Stability of Buildings Part 3 Shear Walls [PDF]

Zitiervorschau

Stability of buildings Part 3: Shear walls

March 2015

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 of the Reviewing Panel E Bennett MEng (Arup) O Brooker BEng CEng MIStructE MICE MCS (Modulus) 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) Acknowledgements The use of Arup internal guidance documents in developing this Guide 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: Figures 2.4, 3.1, 6.7, 6.8, 7.2: Arup Figure 7.11a: The Structural Timber Association Figures 7.11b, 7.14: Milner Associates Figure 8.2b: ‘Reinforced concrete frame with brick masonry infill walls, India’ by A. Charleson (GEM Nexus website [or http://www.nexus.globalquakemodel.org]) is licensed under CC BY 3.0 (http://creativecommons.org/licenses/by/3.0/) Box 3.2: J.K. Nakata, United States Geological Survey Box 3.3: Halcrow Atkins Joint Venture Box 6.3: SKM anthony hunts Boxes 7.1, 7.5, 7.6b: Arup Box 7.3: Wellcome Images Box 7.4: P Buffett Box 7.6a: Frank P Palmer All other photographs and all hand illustrations: A Gardner Published by The Institution of Structural Engineers, 47–58 Bastwick Street, London EC1V 3PS, United Kingdom Telephone: þ44(0)20 7235 4535 Fax: þ44(0)20 7235 4294 Email: [email protected] Website: www.istructe.org First published 2015 ISBN 978-1-906335-27-4 # 2015 The Institution of Structural Engineers

The Institution of Structural Engineers and those individuals who contributed to this Guide have endeavored to ensure the accuracy of its contents. However, the guidance and recommendations given in the Guide should always be reviewed by those using the Guide 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 and its contents is accepted by the Institution, the author, the consultees, their servants or 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 47–58 Bastwick Street, London EC1V 3PS, United Kingdom.

Glossary

The following definitions are provided to explain how the listed terms are used specifically in this Guide. They may differ to definitions found in other documents. Term

Definition

Action or load

An influencing effect, normally external to the structure, that causes movement, deformation and/or internal stresses. The two terms are largely interchangeable; ‘action’ is favoured by the Eurocodes while ‘load’ is more common throughout the design codes of English-language countries. Both terms are used herein.

Braced

Stabilised in sway by other connected elements or systems such that the subject element does not experience a significant sway moment. Structural elements or systems that are not braced are ‘unbraced’. The term braced is not to be confused with ‘bracing’ which is a type of structural component.

Centroid

The point on a cross-section, defined by the intersection of the neutral axes, through which a pure axial load will result in a uniform stress.

Coupled

Two or more elements with joints that resist longitudinal shear and make the flexural stiffness of the system greater than the sum of the parts.

Deflection head

A detail that allows differential vertical movement at the top of a non-loadbearing wall/panel. The detail may or may not provide in- and/or out-of-plane shear resistance.

Effective height

The length of an ideal pin ended wall that would have the same buckling load as the actual wall to which it relates.

Force

A type of action, causing both stresses and strains within a resisting static structure.

Horizontal stability system

An element, frame or assembly orientated in a horizontal or near horizontal plane that transfers lateral actions through the structure (generally connecting the fac¸ade to the vertical stability systems).

Hybrid system

A structure that contains more than one type of vertical stability system. This is usually with a combination of shear walls, framed bracing or portalisation.

In-plane

Characteristics (e.g. stiffness) or effects (e.g. actions) considered in a vertical plane that are orthogonal to a wall’s or wall system’s major axis. For a planar wall, these are the characteristics or effects in the plane of the wall. Out-of-plane characteristics or effects are those orthogonal to a system’s minor axis.

Insulated sandwich panels

Also known as ‘structural insulated panel systems’ (SIPS), a pre-cast composite wall element combining layers of materials to deliver structural and insulation (acoustic and/or thermal) performance. The structural component is typically either reinforced concrete or timber.

Lateral loadThe total structural system that acts to resist lateral loads comprising both horizontal and vertical stability resisting system systems together with fac¸ade elements (windposts, cladding rails, etc.) and the substructure. Length

The longer plan dimension of a wall. For planar walls, this is orthogonal to the major axis.

Loadbearing

A wall that resists vertical actions. Walls that resist in-plane lateral forces but not vertical actions are defined as ‘non-loadbearing’ herein. Meanwhile partitions and fac¸ade elements that only resist out-of-plane local pressures are defined as ‘non-structural’.

Load path

The complete route by which any applied or induced stress is transmitted through a structure to the foundations via a system of interconnected elements.

Modular ratio

The ratio of moduli of elasticity for two composite materials. In the context of reinforced concrete, it is the ratio of the steel modulus divided by the concrete modulus.

Non-structural

An element that can be removed without detrimental impact on the retained structure.

Precast

Used generically for any construction process that is not completed in situ. This includes processes that are more accurately described as pre-formed or pre-assembled.

Secant modulus The average gradient (stiffness) plotted as a straight line between two defined points on a stress–strain curve. It of elasticity differs to the tangent stiffness which is the gradient of a tangent to the stress–strain curve at a given point on the curve. Shear centre

The longitudinal axis through which a transverse shear will cause a linear displacement without twist, and about which a torque will cause pure rotation.

Slender

An element that is prone to buckling at a load less than the material strength would imply. Structural elements that are not slender are ‘stocky’.

Soft storey

Those storeys that have undergone ill-conceived structural alterations leading to a structural system that is particularly highly utilised and vulnerable to failure.

U-value

The thermal transmittance of a material, it is a measure of the power loss per metre squared per degree Kelvin temperature gradient (standard units W/m2/K). It is the inverse of the thermal resistivity.

Vertical stability system

An element, frame or assembly orientated in a vertical or near vertical plane that transfers lateral actions through the structure (generally down towards the ground). These systems form part of the lateral load-resisting structure.

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Notation

The following notation is used for hand drawn figures: An applied force An applied bending moment A movement/displacement An out-of-plane surface pressure Centre of stiffness Lateral restraint Solid wall section Structural lintel beams across wall openings Components of stiffness

The following notation is used in equations. Further notation is defined in the body text and within figures where used. A E G I J L Le b k t

e s t

Cross-section area Young’s modulus of elasticity Shear modulus Section second moment of area Section torsion constant Wall height Effective wall height Wall cross-section length on plan Stiffness Wall cross-section thickness Strain Normal stress Shear stress

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Contents

Foreword vi

7 7.1 7.2 7.3 7.4

Part 3: Shear walls

7.5

Glossary iv Notation

v

Introduction

2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 2.10

Design overview 4 Form and configuration 4 Resistance and force transfer 4 Failure mechanisms 5 Materials 6 Monolithic and jointed construction 6 Coupled behaviour 6 Buckling and buckling restraint 6 Slenderness and effective heights 7 Limit state philosophy and initial wall sizing References 10

3 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8

Requirements of walls 11 Introduction 11 Wall locations 11 Non-structural partitions and non-loadbearing panels 11 Cores 12 Vertical access and transportation 12 Service risers and distribution 14 Insulation and compartmentalisation 15 References 15

4 4.1 4.2 4.3 4.4 4.5 4.6

Elastic theory of thin-walled sections 16 Introduction 16 Complementary shear 16 Torsion 16 Warp and warp restraint 16 Lintel beams in sections subject to torsion 18 Centroid and shear centre 19

5 5.1 5.2 5.3

Modelling and analysis 21 Introduction 21 Modelling simplifications 21 Modelling vertical stability structures 22 5.3.1 1-dimensional element models 22 5.3.2 Grillage models 26 5.3.3 2-dimensional finite element models 28 Modelling horizontal stability systems 30 Manually apportioning actions between vertical stability systems 31 Modelling boundary conditions 31 Elastic and plastic analysis 32 References 32

5.6 5.7 5.8 6 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8

8 8.1 8.2 8.3 8.4

Shear infill panels 53 Introduction 53 Common characteristics of infill systems Masonry infill panels 54 References 56

7.6 7.7 7.8

1

5.4 5.5

7.9

Non-monolithic shear wall construction 40 Introduction 40 Precast construction 40 Precast reinforced concrete wall construction 42 Hybrid precast in situ reinforced concrete wall construction 43 Timber and light gauge steel ‘platform’ frame construction 45 Mass timber 47 Loadbearing masonry 49 Steel plate diaphragm walls in steel framed buildings 51 References 52

1

53

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Monolithic reinforced concrete shear wall construction 33 Introduction 33 Modelling the stiffness of concrete 33 Ultimate and serviceability limit state design of reinforced concrete sections 34 Concrete classes 35 Minimum wall thickness 35 Reinforcement and embedments 35 Construction 36 References 39 The Institution of Structural Engineers Stability of buildings Part 3

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Part 3: Shear walls 1

Introduction

This Guide is the third part in a four-part series on lateral load-resisting ‘stability’ systems for buildings. Its focus is the use, analysis and design of shear walls. Walls have provided stability to buildings intentionally or otherwise for many centuries. They are almost exclusively vertical and are inherently stiff in-plane. However, perhaps more significant to their widespread application, walls are essential components of most buildings to divide space and isolate environmental conditions. This remains as true today as it has done throughout history and it is rare that the structural design of walls is devoid of non-structural criteria. Continuing to evolve are acoustic, thermal and fire criteria together with material technologies and construction techniques. Relatively recent changes in building form have seen an ascendency in open-plan, flexible accommodation, paired with ever taller and larger buildings. Through this evolution, framed structures have come to the fore and walls have become engineered systems that fulfil specific criteria. Modern construction distinguishes between non-structural ‘partitions’, ‘cladding’ and ‘fac¸ade’ elements that are isolated in-plane from the structure on the one hand, and ‘structural walls’ that transfer in-plane forces on the other. Within the subset of walls classed as structural, walls can resist vertical forces, in-plane horizontal forces, out-of-plane horizontal forces or a combination thereof (Figure 1.1). Walls that resist in-

Vertical actions

In-plane horizontal actions

Out-of-plane horizontal actions

Figure 1.1 Actions on structural walls

plane horizontal forces may be termed shear walls, cross walls, spine walls, raking panels or vertical diaphragms. These terms are largely interchangeable, though each has origin in a different material trade. To avoid ambiguity, the term ‘shear wall’ is adopted generally throughout this Guide. A further term ‘shear infill panel’ is used to describe the subset of walls that resist only in-plane lateral loads (i.e. not vertical loads). Meanwhile, the term ‘wall system’ is used herein to discuss any arrangement of coupled shear walls. This Guide discusses walls that are planar, flanged or arranged as a core. The torsional behaviour of these wall systems is given specific attention – with Chapter 4 dedicated to fundamental theory. Chapter 5 discusses modelling techniques focusing mainly on computer analysis methods. This Guide describes common characteristics of shear walls before considering various constructions in turn. These are split into three categories: in situ monolithic shear walls (Chapter 6), non-monolithic shear walls (Chapter 7) and non-vertical loadbearing (non-loadbearing) shear infill panels (Chapter 8). Relevance and aims This Guide is an introduction written primarily for design engineers, particularly those approaching a professional review. Together with Part 1 of the Institution’s sister publication Stability of buildings, Parts 1 and 2: General philosophy and framed bracing, it introduces many generic principles – theoretical and applied – that are associated with shear wall design. However, it is not the intention that this Guide provides detailed ‘how to’ instructions on design, and reading it will not automatically make a designer proficient to work autonomously. Rather, this Guide aims to supplement supervised learning by increasing background knowledge on the topic. To this end, we hope the Guide helps promote a thoughtful attitude towards design that is based on a breadth of knowledge. Finally it is important to note that this Guide is not limited to a discussion of ‘best practice’ systems. Chapters 7 and 8 intentionally include a variety of systems not all of which are in favour, at least in the UK. These systems exist in buildings standing today and many of today’s engineers will be required to carry out designs for retrospective alterations. This is the motivation for including any guidance on controversial systems. Further reading: stability The following text is a recommended source of further guidance: – Institution of Structural Engineers. Stability of buildings. Parts 1 and 2: General philosophy and framed bracing. London: IStructE, 2014 The Institution of Structural Engineers Stability of buildings Part 3

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Introduction Designers’ checklist Actions – applied: Are minimum and maximum gravity load cases considered? Are wind, soil, ground surcharge and hydrostatic lateral forces considered? Are accidental and extreme actions including impact, fire and earthquakes considered? Actions – induced: Will actions result from the restraint of arches, domes, catenaries, nets? Will actions result from initial imperfections? Will actions result from inelastic strains? Will actions result from the restraint of post-tensioning and other elastic strains? Second-order PD effects: Is the structure sway sensitive/do PD effects need to be considered? Combinations of actions: Are all critical combinations for all elements/failure mechanisms evaluated? Accommodating movement: Are viable movements understood and quantified? 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? Does the design take due account of 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 systems? Where the fac¸ade spans onto beams, are they restrained or bending in their minor axis? How do forces acting on the horizontal stability systems transfer to the vertical stability structures? How stiff are both the horizontal stability structures and 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? How are forces transferred from the substructure into the soil? Are the interfaces of the above six line items 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? Are effective heights correctly determined, taking account of relative stiffnesses and joint rotations where necessary? Design – stability, strength, service and robustness: Is the structure in static equilibrium: rotational and linear? Are all elements and connections adequate to transfer the design actions? Are deflections, rotations and the natural frequency each within permissible bounds? Is the structure deemed robust in the event of failure to any of the stability structures? Does the design safeguard against progressive collapse? Construction: Is the disposition of the stability system, and are all design assumptions communicated to the contractor? 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? 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? Can elements within the completed structure be maintained? Figure 1.2 Designers’ checklist for design of lateral load resisting stability systems 2

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Introduction Limitations This Guide does not cover general considerations of lateral load-resisting ‘stability’ systems or the broader topics of actions, movements and load paths. These are discussed in Part 1 of this series. It is recommended that designers familiarise themselves with this before embarking on a stability design. Figure 1.2 reproduces the designers’ checklist from Part 1 for quick reference. Note that the checklist given in Fig. 1.2 is intended to serve as a prompt for designers. It only concerns the design of lateral load-resisting systems and is generic, to be considered with the project context in mind. In line with Part 1 and Part 2 of this series, earthquake design is largely omitted from this Guide. So too are the advanced topics of non-linear and dynamic analysis. Each of these is introduced in Part 1 but is considered too advanced to be catered for in this introductory text.

