conceived as a particular kind of stability failure. This analogy might prove fruitful for the development of approaches for treating progressive collapse based on methods for treating instability.

2.2.6 Mixed-type collapse The types of collapse considered so far are relatively easily discerned and described. Some incidents of progressive collapse that have occurred in the past do not neatly fit into these categories, however. The partial collapse of the Alfred P. Murrah Federal Building (see Section 5.1) exhibited features of not only a pancake-type but probably also a domino-type scenario. A characteristic feature of the latter type is the occurrence in the course of collapse of horizontal forces that lead to the overturning of other elements. Horizontal tensile forces could have been induced in that incident by partially separated falling components that remained connected to the still intact parts of the structure through continuous concrete reinforcing bars. The possible occurrence and the importance of such forces are suggested by the fact that the collapse stopped shortly after a reinforcement discontinuity in a major horizontal element of the structure (see Section 5.3.4). The collapse of the Haeng-Ju Grand Bridge (see Section 1.2) seems to have involved features of the zipper-type and the domino-type categories. The importance of the latter type is underlined by the fact that the debris of this continuous prestressed concrete bridge came to rest in a longitudinally shifted position and remained connected through the continuous post-tensioning tendons which mostly stayed 23



intact. This indicates that the tendons served as a mediating element transmitting the propagating action of a domino-type collapse. But zipper-type features might also have contributed to the collapse because the initial failure of one span must have induced an impulsive redistribution of forces. This, in turn, possibly led to overloading and failure in bending of adjacent spans. The girders and towers of a cable-stayed bridge are in compression. They are braced by the stay cables. Thus, the loss of one or more cables can not only lead to unzipping, as stated above, but also to global stability failure. In such a scenario, the features of zipper-type and instability-type collapses will most likely interact and thus reinforce each other in promoting collapse (see Section 6.2.3). Possible kinds of interaction are (a) a progressive destabilisation through a zipper-like failure of cables and (b) an increase in force concentration in the next element to fail (a zipper-type feature) caused by the vertical displacement increment due to compression (an effect associated with instability). The propagating action in this case is both a force and a destabilisation. In certain kinds of structures, particularly certain kinds of buildings, it even seems possible that features of the four basic categories — pancaketype, zipper-type, domino-type, and instability-type collapse — interact and jointly contribute to failure progression. The importance of pancake-type and domino-type features for the collapse of buildings has already been addressed above. Features of zipper-type collapse could emerge, for instance, in a multi-bay frame structure when the failure of columns leads to overloading and failure of adjacent columns. Because failure progression also tends to reduce stiffness and to eliminate stabilising elements in a progressive manner, and considering that the columns in the latter example can fail due to buckling, the propagating action can partly consist of destabilisation, a feature associated with instability-type collapse. Mixed-type collapse is less amenable to abstracting and generalising treatment because the relative importance of the contributing basic categories of collapse can, in principle, vary. Nevertheless, further study could lead to the definition of other well-defined types of collapse, which might turn out to be combinations of the basic types described here or independent new varieties. This could be the case, for instance, for the alternative mode of pancake-type collapse mentioned in Section 2.2.1 in which only the floors of a building are involved in vertical failure progression and which also exhibits features of a domino-type collapse. 24



2.3

Classes of progressive collapse

The preceding discussion of types of collapse based on their respective mechanisms and characteristic and distinguishing features allows further abstraction and an outline of a hierarchical classification. In doing so, types of collapse are combined into classes. Both zipper-type and section-type collapses are characterised by the redistribution of forces carried by failing elements or cross-sectional parts into the remaining structure or cross-section. These two types are thus subsumed under one class of collapse, for which the term redistribution class is suggested. Pancake-type collapse and domino-type collapses, in comparison, have fewer features in common. For all their differences, however, they share an important characteristic: a substantial amount of gravitational potential energy is transformed into kinetic energy during the fall or overturning of components and is subsequently reintroduced into the structure. The reintroduction of energy occurs more or less abruptly. These two types of collapse are thus combined into one class of collapse, for which the term impact class is suggested. The term ‘impact’ is intended to be understood in a more general sense as it also refers to the abrupt deceleration of overturning elements in a domino-type collapse. Instability-type collapse forms a class of its own. It is characterised by the destabilisation of load-bearing elements in compression caused by the discontinuance of stabilising elements. The transformation of gravitational potential energy plays a role but in a different way than for the types of collapse in the impact class. Finally, mixed-type collapse also constitutes a separate class, for which, however, it is difficult to identify common characteristics other than the fact that features of various types of collapse interact and thus reinforce each other in promoting collapse.

2.4

Collapse-promoting features

2.4.1 Dynamic action and force concentration Despite the differences discerned in the preceding discussion, there are some collapse-promoting features that are shared, to varying extents, by the different types of collapse. Although dynamic action is necessary only for the explanation of a pancake-type collapse, it also plays a role in the other types of collapse. A concentration of force in the next element to fail induced by the failure of the previous element occurs in all the types of collapse 25



discussed, except possibly in the instability-type collapse. This force concentration is another feature promoting failure progression. Both these features are characteristics not of a structure but of the mechanisms of collapse.

2.4.2 Brittle material behaviour Dynamic action and force concentration become more detrimental as the material of the element that is prone to fail next becomes more brittle. Brittle material behaviour can thus be a collapse-promoting feature of a structure. Ductile material, on the other hand, is able to absorb and dissipate kinetic energy, and permits a redistribution of forces resulting in a reduction of force concentration. For this reason, ductile material can be particularly beneficial — or brittle material particularly harmful — when the design aims at increasing the robustness of a structure through the provision of alternative load paths (see Section 5.3.2). This concerns, in particular, the possibility of a zipper-type collapse and countermeasures to prevent it. The beneficial effect of ductile material behaviour can show itself in all types of collapse. This is less obvious regarding the prevention of a domino-type collapse. But even then, it can help to dissipate kinetic energy and to stop the collapse when the overturning of the element concerned, say the tower of an overhead transmission line, would require the failure of ground anchors or a local structural failure above foundation level.

2.4.3 Overstrength and ductile material behaviour Intriguingly, there are also instances where strength and even ductility are detrimental. Consider a domino-type collapse in which the propagating action is transmitted by mediating elements in tension (say a transmission line). This action corresponds to a force in the mediating elements larger than that occurring under normal conditions. To limit that force, the strength of the mediating elements or their connections should be limited, and thus overstrength should be avoided. But even then, the actual strength of a mediating element can result in an excessive force on the next element affected (a tower) that cannot reasonably be designed for. The reason lies in the safety margin required in the design of the mediating element for normal loading conditions and in a possible change of position and force direction of that element. In such a case, the mediating element or its connections should instead 26



be non-ductile in order to minimise the duration of the action and the impulse transmitted to the next element. The inertia of the next element can thus be put to work to resist its overturning. These remarks also apply to a mixed-type collapse with significant involvement of domino-type features. A mediating element that releases at a defined force or moment in a non-ductile manner is a predetermined breaking point. It resembles a fast-blow electric fuse, and can be considered a structural equivalent. This analogy hints at the potential effectiveness of structural fuses for also limiting a zipper-type collapse. In an electric power network, the failure of a component (power station, transmission line, substation) is usually compensated for by a redistribution of electric power flow to other components. This redistribution, however, can lead to overloading and progressive failure of those other components and even to the collapse of the entire network — a mode of failure that resembles in its characteristic features the zipper-type collapse of a structure described here. The redistribution of electric power flow is undesirable in such a case, and must be precluded by activation of electrical protection devices. The collapse of the electric power network thus remains spatially isolated and limited. A zipper-type collapse of a structure can similarly be limited by structural fuses. In more general terms, a well-defined strength and a non-ductile material behaviour can be advantageous in isolating elements that are intended to constitute segment borders. A segment border is an expedient of a design method aimed at limiting the extent of collapse through isolating the collapsing part by means of structural segmentation (see Section 5.3.3). This method is applicable to all types of collapse, although not always in association with structural fuses.

2.4.4 Continuity or discontinuity The discussion in the previous two sections indicates that the advantages and disadvantages of high strength and ductility should be evaluated primarily with reference to the methods used in design and less so in connection with the type of collapse. The same applies to the structural features called continuity and discontinuity. Continuity can be favourable when the design aims at increasing the robustness of a structure by providing alternative load paths. If collapsing parts are to be isolated by structural segmentation, on the other hand, the elements designed as segment borders can achieve their isolating effect not only by continuity and high local resistance 27



but also by discontinuity. The choice between the two design methods just outlined is a fundamental problem that should also be considered with regard to beneficial or harmful interaction and the predictability of the structural response (see Section 5.3.5).

2.4.5 Series or parallel load transfer In the case of series load transfer, the initial failure of any one loadbearing element can be expected to cause collapse. It can occur, for instance, as a pancake-type collapse of a high-rise building. The initially failing element here is the whole of the vertical load-bearing members of a storey. The structure is characterised by a lack of robustness, at least with respect to this assumed initial failure. Series load transfer is therefore undesirable in principle. On the other hand, it is inevitable in some structures, such as slender high-rise buildings. In the case of parallel load transfer, the forces carried by failing elements can be redistributed into the remaining structure and carried by other elements (alternative paths). Collapse can be avoided in this manner. However, redistribution of forces is also a characteristic of zipper-type collapse. Its occurrence requires parallel load transfer. To counter such a type of collapse, a redistribution of forces must be permitted not only by the topology of the structural system, that is, by an adequate degree of connectivity and continuity, but also by making the resulting alternative paths sufficiently strong (see Section 5.3.4).

2.4.6 Spatial orientation, size, and slenderness Structures are often aligned in a primary direction. High-rise buildings are mainly vertically aligned, whereas bridges are mainly aligned along a horizontal axis. Pancake-type collapse is more likely in a vertically aligned structure. This follows from the characteristics of a pancaketype collapse: the impact of separated and falling components on the remaining structure and a failure progression in the vertical direction. A domino-type collapse, in contrast, is characterised by the overturning of elements and a horizontal failure progression; it therefore implies a horizontal alignment of the structure or group of structures. A zippertype collapse typically progresses in the horizontal direction but does not seem to require a distinct primary direction of structural alignment. The latter also applies to the other types of collapse. The susceptibility to progressive collapse increases with the size of a structure. In buildings up to, say, ten storeys built in accordance with 28



modern design standards, the impact loading resulting from the failure of one storey can normally be tolerated by the remaining structure, and does not generally lead to a pancake-type collapse (see Fig. 6.15). The latter seems almost inevitable, though, in buildings higher than, say, 30 storeys (if special measures, such as those described in Section 6.3, are not taken). The reason for this height dependency lies in the ratio of the gravitational potential energy to the elastic potential energy, which increases with height. The other types of collapse require a certain number of elements and a certain structural size in order to be recognised as progressive and disproportionate. The slenderness of a high-rise building goes along with its vertical alignment. It is similarly a structural feature that promotes pancaketype collapse. This is based on the ratio between the extent of accidental circumstances required for the failure of one storey and the susceptibility to failure progression addressed in the previous paragraph. This ratio decreases — and thus the structure becomes more susceptible to a pancake-type collapse — with an increase in slenderness. Because slenderness facilitates failure from overturning and instability, it is a property that also favours domino-type and instability-type collapses. In these cases, it is the slenderness of individual structures or elements, not that of the overall structure, that is of main concern.

2.4.7 Structuredness A further collapse-promoting structural feature appearing in some of the types of collapse discussed is the structuredness (as opposed to compactness) of a structure. This term is already in use in the context of software development.91 Adopting it by analogy, structuredness is the degree to which a structure possesses a definite pattern of organisation of its interdependent load-bearing elements. In this sense, the discrete frame structure of a high-rise building with its organisational pattern of horizontal beams and slabs and vertical columns is highly structured whereas an industrial chimney of the same height designed as a compact reinforced concrete tube is comparatively unstructured. Structuredness is a condition for, or at least favours, pancake-type collapse. This follows from the observation that the characteristic features of this type of collapse — that is, the release and subsequent reintroduction of a large amount of gravitational energy associated with the fall and impact of components — are difficult to develop in a structure lacking structuredness. For a domino-type collapse, the description of which is comparatively specific, structuredness is implied 29



by the defining features. Structuredness is thus important for both types of collapse in the impact class. For zipper-type, section-type, and instability-type collapses, on the other hand, structuredness does not seem to be a necessary condition.

2.5

Summary

Progressive collapse can be produced by various different mechanisms. Based on a discussion of these mechanisms, five distinct types of collapse are identified. The terms suggested for these five categories are pancaketype, zipper-type, domino-type, section-type, and instability-type collapse. These categories are relatively easily distinguishable through their respective features, which are described here. These features can interact, though, in various combinations and to varying degrees. The resulting types of collapse are subsumed under a sixth category, called mixed-type collapse. A higher level of abstraction is achieved by combining the pancake-type and domino-type categories, on the one hand, into a so-called impact class, and the zipper-type and sectiontype categories, on the other hand, into a redistribution class. It is hoped that the typology presented here will not only advance the conceptual treatment of progressive collapse but also help in developing analysis procedures and in quantifying robustness and collapse resistance (see Chapter 7), as well as in developing, classifying, and selecting countermeasures. If little progress has been made to date in achieving these goals, one reason might have been the hitherto lack of differentiation and classification of types of collapse on the basis of a description of the underlying mechanisms. Both the theoretical treatment and appropriate countermeasures will differ for different types of collapse. For instance, if pancake-type collapse can only be treated in a deterministic way, zipper-type collapse might become tractable by probabilistic approaches. Some analogies are given that seem promising to pursue further: the similarity between section failure and zipper-type collapse hints at the applicability of fracture mechanics to the latter type of collapse; the similarity between the definitions of instability and progressive collapse could be explored to develop concepts for treating progressive collapse from approaches for treating instability. As another example of how the basis offered here could be used for future study, collapse-promoting features — and some countermeasures — are outlined and their association with types of collapse are discussed. Salient collapse-promoting features of the mechanisms of collapse are 30



dynamic action and force concentration. Collapse-promoting features of a structure are large size and slenderness, and a certain degree of structuredness, a term suggested and defined here. If the structure is spatially aligned in a primary direction, it is susceptible to particular types of collapse. The influence of other structural features is more difficult to generalise. Although brittle material behaviour can be collapse promoting, it is shown that overstrength and ductile material behaviour can also be detrimental in some cases. Similarly, continuity or discontinuity, and series or parallel load transfer can be beneficial or harmful, depending on the kind of structure, the type of collapse, and the chosen method of design to prevent it. More insights might flow from a further discussion of the types and mechanisms of progressive collapse.

31


3 Current design procedures 3.1

Inadequacy of current procedures

Modern design codes and verification procedures are based on the probabilistic theory of reliability. Actions and resistances are determined statistically from empirical data obtained from observations and measurements and represented by their respective probability density functions. Based thereupon, and after stipulating an allowable probability of failure, the design values for actions and resistances are computed using probabilistic methods. Design using these values promises a uniform level of safety. Such an approach is based on a mathematically sophisticated and sound foundation and is, as it seems, correct. It is reflected in the design codes by partial safety factors and a series of load combination schemes. The application of the accompanying code rules is often cumbersome due to the multitude of load combinations to be considered. The design engineer might still take comfort in the idea that, by working on a rational mathematical basis, a uniform level of safety is achieved. Unfortunately, that idea is illusory because such an approach fails with regard to the identification of a possible susceptibility to progressive collapse and the development of appropriate countermeasures. There are three reasons for this failure.31,92 The first reason lies in the focus on local instead of global failure. Design equations for checking structural safety are usually defined and applied at a local level only (check of stresses, sectional forces, or stability of load-bearing elements). Structural safety, therefore, is also accounted for only at a local level. The structural safety at a global or system level, that is, the safety against the collapse of the entire structure or a major part thereof, is a function of not only the safety against local failure of all load-bearing elements but also of the structural response of the entire system to local failure. The latter effect is neglected. Different structures will respond differently to local failure. The tacit underlying assumption that a uniform safety level of a 32


Current design procedures

structure is achieved by merely providing a uniform level of safety to its elements is therefore not generally valid. When applied to non-robust structures, such procedures produce unsafe designs. (See Section 4.2.1 for a definition of robustness.) The problem can be illustrated by means of a simplified expression for the probability, P(C), of a progressive collapse, C , due to an event, E : PðCÞ ¼ P ðCjLÞ  PðLjEÞ  PðEÞ

ð1Þ

where P(E) is the probability of occurrence of E, PðLjEÞ is the probability of local failure, L, given the occurrence of E, and PðCjLÞ represents the probability of progressive collapse given the occurrence of L.41 The factor PðCjLÞ is not reflected in the verification procedures of current design codes. The possibility of a progressive collapse thus remains out of consideration. If the preceding appears to be critical of the application of the probabilistic theory of reliability, it also holds that there is currently no deterministic design code either that remedies the problem just outlined. Nevertheless, it must be stated that the hope of achieving a uniform level of safety by using reliability theory has not been fulfilled. Although this deficiency is known to professionals familiar with reliability theory, practising engineers are often unaware of it. The second reason for the inadequacy of current design procedures is that accidental circumstances are neglected. Accidental circumstances are events that are unforeseeable or whose probability of occurrence is very low, that is, events, E, for which P(E) is very small. In the context of reliability-based design, neglecting them is necessary because the supporting statistical data, derived from experience and observation, are unavailable.93 For low-probability events, the source data are too scarce. Unforeseeable events, in particular those that have never occurred before, can at best be speculated on. In the case of a nonrobust structure, however, this neglect of accidental circumstances is unacceptable. This follows from the first problem with current design procedures discussed above. For illustration, consider a structure characterised by series primary load transfer, say a slender high-rise building. A relevant initial local failure is the simultaneous failure of all the vertical load-bearing elements of a storey. For the sake of argument, assume that such an initial failure leads to impact forces that cause the building to collapse, that is, PðCjLÞ ¼ 1. For buildings of sufficient height, this assumption will hold for the initial failure of most storeys. The probability of collapse is then of the order of the sum of the failure probabilities of all the 33



constitutive elements, that is, of the individual storeys of the building.31 If the number of storeys is sufficiently large (put simply, if the area of attack of the building is sufficiently large), even very low probabilities of local failure resulting from accidental circumstances can add up to a probability of global failure high enough to be taken seriously. For structures with parallel primary load transfer, in contrast, the probability of global failure is of the order of the product of the failure probabilities of the constitutive elements, and therefore very low. The third reason for the inadequacy of current design procedures is that the underlying probabilistic concept requires the specification of an acceptable probability of failure. The target failure probabilities of probabilistic design codes are usually derived from calibration with previous deterministic design codes. Hence, no new societal consensus seems necessary when probabilistic design is adopted. Considering the huge losses that can result from progressive collapse, however, it is difficult to see how an informed and true societal consensus on the numerical value of the acceptable probability of such an outcome can be reached — a problem that risks of the ‘low probability/high consequence’ type are typically up against.94 This problem can be evaded, but not solved, by not bringing the question to the attention of the public.

3.2

Possible improvements

The first problem outlined in the previous section is not actually inherent in the theory of reliability. As illustrated by Eq. (1) and further explained in Refs 41 and 42, it is, in principle, possible to account for progressive collapse within a probabilistic framework. The difficulty arises from practical limitations that appear when the theory is applied to actual structures. In this process, the structural response to local failure needs to be examined. This response typically involves large deformations and displacements, separation of structural components, falling or overturning components striking other parts of the structure, and other unusual kinds of interaction. Proper treatment of all these effects generally entails a geometrically and materially nonlinear dynamic analysis in the time domain. Even the precise modelling of such scenarios is difficult because some structural properties, such as the behaviour of joints or post-tensioning tendons under extreme and unusual loading, are not well established. These difficulties are compounded by the need to consider many different cases of initial local failure and by the fact that, owing to the nonlinear dependencies arising here, small errors in the modelling assumptions 34


Current design procedures

can produce large deviations in the computational outcome. Even a deterministic analysis of the structural response to local failure poses tremendous difficulties. A probabilistic analysis of this response together with a computation of the safety against global failure adds further dimensions of difficulty, and, apart from special cases, seems out of reach of today’s analysis resources. Regarding the problems of computational tractability and predictability of the structural response, it is of interest that different kinds of structures are susceptible to different mechanisms and types of collapse (see Chapter 2). The latter, in turn, involve varying degrees of computational effort. The amenability to computational treatment in general, and to a probabilistic approach in particular, seems greatest for structures where local failure is unlikely to result in major impact incidents, for instance structures that are susceptible to zipper-type collapse but not to pancake-type collapse. If a probabilistic analysis of particular kinds of structures or structures in general becomes feasible in the future, one could attempt to consider the structural response to local failure by an additional system partial safety factor on the resistance side of the design equations. The framework of current design procedures could thus be maintained. The additional safety factor would take a value of 1 for robust structures and a value smaller than 1 for non-robust structures. Provisions in some design codes aim in this direction. In these cases, however, the reduction of the design values of resistance for non-robust structures is based on engineering judgement rather than on thorough probabilistic analysis. Partial safety factors for considering structural robustness would have to be specified on the basis of parametric analyses of the safety against global failure for all the kinds of structures covered by the respective design code. The robustness of all these structures will vary widely. A classification of structures is thus required in order to assign to each class of structure its respective reduction factor (see also Section 7.2, point 5). Moreover, the reduction factor would have to be specified differently even for different structural elements of structures of the same class according to the respective global consequences of element failure. Such differentiation can be considered as the semi-probabilistic counterpart of the specific-local-resistance method, a deterministic approach discussed in Section 5.2. Another possibility is to pursue a fully probabilistic analysis for a given design task, thus dispensing with the use of safety factors. The second and third problems outlined in the previous section are fundamental challenges to purely reliability-based design. If low 35



probabilities of local failure resulting from accidental circumstances add up to a large probability of global failure, then the probabilities of occurrence of the accidental circumstances need to be known. They are needed as input data for the probabilistic analysis, and cannot be neglected. The determination of the actual values of these probabilities, however, seems extremely difficult, if not impossible. Also, if a societal consensus on the acceptable probability of a major disaster cannot be reached, another basic ingredient to a probabilistic computation is missing.

36


4 Design against progressive collapse 4.1

General

It follows from the preceding discussion that the inadequacy of current design methods are both fundamental and practical in nature, and can only partly be overcome within the framework of reliability theory. The possibilities for improvement that do exist require a major advance in computational methods and extensive numerical studies, and may in the end turn out to be insufficient. Nonetheless, there is a need for immediate guidance. Both a general concept for handling the questions raised by progressive collapse and a procedure for designing collapseresistant structures are urgently required. The following pragmatic approach to tackling these tasks is suggested.55,92,95 As a starting point, the design procedures of current codes are retained. They are based on reliability theory, which is reflected in the codes by partial safety factors and load combination schemes. Where necessary and possible, for instance concerning ship impact on major bridges, this code-based design can be complemented by direct probabilistic analysis and risk assessment. (In view of the inconsistencies of current design procedures outlined above, one could argue that the number of load combinations prescribed by some codes should be reduced because it is exaggerated when compared with the accuracy actually achieved.) In addition, an assessment with respect to progressive and disproportionate collapse is carried out and corresponding measures are taken. The procedure is further described in the following sections. It is anticipated here that this will not be based on the probabilistic theory of reliability but on engineering judgement and on concrete, deterministically defined design objectives that must be established in a decision-making process. Structural analyses will similarly be carried out deterministically. Emphasis is put on performance-based methods. 37



This approach is pragmatic because it lacks the rigour of a purely mathematical basis but still helps to solve the problem at hand. It enables the design engineer to adequately address progressive collapse in the sense that safety and economy are reasonably balanced and the required structural analysis remains tractable. Such an approach has implicitly been used already in the few reported cases where progressive collapse has been considered in the design of actual structures.33 Recent European and American regulations on accidental actions and progressive collapse (see Ref. 70 (Annex A), and Refs 67, 75, and 76) indicate that codification is already moving towards such a pragmatic approach. The same holds for the ASCE Structural Engineering Institute PreStandard Prospectus,81 which is influenced by this proposal. It is hoped that future code development will lead to a clearer description of the design criteria and a more precise and consistent use of language. This presentation of the additional assessment and measures relating to progressive collapse begins with two fundamental definitions. Then follows a listing and discussion of design criteria that reflect the questions at hand, and the provisions to be established before and during the design process. The approach presented here can be applied to both new structures and retrofit projects.

4.2

Two definitions

The terms ‘robustness’ and ‘collapse resistance’ have already been introduced (in Section 1.1). The term ‘robustness’ appears frequently in discussions and publications on progressive or disproportionate collapse. It is used differently by different authors,46,49,53,70 however, and there is no general agreement to date on its precise meaning. The definition of robustness given here and the introduction of the new term ‘collapse resistance’ prove useful for the suggested approach to handling progressive collapse. Before continuing to present that approach, therefore, both terms are defined and discussed in more detail in the next two sections.55,96

4.2.1 Robustness Robustness is defined as insensitivity to local failure. This definition can be understood both qualitatively and quantitatively. The latter requires quantification of the defining terms ‘insensitivity’ and ‘local failure’. These two specifics, however, are, in the end, not quantifiable by resorting to first principles of natural sciences or mathematics but 38


Design against progressive collapse

have to be established in a decision-making process, mostly on a caseby-case basis. The same holds for the design objectives listed in Section 4.3.2. It thus seems convenient to equate ‘local failure’ to the ‘assumable cases of initial local failure’ (design objective 2) and to state ‘insensitivity’ if no more than the ‘acceptable total damage’ (design objectives 3 and 4) results. (The term ‘total damage’ refers to the total amount of all direct and indirect losses.) In this way, the quantitative definition of robustness is rooted in the design objectives that have to be predetermined in a decision-making process. According to the definition suggested here, robustness is a purely structural property in the sense that the cause and probability of local failure — and thus also the nature, extent, and probability of the triggering accidental circumstances — are immaterial. This is in contrast to a broader definition of robustness — as is given, for instance, in Eurocode EN 1991-1-770 — that refers to triggering accidental circumstances. (Note that Eurocode EN 1991-1-7 uses the term in an undifferentiated manner and also in the more specific meaning suggested here.) Such a broader conception is close to the term ‘collapse resistance’ defined next.

