Stability of Buildings Parts 1 and 2_May 2014 by IStructE

Stability of buildings Parts 1 and 2: General philosophy and framed bracing

May 2014

 Author  A Gardner  MEng(Hons) MA(Cantab) CEng MIStructE  (The Institution of Structural Engineers) Consultees P Perry  BSc(Hons) CEng MIStructE MICE MHKIE  (CH2M Hill) Chairman Hill)  Chairman of the Reviewing Panel  E Bennett  MEng  (Arup) O Brooker  BEng CEng MIStructE MICE MCS (Modulus) N D Eckford  CEng FIStructE MICE Dr G J Evans  BSc PhD CEng FIStructE FICE MBCS  (Seawork Marine Services Ltd) Dr A S Fraser  BEng(Hons) PhD CEng MIStructE MICE  (Arup) J Guneratne  BSc(Hons) CEng MIStructE  (CH2M Hill) R Marshall  BEng(Hons) MIPENZ  (Buro Happold) K Moazami  PE FIStructE FASCE  (WSP) Dr M O’Connor  PhD MBA  (WSP) C J O’Regan  BEng(Hons) CEng MIStructE  (The Institution of Structural Engineers) Dr Y Pan  MSc PhD CEng MIStructE  (Sir Robert McAlpine Design Group)  Acknowledgements  Acknowledgements  The use of Arup internal guidance documents in developing this this Guide  Guide is  is gratefully acknowledged.

Photographs and digital imagery have been supplied by courtesy of and are published with the permission of the following organisations and individuals: Figure 4.4 (illustrations): Arup Figure 4.9: J.K. Nakata, United States Geological Survey Figure 8.2 (HSBC building): Arup Figure 11.1 (8 Chifley Square): Arup Figure 11.1 (Bank of China): WiNG Figure 11.1 (Neo Bankside): Native Land/Rogers Stirk Harbor Figure 11.2 (1 Shelley Street): Arup Figure 11.2 (Hearst Tower): The Hearst Corporation Figure 11.2 (Aldar HQ): Stuart Clarke, Arup Figure 11.3: Arup Box 4.2: F Freudenberger Box 4.5: The Technical Office Julio Kassoy and Mario Franco Box 4.6: Arup Box 5.1: Dutch Natio National nal Police, Air Support Unit Box 8.1: P Buffett Box 9.1: Thornton Tomasetti Box 10.1: British Standards Institution (BSI) Box 11.1: Arup

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 All other photographs and all hand illustrations: A Gardner Permission to reproduce extracts from British Standards is granted by the British Standards Institution (BSI). No other use of this material is permitted. British Standards can be obtained in PDF or hard copy formats from the BSI online shop: www.bsigroup.com/Shop or by contacting BSI Customer Services for hard copies only: Tel: þ44 (0)20 8996 9001, Email: [email protected]. Published by The Institution of Structural Engineers, International HQ, 47–58 Bastwick Street, London EC1V 3PS, United Kingdom  Telephone:  T elephone: þ44(0)20 7235 4535 Fax: þ44(0)20 7235 4294 Email: [email protected] Website: www.istructe.org First published 2014 ISBN 978-1-906335-26-7 #

2014 The Institution of Structural Engineers

 The Institution of Structural Engineers and those individuals who contributed to this  Guide  Guide have  have endeavored to ensure the accuracy of its contents. However, the guidance and recommendations given in the Guide the  Guide should  should always be reviewed by those using the  Guide  Guide in  in the light of the facts of  their particular case and specialist advice obtained as necessary. No liability for negligence or otherwise in relation to this  Guide  Guide and  and its contents is accepted by the Institution, the author, the consultees, their servants or agents. Any agents.  Any person using this  Guide  should pay particular  attention to the provisions of this Condition. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means without prior permission of The Institution of Structural Engineers, who may be contacted at International HQ, 47–58 Bastwick Street, London EC1V 3PS, United Kingdom.

 Author  A Gardner  MEng(Hons) MA(Cantab) CEng MIStructE  (The Institution of Structural Engineers) Consultees P Perry  BSc(Hons) CEng MIStructE MICE MHKIE  (CH2M Hill) Chairman Hill)  Chairman of the Reviewing Panel  E Bennett  MEng  (Arup) O Brooker  BEng CEng MIStructE MICE MCS (Modulus) N D Eckford  CEng FIStructE MICE Dr G J Evans  BSc PhD CEng FIStructE FICE MBCS  (Seawork Marine Services Ltd) Dr A S Fraser  BEng(Hons) PhD CEng MIStructE MICE  (Arup) J Guneratne  BSc(Hons) CEng MIStructE  (CH2M Hill) R Marshall  BEng(Hons) MIPENZ  (Buro Happold) K Moazami  PE FIStructE FASCE  (WSP) Dr M O’Connor  PhD MBA  (WSP) C J O’Regan  BEng(Hons) CEng MIStructE  (The Institution of Structural Engineers) Dr Y Pan  MSc PhD CEng MIStructE  (Sir Robert McAlpine Design Group)  Acknowledgements  Acknowledgements  The use of Arup internal guidance documents in developing this this Guide  Guide is  is gratefully acknowledged.

Photographs and digital imagery have been supplied by courtesy of and are published with the permission of the following organisations and individuals: Figure 4.4 (illustrations): Arup Figure 4.9: J.K. Nakata, United States Geological Survey Figure 8.2 (HSBC building): Arup Figure 11.1 (8 Chifley Square): Arup Figure 11.1 (Bank of China): WiNG Figure 11.1 (Neo Bankside): Native Land/Rogers Stirk Harbor Figure 11.2 (1 Shelley Street): Arup Figure 11.2 (Hearst Tower): The Hearst Corporation Figure 11.2 (Aldar HQ): Stuart Clarke, Arup Figure 11.3: Arup Box 4.2: F Freudenberger Box 4.5: The Technical Office Julio Kassoy and Mario Franco Box 4.6: Arup Box 5.1: Dutch Natio National nal Police, Air Support Unit Box 8.1: P Buffett Box 9.1: Thornton Tomasetti Box 10.1: British Standards Institution (BSI) Box 11.1: Arup

þ Partners

 All other photographs and all hand illustrations: A Gardner Permission to reproduce extracts from British Standards is granted by the British Standards Institution (BSI). No other use of this material is permitted. British Standards can be obtained in PDF or hard copy formats from the BSI online shop: www.bsigroup.com/Shop or by contacting BSI Customer Services for hard copies only: Tel: þ44 (0)20 8996 9001, Email: [email protected]. Published by The Institution of Structural Engineers, International HQ, 47–58 Bastwick Street, London EC1V 3PS, United Kingdom  Telephone:  T elephone: þ44(0)20 7235 4535 Fax: þ44(0)20 7235 4294 Email: [email protected] Website: www.istructe.org First published 2014 ISBN 978-1-906335-26-7 #

2014 The Institution of Structural Engineers

 The Institution of Structural Engineers and those individuals who contributed to this  Guide  Guide have  have endeavored to ensure the accuracy of its contents. However, the guidance and recommendations given in the Guide the  Guide should  should always be reviewed by those using the  Guide  Guide in  in the light of the facts of  their particular case and specialist advice obtained as necessary. No liability for negligence or otherwise in relation to this  Guide  Guide and  and its contents is accepted by the Institution, the author, the consultees, their servants or agents. Any agents.  Any person using this  Guide  should pay particular  attention to the provisions of this Condition. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means without prior permission of The Institution of Structural Engineers, who may be contacted at International HQ, 47–58 Bastwick Street, London EC1V 3PS, United Kingdom.

Foreword

Stability is an important and critical aspect fundamental to the design of a building structure. From the inception of an initial concept, through preliminary, scheme and detailed design, it dominates the development of the structural frame; all to inform the construction and form of a safe and serviceable building. Thereafter it remains vital through the operation, maintenance, renovation and eventual demolition demol ition and is often critical critical to the design of  retrospective work.  The Institution of Structural Engineers is keen to ensure that young budding engineers incorporate within their design skills the ability to develop safe economic and coherent stability provision within their building structures.  This   Guide  has been developed to assist structural engineers in the development of this important aspect within the schemes they develop, illustrating the choices available, the process of design development and the detailing of clear and concise aspects of their design. It is relevant to structural engineers at all levels of the industry, to act as both a design guide and the latest technical recommendation to ensure that all parties, whether building owner or design engineer working for either the consultant or contractor, have a reliable source to make reference during their projects.  The  Guide  covers two parts. Part 1 commences with the general philosophy to confirm the definition, the forms and responsibility with regards stability. A  chapter on actions and combinations provides advice on the devel developmen opmentt of the loads loads,, their magnitude magnitude and consideration. A section on the various stability systems defines the suite of considerations when choosing the optimum solution followed by a discussion to highlight aspects during construction and alteration. In Part 2, framed bracing is written up from the initial vertical bracing through analysis, design and specification and concluding with the more unusual forms associated with diagrids and other triangulated forms. Two further parts will follow as standalone texts: Part 3 on shear walls and Part 4 on moment frames.  The  Guide  is illustrated throughout by clear structural philosophy cartoons, case histories, analytical extracts and valuable references for those who wish to be well read on the subject. A  designers’ checklist ensures that more experienced structural engineers can use the  Guide  for quick  reference and as a project tool; others may use it to navigate Part 1. Whether the reader is attempting the Institution’s membership examinations and needs a revision prompt on the subject, or is completing a Stage C report for a scheme and requires a memory-jog for clear concise stability sketch, this   Guide  does the job We would be keen that engineers who read this Guide advise any comment, omissions and additional references for consideration if future revisions of this Guide are progressed. These can be sent to the Institution’s Institution’ s address.

Finally, I would like to offer thanks to the consultees who have assisted in the development of this guidance note, and Dr Gareth Evans, Chairman  Technical  T echnical Publications Panel for managing the draft through its peer review.

Paul Perry Chairman of the Reviewing Panel

Contents

Glossary

iv

Notation

v

7

Desi De sign gner ers’ s’ ch chec eckl klis istt

Part 2: Framed bracing Foreword 1

Int ntrrodu duct ctio ion n

1

3

Stability 3 Defin De finiti ition on of sta stabil bility ity 3 Forms For ms of ins instab tabili ility ty 3 Responsib Resp onsibility ility of desig designn engi engineers neers 3 Refe Re fere renc nces es 5

3 3.1 3.2

Action Acti onss an and d co comb mbin inat atio ions ns 6 Introd Int roduct uction ion 6 Gravity Grav ity actin actingg on on the the super superstruc structure ture 6 3.2. 3. 2.1 1 Ma Mass ss 6 3.2.2 3.2. 2 Thrus Thrusts ts resulti resulting ng from from structura structurall form 7 3.2.3 3.2. 3 Sway imperfe imperfectio ctions ns and equivale equivalent nt horizonta horizontall forces 7 3.3 3. 3 Wi Wind nd ac acti tion onss 8 3.4 Actio Actions ns resultin resultingg from the ground ground and and ground ground water  water  9 3.5 Inel Inelastic astic mate material rial strains ns 10 3.6 Post tensioning oning and applie appliedd elastic elastic stra strains ins 10 3.7 Extre Extreme me actio actions ns and robus robustness tness 10 3.8 PD  sway effects 11 3.9 Part Partial ial factors factors and and combinati combination on cases cases for limit imit state state design 12 3.10 Refe Reference rencess 13 4 4.1 4.2 4.3

4.6 4.7 4.8 4.9 4. 9

Stabil Stab ilit ityy sy syst stem emss 14 Loadd paths Loa paths for for late lateral ral act action ionss 14 Horizonta Hori zontall stabi stability lity syste systems ms 15 Vertical Vert ical stability lity syst systems ems 16 4.3.1 4.3 .1 Int Introd roduct uction ion 16 4.3.2 Plan Planning ning vertic vertical al stabilit stabilityy structure: structure: plan plan layout layout 16 4.3.3 Plan Planning ning vertica verticall stability ity structur structure: e: layout layout through through the height of the building 18 4.3.4 4.3 .4 Sub Substr struct ucture ure 18 Accommodat Accom modating ing move movement ment 20 Bracedd and unbra Brace unbraced ced vertica verticall stabilit stabilityy systems systems 21 4.5.1 4.5 .1 Int Introd roduct uction ion 21 4.5.2 4.5. 2 Brace Bracedd struc structures tures 21 4.5.3 4.5. 3 Unbra Unbraced ced struc structures tures 22 4.5.4 4.5. 4 Hybri Hybridd struc structural tural syste systems ms 22 4.5.5 4.5. 5 Slend Slenderne erness ss of eleme elements nts in compr compressi ession on 23 Earthq Ear thquak uakee des design ign 23 Serviceabi Servi ceability lity perfo performanc rmancee crite criteria ria 24 Non-struc Nonstructural tural requi requiremen rements ts 24 Refe Re fere renc nces es 25

5 5.1 5.2 5.3 5.4 5. 4

Stability Stabil ity dur during ing con constr struct uctio ion n 26 Introd Int roduct uction ion 26 Responsib Resp onsibility ility of of the contrac contractor’ tor’ss structura structurall engineer  engineer  26 Exchan Exc hange ge of inf inform ormati ation o n 27 Refe Re fere renc nces es 27

6

Stabilit Stab ilityy foll followin owing g dete deterior rioratio ation, n, alte alterati rations ons or change of use 28 Planne Pla nnedd alt altera eratio tions ns 28 Deter De terior iorati ation on 28 Refe Re fere renc nces es 29

4.4 4.5

6.1 6.2 6.3 6. 3

33

vi

Part 1: General philosophy 2 2.1 2.2 2.3 2.4 2. 4

30

8 8.1 8.2 8.3 8. 3 8.4 8.5 8. 5

Vertic Vert ical al fr fram amed ed br brac acin ing g Introd Int roduct uction ion 33 Struct Str uctura urall for form m 33 Stif St iffn fnes esss 34 Force For ce tra transf nsfer  er  34 Brac Br acin ingg an angl glee 35

33

9 9.1 9.2 9.3 9.4 9. 4

Analys Anal ysis is of fr fram amed ed br brac acin ing g 37 Static Sta tic ana analys lysis is 37 Approximat Appro ximatee analy analysis sis metho methods ds 37 Computer Comp uter analy analysis sis mode models ls 39 Refe Re fere renc nces es 40

10 Design and Design and spec specifica ification tion of frame framed d braci bracing ng 41 10.1 Intro Introducti duction on 41 10.2 Elem Elements ents 41 10.2.1 10.2 .1 Ties 41 10.2.2 10.2 .2 Strut Strutss 41 10.2.3 10.2 .3 Beams and and columns columns 43 10.3 10. 3 No Nodes des 43 10.3.1 10.3 .1 Conne Connection ction types types 43 10.3.2 Concentric connections 43 10.3.3 Eccentric connections 43 10.3.4 10.3 .4 Centr Central al node in cross braced systems systems 44 10.3.5 Slotted connections connections and translational translational bearings 44 10.3.6 Pinned connections connections and articulation 45 10.3.7 10.3 .7 Colum Columnn baseplates, baseplates, holding down bolts and foundations 46 10.4 Refe Reference rencess 46 11 11.1 11.2 11.3

Diagrids and othe Diagrids otherr triang triangulat ulated ed struct structural ural forms Structural Struc tural forms 47 Character Char acteristic isticss 48 Reference Refe rencess 49

47

1

Intr In tro odu duct ctio ion n

 A structure must not only transfer gravity forces to the ground; it must also stand up against many lateral forces. The combination of elements that keeps the building standing against these lateral forces is referred to as the ‘stability system’ or sometimes the ‘lateral load resisting system’.  These terms each tell half the story story,, one alluding to the load path for lateral forces while the other has a clear association with the destabilising effects of  various actions. This   Guide  focuses primarily on lateral load resisting systems. However the term ‘stability ‘stab ility’’ will be used in place of lateral load resistance throughout this  Guide.  The   Guide  is split into two parts. Part 1 gives an overview of stability systems introducing parameters set by actions, material characteristics, building form, function and construction. Key points are summarised in a designers’ checklist contained in Chapter 7. Part 2 goes on to outline characteristics of  triangulated vertical stability systems, with sections on each of analysis and design.  Two further parts are planned; Part 3 on shear walls  Two and part 4 on moment frames. These will be published as standalone texts, but each of Parts 2, 3 and 4 assume a good grasp of Part 1 contained herein.  The   Guide  acknowledges earthquake actions and design within Part 1, but primarily recommends sources of further reading on this topic. These are listed in Section 4.6. Guidance on fatigue and temporary works are omitted, being specialist topics not core to the work of most design engineers, while extraordinary requirements of high-rise, off-shore and other non-standard structures are not specifically addressed. Motivation

Instability can have significant consequences. Collapse of a structure and resulting loss of life are the most severe consequences but each of design delays, cost over-runs, litigation and criminal penalties may also occur where a design is shown to be inadequate. Unlike many industries, construction is not universally regulated. Alerts on the structural-safety.org website reveal a number of near misses and failures associated with stability shortcomings. This echoes failures of candidates sitting the Institution’s chartered member exam in which unstable solutions are frequently presented. Stability is a core concept, yet it is rarely taught as a subject in itself and evidence suggests it does not come as intuitively to designers as gravity-resistance. It is hoped that by reiterating relatively simple lessons, this  Guide  will increase familiarity with key criteria. Relevance

 This  Guide  is an introduction written primarily for graduate design engineers, particularly those approaching a professional review. It is not the

intention that it provides detailed ‘how to’ instruction, and reading it will not in itself equate to ability (see Box 1.1). Rather this   Guide  aims to supplement supervised learning by increasing awareness and promoting thoughtfulness in design.  The content can be considered to be applicable to all buildings, whether permanent or temporary, and should be considered to have international relevance.