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2

Design overview

2.1

Form and configuration

There are three basic types of structure that include shear walls (Figure 2.1): – Cellular structures with vertical loadbearing shear walls. – Framed structures with vertical loadbearing shear walls. – Framed structures with non-loadbearing shear infill panels.

(a)

Each contains wall elements that are generally much stiffer in one principal axis than they are in the other. However, how these elements behave is largely governed by whether they are isolated (and acting as a uniform planar section) or coupled (and acting as a compound section). Examples of each are shown in Figure 2.2. Within a building, isolated or coupled walls can be arranged in any configuration that provides: – Adequate resistance in two orthogonal horizontal directions – Adequate torsional resistance – Adequate robustness

(b)

Note that, in this context, ‘resistance’ should be interpreted to mean both stiffness and strength. Fig. 2.1 shows the three structural types idyllically in isolation but they can equally contribute to a hybrid system. Two examples are shown in Figure 2.3: one with the different systems acting in a single axis and the other with the different systems acting orthogonal to one another.

2.2

Resistance and force transfer

Shear walls act as vertical stability systems within load paths that extend from a building’s extremities to its foundations. They are generally regarded as primary structure and provide relatively stiff resistance

(c) Figure 2.1 Structural forms: (a) cellular, (b) framed with loadbearing walls, (c) framed with infill walls to vertical and horizontal actions acting in their plane. In this way they transfer forces vertically to their founding structure. This transfer is via an internal stress distribution that results from compatible axial, shear, torsional and flexural strains.

Flanged

Tubular ‘core’ Coupling across openings

                         

Coupling at intersections

(a) Figure 2.2 Wall systems: (a) isolated, (b) coupled 4

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(b)

Design overview

2.3

components, local strengthening with additional elements/reinforcement and/or local restrictions on the placement and size of wall or slab penetrations.

Shear walls Framed bracing

In multi-walled statically indeterminate structures, the relative stiffness of each wall together with its boundary conditions will influence the distribution of forces between walls. The wall-floor connections can be considered as one set of boundary conditions and the founding structure another. None will be of infinite stiffness and collectively there can be significant stiffness variation within a structure. The rotational stiffness of the founding structure and translational stiffness of the floor systems tend to have greatest impact. Note that any movement joints form boundary conditions with zero stiffness in the axis of the free movement. This is critical when devising the stability strategy and is discussed in more detail in Part 1 of this series2.1.

Shear walls Framed bracing / Shear walls Figure 2.3 Example hybrid stability systems The overall height to length aspect ratio of a wall, together with the material characteristics, will often govern whether shear or flexural stresses dominate the global behaviour. Shear tends to govern in short, stocky walls and it is usually acceptable to dismiss in-plane flexural deformation for walls with a height to length (L/b) ratio of less than 2. Conversely, taller more slender walls are dominated by flexure. Joint slip in precast assemblies and local deformations around voids in coupled walls will, however, influence the global behaviour and can lead to complex stress distributions in which plane sections do not remain plane. Actions may apply directly to a wall (e.g. gravity acting on the wall’s mass) but a large component of the total action tends to transfer from the connecting structure (usually via beams and/or the slab at each floor – Figure 2.4). This can cause stress concentrations at the wall-floor connections that extend into both the wall and the surrounding floor. Common options to overcome insufficiencies in these connection regions include increasing the wall/slab thickness, increasing the size of any connection

2.3

Failure mechanisms

The ultimate limit state of a shear wall may be governed by one of four mechanisms shown in Figure 2.5. These mechanisms are additional to the equilibrium failure modes that include ‘rigid-body’ overturning and sliding. The critical mechanism will be dependent on all aspects of the wall: its geometry, loading, material properties, restraint, and construction. While failure could occur anywhere, ill-conceived joints are particularly vulnerable and can create paths of weakness in non-monolithic structures. This is, however, generally to be avoided as it can lead to poor robustness. Note that the failure mechanisms listed are those resulting from vertical (axial) and in-plane horizontal actions only. Walls with significant out-of-plane horizontal actions may also fail in minor axis bending or shear.

2.4

Materials

Reinforced concrete, masonry and timber are the most common materials for shear wall construction worldwide.

(a) Figure 2.4 Wall-floor beam connections showing steel beams and reinforced concrete core wall

(b)

(c)

(d)

Figure 2.5 Structural failure mechanisms: (a) tension and/or compression, (b) horizontal shear, (c) vertical shear, (d) buckling The Institution of Structural Engineers Stability of buildings Part 3

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2.5

Design overview Masonry and reinforced concrete are widely available, have high compressive strength and are noncombustible. They also both allow large, heavy panels to be constructed in situ with manageable constituents. Timber, used mostly as an engineered product, is lightweight and sustainable when sourced from managed plantations. It is however combustible and the least stiff of the materials listed. It also suffers from significant shear deformation and can suffer dimensional instability. Steel diaphragms are used in substitution for reinforced concrete in certain regions including North America and North East Asia. These are suitable for reasonably tall structures. Meanwhile modular steelconcrete hybrid systems (e.g. Tata Corefast2.2) are available and can be favourable where the speed of construction is critical2.3. Plasterboard is a recognised option for sheathed panels in lightly loaded modest structures (e.g. English Building Regulations Class 1 structures2.4) although wood-based sheathing (e.g. plywood) is widely considered more robust. Other materials including glass and composites have been used for structural walls when warranted. These are however highly specialist, non-standard, and are outside the scope of this Guide.

Monolithic and jointed construction

Structural shear walls fall into two categories: in situ and monolithic or precast with joints. Only in situ reinforced concrete leads to structures that can be considered wholly monolithic. All other materials tend to result in structures made up of parts and joints. The implications of each are discussed in more detail in Chapters 6 and 7.

2.6

Coupled behaviour

Many wall systems, monolithic or jointed, contain coupled panels (Fig. 2.2). The panels that make up these systems may be in a single plane framing openings with coupling beams (lintels) above and below the opening; otherwise they may be nonplanar with multiple wall planes joining to form a flanged or channel section in plan. Two neighbouring wall panels can be considered coupled when the interface transfers longitudinal (vertical) shear to resist the deformation mode shown in Fig. 2.5(c). This stress arises whenever a section experiences a flexural or restrained warping stress and its magnitude is dependent on the stiffness of the coupling element. Depending on this stiffness, the performance of a coupled section will fall between that of: – An ideal uniform element of similar gross plan cross-section. – The combined performance of the independent (non-coupled) component parts.

Plan:

Elevation:

Stress: (a) Figure 2.6

2.5

(b)

(c)

(d)

Stress distributions for planar walls: (a) solid, (b) and (c) coupled, (d) discrete

It is important to appreciate that coupling enhances the overall flexural stiffness disproportionately to the shear stiffness. For buildings of equal overall stiffness, one containing coupled walls will deform more in shear (and less in flexure) than one with isolated walls. This change to the deflection bias can heighten the relative sensitivity of the coupled wall structure to second order PD effects2.1. In a similar light, coupling may influence the torsional stiffness disproportionately to the flexural stiffness (see Section 4.5). The coupling effect is illustrated in Figure 2.6 for a series of planar walls, and Figure 2.7 for a non-planar arrangement. Both figures plot the longitudinal stress resulting from a major axis bending moment. In reality, longitudinal shear deformations together with joint slip (where joints are present) can impact on this stress distribution.

Plan:

Elevation:

2.7 Stress: (a)

(b)

(c)

Figure 2.7 Stress distributions for flanged walls: (a) perfectly coupled, (b) partially coupled, (c) discrete 6

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Buckling and buckling restraint

Shear walls and panels subject to in-plane shear and/ or axial compression are vulnerable to buckling failure if slender. Three modes can act: – Euler major axis (in-plane) buckling due to axial compression – Euler minor axis (out-of-plane) buckling due to axial compression

Design overview

Vz Nx

Nx

Pinned

δy

2.8

Rigid or semi-rigid

δy

δz

Rigid x

x

y z

y

Pinned or rigid

x y z

Shear walls

z

Moment frame

Figure 2.9 Comparison of behaviour of shear wall and moment frame structures

Figure 2.8 Buckling modes for walls subject to in-plane shear and axial force

– Lateral torsional (out-of-plane) buckling due to an in-plane (major axis) bending moment

adopted by BS EN 19962.5 and BS EN 19922.6 respectively.

These are shown for a planar wall in Figure 2.8 but may apply to walls of more complicated crosssection geometry.

More recently, the slenderness ratio has also been defined as a function of the resistance without buckling divided by the elastic critical bucking load. This is the definition used, for example, by BS EN 19932.7.

Individual shear walls can often be regarded as statically determinate ‘unbraced’ cantilevers in their major axes. Floor systems will usually provide an inplane link between walls but do not normally provide a significant coupling effect. This differentiates the majority of shear wall structures from moment frames (Figure 2.9).

The slenderness ratio relates to a ‘slenderness limit’ that is the cut-off between elements being classed ‘slender’ (and thus vulnerable to buckling) or ‘stocky’. Both the ratio and the limit must always be taken from the same code. Slenderness of unrestrained wall system The slenderness of an unrestrained wall system concerns global buckling and is a function of the

x

z y

L (Ley = Lez = 2L)

Both lateral torsional buckling and Euler buckling can apply simultaneously, impacting on the axial compression and major axis bending moment capacities of a wall. However, only one Euler mode will govern; whether this is in the major or minor axis is dependent on the effective unrestrained heights and flexural stiffnesses of the wall in each of these axes.

The minor axis may similarly be unbraced, in which case minor axis Euler buckling will always govern over major axis. A single central core is a common scenario when this may apply (Figure 2.10). Alternatively, an individual wall may be restrained at discrete points through its height. Restraint can be to each or either of the major and minor axes of a system. However, in practice, it is almost exclusively applicable to the minor axis of a wall system with low minor axis stiffness (‘low’ stiffness being measured relative to the stiffness of the restraining systems (Figure 2.11).

Figure 2.10 Euler buckling effective heights of an unrestrained system

z

x y Slenderness is a measurement used to combat the buckling in members subject to axial compression. A similar approach is used for walls as is used for columns. The ‘slenderness ratio’ of a wall is traditionally defined as a function of the effective height divided by either the effective thickness or the radius of gyration of the wall section. These definitions are

Lez

Slenderness and effective heights L (Ley = 2L)

2.8

Figure 2.11 Euler buckling effective heights of a system restrained in the minor axis The Institution of Structural Engineers Stability of buildings Part 3

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2.8

Design overview overall height of the wall L. The effective height Le is that of a strut or cantilever that is free at its tip (Fig. 2.10). Slenderness of restrained wall systems and component parts The slenderness of a restrained wall system, or of a restrained component within a system, primarily concerns the spacing of the restraints. Restraint can be provided by floor diaphragms linking between a number of vertical stability systems (Fig. 2.11). Vertical return walls within non-planar coupled wall systems may also provide restraint to individual panels. Thus a single wall panel can be: – Restrained along one edge (Fig. 2.12(a)) – Restrained along two opposite edges (Fig. 2.12(b)) – Restrained along two adjacent edges (Fig. 2.12(c)) – Restrained along three edges (Figs 2.12(d) and 2.12(e)) – Restrained along four edges (Fig. 2.12(f )) These restraint conditions influence the effective height, usually by means of a factor applied to the actual wall dimension and/or restraint spacing. Each of the Institution’s manuals on concrete2.8 (Section 5.6.2.1) and masonry2.9 (Section 5.3.2) define simplified factors for walls restrained along two opposite edges (i.e. one-way spanning braced walls). The latter also defines factors for braced masonry walls restrained on three and four edges. Meanwhile, Clause 12.6.5.1 of BS EN 1992 Part 1-12.6 lists simplified factors for lightly reinforced concrete walls restrained along three and four edges. In accordance with Clause 5.8.3.2(7), these factors may be used for normally reinforced concrete. BS EN 1992 Part 1-12.6 Clause 12.6.5.1(3) and the Institution’s manual for masonry2.9 each give guidance on the disposition of return walls necessary

br >

(a)

(b)

(c)

(d)

(e)

(f)

Notes a Condition (a) is unrestrained and equivalent to the condition shown in Fig. 2.10. b Condition (b) is equivalent to the conditions shown in Fig. 2.11. Figure 2.12 Wall panel restraint configurations to act as vertical edge restraints; further simplified guidance for small buildings of traditional (masonry) construction is contained in the English Building Regulations2.4. Figure 2.13 illustrates the requirements for concrete walls as set out in BS EN 19922.6. Where these, or similar, rules are not achieved by a return wall (i.e. the return wall is too small), the return can be counted as part of the panel’s geometry contributing towards the effective thickness or radius of gyration. To this end, the arrangement shown in Fig. 2.13 may be regarded

L 5 b Restraint from slab diaphragms top and bottom

hr > 0.5h

h

Return wall Subject wall

where: b is the length of the wall L is the height of the wall h is the thickness of the wall br is the length of the return (supporting) wall hr is the thickness of the return wall

L

Short stub wall inadequate as a restraint but may count towards the subject wall’s effective thickness or radius of gyration

Figure 2.13 Illustration to support BS EN 1992 Part 1-1 Table 12.1 and Clause 12.6.5.1(3) 8

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Design overview as two panels, each locally restrained on three sides (Figure 2.14). Carefully located and sized return walls can have a considerable enhancing effect on the slenderness of individual panels. To work most efficiently, return walls should be of sufficient length to provide edge support to the adjoining panel, but not be so long that they become critically slender elements in themselves. When a wall is classed as slender (with the slenderness ratio above the slenderness limit) the design must account for second order effects. This may be conducted via a non-linear second order analysis. Alternatively many codes allow simplified methods. The most common is to design for a moment that must be considered in addition to the actions resulting from first order linear elastic analysis. This additional moment makes allowance for the tendency to buckle by assuming the axial force acts eccentric to the section. BS EN 1992 Part 1-12.6, by example and specific to reinforced concrete, includes two alternative methods to account for this additional moment in Clauses 5.8.7.3 and 5.8.8.2. Further reading: slenderness and effective heights The following text is a recommended source of further guidance on slenderness and effective heights of reinforced concrete shear walls: – The Institution of Structural Engineers (2014) Technical Guidance Note 10 (Level 2) ‘Design of reinforced concrete walls’, The Structural Engineer, 92(4), pp36-40

2.9

Limit state philosophy and initial wall sizing

Analysis at the ultimate limit state (ULS) may consider only those components of the structure that are essential to the principal load path. Meanwhile, analysis at the serviceability limit state (SLS) should consider all components of the structure that may undergo elastic deformation.