4.2.2 Collapse resistance Collapse resistance is defined as insensitivity to accidental circumstances, that is, to unforeseeable and low-probability events. Again, the quantitative interpretation of this term resorts to the design objectives. Just as local failure was equated to design objective 2, the ‘accidental circumstances’ are now equated to the ‘assumable accidental circumstances or actions’, that is, design objective 1. ‘Insensitivity’ is quantified by design objectives 3 and 4, as before. The conjunction with predetermined design objectives also provides a quantitative basis to the definition of disproportionate collapse that was given in Section 1.1 in a qualitative manner. A collapse is disproportionate when assumable accidental circumstances lead to unacceptable total damage. Disproportionate collapse is avoided by ensuring collapse resistance. The latter is a property that depends on both the structure and the assumable accidental circumstances. In this regard, the structural property ‘robustness’ is of particular importance: a robust structure is at the same time collapse resistant. It would limit the range of design choices unacceptably, however, if only those structures were permitted that are clearly robust. Nor is such a limitation necessary, because a non-robust 39



structure — whose response to an assumable local failure is unacceptable total damage — could possibly be made less sensitive to accidental circumstances, and thus collapse resistant, by other means, such as increased structural resistance of so-called key elements. Furthermore, collapse resistance will not be required for every structure. The definitions of robustness and collapse resistance suggested here bring about a clear distinction between the corresponding properties — which is the essential point. As long as such a distinction is retained, these properties could be named differently (if no consensus on a redefinition of the term ‘robustness’ is reached).

4.3

Design criteria

In the assessment of a structural design with respect to progressive collapse, the following design criteria are of importance:55,92,95 I. design requirements II. design objectives III. design methods IV. verification procedures. These criteria and their respective subcriteria are presented in Fig. 4.1 and further examined in the following sections. The design criteria should generally be established according to codified provisions, as long as these exist and are applicable. If applicable design criteria are unavailable in codified form, they must be agreed upon on a projectby-project basis by the contracting and other affected parties. For major projects, a project-related agreement will probably be the rule rather than the exception.

4.3.1 Design requirements First, the design requirements — that is, in particular the question of whether collapse resistance is necessary — should be clarified. The necessity depends on the significance of the structure with respect to the consequences of a collapse. These go beyond the immediate human and material losses and include indirect consequences, such as impairment of the infrastructure and of civil and national defence. In this sense, a storage structure filled with hazardous material can be of greater significance than a building of the same size. Likewise, a short motorway bridge can have a greater significance than a much longer bridge on a secondary road. 40


Design against progressive collapse Design requirements

Significance Exposure

Design objectives

Assumable accidental circumstances or actions Assumable cases of initial local failure Acceptable extent of collapse Acceptable other damage Partial safety factors/combinations of actions

Design methods

Prevent local failure Specific local resistance Non-structural protective measures

Assume local failure Alternative load paths Isolation by segmentation Prescriptive design rules

Verification procedures

Exact procedures Nonlinear dynamic analysis

Simplified procedures Quasi-static analysis Generalised single-degree-of-freedom system

Fig. 4.1 Design criteria for collapse resistance of a structure

Another criterion for establishing the design requirements is the degree of exposure of the structure to accidental circumstances, such as deliberate damage and assault (malicious action), accidents, and human error. Regarding malicious action, a structure can be considered exposed when it is large and vulnerable, is perceived as important, or symbolises a major institution. The exposure to malicious and war 41



action is particularly high for landmark structures, public buildings, major bridges and tunnels, and other lifeline structures. For secondary structures (i.e. those of low significance and exposure), collapse resistance can be dispensed with, in particular when the additional cost would be disproportionate. In the General Services Administration (GSA) guidelines,75 a procedure called the ‘exemption process’ is presented through which buildings with a low probability of collapse or of low significance — this includes small buildings and those with low occupancy — are exempted from further consideration. In addition to answering the question of whether collapse resistance is necessary, the significance and exposure of a structure can serve to establish design and verification requirements that are more differentiated. This leads to a classification with three or more classes of structures. In this context, the term ‘importance factor’ appears in the Multihazard Mitigation Council report.43 Such differentiation resembles the ‘importance classification’ used in the seismic design of bridges as set out in the American Association of State and Highway Transportation Officials specifications.63 Annex A of Eurocode EN 1991-1-770 provides a classification of buildings and stadia according to ‘consequences classes’. These structures are classified into four groups in an attempt to judge their significance with regard to the consequences of a collapse. Class 1 structures, such as agricultural buildings and single-occupancy houses not exceeding four storeys, do not require an additional assessment or specific measures with respect to their collapse resistance. For structures of higher classes, assessment and measures are required to varying degrees. The British Approved Document A,67 though not identical, here closely mirrors the Eurocode. In the classifications according to Refs 67, 70, and 75, indirect consequences for infrastructure and national defence and the degree of exposure are not explicitly considered. These documents cover solely buildings and stadia. A classification that factors in the degree of exposure and indirect consequences for infrastructure, civil defence, and national defence is given in an American Society of Civil Engineers (ASCE) security guideline.97

4.3.2 Design objectives If collapse resistance is deemed necessary, the following design objectives must be established: 1. assumable accidental circumstances or actions 2. assumable cases of initial local failure 42



3. acceptable extent of collapse 4. acceptable other damage 5. applicable partial safety factors and combinations of actions. The term ‘assumable’ means ‘to be assumed in the assessment of a structural design with respect to progressive collapse’. Establishing the assumable accidental circumstances or actions (design objective 1) and the assumable cases of initial local failure (design objective 2) requires a specification of their respective nature and extent. Accidental circumstances include malicious action, war action, natural disasters, fire, accidents, human error, and other hazards. They can involve actions, such as explosive blast, vehicle impact, or simply static overloading, as well as a lack of structural resistance due to design and construction flaws, corrosion or other causes. When choosing assumable cases of initial local failure, the extent of initial failure occurring in each case must also be defined. The cause of failure is irrelevant. Note that design objective 3 refers to collapse and not merely to failure. Design objective 4 refers to damage to the non-collapsed remaining structure, even if extending to virtual failure and loss of serviceability, damage to the surroundings, and indirect losses resulting from an impairment of infrastructure and of civil and national defence. Design objectives 3 and 4 are included in the term ‘acceptable total damage’. The term ‘total damage’ thus refers to the total amount of all direct and indirect losses. It is of particular interest that the design objectives are established deterministically; the respective probabilities of occurrence thus remain undefined. It is anticipated that these design criteria can, at best, only partly be derived from first principles. Quantifying assumable accidental circumstances or actions that result from such circumstances (design objective 1) is particularly difficult. The quantification of design objectives 3 and 4 is not actually an engineering problem, but all the more challenging. Establishing the acceptable total damage can be facilitated by a cost-benefit analysis; however, this tends to become controversial when human life is at stake. Advice can be taken from the insurance industry, which has developed methods and parameters for such considerations. Even so, there will remain the necessity for a judgement and decision-making process when assets, the environment or human life are affected on a large scale. That process can be supported by professionals, but, in the end, must reflect public opinion. Design objectives 1 to 4 can be understood as performance criteria to be given by the client. Progressive collapse is a concern mostly for major 43



projects, which means that public interest is usually affected. The term ‘client’ should then be taken in a more general sense as the publicdecision makers who represent public opinion as well as the parties affected by the project. The decision of the client must be supported by engineering judgement, especially concerning design objectives 1 and 2. To establish design objective 1, a risk assessment should be performed. Annex B of Eurocode EN 1991-1-770 provides some guidance in this regard, in particular a list of potential accidental circumstances. Nevertheless, one must select from a multitude of possible scenarios. That selection can only be done on a project-byproject basis. It is difficult to generalise and to codify, and, therefore, requires professional competence and experience. The verification of collapse resistance can be carried out by verifying robustness, that is, by invoking design objective 2 instead of design objective 1. A definition of design objective 1, therefore, is unnecessary in some cases. This facilitates the process and increases its reliability because design objective 2 can often be established for a given project by engineering judgement in a meaningful and safe manner — in the case of the Confederation Bridge, for instance, as the failure of a bridge pier (see Section 5.3.3). If both objectives are specified, the assumable local failure (design objective 2) must not be smaller than the damage resulting from assumable accidental circumstances (design objective 1). When only design objective 1 is specified, design objective 2 can be derived from it by structural analysis. This would be necessary for the identification of key elements, given that it requires a definition of the assumable cases of initial local failure (see Section 5.1). Design objectives 1 to 4 can be specified in a continuous numerical manner or as discrete conditions. The latter are often more meaningful and better accommodate engineering judgement because structural particularities can be considered. For instance, instead of specifying the acceptable extent of collapse (design objective 3) as an overall numerical ratio to the size of the structure, one could instead define the location of collapse boundaries that constitute interception lines preventing the collapse progressing further. This approach lends itself especially to establishing the design objectives for a particular given project. Such a more specific and descriptive definition also facilitates the design process. Similar comments apply to design objective 2, as already mentioned in the previous paragraph. Furthermore, it is noted that design objectives 1 to 4 may have to be revised after examining the design methods to be considered for a given project. That is, the 44


Design Desig n again against st progr progressive essive collapse

final specification of these design objectives can depend on the available desi de sign gn op opti tion onss (s (see ee Se Sect ctio ion n 5. 5.3. 3.3) 3).. Fi Fina nall lly, y, it sh shou ould ld be me ment ntio ione ned d th that at a furt fu rthe herr di diff ffer eren enti tiat atio ion n of th thes esee de desi sign gn ob obje ject ctiv ives es wo woul uld d be po poss ssib ible le.. Th They ey could be given as more than one set of data or in an interrelated form, for instance, with an acceptable total damage that depends on the extent of initial local failure. Desi De sign gn ob obje ject ctiv ivee 5 is no nott ac actu tual ally ly a pe perf rfor orma manc ncee cr crit iter erio ion. n. It is included in the above list since its specification is likewise needed for thee de th desi sign gn pr proc oces ess. s. Re Reli liab abil ilit ityy th theo eory ry ca can n be of as assi sist stan ance ce fo forr th this is specification, but here also engineering judgement will, in the end, be decisive. This seems unavoidable but admissible. For large and unique stru st ruct ctur ures es,, wh whic ich h ar aree th thee ma main in co conc ncer ern n he here re,, ac achi hiev evin ingg a un unif ifor orm m level of safety is illusory (see Section 3.1). What is required, however, is no nott ne nece cess ssar aril ilyy a un unif ifor orm m le leve vell bu butt a re reas ason onab able le le leve vell of sa safe fety ty.. When Wh en app applyi lying ng the des design ign met method hod ‘spe ‘specifi cificc loc local al resis resistan tance’ ce’ (see (see Sec Sectio tion n 4.3.3), and when deriving design objective 2 from design objective 1 by structural analysis, increased partial safety factors should be used (see Section 5.2.3); when applying the design strategy ‘assume local failure’, reduced partial safety factors are justifiable (see Section 5.4). The concept presented here accommodates the need for public debate by mak making ing the cho choice icess tra transp nspare arent. nt. Th Thee des design ign cri criter teria ia for the Co Confe nfeder deraation Bridge, for instance, specified the acceptable extent of collapse as a cert ce rtai ain n nu numb mber er of co coll llap apse sed d sp span anss with with a co comb mbin ined ed le len ngt gth h of ab abo out 70 700 0m 31,33 outt of a to ou tota tall br brid idge ge le leng ngth th of 12 91 910 0 m. The only alternatives to specifying a certain acceptable extent of collapse would have been to disregard the possibility of progressive collapse in the design process or to abandon the project altogether. These three choices are clear even to a lay person. A societal consensus or an administrative or political decision in regard to such choices is easier than in regard to choosing an abstract mathematical quantity such as the safety index  — even if that consensus or decision means that certain construction projects are better not pursued and some structures remain unbuilt. If the design objectives 1 to 5 are viewed as a framework whose content needs to be specified further, note that some of these specificat fic atio ions ns ar aree al alre read adyy be bein ingg di disc scuss ussed ed43,93 or ar aree in use se.. Eu Euro roco code de EN 199 1991-1 1-1-7 -770 provides details on accidental actions (design objective 1). For some specific accidental circumstances, that is, internal explosions and the impact of road vehicles, rail traffic, ships, or helicopters, the corresponding accidental design actions are specified. Comprehensive provisions on the impact of road vehicles on structures are also given by a Swiss guideline.98 45


Progressive Progr essive collap collapse se of struc structures tures

Also with regard to design objectives 2 and 3, some specifications can be fo foun und d in th thee co code des. s. As Assu suma mabl blee ca case sess of in init itia iall lo loca call fa fail ilur uree in bu buil ildi ding ngss 75 are treated treated in detail in the GSA guidel guidelines ines and in the United Facilities Criteria.76 An Ann nex A of Eur uroc ocod odee EN 19 199 911-11-7 770 spe specifi cifies es des design ign obje ob ject ctiv ivee 2 by re requ quir irin ingg th that at ‘t ‘the he bu buil ildi ding ng sh shou ould ld be ch chec ecke ked d to ensure ens ure tha thatt upo upon n the no notio tional nal rem remov oval al of eac each h sup suppor portin tingg col column umn and each beam supporting a column, or any nominal section of loadbear be arin ingg wa wall ll . . . (o (one ne at a ti time me in each each st stor orey ey of the buil buildi ding ng)) . . . an anyy local damage does not exceed a certain limit’. It remains unspecified whether the ‘notional removal’ should be done slowly or suddenly, that is, whether it should be examined by static or dynamic analysis. Thee re Th reco comm mmen ende ded d li limi mitt of lo loca call da dama mage ge — wh whic ich h co corr rres espo pond ndss to 2 design desig n objective objective 3 — is ‘15% of the the floor, or 100 100 m , whichever is greater, in ea each ch of tw two o ad adja jace cent nt st stor orey eys’. s’. Th Thee co corr rres espo pond ndin ingg pr prov ovis isio ion n in 67 Approv App roved ed Doc Docume ument nt A is si simi mila larr bu butt mo more re na narr rrow owly ly li limi mits ts th thee 2 acce ac cept ptab able le damag damagee to ‘15% ‘15% of the floor floor ar area ea . . . or 70 m , whichever is smaller’. The corresponding limit set forth in the GSA guidelines is likewise likew ise narrower narrower than that of Euroc Eurocode ode EN 19911991-1-7. 1-7. Thee st Th stan anda dard rdss an and d gu guid idel elin ines es ju just st me ment ntio ione ned d ma main inly ly ap appl plyy to buildings. build ings. The Post-T Post-Tensio ensioning ning Instit Institute ute (PTI (PTI)) recom recommend mendation ationss64 state that ‘All cable-stayed bridges shall be capable of withstanding thee lo th loss ss of any one ca cabl blee with tho out th thee oc occu curr rren encce of st stru ruct ctur ural al instability’. Furthermore, loss of cable is to be assumed as sudden so that an impulsive dynamic loading is produced. Design objective 2 is thus explicitly defined as the sudden failure of any one cable at a time. Given that an associated load combination and applicable partial safe sa fety ty fa fact ctor orss ar aree st stat ated ed,, de desi sign gn ob obje ject ctiv ivee 5 is al also so sp spec ecifi ified ed.. Th Thee definition of design objective 3, on the other hand, is less clear. If ‘structura tu rall in inst stab abil ilit ity’ y’ is un unde ders rsto tood od as a to tota tall co coll llap apse se,, th then en a ce cert rtai ain n ex exte tent nt of local damage and large deformations would still be acceptable. Similar recommendations are made in Ref. 65. The acceptable damage to the non-collapsed remaining structure — a constitutive part of design objective 4 — has not yet been specified in codified form. This specification is related to the repairability of the structure and the timescale for recovery of its serviceability. If public interest is not affected, the decision on these issues can be left to the owner (i.e. the client in the more specific sense). In regard to indirect losses, however, the decision on the level of acceptability will generally lie with public decision-makers. Details on partial safety factors and combinations of actions (design objective 5) can be found in Refs 64, 75, and 76. 46


Design Desig n again against st progr progressive essive collapse

4.3.3 Design methods The fo The foll llow owin ingg de desi sign gn st stra rate tegi gies es an and d me meth thod odss to en ensu sure re co coll llap apse se resistance are described in the literature, and have at least partially made their way into design codes: 1. prevent prevent local local failure failure 1.1. speci specific fic local resistanc resistancee 1.2. nonnon-struct structural ural protective protective measures measures 2. assu assume me local local failur failuree 2.1. altern alternative ative load load paths 2.2. isola isolation tion by segmenta segmentation tion 3. prescr prescriptiv iptivee design rules. The two strategies specified in points 1 and 2 (design strategies 1 and 2, respectively, as they are called here for short) lead to so-called direct design methods that start from given design objectives and, except for non-structural protective measures, are based on structural analysis. Such methods are performance-based approaches. Design strategy 1 is pursued by providing an increased level of safety against local failure to the key elements of a structure. Design strategy 2, on the other hand, is based on verifying and limiting the structural response to assumed local failure. Only design strategy 2 aims at verifying or increasing the robustness of a structure. The application of prescriptive design rules is an indirect design method. It does not rely on the verification of design objectives, nor does it require structural analysis. The design strategies and methods are further discussed and compared in detail in Chapter 5. Applicable standards and guidelines, such as the Canadian code73 or the ASCE 7-02 guideline,61 often focus on prescriptive design rules that are intended to provide continuity and ductility, assuming that also robu ro bust stne ness ss or co coll llap apse se re resi sista stanc ncee is th thus us en enha hanc nced ed.. Mo More re de deta tail iled ed spec sp ecifi ifica cati tion onss ca can n be fo foun und d in th thee GS GSA A gu guid idel elin ines es75 and in the United Facilities Criteria,76 where prescriptive design rules are given but also certain cases of assumable local failure are specified aiming at the provision of alternative load paths (see also Section 4.3.4). Eurocode Euroc ode EN 19911991-1-7 1-770 classifies the approaches for handling accidental design situations into strategies based on identified accidental acti ac tion onss an and d st stra rate tegi gies es ba base sed d on li limi miti ting ng th thee ex exte tent nt of lo loca call fa fail ilur uree (caused by unidentified accidental actions). Each of these two strategies can be pursued by three different methods. One of the methods for handling identified accidental actions is providing robustness — a structural property that remains undefined and unquantified. One method 47



for limiting the extent of local failure is to design key elements for a specified accidental design action — which aims not at limiting but at preventing local failure. The scheme thus appears inconsistent, or at least poses some questions. Nevertheless, the design strategies and methods listed above are all addressed in one way or the other, except for ‘isolation by segmentation’. The applicability of the various methods is related to the consequences classes mentioned in Section 4.3.1 above. The Eurocode strategy based on limiting the extent of local failure aligns with Approved Document A.67 The latter refers to BS 595068 and BS 811069 for the design of steel and concrete structures, respectively, concerning details of prescriptive design rules, checking and limiting the effect of local failure, and providing specific local resistance to key elements. The differences between the current European and UK standards on accidental actions and progressive collapse are summarised in Ref. 71. Although the design method ‘isolation by segmentation’ is not yet explicitly mentioned in standards or guidelines, it has already been used in bridge design,33 and can be considered a fully fledged and generally applicable design alternative, as outlined in previous publications by the author.55,99 Instead of segmentation, the term ‘compartmentalisation’ was used there. In this book, the term ‘segmentation’ is preferred, as explained in Section 5.3.3.

4.3.4 Verification procedures The assessment of the collapse resistance of a structure and the application of direct design methods for ensuring this property require suitable verification procedures. The structure is to be examined by these procedures to evaluate its sensitivity to accidental circumstances. The general approach follows from the quantitative definition given in Section 4.2.2 that is rooted in the design objectives presented in Section 4.3.2. If assumable accidental circumstances or actions according to design objective 1 lead to unacceptable total damage according to design objectives 3 and 4, the collapse is considered disproportionate, and the finding would be ‘susceptible to collapse’. Otherwise, the structure is collapse resistant, and verification is complete. Given the deterministic nature of the design objectives, the analyses required for verification are also performed deterministically. If collapse resistance is alternatively verified by verifying robustness, the structure must notionally be modified by inflicting local failure 48



according to design objective 2, and its response to this must be examined. Local failure can be modelled by the removal of one or more load-bearing elements, by cutting connections or cross-sections of members, or by releasing individual structural constraints. The questions about the actual cause and probability of local failure are irrelevant to the assessment of robustness. Thus, increasing the level of safety against local failure is also irrelevant to this assessment (unless this increase is also provided to elements not assumed to fail in a particular case of initial local failure). On the other hand, this approach eliminates the need to make statements about the nature and extent of assumable accidental circumstances. As noted before, this means a substantial simplification, given the intrinsic difficulties in making such statements. Even if the cause and probability of initial local failure do not need to be specified, the assumable cases of initial failure must be properly chosen and modelled realistically. The governing choice will not normally be obvious at the outset. The various cases of initial failure included in design objective 2 must thus be examined one after another. The initial local failure can be modelled in various ways, as specified above. In any case, the removal of elements or similar modifications of the structure should normally be implemented as a sudden event and examined by dynamic analysis. Assuming a delayed instead of a sudden initial failure often, but not always, leads to a smaller dynamic response of the structure (a counter-example is given in Section 5.3.3). If such a delay is justified and quantified based on design objective 1, it can be considered in the dynamic analysis, and a reduced dynamic response possibly results. The response of the structure to the static and dynamic actions (removal of elements or structural constraints, permanent action, and, possibly, parts of non-permanent action) must be examined as realistically as possible. In view of the effects that are typically involved and need to be considered — such as inertia forces, large deformations and displacements, inelastic material behaviour, and damage, as well as separation, fall, and impact of structural components — this examination generally requires a geometrically and materially nonlinear dynamic analysis in the time domain. In particular cases, it can also be performed by model or full-scale tests (see Ref. 30 for an example). The more realistic and accurate the examination, the more confidence can be had in the finding ‘collapse resistant’. Such detailed investigation places high demands on the expertise of the professionals in charge and on the modelling effort. The use of simplified verification procedures should therefore be considered, 49



although their accuracy must be checked. Simplification can be achieved by assuming linear material behaviour or by performing less sophisticated analyses. Dynamic action, for instance, could be handled in a simplified way, and large deformations could be neglected. A nonlinear dynamic analysis in the time domain can, in some cases, be replaced by a quasistatic analysis that is performed in a linear or nonlinear fashion. In this case, the static force in an element or constraint being suddenly removed is multiplied by a dynamic amplification factor and then applied as a static load. The dynamic amplification factor can possibly be determined using a generalised single-degree-of-freedom system, if necessary resorting to response spectra (see Section 5.3.3 for an example). The accuracy of simplified verification procedures must be validated by comparative numerical examination with more accurate methods. Such examination is done for particular structures. The validation, therefore, applies to other structures only if they are sufficiently similar to the structures being examined. This, in turn, suggests that a classification of structures with respect to the accuracy and admissibility of simplified verification procedures should be developed. Such a classification can be based on the governing types and mechanisms of collapse (see Chapter 2). For instance, simplified verification procedures that resort to quasi-static analysis might be admissible for structures that are prone to zipper-type collapse. They are more difficult to justify for structures whose collapse behaviour is affected by impact forces, that is, structures that are susceptible to pancake-type or domino-type collapse. When simplified verification procedures whose accuracy has not been validated are used, confidence can only be had in the finding ‘susceptible to collapse’. Analysis-based but simplified verification procedures are described in the GSA guidelines.75 Their application is limited to buildings where no complex system response is expected. Otherwise, a more sophisticated investigation, such as by nonlinear dynamic finite element analyses, is required. The United Facilities Criteria76 distinguish design and verification requirements according to basically three levels of protection. For the lowest level, only prescriptive design measures are required. For the other levels, alternative paths must be provided. In doing so, three different kinds of analysis can be performed, namely linear static, nonlinear static, or nonlinear dynamic. Static analysis has to be performed for a factored load combination specified in such a way that the analysis is effectively similar to a quasi-static analysis with a dynamic amplification factor of 2.0. Requirements put on nonlinear dynamic analysis are explained. It is not defined, though, which kind of analysis is to be used in which case. 50



The PTI recommendations64 state that in the design of cable-stayed bridges the effect of cable loss can be determined by performing a quasistatic analysis with a dynamic amplification factor of 2.0. Alternatively, a dynamic amplification factor determined by nonlinear dynamic analysis can be used. These recommendations are further discussed in Section 6.2.3. Eurocode EN 1991-1-770 gives guidance on the kind of analysis to be used for determining the effect of vehicle impact. This refers to the structural response to specific accidental actions and not to initial local failure.

51


5 Design methods 5.1

General

Design measures for ensuring collapse resistance can be classified into indirect and direct methods (see Section 4.3.3). Indirect design relies on prescriptive design rules such as, for instance, the requirement of concrete reinforcement continuity. Direct design is a performancebased approach. It is more sophisticated in that it is based on the verification of design objectives and requires structural analysis. In the following, both approaches are presented, starting with the direct design methods, which are the main focus here. Direct design methods can be derived from the definition of collapse resistance given in Section 4.2.2 that refers to the design objectives outlined in Section 4.3.2. If assumable accidental circumstances or actions lead to unacceptable total damage, then the structure is deemed susceptible to collapse, and the design objectives are not met. This deficiency can be corrected by pursuing one of two different strategies. The design measures can be based either on increasing the level of local safety and thus enhancing the effort to prevent an initial local failure (design strategy 1) or on limiting the total damage following an assumed local failure (design strategy 2). The latter requires verification of and design for local failure events or ‘load cases’. If design objective 1 (i.e. the assumable accidental circumstances or actions) has been specified, both routes are viable. If design objective 1 has not been specified — in which case design objective 2 (i.e. the assumable cases of initial local failure) must at least be established — then only the second option remains: limiting the consequences of local failure. For both design strategies, the identification of the so-called key elements is important. A key element is a structural member (or a part of the structure) that meets two conditions: first, it is not larger than the structural part assumed to initially fail at a time (design objective 2); second, its failure, if no countermeasures are taken, results in 52


Design methods

Fig. 5.1 Structural design concept of the Alfred P. Murrah Federal Building (simplified)

unacceptable total damage (design objectives 3 and 4). Thus, by referring to the design objectives, a quantitative and clear definition is also obtained for the term ‘key element’. Applying this definition generally involves structural analysis that should meet the quality requirements outlined in Section 4.3.4. In some cases, key elements can be identified by inspection. Further discussion will be illustrated with examples. The Alfred P. Murrah Federal Building (Oklahoma City, USA) partially collapsed in 1995, following the detonation of an ammonium nitrate—fuel oil mixture equivalent to 1800 kg of TNT inside a truck in front of the building (see Fig. 5.19).9,10 According to the structural design concept, every second exterior column, here referred to as a secondary column, was indirectly supported by a continuous transfer girder that ran across the face of the structure at the second floor (Fig. 5.1). The other exterior columns, here referred to as main columns, extended down to the foundation. For the sake of argument, it is assumed that the detonation caused the immediate destruction of only one main column (Fig. 5.2). (In reality, further main columns might have been directly affected.9) The structure was not able to redistribute the force carried by that column to the neighbouring main columns. The failure of the transfer girder and the failure of the adjacent secondary columns resting on the transfer girder (Fig. 5.3) led to a collapse progression that, possibly promoted by impact loading and horizontal forces (see Section 2.2.6), spread through the neighbouring spans and eventually affected a major part of the structure. For the Alfred P. Murrah Federal Building, the design objectives could have been specified, for instance, as follows: 53



Fig. 5.2 Detonation and destruction of one main column .