Box 1.1

Competence

From planning load paths to understanding the difference between braced and unbraced systems, a thorough awareness of all the topics introduced in Part 1 is fundamental for all practicing engineers; while a familiarity with, and ability to implement, the topics is necessary for all engineers working autonomously. Junior engineers must not see this   Guide  as   as a substitute for  working under the supervision of a more experienced engineer.

Part 1: General philosophy 2

Stability

2.1

Definition of stability

 The word stability is synonymous with steadiness, poise and balance. It is a time-based characteristic meaning resistance to change; a concept illustrated in Figure 2.1. In the context of structural engineering a stable system is one that, when displaced by a small amount, will return to its equilibrium position. Conversely, an unstable system is one which, when displaced by a small amount, will continue to move away from the equilibrium position to the point where it fails.  The European Council Construction Products Directive 89/106/EEC 2.1 defines a building to be stable when, ‘‘The loadings that are liable to act on it during its construction and use will not lead to: (a) Collapse of the whole or part of the work. (b) Major deformations to an inadmissible degree. (c) Damage to other parts of the works or to fittings or installed equipment as a result of major deformation of the loadbearing construction. (d) Damage by an event to an extent disproportionate to the original cause.’’ It should be clear from these statements that stability concerns both safety and function. This  Guide focuses on statements (a), (b) and (c); meanwhile statement (d) is the focus of the Institution’s publication Practical guide to structural robustness  and disproportionate collapse in buildings 2.2.

2.2

Forms of instability

 Actions and reactions must be in equilibrium in each of the six degrees for stability to be maintained; otherwise the system is a mechanism subject to the laws of motion. Instability can occur in an element (‘local’), or a sub-frame or whole structure (‘global’). Where allowed to manifest, it would be perceived as either rigid body movement or deformation of the part or whole. Overturning is a bold example of global instability (see Box 2.1), though each of sliding, racking, and twisting are further lateral instability modes illustrated in Figure 2.3. It should be noted that buoyancy, uplift, slope failure and foundation settlement are each causes of global instability that can be attributed to vertical actions. While consideration of these is of equal importance to the lateral modes, vertical instability is not the focus of this Guide. Local instability includes Euler and lateral torsional buckling. These modes can occur in elements of a lateral load resisting system but are also more widely applicable to any element subject to the necessary actions and restraint conditions.

2.3

Responsibility of design engineers

It should always be the case that one structural engineer is responsible for the overall design of any building structure, with a duty to oversee that the designs and details of all elements and assemblies comply with the stability requirements. This responsibility applies equally where some or all of the structural design and details are developed by others, to new buildings as well as alterations, and to both permanent and temporary structures.

 There are six degrees of freedom for any single point within a static system: three orthogonal component axes for linear displacements and three orthogonal component axes for rotations (see Figure 2.2).

z

y

Stable Figure 2.1

x

Unstable

Inherently stable and unstable massing

Figure 2.2

Degrees of freedom

2.3

Stability Box 2.1

Stability of a rigid body

 A rigid body is stable against overturning provided the resultant of all actions acts within the rigid footprint. Rigid body           













Resultant

The simple frame elements shown act only in vertical shear on the rigid body of the stability system and thus are not counted as part of the footprint being considered.

Where a development could impact neighbouring buildings, engineers have a due diligence to ensure the stability of these properties is not compromised. By example, very tall buildings can detrimentally increase wind loads across a city block, while excavations and tunnelling can cause movement of  the foundations several metres away. In developing a design, the design engineer must consider construction and the means of temporary stability. Though they may not be contracted to design the temporary stability systems, a design must be buildable and maintainable without undue risk or expense (see Box 2.2). As a general rule at least one viable sequence of construction must be identified.  Towards the conclusion of the design, the design engineer must oversee the production of detailed design calculations; a set of coherent workings giving evidence of the rigour to which the stability and lateral load resisting systems have been considered, and the conclusions thereof. The calculations must include narrative adequate to allow other professionals to review and comprehend them, must be free of anomalies, and must reciprocate the construction information portrayed on the drawings and in the specifications.

Figure 2.3

Global instability failure mechanisms: overturning, sliding, racking and twisting

Once the design has been completed, it is recommended that another structural engineer independently appraises the whole design to see that requirements for stability have been incorporated without compromise and can be met throughout construction. Independent appraisals should supplement, and not replace, self-checks of the designer. They are always considered good practice,

Stability Box 2.2

Safety in design

Safety in design is a legislated requirement in many countries. In the UK, construction obligations are defined quite specifically under the CDM Regulations2.3. Other  countries cover the matter with equivalent legislation, or more generally under workplace safety legislation. Irrespective of the nomenclature, the engineer is responsible for  understanding and adhering to the legislation in force at the site of the development.

to foster safe and serviceable structures, but may also be a legal requirement of a project contract or the local legislation in force at the site of the development.  Assumptions of tolerance, material quality, temporary works, construction sequence and workmanship made during the design should be in line with the practical capability of the local construction industry and must be communicated clearly in the design documentation. Information concerning any unusual design feature or a particular vulnerability of the structure must be made available to the contractor, who would normally manage the stability of the building structure during construction (see Chapter 5).

2.4

References

2.1

Council directive of 21 December 1988 on the  approximation of laws, regulations and administrative  provisions of the Member States relating to  construction products (89/106/EEC) . Available at: http://eur-lex.europa.eu/LexUriServ/  LexUriServ.do?uri=CONSLEG: 1989L0106: 20031120: EN:PDF [Accessed: 16 December 2013]

2.2

Institution of Structural Engineers. Practical guide to  structural robustness and disproportionate collapse in  buildings . London: IStructE, 2010

2.3

 

HSC. Managing health and safety in construction:  Construction (Design and Management) Regulations  2007: approved code of practice. L144 . [Norwich?]: HSE Books, 2007

2.4

3

Actions and combinations

3.1

Introduction

 Actions should be considered in accordance with the national, local and occupier requirements, together with environmental conditions. They can be applied, attributed to accelerations and decelerations or induced internally. Designing for lateral stability primarily concerns lateral forces. However, vertical forces must not be ignored as their magnitude will regularly have impact. These may act to either the benefit or detriment of the system, and it may be appropriate to consider the envelope of maximum and minimum values for a given characteristic action.  The following sections discuss common actions, some of which are depicted in Figure 3.1. However this discussion is by no means exhaustive. Using guidance provided in building standards, designers should consider all actions that are appropriate to a building’s function and context.

3.2

Gravity acting on the superstructure

3.2.1

Mass

Gravity always acts in the vertical axis making it wholly independent of the building form. The magnitude of the force is a function of mass and will include components attributed to each of: – Permanent mass (e.g. the structure self weight). – Superimposed mass (e.g. the self weight of finishes and semi-permanent installations). – Imposed mass (e.g. furniture, occupants, snow, sand and other transient installations). Each of these can be considered variable to some extent and may need to be evaluated across an envelope. By example, a metal roof may be taken as 0.5kN/m2 for the rafter design but may be as low as 0.1kN/m2 when the roof sheeting is first installed and exposed to wind actions.  Variability like this may not only change the magnitude of the force but can also impact on the

Dynamic action

Thermal radiation

RC shrinkage

Wind Gravity

Seismic

Differential axial shortening

Terrorism &  accidental impact

Dynamic wind

Differential settlement Thrust

Figure 3.1

Possible actions on the CCTV building, Beijing

Neutral axis imbalance

 Actions and combinations

Flexible supports to barrel roof Figure 3.2

The influence of support conditions on non-planar structural systems

position of the force resultant. This is important in all buildings but is particularly critical where the centre of  gravity lies close to or outside a building’s footprint. 3.2.2

Thrusts resulting from structural form

Significant lateral forces can result from gravity forces where a structure is inclined, pitched, non-planar or acting as an arch or catenary. These forces can be large; potentially larger than the vertical forces to which they are attributed.  The horizontal component of force can be highly sensitive to the geometry and relative stiffnesses of  the structural elements and connections. Hence, it is of paramount importance that the engineer adopts a considered approach when modelling and detailing the support conditions, understanding the broader implications of finite support stiffness and/or movement joints (see Figure 3.2). In the absence of  absolute certainty, it is often necessary to design for a plausible range of support and joint stiffnesses. 3.2.3

Rigid supports to barrel roof

Sway imperfections and equivalent horizontal forces

Sway imperfections are unavoidable. They occur in all structures and must be accounted for in almost all design scenarios.

Imperfections generally occur at random and cannot be modelled accurately for structures yet to be built. Instead, the effects are best accommodated by applying equivalent horizontal forces to an idealised model.  Two sway imperfections should be considered for all structures (see Figure 3.3): – A global imperfection caused by an overall list to a frame. – A local imperfection at element splices or between consecutive concrete pours. Both cause equivalent horizontal forces as a function of the vertical force and are supplementary to other coincident horizontal actions. They should be considered in any direction, to determine design values for both maximum sway and twist (see Figure 3.4), and with load factors matching those applied to the vertical actions. Global and local forces do not need to be combined but the more critical should always be designed for.  Although Figure 3.3 shows the case where the frame is made up of straight elements, a similar system that exhibits a bow will also result in equivalent forces acting on the supports points. BS EN 1993 Part 1-1 Figures 5.4 and 5.6 3.1, by example, depict this. The

N 1

φ1 N  =

φ2N 2 – φ1N 1

φ2

Local

N 2

φ3 N 3

N 3

N 3

N  =

N 4

Figure 3.3

Global and local equivalent forces for small angle sway imperfections

N 4

N 4

φ3( ΣN 4 – ΣN 3 )

Global

3.2

3.3

Actions and combinations with initial alignment imperfections. They are not to be confused with: notional horizontal forces (see Box 3.1); minimum eccentricities or connection offsets that relate to the finite geometries of practical construction details; minimum robustness tie forces; or PD  effects that relate to second order movement and force redistribution (see Section 3.8).

3.3

Sway Figure 3.4

Box 3.1

Wind is a phenomenon of great complexity composed of eddies of varying sizes and rotational characteristics carried along in a general stream of  moving air3.2. Design wind speeds are site specific, dependent on coastal proximity, altitude, terrain, nearby obstructions and the design return period. Corresponding pressures are a function of this speed together with a building’s geometry and scale, envelope permeability, site context and proximity to adjacent obstructions.

Twist

Application of equivalent horizontal forces

Notional horizontal force

The terms ‘notional horizontal load’ and ‘notional horizontal force’ refer to the no longer current British Standards BS 8110 and BS 5950 respectively. They defined horizontal forces, derived as percentages of the vertical forces, intended to set criteria for the minimum design resistance in the absence of more onerous demands. While similar to equivalent horizontal forces in concept, there was no requirement to combine notional horizontal forces with other actions. Hence they tended to dominate in massive structures of concrete or masonry construction with relatively small wind exposure.  As an aside note, notional horizontal forces were used in BS 5950 for the purpose of assessing the sway sensitivity of steel structures. This was, in many ways, an unnecessary relationship that caused confusion. While it was not wrong, there was no rationale to define a building’s sway characteristic by this action. two figures show equivalent uniform and discrete forces respectively. Finally, it is worth emphasising here that these equivalent forces are first order effects associated

Roof

P w

Wind actions

P L

 Actions aggregate both steady and gust components of the wind and a building’s response can be considered as either quasi-static or dynamic. These responses are discussed separately under the following headings. Quasi-static wind response Most low- to medium-rise buildings (those less than 15 storeys) exhibit negligible dynamic response to wind. They can be considered as quasi-static (rigid) barriers in the path of the wind.  The dominant wind force will usually be derived from the combined action of positive windward and negative leeward external pressures, together with frictional drag on side walls and roofs. For each wind direction in turn, pressures can be evaluated for the surfaces of the building and applied at each floor level (see Figures 3.5 and 3.6).  The pressure may be determined with or without an eccentricity. This eccentricity is to account for a non-uniform wind profile that would cause the resultant force to be eccentric to the centre of  area of the envelope. Rules to determine eccentricities are typically defined in wind codes, either as an offset to the resultant force, or as a non-uniform pressure profile. BS EN 1991 Part 1-4 Clause 7.1.23.3, by example, specifies a linear pressure profile.

= =

Floor

Wind

Floor

Floor

P w

P L

= =

Eccentricity of the wind action is measured relative to the centre of area of the building envelope. It is supplementary to any eccentricity that exists between this axis and the centre of stiffness of the structure (see Figure 3.6, eccentricities  e 1  and  e 2  respectively). Dynamic wind response Simple quasi-static treatment of wind actions can be unacceptably conservative for some buildings. Different phenomena give rise to dynamic behaviour including buffeting, vortex shedding, galloping and flutter (each defined in Chapter 5 of  Wind Loading of  Structures 3.4 ).

Floor Windward Figure 3.5

Wind pressure acting on a facade (in elevation)

Leeward

 Tall, slender structures are most prone to exhibit significant dynamic response to wind. Dynamic behaviour becomes critical when the frequency response of the structure interplays with the

 Actions and combinations frequency of the wind gusts, leading to enhancements in the pressure profiles. Codes of  practice define limits on when such methods should be considered; the criteria set by the Canadian National Building Code 2010, Volume 2, Division B, Part 43.5 are listed in Box 3.2. Where dynamic behaviour is significant the first translational mode shape, together with torsional mode shapes, can be used to determine a ‘dynamic magnification’ or ‘dynamic response’ factor. This factor is defined as the increase in force over that of a quasi-static structure.

Box 3.2

Centre of area of the envelope e 2

Dynamic wind response cut off criteria

Resultant force

3.5

The Canadian NBC 2010 sets the following criteria for  when to evaluate dynamic wind effects. Other national codes may vary slightly, though all should be similar. – Buildings whose height is greater than or equal 60m, or  four times the effective width (where the effective width is defined as the sum of areas divided by the sum of heights). – Buildings whose lowest natural frequency is less than or  equal to 1Hz.