Figure 2.14 Restraint conditions for the wall shown in Fig. 2.13 (exploded view)

This is a significant difference, not to be overlooked. Taking a monolithic slab spanning a narrow doorway between walls as an example (Figure 2.15): in the absence of a lintel a slab will contribute very little coupling stiffness between walls. It is generally inadequate to provide meaningful coupling effect and can therefore be ignored at the ultimate limit state. However, in service, the degree of deformation caused by the connection must be assessed for adequacy to ensure the slab does not become unduly strained. Serviceability performance criteria can often govern shear wall design, whether it be movement, acceleration, cracking, another characteristic, or a combination thereof that dominates. Both deflection and dynamic behaviour are related to stiffness which is in turn dependent on geometry and material elastic moduli. Height to length (L/b) ratios are a useful starting point for sizing walls and/or choosing viable systems. Table 2.1 lists guide values for a number of materials and constructions.

Wall

Pinned strut

Slabs

Real structure

SLS model

ULS model

Figure 2.15 Ultimate and serviceability models of a monolithic wall and slab system The Institution of Structural Engineers Stability of buildings Part 3

9

2.9

2.10

Design overview Table 2.1 Typical height to length ratios for common materials Material and construction

Typical L/b ratios

Reinforced concrete – in situ

7 to 10

Reinforced concrete – precast

5 to 8

Masonry – unreinforced

1.5 to 2.5

Timber – cross laminated

3 to 4

Timber – sheathed panels

1 to 2

Steel plate diaphragms

7 to 10

where: L is the overall height of the wall. b is the overall length of the wall on plan. Notes a These are guide ratios only; they are not rules and design solutions may fall outside the ranges given. b Ratios are derived for wall sections without dominant openings (i.e. where the second moment of area, I, is proportional to L4 and vertical shear deformation is not exceptional). c The performance of any specific structure at any nominated ratio will depend on the loading which is usually a function of the tributary load area and/or building mass.

2.10 References 2.1

Institution of Structural Engineers. Stability of buildings. Parts 1 and 2: General considerations and framed bracing. London: IStructE, 2014

2.2

Corus. Bi-Steel design and construction guide. Scunthorpe: British Steel, 1999

2.3

Gough, V. ‘Fast steel cores’. New Steel Construction, 14(5), May 2006

2.4

HM Government. The Building Regulations 2010. Structure: Approved Document A (2004 edition incorporating 2010 and 2013 amendments – for use in England ). London: NBS, 2013

2.5

BS EN 1996-3: 2006: Eurocode 6 – Design of masonry structures – Part 3: Simplified calculation methods for unreinforced masonry structures. London: BSI, 2006

2.6

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

2.7

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

2.8

Institution of Structural Engineers. Manual for the design of concrete building structures to Eurocode 2. London: IStructE, 2006

2.9

Institution of Structural Engineers. Manual for the design of plain masonry in building structures to Eurocode 6. London: IStructE, 2008

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The Institution of Structural Engineers Stability of buildings Part 3

3

Requirements of walls

3.1

Introduction

Together with floor slabs, walls are often integral components in the form, environment and function of a building. In this way they differ from columns, beams and foundations that usually satisfy structural functions only. This chapter introduces a number of non-structural performance requirements. It focuses on the direct and/or indirect effects these have on the structural design.

3.2

Wall locations

The placement of structural walls will always be linked to the architecture and building function. Some buildings present more opportunities for walls than others; cellular single-occupancy dormitory buildings are one extreme while open-plan offices, arenas and industrial buildings are at the other (Box 3.1). Structural engineers should not take for granted that structural walls can be included in the fac¸ade especially where large doorways are required. Natural ventilation and/or daylighting requirements can dictate strict criteria for the geometry of windows, while the installation and maintenance strategy for significant plant or operational equipment may affect the permanence of parts of the fac¸ade. Similarly structural engineers should consider all special storeys that might break the continuity of the vertical structure from one storey to the next. By example ground floors, basement levels and any internal plant floors will often have very different functional requirements to typical floors. These requirements may prevent walls being continuous from one floor to the next and heighten the risk of localised instability (Box 3.2). Box 3.1

Requirements for, and the likelihood of, future layout changes should be considered when planning structural walls. While cellular construction is often efficient as designed, the widespread structure can be prohibitive to future changes of use. This can lead to low whole-life efficiency if the inflexibility of the layout becomes the cause of premature decommissioning or major structural remodelling works. Hence it can be advantageous to design for fewer structural walls especially where the walls are only lightly stressed. Additional partitions can then be added and removed as non-structural items. Note that any remodelling of the structural walls will usually affect the horizontal stability systems and the foundations in addition to walls that form part of the remodelled load paths.

3.3

Non-structural partitions and non-loadbearing panels

Partitions that are temporary are not suitable for use as structural stability elements unless the design specifically allows for the partitions to be removed. Nonstructural partitions should be considered as nothing more than superimposed mass and a surface attracting lateral actions that transfer to the adjoining structure. Walls that are discontinuous from one storey to the next may be used as non-loadbearing shear infill panels within a frame (Chapter 8). They are, however, generally not suitable as vertical load carrying shear walls unless they land upon suitable transfer structures that transfer both vertical and horizontal loads to structural elements continuing below. Any non-structural partitions or fac¸ade elements should be installed with connections that can accommodate in-plane differential movement. This is

Traditional cellular construction

Many cellular buildings including schools, hotels, prisons and student accommodation adopt a regular wall arrangement with transverse ‘cross walls’ between rooms and longitudinal ‘spine walls’ flanking a central corridor. Spine walls are generally punctured by doorways and service routes. Meanwhile the fac¸ade is often non-structural to permit unobstructed glazing, a proprietary fac¸ade system, and/or doorways. Spine wall

Cross wall Non-structural façade Doors and service voids to corridor

The Institution of Structural Engineers Stability of buildings Part 3

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3.4

Requirements of walls Box 3.2

Local storey instability and alterations

A single storey may be the cause of an instability failure where it provides particularly little resistance, measured relative to the action. This can occur in new structures but often comes about through ill-conceived structural alterations to existing buildings (e.g. the removal of walls to create open-plan accommodation). Where alterations have a detrimental effect on the resistance, the resulting storey is often dubbed a ‘soft storey’. Despite the name, a soft storey is not necessarily the weakest storey in a structure. Rather, it is the part of the structure most vulnerable to failure. This could be one of the strongest storeys (e.g. the ground floor storey which is subject to maximum shear force). Further information on structural alterations can be found in Part 1 of this series3.1.

Global sway failure to prevent unintentional load paths that could otherwise lead to premature failure of one or more panels. Removed from the load path, these nonstructural elements must not be relied upon to provide any in-plane resistance or stiffness. However, they must be self-stable in all unrestrained axes and of adequate strength and stiffness to withstand direct actions (e.g. wind pressure) without loss of integrity.

3.4

Cores

Most multi-storey buildings contain at least one core housing communal services including stairs, lifts, toilets and service risers. These often have walls continuous up the height of the building that are most likely suitable to be used as primary components of a building’s structure (Figure 3.1).

Whether a building has centralised or dispersed stairwells is often a function of emergency egress criteria. These criteria, together with the functional brief, inform the initial concept developed by the architect. However, while the building layout is fluid, structural engineers can contribute structural drivers into the mix, collaborating with the wider design team to guide the architect through the early space planning. Important structural drivers may include: – symmetry and/or eccentricities – linear stiffness – torsional stiffness – movement joints – foundation requirements and avoidance of transfers The importance of these is discussed in Part 13.1. When a building’s form can accommodate or favours a non-structural core, the core becomes nothing more than a series of slab penetrations, superimposed actions and non-structural partitions (supported either at intervals through the superstructure or cantilevering from the foundation). Non-structural cores can be advantageous when the structural design is progressing ahead of other disciplines, or when the building services are significant and likely to change markedly during the life of the building (e.g. in industrial buildings). Otherwise, precast non-structural lift (elevator) shafts that are independent of the structure are increasingly common in low-rise steel framed structures (Figure 3.2).

3.5

Figure 3.1 Structural core walls under construction for a 400m tall tower 12

The Institution of Structural Engineers Stability of buildings Part 3

Local member failure

Vertical access and transportation

Counter to the scenario shown in Fig. 3.2, it is convenient in many structural systems to surround stair and lift shafts with coupled structural shear walls in the form of a flanged or tubular core (Fig. 2.2). This minimises the need for walls or bracing elsewhere throughout the structure, while it also increases the efficiency by which fire compartmentalisation can be achieved (if required).

Requirements of walls Where the walls are working hard (typically in taller buildings) there may be no alternative but to use all the available enclosure as structural elements. In this case, care is needed to make the wall spanning the doorways thick enough to accommodate the stress concentrations around the openings. Irrespective of whether the wall containing the doorways is structural or not, it is recommended that doorways are not located immediately adjacent to a structural return wall (Figure 3.3). It is better to have an adequate offset from the flanking wall to: – provide support to the lintel beam – provide rotational stiffness at the lintel to wall junction – decrease the minor axis slenderness of the return wall It should be noted that the decision on the placement of doors is typically at the behest of the architect and not the structural engineer. The engineer should make recommendations to the architect at the earliest appropriate time. Note The steel frame is independently stabilised, in this instance with framed bracing. Figure 3.2 Non-structural precast lift shaft providing support to lift guide rails only

Both lift and stair shafts require access openings, usually regular in size and location at every storey. The result is often a ladder effect, with planar sections of wall punctuated in a regular arrangement, as shown in Figs 2.6b, 2.6c and 3.1. Penetrations the size of doorways and stacked one above another will often have significant impact on the behaviour of a wall, bringing into play the coupling effects introduced in Section 2.6. Where possible there may be advantages in making the penetrated walls non-structural and discounting them from the analysis. Among other benefits, this allows the structural design to proceed in advance of precise locations and sizes of the doors being known. It also allows for delayed construction and the future removal of the non-structural element, possibly needed for the installation and replacement of a lift car. A drawback however is the loss of torsional rigidity that comes with an open section (Chapter 4).

Unrestrained wall end

Lifts Specific to lifts, overruns are often necessary at both the top and bottom and often define the vertical extents of the walls. These may have an impact on the design actions, the global slenderness, and the interfaces with other structural components (the roof, substructure or transfers). Lift systems will often require smooth, accurately formed internal walls, constructed to tight tolerances and without projections (e.g. surface-mounted connections). BS 5655-63.2, by example, recommends that shafts should be sized with a 50mm tolerance zone provided to all four sides for lifts up to 20 storeys, with an additional 1mm per storey up to a maximum of 100mm for lifts over 70 storeys. Although critical, internal shaft dimensions often remain in abeyance through much of the design development until the preferred lift manufacturer is contracted (often past the point at which the architectural space planning becomes fixed). The structural engineer should bear this in mind, stating any assumptions on preliminary drawings, and possibly allowing tolerance when initially sizing the walls to ensure adequate thickness in the event that the internal shaft dimensions increase.

Wall end restrained by return

Short wall return to provide restraint

Lintel continuous into wall

Doorway with lintel

Door with lintel

Wall thickness often governed by lintel

Poor

Improved

Non-structural surround to doorway

Max. flexibility

Figure 3.3 Positioning large penetrations in walls The Institution of Structural Engineers Stability of buildings Part 3

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3.5

3.6

Requirements of walls Box 3.3

Stair core buildability at Bond Street Station, London

The images below show the construction and permanent conditions of the over-site development commissioned as part of the Bond Street Underground Station upgrade in Central London.

Temporary (construction) stage

Permanent stage

Here, stair flights and sections of floor slabs were omitted throughout the duration of the superstructure construction. This was to allow for a temporary crane hall within the stair core footprint that provided construction access to works on the station tunnels below. The omission of the stairs meant that the planar shear wall, which is situated on the perimeter of the building adjacent the site boundary, was unrestrained in the temporary condition. Temporary bracing could not be provided as it would have impeded the crane hall. Instead the wall had to be designed for the temporary unrestrained condition. Temporary loads included all the selfweight of the complete superstructure plus concentrated crane loads from construction equipment supported off the wall.

Stairs More so with stairs than lifts it is important that the structural design engineer understands the sequence of construction, the dependency of the walls on the stairs as means of restraint, and the robustness requirements of any joints3.3. Each can influence the fixings embedded in, or post-fixed to, the walls and the nature, alignment and magnitude of the reaction forces. Short-term buildability logistics should also be thought through. Where stairs are precast or prefabricated they may be craned in from above, or need to be manoeuvred through adequately sized openings in the walls. Other in situ stairs may require formwork or temporary work platforms. Finally, where the stair flight provides permanent lateral restraint to the walls, temporary bracing may be needed prior to the stair being completed. Without temporary bracing, walls may need to be designed for a governing temporary condition (Box 3.3).