. .

.

.

Design objective 1: blast loading corresponding to the size of an explosive charge and the standoff distance as can be determined according to, for example, the American Society of Civil Engineers (ASCE) security guideline,97 or accidental design actions as specified in, for example, Eurocode EN 1991-1-7.70 Design objective 2: sudden failure of a main column. Design objective 3: no collapse progression, that is, no failure of neighbouring main columns and no fall of floors. Design objective 4: any damage to the non-collapsed remaining structure as long as safety and physical integrity of persons are not compromised; light damage to the surroundings; light indirect losses. Design objective 5: increased partial safety factors when using the design method ‘specific local resistance’; reduced partial safety factors when using the design strategy ‘assume local failure’; the combination of actions, in the latter case, consists of the sudden loss of a structural member, permanent loads, and reduced non-permanent loads.

Fig. 5.3 Failure of the transfer girder and secondary columns

54


Design methods

Fig. 5.4 Specific local resistance

Impact loading does not occur as long as design objective 3 is met. It is assumed here that, with these specifications, the lower part of each main column (i.e. the section between the foundation and the transfer girder) becomes a key element.

5.2

Prevent local failure

5.2.1 Specific local resistance Design strategy 1 (prevent local failure) centres on the structural members identified as key elements. Their safety against initial failure is increased. This is preferably achieved by designing the key elements for the actions specified by or resulting from design objective 1. They are thus provided with specific local resistance. In the case of the Alfred P. Murrah Federal Building, this would mean that the lower parts of the main columns are designed for blast loading, or the corresponding accidental design actions, and are thus made particularly resistant (Fig. 5.4).

5.2.2 Non-structural protective measures If specific local resistance cannot be achieved or would require disproportionate effort, the safety against failure of key elements can also be increased by non-structural protective measures that avert harmful events or attenuate detrimental actions (event control). Such measures can include limitation or control of public access, barriers to resist vehicle impact and to increase the standoff distance for reducing blast loading from deliberate attack, sacrificial elements to mitigate blast loading, and other protective measures. Again, the measures to be 55



Fig. 5.5 Bollards protecting a building entrance against vehicle intrusion and increasing the standoff distance (Canary Wharf, London). (Photograph: Stuart Alexander)

taken are guided by the assumable accidental circumstances or actions specified as design objective 1. The example shown in Fig. 5.5 illustrates that protective measures can be designed to be attractive and unobtrusive.

5.2.3 Discussion and further remarks Ensuring high safety against initial local failure (design strategy 1) requires more than the use of high design loads or recourse to protective measures. A local failure can also be caused by occurrences such as corrosion or fire — events that are more effectively counteracted by corrosion protection, regular inspection, fire protection, and firefighting systems (which, in a wider sense, are also non-structural protective measures) than by increasing design loads. In general, the effectiveness of design strategy 1 eventually depends on the completeness and validity of the accidental circumstances and actions specified as design objective 1. Since these concern events that are unforeseeable or occur with very low probability, completeness and validity cannot be verified, and thus may not be ensured. This uncertainty must be countered by encouraging, and enforcing as 56


Design methods

much as possible, a high level of safety consciousness throughout all stages of a project. Soil investigation, structural design, and construction must meet enhanced quality requirements when key elements are concerned. Possible hazards and all possible kinds of detrimental accidental circumstances should be identified using foresight and imagination. This applies, in particular, to events that are associated with accidents or malicious action, but also to local lack of resistance due to human error. Because of both the inventiveness and fallibility of human nature, foresight and imagination are particularly important for tracing those detrimental circumstances that result from human action. Part of such an approach, for instance, is to put oneself in the mindset and position of potential aggressors, taking into account their intentions and resources. Structural engineering knowledge on the part of the aggressor must be assumed as a given. Tracing the corresponding hazards is therefore not only the responsibility of risk consultants but also of structural engineers. The development and codification of accidental design actions to account for accident-related or malicious circumstances are incomplete. Further effort is necessary both in terms of accidental circumstances and types of structures to be covered. Accidental design actions should also be differentiated according to the criticality of the affected structural members, that is, they should be increased for key (i.e. critical) elements. This also applies to the ordinary design loading conditions, such as dead load, live load, wind, snow, and earthquake, which, with low but not zero probability, can occur with more severity than usually considered. For bridges and other structures over water, this list further includes loads from ship collision, waves, current, and drifting ice. The influence of the criticality of the affected structural member can be factored in by differentiating the partial safety factors on the load side accordingly (design objective 5). The partial safety factors for material and soil resistance should likewise be increased for the key elements, which can include certain areas of the subsoil. The construction stages are of particular importance, although it is difficult to cover them in a standardised way. Temporary bracing, auxiliary piers, and other construction devices can now also become key elements. Instead of specifying accidental design actions, an overall increase of safety factors might be more expedient. Alternatively, the requirement can be made to consider specific accidental actions, such as falling construction equipment or collapsing formwork, and to design the key elements for the loading resulting from such occurrences. 57



If such an approach is impracticable, the site safety requirements for the construction stages identified as critical can be raised. In any case, the site manager should be informed and aware of the key elements, identified during design, that exist in the various construction stages and the completed structure. It must be noted that although high safety against initial local failure can be achieved, this safety cannot be absolute, and in the face of unknown future events may not even be as high as hoped for. Since design strategy 1 does not explicitly aim at increasing robustness, a local failure that, despite all provisions, does occur can still cause collapse. Nevertheless, its application is justified in certain cases, in particular when the significance and exposure of the structure are not extremely high, the assumable accidental actions are relatively small, or when the methods based on design strategy 2 (see Section 5.3) are inapplicable — provided the key elements are clearly and fully identifiable. Design strategy 1 can be cost-effective as long as the combined size of all key elements is small compared with the size of the structure. Small to medium-sized buildings with transfer girders providing indirect load transfer, for instance, can be made sufficiently collapse resistant through local strengthening of the main columns (see Section 5.2.1) if the alternatives ‘modification of structural system’ or ‘strengthening of transfer girder’ (see Section 5.3.2) are unsuitable for architectural or other reasons. Likewise, for small to medium-sized bridges up to, say, 1000 m in length, providing high safety against local failure might be preferable to the ‘segmentation approach’ (see Section 5.3.3). For structures characterised by series primary load transfer, the applicability of the methods based on design strategy 2 can be impaired, in which case collapse resistance might better be achieved by following design strategy 1, in particular by providing specific local resistance to key elements (see Section 6.3). However, if design strategy 1 is applied to structures of extremely high significance and exposure, such as, for instance, the Freedom Tower, New York, or the Messina Bridge, Italy, an informed societal consensus must be reached not only on the underlying design objectives but also on the acceptability of the residual risk of collapse. A systematic comparison of design strategies 1 and 2 is given in Section 5.4.

5.3

Assume local failure

5.3.1 General Absolute safety against initial local failure cannot be achieved. Design strategy 1 (prevent local failure), discussed in the previous sections, 58


Design methods

Fig. 5.6 Column failure introduced as load case ‘local failure’

should therefore be applied to extremely significant and exposed structures only when other methods are inapplicable, or in conjunction with other methods. For other types of structures, a high level of safety against local failure might be achievable, and the residual risk acceptable, but the resulting costs of construction and protection are disproportionately high. At least in such cases, it is better to strive for collapse resistance not by high safety against local failure but by taking the alternative route, if viable, offered by design strategy 2 (assume local failure). Accordingly, initial local failure as specified by design objective 2 is postulated, and it is ensured, during design, that the ensuing collapse and damage do not exceed the limits set forth by design objectives 3 and 4. If the key elements have already been identified in accordance with Section 5.1, the further design and verification process can be based on the assumed failure, one at a time, of the key elements only. In this way, collapse resistance is indirectly verified by verifying robustness. In the case of the Alfred P. Murrah Federal Building, the lower part of each main column was identified as a key element. The sudden failure of each of these elements is to be considered as a triggering event, and investigated separately as a dynamic load case. The dashed line in Fig. 5.6 represents one such key element. Verification of robustness and collapse resistance is deemed complete when design objectives 3 and 4 suggested in Section 5.1 are proven to be met. The verification procedure and the corresponding structural analysis should meet the quality requirements outlined in Section 4.3.4.

5.3.2 Alternative load paths As suggested above, the requirement of ‘no collapse progression’ could have been adopted for the Alfred P. Murrah Federal Building as design 59



Fig. 5.7 Modification of the structural system

objective 3. This specification calls for limiting the collapse to the initially failing structural member, that is, to the lower part of a main column. To achieve this objective, at least two different measures are available. On the one hand, the indirect support of the secondary columns by the transfer girder, identified as problematic, could be replaced by direct support (Fig. 5.7). In the modified structure, all columns extend down to the foundation, and are main columns. In the case of failure of the lower part of a column (see dashed line in Fig. 5.7), the upper part of that column becomes a secondary column supported by the lower girder (i.e. the girder at the position of the former transfer girder). The effective span length of that supporting girder after failure initiation is the same as that of the transfer girder of the undamaged original structure. It will thus be possible to design and verify the girder for this loading condition. Although this loading is significantly increased by dynamic action due to the suddenness of the initial failure, the requirements on the design are substantially relaxed, on the other hand, when adopting design objectives 4 and 5 as suggested above. In particular, when damage to the non-collapsed remaining structure is acceptable as long as human safety is not compromised, verification can be restricted to the true ultimate limit state. The ultimate load-bearing reserves due to, for instance, catenary action can thus be fully utilised. Furthermore, reduced partial safety factors can be used on both the load and the material side. In the considered case of failure, the supporting girder becomes part of an alternative load path for the forces otherwise carried by the lower part of the affected column. The existence of alternative paths will simply be referred to as redundancy. The specific meaning of this term in this context is redundancy of the structure with respect to its ability to carry loads. Redundancy is increased by the design modification just 60


Design methods

Fig. 5.8 Strengthening of the transfer girder

described. This assessment is, at least in this case, also intuitively confirmed by the increase in static indeterminacy of the structural system. It should be noted that the suitability of this approach depends on the design objectives. It might be reasonable, for instance, to change design objective 2 for the modified structure by assuming the initial failure of not one but three adjacent columns. In this case, the design modification brings little improvement (if all columns have the same strength as the main columns of the original structure) or may even be detrimental and increase the risk of failure progression (if the columns are designed for smaller forces due to the higher number of columns). Modifying the structural system might be undesirable, in particular when there are architectural or serviceability reasons for indirectly supporting secondary columns on a transfer girder. A second measure could then be implemented as an alternative: the topology of the structural system is retained but the transfer girder is strengthened by designing it for the dynamic loading resulting from the sudden failure of the lower part of a main column (Fig. 5.8). If the lower part of a main column fails, the upper part of that column together with the adjacent secondary columns are then supported by the transfer girder. An alternative load path is provided, and thus structural redundancy is increased also by this measure. Note that in this case, however, the increase in redundancy is not accompanied by an increase in static indeterminacy. In view of the now fairly large span after failure initiation, it may prove difficult to strengthen the transfer girder sufficiently. On the other hand, advantage can again be taken of relaxed requirements on the design when verifying the transfer girder for this extraordinary load case. 61



If the transfer girder cannot be strengthened sufficiently, further design alternatives are available that also retain the topology of the structural system. Instead of supporting the upper part of the affected main column by the transfer girder only, the exterior girders above the transfer girder can be designed to participate in the alternative load transfer and carry their share of column loading. The entire structure, and not just the transfer girder, can now redistribute the forces and bridge the failed member. Furthermore, the structure can be designed not as an ordinary frame but as a special moment-resisting frame,10 a concept also used in seismic engineering. Also in this case, advantage can be taken of a substantial amount of damage being acceptable in the non-collapsed remaining structure. Ultimate total collapse will not occur until the plastic reserves, which are large in such a specifically detailed and highly redundant structure, are exhausted. Activating the other exterior girders and designing the structure as a special moment-resisting frame is also an option when the first approach initially outlined above is taken, that is, when the structural system is modified. Alternative load paths can develop in various ways, and there are a variety of different modes of load transfer and structural members involved. In the aforementioned case, the flexural capacity of the main load-bearing elements and, if necessary, the plastic reserves of the structure are mobilised. In other cases, alternative load paths can form through the mobilisation of axial or torsional resistance. The inversion of flexural load transfer, for instance from hogging to sagging above a failing column, the transition from flexural to tensile load transfer (catenary action), for instance in concrete floors or in steel beams, and the transition from plane to spatial load transfer, for instance in one-way slabs turning into two-way slabs, are all possible. If plastic reserves are used, a sufficient degree of ductility must be ensured. Note that the provision of additional alternative load paths, and thus an increase in redundancy, is often accompanied by an increase in continuity. As shown in the next section, the terms ‘redundancy’ and ‘continuity’ are nevertheless different and should not be used synonymously.

5.3.3 Isolation by segmentation For certain structures, the alternative-paths method will reach its limits. The Confederation Bridge crosses the Northumberland Strait between Prince Edward Island and the Canadian mainland. It is a continuous 62


Design methods

Fig. 5.9 The Confederation Bridge (Canada)

prestressed concrete box girder bridge consisting of 43 main spans of 250 m each and shorter approach spans on either side. The total length is 12 910 m (Figs 5.9 and 5.10). If this structure were to be made robust and collapse resistant by providing alternative paths, an initial local failure to be considered would be the failure of a bridge pier. This failure event, in turn, would require designing a prestressed concrete frame with the double-span length of 500 m — arguably a vain endeavour even if resorting to catenary action. The design method chosen was to isolate collapsing sections, and thus to limit the extent of collapse, by a segmentation of the structure.31—34 The specification of the design objectives for this particular structure illustrates some of the remarks made in Section 4.3.2. The design objectives were established by the design engineer in consultation with the owner and the supervising authority, Public Works Canada. In doing so, the considerations just outlined concerning the available design options and the idea of isolating an incipient collapse were incorporated. Accordingly, the sudden failure of a main bridge pier was to be assumed in the design (design objective 2). For the structural system

k c i w s n t n u r e B m w t u e b N a

% – 2. 3

EI. 40.80 EI. 0.00 (CGD) 0.0%

EI. 59.06

n o i t a g i v a n N a L p C s

% – 2. 1

+ 2. 1 %

EI. 40.80 0.0%

d n a l s I d r a w d t E n e e m c t n u i r b P a

+ 2 .1 %

Bedrock 1320

10 990

600

12 910

Fig. 5.10 Elevation of the Confederation Bridge (not to scale; dimensions in metres)

63



Fig. 5.11 Assumed cases of initial local failure and the acceptable extent of collapse

of the preliminary design, this led to two different cases of initial local failure to be considered (Fig. 5.11, pier B or pier C). The acceptable extent of collapse (design objective 3) was set by specifying the collapse boundaries (pier D and hinge H1); any collapse starting within these boundaries must not transgress them. Further design objectives were not formally established. The verification of the remaining structure outside the collapse boundaries, however, was restricted to the ultimate limit state, and reduced partial safety factors were used. Furthermore, the plastic cross-sectional and system reserves were used. This meant that a certain level of damage to the parts of the non-collapsed remaining structures that lie immediately adjacent to the collapsing section was implicitly assumed to be acceptable (design objective 4). The segmentation method is related closely to the concept of collapse isolation. By specifying collapse boundaries, the structure becomes notionally segmented already. The locations of the actual segment borders, however, do not necessarily have to match those of the collapse boundaries. The segment borders are chosen by the design engineer, and can lie within the collapse boundaries, which are minimum requirements established as design objectives. The segment borders are formed by isolating elements. The structural detail of the isolating elements and their mode of operation as segment borders still need clarification. This design method requires the verification of the segment borders and the remaining structures for the forces resulting from incipient collapse. Particular attention must be paid to the isolating elements that form the segment borders. For the Confederation Bridge, further study showed that they lie in the region between hinge H1 and pier A and the region between hinge H2 and pier D (Fig. 5.11). Although the isolating elements are not key elements in the special sense defined in Section 5.1, their safe performance as collapse-isolating segment borders is likewise crucial for the effectiveness of the method. They are therefore referred to here as relevant elements. An obvious design approach would be to provide these elements with high local resistance. 64


Design methods

Fig. 5.12 Bending failure at cast-in-place joint

Verifying that their resistance is adequate, however, can be difficult because of the mostly large magnitude of the collapse-induced forces. This difficulty is often compounded by uncertainties in the modelling and analysis process. This will be illustrated with the example of the Confederation Bridge. Among other aspects, the response of the remaining structure to the left of hinge H2 (Fig. 5.11) after a sudden loss of support at that hinge was to be investigated. In the preliminary design, the initially affected region, between hinge H2 and pier D, consisted of a 75 m-long cantilever beam and a 100 m-long precast drop-in girder that was monolithically connected to the cantilever beam by a cast-in-place joint and continuous prestressing tendons. Static and dynamic analysis31,33 showed that the sequence of collapse would be marked by the following distinct events: .

.

.

.

.

.

The girder fails in bending under its own weight at the cast-in-place joint (Fig. 5.12). The drop-in girder rotates around this point, remaining connected to the cantilever through the continuity tendons. The free end of the drop-in girder hits the water; the drop-in girder fails in bending due to the inertial forces induced during its sudden deceleration. Large forces are transmitted to the cantilever during this violent event; shear failure occurs at the cantilever end. The continuity tendons cut through the cantilever bottom slab in longitudinal direction, thus crippling the bending resistance of the cantilever. The failure progresses throughout the cantilever towards pier D (Fig. 5.13).

Note that the analysis had to consider not only large deformations and dynamic forces but also unusual kinds of interaction such as the drop-in girder hitting the water or the continuity tendons bearing on the cantilever bottom slab and cutting through it. The results of further analysis therefore depended more and more on the modelling 65



Fig. 5.13 Failure progression towards pier D

assumptions. The analytical prediction of the further course of failure was thus deemed to lack the accuracy and certainty required for design and verification. In any case, it seemed possible that the collapse could progress into the next span, beyond pier D, and then into the further spans, similar to the collapse of the Haeng-Ju Grand Bridge (see Section 1.2). Verification of adequate resistance of the isolating element was not possible because of both the high loading and the analytical uncertainties. Both problems can be solved, or at least mitigated, by selectively eliminating (i.e. breaking) continuity, by reducing stiffness or through ductility. By inserting joints, break-away hinges, or structural fuses, or by providing plastic hinges at the segment borders, the loading on such isolating elements is reduced and the analysis simplified. The mode of effectiveness of the isolating elements in this case is not based on high resistance against forces but on the ability to accommodate large deformations and displacements, and the elimination or reduction of forces or a large energy dissipation capacity thus achieved. A combination of such measures was used in the design of the Tasman Bridge, and proved successful (see Section 1.2). For the Confederation Bridge, it seemed particularly important to interrupt the continuity of the prestressing tendons to allow for an early and safe separation of the falling drop-in girder from the remaining structure, thus avoiding the problems described above. An attempt was made to design a structural fuse within the cast-in-place joint between the cantilever beam and the drop-in girder. However, no convincing way was found to cut the continuity tendons automatically and safely after the onset of collapse, and so the idea was abandoned. Hence, it was deemed necessary to eliminate or, more precisely, reduce continuity at that location. 66


Design methods Monolithic connection H2

Preliminary design Hinge H2

Final design

Fig. 5.14 Insertion of a hinge in every second span

This change was brought about by a permanent modification of the structural system. Compared with the preliminary design, the final design comprises one additional hinge in every second span of the main bridge (Fig. 5.14). Each of these additional hinges replaces an originally planned cast-in-place joint. This means that the drop-in girder in every second span is connected to the cantilever beams by hinges at both ends. In the other spans, which also consist of two cantilever beams and one drop-in girder each, the drop-in girders remain monolithically connected to the structure by cast-in-place joints at both ends. The prestressing tendons are subject to a natural interruption of continuity at the hinges. A reliable isolation of local failure is thus achieved. If the support at hinge H2 is lost, the drop-in girder extending between the inserted hinge and hinge H2 will fall and separate from the remaining structure in a predictable way. The disengagement will be forced and is defined by the geometry of the hinge corbel (Fig. 5.15).

θ θ

Fig. 5.15 Forced disengagement of drop-in girder at hinge

67


Progressive collapse of structures F (t )

12

MN

F dyn(t )

10 F st

8 6 4 2 0 Time

Fig. 5.16 Vertical force at cantilever tip during the fall and separation of a dropin girder

This is also the case when the hinge bearing is not movable but fixed. Hinge corbels with fixed or movable bearings are examples of break-away hinges. As a further measure, the length of the drop-in girders was reduced from 100 m to 60 m, to ensure the separation of a falling drop-in girder before its free end hits the water, and so to avoid the structural and analytical problems associated with this event. This design modification provides two additional benefits for the collapse resistance of the structure. First, the dynamic loading on the remaining structure during the fall and separation of a drop-in girder is reduced. Second, the remaining cast-in place joints are shifted into a position where the collapse-induced sectional forces from the collapse of an adjacent span are smaller. The remaining structure was checked for the impulsive dynamic loading that acts on the cantilever tip during the fall and separation of a drop-in girder. This event and the resulting impulsive loading can now be accurately analysed (Fig. 5.16).31,34 For simplicity and to counter some remaining modelling uncertainties, linear response spectra of a single-degree-of-freedom system were developed for the acting impulsive loading (Fig. 5.17). From this, an overall dynamic amplification factor was determined that was used in a nonlinear quasi-static analysis and verification of the remaining structure. The dynamic amplification factor was 2.6. This is larger than the value of 2.0 that would result for a simple step impulsive loading. The actual load impulse would be more complex (Fig. 5.16). When the support at hinge H2 fails, the vertical force on the cantilever tip suddenly drops 68


Design methods 3.00

2.00

t s

F / ) t η

( n n y i d F m , – η = x ) t a ( n m

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y

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–

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–1.00 0.00

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1.50

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Fig. 5.17 Impulsive dynamic loading and spectra of extreme positive and negative responses

to half of its pre-failure value. After rising again during the rotation of the drop-in girder, it suddenly drops to 0 at the moment of disengagement. If these two sudden events are tuned to a modal frequency of the remaining structure, which would be the case here, a resonance amplification of the structural response occurs. In the nonlinear quasi-static analysis performed for the Confederation Bridge, the formation of plastic hinges was deemed acceptable; plastic cross-sectional and system reserves were used when verifying the collapse resistance of the structure. The validation of such a simplified verification procedure with more accurate methods, as suggested in Section 4.3.4, was not performed because of a tight design schedule. From today’s perspective, with the computational resources and analysis programs now available, a more accurate investigation by nonlinear dynamic analysis in the time domain seems desirable and possible. A detailed account of the progressive collapse study undertaken during the design of the Confederation Bridge is given in Ref. 31; abridged versions can be found in Refs 33 and 34. This section on the segmentation method will be concluded with some more-general remarks. Limiting the effect of local failure without considering the cause or the probability of its occurrence corresponds to the design strategy ‘assume local failure’. It is ultimately also the basis of the alternative-paths method, which is frequently mentioned in the literature and recommended in standards and guidelines.60,67,75 The same goal can be achieved by segmentation, however, which opens up a design alternative that has received little attention so far. 69



Segmentation is performed by specifying and implementing segment borders. The locations of the segment borders are chosen by the design engineer within the scope of the design objectives. The segment borders are formed by isolating elements whose isolating effect is achieved by one of three different modes of effectiveness: 1. the capability to accommodate large forces, that is, by high local resistance 2. the capability to accommodate large deformations and displacements, that is, by eliminating continuity or reducing stiffness, which causes a reduction of forces 3. the capability to accommodate large forces and large displacements at the same time, which usually means by high ductility and a large energy dissipation capacity. Segmenting a structure to isolate an incipient collapse has a functional similarity to dividing a structure into fire compartments to confine a fire to the compartment of origin. For this reason, the term ‘compartmentalisation’ was used in earlier publications by the author55,99 instead of the term ‘segmentation’ used here. Referring to the collapse resistance of a structure, however, the term ‘compartmentalisation’ appears in the literature with different meanings. The mention in the Canadian code73 appears to refer to segmentation in the sense understood here. It is used differently, though, by Corley et al.10 and in the ASCE 7-02 guideline.61 In these publications, it denotes a particular kind of residential building structure consisting of small, box-like compartments made up of monolithically connected reinforced concrete slabs and walls. Similarly to a moment-resisting frame, the increased collapse resistance of such a structure would result from the availability of alternative paths, that is, from redundancy, and not from a deliberate isolation of incipient collapse at defined segment borders. To avoid confusion, and also for brevity, this book uses the term ‘segmentation’ to denote the structural design method discussed in this section. A local elimination of continuity — in the case of the Confederation Bridge, by inserting hinges — reduces the degree of static indeterminacy. The redundancy of the structure was not reduced by this measure, however, because it did not remove any feasible alternative load path — keeping in mind that designing a 500 m span, even though a theoretical option offered by the original structural system, was impracticable. On the other hand, the robustness of the structure, that is, its insensitivity to local failure, and so its collapse resistance 70


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were increased. This shows that associating the degree of continuity or static indeterminacy with redundancy and equating redundancy with robustness or collapse resistance, even if possible for particular types of structures, is not generally justified. It is therefore important not to confuse all these terms, as is sometimes done, but to distinguish between them carefully.