3.4

The following texts are recommended sources of further  guidance on wind actions and design: Quasi-static response  – Institution of Structural Engineers.  Manual for the design of  building structures to Eurocode 1 and basis of structural  design . London: IStructE, 2010 – Cook, N. Designers’ guide to EN 1991-1-4 Eurocode 1:  actions on structures, general actions. Part 1-4: Wind  actions . London: Telford, 2007 Dynamic response and comfort criteria 

– Holmes, J.D.  Wind loading of structures . 2nd ed.  Abingdon: Taylor & Francis, 2007 – National Research Council of Canada. National building  code of Canada 2010 . 13th ed. Volume 2. Ottawa: National Research Council of Canada, 2010 – National Research Council of Canada. User’s guide – NBC  2010 structural commentaries (Part 4 of Division B) . 3rd ed. Ottawa: National Research Council of Canada, 2011

The resultant wind force (on plan)

Actions resulting from the ground and ground water

Earth retaining structures can be subject to significant lateral forces attributed to the weight and pre-compaction of soil retained, together with any surcharge actions on the adjacent ground surface. These forces can become critical to the lateral stability system where there is out of balance across the structure (e.g. across a sloping site or where a basement is immediately adjacent to a neighbouring basement). Where there is potential for buoyancy, the resistance of the substructure against sliding diminishes in proportion to the vertical reaction. In a similar vein, mass foundations intended to provide anchorage against uplift deliver less gravitational resistance when submerged under water or in soil with a high water table (see Figure 3.7).

Dry soil

Stable Figure 3.7

Effect of hydrostatic forces on mass foundations

45º

Envelope for wind direction factor (where applicable) Figure 3.6

Further reading: wind actions

e 1

Wind

Saturated soil

Potentially unstable

3.4

3.5

Actions and combinations

3.5

Inelastic material strains

Materials experience inelastic strains in response to a number of actions. These actions include: – Thermal variations (expansion and contraction). – Moisture variations (e.g. concrete drying shrinkage, clay brick expansion and timber cross-grain shrinkage and swelling). – Chemical reactions (e.g. concrete autogenous shrinkage and rusting of steelwork). – Long term forces. For each of the first three list items the direct strain attributed to the action is independent of stress. However, it is rare that these strains occur in a completely free manner. Rather, counteracting (indirect) strains will often develop where the direct strains are resisted by other parts of a structure or by the boundary conditions. These indirect strains are elastic up to the point of material yield and can lead to very significant forces when elements are of  high stiffness. Whether inelastic strains are free or resisted will depend, in part, on the construction sequence and also the change in climatic conditions from the construction to operational states. Long term forces are included in the list because they are a cause of time related deformations

including creep and foundation movement (see Figure 3.8). Both are inelastic second order effects that can increase sway and cause forces to redistribute internally.

3.6

Post tensioning and applied elastic strains

Post tensioning puts a compressive stress into a structure and causes an elastic strain. In buildings, the method is most commonly associated with concrete floor slabs where the average slab compression should be of the order of 2.0 to 2.5N/mm2. Because vertical stability systems often provide resistance to strains in floor diaphragms (see Section 4.3), they will act with the slab to resist the post tensioning. The force from the tensioning tendons will be apportioned between the slab (where it is intended) and the vertical stability structure based on the relative stiffnesses of the systems (see Figure 3.9).  All other instances of applied elastic strains will have a similar effect to post tensioning and lock stresses into elements of a structure. A common example is that of cables and rods tensioned using turnbuckles to eliminate load reversal. These may be part of a braced stability system (refer Part 2), part of a tied arch or part of a bow-string truss. Further reading: post tensioning concrete slabs

The following texts are recommended for guidance on post tensioning of concrete slabs: – The Concrete Society. Post-tensioned concrete floors:  design handbook . Technical Report 43. 2nd ed. Camberley: The Concrete Society, 2005 – Institution of Structural Engineers.  Manual for the design of  concrete building structures to Eurocode 2 . London: IStructE, 2006

3.7

Figure 3.8 Enhanced PD  sway effects resulting from (a) foundation settlement, and (b) material creep

Extreme actions and robustness

Extreme actions can be defined as those resulting from exceptional conditions. By nature, they tend to be of uncertain magnitude and low probability. Examples include terrorism, explosions, fire, vehicle, train or boat impact and extreme natural events including earthquakes (see Box 3.3) and floods. Box 3.3

Earthquake actions

Earthquakes are extreme events that dictate the governing actions in many regions of the world. For most buildings, they are usually considered at the ultimate limit state only.

Σ(Stiffness × Strain)slab + Σ(Stiffness × Strain)vertical stability systems = Σ(Post tension force) Figure 3.9

Post tensioning of restrained floor slabs

 Although some codes permit a quasi-static method for  evaluating earthquake base shear in low seismic zones (e.g. the Australian Standard AS 1170 Part 4 3.6 ), a more accurate evaluation requires a dynamic analysis. This will be dependent on each of the structural form and soil/rock  characteristics. Further reference to earthquake design is given in Section 4.6.

 Actions and combinations Some structures are particularly at risk of being damaged by extreme actions (e.g. embassy buildings as the target of terrorism), while the consequence of  damage to other buildings has disproportionate impact on society (e.g. damage to emergency facility such as a hospital, a service-supply facility such as a water treatment plant, or a building containing hazardous or toxic materials such as a nuclear power station). These ‘high risk’ buildings often necessitate a project-specific risk assessment approach to determine suitable parameters for the design actions. Further information is provided in the Institution’s publication, Manual for the systematic risk   assessment of high-risk structures against  disproportionate collapse 3.7. In preference to such a lengthy procedure, codified robustness criteria are defined for the majority of  structures. Most national regulations, codes or standards define building risk categories (or building classes) that help define when and how these criteria should be adopted. It is worth noting here that extreme actions should not be confused with many accidental yet probable actions such as the impact of moving plant on unprotected columns. Where relevant, the latter should be applied in a manner similar to other variable actions.

3.8

Box 3.4

Sway sensitivity

– All structures should be checked for sensitivity. – Sway effects can be caused by each of lateral and vertical actions, and can be either linear or torsional in nature. All modes should be evaluated. – Each storey should be evaluated for each combination of actions. – Frames may prove to be sway sensitive for one combination of actions, yet not for another. – The worst sway case should be used to determine the P D effects for the whole building. It should be noted that sway sensitivity can vary significantly for structures of similar overall stiffness. Structures governed by low shear stiffness have a greater sensitivity than those governed by flexure. Hence sway instability can be just as prevalent in low-rise stocky structures as it is in high-rise slender ones. δ

Flexural

PD  sway effects δ

Section 3.2 identified that gravity always acts vertically, independent of the alignment of notionally ‘vertical’ columns and walls. As a building is displaced laterally under applied actions, the added list increases the lateral force component that is necessary to maintain equilibrium. This is a destabilising second order effect, commonly referred to as the global P D  (or P-delta) effect. While all structures are subject to P D  effects, structures prone to significant P D  effects are traditionally said to be ‘sway sensitive’ (see Box 3.4). PD  effects can be determined using non-linear second-order analysis. While this is impractical without the aid of a computer, most analysis platforms offer it as a function. A drawback to using it is the demand on computing power. Not only does it make the analysis iterative but it also rules out the opportunity to use superposition of results, increasing the analysis cases to include each combination of  actions in turn.  Alternatively, many design codes allow an approximate method for sway whereby a modification factor is applied to the horizontal actions within first order analysis. Box 3.5 works through the derivation of a modification factor in line with BS EN 1993 Part 1-1 Clause 5.2 3.1. This derivation is included here to make clear how the modification factor relates directly to actions on a structure. It should be noted that any oblique actions should be split into vertical and horizontal components so that the modification can be applied to the horizontal component only. And while Box 3.5 shows the effects with an applied horizontal force, a similar effect can be caused by a vertical action acting on an asymmetric structure.

Shear

Deformed shape

Buckled mode shape

 The method shown in Box 3.5 is only deemed appropriate where: – Sway is not approaching the unstable limit. BS EN 1993 Part 1-1 Clause 5.2 3.1 defines a lower limit of  a cr  3. – The frame is not governed by a global torsion buckling mode. – Local second order effects (e.g. the axial strain of  elements including columns) are inconsequential, having negligible impact on the individual element buckling lengths. In the absence of a fully iterative second order analysis, PD  effects in frames with or without local second order effects can be determined using the ‘equivalent column’ method as described in BS EN 1993 Part 1-1 Clause 5.2.2 3.1. This is a third option, outside the scope of this  Guide

3.8

3.9

Actions and combinations Box 3.5

Sway modification factor derivation

The following shows a simple representation of a frame. The spring, shown of stiffness  k , represents the total lateral resistance between adjacent storeys. δH,Ed δH,Pδ

k

k

V  Ed

H Ed

H Ed

V  Ed

k 

H Ed

H Ed.Pδ

h 

V  Ed

V  Ed

Initial state

First order state

( δ  ) H,Pδ

h 

V  Ed

Second order state

From second order equilibrium: H Ed.Pd

¼ k d H,Pd

H Ed.Pd

and

¼ H Ed þ V Ed

dH  P d

  ;

h 

These two equations can be combined to show second order equilibrium is satisfied when: H Ed.Pd ¼ H Ed

where: H Ed.Pd H Ed

is is is is is

V Ed h  d H,Pd

2 4

1 V Ed 1 kh 

3 5

the resultant horizontal force transferred by a storey the total horizontal design force including equivalent sway forces acting on a storey the total vertical design force acting on a storey the storey height the inter-storey second-order horizontal displacement

This is an asymptotic equation. Where  kh  tends to infinity (high stiffness),  H Ed.Pd  tends to  H Ed  and second order effects tend to zero. Conversely, where  kh  tends to  V Ed ,  H Ed.Pd  tends to infinity and the structure becomes critically unstable. Defining  V cr  ¼ kh , and  a cr  ¼ V cr  / V Ed  allows the equilibrium expression to be rewritten: H Ed.Pd ¼ H Ed

2 64

1

1

1 acr

3 75

Thus the modification factor to be applied to the first order horizontal force is:

2 64

1

1

1 acr

3 75

a cr  can be determined through first order analysis using the equilibrium equation: acr ¼

H Ed h  V Ed dH Ed ;

where: d H,Ed

is the inter-storey first-order horizontal displacement.

In most circumstances, it is widely accepted that PD  effects may be ignored where it is proven that the PD  components are less than 10% of the coincident first order actions (i.e. when  a cr . 10 for sway modes)3.8. Finally, it is worth noting that sway is only one cause of PD  effects. Similar effects can arise from other movements, such as the axial shortening of an arch or the extension of a catenary.

3.9

Partial factors and combination cases for limit state design

Partial factors and combination cases are codespecific and not covered explicitly in this  Guide. Fundamental to the limit state design of all structures is that engineers design all failure mechanisms along load paths for the worst credible scenario of  coincident actions.

 Actions and combinations

C  L

 Additional superimposed mass to buttresses

Resultant outside of footprint

Minimum load (min envelope) – Stable Figure 3.10

Intermediate case – Unstable!

Maximum load (max envelope) – Stable

Stability of buttress walls to arched or pitched roofs, subject to variable vertical actions

For lateral stability systems, the most onerous combination is not always clear and will most likely vary between elements. Combination cases should look to combine the most onerous detrimental actions with the least beneficial actions. However, considering mass as an example: it can be both beneficial, providing anchorage, but also detrimental, increasing the equivalent sway and second order P D effects. Thus, should the engineer consider maximum or minimum mass? The answer can only be determined by checking the specific cases. Some codes, including Eurocodes, define different partial factors for equilibrium and strength limit states (these are denoted ‘EQU’ and ‘STR’ in BS EN 19903.9 ). The engineer m ust be aware of  these and use the correct factors in the correct instances. The design of the whole or parts of the stability systems should be completed adopting the strength partial factors; but further checks of the stability of the whole or parts of the system should also be checked for the equilibrium factors. Engineers must complete checks to eliminate any doubt over which combination of actions is critical.  These checks may be by inspection, approximate hand calculations or detailed analysis. Subsequently, the engineer should analyse critical cases in detail in order to determine design parameters. In practice, engineers may simply choose to analyse all applicable combination cases in detail. This is potentially the safest way of working as it increases the likelihood that critical cases are captured. However, the approach can lead engineers towards enveloping results; a practice that may mask critical results or lead to inefficient designs. Figure 3.10 shows a classic example where the envelopes exhibiting both maximum and minimum vertical actions would be adequate but not the intermediate case. Such a scenario may often occur during the construction as suggested by the figure but could also manifest during operation, maintenance or remodelling works.

3.10 References 3.1

BS EN 1993-1-1: 2005: Eurocode 3: Design of steel  structures. Part 1-1: General rules and rules for  buildings . London: BSI

3.2

Mendis, P.  et al . ‘Wind loading on tall buildings’. Electronic Journal of Structural Engineering , Special Issue: Loading on Structures, 2007, pp41-54.  Available at: http://www.ejse.org/Archives/Fulltext/  2007/Special/200704.pdf [Accessed: 16 December  2013]

3.3

BS EN 1991-1-4: 2005 þ  A1: 2010: Eurocode 1:   Actions on structures  Part 1-4: General actions –  wind actions . London: BSI, 2010

3.4

Holmes, J.D.  Wind loading of structures . 2nd ed.  Abingdon: Taylor & Francis, 2007

3.5

National Research Council of Canada.  National building  code of Canada 2010 . 13th ed. Volume 2. Ottawa: National Research Council of Canada, 2010

3.6

AS 1170.4-2007 Structural design actions. Part 4:  Earthquake actions in Australia.  Sydney: Standards  Australia, 2007

3.7

Institution of Structural Engineers.  Manual for the  systematic risk assessment of high-risk structures  against disproportionate collapse . London: IStructE, 2013

3.8

BS EN 1992-1-1: 2004: Eurocode 2: Design of  concrete structures – Part 1-1: General rules and rules  for buildings . London: BSI, 2004

3.9

BS EN 1990: 2002 þ  A1: 2005: Eurocode – basis of  structural design . London: BSI, 2005

3.10

4

Stability systems

4.1

Load paths for lateral actions

 A structure is a system that transfers actions from the point of action to points of reaction, adhering to the laws of statics. ‘Load paths’ are required for all actions (vertical and horizontal) and must be continuous through elements and connections. Planned load paths should be communicated in the design calculations, clearly illustrating the primary systems of resistance (see Box 4.1). At least one load path is needed to resist each action, though many actions will share common load paths or parts of load paths. Full load paths to resist lateral forces will often include: the fac¸ade, cladding rails, windposts, beams and columns, horizontal stability systems, vertical stability systems, substructure and foundations, and

Box 4.1

Sketching load paths

The practice of sketching load paths is recommended and widely regarded fundamental to design, both for  communicating and exploring/developing ideas. Load path sketches can be global (see Figure 4.1) or narrowed down to show a specific system or detail (see Figures 10.7 and 10.8 by way of examples).

Horizontal bracing

all connections/interfaces between these elements listed (see Figure 4.1). For the ultimate limit state, it is good practice to establish simple load paths that may neglect the contributions of redundant elements (e.g. two walls connected by a monolithic beam may be designed as independent elements ignoring the coupling effect of  the beam). This is an ‘upper lower bound’ approach to modelling that allows the design to be completed with only limited concern for each of relative stiffnesses, locked in stresses, tolerances and the construction sequence. It tends to result in conservative solutions that are simple to erect and robust. Even when planning simplified load paths the true distribution of stresses can remain critical, at least at the serviceability limit state. In reality, load paths will develop through all elements that resist movement of  the structure and unintentional load paths can lead to premature failure of inadequate elements. While these failures will seldom threaten the adequacy of the structure (provided adequate ‘upper lower bound’ load paths have been designed), they are rarely acceptable.  To overcome any unintentional load paths, many vertical planar elements including partitions, glazing and cladding (each of high in-plane stiffness but low failure strength) are often installed with connections

Beams

Wind posts Floor slab diaphragms

Vertical bracing

Load Foundations

Figure 4.1

Load paths from facade to ground (shown for horizontal loads in the single axis only)

Stability systems that can accommodate in-plane movement. Removed from the load path, these elements must not be relied upon to provide any in-plane resistance or stiffness.