Non-structural partitions to risers

Penetrations to partitions

Structural core

Penetrations in slab diaphragm Figure 3.4

Penetrations to service risers 14

The Institution of Structural Engineers Stability of buildings Part 3

3.6

Service risers and distribution

Service risers are shown on architect’s drawings as box-outs, cupboards or small rooms, typically with door or hatch access from each floor. Traditionally they were quite small. However this has changed as buildings have become more heavily serviced and safe installation and maintenance provisions have become mandatory. Risers are often clustered around stair and lift cores: – to minimise impact on a building’s plan layout – to be close to the main circulation routes – to be accessible from communal areas While functionally ideal, this is not without challenges to the structural engineer. Most risers require large voids in the floor diaphragm to fulfil their function and allow vertical service distribution through the height of the building. Voids in the walls (additional to any doors) are also required to allow horizontal distribution of the services out to the floors (mostly into false floor and ceiling voids). These wall voids often limit the opportunity to use riser walls as structural elements. However, the voids in the floor diaphragms which are close but external to a structural core can be equally troublesome, impacting on the load path between the wider floor diaphragm and the structural walls (Figure 3.4). Horizontal service distribution routes to each storey generally follow circulation corridors above ceilings and below floors. They invariably track into the cores, passing through, under or over critical lintel beams. Any services passing across structural wall lines should be thoroughly coordinated by the different engineering disciplines. This is best conducted by first setting clear parameters early in the concept stage to define the zones that can and cannot be assumed by the different engineering disciplines. Zones overcome

Requirements of walls the need to know exact penetration sizes. However, it is recommended that structural engineers do understand the nature of absolute penetration dimensions to better identify and collaboratively resolve conflicts. Insulation, isolation and minimum separation distances3.4, together with practical installation tolerances3.5, can add significantly to the dimensions of ducts, pipes and cable trays typically cited on the service engineer’s drawings. Further reading: vertical transportation and service integration The following texts are recommended sources of further guidance on service integration: – McKenna, P.D. and Lawson, R.M. Design of steel framed buildings for service integration: interfaces. SCI Publication 166. Ascot: SCI, 1997 – Co-Construct. Services integration with concrete buildings – Guidance for a defect-free interface. IEP 3/2004. Bracknell: BSRIA, 2004 – Co-Construct. Services coordination with structural beams. IEP 2/2003. Bracknell: BSRIA, 2003

3.7

achieved by meeting minimum cover and concrete class criteria; for steel it may be via an insulating barrier layer (e.g. intumescent paint or a solid boxout); meanwhile for timber, a sacrificial char layer or an insulating barrier are common. Finally a need for moisture resistance may be defined either by the serviceability requirements of the accommodation or by any degrading effects of moisture on the material of the construction (e.g. rusting of steel, leaching of calcium from mortar, rotting of timber, etc.). Further reading: moisture and water resistant wall construction The following texts are recommended sources of further guidance on moisture and water resistant wall construction: – Institution of Structural Engineers. Design and construction of deep basements including cut-and-cover structures. London: IStructE, 2004 – Mott MacDonald Special Services Division. Water-resisting basement construction – a guide – safeguarding new and existing basements against water and dampness. CIRIA Report 139. London: CIRIA, 1995

Insulation and compartmentalisation

Requirements for thermal insulation, acoustic insulation, moisture resistance and fire compartmentalisation often impose performance criteria on walls. Each of these is typically dependent on the complete wall construction (including non-structural parts such as insulation and protective coatings) and can benefit from cavity or sandwich wall systems. The peripheral detailing can also be influential: voids, edge details and anything that detrimentally ‘bridges’ the favourable constituents of the wall will often govern. Thermal insulation is usually defined by a system’s U-value. Design values are normally established by a mechanical or building environment engineer and should satisfy legislated requirements (e.g. those criteria set by the English Building Regulations Part L3.6). Acoustic insulation is similarly defined by a sound reduction index (SRI) which is a logarithmic function of the construction’s transmission coefficient (the ratio of incident to transmitted sound energy)3.7. The design value is normally established by an architect, possibly in consultation with an acoustics specialist, and may be based on occupancy-specific guidance such as that published in Building Bulletin 933.8. Meanwhile, fire performance is defined by a timebased rating that concerns each of: – the structural adequacy (i.e. the ability to fulfil a structural function) – the integrity of the system (i.e. the ability to compartmentalise a space without breach) – the insulation of the system (i.e. the ability to contain heat) The fire rating is usually established by the architect, often in consultation with a fire engineer, the client’s insurance manager, mechanical engineers (involved in the design of a sprinkler system), and the local fire authority. It will often have a direct impact on the structural design, the detail of which varies by material. Fire rating for concrete components may be

3.8

References

3.1

Institution of Structural Engineers. Stability of buildings. Parts 1 and 2: General philosophy and framed bracing. London: IStructE, 2014

3.2

BS 5655-6: 2011: Lifts and service lifts – Part 6: Code of practice for the selection, installation and location of new lifts. London: BSI, 2011

3.3

Billington, C. ‘Achieving robustness of precast concrete stairs using proprietary cast-in inserts’. The Structural Engineer, 92(2), February 2014, pp34-36

3.4

Ministry of Defence. Space requirements for plant access, operation and maintenance. Defence Works Functional Standard Design & Maintenance Guide 08. London: HMSO, 1996

3.5

BS 8313: 1997: Code of practice for accommodation of building services in ducts. London: BSI, 1997

3.6

HM Government. The Building Regulations 2010. Approved Document L1A: Conservation of fuel and power in new dwellings; Approved Document L2A: Conservation of fuel and power in new buildings other than dwellings [2013 edition for use in England]. London: NBS, 2014; Approved Document L1B: Conservation of fuel and power in existing dwellings; Approved Document L2B: Conservation of fuel and power in existing buildings other than dwellings (2010 edition incorporating further 2010 and 2011 amendments). London: NBS, 2011

3.7

BS 8233: 2014: Guidance on sound insulation and noise reduction for buildings. London: BSI, 2014

3.8

Department for Education and Skills. Acoustic design for schools: a design guide. Building Bulletin 93. London: The Stationery Office, 2004 [Section 1 updated by Education Funding Agency. Acoustic performance standards for the priority schools building programme. 2012. Available at: https://www.education.gov.uk/ publications/standard/publicationDetail/Page1/BB93] The Institution of Structural Engineers Stability of buildings Part 3

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3.7

4

Elastic theory of thin-walled sections

4.1

Introduction

Often subject to both linear and torsion actions, shear wall systems experience various stress components. How these interact and cause compatible deformations (strains) is critical to the behaviour and must be captured in the analysis. A wall system can be considered analytically as a collection of 2-dimensional elements. However, most wall systems can also be approximated as thinwalled 1-dimensional elements that are regular along their vertical (longitudinal) axes. In this way classical beam theories can be applied.

4.2

Complementary shear

As thin-walled systems, it is acceptable to neglect through-thickness stresses in most walls. However, complementary stresses must be considered inplane; anywhere a shear is applied (from either a linear or torsional action), an equal shear stress must occur on all four through-thickness faces of a infinitesimally small cut block. This is to maintain equilibrium (Box 4.1). Box 4.1

2-dimensional complementary shear of a thin-walled structure

Consider an infinitesimally small block subject to uniform shear stress t1:

t

Longitudinal shear due to flexure is one example of complementary shear. Box 4.2 gives the general equation for an ideal 1-dimensional element; all elements that maintain a plane section when subject to flexure must be able to transfer a stress derived in accordance with Equation 4.1 through any longitudinal plane. A similar longitudinal shear stress acts in all walls subject to flexure. However the magnitude of the stress deviates from that given in Equation 4.1 if plane sections deform. This deviation is critical to the analysis of coupled wall systems. Anywhere a lintel beam or joint is less stiff than the equivalent solid section, the shear stress across the weakened section will decrease while the shear stresses in the monolithic sections will increase (Figs 2.6 and 2.7). Overall this ensures shear equilibrium but equates to a loss of gross section stiffness.

4.3

Torsion

Box 4.3 shows two mechanisms by which torsion is resisted within elastic sections. The first is with a linear stress profile that acts through the thickness of all parts of the cross-section (Box 4.3a). This is referred to as St Venant’s resistance and it acts irrespective of whether the section is open or closed. The second mechanism has a uniform stress profile and acts only within closed sections (Box 4.3b). The second mechanism generates a resistance which is proportional to the square of the area enclosed by the closed section and tends to dominate over St Venant’s resistance where applicable.

4

4.4

Warp and warp restraint

1

a

Complementary longitudinal shear stresses exist with both resistance mechanisms introduced in Section 4.3. Where unrestrained, these stress profiles cause warp: a minimum-energy longitudinal deformation that distorts plane sections.

3

2

b For vertical equilibrium:

t1at ¼ t3at

!

t1 ¼ t3

For moment equilibrium: b 2

b 2

a 2

a 2

t1 at þ t3 at ¼ t2 bt þ t4 bt ! t1 þ t3 ¼ t2 þ t4 For horizontal equilibrium:

t2bt ¼ t4bt

!

Hence:

t1 ¼ t2 ¼ t3 ¼ t4 16

The Institution of Structural Engineers Stability of buildings Part 3

t2 ¼ t4

Open sections that are subject to torsion and are free to warp exhibit uniform deformation along their length. However, when warp is restrained with one or more sections held plane, the deformation cannot be uniform and axial stresses develop proportional to the restraint stiffness.

Elastic theory of thin-walled sections Box 4.2

Transverse and longitudinal complementary shears resulting from flexure

Vz

Cross-section area A Neutral axis of gross cross-section

z Vz t

Longitudinal complementary shear

Myy

Vz

Shear stress Vertical normal stress

For elements that deform such that plane sections remain plane, the longitudinal shear stress tx can be derived by evaluating Equation 4.1:

t2 ¼

Vz Az Iyy t

. . .Eqn 4.1

where: Vz is the applied transverse shear force Az is the first moment of area of the cut section measured about the neutral axis of the gross section Iyy is the second moment of area of the gross section t is the thickness of the cut section Both Az and Iyy should be measured about an axis orientated perpendicular to the shear force.

Box 4.3

Shear stresses resulting from torsion for (a) an open section and (b) a closed section

Enclosed area Ω to centre of walls Cross-section:

(a) Open section

(b) Closed section

Through-thickness stress: St. Venant’s stress

St. Venant’s + Uniform stress stress

St. Venant’s stress The shear stress at the extreme fibres tmax and the torsion constant J are given by Equations 4.2 and 4.3 respectively: 3T bt 2

. . .Eqn 4.2

n 1X bt 3 3

. . .Eqn 4.3

tmax ¼ J¼

The Institution of Structural Engineers Stability of buildings Part 3

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4.4

4.5

Elastic theory of thin-walled sections Box 4.3

Continued

Note that Equations 4.2 and 4.3 apply where b
t and for small rotations where the global flexural stresses due to rotational deformations (Figure 4.1) are small. Uniform stress of a closed section The uniform component of shear stress t and the corresponding torsion constant J are given by Equations 4.4 and 4.5 respectively:

t¼

T 2T V

. . .Eqn 4.4

4V2 J ¼ð 1 ds t where: T t b V Ð ds

is is is is is

. . .Eqn 4.5

the applied torque the section thickness the cross-section length of the elements that make up the section the area enclosed by the centrelines of the walls forming a closed section the line integral of elements within a section

Thus warp restraint is a third mechanism by which torsion can be resisted. The resulting stress profile is additional to those shown in Box 4.3 and is commonly known as ‘warping stress’. It is associated with the local in-plane bending resistance of the individual wall panels as the section twists (Figure 4.1). Importantly, warp restraint increases the rotational stiffness of a section but in doing this it adds to the longitudinal stresses in the wall. Stresses tend to peak close to the restraint and diminish moving towards unrestrained ends (Figure 4.2). Shear walls extending to foundations are generally considered fully restrained at the base and free to warp at the top. Other shear walls (e.g. those terminating on transfer beams, or infill panels situated within a framed system) may have less rigid warp restraint as a function of the supporting element’s stiffness. In either instance, the longitudinal stresses should be

Flanges bend as section twists

Figure 4.1 In-plane bending of individual wall panels due to twist 18

The Institution of Structural Engineers Stability of buildings Part 3

considered in the walls and also as actions on the supporting structure (Figure 4.3). Longitudinal stresses due to restrained warp are most pronounced in open sections and can be of similar order to stresses resulting from flexure. Closed sections have significantly larger torsional resistance (Box 4.3) rendering the effect of restrained warp usually negligible, while circular sections are the only sections where restrained warp causes zero additional stress (as circular sections do not warp).

4.5

Lintel beams in sections subject to torsion

When an open channel twists, the section naturally wants to warp causing the wall ends to displace longitudinally in opposite directions. This longitudinal unrestrained movement is vertical in walls (Figure 4.4). Lintel beams locally close the section and partially restrain this movement forcing compatibility of stresses and strains across the opening. In doing this, they resist warp and can add significant torsional stiffness. The lintel beam experiences significant inplane (vertical) shear and bending; stresses that induce a complementary horizontal shear. This circulates through the closed section causing an increased torsion constant locally in the section with the lintel (Box 4.3). In turn, this enhanced stiffness reduces the tendency for rotation and warp, increasing the overall torsional stiffness of the whole system. The vertical stresses in walls resulting from torsion will vary significantly with the stiffness of the lintel beam. Even relatively shallow lintel beams can result in a considerable increase in overall torsional stiffness, resulting in an equally considerable drop in vertical warping stress in the walls and acting on the restraining foundations or transfer structures. However, engineers must be mindful that any weaknesses in the lintel (e.g. those resulting from

Elastic theory of thin-walled sections

Original shape

Free

4.6

Height

Approaches constant shear

Approaches constant rate of rotation

Rota t

ion

Section deforms through full height with constant shear and rate of rotation

r

Shea

Restrained Shear rotation Free to warp

Restrained warp

Figure 4.2 Free and restrained warp of an open channel section service penetrations) can have a significant detrimental effect. This sensitivity emphasises the importance of developing a coordinated scheme that makes adequate provision for service distribution voids and doorways alike (Chapter 3).