5.3.4 Redundancy versus segmentation Apart from the Confederation Bridge and the Tasman Bridge (see Section 1.2), the segmentation approach has so far only been mentioned sporadically in the literature72,73 and without discussing the mode of operation and the structural details of the segment borders. Nevertheless, other past applications in bridge design are probable, but may have gone unpublished. The application to the design of the Confederation Bridge was substantiated by the difficulty of providing alternative load paths. This approach may still be preferable, though, even when alternative paths can be provided. To word this more strongly, the increase in continuity that often accompanies the provision of alternative load paths may, in certain cases, promote rather than prevent failure progression.92,99 This view is supported by eye-witness accounts of fire fighters and controlled demolition experts who have observed the collapse of buildings.43,52 According to these accounts, local failure may actually pull down a greater portion of the building when structural components such as frames or diaphragms are tied together too well. Such observations seem plausible, considering that failure progression requires a certain level of interaction, which, in turn, could mean a certain degree of connectivity and continuity, between structural components. In the light of these considerations, the Ronan Point incident, an often cited example of progressive collapse, can be interpreted differently. Triggered by a gas explosion in one of the upper storeys, one corner of the building collapsed over nearly its entire height. The larger part of the building, however, remained undamaged (Fig. 5.18). The progressive collapse of floor slabs in this incident has been ascribed to a lack of continuity in the slab reinforcement. On the premise that the collapse of a major part or the whole of a building must be prevented, however, and contemplating the segmentation approach, such a lack of continuity does not seem so unreasonable after all. At least it would be an alternative in a design where alternative paths cannot be provided safely. 71



Fig. 5.18 Partial collapse of the Ronan Point building triggered by an internal gas explosion (London, 1968)

Stimulated by the Ronan Point incident, requirements for enhanced structural continuity have been included in building codes (e.g. Refs 67, 70, 73, and 74) in the form of prescriptive design rules (see also Section 5.5). These provisions are intended to lead to an overall increase in robustness and collapse resistance. They appear to have been successful in the UK against the kind of event experienced in the IRA bombing campaigns. Nevertheless, they may not be appropriate for other kinds of events and other types of structures. In any case, the objective of increased robustness and collapse resistance is not achieved if the alternative load paths resulting from enhanced continuity become overloaded. In this context, an observation made by Corley et al.9 concerning the partial collapse of the Alfred P. Murrah Federal Building is of interest. If only one main column was destroyed by direct blast action (one of the 72


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Fig. 5.19 Partial collapse of the Alfred P. Murrah Federal Building (Oklahoma City, 1995)

possibilities discussed in Ref. 9), it is argued that the two neighbouring main columns could have been pulled down by their connections to the falling structural components in between them (see also Section 2.2.6). This assessment is supported by the fact that the collapse stopped at another main column located next to a discontinuity in the top reinforcement of the transfer girder (Fig. 5.19). Regarding the actual mechanism of collapse of the Alfred P. Murrah Federal Building, a reevaluation recently presented by Osteraas100 is of interest: this study confirms the possibility that only one main column may have been destroyed by direct blast action. Two more examples where structural segmentation accomplished by discontinuity has possibly prevented widespread disproportionate collapse are the Pentagon Building in Washington, DC, and the Charles de Gaulle Airport Terminal in Paris. The Pentagon Building consists of three nested building rings, each divided into five segments, and thus made discontinuous, by expansion joints. On 11 September 2001, the aircraft impact near an expansion joint caused the destruction of several columns on both sides of the joint.101 The more affected part of the outer ring, to the right of the joint (Fig. 5.20), partly collapsed while the less affected part, to the left of the joint, did not. Continuity instead of joints would in all likelihood have promoted a collapse progression, since the part to the left of the joint was heavily damaged as well and would not have been able to carry additional loads. The isolation of the collapsing section at the other end was achieved by strong structural components with high local resistance that withstood the 73



Fig. 5.20 Partial collapse of the Pentagon Building (Washington, DC, 2001)

collapse-induced forces and likewise acted as isolating elements and formed segment borders. The partial collapse of the Charles de Gaulle Airport Terminal 2E was initiated by the failure of a portion of the roof, possibly owing to design flaws and poor workmanship (the investigation into what caused the incident is ongoing). The collapse came to a halt at joints on both sides of the collapsing section, which was (unintentionally) isolated from the adjacent sections by these structural discontinuities (Fig. 5.21). If continuity had been provided, it seems unlikely that the forces that occurred during collapse could have been supported by the adjacent sections since these were structurally deficient as well. A further progression of the collapse would then have been possible. Finally, the Tasman Bridge failure incident is again considered. The bridge partially collapsed due to the impact of a ship (see Section 1.2). The collapse was limited to the three spans that were supported by the two bridge piers directly destroyed by the ship impact. The absence of collapse progression apparently resulted from the interruption of continuity of the superstructure prestressing tendons at the bridge piers, that is, from discontinuity and segmentation. The potential value of continuity will not be called into question. It must be kept in mind, however, that continuity can be harmful when 74


Design methods

Fig. 5.21 Partial collapse of the Charles de Gaulle Airport Terminal 2E (Paris, 2004). (Source: AP Photo. Photograph: Jerome Delay)

the alternative load paths that result from continuity are not provided with the strength required to withstand the actual forces occurring in an incipient collapse. This remark also applies to prescriptive design rules that aim at providing alternative paths through an overall increase in continuity (see Section 5.5). If it is impossible or prohibitively expensive to provide alternative paths with sufficient strength, the segmentation method — implemented, if necessary, by selectively eliminating continuity — has the advantage. This is also the case if alternative paths are strong enough, but the corresponding structural analysis and verification prove difficult or unconvincing. Such a problem can result from a variety of reasons: high structural complexity, large displacements, unusual kinds of interaction, or high dynamic forces (see the discussion concerning the Confederation Bridge in Section 5.3.3). Incidentally, a similar statement can be made with respect to the three different kinds of isolating elements used in the segmentation method: eliminating continuity, when compared with the alternatives of providing high local resistance or large energy dissipation capacity, will usually have the advantage of facilitating analysis and verification. The alternative-paths method, on the other hand, has the advantage when the fall of structural components or debris must be prevented by 75



any means — provided that alternative paths can be made available at all and shown to be sufficiently strong. This applies particularly to cases in which falling parts could lead to impact loading on key elements of the remaining structure. This is because such loading is usually high, and designing for it is difficult, afflicted with uncertainties, and normally out of the question. Such conditions are typically found in structures that are aligned along a vertical axis and susceptible to pancake-type collapse, that is, in high-rise buildings. Impact loading is less of a concern in structures mainly aligned along a horizontal axis such as bridges and low-rise buildings (see Chapter 6 for a more differentiated discussion). The suitability of the two design approaches compared in this section thus depends on the type of structure and its orientation in space. The alternative-paths method requires an increase in either, or both, continuity and structural resistance. Segmentation, on the other hand, can be accomplished by less continuity or more resistance. Other differences between these two methods concern the spatial distribution of the resulting design measures, the extent of collapse, and the dependency of their effectiveness on the size of the initial local failure. The alternative-paths method leads to design measures that are distributed throughout the structure; the extent of collapse increases and the effectiveness of the method decreases with an increase in initial failure size. It is therefore preferable when the size of the initial failure is assumed to be small. The segmentation method requires design measures at discrete locations within the structure; the extent of collapse and the effectiveness of the method are insensitive to the size of the initial failure (provided the segments are not too small); the extent of collapse, however, is relatively large. This method is thus preferable when the initial failure size is also assumed to be large. These dependencies indicate that the choice between the two design methods compared here in the end also depends on the given design objectives. Furthermore, both methods can be combined in different ways. If the structure is segmented and, additionally, alternative paths are provided within the segments, then the extent of collapse will not be substantially larger than a triggering initial failure for both small and large initial failure sizes. This allows more differentiated design objectives to be considered in which the assumable initial local failure and the acceptable extent of collapse are given as more than one pair of data or in an interrelated form. Another way of combining both design methods is to resort to alternative paths for the design and verification of the remaining structure outside a collapsing section that is isolated by 76


Design methods

segmentation. Such an approach was implicitly taken in the design of the Confederation Bridge when using the plastic cross-sectional and system reserves for the verification of the remaining structure (see Section 5.3.3).

5.3.5 Interaction and progressive collapse As stated in the previous section, failure progression requires a certain degree of interaction between structural components. Because interaction is of fundamental importance to the phenomenon of progressive collapse, and a complex phenomenon in itself, a separate section is dedicated here to this topic.102 Interaction is a term originating from sociology and psychology, and refers to the interdependency between acting parties. When adopting the term for technical systems, interaction denotes the interdependency between the various components of a system and between a system and the environment. Considering interaction according to this definition is nothing new in structural engineering. The influence of the structural members on each other in a statically indeterminate structure, for instance, is taken into account as a matter of course. Another example at an even more elementary level is the dependency of the applied loads on the structural dimensions, which is likewise considered in design. Nevertheless, interaction is usually accounted for in an incomplete manner. On the other hand, many kinds of interaction are negligible or difficult to quantify. It is thus essential in structural design to consider all possible kinds of interaction, to discern the important from the unimportant, and to describe the important ones with sufficient accuracy. In addition to this aspect of examination and analysis accuracy, there is another problem that is more fundamental and therefore more interesting, namely the question of whether and where interaction is beneficial or harmful and whether it should be promoted or prevented by design measures. In progressive collapse studies, all of the important kinds of interaction within a structure and between the structure and the environment must similarly be adequately considered to ensure the accuracy of examination and analysis. Compared with more ordinary structural design tasks, however, the calculability and predictability of the structural response can be compromised. This difficulty, in turn, can have an indirect effect on the design. These problems result from the fact that the interactions that develop during a collapse can far exceed those that occur under normal 77



construction and operation conditions. The structural analysis must now consider many and unusual kinds of interaction, such as the partial or complete separation of structural components and their fall and impact on the remaining structure or the surroundings. This also includes unusual kinds of action on the structure and material (e.g. cutting action on a reinforced concrete slab, and lateral action on prestressing steel: see below) and non-structural action — in particular, fire. When considering such interactions, specifics must be taken into account that are otherwise irrelevant or at least do not occur all at the same time: dynamic action and behaviour, large deformations and displacements, thermal action and behaviour, plastification, and partial destruction of the structure. For complex structures, an accurate and reliable analytical coverage of all these possible kinds of interaction will only succeed, if at all, by performing a geometrically and materially nonlinear dynamic analysis in the time domain. If there remains any doubt concerning the validity of analysis and verification, it may be necessary to reduce excessive interaction to a manageable level by changing the design. For illustration, reference is again made to the design of the Confederation Bridge (see Section 5.3.3 and Refs 31 and 33). There was some doubt as to the interaction of the continuous prestressing tendons with the enveloping reinforced concrete box girder that forms the cantilever. When studying a certain failure scenario and analysing the corresponding sequence of collapse, it was assumed that the tendons come to bear directly on the bottom slab of the box girder, cut through the slab in the longitudinal direction, and thus eliminated the bending resistance of the cantilever (see Figs 5.12 and 5.13). The assumption that such cutting would occur, and not be prevented by the rupture of the tendons due to the unusual lateral loading, is justified by the collapse of the Haeng-Ju Grand Bridge. In that incident, most of the superstructure tendons resisted the stresses caused by the rupture of the encasing reinforced concrete and the failure and fall of structural components (see Section 1.2). A quantitative description of such a process, however, is difficult. For the Confederation Bridge, at least, it could not be achieved with the required accuracy and certainty. It remained unclear how much energy would be dissipated by the cutting of the box girder bottom slab, where this cutting and the destruction of the cantilever would come to a halt, and, therefore, what the effect would be on the next span. By inserting hinges (see Fig. 5.14), and hence interrupting the continuity of the tendons, the interaction described above between 78


Design methods

the tendons and the bottom slab was eliminated. Accurate analysis and a reliable verification of collapse resistance were thus made possible. The length of the drop-in girder (i.e. the section between the two hinges in the lower part of Fig. 5.14) was reduced to such an extent (and the position of the hinges was shifted accordingly) that the drop-in girder separates from the remaining structure (see Fig. 5.15) before its free end hits the water. This design modification was likewise based on the intention to avoid a violent interaction (i.e. between the structure and the water) that is difficult to determine by analysis. It is of interest that, here, interaction influenced design decisions in an indirect manner, that is, by compromising predictability. However, the nature and degree of interaction first of all have a bearing on the structural response and thus also directly relate to design issues, in particular to the choice between the alternative-paths method and the segmentation method. While both approaches arise from the assumption of an initial local failure, they follow contrary lines of thought. Alternative paths create redundancy through the ability of redistributing forces. This approach usually requires a certain degree of structural continuity and takes advantage of the interaction between structural members. The attempt to isolate collapsing sections by segmentation, on the other hand, aims at reducing interaction. In this approach, isolating elements prevent the interaction of the collapsing section with the remaining structure. The reduction of interaction becomes particularly apparent when continuity is eliminated by the insertion of hinges or joints. Concerning the design of robust and collapse-resistant structures, each of these two contrary design methods will find its respective fields of application (see Section 5.3.4). Thus, depending on the design task at hand, either a reduction or an increase in structural interaction can be reasonable (provided excessive interaction does not compromise predictability). The overall goal of the design measures must be to promote beneficial interaction and to prevent harmful interaction. Incidentally, there are kinds of interaction concerning progressive collapse that are beyond the usual structural engineering considerations. The question of whether collapse resistance is necessary for a given structure, for instance, must be decided after also considering the exposure of the structure to circumstances such as malicious action and war (see Section 4.3.1). From a technical standpoint, however, such a relationship between design requirements and exposure could simply be interpreted as a more general form of the 79



above-mentioned dependency of the applied loads on the structural dimensions.

5.4

Local failure: prevent or assume?

Direct design methods are based on one of two strategies. They can either aim at preventing initial local failure (more precisely, making it less probable) by locally increasing safety (design strategy 1) or at limiting the total damage that follows an assumed initial local failure (design strategy 2). Each of these two strategies leads to at least two design methods, as outlined in the preceding sections. If collapse resistance is to be achieved by preventing initial local failure, the design methods ‘specific local resistance’ and ‘non-structural protective measures’ are available to ensure a high level of safety against local failure. These methods do not aim at increasing the robustness of the structure (although locally increasing its resistance may also increase its robustness). On the other hand, if a local failure is assumed, the design methods ‘alternative load paths’ and ‘isolation by segmentation’ can be used, either separately or combined, to make the structure robust and to limit the total damage to an acceptable extent. In both cases, the structural behaviour and the safe performance of key elements (design strategy 1) or other important elements (design strategy 2) is crucial. The significance and role of these elements exhibit interesting differences, which allow conclusions to be drawn regarding the application and evaluation of design methods. The key elements in design strategy 1 are to be designed for design objective 1, that is, for assumable accidental circumstances or actions. The relevant elements in design strategy 2 are alternative load paths or isolating elements that are to be checked for the actions resulting from incipient collapse. In the latter case, design objective 1 does not need to be specified. Hence, the uncertainty associated with such a specification has no bearing on the effectiveness of methods that are based on design strategy 2. This justifies the use of different partial safety factors for the different design strategies, as suggested in Section 4.3.2. Another interesting difference is that the relevant elements in design strategy 2, unlike the key elements in design strategy 1, can be chosen by the design engineer within certain limits. They are defined by the choice and the corresponding design of alternative load paths or segment borders, respectively. The extent of this design freedom depends on the design objectives. The number of relevant elements can be minimised and be kept comparatively small, in particular when using 80


Design methods

the segmentation method whose relevant elements are the isolating elements that form the segment borders. Both aspects favour methods that are based on design strategy 2 in terms of the safety-cost ratio.55,95 To illustrate, two fictitious structures S and R are considered for which the following assumptions are made: the collapse resistance of structure S is achieved by segmentation, and that of structure R by specific local resistance; both structures are similar and suitable in principle for both design methods; the probability of failure of the isolating elements of structure S, in their role as collapse isolating segment borders, is as high as the probability of initial failure of the key elements of structure R. This leads to another tentative assumption: the probabilities of progressive collapse of structures S and R, and thus their levels of safety, are of the same order of magnitude. For structure S, however, this safety comes at a lower cost. This is because the actions to be applied in the verification of the relevant elements of structure S are not due to accidental circumstances but to collapse actions. These can be determined with a relatively high degree of accuracy and certainty, and therefore be taken into account with lower partial safety factors. This advantage would also benefit a fictitious structure A, whose collapse resistance is achieved by alternative load paths. Structure S has the additional advantage, not shared by structure A, that the isolating effect of the isolating elements can be achieved not only by making them highly resistant but also by eliminating continuity — a measure that, for the same probability of failure, is attainable at a lower cost. It was tentatively assumed in this example that the probabilities of progressive collapse of structures S and R are of the same order of magnitude. In reality, however, this probability will mostly be lower for structure S (and structure A) than for structure R, which further shifts the safety:cost ratio to the detriment of the latter. This is a direct result of the underlying design strategies, according to which a complete collapse of structure S requires the progressive failure of all isolating elements, whereas a complete collapse of structure R could be triggered by the initial failure of any one key element. The mode of global load transfer (i.e. series versus parallel) and its effect on the probability of a progressive collapse was discussed in Section 3.1. Similar reasoning can be applied here to substantiate the assertion of the previous paragraph. For structure R, the probability of collapse is of the order of the sum of the initial failure probabilities of all the key elements. This holds, at least, in the extreme case that the failure of any one key element leads to complete collapse. The 81



probability of collapse, therefore, increases with the number of key elements, and can become relatively high. For structure S, in contrast, the probability of collapse is of the order of the product of the failure probabilities of the isolating elements, in their role as collapse-isolating segment borders, multiplied by the probability of an initial local failure anywhere in the structure. Thus, in this case, the probability of collapse decreases with the number of isolating elements, and hence with the number of segments, and will be relatively low. For these reasons, design methods based on the assumption of an initial local failure (design strategy 2) are preferable for structures of high significance and exposure, especially if the assumable cases of initial local failure (design objective 2) can be meaningfully and safely established by engineering judgement, and provided the structure is, in principle, suitable for these methods. In comparison with design methods aimed at preventing initial local failure (design strategy 1), they provide a high level of safety against progressive collapse at a relatively low additional cost. Moreover, they are more satisfactory from a reliability standpoint because their effectiveness is comparatively insensitive to the probability of failure of relevant elements. Uncertainties associated with accidental circumstances (design objective 1) are altogether irrelevant. These methods, therefore, remain largely unaffected by the difficulty of assessing failure probabilities. On the other hand, design strategy 1, and in particular the specificlocal-resistance method, are of interest for structures that are poorly suited for other methods. They can be preferable, for instance, for providing collapse resistance to the primary load transfer system of slender high-rise buildings, even those of high significance and exposure (see Section 6.3.2). Furthermore, these methods can be preferable for smaller structures, for structures with only a few and clearly identifiable key elements, and in cases where the extent of assumable accidental circumstances is small. More remarks on the application of design strategy 1 can be found in Section 5.2.3. The relationship between design strategies 1 and 2 is in some respects analogous to the relationship between the alternative-paths method and the segmentation method. As outlined in Section 5.3.4, these two design methods differ with respect to their sensitivity to the size of the initial local failure (design objective 2). When comparing design strategies 1 and 2, their different sensitivities to accidental circumstances (design objective 1) instead become apparent. The choice between these two design strategies will again be influenced by the design objectives. 82


Design methods

Again, design strategies 1 and 2, and their respective design methods, can favourably be combined in different ways. While the primary load transfer system of a slender high-rise building is possibly made collapse resistant by specific local resistance (R) (a method in design strategy 1), the design of its secondary load transfer system can be based on providing alternative paths (A) or by segmentation (S) (methods in design strategy 2) (see Section 6.3.2). When all three methods are combined in the design of the same system or subsystem, disproportionate collapse can be averted for small (R), medium (A), and large (S) accidental circumstances or initial local failure.

5.5

Prescriptive design rules

The design methods discussed above require detailed examination. The response of the structure to accidental actions or to the removal of selected structural elements is analytically (or, in exceptional cases, experimentally) determined and compared with the design objectives (direct design). Such a direct approach demands a great deal of time, skill, and computational resources on the part of the design engineer. For small to medium-sized structures, such a level of commitment may become disproportionate. If, consequently, a detailed examination is dispensed with, it may nevertheless still be desirable to achieve at least a certain degree of collapse resistance, preferably by following prescriptive design rules that are codified and simple to use (indirect design). Such an indirect approach does not rely on an analytical verification of specified design objectives, nor can it take design objectives into account. Prescriptive design rules are mostly simple and all-encompassing directions concerning structural detailing. To what degree collapse resistance is achieved remains unclear. If this approach proves unsuccessful, on the other hand, the consequences are less serious, as long as its application is limited to structures of relatively minor significance. For building design, a number of prescriptive design rules have emerged and made their way into standards and guidelines.61,67—70,73—76 An overview is given by Dusenberry and Juneja.72 The three most common rules are: 1. providing tension ties 2. enabling catenary action 3. ensuring ductility. The main structural members are required to be tied together horizontally and vertically by tension ties. According to the American 83



Concrete Institute Committee 318 requirements for the design of reinforced concrete buildings,74 a certain portion of top and bottom reinforcement in perimeter and spandrel beams is to be made continuous to provide a continuous tie around the structure and enhance its so-called ‘overall integrity’ (i.e. its robustness and collapse resistance). Precast concrete elements are to be connected by tension ties in all directions and around the perimeter of the structure to effectively tie elements together. Eurocode EN 1991-1-770 requires horizontal and vertical ties for the transfer of accidental design tensile forces, which are derived from the ordinary design loads. Similar provisions can be found in Approved Document A67 when read in conjunction with the applicable British standards.68,69 By enabling catenary action, a transition from flexural load transfer to tensile load transfer becomes possible. It can be activated in both beams and slabs and in both steel and concrete structures. In the event of failure of an intermediate column, catenary action allows the failed column potentially to be bridged, and thus a failure progression to be averted. Arguably, its most beneficial effect is in preventing the fall of failed structural components. If, for instance, a floor slab is destroyed in an incipient collapse, the debris is held in place by the tensile forces within the sagging remnants of the slab. A pancake-type collapse resulting from the impact of falling debris on the floor below is thus avoided. Catenary action is enabled by providing for horizontal continuity within and between flexural members. In concrete members, this is done by making the top and bottom reinforcement continuous. The continuity of the bottom reinforcement is required because the top reinforcement over a failing column tends to tear out of the concrete.74 As an alternative, additional untensioned steel cables within or outside floor slabs have been proposed by Astaneh-Asl.103 Ductility in structural members and connections is achieved through proper detailing. In the event of a local failure, it enables plastic crosssectional and system reserves to be used and energy to be dissipated. Stimulated by the ductility requirement, the suitability of seismic design rules for design against progressive collapse has been discussed by Hayes et al.48 and Corley.104 All prescriptive design rules, as far as specified in design codes, aim at ensuring collapse resistance through continuity and the provision of alternative load paths. Therefore, and in light of the discussion in Section 5.3.4, these rules should be applied with prudence and only to structures within the scope of the respective standard or guideline (i.e. to particular types of buildings and construction methods). This 84


Design methods

is because prescriptive design rules may increase the number of potential alternative paths but do not guarantee their quality, that is, they have sufficient structural resistance. Thus, if potential alternative paths are not provided with the strength required to effectively withstand and transfer the forces occurring in an incipient collapse, then a collapse progression is possibly not prevented but, rather, promoted. When using direct design methods, such a possibility is identified and excluded since the transfer of forces assigned to alternative paths is verified down to the foundations. Such a verification should preferably also be performed when alternative paths are provided and forces are assigned to them implicitly by prescriptive design rules. When tension ties, catenary action, plastic hinges, etc. are provided through prescriptive design, the forces whose transfer is to be verified should be determined based on the overstrength of the respective tensile elements or the overstrength plastic moments of the plastic hinges. The idea of isolating collapsing sections by a segmentation of the structure has been mentioned sporadically in the literature72,73 but has not yet led to any prescriptive design rules. Such rules could be useful when safety concerns, as outlined above with respect to prescriptive design aiming at continuity and alternative paths, are more easily met by specifying segmentation. This is possible, in particular, if the isolating effect of the isolating elements is achieved by eliminating continuity. For the development of prescriptive design rules based on segmentation, the scope of application, the appropriate size of the segments, and the detailing of the isolating elements would have to be investigated and specified. For structures of high significance and exposure, direct design methods are generally preferable to prescriptive design rules. They take into account the structural diversity and complexity inherent in such structures and ensure collapse resistance in a more or less reliable and verifiable manner. Moreover, not only safety but also cost-effectiveness can be impaired by applying prescriptive design rules. This is certainly true for large, unique, and expensive structures. In such cases, it is altogether more economical to spend effort and cost on detailed study and a design adapted to the conditions of the given project, that is, on direct design.

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6 Applications 6.1

General

In Chapters 4 and 5, an approach to the handling of questions arising from the phenomenon of progressive collapse was presented, and methods for the design of collapse-resistant structures were discussed. Both direct design methods and prescriptive design rules were examined. Direct design is more sophisticated in that it is based on design objectives and structural analysis. Greater emphasis was put on the direct design methods. They were illustrated by examples of building and bridge structures. For the justification and comparison of these methods, failure incidents and project-related design tasks were considered. The suitability of this approach will now be tested through a systematic application in two areas of structural engineering, namely large bridges and high-rise buildings. In Section 6.2, the most important types of large bridges are examined, and recommendations for the collapse-resistant design of such structures are derived. A somewhat different goal is pursued in Section 6.3, which is dedicated to the design of high-rise buildings. Only extremely tall and slender structures, comparable, say, to the collapsed towers of the World Trade Center (WTC), are considered. The possibility of designing such structures to be collapse resistant are explored using the tools developed in Chapters 4 and 5. Economic aspects are treated here as secondary to the question of the possibility, in principle, of achieving a collapseresistant design. Common features of large bridges and high-rise buildings are high significance and exposure, large internal forces, and a high degree of structural interaction. Prescriptive design rules cannot normally meet the particular demand for collapse resistance, and do not properly account for the structural diversity and complexity inherent in such structures. In addition, large bridges and high-rise buildings are generally unique and expensive. In terms of both safety and economy, direct design methods are therefore preferable for such structures over 86


Applications

prescriptive design rules (see Section 5.5). The study which follows in Sections 6.2 and 6.3 is therefore limited to direct design methods.