4.2

Modified Fink to eaves

Horizontal stability systems

Horizontal stability systems are those systems that are in a horizontal, or near horizontal plane (typically associated with floor and roof planes). They are needed to transfer lateral forces to the vertical stability elements.  There are two types of horizontal system: diaphragms and triangulated bracing (the latter being sometimes referred to as a wind girder). Concrete floor slabs are often sufficient to act as diaphragms. However, scenarios where their shear capacity may be inadequate can include those shown in Figure 4.2. Profiled metal liner trays or plywood sheathing can each provide diaphragm action but only when appropriately specified. Where adopted, the engineer needs to satisfy themselves that each of the sheets and their fixings are adequate to transmit the required forces (often necessitating thicker sheets and many more fixings than are needed to resist out-of-plane actions alone). They will also need to consider the temporary stability of the frame in advance of the diaphragm’s installation. Horizontal bracing can be provided in the absence of  an adequate diaphragm. It is commonly used for lightweight (non-concrete) roofs, especially in steel framed buildings. Bracing is usually arranged in either Modified Warren or Modified Fink truss formats; the

Modified Warren to gables Orthogonal beams form part of the bracing system Note  this particular arrangement of Modified Warren and Fink trusses is to illustrate the different options only

Figure 4.3

Standard forms of truss

latter being suited to tension bracing (see Part 2). In both configurations floor or roof beams act as part of  the truss and are subject to either tension or compression in addition to any shear and bending moment (see Figure 4.3). Where the vertical stability systems provide three or more points of support, the stiffness of the horizontal diaphragm or bracing will influence the force distribution to the vertical elements (see Section 9.2).  The inclusion of large voids in floor diaphragms adjacent to shear walls and eccentricities between members can each impact on the stiffness of a connection and hence the percentage of the force transferred.

Link with no shear stiffness Isolated core

Limited stiffness

Unstable

Voids

.   M. J

Limited stiffness

Cracking

Figure 4.2

Examples of defective slab diaphragms

Limited shear resistance between precast units

4.2

4.3

Stability systems  The span to depth ratio (where ‘span’ is the distance between vertical stability systems and ‘depth’ is the in-plane horizontal depth) can be used to provisionally size systems. For braced systems, this may influence the spacing of primary beams where these act as the chords to the truss. Meanwhile, in long narrow buildings the depth of the floor plate could dictate the maximum spacing of vertical stability systems.

4.3

Vertical stability systems

4.3.1

Introduction

 As systems they must always: – Provide linear resistance in two orthogonal horizontal axes. – Provide torsional resistance about a vertical axis. – Provide said resistance to all parts of the structure.

 

e 3

Planning vertical stability structure: plan layout

Figure 4.4 identifies and rates eight basic layouts for vertical stability structures. While these are illustrated for an idealised rectangular building, the six column headings used to evaluate the layouts remain the key considerations for all building forms. These headings are explained in Figure 4.5. Figure 4.4 layout 1 has the minor axes of all stability systems intersecting at a common point. It is therefore unstable with no torsional resistance. The same is true for any configuration of radial systems irrespective of whether the intersection of the stability system axes is central to, or offset from, the centre of  the building.

 Vertical stability systems are those in a vertical or near vertical plane. They are the only parts of the structure that intentionally transfer lateral forces acting on or within the suspended floors and roof down through the structure. The primary systems will comprise one or more vertical cantilevers, with individual elements pinned or fixed at the foundations.

e 2

4.3.2

Figure 4.4 layouts 2 and 5 each indicate minimum requirements for a stability system, relying on the combined contribution of torsion and linear resistance. Both are common and layout 2 is not dissimilar to the three-sided layout used at ground floor for open-plan terraced shops (see Figure 4.6).  All other layouts shown in Figure 4.4 are generally improvements on layouts 2 and 5, though each is not without its own characteristic shortcomings.

Load eccentricity

Stability

e 1

Torsional resistance requires multiple stiff elements positioned such that the minor axes of the elements are not radially aligned. Resistance increases proportionally with the offset between the axes of the elements and the global centre of stiffness ( e 1, e 2, etc). Locating resistance at or near the extremities of the structure maximises the torsional effectiveness.

Restrained slab



All structures must exhibit two axes of linear and torsional resistance.

Service Floor and roof structures become restrained where there is an offset between stiff axes of individual stability systems. Restraint stresses increase approximately linearly with i ncreasing offset distance for any given action.

Where the stability system is uniform through the height of a building, stresses due to shrinkage or post tensioning of concrete slabs are likely to be most significant through the lower storeys; while those due to solar radiation are pronounced at the upper most storey. Other features of a building (e.g. unconditioned car park storeys) can also concentrate thermal or moisture-induced stresses.

Possible movement  joint

Redundancy

Localised failure



Residual systems

Where a stability system contains redundancy, robustness requirements can be satisfied by ensuring adequacy (in terms of strength and stability) of residual load paths. This approach is most suited to structures containing isolated walls, bracing or portal frames. Distributing the stability systems, so that they are not closely situated nor share common columns, reduces the risk of multiple systems being impacted by a given event. Where it is impractical to provide redundancy within the stability system, stability elements should be designed and justified to withstand extreme actions determined via a systematic risk assessment. This is the usual approach taken for buildings with stability cores.

Note  The notation used in this figure is defined in the legend to Figure 4.4.

Figure 4.5

Vertical bracing criteria

Stability systems Plan layout

Stability Resistance in two orthogonal axes

Distributed systems

to



Depending on building plan shape, dimensions and scale

But slab movement may cause minor axis bending of the stability systems







to



Resistance in two orthogonal axes

Unstable



No redundancy







But slab movement may cause minor axis bending of the stability systems





to





to

to



8



to

Failure at a corner would impact on two systems leaving only two intact

Failure at a corner would impact on two systems leaving only two intact

Single concentrated system

No redundancy. The No redundancy. The core is a key element core is a key element

Single concentrated system

No redundancy. The No redundancy. The core is a key element core is a key element

Single concentrated system

No redundancy. The core is a key element









Depending on building plan shape, dimensions and scale

7





Depending on building plan shape, dimensions and scale



No redundancy

Depending on building plan shape, dimensions and scale



Restrained between systems

Depending on building plan shape, dimensions and scale

Residual torsional resistance



Restrained between systems

Depending on building plan shape, dimensions and scale

4

6

Slab free to move



Unstable

3

5

Torsional resistance

Redundancy



1

2

Service

4.3



Large lever arm between the centres of stiffness and mass



Restrained between systems

No redundancy. The core is a key element

Large lever arm between the centres of stiffness and mass

Legend   Denotes inherently good performance. Denotes unwelcomed characteristics that may or may not be critical (depending on the plan geometry) and may be alleviated via careful detailing. Denotes instability in the event that a single stability structure fails. Design parameters for the stability elements must be justified based on an assessment of risk. Denotes inadequate performance. Note  Compatible combinations of the above layouts may be adopted to combine favourable characteristics.

Figure 4.4

Vertical stability layouts on plan

4.3

Stability systems 4.3.3

Planning vertical stability structure: layout through the height of the building

 Vertical stability structures of one, or a compatible combination of forms must provide stability throughout the height of a building to the uppermost extents of the structure including spires, chimneys, pitched roofs and plant screens.  Although lateral forces accumulate down through the height of a building and peak at foundations, the failure mechanisms shown in Figure 2.3 can occur at any level (see Figure 4.7).

Figure 4.6 floor 

Terraced shops with three-sided stability at ground

While not always possible, it is generally most efficient to have all primary stability structures continuous to the foundations. Although this concentrates forces into particular columns, walls and foundations, it eliminates the need to transfer accumulated shear forces from the base of one system, through a horizontal system, to further vertical systems continuing below (see Figure 4.8 by way of example). Not violating the last statement, it can be beneficial to have a greater density of stability structures providing enhanced stiffness at lower storeys. Such bolstering of the structure responds directly to the accumulating bending moment and shear force down through a vertical cantilever. Possible techniques include buttressing to core walls (see Box 4.2), additional bracing, outrigger systems or a combination thereof.

Figure 4.7

Example failure modes at critical storeys, not necessarily ground d  H 

h 

H  H  H  H 

Some structures require local secondary stability systems in addition to the primary systems that extend through the height of the building. These are common where a floor plate steps, is discontinuous between primary systems or meets the primary system away from a stiff node (see Figure 4.10).

5H  15Hh 

15Hh 

d 

d 

Where the functional requirements dictate a change to the stability structure from one floor to the next, particular care is needed to avoid a soft storey scenario. ‘Soft storeys’ are those that provide particularly little resistance. They can be present in new structure (e.g. to accommodate parallel carports at the base of a residential building  see Figure 4.9) but often come about through ill-conceived structural alterations to existing buildings (e.g. the removal of  walls to create open-plan accommodation). It is always best practice to avoid soft storeys by ensuring a reasonably constant utilisation ratio for the resistance at each storey.

d  H  h 

It is beneficial in most instances to have sufficient permanent vertical mass acting on stability structures such that net tension is avoided in the columns. This can usually be achieved in multi-storey buildings via well-conceived framing to the floor plates and by avoiding superfluous columns at close centres to the stability system. Anywhere where column tension cannot be avoided, each of the superstructure, substructure and soil-structure interface need to be checked for adequacy in tension.

H  H  H 

4H 

H 

4.3.4

Substructure

5H  6Hh 

6Hh 

9Hh 

9Hh 

d 

d 

d 

d 

Figure 4.8 Building elevations showing an example of the impact of discontinuous vertical stability systems ( d  and  h  are consistent to all bays/storeys)

 The cumulative shear force, compression and tension in the vertical stability structures must be transferred to the ground via the substructure. Forces may transfer to the ground via local foundations immediately below the superstructure elements, or

Stability systems Box 4.2

4.3

Buttressed cores to the Burj Khalifa

Currently the world’s tallest building, the Burj Khalifa adopts a reinforced concrete buttressed core throughout its height. The buttresses radiate further with additional cross walls as the forces increase down the height of the tower.

through wider-spreading structures including stiff  basement boxes (see Box 4.3) or raft slabs.  The ground surrounding the substructure provides the final resistance to all actions and the structural engineer must adopt appropriate design parameters for the soil-structure interface. These must be site specific, taking account of the immediate ground conditions.  The soil parameters will ultimately dictate the nature of the substructure system; principally its form, stiffness and load distribution characteristics. It is likely that the parameters will be non-linear and it may be necessary to consider values across a range (allowing for uncertainty or variation of the ground). Sensitivity studies can be used successfully to determine design actions for an envelope.

Figure 4.9

Soft storey failure at ground floor 

It is worth noting here that, in the common scenario where there is a division of responsibility (e.g. when a specialist piling designer is appointed), a clear and comprehensive transfer of information must take place to enable the different contracted parties to complete their design packages. The collapse of the Lotus Riverside building, Shanghai, in 2009 is a stark  reminder of the consequences of a foundation failure; in this instance caused by earthworks conducted by an unqualified contractor 4.1 and not in accordance with the substructure design assumptions.

Local stability system at step in floor diaphragm

Figure 4.10

Primary stability system

Secondary vertical stability systems (in elevation)

Local stability to isolated floor

4.4

Stability systems

Box 4.3

Substructure load paths

Where the building has a stiff basement box, lateral forces can be transferred at the foundation level and at any slab levels where the slabs are detailed to act as props or diaphragms spanning to the surrounding basement walls. One or more slabs, together with the foundations can form a couple resisting the overturning bending moment acting in the stability superstructure. It is worth noting that this couple can cause horizontal forces in the slabs and on the foundations in excess of the total horizontal shear on the building. With movement joint at ground floor

Monolithic construction Horizontal reaction force dependent on the ground stiffness

Large couple and shear on the foundation

Couple in slabs reduces the couple on the foundation

Note  that a load path via the front and back basement walls (those parallel to the action) is a further means of resistance not shown in the above figure.

4.4

Accommodating movement

Movements can be influenced by, and have influence on, both design actions and load paths (see Box 4.4). How they are to be accommodated is a decision that needs to be made by the engineer and is inseparable from the development of a stability system.

Box 4.4

Free movement and load paths

For a particular degree of freedom (see Figure 2.2) free movement can only be provided at the expense of a load path. The two are incompatible. This is rarely misunderstood by engineers. Yet it is often overlooked or paid inadequate attention especially where a movement joint is incorporated late in the design development. Whether a movement joint provides one or more degrees of free movement will be dictated by the detailing of the joint. A carefully detailed movement joint can transfer shear and/or  bending moments in certain axes, while providing movement in others.

While all structures can and will accommodate some restrained movement, it is often necessary to provide movement joints through large horizontal structures. This is to release forces that would otherwise develop from strains (see Sections 3.5 and 3.6). Horizontal movement joints bifurcate the diaphragms or horizontal bracing systems in which they are present, and can be temporary (allowing for rapid irreversible strains only) or permanent. Where used, structures to either side of a joint must be independently stabilised for the duration that the joint allows unrestrained movement (see Figures 4.5 and 4.11 and Box 4.5).  Vertical movement joints are less common within the primary structure. Where provided, they are usually at the junction of vertical loadbearing and nonloadbearing systems (e.g. wind posts connecting to floor beams), or between structures vulnerable to differential foundation settlement. It is more common that vertical movements in the primary structure (resulting from elastic deformation, creep and shrinkage) are accommodated within uninterrupted load paths.  Any locked-in differential movements will have adverse effects on both vertical and horizontal systems, resulting in a second order redistribution of stresses. The structure must be able to withstand these effects but engineers can mitigate against exacerbated P D  effects with wellconceived compensatory measures 4.3. Compensatory measures may also be necessary for serviceability criteria.

Further reading: movement

Figure 4.11

Horizontal roof bracing and parallel rafters either side of a movement joint

The following texts are recommended sources of further  guidance on movement: – CIRIA. Design for movement in buildings. C734 . London: CIRIA [due for publication in 2014] – The Concrete Society. Movement, restraint and cracking in  concrete structures . Technical Report 67. Camberley: The Concrete Society, 2008 – Rainger, P.  Mitchell’s movement control in the fabric of  buildings . London: Batsford, 1983

Stability systems Box 4.5

Pa´ tio Malzoni Building, Sao Paulo Block 3 Block 2 Block 1

Movement  joints

Completed in 2012, the 21 storey Pa´ tio Malzoni Building is 150m long, 84m high and of reinforced and post tensioned concrete construction4.2. The building is split into three blocks to accommodate horizontal shrinkage; each self stable and separated by 20mm wide, neoprene filled movement joints (shown red in the figure). The two outer blocks are braced systems stabilised by traditional core structures (each similar to Figure 4.4, layout 6). However, due to site constraints, accommodation in the middle block is suspended 30m above ground with 14 floors supported on just eight unbraced columns to ground. Ultimate limit state stability to the central block is provided by portal behaviour of the unbraced columns, with expected displacement of the order of 120mm. However resistance in the longitudinal direction at both the ultimate and serviceability limit states is also allowed for in the flanking blocks with each designed to withstand the additional load from the middle block. This is essential, owing to the difference in stiffness between the braced and unbraced systems.

4.5

Braced and unbraced vertical stability systems

commonly associated with concrete construction their meaning and application is appropriate to all materials. Examples are shown in Figure 4.12.

4.5.1

Introduction

4.5.2

 Vertical stability systems can be classified as either ‘braced’ or ‘unbraced’. While these terms are most

Braced structures

 A ‘braced’ structure is one in which defined systems (elements or assemblies) are assumed to

Moment connections

Wall

Bracing Braced

Moment connections

Unbraced

Wall or bracing

Single axis hybrid Figure 4.12

Braced, unbraced and hybrid structural systems

Braced

Unbraced

Hybrid in orthogonal axes

4.5

4.5

Stability systems contribute resistance to the overall lateral stability of a structure, while other elements specifically do not4.4.  The resisting systems are typically multiple orders of magnitude stiffer than the general frame. This is a form that facilitates simple (pinned) frame construction in the extreme and allows general frame elements to be considered restrained at storey levels. 4.5.3

Unbraced structures

 An ‘unbraced’ structure is one in which the vertical and horizontal frame elements provide lateral stability via rigid connections of sufficient stiffness to resist rotation.  These structures rely solely on the bending stiffness of the frame elements and connections to maintain rigidity (otherwise known as portal or vierendeel behaviour). Hence, systems of comparable frame tonnage tend to be more flexible when unbraced than when braced.