4.6

Centroid and shear centre

Two centres govern the behaviour of a section: the centroid and the shear centre:

– The centroid is significant for axial (vertical) forces; an axial force through the centroid results in pure axial strain – The shear centre is significant for transverse (horizontal) forces; a horizontal force through the shear centre results in pure shear (without torsion) It should be noted that torsion and warp relate to the vertical axis that runs through the shear centre equivalent to how flexural deformations relate to a section’s neutral axes. Both centres lie on axes of symmetry and are only coincident when a section is doubly-symmetrical. The

Original shape

Wall

Restrained warp stresses across interface

Restraining structure (substructure or transfer) Figure 4.3 Warp restraint reactions (exploded view)

Open section

Closed section

Figure 4.4 Warp deformations across openings with and without lintel beams The Institution of Structural Engineers Stability of buildings Part 3

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4.6

Elastic theory of thin-walled sections shear centre can be derived by considering the equilibrium of complementary shear stresses in a section subject to a transverse shear. A simplified statically-determinant example for an open channel section is shown in Box 4.4. In practice the shear centre of a flanged or tubular wall system will be dependent on the stiffness of the coupling within the section. The shear centre may also vary through the height of the building if the wall section changes.

Box 4.4

Shear centre of a regular channel section

The following is a simplified derivation for the shear centre of a regular channel section with constant thickness t and equal flange lengths B. It simplifies the minor axis inertia of the channel to that of the two flanges only. It is accurate when the minor axis inertia of the web, measured about the section’s neutral axis, is negligible.

F

Further reading: elastic theory

A

The following texts are recommended sources of further guidance on elastic theory: – Millais, M. Building structures: from concepts to design. 2nd ed. Abingdon: Spon Press, 2005 – ACI 445.1R-12: Report on torsion in structural concrete. Farmington Hills, MI: ACI, 2012

B QF t

D/2

D/2

Qw

QF Shear in flanges: from

ð

t dA ! QF ¼

FB 2D

Shear in web: from vertical equilibrium Qw ¼ F Moments about shear centre: FB B D  FA ¼ 0 ! A ¼ 2D 2

20

The Institution of Structural Engineers Stability of buildings Part 3

Introduction

A model is a tool for analysis being a representation of a structure, its physical behaviour and the forces and environmental conditions to which it is subject. All models are a simplification in one way or another: whether they only represent part of the structure, part of the behaviour, or part of the exposure conditions. In most cases, the simplest possible model to achieve the goal should be used. This will usually be the easiest model to interrogate, update and (perhaps most importantly) check. The method of analysis and modelling should be actively planned by the lead structural engineer. Decisions should be recorded to assist both colleagues and checkers. This is best done by way of a documented modelling plan contained within the calculations and model files. In planning a model, it is important the engineer considers all parameters that could be critical (Box 5.1). Knowing how sections behave when loaded and how behaviours are represented by various model techniques is fundamental; Chapter 4 provides important background reading relevant to the discussion that follows on 1-dimensional element models. Box 5.1

5.2

Modelling simplifications

The analysis of shear walls is a key part of a project’s design development, from concept right through to detailed production information and checking. The rigour with which a structure is modelled should reflect the design stage, certainty and risk. Figure 5.1 presents possible model options; these options make reference to element dimensions defined in Box 5.2.

Single 1-D element approximation

There is very little dispute that computer analysis can be far more powerful than more traditional methods. However, while the following sections refer mostly to computer methods, there is rarely a project that cannot start with simple hand calculations as part of the conceptual design. These should not be underestimated. Not only do they provide focus leading to coherent concepts but they also provide information against which more detailed computer outputs can be appraised. Parts of the discussion herein can be applied to hand calculations just as it can to computer methods. Note that differences between computer output and results obtained via hand calculations must always be examined and justified.

1-D element grillage approximation

2-D finite element approximation Limit on model accuracy Real-world structure testing

Modelling parameters

The following is a list of common modelling parameters and associated considerations that can influence the accuracy of a model: – Applied actions: type, location, relationship to original and deformed geometry, variability – Boundary conditions: location, stiffness/fixity, strength, variability – Imperfections of the structure: material moduli, densities, setting out errors, out-of-plumb errors, locked in assembly/ casting stresses – Construction sequence: staged loading, temporary conditions – Material behaviour: elastic, plastic, brittle, ductile – Non-linear behaviour: material non-linearity (including shrinkage, creep and cracking), action non-linearity (including PD effects), reaction non-linearity, element buckling, global buckling, plastic hinge failure – Model compatibility: are the parameters compatible across all models being used to analyse a structure?

Increasing computing power

5.1

Simplifications

Modelling and analysis

Ease of interpretation

5

Figure 5.1 Modelling options and complexity

Box 5.2

Modelling dimensions

Wall sections are typically modelled using 1- or 2-dimensional elements. These element dimensions have no relation to the dimensions of the model as a whole: – 1-dimensional elements connect two node points defining a line. They usually exhibit constant properties along their length and closely resemble linear elements within a frame structure – 2-dimensional elements connect three, four, six or eight points arranged as either a planar triangle or quadrilateral. They exhibit properties in two orthogonal axes and can closely resemble both walls and floor slabs.

1-D element

2-D element

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5.3

Modelling and analysis

Real structure Figure 5.2

(a)

(b)

(c)

1-dimensional element models of a structure: (a) grillage model, (b) single element per wall system model, (c) single element amalgamated model

It is worth noting that it is often advantageous in more complex structures to use more than one of the modelling options through the different stages of the design development and/or in the checking. Testing different models against one another is often far more efficient than directly checking a single model for errors and can unearth fundamental shortcomings that would not otherwise be apparent. Engineers must also not confuse nor automatically associate modelling complexity and/or simplifications with model accuracy. It is possible to have a highly accurate simple model, just as it is possible to have an inaccurate complicated model. The accuracy of a model ultimately comes down to the cumulative impact of the simplifications, not the simplifications in themselves. Modelling elements and joints as perfectly elastic is a common simplification; uniform actions and perfectly rigid boundary conditions are others.

5.3

Modelling vertical stability structures

5.3.1

1-dimensional element models

1-dimensional element modelling originates from classical beam theory and was favoured with early software. Today these models are valued for hand calculation methods and are well suited to fast conceptual work. They remain a fall-back when 2-dimensional finite element (FE) modelling is not available and provide a means of checking more complicated results. A significant advantage is that the output is readily intelligible and can be used for element design with very little post-processing. Individual wall systems can be represented with either a grillage or single element representation (Figures 5.2(a) and 5.2(b)). Models can be simplified further with a single element to represent the amalgamation of all stability systems across a building (Fig. 5.2(c)). With reference to Fig. 5.2, methods exist to determine equivalent properties for simplified models: – Box 5.3 outlines a method for approximating the equivalent single-element properties of a coupled wall (i.e. changing from Fig. 5.2(a) to 5.2(b)). – Box 5.4 outlines how properties of elements shown in Fig. 5.2(b) can then be combined to determine the amalgamated properties for the single element shown in Fig. 5.2(c). 22

The Institution of Structural Engineers Stability of buildings Part 3

Each simplification requires that the properties of the more complicated model are known. Thus the simplifications are rarely useful for design development but are valued techniques for checking. For design development, it is most likely the models are used in the reverse of the order shown in Fig. 5.2. The single element amalgamation shown in Fig. 5.2(c) is useful as a concept, if not formally modelled, to gain a handle on the gross requirements of the stability system in the early concept development stage. The representation shown in Fig. 5.2(b) then becomes more useful once the stability systems have been located. It allows the structural engineer to quickly experiment with the properties of the individual systems and evaluate the influence of minor adjustments. Finally, the grillage model shown in Fig. 5.2(a) is the most detailed 1-dimensional element model and is best suited to element verification within the detailed design. Techniques to model an accurate grillage are discussed in more detail in the next section.

Modelling and analysis Box 5.3

Single element representation of a pierced wall

It should be noted that the following representation is appropriate for modelling global behaviour. It fails to capture the local stress concentrations that would be apparent in and around the lintel beams and also the effect of any localised buckling in the wall ends adjacent to the openings. Torsional stiffness

Un-stressed Equivalent shear diaphragm Lintel beam

Deformed

δw Thickness tw δb

h Beam of flexural stiffness EI b and shear stiffness GA b

Diaphragm of shear stiffness GAw

V

V

Lb

Lb True structure

Representation

Thickness of the equivalent diaphragm:

db ¼

VL b 3 VL þ b 12EI b GA b

dw ¼

VL b GA w

A w ¼ ht w !


2 1 L G ¼h b 12I b E tw |fflfflffl{zfflfflffl}

flexural deformation of beam

where: Ab E, G Ib Lb h tw

þ

1 Ab |fflfflfflffl{zfflfflfflffl}



. . .Eqn 5.1

shear deformation of beam

is the shear area of the lintel beam are the material moduli of the lintel beam is the second moment of inertia of the lintel beam is the lintel beam length is the height of the equivalent diaphragm is the thickness of the equivalent diaphragm The Institution of Structural Engineers Stability of buildings Part 3

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5.3

5.3

Modelling and analysis Box 5.3

Continued

Torsion constant J: J¼

1X 3 bt 3 |fflfflfflffl{zfflfflfflffl}

þ

V2 L=t w |fflfflfflfflfflfflfflffl{zfflfflfflfflfflfflffl ffl}

. . .Eqn 5.2

t w  treal walls [ L /t w dominates

for real walls only

where: b is the length of the perimeter walls excluding length Lb V is the area enclosed by the perimeter walls, measured to the centre of the walls Flexural stiffness A conservative approximation of the flexural stiffness in both the major and minor axes can be approximated by considering the net wall section taken from a cut through the wall at a level that bisects the largest wall penetrations. This will result in a section of least stiffness.

Iyy Izz

It should be noted that the centroid will be influenced by the presence of the penetrations. Shear stiffness for solid ‘webs’:

d¼

Un-stressed

Vw L GA w

for beams:

d¼

V bL b V bL b3 þ GA b 12EI b

combined:

d¼

VL GA

(neglecting flexural component)

where V ¼ Vw þ V b ,

Solid ‘web’


 Lb L 3 L þ ðGA w Þ þ b ðGA b Þ 12EI b ! ðGAÞ ¼ 
Lb L 3 þ b ðGA b Þ 12EI b

Deformed

where: GA is the gross equivalent shear stiffness GA w is the shear stiffness of the solid wall GAb is the shear stiffness of the lintel beam EI b is the flexural stiffness of the lintel beam L is the overall depth of the wall system

Lintel beam

L δ

... Eqn 5.3

δ

V

Lb

Box 5.4

Assume all deformation of the coupled wall occurs in the lintel beam

Notes for amalgamating multiple linked structures into a single element

The following characteristics refer to the amalgamated element. Flexural stiffness I is quoted as a simplification to the combined effect of flexure and shear. This can be changed throughout to a more general stiffness k. Lower case subscripts i,uu and i,vv are used to denote the stiffnesses of the i’th element in its principal major and minor axes respectively, and i,xx i,xy and i,yy are used for the stiffnesses of the i’th element about a common global coordinate system. Upper case subscripts are used for the single amalgamated system: XX, XY and YY define stiffnesses in the global coordinate system while UU and VV define stiffnesses in the amalgamated system’s principal axes. 24

The Institution of Structural Engineers Stability of buildings Part 3

Modelling and analysis Box 5.4

Continued

Cross-section area A

This model should not be used for axial loads and the area of the section is largely irrelevant.

Principal second moment of area stiffness properties I UU, I VV

The principal inertias I i,uu, I i,vv of the individual contributing components must first be converted to I i,xx, I i,yy, and I i,xy about a common global axis set. These can then be summed in turn to determine I XX, I YY and I XY for the amalgamated element. Finally, I UU and I VV can be calculated.

v

y

y u x

y x

Single element stiffness: IXX, IYY, IXY x Notes a I i,uu and I i,vv of the components must not be summed where they do not share a common axis set. b I i,uu, and I i,vv can be related to I i,xx, I i,yy and I i,xy, and I XX, I YY and I XY to I UU and I VV using Mohr’s circle. Torsional stiffness J

The amalgamated torsional stiffness is the sum of: P – The local torsional stiffness of the contributing components J i – The product of the translational stiffness of the contributing components and the eccentricity of this stiffness from the global centre of stiffness

xi

y

xs

xs

yi ys

Single element torsional stiffness J

ys

x Arbitrary origin J¼ Position

P

[J i ] þ

P

[I i,xx(yi  ys )2 þ I i,yy(x i  xs )2  2I i,xy(x i  x s )( y i  y s )]

. . .Eqn 5.4

The single element should be positioned at the equivalent shear centre of the systems (xs, ys), otherwise known as the global centre of stiffness. The coordinates can be determined relative to a reference origin by evaluating a torsion about the origin that results in a unit linear displacement in each of the x and y axes: P [I i,xy x i  I i,xx y i ] . . .Eqn 5.5 Tx ¼ P [I i,yy x i  I i,xy y i ] . . .Eqn 5.6 Ty ¼ x s ¼ (I XX Ty  I XY T x ) / (I XX I YY  I XY 2 )

. . .Eqn 5.7

y s ¼ (I YY T x þ I XY Ty ) / (I XX I YY  I XY 2 )

. . .Eqn 5.8

Further reading: An understanding of Mohr’s circle is required for the stiffness components. For further guidance refer to: – Hulse, R. and Cain, J.A. Structural mechanics: worked examples. Basingstoke: Palgrave Macmillan, 2009 – Parry, R.H.G. Mohr circles, stress paths, and geotechnics. 2nd ed. London: Spon, 2004

Limitations of 1-dimensional elements Critical to the performance of the model shown in Fig. 5.2b is the software’s representations of the restrained warping stiffness and the shear centre. Few software packages apply a restrained warping stiffness to 1-dimensional elements. This is critical for open sections where restrained warping stiffness is often several orders of magnitude greater than pure The Institution of Structural Engineers Stability of buildings Part 3

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5.3

5.3

Modelling and analysis St Venant’s torsion stiffness. Failure to acknowledge the restrained warping stiffness in these sections can render a model overly flexible. More importantly, it may dramatically underestimate the element stresses and reactions on supporting structures. It is for these reasons that Fig. 5.2b shows a two-column grillage for the channel section. Each column of elements represents half the gross cross-section of the wall (in this case, each is an ‘L’ section) and collectively the flexural stiffness of these elements, together with the shear resistance of the horizontal elements and the two support nodes, go some way to replicate the warp restraint. This approach is recommended for all non-planar open sections when warping stiffness is not accounted for in the software. With regard to the shear centre, many software packages incorrectly assume it is coincident with the centroid irrespective of cross-section geometry. This assumption is again critical to open sections when represented by single elements. Loads in the real world are invariably applied to the physical structure (not the academic shear centre) and failure to acknowledge an offset to the shear centre can dramatically reduce the torsion recorded. Modelling the core so that it is centred at the shear centre can improve the accuracy of the model provided the lateral forces are applied correctly through the true core alignment (i.e. at an offset to the core elements as modelled (Figure 5.3)). With this approach, and where the core cross-section changes with height, the modelled core elements may need to move on plan to coincide correctly with the changing shear centre. Two layers of rigid links, spaced with rigid stub columns, can be used to best maintain continuity in such circumstances (Figure 5.4). It should be noted that this detail is only needed where continuity of each of the wall’s rotational and translational deformation is needed across the step. This is the case for changes of cross-section within the height of a wall. However, in the scenario where a wall is simply supported on an offset transfer system, a single layer of rigid links is sufficient to ensure compatible translational deformations only (Figure 5.5).