6.2

Design of collapse-resistant bridges

6.2.1 General While there are now a number of design standards and guidelines for buildings aimed at preventing progressive collapse (see Sections 1.4 and 4.3), almost no such regulations as yet exist for bridges. Notable exceptions are the corresponding details in the Post-Tensioning Institute (PTI) recommendations 64 and in Ref. 65, which, however, do not exhaustively treat the problem and are relevant only for cablestayed bridges. Other regulations applicable to bridges are mostly limited to general safety recommendations 105 or the specification of design actions for accidental circumstances. The focus of the latter is the impact of road, rail, air, or water vehicles in order to prevent initial local failure.70,98 Nonetheless, the Swiss guideline on the impact of road vehicles98 advises choosing structural systems that are robust. The few non-standard publications addressing the collapse-resistant design of bridges are mostly limited to the prevention of initial local failure due to previously disregarded accidental circumstances such as malicious explosion.28,106,107 Exceptions to this are Refs 30, 31, and 96. The discussion in Chapter 5, on the other hand, shows that there are at least four generally applicable direct design methods to choose from or to combine for the design of a structure against progressive collapse. Furthermore, it was noted that the suitability of the different methods depends on the design objectives, and on the type of structure and its orientation in space (see, in particular, Section 5.3.4). The understanding of these dependencies is still rudimentary. An obvious characteristic feature of bridges, however, is that they are mainly aligned along a horizontal axis. Impact loading caused by falling structural components or debris is therefore less of a concern for bridges than for buildings. It follows that in bridges there is less need to provide alternative load paths and to tie together structural components in order to prevent their fall and impact. This is just as well as it is usually difficult to provide alternative paths in structures that are aligned along one axis, as is the case for bridges. Other general features and conclusions with respect to progressive collapse are hard to find. The following discussion is therefore directed at specific types of large bridges. 87



6.2.2 Continuous girder bridges Relevant examples of continuous girder bridges are the Viadotto Cannavino and the Haeng-Ju Grand Bridge, which collapsed in a progressive manner following an initial failure, and the Tasman Bridge, where an initial failure did not trigger a progressive collapse (see Sections 1.2 and 2.2.6). Another example is the Confederation Bridge, for which the requirement to provide collapse resistance was part of the design criteria (see Section 5.3.3). Out of this experience and the preceding discussion in Chapter 5, two suitable design approaches emerge to ensure collapse resistance in continuous girder bridges. The first one is the segmentation method. For the bridge type considered here, selected piers or the regions around those piers should be chosen as segment borders. For short spans up to, say, 40 m, it will be possible to provide these piers or regions with high local resistance to enable them to act as isolating elements. A historical example is the Chaumont Viaduct, France, a 600 m-long railway bridge completed in 1856 consisting of 50 masonry arch spans. Every fifth pier is designed as an abutment pier, with twice the cross-sectional dimensions in both directions as the normal piers. This arrangement facilitated construction because every five-span segment could be built independently of the others. Even if providing robustness was not an original design intent, the structure proved to be robust during World War II, when four piers were dynamited but this damage did not lead to progressive collapse. For longer spans, the segmentation method requires selective elimination of continuity at the envisaged segment borders. This can be accomplished in a reliable manner by the insertion of break-away hinges. Further methods to eliminate continuity and to form isolating elements and segment borders are described in Section 5.3.3. The second approach aims at preventing initial local failure by increasing the level of safety of the key elements — either by providing specific local resistance or through non-structural protective measures. Thought must be given to possible accidental circumstances that could endanger key elements. The probability of occurrence of such circumstances should be minimised. Actions resulting from assumable accidental circumstances must be considered in design. Examples include: the impact of a ship or an aircraft on a pier or the superstructure; unexpectedly strong ice floes striking a pier; scour undermining a foundation; fire caused by a traffic accident that could damage, for instance, the prestressing tendons in a prestressed concrete 88


Applications

bridge; a bomb blast at a vulnerable location; other accident-related or malicious detrimental circumstances; deficiencies in design or construction; or, simply, corrosion. For the design of major bridges over water, the probability of ship impact and the corresponding design loading are usually evaluated by specialist consultants. The decision to protect the bridge piers through strengthening or through external impact-resistant barriers can be based on such an assessment. The normal design loading for ship impact and other actions should be increased when designing key elements. The construction stages must also be considered. Further information on the application of the design strategy ‘prevent local failure’ can be found in Section 5.2.3. As noted there and in Section 5.4, the choice between the two design approaches suggested here depends, in particular, on the size of the structure and the design objectives.

6.2.3 Cable-stayed bridges 6.2.3.1 General Cable-stayed bridges are a good illustration of the statement made in Section 5.3.3 that the terms continuity, redundancy, and robustness should be carefully distinguished. Although such structures possess a high degree of static indeterminacy and internal continuity, this does not mean that they are redundant or robust. The sudden failure of one or more stay cables and a possibly ensuing zipper-type failure progression and collapse (see Section 2.2.2) are of particular concern. The cables should be seen as potential key elements (see Section 5.1) of this type of bridge. The problem is aggravated by a number of factors: the cables are often easily accessible and exposed to accident-related or malicious detrimental action (Fig. 6.1); their cross-section is relatively small, which makes it difficult to provide them with specific local resistance against lateral action; cable failure could occur nearly instantaneously, and thus produce an impulsive dynamic loading; unzipping of cables is likely to interact with and be reinforced by a stability failure (i.e. buckling) of the bridge girder and pylons that are in compression (see Section 2.2.6); and the structure could respond in a non-ductile manner. To meet such concerns, the PTI recommendations 64 require that a cable-stayed bridge shall be designed so that the sudden loss of a cable does not lead to collapse. A load combination associated with such loss-of-cable events or ‘load cases’ and applicable partial safety

89



Fig. 6.1 Exposure of stay cables to accident-related or malicious action

factors are specified. The loss of any one cable shall successively be considered. Similar recommendations are made in guidelines issued by the International Federation for Structural Concrete (fib). 65 In contrast to the fib guideline, the PTI recommendations also specify a verification procedure: the structural response to the impulsive dynamic loading that results from the sudden failure of a cable is recommended to be determined in a quasi-static analysis using a dynamic amplification factor (DAF) of 2.0. These recommendations have been applied to the design of cablestayed bridges erected in the USA over the past years. It was found that the loss-of-cable events in conjunction with quasi-static analysis often become controlling load cases in the design of the bridge girder, thus leading to increased construction costs. The corresponding clause was therefore amended in the fifth edition of the PTI recommendations:64 the DAF to be used in quasi-static analysis can alternatively 90


Applications

Fig. 6.2 Structu Structural ral model for analysis of loss-of-cable loss-of-cable events

be determined by nonlinear dynamic analysis; it should not be taken as smaller, small er, howev however, er, than 1.5.

6.2.3.2 Numerical study of loss-of-cable events The effects of sudden cable failure and the corresponding verification proc pr oced edur ures es we were re st stud udie ied d in a re rese sear arch ch pr proj ojec ectt su supe perv rvis ised ed by th thee 108—110 author. Numerical studies were performed for a five-span symmetric met rical al cable-st cable-staye ayed d bri bridge dge with a mai main n spa span n of 600 m, side spa spans ns of 210 m, and end spans of 60 m. In thi thiss str struct ucture ure,, the two cable cable planes planes are anchored along the edges of the bridge girder and slightly inclined inwards in the transverse direction. They consist of 80 cables each in a semi-fan configuration. The cable anchors in the bridge girder are spac sp aced ed at 15 m. The br brid idge ge gi gird rder er co consi nsist stss of an or ortho thotr trop opic ic de deck ck suppor sup ported ted on two 2.60 m-d m-deep eep steel edge beams. beams. The response response of the structure to the failure of any one cable was investigated by nonlinear dynamic analyses of a spatial model of the structure (Fig. 6.2). Cable sag, large deflections and their effect on equilibrium were taken into accoun acc ount. t. Mat Materi erial al non nonlin linear earity ity was con consid sidere ered d for col collap lapse se ana analys lyses, es, which are addressed further below, but not for the computation of DAFs. The failure of a cable was modelled as a sudden event, causing a step impulsive impul sive loading, loading, and the ensuing extreme responses responses of the state variables (i.e. of the displacements and sectional forces) were determined. By rel relati ating ng the these se ext extrem remee dyn dynami amicc res respon ponses ses to the cor corres respon pondin dingg static responses to cable failure, DAFs were derived that could be used in quasi-static analysis. Because the comparison of dynamic and static responses must be carried out case by case for individual cable failur fai lures es and ind indivi ividua duall sta state te var variab iables les,, eac each h res result ulting ing DAF is val valid id only for the case considered, and will generally be different for other cable failures and state variables. variables.

91


Progressive collapse of structures 4.0 3.0 F A 2.0 D

1.0 0

0 (a)

Anchor pier

Pylon

60

270

Anchor pier

Pylon

60

270

Centre of bridge 570

–30 m N–20 M : y

–10

M

t n 0 e m o 10 m g 20 n i d n 30 e B

40

0

Centre of bridge 570

Longitudinal bridge axis: m (b) All cables intact Minimum dynamic response (envelope) Corresponding Correspondin g minimum static response

Maximum dynamic response (envelope) Corresponding Correspondin g maximum static response

Fig. 6.3 (a Fig. (a)) Th Thee DA DAF F for positi positive ve ( h ) and negative (g ) bending moments. (b) Bending moments in the bridge girder due to permanent loads and extreme bending moments due to permanent loads plus the governing loss-of-cable load case

The numerical results confirmed that it is impossible to specify an overall DAF. The DAF, in fact, strongly depends on both the location of the failing cable and the location and nature of the state variable considered. Regarding the vertical displacement of the bridge girder at and in the vicinity of cable failure, the DAF is between 1.5 and 1.8, depending on the location of the failing cable. For the forces in the cables adjacent to the failing cable, the DAF is between 1.35 and 2.0. It is between 1.3 and 1.6 for the positive bending moments, and between 1.4 and 2.7 for the negative bending moments, in the bridge girder in the vicinity of the failing cable (Fig. 6.3). More precisely, these values refer to the bending moments in the bridge girder edge beam in the plane of cable failure. For state variables at locations distant from the failing cable, the DAF can generally be much larger than 2.0. This, however, simply results from the fact that the corresponding static 92


Applications

response used as a reference value is usually small at distant locations — and not from a particular large or governing dynamic response. The numerical values of DAFs just stated were determined for an undamped structure. The attenuating effect of damping was found to be small. Based Bas ed on the these se res result ults, s, on overa overall ll DAF DAF of 2.0 2.0 seems seems appro appropri priate ate for for the safe evaluation of design cable forces. Regarding the bending moments in the bridge girder, the DAF is noticeably smaller than 2.0 for a wide range of locations. Thus, the reduction of design bending moments sought by the am amen endm dmen entt in th thee fif fifth th ed edit itio ion n of the PT PTII re reco comm mmend endat atio ions ns is partly possible. On the other hand, a DAF larger than 2.0 is obtained forr th fo thee ne nega gati tive ve be bend nding ing mo momen ments ts at so some me lo loca cati tion ons. s. It thu thuss se seem emss nece ne cess ssaary to ad adop optt va valu luees la larg rger er th than an al allo low wed by th thee cu curr rren entt PT PTII recommendations64 for the corresponding design bending moments. Furthermore, Furthe rmore, it stands out that the DAFs for the bending moments moments in the pylons result much larger (i.e. by one order of magnitude) than 2.0. The corresponding static responses used as reference values are small. The si situ tuat atio ion n thu thuss se seem emss to re rese semb mble le th that at of st stat atee va vari riab able less in the bridge girder at locations distant from the failing cable. In contrast to tho th ose fin findi ding ngs, s, ho howe weve ver, r, no nott on onlly th thee DA DAFs Fs bu butt al also so th thee ab abso solu lute te dy dyna nami micc responses are large in the pylons, and can govern the design (Fig. 6.4).

200

All cables intact Minimum dynamic response (envelope) Corresponding minimum static response Maximum dynamic response (envelope) Corresponding maximum static response

150 m : t h g i e h 100 n o l y P

50

0 –100

–50 0 50 Bending moment M y : MNm

100

Fig. 6. Fig. 6.4 4 Ben Bendin dingg mo mome ments nts in py pylon lon leg legss due to per perma manen nentt lo loads ads and ex extr trem emee bending moments due to permanent loads plus the governing loss-of-cable load case

93



Again, the results just stated were determined for an undamped system. The attenuating effect of damping was found to be more pronounced for the pylon moments than for the other state variables, but not enough to eliminate the problem. When assuming a damping ratio to critical of 1%, the design bending moments are reduced by approximately 15%. These remarkable findings indicate that, for the bending moments in the pylons due to cable failure, a quasi-static analysis with a DAF of 2.0 can be unsafe and should be replaced by proper dynamic analysis. It was further determined that the sudden failure of one cable can indeed result in bending moments that govern the design of the bridge girder but does not lead to collapse (even if loss-of-cable load cases were neglected in design) nor to particularly high cable forces. In the case of the simultaneous sudden failure of two adjacent cables, however, the ultimate load is notionally reached in the adjacent cables. Nevertheless, when effects such as ductile material behaviour or non-simultaneity of cable failures are taken into account, failure progression requires a still larger number of initially failing cables. To simulate the actual collapse progression and to explore the true ultimate capacity of the bridge, the material nonlinearity of all structural members was incorporated in the analytical model. It turns out that the simultaneous sudden failure of three adjacent short cables results in immediate collapse due to buckling of the bridge girder where it becomes unbraced (Fig. 6.5). Only one additional cable snaps during buckling, so that there is no pronounced zipper-type failure progression but mainly an instability-type collapse. It is maintained, though, that, for other cable-stayed bridge configurations, failure could also progress as a mixed-type collapse (see Section 2.2.6) in which the features of zipper-type and instability-type collapses interact. Further findings concerning the effect of sudden cable failure are presented in Refs 108—110. The effect of delayed (i.e. non-sudden) cable failure is examined in Ref. 110. All these results were obtained for a long-span multi-cable bridge with two cable planes and steel girders. It still needs to be examined to what degree they are representative for cable-stayed bridges in general. Results of dynamic analyses of cable failure for another, though similar, cable-stayed bridge are presented in Ref. 111. Instead of performing a quasi-static analysis with predetermined DAFs, it might soon become possible and more convenient for the design 94


Applications

Fig. 6.5 Instability-type collapse triggered by the failure of three short cables (pylon omitted for clarity)110

engineer to directly determine the design forces by nonlinear dynamic analysis, at least for selected cases of cable failure.

6.2.3.3 Initial failure of multiple cables When applying the PTI recommendations, 64 the assumable cases of initial local failure (design objective 2) follow from the condition that the loss of any one cable at a time shall be considered. The question arises whether the assumption of just one cable failing at a time is always sufficient, in particular when the cable anchors in the bridge girder are closely spaced. Considering traffic accidents as possible triggering events, it seems sensible to assume the sudden and simultaneous failure of all cables anchored within a segment of certain length placed anywhere along the bridge girder. In the design of the Taney Bridge, a recently erected cable-stayed bridge in Ireland carrying two tracks of the Dublin Light Rail Transit system, the length of that segment was set at 10 m, measured along the cable anchors. Accordingly, the sudden and simultaneous failure of any two adjacent cables needed to be assumed in the design of that bridge.112 These dynamic load cases were examined by quasi-static analysis using a DAF of 2.0. They were combined with a specified set of additional actions, including live load on the track next to the failing

95



cables. A specified set of load and resistance partial safety factors was used. As a further combination of actions, the failure of any two adjacent cables was considered statically in combination with live load on both tracks. This was to account for the possibility that a second train would cross the bridge soon after the failure of the cables while the first train is still standing on the bridge. These design criteria were developed jointly by the design engineer and the owner.

6.2.3.4 Other design methods Verification of and design for loss-of-cable load cases is an application of the alternative-paths method, one of the design approaches to providing collapse resistance discussed in Chapter 5. When examining other approaches, it turns out that the segmentation method is usually inappropriate for cable-stayed bridges. Except for multi-span structures, the minimum segment size, and thus the minimum extent of collapse, corresponds to the size of the entire bridge (or at least half of the bridge when a centre hinge is inserted in a three-span structure). The specific-local-resistance method, too, seems inappropriate, at least for the currently preferred multi-cable systems with narrow cable spacing. This is due to the small cross-sectional area of the load-bearing elements of the cables, their comparatively small resistance to accidentrelated or malicious actions in the lateral direction, and their significant impact on construction costs. This design method is suitable, at best, after a change of structural system: if the multi-cable configuration common today is replaced by a few widely spaced large-diameter cables, these would also exhibit a higher local resistance to lateral action. On the other hand, such change of system could impair the formation of alternative paths in the case of cable failure. Instead of by providing specific local resistance, the design strategy ‘prevent local failure’ can also be pursued through providing nonstructural protective measures. This method is applicable to cablestayed bridges, and should be employed more, not as a substitute for but rather as a complement to the alternative-paths method, that is, to verifying and designing for loss-of-cable load cases. Local protective measures include barriers to fend off vehicles, such as concrete barriers, guard rails, or crash cushions, 98 fencing to deter trespassers from approaching the cables, and measures that protect against explosions. The last could be a thick composite-material sheath to mitigate the effect of a shaped charge mounted directly on a cable. The sheath would have to be applied to the cables up to a

96


Applications

certain height (say 5 m) above deck level. To prevent sudden or delayed cable failure due to corrosion, efficient corrosion protection systems for cables and anchors, and regular inspection, ideally complemented by constant monitoring, are needed. For particularly significant and exposed bridges, non-local measures such as aerial surveillance or anti-aircraft defence may be required. Again, further information on the application of the design strategy ‘prevent local failure’ is given in Section 5.2.3.

6.2.4 Suspension bridges The hangers of a suspension bridge are secondary load-bearing elements, in contrast to the cables of a cable-stayed bridge, which are constitutive elements of the primary load transfer system. Nevertheless, the sudden failure of one or a few hangers would similarly produce an impulsive dynamic loading on the structure that could lead to zipperlike failure of further hangers and collapse. 113 Such a failure progression can be seen in the footage of the Tacoma Narrows Bridge collapse in 1940. After the first hangers snapped due to excessive wind-induced distortions of the bridge girder, the entire girder peeled off from the hangers and suspension cables (see Fig. 2.2). In the case of a self-anchored suspension bridge, where the bridge girder is in compression, any unzipping tendency is likely to be reinforced by the susceptibility of the bridge girder to buckling. As found above for cable-stayed bridges, a mixed-type collapse can thus occur in which the features of zipper-type and instability-type collapses interact and reinforce each other. Progressive collapse initiated by the sudden failure of one or more hangers seems not to have been a major concern in the past. At least, it is not regularly checked in design. With the recent advent of new kinds of threats, a different stance should be taken. The challenge can be met by making hanger failure less probable and by simultaneously designing for such a scenario. The design and verification measures for cable-stayed bridges outlined in the previous section are similarly applicable. For earth-anchored suspension bridges, there is a further possible design approach that is impracticable for cable-stayed bridges and self-anchored suspension bridges: the bridge girder could be provided with a number of break-away hinges that give way at the beginning of collapse and thus allow for a safe separation of the falling part of the girder. In other words, the segmentation method can be used; 97



the segment borders are formed by the inserted break-away hinges. A collapse of the bridge girder initiated by hanger failure or another event would thus be isolated by the hinges and limited to one segment. The primary load transfer system of a suspension bridge is formed by the suspension cables, which generally are continuous over the length of the bridge. The failure of a suspension cable will usually be equivalent to collapse. Applying the segmentation method to the primary load transfer system to confront this possibility is, at best, an option only for multi-span systems. Each segment would consist of a self-contained two-span or three-span suspension bridge. The alternative-paths method, on the other hand, is more generally applicable, as long as the force carried by a failing suspension cable can be redistributed to neighbouring cables. To enable such a force redistribution while at the same time limiting the resulting costs, a number of cables would be required. This design method, therefore, is more appropriate for large suspension bridges, where more than two cables are already envisaged or where the number of cables can more easily be raised without major disadvantages. Applying the specific-local-resistance method to the primary load transfer system would require a strengthening of the load-bearing elements of the suspension cables. This can be an appropriate measure for small suspension bridges. For large long-span suspension bridges, it is not a reasonable option, because the design of such bridges is mostly cost driven, and a major share of construction costs is related to the suspension cables. On the other hand, the suspension cables of long-span bridges have large cross-sections and masses already, which provide them with high local resistance, including against lateral action, even without further strengthening. Furthermore, their resistance is less affected by isolated wire breaks because each suspension cable consists of many wires and even a broken wire will carry load again at a certain distance from the breakage point. In view of the emergence of new kinds of threats, however in particular aggressive and well-resourced malicious action, it is advisable to take non-structural protective measures to guard suspension cables against such threats, regardless of cable size. For bridges of high significance and exposure, these measures should include appropriate physical shielding and electronic security systems to reliably deter trespassers from approaching the suspension cables. This applies especially to locations where the cables are easily accessible (mid-span) or where their load-bearing elements are exposed (splay chamber). 98


Applications

6.2.5 Arch bridges Arch bridges have similarities to suspension bridges in terms of topology and the flow of forces. Much of what has been presented in the previous section can be directly applied or readily adapted to arch bridges. A through-arch bridge, in which the bridge girder is carried below the arch, has hangers like a suspension bridge, and the same potential problem of a zipper-type collapse. Similar design approaches can thus be used. As for a self-anchored suspension bridge, segmentation of the bridge girder is not an option for a tied-arch bridge. In a true arch, the bridge girder is supported above the arch by columns and not suspended under the arch by hangers. Since the columns, in comparison with hangers, are more resistant to lateral action and not exposed to traffic, column failure due to accidents is less probable. On the other hand, they are also more hidden from public view, which facilitates malicious action. Regarding the primary load transfer system, there are two important differences between the arches of an arch bridge and the suspension cables of a suspension bridge. First, an arch can suffer global stability failure, which can occur in the plane of the arch or in the lateral direction. This opens up further possibilities of failure initiation and progression. Second, various kinds of material and cross-sections are possible and in use for arches. These design options should be evaluated with respect to assumable accidental circumstances, in particular those that induce local lateral action. Local failure caused by lateral action can be facilitated by local instability (i.e. plate buckling), and can lead to global instability and collapse. In this regard, solid cross-sections are more resistant than thin-walled or hollow ones, and reinforced concrete is preferable to steel. The susceptibility of a hollow steel tube arch to local lateral action can, on the other hand, be reduced by partially filling the tube with concrete. The filling can be limited to the regions that are accessible to traffic or trespassers.

6.3

Design of collapse-resistant high-rise buildings

6.3.1 General The Federal Emergency Management Agency (FEMA) report on the collapse of the WTC towers 11 concludes with a call for studies to determine ‘whether there are feasible design and construction features that would permit such buildings to arrest or limit a collapse, once it 99



began’. An attempt is made here to answer this call. The phenomena to be dealt with are unforeseeable and low-probability events (accidental circumstances), local failure, and progressive collapse. The tools for handling these phenomena were provided in Chapters 4 and 5, which include the discussion of generally applicable design methods. These findings are now applied to structures that are comparable to the collapsed WTC towers, that is, to high-rise buildings with a large height-to-width ratio, a large number of storeys, and a high degree of significance and exposure.114 Furthermore, it is assumed that the design criteria call for assuming substantial accidental circumstances or major local failure, as detailed later. The study is not limited, however, to specific accidental circumstances, and its results apply to all kinds of events, including fire. The primary objective is to identify design alternatives that increase the collapse resistance as much as possible and minimise the probability of a progressive collapse — even if they seem unusual or are more costly in comparison with present practice. To this end, each of the four design methods ‘specific local resistance’, ‘non-structural protective measures’, ‘alternative load paths’, and ‘isolation by segmentation’ is examined in a separate section with regard to its suitability to provide adequate collapse resistance of the primary load transfer system, which is responsible for the global load transfer of all vertical and horizontal loading. Measures and structural systems that result from this examination are suggested where possible. Indirect design (prescriptive design rules) seems inadequate for the type of structure contemplated here, and is not considered further (see Sections 5.5 and 6.1).

6.3.2 Specific local resistance 6.3.2.1 General This design method aims at enhancing local safety by increasing the structural resistance of key elements. These have to be identified first. In principle, this is carried out based on a structural analysis in which the assumable initial local failure is modelled, and the ensuing total damage is then determined and compared with the acceptable total damage (see Section 5.1). In this process, both the assumable cases of initial local failure and the acceptable total damage are design objectives that must first be established. Alternatively, the assumable cases of initial local failure can be

100


Applications

derived by structural analysis from the assumable accidental circumstances (see Section 4.3.2). This implies that the assumable accidental circumstances are clearly defined, for instance as an internal gas explosion, and the corresponding actions can be determined or are directly given. If the calculated total damage is acceptable, the structural members initially modelled as failed do not qualify as key elements, and they do not require specific local resistance. However, if the acceptable total damage is exceeded, these members are key elements. They can then be designed for the assumable accidental actions, and thus be provided with increased structural resistance — again, on the assumption that the assumable accidental circumstances are clearly defined and the corresponding actions can be determined or are given. It will often be difficult, however, to establish and agree on the assumable accidental circumstances or actions. This applies, in particular, to structures of high significance and exposure because malicious action must be included in the list of assumable accidental circumstances. Malicious action, however, is hard to anticipate due to the inventiveness that any human aggressor must be assumed to possess. In such cases, the initial local failure should be chosen to be as large as reasonably possible. For the type of structure considered here, this means the initial failure of the structure is assumed to extend over the whole of one storey. The adequacy of this assumption is emphasised by the collapse of the WTC towers. It can be expected that such an initial failure leads to a pancake-type collapse (see Section 2.2.1) if no countermeasures are taken. Despite the apparent size of the assumed initial failure, the collapse would, nevertheless, be disproportionate. The part of the structure assumed to be initially failing here, that is, all the vertical load-bearing members of one entire storey, thus qualifies as a key element. This conclusion holds for all storeys (except for the uppermost ones, whose failure does not necessarily result in intolerable impact forces). All these key elements are contiguous. It follows that the whole primary load transfer system must be provided with specific local resistance over nearly the entire height of the structure. The corresponding design ultimately does require a decision on the assumable accidental circumstances or actions. Independently from that decision, which must be made on a case-by-case basis, general conclusions concerning the configuration of the primary load transfer system can, however, be drawn from the preceding discussion. In consideration of conceivable accidental circumstances — accidental or malicious explosion, vehicle or aircraft impact, missile impact and 101



blast, or fire — it is concluded that the structural members composing that system should be as compact as possible. The surface area exposed to attack is thereby reduced to a minimum and the resistance against local action is increased to a maximum. The design concept presented below results from opting to ensure the collapse resistance of the primary load transfer system through specific local resistance and from the ensuing demand for compactness of that system. In the next section, the primary load transfer system itself is treated. The other parts of the structure (secondary load transfer system, façade) are covered in subsequent sections. It is found that their collapse resistance must be ensured independently of the primary system. The design approaches to be considered for this task are therefore not limited to the specific-local-resistance method.