Box 4.6

4.5.4

Hybrid structural systems

Many structures contain a mix of vertical stability systems to best suit the building requirements and form. It is not uncommon to have vertical systems of  differing nature providing stability in the two orthogonal plan axes, e.g. portal frame warehouses with bracing along the side elevations. Being orthogonal, these systems will act largely independently, keeping the load paths unambiguous for most building forms. Structural form and/or constraints sometimes dictate that multiple systems are needed in a single axis to achieve the necessary level of resistance. This is often the case in tall buildings due to their slenderness (see Box 4.6) but is not uncommon in lower-rise buildings, especially those with mixed-use functional requirements. Wherever multiple systems interact to share forces, care is needed to ensure the modelled stiffnesses are

Hybrid stability system to One One One Eagle Street, Brisbane

One One One Eagle Street is a 200m tall office tower that uses an eccentric reinforced concrete core together with a grillage of non-orthogonal perimeter columns to resist lateral forces. The freeform nature of the perimeter columns is both visually striking and structurally significant. The irregular geometry contributes to the overall stability of the tower, significantly increasing the torsional resistance. Columns become more inclined as vertical forces reduce up the building, making the perimeter frame increasingly effective as a lateral force resisting system. This counters a reduction in the concrete core stiffness as lift shafts terminate. Structural core walls

Edge thickening resolving forces between columns

Perimeter column grillage

Stability systems

Systems oppose one another at top

Shear resisted by frames

Shear resisted by walls

Total shear Unbraced system Figure 4.13

Braced system

Combined

Combined behaviour of a moment frame – braced frame dual system

reflective of the as-built structure. Figure 4.13, by example, illustrates how frame and wall elements work independently under force, and how these can be united to share a lateral force. No units are given for the graphical distribution and each of the relative stiffnesses of the elements, the failure strains of  different materials, the degree of inelastic movement or slip in any joints, the construction sequence, and the magnitude of locked-in construction stresses can influence the load distribution between systems. 4.5.5

Slenderness of elements in compression

 A ‘slender’ element is one which is vulnerable to buckling failure when experiencing a compressive stress less than the yield stress. Non-slender elements are said to be ‘stocky’. Whether an element is slender or stocky is influenced by whether a frame is braced or unbraced. Elements in a braced frame typically have effective lengths less than or equal to their true length, while elements in an unbraced frame typically have effective lengths larger than their true length. Slenderness can render plastic analysis and design methods inappropriate. Also, while slenderness has no intrinsic link to the theory behind P D  effects, a frame comprising slender elements would have less resistance to deformation than an equivalent stocky frame, making it more sway sensitive. Further discussion on effective lengths is contained in each of Parts 2 (contained herein), 3 and 4 for framed bracing elements, shear walls and moment frames respectively.

4.6

Earthquake design

Earthquake design requires attentive initial planning of form and careful detailing. Adequate

strength is usually not sufficient in isolation to impart effective resistance, and designing to avoid yield is widely accepted as uneconomical and unjustified. Rather, designs should exhibit ductile post yield behaviour. Each of steel, timber, reinforced concrete and post tensioned concrete can be designed with adequate ductility when suitably detailed. Figure 4.14 highlights the primary pros and cons of common systems.  Vulnerable structures must be not only ductile but also suitably stiff to ensure that plastic deformations do not cause insurmountable P D  effects. Other considerations include: – The building layout should be relatively symmetrical, and vertical discontinuities minimised to avoid soft storey stress concentrations that can otherwise amplify local deformation. – Mass of fixed plant and equipment should be positioned through the height of a building to best suit the dynamic behaviour. – Neighbouring buildings and structures across movement joints should be spaced adequately to prevent collisions during dynamic sway. This is especially critical where adjacent floor plates are not vertically aligned and could impact on unrestrained lengths of adjacent columns. Further reading: earthquake engineering

The following texts are recommended sources of further  guidance on earthquake actions and design: – Institution of Structural Engineers.  Manual for the seismic  design of steel and concrete building to Eurocode 8 , London: IStructE, 2010 – Booth, E.  Earthquake design practice for buildings . 3rd ed. London: ICE Publishing [due for publication in 2014] – Dowrick, D.  Earthquake resistant design and risk  reduction . 2nd ed. Chichester: Wiley, 2009

4.6

4.7

Stability systems Generally ductile and have low natural frequency making unbraced systems less prone to resonance. However often sway sensitive with dominant P Δ effects.

Unbraced

Stiff, but often governed by non-ductile buckling failure. Ductility can be increased by providing restraint to elements against buckling.

Braced Stiff and generally ductile, but penetrations and lintel beams can be critical.

Hybrid structures look to combine the ductile mechanisms of unbraced frames with the stiffness of braced systems. Hybrid

Control elements (or ‘fuses’) can be used to yield in preference to more critical elements. This is the basis of the widely adopted ‘weak beam – strong column’ approach.

Figure 4.14

4.7

Earthquake performance of unbraced, braced and hybrid stability systems

Serviceability performance criteria

Serviceability performance criteria play no part in stability. However, the sizing of stability systems will often be governed by stiffness criteria that must not be assumed adequate or overlooked. Each of a building’s materials (including fac¸ade elements, partitions and finishes), services, equipment, operations and human comfort can dictate limits on sway, inter-storey drift and torsional rotations.  The Institution’s Manual for the design of building structures to Eurocode 1  recommends that both total sway and inter-storey drift should not exceed height/  5004.5. This is more prescriptive than guidance listed in the ASCE/SEI 7-10 Clause CC.1.2 4.6 which suggests a limit in the range of height/400 to height/  600. Ultimately, these are only guide values, proven to prevent visible distress or impair service distribution and lift (elevator) operation in most buildings. It is however up to the engineer and wider design team to refine these limits as necessary and see that they are appropriate. A number of common features of buildings, some of which may impact the criteria, are listed in Section 4.8. Horizontal acceleration can be as critical as absolute movement. This is particularly true in high-rise buildings (those over 15 storeys) subject to dynamic loads such as wind. Acceleration is intrinsic to oscillatory movement and is a function of building height and natural frequency. Meanwhile perception is a function of activity. Instances of the order of 0.5% gravity (0.05m/s2 )4.7 can be perceptible by humans, though this is not to say it should be the design criterion. Equipment (including medical scanners, laboratory testing systems and other precision instruments) can

dictate operating requirements. Where applicable, the requirements are usually stipulated by the manufacturer and can vary markedly between similar products. Further reading: acceleration performance criteria

The following texts are recommended for guidance on acceleration performance and comfort criteria: – Breeze, G. Dynamic comfort criteria for structures: a review of UK codes, standards and advisory documents. FB 33. Watford: IHS BRE Press, 2011 (and references listed therein) – National Research Council of Canada.  National building  code of Canada 2010 . 13th ed. Volume 2. Ottawa: National Research Council of Canada, 2010 – National Research Council of Canada.  User’s guide – NBC  2010 structural commentaries (Part 4 of Division B) . 3rd ed. Ottawa: National Research Council of Canada, 2011

4.8

Non-structural requirements

Structure cannot be considered in isolation and there are usually many requirements of the design that may have an impact on the structural efficiency. A design engineer should recognise and appreciate these, be able to communicate the significance of conflicts, and work collaboratively with project teams to develop solutions without unsatisfactory compromise in any one area. Some common features of buildings that may impact on the stability system design are listed opposite. These may influence the layout and form of the stability structure (see Sections 4.1, 4.2 and 4.3) or influence the serviceability criteria (see Sections 4.4 and 4.7).

Stability systems Building layout  – The size, layout and quantity of stair and lift (elevator) shafts, and the requirements for fire compartmentalisation of such features. – The size and disposition of service risers, particularly where these require significant penetrations for service distribution, both horizontally and vertically. – Horizontal service distribution across movement  joints and beam lines (particularly t hose beams, including lintels, forming part of a coupled stability system). – Storey heights. – Open-plan or cellular layouts and column free spaces. – Floor plan layout repetition between storeys, and discontinuity of vertical structure. – Any prerequisites for future flexibility and the likelihood of change. – The storey or foundation level at which the stability system is restrained by the ground and the nature of this restraint. – The thickness, alignment and construction of  internal non-structural partitions. Operational performance – The requirements of the fac¸ ade for natural daylight, access, insulation and thermal isolation. – The inclusion of brittle finishes including glass and masonry. – The sensitivity of equipment and plant to movement. – The inter-storey drift that can be accommodated by lift cars, escalators and vertical service distribution. – Environmental conditions and variability (both thermal and moisture). Construction – The degree of prefabrication. – Site access for materials and plant including cranes. – Workmanship and material quality control. – The construction programme (speed and sequence). Further specific features of a project will almost certainly add items to this list. Many of these will be identified in the conceptual planning but others may only become apparent later in the design development. Usually the earlier any requirements are identified and addressed the more coherent the solution.

4.9

References

4.1

BBC News. ‘Jail terms for Shanghai collapse’. 22 April 2010. Available at: http://news.bbc.co.uk/1/  hi/world/asia-pacific/8636446.stm [Accessed: 16 December 2013]

4.2

Franco, M. ‘Sao Paulo building for the future freezeframes Brazil’s past’.  ICE Proceedings, Civil  Engineering . Special Issue, 166(CE6), November 2013, pp13-19

4.3

Cargnino, A.  et al . ‘Axial shortening compensation strategies in tall buildings. A case study: the New Piedmont Government Office Tower’.  Structural  Engineering International , 22(1), February 2012, pp121-129

4.4

BS EN 1992-1-1: 2004: Eurocode 2: Design of  concrete structures – Part 1-1: General rules and rules  for buildings . London: BSI, 2004

4.5

Institution of Structural Engineers.  Manual for the  design of building structures to Eurocode 1 and basis  of structural design.  London: IStructE, 2010

4.6

ASCE/SEI 7-10: Minimum design loads for buildings  and other structures . Reston, VA: ASCE Press, 2010

4.7

National Research Council of Canada.  User’s guide –  NBC 2010 structural commentaries (Part 4 of Division  B) . 3rd ed. Ottawa: National Research Council of Canada, 2011

4.9

5

Stability during construction

5.1

Introduction

Most instances of instability in structures and buildings occur while undergoing construction. By its very nature, this is a period in which the structure is in a state of flux. It is also the period in which design information is being most intensively communicated to, and interpreted by, those parties not involved in the design. Failure of the FC Twente stadium roof in 2012 was a shocking example of a failure that resulted in international media attention. It has since been attributed to a number of generic errors, any one of  which could cause similar failure elsewhere (see Box 5.1).  This chapter is written primarily to guide the design engineer and should be read in conjunction with Section 2.3. It is an introduction, to help designers understand their responsibilities in the context of the wider team.

Box 5.1

Construction failure at FC Twente stadium, 2012

 A Structural-safety.org paper attributed failure of this stadium roof to each of the following 5.1: – Concurrent activities took place without management to ensure stability at all times. The overlap of activities was in part due to an overly tight programme. – Necessary tolerances were not allowed for in the design, or conversely the accuracy assumed in design was not communicated to the contractor. – Elements were installed in a manner that they were not designed for. – Elements critical for temporary and permanent stability were not installed in sequence. – The structure was loaded in its temporary condition prior  to completion of necessary stability, with forces of such magnitude that the temporary condition was more onerous than the permanent condition.

5.2

Responsibility of the contractor’s structural engineer

Construction works should be undertaken only by those who will exercise their duty to carry out and supervise work to ensure that: – The requirements of the design and specification for materials and workmanship are achieved. – The stability of the temporary and permanent works is maintained at all times. – The construction is completed in a safe manner that does not expose anyone to unnecessary risk  of injury or long term health implications. Once on site, responsibility for the stability of the structure and all associated temporary works usually resides with the main contractor (see Box 5.2). It is recommended that one of the contractor’s site engineers, or an appointed temporary works coordinator (TWC), oversees this responsibility and all associated tasks. These will include: – Overseeing the preparation of construction method statement(s). – Coordinating the activities of all subcontractors. – Coordinating temporary works. – Managing the design of temporary works structures. Where appointed, subcontractors will typically take responsibility for the stability of works packages for which they are appointed, throughout the duration of their involvement. However, by the very nature of works packages, the subcontractor’s responsibility rarely extends to all aspects of the development and it should not be relied upon by third parties until signed off as adequate or complete. Where more than one subcontractor is operating on site, there is a heightened need for the activities to be coordinated. Each subcontractor should identify an individual as their temporary works supervisor, to report to the main TWC.  The TWC must pay special attention to all aspects of  stability highlighted by the design engineer. This information should include, but may not be limited to, any features of the stability systems that cross between multiple works packages or stages. They must appreciate that the preferred construction sequence may not match that assumed (and documented) by the design engineer and that changes to either the sequence or programme may influence both the temporary conditions and locked in

Box 5.2

Contractual responsibility

The design engineer must always check, and amend where necessary, the division of responsibility proposed in the contract documents. While temporary stability is usually the responsibility of the contractor, this is not always the case and must not be assumed. In no circumstance shall an engineer agree to temporary works or other responsibilities if outside their competence.

Stability during construction

stresses. Any deviations from the designer’s assumptions need to be approved by the designer in advance of works starting on site.

5.3

Exchange of information

Design information must be unambiguous, precise and appropriate to the particular project. Before any works start the following exchange of information must take place so that all concerned parties understand what needs to be done. Information from designer to contractor   The designer must provide information detailing all facets of the design and any underlying principles and assumptions. Information should be concise and relevant to the project 5.2. In addition to drawings and specifications, this may include the following information specific to stability: – Design actions, particularly those needed for contractor-designed elements. – Details of the envisaged/assumed construction sequence, including demolition works where applicable. – Details of lifting points for elements and assemblies. – Temporary or final capacities of elements. – Critical hold points and/or dependencies for the sequence of construction. – Details on the positions of construction joints. – Details of predicted movements. – Details of any unique and significant residual risks that cannot be mitigated against by the designer and must be accommodated by the contractor. Information from contractor to designer  In return, the main contractor should provide a method statement to include: – Construction or erection procedures. – Use, weight and location of plant. – Programme of works. – Sequence of construction. – Details of temporary works (e.g. props and bracing) to be used to ensure stability, including details of  the timing of installation and removal. – Details of holes to be drilled in, fixings to be attached to, and cast-ins within elements of the permanent structure.

Furthermore, the contractor must provide information relating to any contractor-designed elements. This should include: – Details of the design parameters adopted. – Calculations. – Fabrication or assembly drawings. It is worth noting that the exchange between designer and contractor may vary by project (depending, for example, on whether the project procurement is traditional or design and build). However, terms of contracts must never stand in the way of technical requirements and safety. Box 5.3 alludes to the underlying need for collaboration and clear, convenient methods of communication between contracted parties.

Box 5.3

Divided responsibility and inadequate communication

Structural-Safety.org receives many reports concerning failures and near-misses attributed to divided responsibility and inadequate communication. One such report concluded: ‘‘The need for temporary bracing must be identified by the engineer if they are aware that the sequence of works requires it. Instability introduced by a change in the contractors’ method of construction is however out of the engineer’s hands if they are unaware of the change. Some contractors may not have the expertise to identify problems, especially when the structure is unusual; meanwhile some designers may not be sufficiently conversant with erection processes so that potential problems may not be identified’’ 5.3.