5.3.2

Grillage models

The grillage method shown in Fig. 5.2a uses vertical and horizontal elements to represent components within a wall system. Figure 5.6 shows a close up of a closed core section. A vertical tower of elements represents each solid planar wall section. These should be centrally located and of dimensions and orientation true to the solid section of wall they represent. Horizontal elements trace the path of the wall system’s cross-section, connecting the vertical elements and joining at the corners. These elements reproduce the shear stiffness between wall sections and ensure geometric compatibility is maintained during deformation. Not being wholly representative of the continuum of the wall, their properties must be modified somewhat (as set out in Box 5.5). Lintel elements are an exception and should not adopt the modified properties of other horizontal elements. These should remain true to the real geometrical properties of the structure. The overall length of lintel beams is also critical. Modelling lintel beams to the centrelines of the walls will underestimate the system stiffness, while assuming full fixity at the face of the opening will be an overestimate. Rather, the position of full fixity should depend on the construction. In monolithic construction (i.e. structures without joints) full fixity may be assumed at 0.6h past the face of the opening, where h is the effective depth of the coupling beam5.1 (Figure 5.7). This is reasonably accurate in most cases, although it becomes conservative where the beam is relatively deep (Box 5.6). At no point should the fixity be beyond the centre of the adjacent vertical wall panels. It is typical to model vertical elements spanning between nodes located at floor levels, allowing the horizontal elements, including lintel beams, to be at storey intervals. This is reasonably accurate in all but short stocky structures (Section 2.2), or open flanged sections subject to large torsion. In both instances, shear deformation dominates and can be better

Deformed shape

True position of structure

Offset modelled element

Correct shear centre Load through centroid

Rigid link element centroid to load

a




Rotation + translation

a



Translation only

Figure 5.3 Correcting for shear centre errors in 1-dimensional element models 26

The Institution of Structural Engineers Stability of buildings Part 3




Approximate rotation + translation

Modelling and analysis

5.3

Wall section 2 Section 2

Floor elements or rigid links Flexurally rigid stub column

~1/10th storey height

Section 1

Auxiliary rigid links between nodes Wall section 1

Viewed end on Shear centre axes Structure

Model

Figure 5.4 Linking offset 1-dimensional element where rotational continuity is needed

Wall

Wall

Transfer beam

Rigid links Transfer beam into page

Structure

Model

Viewed end on

Figure 5.5 Linking offset 1-dimensional element where a pinned joint is appropriate

Box 5.5

Horizontal element property modifiers

The following apply to horizontal elements other than lintel beams in a grillage model: (1) The material property and section thickness should be as per the vertical elements (2) The section depths should be equal to the vertical spacing of the elements (3) The major axis (in-plane) flexural stiffness should be increased to minimise flexural deformation (4) The torsional stiffness should be decreased so as not to relieve vertical elements of out-of-plane bending actions (5) The mass should be set to zero so as not to double count gravity loads and/or affect the natural frequency

Nodes at all intersections

Horizontal ‘modified’ elements (shown red)

Note that the torsional stiffness of the vertical elements should also be decreased so as not to relieve the horizontal elements of out-of-plane bending actions. Initial modification factors of the order of 103 are recommended for each of (3) and (4) and the torsional stiffness of the vertical elements as listed. The sensitivity of the model with respect to these factors should, however, be reviewed in the software being used. Extremely large or small factors, as well as a 0% factor, can cause numerical errors in the analysis engine depending on the algorithm and numerical rounding.

Vertical elements with properties of wall sections

Elements with properties of lintel

Figure 5.6 1-dimensional elements used in a grillage configuration The Institution of Structural Engineers Stability of buildings Part 3

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5.3

Modelling and analysis Box 5.7

b2/2

b1/2

Modified horizontal element

Lintel element

h

Corner node to return wall

0.6h

t /2 Figure 5.7

b2/2 < 0.6h ∴lintel extends to wall node

Vertical wall element

b2

b1

t /2

Modelling lintels with 1-dimensional grillage elements

captured in the model with additional mid-storey horizontal elements. 5.3.3

Modelling clarity, complexity and verification

It is not uncommon for automated software to lead to unnecessarily complex models developed without clear intent or focus on specific output. Engineers should be wary of this as overly complex models can be a catalyst for oversights and misinterpretation of results; they can also be a cause of inefficient working practice. Models should be: – planned based on clear objectives – developed in a manner that is fit for purpose and within the limitations of the software – verified It is important for engineers to recognise that software does not relinquish any responsibility – and ignorant dependency on software is an example of working without due diligence. Hand calculations or simple models can almost always be undertaken to demonstrate that a complex model is giving reasonable results. These checks should always be carried out.

(Box 5.7), not least because FE models can produce an overwhelming amount of information which the engineer must decipher.

2-dimensional finite element models

2-dimensional finite element (FE) modelling is potentially the most detailed technique, being the truest representation of the structure (Figure 5.8). It is also increasingly one of the most convenient techniques, with software developers continually improving and adding new automated links between analysis, design and documentation software packages. However, this convenience tends to play down the engineer’s responsibility and workload

Box 5.6

Deep beam lintels

Grillage models are not suitable for structures containing lintels classified as ‘deep beams’ (where the span is less than three times the depth)5.2. The behaviour of these beams is dominated by shear deformation and is better modelled within a 2-dimensional finite element model.

Element type and meshing Choice of element type and their conditioning is critical within FE modelling. Shear wall elements can be modelled as plane-stress elements when in-plane stresses dominate, otherwise shell elements need to be used when both in- and out-of-plane stresses need to be considered. Plate elements which ignore in-plane stresses are not appropriate and plane strain elements are inappropriate in all but 2-dimensional cross-section models (the likes of which may be used to determine the necessary area of reinforcement in a concrete section, but not to determine the design actions on the section). Note it is essential that engineers understand the default element settings adopted by the specific software they will be using. By adopting plane-stress elements the design engineer dictates that a model will resist all forces by in-plane stiffness only (i.e. walls bending in their minor axes have zero stiffness and attract no force). This approach is valid where redistribution is justifiable and followed through with adequately ductile detailing of joints and/or reinforcement. Otherwise, shell elements are needed to incorporate out-of-plane stresses. These stresses can be manually redistributed or designed for but cannot be ignored. 1-dimensional auxiliary elements can be used in conjunction with 2-dimensional elements. These may be to enhance the accuracy of a model by replicating a property of the structure (usually a stiffness) that is not adequately replicated by the 2-dimensional elements. Two common instances where these auxiliary 1-dimensional elements are used are introduced in Box 5.8.

Figure 5.8 2-dimensional element model 28

The Institution of Structural Engineers Stability of buildings Part 3

It is typical to use quad 2-dimensional elements for planar walls. The ideal shape of these is square and the further the elements deviate from this (either in the aspect ratio or interior angles) the less accurate they become. As a guide, the length of the smallest side

Modelling and analysis Box 5.8

5.3

1-dimensional auxiliary elements in 2-dimensional models

Auxiliary elements are needed with plane-stress 2-dimensional elements to provide stiff anchorage to out-of-plane actions or to in-plane rotations. They can be used to ensure continuity between wall elements and floor beams, as shown below:

1-D element to lintel beam

1-D element to floor

Auxiliary elements

Auxiliary elements Auxiliary elements can also be used to recreate a torsion constant J of an open section. Plane-stress elements cannot represent this stiffness and, while small relative to the warping stiffness, the stiffness can attract stresses that may otherwise be redistributed. A single vertical column of 1-dimensional elements can be used, with each element being assigned a constant J representative of the system:

Single column of 1-D auxiliary elements with J = Jwall, Ix = Iy = 0 It should be noted that 2-dimensional FE models consider restrained warping stiffness intrinsically and do not require any special consideration in this regard.

should not be less than half the length of the longest side. The size of elements should be such that the stress does not vary significantly across the side length. Significant stress discontinuities across the boundaries of neighbouring elements are tell-tales that the density of elements should be refined. Elements are typically refined locally for in-plane stress concentrations at abrupt changes in the geometry (Figure 5.9). Trapezoidal or irregular elements are unavoidable in such instances and it is essential that all nodes of all elements meet with nodes of adjoining elements where present.

Min. four elements across wall

Trapezoidal elements

It is worth noting that Fig. 5.9 shows a regular array of elements (collectively making a ‘mesh’) in a format that is convenient to generate manually. Many software programmes provide auto-meshing functions and these tend to produce a far less regular, ‘organic’ mesh pattern. Either is suitable provided the sizes of the elements (the ‘mesh density’) are reflective of the stress concentrations. Lintels are governed by flexure and should be divided to portray the stress flow. Four elements through the depth and six across the span are recommended as the minimum. However, good element aspect ratios should be attained and this may lead to significantly

Min. six × four elements to lintel

Figure 5.9 2-dimensional element mesh The Institution of Structural Engineers Stability of buildings Part 3

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5.4

Modelling and analysis

more elements either across the span or through the depth (depending on the geometry of the beam). Output Raw output from a 2-dimensional FE model consists of a stress field for each element which is often integrated by the software over the area of the individual elements. This integration returns stress resultants (forces and moments), shown in Figure 5.10 for a shell element. However, further post-processing is needed to obtain values representative of the wall as a whole or part that are suitable for design. Increasingly software packages automate this but engineers should verify that this is being completed appropriately.

Ny

where: Nx,i is the force on element i bi is the side length of element i NX is the force per unit length – Moments must include allP components acting on the elements, e.g. MXX ¼ (Mxx,i þ |Mxy,i|) / bi where: Mxx,i and Mxy,i MXX

5.4

M yx

N yx

– The mesh element size is considered where a force per metre P length of wall is needed, e.g. NX ¼ (Nx,i / bi)

Modelling horizontal stability systems

M yy

N yz

N xy

Horizontal stability systems that link vertical stability systems may be modelled using elements true to the structure or by using rigid constraints; the latter is shown in Figure 5.11 for the models previously shown in Figs 5.2 and 5.8.

M xx

N xz Nx

M xy

Figure 5.10 Stress field for 2-dimensional shell element When post-processing mesh results, care must be taken to ensure:

These elements or constraints will distribute forces internally and allow actions to be applied to a global model independently of either the stiffness or layout of the resisting structure. Fig. 5.11 shows forces applied to nodes located at the centre of area for each storey as would be used for uniform wind load.

Rigid constraints

Figure 5.11 Modelling horizontal stability systems using rigid constraints 30

are the components shown in Fig. 5.10 is the moment per unit length

The Institution of Structural Engineers Stability of buildings Part 3

Modelling and analysis Further nodes could be positioned and loaded at an eccentricity (for non-uniform actions) or at the centre of mass (for equivalent horizontal and static earthquake actions). Rigid constraints are the simplest way of connecting discrete stability walls to the point or points of loading. The decision to use them should be based on two questions: – How stiff is the horizontal structure and is an infinitely rigid approximation appropriate considering each of: any penetrations, narrow sections and the stiffness of the slab to wall connections? – What actions are being modelled? Rigid constraints must not be used when applying stresses resulting from internal strains (e.g. thermal strains or posttensioning), or when using a model to evaluate forces in the horizontal system. Particular care should be taken not to over-constrain any elements of the structure. Rigid constraints should only link nodes of the core that are directly connected to the diaphragm or horizontal bracing and should generally only provide constraint in horizontal planes. Neither should they run parallel to (or bridge) elements that are being investigated, nor connect to fixed ‘boundary’ nodes. Where the floorplate is instead modelled using elements representative of the structure, it is typical to use 2-dimensional elements for diaphragm slabs. Elements can be of plane-stress type when modelled solely for the purpose of assessing the diaphragm action. The mesh density should be reflective of the stress concentrations, especially locally around the shear walls. Otherwise, where the model will be used for load takedown or slab design, or where the slab contributes to the stiffness of the vertical structure (e.g. by contributing to frame action), shell elements must be used. The mesh should be suitably dense in all spans and around vertical supports to allow the flexural and shear behaviour to be determined. This typically requires not less than six elements across each span.