6.3.2.2 Primary load transfer system The primary load transfer system (or, for short, the primary structure) is envisaged as a massive tube forming the vertical spine of the building (Fig. 6.6). Because it is assigned the entire vertical and horizontal load transfer, the tube must be larger in its outer dimensions than the core of a core and outrigger system. To maximise its compactness, the tube should have as few openings as possible and the openings should be small. For this reason, the tube does not lend itself to forming the façade but must be placed inside the outer perimeter of the building. The usable floor space is located mainly between the tube and the façade. The tube consists of reinforced high-strength concrete or of structural steel members embedded in reinforced concrete. It features a substantial wall thickness of the order of 1 m or more to ensure adequate resistance against local action. The wall thickness and the further detailing of the tube depend on the assumable accidental circumstances and actions that must be specified on a project-by-project basis. The number and size of openings are limited to the minimum necessary to allow access from the vertical lines of traffic and supply (lifts, staircases, service risers) located inside the tube to the floor space on the outside. The openings are staggered between successive storeys, to minimise weakening of the global structural resistance. To prevent the undetected placing of large amounts of explosives, which could be done incrementally over an extended period of time, the inner and outer faces of the tube should be permanently accessible for inspection or be entirely open to the public.

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Primary load transfer system

A

A Secondary load transfer system

Façade

Vertical section

Section A–A

Fig. 6.6 Primary load transfer system: vertical and horizontal sections

An explosion inside the tube — caused accidentally or by smaller amounts of explosives brought into the building shortly before detonation — can lead to a substantial pressure build-up within the enclosed inner space of the tube, a loading for which the tube should be designed. This can be facilitated by choosing an annular cross-section for the tube 103


Progressive collapse of structures Primary load transfer system Façade

Section A–A

Fig. 6.7 Annular cross-section of the primary load transfer system

(Fig. 6.7). Prestressed reinforcement could be provided for carrying the sectional forces in the circumferential direction. The pressure build-up inside the tube could be reduced by permitting venting through the access openings and by providing additional vents at the top and base of the building. The design features of the primary structure just outlined result from applying the specific-local-resistance method that aims at preventing a triggering initial failure. Although such a strategy does not exactly correspond to the call of the FEMA report cited in Section 6.3.1, the collapse resistance achieved in this way is high. The structure presented here is deemed to exhibit the maximum collapse resistance achievable by this design method. In terms of tolerable accidental circumstances, it is surpassed only by the design alternatives presented in Section 6.3.5.2, which are based on vertical segmentation. In addition, it is of interest that the solid and compact structure described here, when compared with non-compact column—beam structures, also seems more robust, that is, less sensitive to local failure. This assumption is based on its lower degree of structuredness, a collapse-promoting structural feature discussed in Section 2.4.7.

6.3.2.3 Secondary load transfer system The primary load transfer system is responsible for the global load transfer of all vertical and horizontal loading. The primary structure suggested in the previous section performs this task and, moreover, exhibits a high degree of collapse resistance. In order not to compromise this desirable property by possibly harmful interaction, the other parts of the structure should not participate in the global load transfer. The secondary load transfer system (or, for short, the secondary structure) is therefore conceived as floors cantilevering out from the vertical tube that forms the primary structure or spanning its inner faces (Fig. 6.8).

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Fig. 6.8 Secondary load transfer system

The current practice of floor design using beams or slabs is, in principle, suitable. However, a self-contained progressive collapse of the secondary structure is still possible, and must also be prevented. Such a collapse could occur as a failure of floors that progresses in the vertical direction without affecting the primary structure. This was called an alternative mode of pancake-type collapse in Section 2.2.1. Since the primary structure is independent of the secondary structure with respect to its collapse resistance, the entire set of design methods can be considered for providing collapse resistance to the secondary structure. Specific local resistance is more difficult to provide than it is for the primary structure. This is because the elements of the secondary structure are intended for local load transfer only, and consequently have smaller cross-sectional dimensions while at the same time they exhibit large surface areas exposed to attack. Designing the secondary structure for assumable accidental actions in all likelihood would lead to crosssectional dimensions that are impracticable. Because of the large surface area exposed to attack and the multitude of conceivable accidental circumstances and actions, non-structural protective measures seem likewise inappropriate (see also Section 6.3.3). It is therefore better to accept a local failure of the secondary structure as inevitable but to limit the ensuing failure progression to an acceptable extent: in other words, to resort to the design strategy ‘assume local failure’. If the horizontal extent of the assumable accidental actions cannot be convincingly limited, initial failure and fall of an entire cantilever floor should be assumed. The loading of this floor can be analytically applied 105



to the cantilever floor below. Thus, an alternative load path beneath the initially failing element is provided for that loading. A two-step capacity design approach is suggested. Consider a cantilever floor that is deflected by the impact of the failing floor above (Fig. 6.9(a)). Assume the outer edge of the deflected floor barely touches the floor below, and that the collapse is arrested in that position. For this to be a reasonable assumption, it must first be ensured that the elastic and plastic energy required for the deflection is larger than the released gravitational energy. The latter approximately equals the total weight of one floor, including a reduced live load

Failing floor Plastic hinge Floor bent down by the impact of floor above

(a)

Failing floors

Plastic hinges

Floors bent down by the impact of floors above

(b)

Fig. 6.9 Assumed initial local failure and the acceptable extent of collapse of the secondary load transfer system

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allowance, multiplied by the vertical distance of the floors and 1.5. The factor 1.5 accommodates the additional gravitational energy released by the lowering of the deflected floor itself. Secondly, the rotational ductility capacity in the plastic hinge regions must be sufficient to allow for such a deformation without a significant reduction of the bending moment in the plastic hinge. Progressive collapse initiated by the fall and impact of a floor is thus prevented. Numerical studies show that the required rotational ductility capacity is probably difficult to achieve with reinforced concrete beams but that it is attainable with haunched steel girders. 115 The analysis can be refined by assuming initial failure and the fall of more than one floor, by increasing the weight of the falling floors by the weight of a possibly incoming aircraft, and by considering larger degrees of deformation when establishing the elastic and plastic energy contributions. The impact of two consecutive floors above, for instance, could be assumed to affect two consecutive floors below (Fig. 6.9(b)). A refined analysis should also account for the interaction between bending moments and axial forces in the plastic hinge regions. An incoming aircraft would result in a concentrated additional vertical load, and thus require sufficient circumferential load distribution capacity. This can be provided by a perimeter beam, situated at the outer edge of each cantilever floor, that works in bending and, for higher loads, is capable of catenary action. The design approach described here applies to the cantilever floors. A similar capacity design approach can be developed for the floors spanning the inner faces of the tube. If the horizontal extent of the triggering accidental actions is assumed to be limited, then the collapse resistance of the cantilever floors can also be ensured through load distribution in the circumferential direction. The latter can be enhanced by, again, providing perimeter beams. Such an approach corresponds to the provision of alternative paths lateral to the initially failing elements. In this case, the fall of structural components and impact loading do not need to be considered. There is an alternative design option, in lieu of providing alternative paths, to limit the failure progression. Collapsing sections can be isolated by an appropriate segmentation of the secondary load transfer system. As outlined in Section 5.3.3, segmentation is achieved by isolating elements that can accommodate large displacements or large forces, or both. For the secondary structure suggested here, isolating elements that allow for large displacements are relatively easily formed by joints in the 107



Floor segment Joint

Fig. 6.10 Horizontal segmentation of the secondary load transfer system by joints

cantilever floors. Each floor contains a certain number of joints running perpendicular to the core (Fig. 6.10). In this way, each cantilever floor is horizontally segmented and divided into a number of structurally independent cantilever floor segments. The joints of all floors are vertically aligned, that is, placed at the same location in plan. If one floor segment fails and falls, the ensuing collapse would be limited to the floor segments located below the failed segment — a partial collapse similar to the Ronan Point failure (see Fig. 5.18). For this kind of horizontal segmentation, the horizontal extent of the assumable accidental actions must be limited. Compared with the alternative-paths and capacity design approach discussed earlier, the extent of collapse is generally greater. Both approaches can be combined: the floors can be designed to carry impact loading following the alternative-paths approach outlined above, and at the same time they can be segmented by joints, as described in the previous paragraph. Circumferential load distribution is eliminated through the insertion of joints. The concentrated vertical aircraft load, therefore, does not need to be considered in the capacity design of the cantilever floors, provided that for this accidental action the collapse of all segments located below a failing segment is acceptable. The isolation of collapse within the secondary load transfer system can also be achieved through vertical instead of horizontal segmentation. In this case, the isolating elements must extend in the horizontal direction instead of being aligned vertically. Furthermore, they must be able to transmit large forces instead of allowing for large displacements. This suggests that a certain number of floors should be selected as isolating elements and designed as ‘strong floors’ that are able to bear 108


Applications

the impact loading from failing segments above. In the case of such a vertical segmentation, the horizontal extent of the assumable accidental actions does not need to be limited. The idea will be taken on in a modified form in Section 6.3.5.2, applying it to the primary load transfer system. Note that the approaches for horizontal and vertical segmentation of the secondary load transfer system described here can also be combined with each other.

6.3.2.4 Façade structure In addition to the primary and secondary load transfer systems, the façade (or building envelope) structure requires attention. A progressive collapse of the façade structure could remain self-contained or occur in interaction with the secondary load transfer system. Windows and glazing, cladding panels, and other façade elements can be mounted either directly or by means of light framing on the cantilever floors (curtain wall). When the collapse resistance of the secondary load transfer system is ensured by designing all or a few selected floors for impact loading from failing segments above — two of the design approaches outlined in the previous section — the contributory weight of the façade must be taken into account when determining the released gravitational energy. For a capacity design of the secondary structure according to Fig. 6.9, further measures concerning the façade need to be taken. When a deflecting floor approaches an undeflected floor below, no excessive forces must be transmitted from the façade to the floor below. This can be achieved by a vertically overlapping or staggered arrangement of the façade elements. Alternatively, the vertical force associated with the destruction of the façade can be considered as a quasi-static load, together with a dynamic amplification factor, in the elastic design of the cantilever floors. When achieving collapse resistance of the secondary structure through horizontal segmentation, the floor joints that run perpendicular to the core and serve as isolating elements must be complemented by continuous vertical joints in the façade. Alternatively, the façade can be designed as a self-supporting structure. For the type of building considered here, a collapse of the façade potentially causes great damage and compromises human safety in the surroundings of the structure. Thus, a self-supporting façade must usually be provided with collapse resistance of its own. This can be achieved by providing alternative paths or by isolating collapsing sections through horizontal segmentation brought about by the

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insertion of vertical joints. The provision of alternative paths, for instance by designing the façade as a moment-resisting frame with sufficiently stiff and strong horizontal spandrel beams, has the advantage of a presumably smaller extent of collapse and other damage. A self-supporting façade must be structurally connected to the cantilever floors of the secondary structure to provide for wind load transfer and out-of-plane stability of the vertical load-bearing elements of the fac ¸ade. Only horizontal forces need to be transferred by these connections. Nevertheless, such connections could lead to an interaction between the façade and the secondary structure that compromises the collapse resistance of the latter. To avoid this, the connections should preferably be detailed such that only horizontal load transfer takes place and they freely disengage at a specified relative vertical displacement. A full connection would also be possible, provided it releases safely at a specified vertical force (structural fuse). With such decoupling mechanisms, the collapse resistance of the façade and the secondary structure can largely be independently ensured by different design methods. Without a decoupling mechanism and not being designed as a curtain wall, the façade becomes a load-bearing part of a more complex secondary load transfer system. It seems better, in this case, to design for and make use of the vertical load transfer between the façade and cantilever floors. The floors are then supported at both ends and work in beam instead of by cantilever action. The collapse resistance of such a combined secondary structure can be achieved by alternative paths, by horizontal segmentation through the insertion of vertical joints, or by a combination of both measures. The structural response of such combined systems to assumable cases of initial local failure is more difficult to assess than for a secondary structure that relies solely on cantilever action. Consider, for instance, the case that the horizontal extent of triggering accidental actions and initial local failure is assumed to be unlimited in such a combined floor—façade secondary structure. Its collapse resistance is therefore based on the provision of alternative load paths beneath the initially failing floor. Accordingly, a capacity design approach similar to that introduced in the previous section can be developed. In this case, however, the vertical load-bearing elements of the façade must carry their share of the forces induced by the fall and impact of one or more floors, a corresponding part of the façade, and aircraft debris on the floor below (Fig. 6.11). When the initial failure is assumed to be unlimited in the horizontal direction and to occur everywhere at the same 110


Applications

Failing floors and façade structure

Plastic deformation due to impact from above

Primary load transfer system

Secondary load transfer system

Fig. 6.11 Assumed initial local failure and the acceptable extent of collapse of a combined floor—façade secondary load transfer system

time, no alternative paths can be made available within the façade: the impact forces act on a non-redundant structure, corresponding to a column under axial compression, and must be transmitted elastically. The floor design, on the other hand, benefits from an increased number of plastic hinges, thus requiring less ductility capacity per hinge. The floors above the failing floors lose their outer edge support from the façade. Therefore, they must be able to carry their dead and live load, as well as the impulsive dynamic loading due to the sudden discontinuance of the outer support, in cantilever action. The primary load transfer system must be capable of supporting these vertical loads but also of carrying the concurrent horizontal loads. The distribution of the impulse dynamic loading to all floors causes short-term vertical tension in the façade above the zone of failure for which the façade must be designed. On the other hand, the load-carrying capacity of the façade in vertical tension can also be used to keep up the outer edge support of the floors above the zone of failure. The vertical loadbearing elements of the façade in this region convert from compression members to hanger-type tension members. The vertical tension in the façade can, in this case, be transferred to the primary structure by 111



outrigger trusses at the top of the building — a load path that developed in the towers of the WTC. 11,12

6.3.2.5 Overall structure The design alternatives discussed in the previous sections flow from the initial choice to provide for collapse resistance of the primary load transfer system by using the specific-local-resistance method. In contrast to the other design methods discussed in the following sections, a hierarchical arrangement of largely independent primary, secondary, and, possibly, tertiary load transfer systems results from that choice. As stated above, the tube constituting the primary structure is placed inside the perimeter of the building for reasons of serviceability. Such a location is also advantageous, however, for the collapse resistance of the primary structure: it is less exposed to actions from impact events or external explosions because the façade and the floor structure between the façade and tube serve to mitigate and distribute the resulting effects.116 This benefit results from energy dissipation and the fragmentation of incoming aircraft or projectiles. Another advantage of such a hierarchical structural system is a large degree of architectural freedom in the design and subsequent modification of the façade and floor plan. This freedom is maximised when the façade is not made a load-bearing part of a combined secondary load transfer system.

6.3.3 Non-structural protective measures Non-structural protective measures for increasing the safety against local failure include barriers to shield against vehicle impact or explosive blast, control or limitation of public access, and other protective measures, such as aerial surveillance or the provision of anti-aircraft systems. In that the structure must be protected against attacks from both the outside and the inside, a combination of such measures would be required. Relying on anti-aircraft defence will not find lasting favour with those being protected in this way, that is, the users of the building, who are generally civilians. Control or limitation of public access impairs the serviceability and the cost-benefit ratio of the building. A large amount of explosives could be smuggled into the building in small quantities over an extended period of time. Trying to counter such a tactic by scrutinising and searching every person entering the building 112


Applications

every day would cause the activities the building is intended for to grind to a halt. It is concluded that non-structural protective measures can complement other (i.e. structural) measures but are unsuitable as stand-alone methods to impart collapse resistance to large permanent civilian structures such as those considered here. The particular role of fire protection and fire fighting is addressed in Section 6.3.6 below.

6.3.4 Alternative load paths This approach aims at creating a redundant load transfer system by providing alternative paths for the forces normally transmitted by failing load-bearing elements. The focus is on the elements identified as key elements, that is, those elements whose failure, if no countermeasures are taken, causes total damage greater than what is acceptable. For the type of building considered here, it was argued in Section 6.3.2.1 that the whole of the vertical load-bearing members of any one storey has to be designated as a key element if no agreement upon the nature and extent of the assumable accidental circumstances or actions can be reached. It is concluded that, in such a case, no alternative paths can be made available for the global load transfer. Again, the assumption ‘failure of an entire storey’, which underlies the radical conclusion ‘no alternative paths available’, is corroborated by experience, and is not far-fetched. It could be argued that much has been learned from the collapse of the WTC towers and that for the design of future high-rise buildings such an assumption is excessive owing to improvements in structural design and fire protection. Such arguments would refer not to the robustness of the structure but to the probability and the extent of an initial local failure. The lessons learnt from the events of 11 September 2001 can help to increase the safety against local failure. It should be appreciated, however, that these lessons are drawn from circumstances and actions that have occurred in the past. The future is unknown. Despite these reservations, assumable accidental circumstances or actions could possibly be established. As outlined in Section 4.3.2, such a specification requires a judgement and decision-making process that reflects public opinion and, in the case of major structures, is arrived at on a project-by-project basis. Selected structural members can then be designed for the assumable actions, and other structural members that are not designed to withstand such actions can be specified as initially failing elements. The latter specification can also 113



be arrived at directly within the judgement and decision-making process, as design objective 2 according to Section 4.3.2, but entails more arbitrariness in the type of structure considered here than in the case of, for instance, continuous-girder bridges. When the initial local failure determined in this way does not extend to all the vertical load-bearing members of one storey, alternative load paths can, in principle, exist or be made available. This applies to all structural systems currently in use for high-rise buildings such as frame, shear wall, core and outrigger, or tubular systems. The redundancy of core and outrigger systems is evidenced by the pre-collapse response of the WTC towers to aircraft impact. 11,12 Identifying those structural systems that are particularly suitable for providing alternative paths needs further analytical study. Requirements for such verification are outlined in Section 4.3.4. The starting points of the corresponding structural analyses are the assumable accidental circumstances or cases of initial local failure that are to be defined as design objectives. Conclusions on the suitability of particular structural systems will, therefore, also depend on the design objectives. As stated above, preventing the initial failure of an entire storey is likely to require the strengthening of selected structural members. In the design of the primary load-bearing system of high-rise buildings, therefore, the alternative-paths method can usually only be applied in conjunction with the specific-local-resistance method.

6.3.5 Isolation by segmentation 6.3.5.1 Horizontal segmentation The damage and collapse following an initial local failure can be limited to an acceptable extent by another measure. Collapsing sections can be isolated by an appropriate segmentation of the structure. Such an approach seems most suitable for structures that are aligned along a horizontal axis, such as continuous girder bridges, where the collapse progression in the longitudinal direction is arrested at predefined locations, and isolation is safely and easily achieved by a well thought out insertion of hinges (see Section 5.3.3). A similar approach was discussed in Section 6.3.2.3 for the secondary load transfer system of a building. Instead of hinges, joints within the floor structure were envisaged as limiting and isolating elements. Extending this approach to the overall structural system leads to horizontal segmentation brought about by continuous vertical joints

114


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that run throughout the structure. In the case of an incipient collapse, horizontal pushing forces can still be transmitted by the joints. Due to the small width of the joint gap, however, these do not occur as impulsive dynamic loading. It is thus improbable that a domino-type collapse would be induced by such forces. A failure within one segment therefore remains limited to the same segment, and there would be no further collapse progression in the horizontal direction — at least not for buildings with a small height-to-width ratio. For tall and slender buildings, which are the focus here, this conclusion might not hold. To keep the extent of the damage reasonably limited, the segments should be small and many. A horizontal segmentation of the overall structure through the insertion of vertical joints, therefore, is less appropriate here. The segments would become too slender to be self-supporting. Detailing the joints to allow for the cross-boundary interaction needed for stability and the transfer of horizontal and shear forces is difficult. After the failure of individual segments, these segments would cease to stabilise the remaining structure. Furthermore, the tolerable accidental actions decrease with the segment size, so that failure may not be limited to one segment. If, again, the whole of the vertical load-bearing members of a storey is designated as a key element, horizontal segmentation would, in the end, be ineffective. As indicated before, horizontal segmentation becomes more appropriate the smaller the height-to-width ratio of a building. Horizontal segmentation through expansion joints apparently helped to prevent a collapse progression in the Pentagon Building on 11 September 2001 (see Section 5.3.4). Instead of by inserting joints, horizontal segmentation can also be achieved through isolating elements that are sufficiently strong and capable of resisting the forces induced by the collapse of an adjacent section — an alternative that likewise was present and proved beneficial in the Pentagon Building. This opens up an interesting line of thought that is pursued further in conjunction with vertical instead of horizontal segmentation in the next section.

6.3.5.2 Vertical segmentation The pancake-type collapse of the WTC towers progressed in a vertical direction (see Section 2.2.1). Once set in motion, the collapse could have been arrested only by horizontal lines of interception. A design idea based on this observation is to isolate collapsing sections, and so to limit the extent of damage, by means of vertical segmentation of

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the overall structure. The applicability of this approach is not limited to specific structural systems within a segment. The structural characteristics inside the segments are therefore not further considered here, and attention is focused on the isolating elements that form the segment borders. Regarding the mode of effectiveness of the isolating elements, three alternatives and corresponding design measures were stated in Section 5.3.3. Providing the capability to accommodate large displacements by eliminating continuity is out of the question here. But strengthening and the ensuing capability to accommodate large forces also does not seem to be a viable option. The corresponding vertical resistance would not only be required locally, that is, within the segment borders, but also in the remaining structure above and below the failing segment, which finally means it is required in the entire structure. This resistance would have to be very high because it must be designed for impact loading. The resulting dimensions of the vertical load-bearing elements would further increase mass and impact loading, so that this alternative seems unpromising. Thus, only the third alternative for creating isolating elements remains, which relies on the capability to accommodate large forces and large displacements at the same time. Such capability brings about high toughness at the segment borders. It can be achieved by providing ductility and a large energy dissipation capacity. Although the resulting forces are large, they are substantially smaller than those arising in the second alternative discussed above. The height of one segment is first assumed to be a certain fraction, say one-tenth, of the building height (Fig. 6.12). Each segment comprises the entire floor area, and is limited at the top and bottom by horizontal segment borders that likewise extend over the entire floor area (except the uppermost segment, which is limited by one border at the bottom only). When all the vertical load-bearing elements of one or more contiguous storeys fail, two failure fronts will propagate in the vertical direction — one downwards and the other upwards — from the location of the initial failure to the two adjacent segment borders. At the same time, the upper part of the building (i.e. the part above the failing segment) moves downwards as a rigid body. The rotational motion component (i.e. tilting) is presumably small — a preliminary assumption suggested by the collapses of WTC 1 and 7 that, however, requires further study (see also Ref. 14). During the fall of the upper part of the building, the segment border below the failing segment is already 116


Applications

Segment height

Detail A (see Fig. 6.13)

Shock absorbing zone

Segment border

Fig. 6.12 Vertical segmentation of the overall structure

Shock absorbing device

Segment border

Detail A

Fig. 6.13 Shock-absorbing segment border

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being loaded by the impacting debris of the failing floors above it. The main impact occurs when the upper part of the building strikes the accumulated debris on the lower segment border. Both the upper and lower parts of the building will remain internally intact until then. The impact causes large forces that act in addition to the gravitational forces. The impact forces must be reduced by appropriate measures. For this purpose, the segment borders incorporate shock-absorbing zones with large energy dissipation capacity (Figs 6.12 and 6.13). A segment border consists of two slabs, placed at a storey height or less apart, connecting structural members, and shock-absorbing devices between the two slabs. The remaining space between the two slabs of a segment border can be used like regular floor space or it can house equipment and appliances or serve as a storage area. The slabs of a segment border must be stiff and strong enough to distribute the occurring forces and to withstand them. As the points of load application are not exactly known but an effective load distribution must nonetheless be achieved, they are envisaged as massive reinforced or prestressed concrete slabs of substantial thickness (of the order of 0.40 m). They are preferably made of high-strength lightweight concrete to reduce weight and thus the impact forces. Openings in the slabs are limited to the minimum required for the vertical lines of traffic and supply. The two slabs of a segment border are connected by vertical structural members. These must be designed for the forces from the ordinary (i.e. non-collapse) loading conditions. A further requirement is that these members fail under smaller vertical forces than the vertical load-bearing elements outside the segment borders. It is thus ensured that at the start of a collapse the parts of the structure outside the failing segment remain intact, whereas the connecting structural members inside the adjacent segment borders give way to the impact forces. When this occurs, the two slabs of each adjacent segment border will approach each other, that is, there will be a relative vertical displacement between them. The shock-absorbing devices are being compressed during this approach movement, in which a large amount of energy must be dissipated in a calculable way. To minimise the impact forces, the movement should be smooth and take up the entire clear space between the two slabs. The shock-absorbing devices should meet these requirements. They are preferably placed around the columns or close to walls (Fig. 6.13). They can consist of telescoping large-diameter steel tube segments provided with a compressible filling (Fig. 6.14). The 118


Applications

A

A

Compressible filling

Section A–A

Fig. 6.14 Shock-absorbing device: telescoping steel tubes with a compressible filling

filling material must allow high volumetric compressive strain along with large plastic or fracture energy. Candidates for such material are scrap metal, metal foam, or even a mineral such as porous tuff gravel. Metal honeycomb structures are suggested in Ref. 117 for similar purposes. Numerical studies confirm that shock-absorbing devices with sufficient performance and moderate space requirement can, in principle, be produced and that the underlying concept, at least with regard to the required energy dissipation capacity, is applicable to the type of structure considered here.115 The energy to be dissipated in the shock-absorbing devices of the two adjacent segment borders corresponds to the released gravitational energy of the failing segment and the impacting upper part of the building minus the energy dissipated by the destruction of the failing segment and the connecting structural members. The energy dissipated in the failing segment is mainly fracture energy. It can be estimated from the observed vertical acceleration of building collapses. 15 This share of energy is larger the more the acceleration falls short of the acceleration of free fall. 119



Some uncertainty in forecasting the failure progression and designing the segment borders arises from the requirement, mentioned before, that the connecting structural members are designed to fail under smaller vertical forces than the vertical load-bearing elements outside the segment borders. Instead of the failure progression described above, in which first two failure fronts propagate inside the failing segment, it is conceivable that the connecting structural members give way almost immediately because the pressure waves induced by the initial failure travel much faster than the failure fronts. The shock-absorbing function of the segment borders would then be activated earlier than assumed above. Furthermore, the shock-absorbing function of remote segment borders could be activated simultaneously. These effects would probably have an attenuating influence on the failure progression, which can now come to a halt inside the failing segment before arriving at the segment borders. In the design concept indicated in Fig. 6.12, each segment consists of a number of storeys, and is comparatively large. The maximum extent of damage corresponds to one segment and, therefore, is large as well. If the maximum extent of damage is to be reduced, the segment size must be decreased. This consideration leads to a design alternative in which each segment consists of just one storey. In view of the reduced drop height, there is less time now for tilting and less uncertainty concerning the prediction of the failure progression, which is an additional advantage. In this alternative, every floor must be designed as a segment border, that is, as a massive concrete slab. Because the failing segment and the drop height of the upper part of the building are smaller, the floor slabs can be of less substantial thickness (say of the order of 0.25 m). On the other hand, shock-absorbing devices must now be provided in every storey. Due to the reduced drop height, however, the released gravitational energy is smaller. Therefore, the combined energy dissipation capacity requirement of all shock-absorbing devices is approximately the same as before. This means that the cost of these devices and the ensuing usable floor space reduction are also about the same. The total mass is likely to be somewhat larger due to massive concrete slabs now being required for every floor. In sum, this design alternative provides for a smaller extent of damage and better predictability of the failure progression at the same or only slightly increased cost, and thus seems preferable. A similar concept and supporting numerical studies are presented in Ref. 117. Partial mid-storey building failures occurred during the 1995 Kobe and other earthquakes, in which the vertical load-bearing elements 120


Applications

Fig. 6.15 Failure of an entire storey without collapse progression (Kobe, 1995). (Source: Eos, 1995, 76, No. 6. Photograph: Paul Somerville, # AGU)

of entire storeys failed without leading to pancake-type collapse (Fig. 6.15). Such incidents show that it is, in principle, possible to arrest a collapse in its early stages at horizontal lines of interception. Finally, it is noted that vertical segmentation may seem unusual, but it is the only approach that does not impose limits on the tolerable accidental actions, at least not in the horizontal direction.