Further reading: construction responsibilities The following text is recommended for guidance on responsibilities during construction: – Institution of Structural Engineers. Structural design  the  engineer’s role . London: IStructE, 2011 The Temporary Works Forum (www.twforum.org.uk) is recommended as a source of further guidance on temporary works and construction.

5.4

References

5.1

  Structural-Safety. FC Twente stadium roof  collapse  learning from the fatal consequences . SCOSS Topic Paper . Available at: http://www.structuralsafety.org/media/24662/280_FC_twente_stadium_ roof_collapse_final_3_Oct_12.pdf [Accessed: 16 December 2013]

5.2

Ove Arup & Partners. CDM2007 – Construction work  sector guidance for designers: taking account of  CDM2007 and its ACoP L144. C662 . 3rd ed. London: CIRIA, 2007

5.3

  Structural-Safety. Split responsibilities on temporary  bracing of steelwork .  Report ID 204 . Available at: http://www.structural-safety.org/publications/viewreport/?report&equals=3177 [Accessed: 16 December  2013]

5.3

6

Stability following deterioration, alterations or change of use

6.1

Planned alterations

 Alterations to a structure or building fabric may reduce the stability systems to such an extent that, in the extreme, localised or widespread collapse may occur. Planned alterations can be anything from the removal of a wall, to major extensions or the retention of a fac¸ ade with an otherwise new development (see Box 6.1). Some alterations provide new lateral resistance to existing structures, e.g. fixing an existing fac¸ade to a new frame, while others may utilise and add force to existing lateral stability systems, e.g. adding a new storey to an existing building. Engineers completing the design of alterations have a duty to ensure the adequacy of all structures impacted by the works, irrespective of whether the element or system is altered. Procedures to be observed include: – Where available, assemble and appraise historical documents including: as-built drawings, design parameters and specifications, details of  modifications or additions subsequent to the original construction, and records of maintenance work. These may be held by the building owner, building control or other local authority offices. Further guidance on sourcing such documents is available in the paper ‘Researching drawings and records for an existing building’ 6.1. – Undertake a structural appraisal of the existing structure. This may involve testing, and/or intrusive works to establish the anatomy of the structure. Further guidance on this is contained within the Institution’s publications Appraisal of existing structures6.2 and Guide to surveys and inspections of buildings and associated structures 6.3. – Undertake an appraisal of the future actions to be exerted on the original structure (see Chapter 3) and check the adequacy of the structure. – Develop solutions for any new, adapted, strengthened or stiffened structures. – Prepare a method statement detailing the sequence of work, the type of construction plant to be used, and the precautions to be taken (including monitoring and temporary bracing) at each stage to guard against instability. In planning work, engineers should appreciate that removing mass can be critical where lateral forces or tension uplift occur (see Figure 3.10), and that removing structure can remove necessary restraint to retained elements. Furthermore, locked in stresses should be acknowledged and managed when developing strengthening details, and interfaces between the new and existing structure should consider each of tolerances and movement. Finally, the stability of an altered superstructure must never increase the dependency on, nor restrict

Box 6.1

Temporary bracing to a retained fac¸ade

The photo shows temporary horizontal stability bracing supporting a retained fac¸ade during construction. It is important to note that, in this instance, the bracing cantilevers from the adjacent property. The client would have had to have requested the permission of the adjacent property owner to adopt this approach and either the design or temporary works engineer would have been responsible for  checking the adequacy of the existing neighbouring structure. In the permanent state, the retained fac¸ade will be stabilised by the new structure.

future alterations to, neighbouring third-party properties without explicit approval of the neighbouring property owner. This is true even where the properties are inter-connected (e.g. masonry terraces, see Figure 4.6). Often where one vertical stability system is removed, another must be provided. The replacement must have comparable stiffness to the system it replaces, and must be adequately fastened to the horizontal stability system (which may also need to be altered) to restore the load path.

6.2

Deterioration

Most materials suffer some form of environmental or fatigue induced deterioration. This can lead to loss of  performance and failure of components. Lateral load resisting structure should be designed for a design life equal to that adopted for the vertical load resisting structure. Where this is not practical, the design must facilitate a maintenance strategy.

Stability following deterioration, alt erations or change of use Scenarios that can accelerate deterioration include: – Exposure to moisture. – Exposure to chemicals including salts, chlorine, acids and alkalis. – Exposure to UV (solar) radiation. – Exposure to extreme temperatures and thermal cycles. – Cyclic, pounding and reversible actions (e.g. tension-compression cycles). – Movements and abrasion (including those within planned movement joints). – Endurance of accidental actions (e.g. vehicle impacts causing spalling of concrete). Signs of deterioration often emerge in the form of  rotting, rusting, cracking and spalling. These are not in themselves indicators of impending instability but can provide visual clues well before any significant instability becomes noticeable. Fire exposure is an exceptional condition that may lead to very rapid deterioration. The Institution’s publication Practical guide to structural robustness  and disproportionate collapse in buildings 6.4 discusses this in more detail.

6.3

References

6.1

Perry, P. and Thomas, R. ‘Researching drawings and records for an existing building’.  The Structural  Engineer , 87(4), 17 February 2009, pp22-27

6.2

Institution of Structural Engineers.  Appraisal of existing  structures . 3rd ed. London: IStructE, 2010

6.3

Institution of Structural Engineers.  Guide to surveys  and inspections of buildings and associated structures . London: IStructE, 2008

6.4

Institution of Structural Engineers.  Practical guide to  structural robustness and disproportionate collapse in  buildings . London: IStructE, 2010

6.3

7

Designers’ checklist

Note  the

checklist given in Figure 7.1 is intended to serve as a prompt to the designer. It only concerns the design of lateral load-resisting systems and is generic, to be considered with the project context in mind. Consideration

Section reference

 Actions – applied:

 Are minimum and maximum gravity load cases considered?

3.2.1

 Are wind, soil, ground surcharge and hydrostatic lateral forces considered?

3.3, 3.4

 Are accidental and extreme actions including impact, fire and earthquakes considered?

3.7

 Actions – induced:

Will actions result from the restraint of arches, domes, catenaries, nets?

3.2.2

Will actions result from initial imperfections?

3.2.3

Will actions result from inelastic strains?

3.5

Will actio ns result from the restraint of post tensioning and other elastic strains?

3.6

Second-order P D  effects

Is the structure sway sensitive/do P D effects need to be considered?

3.8

Combinations of actions:

 Are all governing combinations for all elements/failure mechanisms evaluated?

3.9

 Accommodating movement:

 Are movements understood and quantified?

3.5, 3.6

 Are any movement joints necessary and/or incorporated?  Are these accurately portrayed in the analysis?  Are significant movements resisted by the structure?  Are corresponding forces (actions and reactions) allowed for throughout the load path?

4.4

Does the design acknowledge force redistribution resulting from creep or ground movement?  Are all parts of the structure adequately served by load paths to ensure stability, noting load paths and movement joints are irreconcilable? How many independent structures exist; is each one stable? Load paths:

How do forces acting on the fac¸ ade transfer to the horizontal stability structures? Where the fac¸ade spans onto beams, are they restrained or bending in their minor axis? How do forces acting on the horizontal stability structures transfer to the vertical stability structures? How stiff are the horizontal stability structures and also the connections from the horizontal to vertical stability structures? How do forces transfer through the vertical stability structures? How are forces transferred from the superstructure into the substructure?

4.1, 4.2, 4.3

How are forces transferred from the substructure into the soil?  Are the interfaces of the above six line items each adequate?  Are there any aspects of the structure, small or large, that do not follow the normal pattern? Do these have suitable load paths of resistance?  Are all eccentricities accounted for in the analysis? Braced or unbraced:

Is the structure braced, unbraced, or a hybrid?

4.5

 Are effective lengths correctly determined, taking account of relative stiffnesses and joint rotations where necessary?

4.5.5

Design – stability, strength, service and robustness:

Is the structure in static equilibrium: rotational and linear?

2

 Are all elements and connections adequate to transfer the design actions?

4

 Are deflections, rotations and the natural frequency each within permissible bounds?

4.7

Is the structure deemed robust in the event of failure to any of the stability structures? Does the design safeguard against progressive collapse?

4.3.2

Designers’ checklist Consideration

Section reference

Construction:

Is the disposition of the stability system, and are all design assumptions communicated to the contractor?  Are all parties clear and in agreement on their responsibility? Is the transfer of information understood by and compatible to all parties. E.g., are actions characteristic or  factored values?

5

Where existing structures are involved, is the stability of these understood before demolition works start?  Are new and existing parts to be connected or isolated from one another?  Alterations and maintenance

Will new structure provide support to, or act on existing structures?  Are ‘as built’ records available for the existing structure?  Are these accurate to the structure and inclusive of any previous modifications?

6.1

Can elements within the completed structure be maintained?

6.2

Figure 7.1

Designers’ checklist for stability systems

Part 2: Framed bracing 8

Vertical framed bracing

8.1

Introduction Beam

‘Framed bracing’ (or simply ‘bracing’) is often the most material-efficient method of providing lateral stability in a framed structure. It is one of the two common systems that generally results in a structure being classified as braced (the other being shear walls; see Section 4.5), and is widely used to achieve both permanent and temporary stability. Similar to a cantilevered truss, bracing refers to diagonal elements that triangulate a frame (see Figure 8.1). This achieves a geometrically stable form with component elements working predominantly or purely in tension and compression. The result is a system with high major axis (in-plane) shear and flexural stiffness.

8.2

Structural form

Brace Column

Braced column set Figure 8.1

Braced column sets in elevation

steel construction where steel bracing elements are fabricated and erected as part of the frame contract. However, bracing is suitable in many more systems. Columns are typically continuous and there is no reason why bracing cannot be used in combination with continuous floor frames and/or rigid beam to

Bracing can be anything from temporary straps to mega-bracing. Figure 8.2 shows it in a number of  guises. All share similar fundamental characteristics. Permanent bracing is most often in the form of  storey-height ‘braced bays’. These are regular column and beam bays within framed structures that incorporate one or more diagonal elements. Once braced, the two flanking columns can be said to be a ‘braced column set’, and each of the columns, beams and diagonal braces that immediately make up the triangulation are component elements of the system; each subject to force resultants from horizontal and vertical actions. Braced bays may be subject to reversible actions. ‘Strut’ systems are those where all elements of the system can resist both tension and compression.  These systems require just three elements (one locked triangle) to resist reversible actions. ‘Tied’ systems are the common alternative having an element (usually the diagonal) that can only resist tension. These are only stable when the tie is in tension. Hence, structures incorporating ties must overcome load reversal by either incorporating crossed-ties within a single column set (‘cross bracing’) or by providing mirrored systems (see Figure 8.3 and Box 8.1). Strut systems can be crossed to increase the rigidity of a bracing bay and reduce individual element forces. This can have the added advantage of  reducing both the major and minor axes effective lengths of the elements (see Section 10.2.2). Bracing lends itself to use in ‘simple’ (pinned or nominally pinned) frame structures, particularly of 

Figure 8.2

Examples of vertical bracing

8.3

Vertical framed bracing

First

Ground

Figure 8.3 Vertical bracing configurations: three stable configurations, each showing tied bracing at first floor and strut bracing at ground floor, arranged to accommodate the doorways as shown

column moment frames. These approaches can achieve material savings, greater robustness and greater ductility but may add complexity to each of  the analysis, fabrication and erection. Bracing can be used with frames of all construction materials, though ties in the permanent works are almost exclusively steel (carbon or stainless). Ties are typically either flats, angles, rods or cables; each being sections that exhibit much higher tensile than compressive capacity. Struts are usually universal column (UC) or hollow sections when steel, or solid sections when timber or reinforced concrete. Irrespective of material, it is important that struts can withstand both tension and compression forces and are resistant to buckling when unrestrained.  A mix of both ties and struts can be used within a single building structure. Ties are slender elements that can be concealed within narrow stud partitions, positioned flat against solid walls (possibly within a cavity), or exposed in front of glazing. However, crossed ties will effectively block all corners to a structural column bay. Struts are often necessary in instances where doors, windows, or other penetrations are required (see Figure 8.3).  Ties are often used in preference to struts in low-rise frames where sway deformations are small. Taller structures, however, benefit from the added stiffness that struts achieve (see Section 8.3) and struts become the dominant choice for buildings greater than five or six storeys.

Box 8.1

8.3

Stiffness

Where sized for strength, struts are usually axially stiffer than ties. This is owing to the fact that struts are usually sized for unrestrained compression while ties are sized for tension.  The stiffness of ties can be enhanced for a given strength by adopting a lower grade of steel for these elements. This may be economical where the different grades are readily available. However, care is needed where grades are mixed within a single project. If the decision is made that a tie is to be a certain grade, then this should be applied as a rule to all ties on the job. Note  that,

though increasingly rare, material grade errors can occur at any stage in the fabrication/  erection supply chain. Hence, incidents are not limited to geometrically identical elements.

8.4

Force transfer

Figure 8.3 shows typical bracing systems where nodes coincide with the horizontal structure to the floors and roof. This is important, ensuring that the predominant actions transfer from the horizontal stability system directly into the bracing. Ignoring the stiffness of any continuous elements and/or rigid joints, axial forces are transferred through a system as shown in Figure 8.4.

Tied Melbourne Westpac Centre (formally the Melbourne Olympic Swimming Hall)

The Melbourne Westpac Centre is a symmetrically tied structure with ties on each of the two flanks to ensure stability during asymmetric load conditions. In this instance the ties are vertical. Flexural roof truss also acts as a tie

Tie

Strut

Strut Pool

Mass foundation

Thrust below pool tank 

Tie

Vertical framed bracing It should be noted that the tied system shows only tension taken in the ties. This is representative of  recommended modelling practice (see Section 9.3) for systems where the ties are able to bow or go slack.

Pinned connections

8.5

Slack ties sagging under self weight

Figure 8.4 illustrates how braced systems are compatible with simple foundation connections without moment transfer. Uplift, shown owing to the applied lateral forces, must be resisted by either the permanent mass of the structure (including the weight of the foundation) or a tensile resistance of the soil-foundation interface. Meanwhile the lateral shear force (often concentrated through one of the columns) must be resisted by friction and passive soil pressure on the foundation. It is common practice to provide a reinforced concrete ground beam across the column set to ensure the shear always acts on the more heavily loaded column, irrespective of load direction or brace configuration. A beam will also prevent differential lateral movement of the columns. Ground beams are included in Figure 8.3. While not included in Figure 8.4, local actions should not be overlooked. These may result from eccentric connections (see Section 10.3) or from actions applied directly to the constituent elements (see Figure 8.5 by way of example). In many instances, they will induce moments or torsional effects in elements which can critically impact the axial and shear capacities and must not be neglected. It is not advisable to have significant actions, such as those from a floor slab, acting on a bracing structure away from a braced node. A situation where this may be mistakenly overlooked is that of a braced stair core with half landing beams in the plane of the bracing (see Figure 8.6). Similar situations include multi-storey car parks with split level slabs and folded or pitched roofs.

8.5

Strut system

Tied system

Note 

Ties are shown slack and sagging under self weight where not subject to tension. This is i ntentionally shown exaggerated. Figure 8.4

Load path diagrams for tie and strut bracing systems (foundations not shown)

Wind

Bending moment in columns, loaded by cladding rails

Bracing angle

Bracing is most efficient where diagonal elements are inclined between 35  and 50  to the horizontal. This ensures relatively modest element forces and compact connection details. Narrow bracing systems with steeply inclined diagonal elements have less flexural stiffness, increased column forces and will increase the sway sensitivity; meanwhile wider bracing systems will increase element effective lengths (critical to diagonal struts and unrestrained horizontal beams) and often result in greater eccentricity at the nodes. 8

Local wind suction on side walls

8

Note 

The bending moment in the cladding rails is not shown. Figure 8.5

Local bending on fac¸ade columns coincident with bracing actions

8.5

Vertical framed bracing

Bracing to floor and stair slabs

No bracing to main floor slabs Poor detailing

Recommended detailing

Note 

The recommended arrangement may not be clear when shown on a plan drawing alone. Elevation drawings are recommended. Figure 8.6

Bracing to stairs with half-landing beams

9

Analysis of framed bracing

9.1

Static analysis

geometry and the stiffness of the individual bracing frames only.