5.5

Manually apportioning actions between vertical stability systems

Box 5.9

Apportioning actions between systems linked by a rigid diaphragm Py

y

Local shear centre of wall

e k y,n k x,n

yi x

k θ,n

xi

The apportioned action Py,n acting on a system is given by:
 k y;i ek y;i x i +P Py;n ¼ Py P k y;i ðk y;i x i 2 þ k x;i y i 2 þ ku;i Þ

. . .Eqn 5.9

where: is the applied (global) action Py e is the eccentricity of the applied action measured from the global shear centre ky,i is the stiffness of the i’th system parallel to the action is the distance to the shear centre of the i’th system measured from the global xi centre of stiffness and orthogonal to the action kx,i is the stiffness of the i’th system perpendicular to the action yi is the distance to the shear centre of the i’th system measured from the global centre of stiffness and parallel to the action ku,i is the local torsional stiffness of the i’th system Note that the global centre of stiffness is analogous to the shear centre of the individual wall elements. It is the point through which a transverse load will cause pure shear (without torsion). Its position can be found using Equations 5.5 to 5.8 (Box 5.4).

and should be commensurate with the general accuracy of the analysis. Flexibility at the boundary nodes should be considered in each of the six degrees of freedom (Figure 5.12). Any variability (e.g. of the founding soil stiffness) or uncertainty (e.g. where founding on an existing structure of unknown design) should be captured in an enveloping sensitivity study.

z

Box 5.9 details how loads can be manually apportioned between vertical stability systems linked by a stiff diaphragm.

y Although quite simple in theory, the calculation can quickly become unwieldy in practice. The stiffness of the individual wall systems ki is dependent on both shear and flexural stiffness and can vary through the height of the building. This can have a knock-on effect on the global centre of stiffness, and collectively will cause the loads to redistribute.

5.6

Modelling boundary conditions x

The rigour with which the boundary conditions are modelled can have significant impact on the results

5.5

Figure 5.12 Degrees of freedom The Institution of Structural Engineers Stability of buildings Part 3

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5.7

Modelling and analysis

5.7

Elastic and plastic analysis

Analysis can be elastic, rigid-plastic or elastic-plastic. Elastic analysis is normally adopted for the derivation of forces throughout shear wall systems. It is appropriate for all materials that exhibit homogeneous behaviour at both the serviceability and ultimate limit states (Figure 5.13(a)), and is applicable irrespective of the structural form and/or the failure mechanism. Rigid-plastic analysis is rarely appropriate for global shear wall analysis. It relies on stable and predictable post-elastic deformation with neither fracture nor buckling causing premature failure.

Note that plastic analysis as discussed in this section is different to plastic section design. The latter is widely used to justify resistance of elements at the ultimate limit state and is applicable in conjunction with elastic, rigid-plastic, or elastic-plastic analysis. It is important that designers distinguish analysis from element design in this way.

5.8

References

5.1

Irwin, A.W. Design of shear wall buildings. CIRIA Report 102. London: CIRIA, 1984

5.2

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

Elastic-plastic analysis is, however, common at the ultimate limit state for walls with lintel beams. These relatively shallow beams can often be designed with sufficient ductility and stability to form predictable plastic hinges. Hinges can either be assumed by the designer (and modelled as springs of constant rotational stiffness) or found by non-linear iterative elastic-plastic analysis. Both techniques should lead to a hinge pattern similar to that shown in Fig. 5.13(b). Alternatively, the in-plane stiffness of lintels can often be omitted outright at the ultimate limit state where the lintels are not necessary for overall stability (Fig. 5.13(c)). This is an elastic-plastic approach, equivalent to assuming plastic hinges that are of negligible rotational stiffness. It has the advantage of being able to simplify the model to one that can be analysed elastically.

Plastic hinge

Strut (of zero flexural stiffness)

Modelled

Deformed

(a)

(b)

(c)

Elastic

ULS with plastic hinges

ULS with lintels omitted

Figure 5.13 Modelling the elastic and plastic behaviour of shallow lintels 32

The Institution of Structural Engineers Stability of buildings Part 3

6

Monolithic reinforced concrete shear wall construction

6.1

Introduction

Modelling the stiffness of concrete

Stiffness is critical to serviceability deflection limits but also to the load distribution within a structure. It is dependent on the material elastic modulus, tension stiffening, creep and the effective section. Modulus of elasticity, tension stiffening and creep The modulus of elasticity E for concrete is a variable usually defined at 28 days in line with the 28 day compressive strength (Box 6.1). These variables are co-dependent; both are characteristics of the concrete mix and both are age (‘maturity’) dependent. Figure 6.1 plots their development for a C35/45 Class R concrete6.2. This graph has been derived in accordance with Clause 3.1 of BS EN 1992 Part 1-16.3 and plots the secant modulus. It shows that both the strength and stiffness are asymptotic over time. Box 6.1

Specification of concrete strength and stiffness

The 28 day strength has traditionally been and remains the principal parameter for design and specification. There is, however, an increasing trend to measure and limit variation of stiffness where sway, creep, differential shortening and/or PD effects are significant. Monitoring of stiffness is often specified up to 56 days, at which point it is approximately 95% of the asymptotic value when Portland cement is used (this may vary where cement replacements such as fly ash are specified within the mix6.1). In addition to this time-based development of stiffness, load duration and/or load cycles influence tension stiffening and creep (also known as ‘relaxation’). BS EN 1992 Part 1-1 Clause 7.4.3 gives factors of 1.0 for short-term loads and 0.5 for sustained or cyclic loads in recognition of this. The Concrete Society gives guidance on when to use the long- and short-term factors6.4. It concludes that the long-term factor should be used for all loads anticipated to last more than approximately 20 days. Effective section The effective section is a function of the area and placement of reinforcement and the extent to which the concrete is cracked. Cracking is a brittle mechanism of limited predictability. It is dependent on the most severe historical load condition experienced by a section (not always related to the load condition being investigated). However, only cracks in the tension zone need to be considered for any given load case.

Cracked section properties are typically modelled by reducing the second moment of area I of the solid wall. This can be carried out in most software packages with either a property modification factor or by overriding the default value (the default having been derived from the gross geometry of the element). Either method has no impact on other properties. However, note that it would be wrong to change the explicit section geometry (which would influence the area and axial stiffness). Meanwhile it is common practice to apply the effects of tension stiffening and creep by virtue of a modified modulus of elasticity E. This is usually applied uniformly to the whole structure and can be via a modification factor or override to a default material property, or by adopting a user-defined material property.

55

40

50

38

45

36

40

34

35

32

30

30

25

f cm(t ) E cm(t )

20 15 1 10 Age of concrete (days)

28

26 24 1000

56 100

Figure 6.1 Development of stiffness and strength with concrete age The Institution of Structural Engineers Stability of buildings Part 3

28

33

Modulus of elasticity E cm(t ) (×103 N/mm2 )

6.2

Cracked properties can be applied uniformly to all elements within a model, banded through the building height, or applied on an element-byelement basis following an initial or iterative appraisal of the tensile stresses. A uniform application is by far the simplest but is likely to underestimate the stiffness of the structure. An element-by-element application is more accurate, though may prove impractical without a semi or fully automated iteration script to determine the extent to which each section is in tension. It may also lead to a false sense of accuracy, potentially not taking account of the true load conditions or locked in stresses. A banded application is a middle road approach. Here, the degree of cracking is applied incrementally through the height of the structure and is based on the approximate extent of tension at representative sections to each band.

Compressive strength f cm(t ) (N/mm2 )

This chapter looks at characteristics of in situ reinforced concrete walls. These tend to be monolithic and loadbearing. They are usually designed as compression elements under the combined action of in-plane bending and axial forces.

Modelling variable parameters In many instances the engineer may find it necessary to carry out analysis across a range of material moduli and with upper and lower bound criteria for the section properties (see the example family of models shown in Table 6.1).

6.3

Monolithic reinforced concrete shear wall construction Table 6.1

Example modelling matrix for concrete

Material moduli

Effective section Lower bound crackingb I walls  90% I gross I lintel  50% I gross

Short-term Ecm(t ) Long-term 0.5Ecm(t )

Upper bound crackingb I walls  50% I gross a I lintel  30% I gross 3 A

3 A (Model 4)

(Model 2)c

3 A

3 A

(Model 3)

(Model 1)

For short-duration static and low frequency dynamic actions For long-duration and permanent static actions

c

Notes a Value taken from ACI 318M-116.5. b Percentages given for the effective lower and upper bound cracked section are guide values recommended for an initial assessment. They should be reviewed against the stresses determined within the analysis and revised as necessary. c The upper bound cracking models (Models 1 and 2) should be used to determine PD effects at the ultimate limit state.

Further reading: design properties of concrete The following texts are recommended sources of further guidance on the design properties of concrete: – Reynolds, C.E., Steedman, J.C. and Threlfall, A.J. Reynolds’s reinforced concrete designer’s handbook. 11th ed. Abingdon: Taylor & Francis, 2008 – Neville, A.M. Properties of concrete. 5th ed. Harlow: Pearson, 2011 – Bamforth, P.B. et al. Properties of concrete for use in Eurocode 2: how to optimise the engineering properties of concrete in design to Eurocode 2. CCIP-029. Camberley: The Concrete Centre, 2008

6.3

Ultimate and serviceability limit state design of reinforced concrete sections

Reinforced concrete shear walls can be designed using methods set out in codes of practice for

ε

Increasing curvature

σ

Elastic – perfectly plastic

ε

σ

Rigid – perfectly plastic

Figure 6.2 Elastic, elastic-perfectly plastic and rigid-perfectly plastic stress block models (shown for flexure) 34

Adequate reinforcement must be provided to resist the combination of normal (predominantly vertical) and shear stresses to all sections. Special attention should be given to stress concentrations including those at re-entrant corners around openings and at slab junctions. The strut and tie design method is recommended for regions in which cross-sections undergo non-planar deformation. Most codes allow an idealised plastic stress block model for section design at the ultimate limit state (Figure 6.2). This is a simple, proven technique for determining lower bound plastic strength. However, it is important engineers appreciate that it assumes large strains equivalent to the stresses. This is reasonable in many scenarios but can be critical when either second order PD effects or load sharing is significant. The Institution’s Manual for the design of concrete building structures to Eurocode 2 Section 5.6.4.16.6 provides a simplified rigid-perfectly plastic calculation for the vertical reinforcement in a wall not subject to significant minor axis bending.

σ

Perfectly elastic

ε

coincident compression or tension with flexure and shear.

The Institution of Structural Engineers Stability of buildings Part 3

An elastic stress method is an alternative approach at the ultimate limit state and is necessary for the serviceability limit state designs. It can be advantageous for the ultimate strength design where: – A wall is particularly slender with heightened risk of buckling instability – A wall has particularly complicated geometry with an irregular arrangement of reinforcement. An elastic calculation requires the modular ratio for the concrete and reinforcement. This will vary depending on the modulus of elasticity of the concrete. The modulus of elasticity of steel is constant irrespective of load, but the design value does vary by region. It typically lies in the range of 200  103 to 210  103 N/mm2. Elastic stresses must remain below the elastic limits of the materials, i.e. the yield stress for steel reinforcement and the compressive strength for concrete. These limits are critical at the ultimate limit state. Reinforcement tensile stress is commonly used to define elastic design parameters for the serviceability limit state. The limiting stress is a variable for a given

Monolithic reinforced concrete shear wall construction steel grade, dependent on each of: the allowable crack width, the cover, the bar diameters and the bar spacing. A larger quantity of closer spaced, smaller diameter bars permits higher stresses but may have implications on construction6.6.

6.4

Concrete classes

Readily available concrete classes (otherwise referred to as ‘concrete grades’) vary by geographic region. As a general rule, higher classes are more economically available in urban areas where there is steady demand justifying large scale production. However, underpinning the availability and cost of high strength mixes is the availability of raw materials. The strength of aggregate is fundamental to the strength of the concrete and is a function of the geology of the quarry from which it is sourced. Likewise the availability of cement replacement materials such as ground granulated blast furnace slag, fly ash and silica fume is influential. The highest class concretes often need fractions of these components as part-replacement to Portland cement to achieve enhanced densities with lower void ratios. Whether raw materials can be sourced locally will influence the delivery cost. For most moderate to high-rise buildings, it is common practice to use a mix that is one or two classes stronger for the vertical elements than is used for the floor slabs. In this common scenario, care is needed to ensure that either the higher strength concrete is continuous through the floor-wall intersection or that the lower strength concrete and local reinforcement is adequate. Which of these approaches is adopted is often dependent on the construction: continuing the wall through the floorslab is convenient for slip- and jump-forms but less so for traditional shuttered lifts (Section 6.6). Most codes of practice list common strength classes, and some go further to list standard mix designs. Engineers should recognise how these ranges relate to the applicability of the code. Extreme care should always be taken where a design uses materials that are outside the scope of the code. Further reading: concreting and concrete mixes The following text is a recommended source of further guidance on concreting and concrete mixes: – The Concrete Society. Concrete practice: guidance on the practical aspects of concreting. Good Concrete Guide 8. Camberley: The Concrete Society, 2008

6.5

Minimum wall thickness

Global strength and stiffness, local stress concentrations, fire resistance, thermal and/or acoustic insulation, the need for chase-outs or embedded fixings and durability can all influence the minimum wall thickness. Once these points have been considered, it is worth sketching out, to scale, the critical sections with the most congested reinforcement. These will usually be within lintels, at junctions to floor beams or slabs, and

at laps. Overly thin and congested sections will lead to challenges when placing and compacting the concrete. The consequence of this can be special mix requirements, slow progress on-site, honeycombing and poor surface finish quality (Box 6.2). Box 6.2

Constraints on construction

Constraints imposed on the construction by a design decision should be clearly described in the contract documents and/or on the drawings. Thin walls, especially those requiring a good finish quality, can restrict pour heights and limit the maximum aggregate size. These are both measures necessary to avoid segregation and honeycombing but often incur a cost premium. The Institution’s publication Standard method of detailing structural concrete6.7 recommends that in situ walls are no thinner than 150mm. Walls of this thickness should be detailed and constructed with lifts not exceeding 1.8m to ensure dense placement. Reinforcement is almost certainly limited to a single layer each way positioned centrally in the wall. Not only is this inefficient, but it is also difficult to secure in place and may not be adequate to control surface cracking. 180mm is a more practical minimum thickness6.6, allowing storey-height walls to be cast in single pours. These walls can generally accommodate two layers of vertical and horizontal reinforcement (one fixed near each face) and span clear heights of the order of 3m.