6.3.6 Fire protection, fire fighting, and evacuation Whatever approach is taken in structural design, thought must be given to non-structural protective measures for fire protection and fire fighting. In addition, rapid and safe egress from the building must be assured, as underlined by the WTC tragedy. The measures taken for these purposes comprise physical provisions and emergency procedures. Both must be developed further, not only considering effectiveness but also in terms of robustness. In this context, robustness means that these provisions and procedures remain operative even in the case of local damage or partial collapse. Fire fighting in high-rise buildings usually depends on water that is pumped up from ground level through standpipes and supplied by hoses. Even if complemented by secondary supply from water tanks within the building, the automatic and manual fire-fighting capabilities 121



of such a system might become inoperative through the same event that ignites the fire. Such conventional fire-fighting systems seem best suited to the specific-local-resistance method as applied in Section 6.3.2: standpipes are fed through the massive tube that forms the primary load transfer system, which means they are relatively well protected against physical damage; the same holds for the staircases and lifts. All these elements, however, could still be affected by accidental circumstances inside the tube that leave the structure intact. To create redundancy for, and increase the robustness of, fire fighting and evacuation, the tube should therefore be partitioned by vertical inner walls. Each compartment created in this way would house independent standpipes, staircases, and lifts. Nevertheless, it is desirable that novel fire-fighting systems are developed that allow for a higher degree of robustness. Instead of water, other fire-extinguishing agents such as carbon dioxide or foam can be used. The constituents are relatively light and need little energy and only light equipment to discharge them. They can be distributed in a decentralised manner over the entire building, with the effect of creating autonomous and redundant systems that are independent of an external energy supply and the normal functioning of standpipe systems. Finally, the provisions and procedures for evacuation need to be improved. As noted above, staircases should be physically protected and be made redundant. The same applies to lifts, which could be used not only for fire fighting but also for evacuation, in particular of disabled occupants (see also the Institution of Structural Engineers report on safety in tall buildings 118). In addition, alternative evacuation methods should be developed. Helicopter rescue from the roof might become more of a viable option if special equipment (e.g. multipleperson rescue baskets) is developed and procedures are improved. For special structures, such as some towers and special manufacturing environments, controlled descent devices are permitted by the Life Safety Code119 to provide escape routes. Occupants could also be evacuated to neighbouring buildings by zip lines and breeches buoys, as used for the rescue of sailors from ships.

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7 Measures of robustness and collapse resistance 7.1

General

In Chapters 4 to 6, a pragmatic approach was presented that allows a reasonable balance of safety and economy to be reached in the design of structures susceptible to progressive collapse. This approach still lacks an objective mathematical basis. Its use requires engineering judgement, imagination, and experience. The further development of this approach should, where possible, go beyond this subjective basis towards more objective procedures in order to advance its applicability and general acceptance. The terms ‘robustness’ and ‘collapse resistance’ as defined in Section 4.2 offer the possibility for this development. According to these definitions, robustness means insensitivity of a structure to local failure, and collapse resistance is insensitivity to accidental circumstances. The defining terms ‘insensitivity’, ‘local failure’, and ‘accidental circumstances’ used here are quantifiable by referring to the design objectives set out in Section 4.3.2. In the following, the formulation of measures for describing robustness and collapse resistance quantitatively is discussed.

7.2

Areas of application

A quantification of these properties based on the definitions and design criteria mentioned above would have various advantages and possible applications: 1. Design requirements for robustness or collapse resistance could be specified numerically in standards and guidelines. This could also account for the type of structure and its significance and exposure. 2. Measures of robustness or collapse resistance could serve as verification tools with the calculated value of a measure being checked 123



3.

4.

5.

6.

agains agai nstt a re requ quir ired ed va valu lue. e. Pr Proj ojec ectt-re rela late ted d de desi sign gn cr crit iter eria ia ca can n be factored into the calculated or required value. It follows follows that such measures measures could also be used for optimising optimising the design concerning the balance between cost on the one hand, and robustness or collapse resistance, on the other. A mea measur suree of robustne robustness ss cou could ld provide provide guidance guidance on the choice choice of design method. For markedly non-robust structures, for instance, particularly those deemed significant and exposed, methods aimed at limiting the extent of collapse could be indicated to be preferable to methods aimed at preventing initial local failure. As outlined outlined in Section 3.2, 3.2, it might be possible to augment augment convenconventional design procedures, which use partial safety factors, with an additional system partial safety factor on the resistance side of the design equations to account for the response of the structure to local failure and thus its robustness. If this additional factor could be derived easily on the basis of a measure of robustness, then this would woul d cons constitute titute a further further step towards towards a standardised standardised and simplifie simplified d treatment of progressive collapse. Fina Fi nall lly, y, a qu quan anti tific ficat atio ion n in co conn nnec ecti tion on wi with th a cl clas assi sific ficat atio ion n of struct str ucture uress ope opens ns up the pos possib sibili ility ty of cat catalo alogui guing ng the num numeri erical cal values of measures of robustness and collapse resistance for the variou var iouss typ types es of str struct ucture ures. s. The usa usabil bility ity of the afo aforem rement ention ioned ed applications would be improved by such a classification.

7.3

Requirements

The val The validi idity ty and use useful fulnes nesss of mea measur sures es of rob robust ustnes nesss and col collap lapse se 120,121 resistance are linked to certain requirements: 1. Expressive Expressiveness: ness: the measures should completely completely and solely express express robustness or collapse resistance and should not be influenced by othe ot herr as aspe pect cts. s. Th Thee me meas asur ures es sh shou ould ld pr prov ovid idee cl clea earr di dist stin inct ctio ions ns betw be twee een n ro robu bust st an and d no nonn-ro robu bust st or co coll llap apse se-re -resi sista stant nt an and d no nonncollapse-resistant structures. 2. Obje Objectivi ctivity: ty: the measures should be independen independentt of user decisions. decisions. Under unchanged conditions, the values of the measures should be reproducible. 3. Simp Simplicit licity: y: the measures measures should be defined defined in as simpl simplee a manner as possible. This is in order to gain acceptance with users and in the interest of objectivity and generality. 4. Ca Calc lcul ulab abil ilit ity: y: it sh shou ould ld be po poss ssib ible le to de deri rive ve th thee me meas asur ures es fr from om the pro proper pertie tiess or beh behavi aviour our of the str struct ucture ure.. All req requir uired ed inp input ut 124


Measures of robustness and collapse resistance

parameters must be quantifiable. A sufficiently accurate numerical calculation should be possible and not require excessive effort. 5. Gene Generality rality:: the measures should, should, as far as possible, possible, be applicable applicable to any kind of structure. These requirements are partly in conflict with each other, so that it may not be possible to meet them all at the same level at the same time. For instance, an evaluation of the approaches proposed so far (see Section 7.4) suggests that a high level of expressiveness can be achieved, but at the cost of calculability. Thus, the above requirements may need to be moderated. This seems just ju stifi ifiab able le an and d ac acce cept ptab able le,, at le leas astt fo forr th thee ge gene nera rali lity ty re requ quir irem emen entt because different kinds of structures are susceptible to different types of collapse (see Chapter 2). Hence, different kinds of structures may be better described by specifically defined measures that reflect different mechanisms of collapse.

7.4 7. 4

Pres Pr esen entt ap appr proa oach ches es

To date, there is no unified theory of progressive collapse nor is there agreem agr eement ent on ter termin minolo ology. gy. Acc Accord ording ingly, ly, a lar large ge var variet ietyy of dif differ feren entt approaches for quantifying the relevant characteristics and structural features have been suggested in the literature. This includes both deterministically defined54,56—58,120,122—125 and probabilistically defined54,121 measures. They are mostly based on assuming damage (an interesting exception to this is presented in Ref. 126) and on either comparing the properties of the damaged and undamaged structures or examining the response of the structure to such initial damage. When Wh en th thee pr prop oper erti ties es of da dama mage ged d an and d un unda dama mage ged d st stru ruct ctur ures es ar aree comp co mpar ared ed,, th thee co comp mpar aris ison on is ba base sed d on th thee re resp spec ecti tive ve lo load ad-c -car arry ryin ingg 54,58,122—124 57,120,125 54,121 capacities, stiffnesses, or probabilities of failure. When the response of the structure to initial local damage is examined, thee re th resu sult ltin ingg ex exte tent nt of co coll llap apse se or to tottal da dama mage ge ca can n be qu quan anti tifie fied, d, an and d ca can n be further related, for instance, to the initial damage and the size of the structure.120,125 Th This is req require uiress an ana analyt lytica icall inv investi estigat gation ion of co collap llapse se scenarios, which in most cases is complex and costly. The analysis of the failure progression can be facilitated by topological considerations57 or by energy-based approaches.56,120,125 Furthermore, the measures suggested have different purposes. Verification of whether the design objectives have been achieved is not always sought. A detailed review120,127 shows that the definitions of 125



the measures and analysis approaches suggested so far meet the requirements specified in Section 7.3 to varying degrees. No approach stands out as clearly superior and practical. For further illustration, examples of three basic approaches are presented below.

7.5 7. 5

Stif St iffn fnes esss-ba base sed d me meas asur ures es of ro robu bust stne ness ss

A simply defined and easily calculable measure follows from examining the static stiffness of the structure: Rs ¼ min j

det K j det K0

ð2Þ

where Rs is the stiffness-based measure of robustness, K j is the active system sys tem sti stiffn ffness ess mat matrix rix of the str struct ucture ure aft after er rem removi oving ng a str struct uctura urall element or constraint j, and K0 is the active system stiffness matrix of the inta intact ct struct structure. ure. Further examination shows that Eq. (2) must still be calibrated, or at least normalised, to obtain a practical and plausible measure with a rang ra ngee of va valu lues es be betw twee een n 0 an and d 1.120 A va valu luee of 1 re repr pres esen ents ts th thee maximum possible robustness, while 0 corresponds to a total lack of robustness. Intermediate values are intended to be quantitative and expressive measures of robustness. Verification of this approach was carried out based on ultimate load analyses of simple frame structures. It turns out that the reduction in load capacity due to the removal of structural elements does not correlate la te ve very ry we well ll wi with th th thee co corr rres espo pond ndin ingg va valu lues es of Rs . So So,, th thee ex expr pres essi sive vene ness ss of the stiffness-based measure of robustness, at least in its present form, is not sufficient. It is more a measure of the connectivity of the system than of the robustness of the structure.120 The advantages of simplicity and ease of calculation, on the other hand ha nd,, ma make ke it se seem em wo wort rthw hwhi hile le to fo foll llow ow up on th thee as asse sess ssme ment nt of ro robu bust st-ness through system matrices. In addition to stiffness, other structural proper pro pertie ties, s, suc such h as str streng ength, th, loa load d cap capaci acity ty uti utilis lisati ation, on, duc ductil tility ity,, and masss dis mas distri tribut bution ion,, can als also o be des descri cribed bed by cor corres respon pondin dingg mat matric rices es and used in such an assessment. Further refinement is also possible by taking into account the system topology.57 All these approaches seek to assess in a simplified manner the load capacity remaining after the removal of structural elements, and thus thee ca th capa pabi bili lity ty of th thee st stru ruct ctur uree to re redi dist stri ribu bute te th thee fo forc rces es ca carri rried ed by these elements into alternative load paths. Based on the description of mechanisms and types of collapse presented in Chapter 2, it can 126



therefore be concluded that these approaches are, in principle, suitable for structures that are susceptible to zipper-type collapse. They are not suitable for structures whose collapse behaviour is governed by impact loading, that is, structures that are susceptible to pancake-type or domino-type collapse, because such loading is not reflected in structural properties such as stiffness.

7.6

Damage-based measures of robustness

This is an approach that is based on the quantification of the extent of collapse or total damage resulting from initial damage. It can easily be aligned with the definition of robustness suggested in Section 4.2.1. Consequently, and in contrast to the measure presented in the previous section, adequate expressiveness can easily be ensured. In doing so, it makes sense to include the design objectives listed in Section 4.3.2 in the definition of the measure of robustness. A suitable formulation is based on the complement of the dimensionless total damage: Rd ¼ 1 

p plim

ð3Þ

where Rd is the damage-based measure of robustness, p is the maximum total damage resulting from the assumable initial damage (which, more precisely, can be any of the assumable cases of initial local failure), and plim is the acceptable total damage. Note that p and plim refer to damage occurring additionally to the initial damage. The quantification of damage required here can be performed by reference to the affected masses, volumes, or floor areas (in buildings), or even to the resulting costs. Since this measure is directly related to design objectives 2 to 4 in Section 4.3.2, it can be used as a design and verification tool in achieving these objectives. A value of 1 is obtained when no additional damage occurs; it thus indicates perfect robustness. For values between 1 and 0, the design objectives are met to a greater or lesser degree. Negative values are generated when p > p lim , and indicate that the design objectives are not met. As said before, the measure of robustness defined by Eq. (3) is related to design objectives, which ensures its usability as a design and verification tool. The design objectives, however, must be predetermined in a decision-making process and cannot be derived from first principles. If expressiveness and objectivity are targeted not only within the context of given design criteria but in a more general sense, then the relationship 127


Progressive collapse of structures d (i )

1 A d

B

d – i

C

i

i

1

i

Fig. 7.1 Maximum total damage d(i) as a function of the initial damage i

to design objectives must be abandoned. The question then arises: what is the extent of the assumable initial damage? Pondering this question leads to the following integral measure:

ð 1

Rd;int ¼ 1  2

0

½dðiÞ  i di

ð4Þ

where Rd;int is the integral damage-based measure of robustness and dðiÞ is the maximum total damage resulting from and including the initial damage of extent i. Both dðiÞ and i are dimensionless variables obtained by dividing the respective reference value (mass, volume, floor area, or cost) by the corresponding value of the intact structure. The dimensionless extent of initial damage i lies between 0 and 1. Because the integration extends over the whole range of values of i, selecting the assumable initial damage is no longer required. If only direct structural damage is taken into consideration, and damage to the surroundings and indirect losses are excluded, then the value of dðiÞ also lies between 0 and 1. Figure 7.1 shows three different curves for dðiÞ, each referring to a different structure of different robustness. Curve A describes a nonrobust structure; even a small amount of initial damage results in significant total damage. Curve B illustrates a comparatively robust structure; major additional damage only occurs after significant initial damage. The maximum total damage dðiÞ as a function of the initial 128



damage i can only take values in the grey area above the straight line described by the equation dðiÞ  i ¼ 0. The value of Rd;int therefore lies between 0 and 1. Similarly to the stiffness-based measure of the previous section, a value of 1 indicates maximum possible robustness, and a value of 0 indicates a total lack of robustness. Now consider curve C. Compared with curve B, it indicates a greater sensitivity to minor initial damage. Since R d;int is also a measure of the convexity of the curve dðiÞ, the measures of robustness resulting from curves B and C are of the same order of magnitude. Thus, Rd;int does not adequately reflect the relatively greater importance of the effect of minor initial damage. This weakness can be remedied by weighting the initial damage so as to increase the importance of minor initial damage in conjunction with renormalising the measure to a range of values between 0 and 1. Modified definitions of damage-based measures of robustness are presented and compared by Haberland.120 The requirements of expressiveness and simplicity, and in principle also the requirement of generality, can be met by these types of approaches. Incidentally, they are not only generally applicable to any kind of structure but also generally compatible with any kind of design method. Among the approaches presented here, they are possibly the only ones that can capture the influence of the design method ‘isolation by segmentation’. The question of calculability, on the other hand, is more difficult to answer. Determining the total damage that results from initial damage requires an examination of the failure progression, which in turn can involve geometrically and materially nonlinear dynamic analyses in the time domain (see Section 4.3.4). In particular, the initial damage must generally be modelled not as a static removal of the affected structural element or constraint but as a sudden or possibly delayed event, that is, as a dynamic process. The analysis becomes particularly difficult when the separation, fall, and impact of structural components needs to be considered. Depending on the type of structure and the governing type of collapse, the analysis required here can become intractable or, for all practical purposes, too complex. This applies especially to structures that are susceptible to pancake-type or mixed-type collapse. When it comes to calculability, and hence applicability in practice, therefore, generality can also be affected. Nevertheless, high computational cost is not necessarily a barrier to the possible applications listed in Section 7.2. In particular, the possibility of a classification of structures as mentioned under point 6 must 129



be emphasised. The identification and cataloguing of numerical values of measures of robustness would be done on the basis of selected representative structures. This work would need to be carried out only once, so that the anticipated high computational cost is of less importance.

7.7

Energy-based measures of robustness

The above discussion shows that stiffness-based and damage-based measures of robustness are either easy to calculate or expressive, but not, from the outset, both. Approaches based on energy considerations might be capable of meeting both requirements to the same degree. The following simple approach is based on the comparison of the energy released during an initial failure and the energy required for failure to progress: Re ¼ 1  max j

Er; j Ef ;k

ð5Þ

where Re is the energy-based measure of robustness, Er; j is the energy released during the initial failure of a structural element j and contributing to damaging a subsequently affected element k, and Ef ;k is the energy required for the failure of the subsequently affected element k . Design objective 2 specified in Section 4.3.2 can be taken into account when choosing the initially failing structural elements. Design objectives 3 and 4, that is, the acceptable total damage, cannot be accounted for in this simplest formulation. Instead, only the possibility of a failure progression is examined. A value of 1 indicates perfect robustness. Values between 1 and 0 are acceptable to a greater or lesser degree. Negative values indicate failure progression. For the sake of argument, it is assumed that failure progression is equivalent to complete collapse. The measure of robustness defined by Eq. (5) seems at first sight to meet the simplicity requirement and, regarding the possibility of complete collapse, also the requirement of expressiveness. A difficulty, however, arises in determining the value of Er; j , which can be over- or underestimated. The energy released during the initial failure of a structural element consists of several parts. In structures susceptible to pancake-type or domino-type collapse, the gravitational potential energy of separating or overturning elements that is transformed into kinetic energy makes a major and possibly dominant contribution to the total released energy. In such cases, a numerical estimation can be easy and valid. However, in structures susceptible to other types of 130



collapse, ordinary external forces such as gravity loads contribute significantly to Er; j . They perform work over the elastic and plastic displacements occurring during the initial failure. This contribution can only be determined by a complete structural analysis. Furthermore, Er; j should include only that part of the energy which contributes to damaging the subsequently affected element k. This condition again is most easily met in structures that are susceptible to pancake-type or domino-type collapse. The separation, overturning, and impact events that govern such scenarios occur in a discrete and concentrated manner, so that the released energy is reintroduced into the structure in a similarly concentrated manner, that is, without major losses, and is therefore easy to calculate. Overall, it is anticipated that such structures are the most suitable for the application of energybased measures of robustness. In the simple form of Eq. (5), the measure is truly expressive only for structures in which the failure of the subsequently affected element k results in complete collapse. This applies, in particular, to structures in which the elements j and k are similar, and which are composed entirely of such elements. In such structures, the number of cases of initial and subsequent failure to be examined is relatively small, which enhances calculability. Examples are rows of overhead transmission line towers, where each tower is an element, and high-rise buildings, where an element could consist of all the vertical load-bearing members of any one storey. Equation (5) is, moreover, based on the assumption that the energy of the event that triggers the initial failure is completely absorbed by that failure, or at least that the excess energy does not contribute to damaging the subsequently affected element. Modified definitions of energy-based measures of robustness and collapse resistance that attempt to overcome these limitations are presented by Haberland.120 A different energy-based approach in which the work done by external forces and possible failure sequences are also examined is taken by Smith.56 This leads to higher computational cost, but could make the method applicable to structures that are susceptible to zipper-type collapse.

7.8

Summary and future directions

Damage-based measures of robustness or collapse resistance account for the actual response of a structure to initial local failure or accidental circumstances. They can thus easily be aligned with the definitions of 131



robustness or collapse resistance (which might require the choice of design objectives) and, in principle, also meet the requirement of generality. For the same reason, however, they are computationally costly. Measures based on stiffness or other structural properties and energy-based measures are not, a priori, expressive and general but are easier to calculate. Improved formulations of such measures could be used as alternatives to more precise damage-based measures, provided they can be shown to be expressive. This verification would have to be done by parametric analyses of representative structures. Both the damage-based measures and the improved alternative formulations based on properties or energy would have to be computed and compared. Alternative formulations prove useful when they correlate well with damage-based measures in this comparison. Such analyses would be representative for the classes of structures being represented by the examined structures. The structures of each class are susceptible to different types of collapse, which in turn will best be reflected in different measures. It can therefore be expected that such improved alternative formulations would be expressive only for specific classes of structures.