 The static analysis of framed bracing systems can be straight forward when there are clearly defined load paths created by the discrete elements. It should take account of all critical combinations of actions and be either first order, first order with sway modifiers, or second order, as required to take account of P D effects (see Section 3.8).

 The centre of stiffness and forces acting on each bracing frame can subsequently be calculated using Equations 9.1 and 9.2. Both equations reference parameters labelled in Figure 9.2.

Note  that

Pð  ¼ P

a dynamic analysis may be required where a structure is subject to dynamic wind and/or seismic actions. Discussion of this is outside the scope of this Guide. Refer to the sources of further reading listed in Sections 3.3 and 4.6.  Apportioning actions between the individual bracing frames is typically the most demanding aspect of  static analysis as invariably there is indeterminacy in the system. Accurate apportionment requires evaluation of stiffness of each of the vertical bracing frames together with the stiffness of the horizontal diaphragm or horizontal bracing systems. With modern computer analysis methods, and numerous combinations of actions to be considered, this is often sufficient reasoning to evaluate a structure using a 3-dimensional computer model. General notes on modelling follow in Section 9.3.

Centre of stiffness, measured from an arbitrary datum:  x 

 x n 0 k n Þ  k n

Stiff diaphragm

Eqn 9:1

Orthogonal braces ignored

Independent structure across a movement joint considered separately

 .       J  .       M

Where hand calculations or simplified 2-dimensional models are preferred, methods exist to simplify the analysis. These are useful, in the least, for validating 3-dimensional computer analysis results; an exercise that all engineers should endeavour to undertake in all instances. The following section describes a simplified approach in more detail.

Stiff beam to represent floor diaphragm

Spring supports Figure 9.1

9.2

On-plan simplifications of structure

Approximate analysis methods ′

x n

 The guidance within this section should result in conservative, yet justifiable results for wellconditioned structures where the overall centre of  stiffness is within the middle third of the building.

x  x 

 Apportioning actions between vertical stability  systems  Two approximations can be made which reduce the complexity of the analysis significantly: – It is often acceptable to discount bracing systems that are perpendicular to the action where they are not essential for equilibrium. This leaves the engineer to consider only those bracing systems which provide a component of resistance in the direction of the action. – Where braced in plane or acting as a stiff  diaphragm, assume the horizontal structure is rigid. Otherwise, assume it is simply supported between vertical bracing systems.

x n

k n

e  P 

 These simplifications are shown in Figure 9.1, leaving a statically determinate structure that is dependent on

Figure 9.2

Apportioning actions between systems

9.2

Analysis of framed bracing

∆flexure

F 

∆shear

+

Elevation

∆

= Section  Acol

Acol d 

Figure 9.3

Frame stiffness

Figure 9.4

For systems with equal columns:

Force acting on the n’th bracing frame, P n  ¼

Pk n Pex n k n +  k n ð x n 2 k  n Þ

P

P

Parallel axis theorem

Eqn 9:2

where:  k n is the stiffness of the n’th element P  is the applied design force e is the offset of the applied design force from the centre of stiffness  x n0 is the offset of the n’th element from the datum  x n is the offset of the n’th element from the centre of stiffness. It is worth noting that all dimensions listed must be orthogonal to the direction of the action, and the stiffnesses must be the components parallel to the action. Evaluating stiffness System stiffness comprises a flexural component and a shear component. The flexural component will tend to dominate in taller, more slender braced column sets while shear will dominate in short, wide systems.  The stiffness of each stability system can be determined in turn by analysing the displacement resulting from an arbitrary force  F  applied to the system in isolation (see Figure 9.3 and Equation 9.3).

I  

 A col d 2 2

Eqn 9:4

where:  Acol is the cross sectional area of one column d  is the spacing of the columns.  The shear stiffness, GA s, can be approximated for common bracing systems using Equations 9.5 and 9.6. Both equations reference parameters labelled in Figure 9.5. For ‘K’ brace systems: GAs    sin 2 u cos uEAd

Eqn 9:5

For single strut systems: GAs  

cos u



1

sin2 uEAd

Eqn 9:6

  u sin EAh

þ

where:

u

is the angle measured between the diagonal and the vertical is the area of the diagonal is the area of the horizontal.

 Ad  Ah

Equation 9.6 for a single strut system simplifies to Equation 9.5 of a ‘K’ brace system when the beam is of high stiffness (i.e. when EAh  is much larger than EAd ).

Stiffness:  k n  ¼

 F  F   ¼ D ðDflexure þ DshearÞ

Eqn 9:3

where: D is the total displacement Dflexure is the flexural component of displacement, proportional to EI  Dshear is the shear component of displacement, proportional to GA s.  The major axis (in-plane) flexural second moment of  area, I , of individual bracing systems can be approximated using the parallel axis theorem, considering the cross sectional areas and spacing of  the columns (see Figure 9.4 and Equation 9.4).

 Ah

 Ah

θ  Ad

Av

Ad

θ

Figure 9.5

Shear stiffness

Av

 Analysis of framed bracing

Equations 9.5 and 9.6 are approximations, neglecting axial strains of the columns. Where column shortening is sufficient to cause ties to buckle or struts to experience significant permanent compression, a buckling analysis should be performed.

9.3

Note  that

    v

Skew bracing  The method described so far in Section 9.2 can only be used for components of stiffness parallel to the action. These can be evaluated for any skew stability system using equations derived from Mohr’s circle of  stress9.1. Equations 9.7, 9.8 and 9.9 are simplifications, true for systems that have negligible minor axis resistance. They reference parameters labelleled in Figure 9.6. I x x.n  ¼  cos2 fnI u u . n 2

    u

φ

.

x

Where φ = 90º  0 I xx = I vv I yy = I uu .

Eqn 9.7 Figure 9.6

I y y.n ¼  sin fnI u u . n

Eqn 9.8

I x y.n ¼  sin fn cos fnI u u . n

Eqn 9.9

where: I u u . n is the major axis stiffness for the n’th element is the angle to the major axis of the n’th fn element, measured anticlockwise from the global x-axis.  The parallel components of stiffness of multiple bracing elements (I x x.n, I y y.n  and  I x y.n ) can be combined by simple addition. Once this addition is performed, Mohr’s circle can be used to calculate the principal axes and magnitudes of stiffness of an entire structure.

9.3

Where φ = 0º I xx = I uu I yy = I vv  0

y

Computer analysis models

It is not the intention of this Guide to be a comprehensive resource for modelling best practice. Rather, this section identifies a number of practical and common lessons specific to the modelling of  bracing. Ties are non-linear   Ties are not linear-elastic in their behaviour when subject to compression. Few software packages take account of the buckling failure that causes this behaviour and will attribute elastic stiffness to even the most slender elements. This is false and it is important that ties are not modelled as normal linear perfectly-elastic elements. Instead, ties should be modelled as ‘tension only’ elements with non-linear material properties (see Figure 9.7). Most software packages allow this with either a toggle on the material properties or a toggle on the element type. Otherwise it may be possible to manually define a non-linear stress-strain characteristic for a user defined material.  An important consequence of this tension only behaviour is that it makes the whole model non-linear.  This invalidates superposition of results which necessitates that actions are combined prior to analysis, and each load combination analysed in turn. Engineers should check that this is correctly conducted by the software. Where a designer does not have access to software allowing tension only elements or materials, the same

Components of stiffness for non-orthogonal bracing (where I v v . n   0)

outcome can be achieved by modelling multiple copies of the structure, each one only containing the tie elements that are in tension for a given combination of actions. Connection eccentricities Models often represent ideal geometries and neglect connection eccentricities (see Box 9.1). Eccentricities will invariably lead to more onerous local effects to be considered in design and may also impact the stiffness of the assembly. Offsets provide one method of allowing for eccentricities without adding stub elements throughout a model. They can be used effectively to determine stress resultants (forces and moments) in elements but must not be used to over-simplify joints. Even with offsets, it is important the model includes sufficient nodes to represent each individual connection in turn. Where a brace fixes to a beam which fixes to a column, two nodes are needed: one for the brace-beam joint and one for the beam-column junction. Where a connection is particularly complicated or highly stressed, a stress design method may be necessary. 3-dimensional finite element models that are representative of the connection geometry are usually adopted in these instances. Connection defaults Some software packages assume continuity of  elements through nodes as a default. This is most common in the more traditional analysis packages which attribute section properties to 1-dimensional elements. To the contrary some of the more modern packages tend to model structural components and

ε

ε

σ

Linear perfectly-elastic

σ

Non-linear (tension only)

Figure 9.7 Linear and non-linear perfectly-elastic material stress strain graphs

9.4

Analysis of framed bracing Box 9.1

Braced node failure: Hartford Civic Center, Connecticut, USA, 1978

The collapse of the roof at Hartford Civic Center was in part attributed to incorrect modelling of braced nodes9.2. Local eccentricities, together with the weight of the node assemblies, were both overlooked.

floor beams across braced bays. They are also inappropriate where evaluating forces in horizontal systems, where considering transfer structures, or in instances where the effect of any kind of movementinduced actions (e.g. thermal expansion or post tensioning) is being assessed. Mass When modelling space frames and other highly efficient, lightweight structures, the additional mass at the nodes can be significant to the overall weight of  the structure. This is rarely included for in computer software and must be added as a superimposed action.

Further reading: computer modelling and analysis  As designed

 As built

The following texts are recommended sources of further  guidance on computer modelling and analysis: – Brohn, D. et al .  Modelling of steel structures for computer  analysis. SCI Publication 148 . Ascot: SCI, 1995 – MacLeod, I.A. Modern structural analysis: modelling  process and guidance . London: Telford, 2005

may have different connection/continuity defaults for components recognised as each of columns, beams and braces. Irrespective of the software, it is important the engineer understands the way in which element continuity and/or connections are modelled and corrects the defaults as necessary. This includes making allowance for any slotted (movement) connections and constructability details such as column splices. It is worth noting here that unstiffened fin plate connections offer very little minor axis moment resistance and should be modelled as pinned about the plate’s minor axis. Rigid constraints It can be common practice to use rigid constraints to model horizontal stability systems, linking all nodes within a single storey often to a common point of  loading. This is reasonable where a concrete slab or similar floor plate provides a stiff diaphragm (see Section 4.2). Engineers should be aware that rigid constraints between nodes on a floor plate mask axial forces in

9.4

References

9.1

Timoshenko, S.P. and Goodier, J.N. Theory of elasticity . 3rd ed. New York: McGraw-Hill, 1970

9.2

Johnson, R.G. Hartford Civic Center (Jan. 18, 1978) .  Available at: http://failures.wikispaces.com/  Hartford+Civic+Center+%28Johnson%29 [Accessed: 16 December 2013]

10 Design and specification of framed bracing

10.1 Introduction  This chapter considers the elastic design of bracing considering elements and nodes in turn.  Anet

Both elements and nodes should be designed for design actions determined via analysis, combining global actions with any local actions or effects, minimum eccentricities, minimum robustness forces and other code requirements.

 Agross (= A )

Note 

10.2 Elements

BS EN 1993 Part 1-1 Clause 6.2.310.1 requires that engineers check the resistance as:

(

N Rd =  A

10.2.1 Ties

 Ties should be designed for pure tension, considering each of the material yield strength and the material tensile strength at critical sections (each with appropriate material safety factors). Allowance must be made for bolt holes as these will lead to a reduced net section area, A net  (see Figure 10.1).  The engineer should consider the strength grade of  materials available for the sections considered. The primary production grades for steel flats and angles are often milder than those of beams, columns and closed sections. Meanwhile cables tend to be proprietary products, typically available with compatible fixings and turnbuckles in non-standard grades. Technical properties depend on the cable construction (see Figure 10.2) and the tensioning cycles sustained during manufacture. Capacities are usually quoted by manufactures often with values for both the yield and breaking point. In most applications, engineers should adopt the yield value (with further material factors of safety applied). When designing with cables, designers should be wary of the magnitude of embedment creep that a particular cable may experience when first loaded.  This is the extension over time resulting from the tightening up of the weave. Staged tensioning may be required to overcome this initial movement, often over a period of several months 10.2.  The design of rods is in many ways a middle ground between that of cables and plate. Rods are solid and do not experience the embedment creep associated with cables. They can be supplied by structural steel fabricators with welded plate connections.  Alternatively architectural-grade rod is available in much the same manner as cables. Where needed, this should be clearly specified by the designer. Rods may be used in preference to cables because they are axially stiffer. Cables are however easier to handle and can be transported in unrivalled lengths 10.3. Flats and angles are used primarily where aesthetics are inconsequential. They are also more common where forces are high; it is unusual to use cables and rods much larger than 30mm diameter in buildings, not least because the connections become unwieldy.

f y γM1

, 0.9 Anet

f u

 )

γM2 lesser

where:  A  Anet f y f u γM1, γM2

is the gross cross section area away from any holes is the net cross section area taking account of holes is the material characteristic yield strength is the material ultimate tensile strength are material partial factors.

Figure 10.1 Critical section checks for steel bracing, using Eurocode nomenclature

Figure 10.2

Cable constructions

Due to imperfection in the erection of a structure, one of the diagonal ties may be slack on erection.  Turnbuckles or threaded connectors can be used with rods and cables to overcome this tolerance (see Figure 10.3). Meanwhile flats and angles can have holes drilled on site. These measures can create a more aesthetically pleasing and visually reassuring structure but often have little impact on the stiffness. Where chosen, they should be specified by the designer. 10.2.2 Struts

Struts must exhibit resistance against buckling. Hence, they must possess flexural stiffness and their design is somewhat dependent on the connections. Where struts are nominally or truly pinned, they can be analysed and designed as pure-axial elements

10.2

Design and specification of framed bracing

with an effective length factor of 1.0 for compression in both the major and minor axes. Their length is typically measured between intersections of the column and beam axes; this will be longer than the length between connections, but allows for the finite buckling resistance provided by the beam, column and gusset plate.

Threaded U-bolt

With all other connection types, struts must be designed to resist the combined actions (forces and bending moments) transferring through the end connections. In such cases, the effective length of an element in compression will depend on the relative stiffnesses of its connections and connecting members.

Turnbuckle

Crossed struts with a central connection will have significantly different in- and out-of-plane effective lengths. Most benefit of the connection is to the in-plane effective length which will be approximately halved. Meanwhile the out-of-plane effective length will be reduced as described in Box 10.1.