132


8 Conclusions 8.1

Synopsis

Progressive collapse of structures is a complex and multifaceted problem for which the existing terminology and procedures are inadequate. Perhaps the best example for illustrating this is the undifferentiated classification of quite different collapse scenarios under the one term ‘progressive collapse’, as is customary today. Hence, the various types and mechanisms of progressive collapse are first of all distinguished and described in this book, and a terminology is suggested (Chapter 2). Next, the terms ‘robustness’ and ‘collapse resistance’ are defined, which brings about a further conceptual refinement. Thus, robustness is insensitivity to local failure, and collapse resistance is insensitivity to accidental circumstances. According to this definition, robustness is a purely structural property, in the sense that the cause and probability of local failure — and therefore also the nature, extent, and probability of triggering accidental circumstances — are immaterial. A robust structure is at the same time collapse resistant, but not vice versa. A quantitative interpretation of these definitions can be obtained by relating them to given design objectives. The need for special considerations for progressive collapse can be demonstrated by studying current design procedures and referring to the probabilistic theory of reliability. It becomes clear that non-robust structures are particularly susceptible and require special attention (Chapter 3). However, a purely reliability-based verification of actual structures where progressive collapse comes into play is almost impossible, at least for the time being, because of the number and complexity of influencing factors that arise during a collapse. That this might be more than a passing problem follows from the fundamental difficulties in describing and quantifying accidental circumstances or actions and in reaching an informed consensus on the acceptable probability of a major disaster. The semi-probabilistic design codes and verification 133



procedures in use today are based on reliability theory, and hence are also inadequate to ensure collapse resistance. Possible future improvements of procedures that are nonetheless based on reliability theory are outlined. On the other hand, both a general concept for handling the questions raised by the phenomenon of progressive collapse and a procedure for designing collapse-resistant structures are urgently required. To this end, a pragmatic approach is suggested in which the design procedures currently used are complemented by an additional assessment and measures to ensure the collapse resistance of the structure (Chapters 4 and 5). This approach allows a reasonable balance of safety and economy to be achieved without requiring excessive analysis effort. The additional assessment for collapse resistance calls for the consideration of design requirements, design objectives, design methods, and verification procedures. It is no longer based on reliability theory but on engineering judgement and on concrete, deterministically defined design objectives that are to be understood as performance criteria and must be established in a decision-making process. The most important design objectives are the assumable accidental circumstances, the assumable cases of initial local failure, and the acceptable extent of collapse. For ensuring collapse resistance, a number of methods are available, which are presented and systematically compared. They are either based on increasing the level of safety against initial local failure or aim at limiting the extent of collapse following an assumed local failure. The corresponding structural analyses required for assessment and verification are carried out deterministically. Quality requirements for such analyses are outlined. In general, nonlinear dynamic analysis in the time domain is required. The feasibility and validity of simplified analysis and verification procedures are discussed. Prescriptive design rules, which do not require structural analysis, are also examined, but it is found that they are not generally to be recommended for major structures. Recent European and American standards and drafts indicate that codification is moving towards such a pragmatic approach already. It is hoped that future code development leads to a clearer description of the design requirements, design objectives, design methods, and verification procedures, as well as to a precise and consistent use of language. Even if it is difficult to base the conceptual and practical treatment of the present problem on reliability theory, it can play an important role in 134


Conclusions

the further development of the pragmatic approach presented here. A more in-depth comparison of the design methods discussed and a specification of design criteria such as the exposure of a structure, the assumable accidental circumstances, and the applicable safety factors could thus be made. Nevertheless, these and other design criteria can, at best, only partly be derived from first principles. Instead, they need to be established in a judgement and decision-making process that can be supported by professionals, but in the end must reflect public opinion. The concept presented here accommodates the need for public debate by making the choices — for instance concerning the acceptable extent of collapse — relatively transparent. If collapse resistance is to be achieved by increasing the level of safety against initial local failure, the design methods ‘specific local resistance’ and ‘non-structural protective measures’ are available. These methods do not aim at increasing the robustness of the structure. If collapse resistance is to be achieved by limiting the extent of collapse following an assumed local failure, the design methods ‘alternative load paths’ and ‘isolation by segmentation’ can be used. In this way, the structure is made both robust and collapse resistant. In the specific-local-resistance method, key elements are designed for the actions resulting from assumable accidental circumstances. A key element is basically a structural member whose failure would trigger an unacceptable extent of collapse. The safety of key elements can also be increased by non-structural protective measures. The effectiveness of both methods depends on the completeness and validity of the accidental circumstances specified as one of the design objectives. Since these events are unforeseeable or occur with very low probability, completeness and validity cannot be verified and might not be ensured. Nevertheless, these methods are of interest for structures that are poorly suited for other methods. Furthermore, they can be suitable for smaller structures and for structures with only a few and clearly identifiable key elements. The alternative-paths method aims at increasing the redundancy of the structure. It requires an increase in either continuity or structural resistance, or both. This method, and the prescriptive design rules based on the same idea, must be applied with prudence. Forces resulting from alternative paths should be verified down to the foundations. In the case of prescriptive design rules, they should be determined based on the overstrength of the structural members and connections that provide the alternative load transfer. The segmentation method aims at isolating collapsing sections, and thus limiting the extent of collapse, by a segmentation of the structure. 135


Progressive Progr essive collap collapse se of struc structures tures

The isolating elements can work in one of three ways: by high local resistance, and thus the capability to accommodate large forces; by a break bre ak in con contin tinuit uity, y, and thu thuss the cap capabi abilit lityy to acc accomm ommoda odate te lar large ge displacements; or by high ductility and large energy dissipation capacity, and thus the capability to accommodate large forces and large displacements at the same time. For some structures, structures, segmentation segmentation is the more suitable approach to prevent progressive collapse, a fact that has been given little attention so far. This may be because the terms ‘continuity’, ‘redundancy’, and ‘robustness’ are intuitively equated, a tacit assumption that is justified, at best, for only particular types of structures. The suitability of the different design methods depends on the design objectives and on the type and features of the structure, for instance its orientation in space. Bridges are mainly aligned along a horizontal axis. Buildings can be aligned along a vertical or horizontal axis. Structural components that separate from the structure and fall down could lead to impact loading on key elements of the remaining structure below. Such impact events are more of a concern for high-rise buildings than for bridges or low-rise buildings. The need for continuity to prevent separation, fall, and impact of components thus varies for different types of structures, and different design methods will be preferable. The effectiveness of the various design methods depends on the accuracy of analysis and the adequacy of the specification of design objectives, such as assumable accidental circumstances and assumable initial local failure. This dependency is greatest for the specific-localresistance method and for non-structural protective measures (which are both based on increasing the level of local safety). It is reduced for the alter alternativ native-pat e-paths hs method, and at a minim minimum um for the segme segmentantation tio n met method hod (w (whic hich h both both aim aim at lim limiti iting ng the ext extent ent of of col collap lapse) se).. Furth Further er information on the application of design strategies and methods can be found in Sections 5.3.4 and 5.4 and in Chapter 6. The discussion in Chapter 6 is directed at specific types of structures and demonstrates the suitability of the concept presented in Chapters 4 and 5. In applying the concept to bridges, the most important types of large bridges are examined, and recommendations for their collapseresistant design are developed. A different goal is pursued in applying it to the design of high-rise buildings. The focus here is not so much on the development of concrete recommendations but, rather, on the possibility, in principle, of a collapse-resistant design of extremely tall and slender structures by using the approach set forth in this book. This approach is essentially based on engineering judgement, imagination, and experience. The possibility of moving to more objective and 136


Conclusions

quanti quan tifia fiabl blee pr proc oced edur ures es is ex exam amin ined ed in Ch Chap apte terr 7. In pa part rtic icul ular ar,, describing robustness and collapse resistance by quantitative measures seems see ms app approp ropria riate te and ach achiev ievabl able. e. Sim Simple ple exp expres ressio sions ns for sti stiffn ffness ess-base ba sed, d, da dama mage ge-b -bas ased ed,, or en ener ergy gy-b -bas ased ed me meas asur ures es of ro robu bust stne ness ss ar aree presented. It turns out that the requirements to be made on such measures cannot all be met at the same level at the same time. In particular, measures that are easy to calculate lack expressiveness and generality, and measures that are expressive and general lack calculability. Furthermore, it is found that structures that are susceptible to differ dif feren entt typ types es of col collap lapse se are bes bestt des descri cribed bed by dif differ ferent ently ly defi defined ned measures measu res of robus robustness tness or colla collapse pse resist resistance ance..

8.2

Outlook

This book has set out to refine the terminology and to develop a sound conceptual framework for the treatment of progressive collapse. This approach has proved applicable and successful, so far. Future development me ntss co coul uld d ai aim m at fu furt rthe herr re refin finem emen ents ts in te term rmin inol olog ogyy an and d th thee identi ide ntifica ficatio tion n of add additi ition onal al con concep ceptua tuall rel relati ations onship hips. s. On the oth other er hand, they should provide insights and methods that are useful in structural design practice. Important relationships exist between the concepts discussed here, and are illustrated in the diagram of Fig. 8.1. They are partly explained in this book, but deserve further study and clarification. In this system of mu mutu tual al re rela lati tion onsh ship ips, s, th thee ty type pess of co coll llap apse se an and d th thee re resp spec ecti tive ve propagating actions seem to hold a central position. In any case, a careful description of types of collapse and propagating actions leads to insights into collapse-promoting structural features, the types of structures affected, and possible design methods, as demonstrated in Section 2.4. As shown there, structural features that have a bearing on the occurrence and type of progressive collapse are the strength, ductility, continuity, mode of load transfer (series or parallel), spatial orientation, and structuredness of a structure. This could be the starting point for a future classification of structures. The description of types of collapse also provides hints at a number of analogies. These could be pursued further to advance the conceptual framework and design procedures. This includes the analogy between prog pr ogre ressi ssive ve co coll llap apse se an and d in inst stab abil ilit ityy (S (Sec ecti tion on 2. 2.2. 2.5) 5) an and d be betw twee een n zipper-type collapse and fast fracture (Section 2.2.4). Concerning the needs of design practice, the future development of a comprehensive and sufficiently differentiated classification of structures 137


Progressive Progr essive collap collapse se of struc structures tures Classification of structures

Collapse-promoting structural features

Types of collapse Propagating actions

Design methods

Measures of robustness

Verification procedures

Measures of collapse resistance

Design objectives

Fig. 8.1 Conce Conceptual ptual relationships relationships in the desc description ription and prevention prevention of progre progressive ssive collapse

for progressive collapse is particularly important. As far as possible, such a classification should be linked to recommendations on appropriate design methods and simplified verification procedures. Furthe Fur thermo rmore, re, obj object ective ively ly qua quanti ntifiab fiable le cri criter teria ia and pro proced cedure uress for evalua eva luatin tingg and cla classi ssifyi fying ng str struct ucture uress wou would ld be des desira irable ble for des design ign practice. It became clear in Chapter 7 that the types of collapse play a leading role also in a quantitative description of the robustness and collapse resistance of a structure. The further development of measures of ro robu bust stne ness ss an and d co coll llap apse se re resi sist stan ance ce mu must st be ac acco comp mpan anie ied d by parametric analyses of representative structures. In this, the parameters to be varied are the structural features that have a bearing on the occu oc curr rren ence ce an and d ty type pe of co coll llap apse se as we well ll as th thee de desi sign gn ob obje ject ctiv ives es.. Thes Th esee an anal alys yses es wo woul uld d se serv rvee to ve veri rify fy th thee en envi visa sage ged d me meas asur ures es of robustness and collapse resistance, and to assign applicable definitions of measures to each class of structure. Finally, they could be the basis for cataloguing the numerical values of these measures and for calibrating them for use as part of a standardised and simplified treatment of progressive collapse.

138


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Index

Page numbers in italics denote figures. Acceptable extent of collapse 43, 54, 64, 111 acceptable total damage design objectives, 39, 43 high-rise buildings, 100—101 robustness measures, 127 see also total damage accidental circumstances, 1 assumable, 43—44, 101, 113—114 cable-stayed bridges, 89, 90 definition, 39 design actions, 45 design procedures, 33—34, 36 Eurocode EN 1991-1-7, 45 exposure to, 41—42 identified actions, 47 insensitivity to see collapse resistance prevent local failure, 56—57 see also triggering events Alfred P. Murrah Federal Building, 2, 4 collapse typology, 23 design methods, 53—54, 53—55, 59— 62, 59—61, 72— 73, 73 alternative load paths, 4, 47, 59—62, 80, 82—83, 135 bridge design, 87, 96, 98 high-rise buildings, 106— 108, 110, 113—114 interaction, 79 prescriptive design rules, 84— 85 segmentation and, 71, 75—76 American Society of Civil Engineers (ASCE), 8, 10, 42 Analogies 19, 23 analysis-based verification, 50—51 future directions, 132 interaction, 78 present approaches, 125—126 research publications, 6 —7 segmentation, 65— 66, 69 anchored elements domino-type collapse, 18

zipper-type collapse, 15 annular cross-sections, 103—104, 104 applied design methods, 86—124 Approved Document A 9, 46, 48 arch bridges, 99 ASCE (American Society of Civil Engineers), 8, 10, 42 ‘assumable’, definition, 43 Assumable initial local failure, 42, 54, 64 , 111 assume local failure strategy, 47, 54, 58—83 bridge design, 95—96 design objectives, 43—44, 46 high-rise buildings, 100—101, 106—107, 106, 111 , 113—114 bending failure, cast-in-place joints, 65 bending moments, cable-stayed bridges, 92 , 93, 94 Best Practices for Reducing the Potential for Progressive Collapse in Buildings, 9 bracing, 21 break-away hinges, 66, 97—98 see also hinge insertion bridges cast-in-place joints, 65 collapse-resistant design, 86—99 Confederation Bridge, 44—45, 62—67, 69—71, 77—79, 88 corrosion protection, 97 damping effect, 93 design methods, 62—66, 64—67, 69— 71, 74, 77—79 design objectives, 46 failure incidents, 3— 4 Haeng-Ju Grand Bridge, 3, 23—24, 66, 78, 88 instability-type collapse, 21 Mississippi River Bridge, 4 mixed-type collapse, 23—24 section-type collapse, 19 —20

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Progressive collapse of structures bridges (continued ) standards/guidelines, 8 Tacoma Narrows Bridge, 14, 14 , 97 Taney Bridge, 95—96 Tasman Bridge, 3—4, 66, 71, 74, 88 verification procedures, 51 zipper-type collapse, 14 see also individual named bridges British Standards, 8, 46, 48 brittle fractures, 18—20, 25 brittle material behaviour, 26 BS 5950, 8, 48 BS 8110, 8, 48 buckling, 21—22 building design standards, 8 —10 see also design . . . ; high-rise buildings building envelope, 109—112 cable net, 16 cable-stayed bridges accidental circumstances, 89, 90 collapse-resistant design, 89—97 design objectives, 46 mixed-type collapse, 24 section-type collapse, 19—20 standards/guidelines, 8 verification procedures, 51 zipper-type collapse, 14 calculability requirement, 124—125, 129 Canadian code, 9, 70 cantilever floors, 106—109 cantilever tip, drop-in girders, 68 , 69 capacity design approach, 106—107, 109, 111 cast-in-place joints, bridges, 65 catenary action, 62, 84 CEB-FIP Model Code 1990, 7 Charles de Gaulle Airport, 73—74 Chaumont Viaduct, 88 classes of collapse, 11, 25 classes of structures, 137—138 design procedures, 35 design requirements, 42 robustness measures, 124, 129 —132 verification procedures, 50 clients, design objectives, 43—44 code-based design see design procedures collapse boundaries, 64 collapse-promoting features, 11, 25—30 collapse resistance, 2 bridge design, 86—99 continuity and, 4 definition, 38, 39—40, 123 design criteria, 40, 41 high-rise buildings, 86—87, 99—122, 136 interaction, 79 measures of, 123—132, 137—138

148


requirements of measures, 124—125 verification, 44, 48—51, 59 column failure, 53, 54 , 59 , 60—61 combination of actions, 43, 46, 95 compactness, 29, 102 compartmentalisation, 70 see also segmentation compressible filling, shock-absorbers, 119, 119 compression loading, 22 computational cost, robustness measures, 129—131 computational tractability, 35 conceptual relationships, 137, 138 Confederation Bridge, 63 collapse-resistant design, 88 design methods, 62—66, 64—67, 69— 71, 77—79 design objectives, 44—45 consequences classes, 42 construction-stage design methods, 57—58 continuity, 27— 28 failure incidents and, 4 redundancy vs, 62 segmentation and, 66—67, 70—76, 88 continuous girder bridges, 3, 21, 88—89 corrosion protection, bridges, 97 costs computational, 129—131 safety-cost ratio, 81, 85 cross-section collapse, 18—20 cutting action, 78 DAF (dynamic amplification factor), 90—95, 92 damage see total damage damage-based robustness measures, 125, 127—130, 131—132 damping effect, bridge design, 93 decoupling mechanisms, 110 deflection of floors, 106—107, 109 design criteria, 40—51, 41 see also design methods; design objectives; design requirements; verification design methods, 47—48, 52—85 applications, 86—122, 123—124 collapse-promoting features, 27—28 local failure, 2 research publications, 5—7 standards/guidelines, 8—10 synopsis, 134—136 see also design criteria; design procedures design objectives, 42—46 Alfred P. Murrah Building, 53—54 direct design methods, 52 key elements, 52—53

Index robustness measures, 127— 128, 130 see also design methods design procedures accidental circumstances, 33—34, 36 current, 32—40 improvement potential, 34— 37 inadequacy of, 32—34 see also design methods design requirements, 40 —42, 123 destabilisation see instability-type collapse deterministic analysis, 35, 37, 125 detonation effects, 53, 54 see also explosion-triggered collapse DIN 1055-100 standard, 8 direct design methods, 47, 52 alternative load paths, 85 applications, 86—122 local failure, 80, 83 see also assume local failure strategy; prevent local failure strategy discontinuity, 27—28, 73—74 see also continuity discrete conditions, 44— 45 disproportionate collapse definition, 1, 39 instability-type, 21, 23 domino-type collapse, 16 —18, 19 classification, 25 energy-based robustness, 130—131 mixed-type, 23—24 promoting features, 26— 30 drop-in girders, 66, 67—68, 69, 79 ductility high-rise building design, 107, 116 material behaviour, 26 —27 prescriptive design rules, 84 dynamic action, 25—26 instability-type collapse, 22 segmentation method, 68, 69 verification procedures, 49— 51 dynamic amplification factor (DAF), 90—95, 92 earth-anchored suspension bridges, 97—98 earthquake effects, 2, 12 , 121 elastic energy, 13, 22, 107 electric power networks, 27 Ellingwood, B. R., 5 energy-based robustness measures, 125, 130—131 energy dissipation, high-rise design, 116—120 Eurocodes EN 1990, 8 EN 1991-1-7, 9, 39, 42, 44—48 evacuation procedures, 121— 122 events see triggering events

event control, 55 exemption process, GSA guidelines, 42 explosion-triggered collapse, 6, 102—103 see also detonation exposure to accidental circumstances, 41—42 expressiveness requirement, 124, 126—127, 129 façade structure, high-rise buildings, 109—112 failure incidents, 2— 5 see also local failure failure probabilities see probabilistic theory fast fracture, 18—20, 25 Federal Emergency Management Agency (FEMA) report, 4, 99—100, 104 fib guidelines, 90 fire fighting/protection, 121—122 floor design, high-rise buildings, 105—111, 111, 120 force concentration, 25 —26 fracture energy, high-rise collapse, 119—120 fracture mechanics, 19— 20 General Services Administration (GSA), 42, 46—47, 50 generality requirement, 125, 129, 132 girders Alfred P. Murrah Building, 53, 54 , 60—62 strengthening, 58, 61 global failure 1, 21 arch bridges, 99 local failure vs, 32 gravitational energy, 13, 22, 107 Gross, J. L., 5— 6 GSA (General Services Administration), 42, 46—47, 50 guidelines, 7— 10 bridge design, 87, 90 design methods, 47 design objectives, 46 design requirements, 42 prescriptive design rules, 83—84 see also standards Haeng-Ju Grand Bridge, 3, 23—24, 66, 78, 88 hangers, suspension bridges, 97 hierarchical structures, 112 high-rise buildings acceptable total damage, 100—101 collapse-promoting features, 28—29 collapse-resistant design, 86—87, 99—122, 136

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Progressive collapse of structures high-rise buildings ( continued ) load transfer systems, 82—83, 101—112, 103—106, 108 , 110, 111 see also individual named buildings hinge insertion, 58 interaction, 78—79 segmentation method, 66, 67 , 70 suspension bridges, 97— 98 horizontal load transfer, high-rise buildings, 102, 103, 110 horizontal segmentation, 108—110, 108, 114—115 human error, 41, 57 identified accidental actions, 47 impact class collapses, 25 see also domino-type collapse; pancaketype collapse impact forces domino-type collapse, 16 pancake-type collapse, 13 vertical segmentation, 116—118 importance factor, 42 see also significance of structure impulsive loading, 68, 69 indirect design methods, 47—48, 52, 83 see also prescriptive design rules initial failure see local failure insensitivity, 123 CEB-FIP Model Code, 7 definition, 38—39 see also collapse resistance; robustness instability-type collapse, 20—23 cable-stayed bridges, 94, 95 classification, 25 mixed-type, 24 promoting features, 26, 29 suspension bridges, 97 interaction, 77—80 International Federation for Structural Concrete (fib), 90 isolating elements, 64, 70 bridge design, 64, 66, 70 high-rise buildings, 108—109 local failure, 80—81 see also segmentation joints bridge design, 65 high-rise buildings, 108 , 114—115 journal articles, 6—7 Kersken-Bradley, M., 6 key elements, 52—53, 80, 101 Kobe earthquake, 121 Lap splice, 20

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large bridges see bridges lateral action, local failure, 99 Leyendecker, E. V., 5 Life Safety Code, 122 lifts, 122 limiting local failure, 47— 48 load cases see local failure load combination, 32, 43, 46, 95 load transfer arch bridges, 99 collapse-promoting features, 28 design methods, 81—83 high-rise buildings, 101—112, 103—106, 108, 111 pancake-type collapse, 12—13 suspension bridges, 98 zipper-type collapse, 16 see also alternative load paths local failure, 1—2 assumable initial, 42, 54, 64 , 111 column failure, 59 definition, 38—39 design procedures, 32—36 direct design methods, 52 high-rise buildings, 100—101, 106—107, 106, 111 , 113—114 insensitivity to see robustness lateral action, 99 limiting, 47—48 multiple cables, 95—96 preventing, 47, 55—58, 80—83, 88—89, 96—97 segmentation method, 76 verification procedures, 49 see also assume local failure strategy loss-of-cable events, 89— 90 modelling, 91 numerical studies, 91—95 McGuire, W., 5—6 main column design, 53, 54, 55, 59—61 malicious action, 41, 57 cable-stayed bridges, 89, 90 exposure to, 41—42 high-rise buildings, 101 prevent local failure, 57 suspension bridges, 98 material behaviour brittle, 26 ductile, 26—27 mediating elements, 17, 26— 27 membrane structure, 16 Mississippi River Bridge, 4 mixed-type collapse, 23 —24 bridges, 94, 97 classification, 25 promoting features, 27

Index modelling local failure, 49 loss-of-cable events, 91 modification of structural system, 58, 60 , 61, 67 moment-resisting frames, 62, 70, 110 Multihazard Mitigation Council report, 6 multiple-cable failure, 95—96 National Institute of Standards and Technology (NIST), 9 nonlinear analysis, 69, 91, 95 non-structural protective measures, 47, 55—56, 56 , 80, 135 bridge design, 96—97 high-rise buildings, 112—113, 121—122 numerical studies, 91—95 see also quantification objectivity requirement, 124, 127 orientation (spatial), 28— 29 overhead transmission towers, 17—18, 19 overstrength, 26—27 overturning susceptibility, 17—18 see also domino-type collapse pancake-type collapse, 12 —14, 12 classification, 25 design applications, 101, 105, 115— 116, 121 energy-based robustness measures, 130—131 mixed-type, 23—24 promoting features, 25, 28—29 parallel load transfer, 16, 28, 34, 81 partial safety factors assume local failure, 54 design objectives, 45 design procedures, 35 prevent local failure, 57 robustness measures, 35, 124 Pentagon Building, 73— 74, 74 , 115 performance-based approaches see design methods; design objectives plastic energy, 107 Post-Tensioning Institute (PTI), 46, 51, 87, 89—90, 93 ¨tzl, M., 6 Po power networks, 27 pragmatic approach, 38, 123, 134—135 Prendergast, J., 4 prescriptive design rules, 47—48, 52, 83—85 continuity, 72 direct design vs, 86—87, 100 synopsis, 134—135 pressure waves, 120 PreStandard Prospectus, 10, 38

prevent local failure strategy, 47, 55—58, 80—83, 88—89, 96—97 primary load transfer system arch bridges, 99 design methods, 82—83 high-rise buildings, 101—104, 103—104, 111—112 pancake-type collapse, 13 suspension bridges, 98 zipper-type collapse, 16 probabilistic theory, 32—37, 81—82, 125, 133—134 progressive collapse classes, 11, 25 conceptual relationships, 137, 138 definition, 1 designing against, 37 —51 present approaches, 125—126 types, 11—31 propagating action, 11 conceptual relationships, 137, 138 domino-type collapse, 17—18 instability-type collapse, 22—23 mixed-type collapse, 24 pancake-type collapse, 13 zipper-type collapse, 15 protective non-structural measures, 55—56, 56, 80, 135 bridge design, 96—97 high-rise buildings, 112—113, 121—122 PTI see Post-Tensioning Institute public access, high-rise buildings, 102, 112—113 pylons, cable-stayed bridges, 93, 94 quantification design objectives, 43 robustness definition, 38—39, 123—124, 137 see also numerical studies quasi-static analysis, 50—51, 90—95 redistribution class collapses, 25 see also section-type collapse; zipper-type collapse redundancy, 60—62, 70—77, 122 relevant elements, 64, 80—81 reliability theory, 32—33, 35—37, 45, 133—134 research publications, 5—7 resistance see specific local resistance risk assessments, 44 robustness, 2 acceptable total damage, 127 continuity and, 4 definition, 38—40, 123—124, 137 design objectives, 127—128, 130

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Progressive collapse of structures robustness (continued ) fire-fighting systems, 121—122 measures of, 123—132, 137—138 requirements of measures, 124—127, 129—130, 132 research publications, 6—7 standards/guidelines, 8 Tasman Bridge, 3 verification, 48—49, 59 Ronan Point incident, 2, 8, 108 collapse typology, 14 design methods, 71—72, 72 safety construction stages, 58 cost:safety ratio, 81, 85 index, 45 partial safety factors, 35, 45, 54, 57, 124 structural safety, 32 —33 Sampoong Superstore, 3 Scheer, J., 3 secondary column design, 53, 54 , 60—61 secondary load transfer system, 83, 104—110, 105—106, 108 , 111 secondary structure requirements, 42 section-type collapse, 18 —20, 25 segment borders, 27, 64, 70, 117—120, 118—119 segmentation, 47—48, 62—71, 80—83, 135—136 bridge design, 88, 96, 97—98 high-rise buildings, 107—110, 108 , 114—121 interaction, 79 prescriptive design rules, 85 redundancy vs, 71—77 self-anchored suspension bridges, 97 self-supporting façades, 110 series load transfer, 13, 28, 33, 81 ship impact, bridges, 89 shock-absorbing devices, 117—120, 118—119 significance of structure, 40—42 see also importance factor simplicity requirement, 124, 129—130 simplified verification procedures, 50 size of structure, 28—29 slender structures, 28 —29 see also high-rise buildings societal consensus, 34 soil investigation, 57 spatial orientation features, 28—29 specific local resistance, 45, 47, 55, 80—83, 135 Alfred P. Murrah Building, 54, 55 bridge design, 96, 98

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high-rise buildings, 100—112, 122 research publications, 5 stability failure, 22 see also instability-type collapse staircases, redundancy, 122 standards, 7—10, 134 bridge design, 87 design methods, 47 design objectives, 46 prescriptive design rules, 83— 84 see also guidelines static analysis, 50—51, 90—95 stiffness-based robustness measures, 125—127 strain energy instability-type collapse, 22 pancake-type collapse, 13 strengthening transfer girders, 58, 61 vertical segmentation method, 116 see also overstrength Structural Engineering Institute PreStandard Prospectus, 10, 38 structural fuses, 27, 66, 110 structural integrity standards, 8 see also robustness structural safety, 32 —33 structure classes, 35, 42, 50, 124, 129—132, 137—138 structuredness, 29— 30, 104 suspension bridges, 97 —98 see also bridges Swiss guidelines, 87 Tacoma Narrows Bridge, 14, 14 , 97 Taney Bridge, 95—96 Tasman Bridge, 3—4, 66, 71, 74, 88 telescoping segments, 118—119, 119 tension ties, 83—84 titling of structures, 116—117 total damage definition, 39, 43 high-rise building design, 100 —101 robustness measures, 127—129, 128 tractability, computational, 35, 66, 77—79 transfer girders Alfred P. Murrah Building, 53, 54 , 60—62 strengthening, 58, 61 transmission towers, 17— 18, 19 triggering events, 1 see also accidental circumstances tubular structures, 102—104, 112 typology of collapses, 11—31 United Facilities Criteria, 46— 47, 50 US standards/guidelines, 8—10

Blast Effects on Buildings, 2nd Edition-D. Cormie

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