Threaded rod

Figure 10.3 Box 10.1

Rod and cable connection details

Out-of-plane effective buckling length of crossed struts

The effective length of struts can be calculated from the elastic critical buckling force ( p 2E I  / ‘ 2 for a simple strut). Where struts are crossed, this can be established by considering the compression brace as a continuous strut with a central spring support. Effective length factors,  b  for crossed struts are contained within Annex D of BS EN 1993 Part 2 Table D.210.4. Factors are a function of each of the properties of the two brace elements, the ratio of forces and the connection condition at the intersection. Lines 1, 4 and 5 of the table are the cases most applicable to bracing. These lines are reproduced below: Z   ℓ 1 /2

N 

1

1

 /2  ℓ 

s k 

 ℓ 1 /2

b¼

 /2 ℓ 

N 

I 1

b¼

 ℓ 1 /2  ℓ   /2

ℓ   /2

I ‘1 3

s  ffiffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi 1  0:75

Z ‘ N ‘1

N 

but  b  0:5

s k 

 ℓ 1 /2

I 1 ‘3

but  b  0:5

Z 

N

3 Z ‘ 4 N ‘1

1þ

I 

Z 

4

v  uu ffiffi ffi ffi ffi ffi ffi ffi ffi ffi ut

I 1 Z 

Z 

b ¼ 0:5

 ℓ 1 /2

 /2  ℓ 

N

5

 /2 ℓ 

N 

I 1 Z 

where: out-of-plane second moment of area of the compression strut out-of-plane second moment of area of the tension strut

N  design compressive force Z 

N ‘1 1 Z ‘

s k 

 ℓ 1 /2

I  I 1

when

‘

coincident design tensile force length of the compression strut

‘1

length of the tension strut

b effective buckling length factor 

or when

EI 1 

3Z ‘1 2 4p2





N ‘1 1 Z ‘

Design and specification of framed bracing

It is uncommon to assume any partition or infill provides buckling restraint to a strut. This is due to the fact that the structural frame, and likely the floor slabs and external fac¸ ade, will be erected in advance of internal partitions. It is common therefore for single (non-crossed) struts to have similar major- and minoraxis stiffness except where the joints provide restraint or transfer significant bending moments. Circular and square hollow sections and open universal column sections are the most common for this reason. Other materials including timber and reinforced concrete tend to be solid sections. In most instances, struts must be designed for load reversal and tension should not be overlooked.  Though this is not typically critical in steel it can be significant in jointed timber or precast construction, or indeed in (albeit rare) braced  in situ concrete frames. Fatigue may need to be considered in severe cases of force reversal. This is outside the scope of this Guide. For an introduction, refer to the Institution’s Introduction to fatigue  technical guidance note 10.5. 10.2.3

Beams and columns

Beams and columns are key elements of a braced column set. They must be designed to resist the envelope of forces resulting from both vertical and horizontal actions, including axial compression or tension, bending and shear.  Away from braced column sets, beams may be subject to axial forces where transferring actions from the fac¸ade to a bracing bay (see Figure 4.1), contributing to a horizontal stability truss (see Figure 4.3), or transferring shear between bracing bays (see Figure 4.8).

10.3 Nodes 10.3.1

Connection types

Nodes can be monolithic but more often comprise connections between discrete elements. These can be pinned, semi-rigid or fully rigid. Wherever possible they should be of a standard type, suitable to the material. Connections that are truly pinned transmit only axial and shear forces. All other connections may also transfer some moment, the magnitude of which will depend on the stiffness of the connection and the connecting elements.

Intersection point of element axes

Figure 10.4 ‘noding-out’

Concentric connection showing elements

Even where a strut is assumed to be pinned, moments and/or buckling resistance may need to be designed for in the connection, especially where it is at a large eccentricity to the theoretical ‘pin’. Particular care should be taken when designing fin plate connections subject to large compression forces to ensure adequate minor axis (plate bending) capacity. 10.3.2

Concentric connections

 A concentric connection has the longitudinal axes of  all elements ‘noding-out’ at a common intersection point (see Figure 10.4). In an ideal form, this geometry enables actions to be resisted through pure axial forces only.  A concentrically connected frame can have all elements with pin connections. This is common in space frames (see Chapter 11) though is rare in standard bracing bays where at least the columns are typically continuous through the connection. Moments and shear can develop in a concentrically connected system, though only where joints are rigid or semi-rigid. Any such stress resultants are typically small owing to the flexural stiffness of elements being much less than their axial stiffness. 10.3.3

Eccentric connections

 Truly concentric connections are often hard to achieve in practice. They can lead to large gusset plates, especially where beams are deep and the bracing is at a shallow angle (both common traits of  wide column grids). In other circumstances nodingout is simply not practical, for example when using precast concrete where cover zones restrict the placement of anchors and tolerance is needed for erection. In such circumstances it can be either advantageous or essential to design for vertical eccentricities within a node (see Figure 10.5).

Further reading: standard connection details The following texts are recommended sources of further  guidance on connection details: – BCSA. Steel details . Publication 41/05. London: BCSA, 2005 – SCI and BCSA. Joints in steel construction: simple joints to  Eurocode 3 . SCI Publication 358. Ascot: SCI, 2011 – Institution of Structural Engineers and Concrete Society. Standard method of detailing structural concrete: a manual  for best practice . 3rd ed. London: IStructE, 2006 – TRADA. Concise illustrated guide to timber connections . High Wycombe: TRADA Technology Ltd, 2012

Figure 10.5

Vertically eccentric connections

10.3

10.3

Design and specification of framed bracing

Slack tie members

Figure 10.6 Eccentric connections for concentric elements, showing 1-D elements as they might be modelled

It is worth noting that local eccentricities can arise in the load path through connections even where the lines of action of the different elements are concentric. Examples are shown in Figure 10.6.  Vertical eccentricities change the geometry of bracing from inherently rigid three-sided triangles to flexible four-sided mechanisms. When included, structures must exhibit flexural stiffness (local portalisation) if  they are to resist deformation. This is usually achieved by providing columns that are continuous through a number of storeys and capable of resisting the local shear forces and bending moments (see Figure 10.7).  This provision will generally allow beams and diagonals to have simple connections. Separate to the above, there can be drivers to offset bracing on plan. Columns are typically wider than infill walls and it is often advantageous to the space planning to limit column outstands to one side of the

T  = Fe 1

Note: fin plate connections to tie beams provide little torsional resistance

e 1

Minor axis bending of beams transferred to slab via shear studs at eccentricity e 3 (slab not shown)

e 2

Torsion transferred to beams via bolts at eccentricity e 2. Results in minor axis bending of beams.

F 

Figure 10.8

wall only. Hence architects may ask to offset the bracing diagonals from the structural grid and column centreline. Such eccentricity can create local torsion and additional bending in the elements that must either be resisted in the frame or transferred into the slab (see Figure 10.8). Eccentricities should be considered whenever they have a significant impact on the elements and connection utilisation. As a guide, a 5 to 10% change in the utilisation factor is generally regarded significant, depending on the limiting utilisation factor throughout the design. 10.3.4

e 3

Tie beam

Figure 10.7 Bending moments with continuous columns and eccentric bracing (not shown, shear is the differential of the bending moment)

Resolving on-plan eccentricity via shear transfer into the slab

Central node in cross braced systems

Cross braced systems may or may not include a physical connection at the intersection of the diagonal elements. While a connection is of benefit to the effective lengths of struts, there is generally no structural need for a connection in tied systems. Rather, common reasons for connecting tie elements include: – To prevent elements bowing and colliding with one another, creating noise. – To avoid abrasive damage including damage to surface treatment. – To accommodate crossing elements in a single plane.  The nature of the connection varies depending on the nature of the elements. Three examples are shown in Figure 10.9. The first has elements continuous past the connection and would need the connection pin to transfer only a nominal force. Meanwhile the connections in the other two examples form part of  the load path and must have strength and stiffness appropriate for the forces in the bracing elements. 10.3.5 Slotted connections and translational bearings

Slotted connections and translational bearings bring a degree of freedom to a joint, allowing movement at the expense of shear transfer. Used incorrectly, they can cause a triangular frame to behave as a foursided mechanism. For this reason, they should be

Design and specification of framed bracing

Plates Figure 10.9

Rods/cables

UC or hollow sections

Central node connections in cross braced systems

detailed with extreme care when used between bracing elements. Despite the challenges, translational movement is sometimes beneficial in bracing frames. Figure 10.10, by example, identifies a scenario where the provision of a free movement joint may be needed to prevent vertical restraint between the bracing and the flexural floor structure. In this scenario, vertical fixity is often undesirable when using steel bracing with a reinforced concrete floor structure, or when postfixing bracing to an existing structure (be this either for secondary elements in a newly built frame or new structure being added to a historic frame as part of  remodelling or strengthening works). Bearings can be proprietary products or bespoke assemblies with contact surfaces usually coated with low-friction PTFE or bonded nylon. They are suitable for a wide range of forces but often require maintenance. They may also need to be detailed with ‘end stops’ to satisfy robustness criteria. Slotted or elongated bolt holes provide a more simple solution. However, they can have unpredictable friction and a tendency to lock or ‘bed-in’ when subjected to large or permanent forces.

Both slotted connections and bearings can be modelled for analysis using translational releases in the direction of the free movement. Analytically determined deflections at the appropriate limit state should be used to specify the length of travel. This must be specified together with the initial setting-out in the design documentation. 10.3.6

Pinned connections and articulation

In contrast to slotted connections, pins allow rotational movement and are easily accommodated in most triangulated structures. Pinned connections have little impact on the performance of bracing except where the structure includes significant eccentricities, or where the elements have particularly high bending stiffness that contributes greatly to the rigidity. While many fin-plate connections are nominally pinned, it can be advantageous to include true pins where significant articulation is anticipated. This may be prevalent where, for example, a steel diagonal brace is used in combination with a timber frame that will experience seasonal movement. True pins are also essential in any form of demountable structure.

Beam free to flex Detail A Slotted connection Rigid strut to strut connection Detail A – Option 1 (allowing deflection)

Struts rigidly connected or pinned to beam Detail A – Option 2 (fully fixed or pinned) Figure 10.10

Chevron brace to beam connection with and without a deflection head detail

10.3

10.4

Design and specification of framed bracing

10.4 References

Figure 10.11

10.1

BS EN 1993-1-1: 2005: Eurocode 3: Design of steel  structures. Part 1-1: General rules and rules for  buildings . London: BSI

10.2

Berenbak, J. et al . ‘The British Airways London Eye. Part 2: Structure’. The Structural Engineer , 79(2), 16 January 2001, pp19-28

10.3

Thornton, J.A. ‘The Design and construction of cablestayed roofs’. The Structural Engineer , 62A(9), September 1984, pp275-284

10.4

BS EN 1993-2: 2006: Eurocode 3: design of steel  structures. Part 2: Steel bridges . London: BSI, 2006

10.5

‘Introduction to fatigue. Technical Guidance Note 25 Level 1’. The Structural Engineer , 91(4), April 2013, pp36-37

Baseplate details for non-monolithic construction showing shear details

10.3.7

Column baseplates, holding down bolts and foundations

Braced columns and holding down bolts must transmit coincident horizontal shear and compression forces into the foundation. Where there is insufficient mass acting on the column to resist uplift, the connection will also have to transmit coincident shear and tension. Foundations are concrete in most instances. Where the superstructure is timber, steel or precast concrete, columns are traditionally anchored via bolted or dowelled column baseplates. Holding down bolts may be cast in or post-fixed and must have adequate tension capacity to resist pull-out from the foundation. The baseplate should be packed up off  the cast face of the foundation by 25 to 40mm to provide tolerance. This gap should be grouted once the frame is lined, levelled and tightened. It is not recommended that bolts are relied on to transfer shear. Friction between the baseplate and the grout may be used where the column is always under adequate compression. However, more robust details have the column base set into a pocket, or a shear key on the underside of the base plate extending into a smaller pocket (see Figure 10.11). With either detail, the brace should be connected to the column/  baseplate and not directly to the foundation.

11 Diagrids and other triangulated structural forms

11.1 Structural forms

of the fac¸ ade line. Here it is used on more modest medium-rise buildings.

 The triangle is a unique shape. Bounded by straight sides of fixed length, it is inherently stable and always planar without warp. Having previously defined framed bracing as the triangulation of a structure, this chapter introduces three framing systems that exploit the characteristics of triangles.

Diagrids and gridshells ‘Diagrids’ and ‘gridshells’ do away with conventional vertical columns, utilising the diagonal elements, together with the horizontal floor structure, to resolve both horizontal and vertical forces. Examples of  diagrids are shown in Figure 11.2.

Megabracing ‘Megabracing’ is conceptually an extension of the standard systems discussed thus far in Part 2. Here, the 2-dimensional planar triangulation that was introduced in Chapter 8 is scaled up and spans multiple storeys and/or column bays. Figure 11.1 shows three example projects.

Like megabracing, a diagrid is a planar or near-planar structure that requires orthogonal restraint from the connecting structure. Conversely, a gridshell is a 3-dimensional system. In a pure form, a gridshell can resist both in- and out-of-plane actions relying on curvature much like a membrane, dome or net to achieve stability.

Megabracing is most common in high-rise buildings where it is used to engage the full plan dimensions and maximise the stockiness of the stability structure. Neo Bankside however illustrates how it can be used to remove bracing entirely from both the envelope and the internal accommodation by placing it proud

Space frames ‘Space frames’ consist of 3-dimensional triangulation to create a stable form that can eradicate the need for both columns and beams. Though traditionally regular in form, elements can be arranged in many regular or irregular tessellating arrangements.

Figure 11.1

Examples of megabracing. From left to right: 8 Chifley Sq, Sydney; Bank of China, Hong Kong; Neo Bankside, London

Figure 11.2

Examples of diagrid structures. From left to right: 1 Shelley St, Sydney; Hearst Tower, New York; Aldar HQ, Abu Dhabi

11.2

Figure 11.3

Diagrids and other triangulated structural forms

Examples of space frame structures. From left to right: The Water Cube, Beijing; Federation Square, Melbourne; Stansted Airport, London

Figure 11.3 shows this variation, and also variation in the scale of the tessellating module.

11.2 Characteristics Each of the three framing systems introduced in the last section has a tendency to exacerbate particular characteristics of a braced frame. Some of these will pose specific challenges to designers 11.1. The following is an introductory list: – Standard robustness and fire guidance may not be applicable, increasing the likelihood that design parameters are project specific, determined via a risk assessment. – Eccentricities of large elements can cause substantial local forces and secondary effects. – Relative movements can be significant between elements of different scales, environmental exposure, actions and material.

Box 11.1

– Forces at corners of the building and discontinuities of the frame must be resolved. Floor diaphragms may not be adequate to restrain elements of the frame. Local stresses at connections between the frame and floor diaphragms must not be overlooked. – Secondary vertical stability systems may be necessary to stabilise storeys bypassed by the primary elements. – Thermal isolation and/or insulation may be required where elements of the structure are external. – Where differing to suit environmental conditions, internal and external metals must be compatible avoiding bimetallic corrosion. – Fabrication, transportation, and erection challenges may influence element and node designs, dictating maximum dimensions/weights. – The critical design conditions may occur during construction and may be highly sensitive to the erection sequence. Box 11.1 illustrates a number of these issues in the context of the Leadenhall Building.

The Leadenhall Building, London

The Leadenhall Building 11.2 contains a lateral and vertical force-carrying frame comprising both diagrid and megabracing systems. This nodes-out at every seventh storey, setting a module to the building’s form. A secondary chevron bracing system is provided to stabilise individual floors between the main node levels.

The primary frame is external to the building envelope, located within a ventilated fac¸ade. Differential thermal movements are significant and accommodated via sliding bearings to many of the floor connections. These allow horizontal movement where restraint is not necessary. Nodes bring together up to six in-plane elements, together with a perpendicular floor beam. Node units weigh up to 30 tonnes and were analysed using 3-dimensional finite element models. Elements are spliced using large diameter high tension threaded rods housed within the web of the section. Nuts were installed using compact tensioners that could be operated safely on site.

Diagrids and other triangulated structural forms

11.3 References 11.1

Hewitt, J. and Edwards, A. ‘The Structural design of One Shelley Street, Sydney’.  The Structural Engineer , 88(20), 19 October 2010, pp18-24

11.2

Annereau, N.  et al . ‘The Leadenhall Building’.  The   Arup Journal , Issue 2, 2012, pp67-76

11.3

Notation

 The following notation is used for hand drawn figures:  An applied force.  The dominant wind action.  An internal axial stress resultant acting through an element (shown here to represent compression).  A bending moment acting along an element (plotted on the tension face of the element). Transverse shear (not plotted) is the differential (gradient) of the bending moment.  A movement/displacement. Where shown in plan or 2-dimensional isometric, a vertical stability system (of either a framed brace, shear wall or moment frame unless defined). The  Guide  assumes such elements have no minor axis stiffness. Centre of stiffness. M.J.

Movement joint.

 The following notation is used in equations. Further notation is defined in the body text and within figures where used. Cross section area Shear area Young’s modulus of elasticity E  Shear modulus G Section second moment of area I  ei   Eccentricity  k    Stiffness e   Strain s   Stress f,  u Angle/Angular rotation d   Displacement  A

 As