6.6

Reinforcement and embedments

Both minimum and maximum amounts of reinforcement in each of the vertical and horizontal axes are typically defined by codes of practice. The definitions are usually given as ratios of the gross concrete area for a section taken orthogonal to the reinforcement. Minimum reinforcement ratios are dependent on the design requirements (stress resultants, crack control, durability and fire resistance) and the construction method. Meanwhile, maximum reinforcement ratios are governed primarily by buildability with limits set to prevent over-congestion and poor concreting. Both minimum and maximum ratios apply throughout elements but maximum ratios tend to only be critical locally at junctions with starter bars or where bars are lapped. Over-reinforcing the tension zone of shear walls (so that they would fail in flexure by concrete crushing) is rare; most shear walls in building structures are without significant out-of-plane actions and are designed with equal reinforcement to each face. This is both to accommodate load reversal and to simplify construction. Wall reinforcement should be detailed in accordance with codified rules and guidance given in the Institution’s manual Standard method of detailing structural concrete6.7. Salient points include: – Vertical bars should always be in a layer that allows the horizontal bars to be tied once the vertical bars are in place (Figure 6.3). This can have significant The Institution of Structural Engineers Stability of buildings Part 3

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6.4

6.7

Monolithic reinforced concrete shear wall construction

Cage built before forms are added Both forms installed only when reinforcement cage is complete

(a) Symmetrical placement

Form installed last

Cage built off formed face (b) Placement away from a formed surface

Form installed first

Note that (a) is standard for shear walls but (b) is more efficient where a dominant unidirectional lateral force is acting (e.g. soil pressure on retaining walls). Figure 6.3

Cross links to vertical bars

Wall reinforcement layering (sections shown on plan) impact on the effective depth (critical in walls that are slender, and/or that are subject to significant out-of-plane actions) – Cross links may be required at wall returns (Figure 6.4) and across heavily reinforced sections (Figure 6.5) to overcome bursting forces – Diagonal bars should be positioned across re-entrant corners (i.e. corners around openings – Figure 6.6). These are usually adequate if designed for a tensile force equal to twice the horizontal shear force in the vertical component of the wall, but should not be less than two 16mm diameter bars across each corner of the opening6.6 – Laps should be detailed to avoid localised congestion (e.g. with staggering)

Note Horizontal bars omitted for clarity. Figure 6.5 Cross links in heavily reinforced walls construction sequence. Laps in the wall reinforcement should generally avoid these areas to prevent unnecessary congestion. Finally, it is worth noting that the Institution’s detailing manual6.7 stipulates a maximum bar spacing of 400mm, in line with BS EN 1992 Part 1-1 Clause 9.6.36.3. However it is considered best practice to limit this to 300mm. This limit is enforced by BS EN 1992 Part 1-1 Table 7.3 which lists maximum serviceability bar stresses for bar spacings up to 300mm only.

6.7 Additional local reinforcement (starter bars) and/or embedments (Box 6.3) are usually essential where floor beams frame into walls. These can be junctions of high local stress and design intricacy. Early coordination across disciplines should try to avoid service penetrations in these zones. Subsequently, close attention during the detailed design needs to be given to the forces being transferred, to the tolerances of the individual systems and to the

Cross links to corner

Construction

The construction method is usually a contractor’s proposal with little impact on the completed structure. However, the choice of method can have significant impact on the appropriateness of a design. The following paragraphs describe common methods of construction of in situ reinforced concrete walls.

Diagonal bar across re-entrant corner U-bars at wall edges lapping to main vertical and horizontal bars

Figure 6.4 Cross links at wall returns (section shown on plan) 36

The Institution of Structural Engineers Stability of buildings Part 3

Figure 6.6 Diagonal reinforcement across re-entrant corners including penetrations (shown in elevation)

Monolithic reinforced concrete shear wall construction Box 6.3

Embedment plates

Embedment plates are commonly used for the connection between a steel structural frame and a reinforced concrete shear wall. They typically transfer both vertical and horizontal actions from the frame to the wall. The photographs (below) from 1 Grafton Street6.8 show the embedment plates before and after concreting. In reinforced concrete construction, an embedment plate is an assembly made up of a flat steel plate with shear studs and/or reinforcement welded to the rear that projects into the wall. A fin plate that projects out from the wall and is necessary for the beam connection (Fig. 2.4) is site-welded once the concrete is cast and formwork removed. Site welding allows the fin plate to be positioned accurately; omitting the fin plate during the initial installation also means that the cast-in assembly can be set flush with, or nominally in from, the face of the wall without impacting on the formwork.

Embedment plates

Embedment plates are generally oversized to allow for tolerance in the concreting. Their design should assume the fin plate is welded in the most onerous conceivable position relative to the shear studs, that reinforcement is welded to the rear of the embedment plate, and that the bolted connection to the beam is at the maximum eccentricity from the wall. Embedment plates should always be shown on reinforcement drawings to be fixed with the wall reinforcement.

Traditional shuttered lifts Traditional shuttered lifts may be used when other methods are not justified. This may be because the total number of walls in the building is small, or because they exhibit little or no repetition. Otherwise the technique may be used to achieve a premium finish quality or texture. The method of construction has the walls formed one storey at a time, often in parallel with the columns. It is slower than other methods listed but can accommodate the greatest variation between panels. Construction accuracy is influenced by: – The degree to which the formwork is erected out of plumb – The setting out and alignment of one wall immediately above the one below – The spacing of the forms (dictating the wall thickness) – The stiffness of the forms (to withstand the pressures during and after concrete pouring) – The spacing and alignment of reinforcement Acceptable limits and/or criteria should be set out for each of these points via a project or industry/ national specification, e.g. the UK National structural concrete specification6.9. The design may also include features such as ‘kickers’ (Box 6.4), while rationalised reinforcement spacing and/or cover zones is often favoured to decrease the risk of errors on-site. Slipform Slipforming is a method of concrete placement whereby a moving form is used to create a continuous wall extrusion. When used for a wellsuited structure, it is very efficient achieving unparalleled speed.

Box 6.4

Kickers

Kickers are small upstands cast ahead of the wall (typically 75mm high and cast with the floor slab) that provide a useful surface to secure formwork against. In this way they can improve the quality of the column aiding both the setting out accuracy and the seal at the base of the form.

Wall above (Pour 3) Pour joints

Kicker (75mm typical)

Slab (Pour 2 with kicker) Wall below (Pour 1) However, forming kickers is in itself not without challenge. Scrutiny is needed during concrete placement as the kickers can be prone to poorly placed/compacted concrete, debris in the construction joints and/or weak concrete slurry. Kickers can also be unsightly and are often unpopular with both clients and architects where columns will remain fair faced in areas without a raised floor. Kickerless construction can overcome these quality issues but can exacerbate issues including grout leakage from the base of the column formwork. It is recommended that the two techniques are considered by the design team and contractor jointly. It should be noted that the inclusion or omission of kickers can impact the reinforcement bar scheduling and unannounced site changes must be avoided. The Institution of Structural Engineers Stability of buildings Part 3

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6.7

6.7

Monolithic reinforced concrete shear wall construction Jump form Jump form, or climbing form, is a method of construction whereby the walls are cast in discrete lifts. It is a stop-start process with day joints formed at each lift level. At its optimum, storeys can be cast on a 24 hour cycle. This requires standard concrete with 28 day cylinder strength not less than 40N/mm2 to achieve strengths of 15N/mm2 at the striking time (typically after just 14 hours)6.10. Like slipforming, jump forming is only efficient where there is significant repetition in the structure through a number of floors. It is most applicable in mediumand high-rise buildings of ten or more storeys.

Figure 6.7 platform

Slipformed cores under construction shown with and without the climbing

Flanged and core wall systems are generally suited to slipforming where they are of regular section through multiple storeys (Figure 6.7). Floor connection details (embedments and/or starter bars), doorways, blockouts, steps in thickness, tapers and dense reinforcement can add complication and lead to reduced efficiency. In general, slipforming is chosen where speed is the key driver and compromises to achieve vertical regularity can be incorporated in the design. An efficient slipform will progress at a rate in excess of 6m per 24 hours with non-stop working day and night. The technique is less well suited at sites with night time restrictions on work, where weather is likely to be prohibitive or material supply is unreliable. Accuracy and minimum wall thicknesses are comparable to traditional formwork methods, however the construction can impact on the area and disposition of the reinforcement. Aesthetically, slipforming gives a rough finish with vertical streaks caused by abrasion of the form on the walls. Horizontal banding can also be apparent, resulting from minor variations in the concrete supply. Thus, it is generally not suitable for fair faced walls.

However, unlike slipforming, jump form can incorporate discrete features other than simple extrusions. This makes it better suited to lift cores in particular where anchors for the lift guide rails must be positioned with high accuracy. Jump form is also far better suited to day-time only work hours and is less sensitive to unplanned events causing a halt on the programme. A key disadvantage of jump form relative to slip form is the inclusion of lots of day joints; each can be a cause of defects during construction by virtue of poorly placed/compacted concrete and debris at the joint. These joints can also cause obvious banding in the concrete (Figure 6.8). Tunnel form Tunnel form construction uses a formwork system to cast slabs and walls as a single pour operation. It is economical for cellular structures with repetition of the structure both horizontally and vertically (Box 3.1). Hotel buildings, with many identical cellular rooms, are ideally suited. Construction progresses vertically and horizontally simultaneously, with an inclined work front stepping back at each level up the building. As with jump form, ‘tunnels’ can be poured on a minimum 24 hour cycle, before the wall forms are struck and relocated to the next bay.

A slipformed wall will always progress in advance of the surrounding structure and the design must consider the temporary condition. Although the dead weight of the slipform structure and the platform is relatively small, where pull-out bar boxes are used at floor slab levels the effective thickness of the wall can be reduced locally by up to 80mm in advance of the slab being poured. This can be critical while the concrete is green and the walls unrestrained. Where walls are inadequate without the restraint of the slabs, temporary bracing (fixing to cast-in plates) may be necessary to brace between panels. The installation of this bracing can be a key consideration and must be factored into the slipform operation. Even with temporary bracing, the early strength gain of the concrete can dictate the maximum speed of the form and the mix design can have a critical impact on the programme. 38

The Institution of Structural Engineers Stability of buildings Part 3

Figure 6.8 A jump formed core under construction

Monolithic reinforced concrete shear wall construction The method requires significant free space to swing out large units of formwork and should have 28 day cylinder strength not less than 40N/mm2 for the same reason given for jump form. Further reading: in situ reinforced concrete construction The following texts are recommended sources of further guidance on in situ reinforced concrete construction techniques: – The Concrete Society. Slipforming of vertical structures. Good Concrete Guide 6. Camberley: The Concrete Society, 2008 – The Concrete Centre. High performance buildings: using tunnel form concrete construction. TCC/04/02. Camberley: The Concrete Centre, 2004

6.8

References

6.1

The Concrete Society. Concrete practice: guidance on the practical aspects of concreting. Good Concrete Guide 8. Camberley: The Concrete Society, 2008

6.2

Narayanan, R.S. and Goodchild, C.H. Concise Eurocode 2: for the design of in-situ concrete framed buildings to BS EN 1992-1-1:2004 and its UK National Annex: 2005. CCIP-005. Camberley: The Concrete Centre, 2006

6.3

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

6.4

The Concrete Society. Influence of tension stiffening on deflection of reinforced concrete structures: report of a Concrete Society working party. Technical Report 59. Camberley: The Concrete Society, 2004

6.5

ACI. ACI 318M-11: Building code requirements for structural concrete (ACI 318M-11) and commentary. Farmington Hills, MI: ACI, 2011

6.6

Institution of Structural Engineers. Manual for the design of concrete building structures to Eurocode 2. London: IStructE, 2006

6.7

Institution of Structural Engineers and The Concrete Society. Standard method of detailing structural concrete: a manual for best practice. 3rd ed. London: IStructE, 2006

6.8

Perry, P. ‘Development over London Underground tunnels: No. 1 Grafton Street’, Proceedings of the Institution of Civil Engineers – Structures & Buildings, 2014 [Online]. Available at: http://dx.doi.org/10.1680/ stbu.11.00025 [Accessed: 12 January 2015]

6.9

Construct. National structural concrete specification for building construction. Fourth edition complying with BS EN 13670:2009. Camberley: The Concrete Centre, 2010. Available at: http://www.construct.org.uk/media/ National_Structural_Concrete_Specification_for_ Building_Construction.pdf [Accessed: 12 January 2015]

6.10

The Concrete Centre. Concrete framed buildings: a guide to design and construction. TCC/03/024. Camberley: Concrete Centre, 2006

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6.8

7

Non-monolithic shear wall construction

7.1

Introduction

Non-monolithic walls are often of precast construction, arranged as storey-height units with horizontal joints coinciding with floor slab connections. Common material systems include: – Precast reinforced concrete (including tilt-up construction) – Hybrid precast in situ reinforced concrete – Timber and light gauge steel platform frame construction – Cross laminated timber (CLT) Section 7.2 discusses general characteristics of these systems, with Sections 7.3–7.6 focusing on the additional characteristics of the systems listed in the previous paragraph, in turn. Each of these sections has a bias towards the joints which are key elements in the design. Introductions to both loadbearing masonry and steel plate diaphragm walls are also included in Sections 7.7 and 7.8. Both systems differ significantly to those listed here as well as from one another. Discussion of proprietary modular ‘system builds’ (e.g. Tata CorefastTM 7.1) is omitted. These systems are generally developed via a manufacturing approach to research, design, testing and product iteration, and are often procured complete with specialist in-house design services.

The pros and cons mean that off-site fabrication generally favours buildings with highly repetitive functional requirements including bedroom blocks for hotels, universities and prisons. In each of these examples, there is a clear advantage to the building owner/occupier if the rooms are standardised, while the repetition means that large savings are possible from relatively minor design refinement. Aesthetically, off-site fabrication can achieve unparallelled favourable results in terms of surface finish quality. It is however very hard to mask an assembled structure where the components are on display. Hence joint patterns can be as important as overall form to the appearance of a structure (Figure 7.2). This should be brought to the attention of both architect and client. The economic viability of these systems varies significantly internationally. Local production facilities and market competitiveness, raw material availability, skilled labour and international financial exchange rates can have an impact. Meanwhile transport, site access and craneage restrictions can influence whether an off-site fabrication option is viable at a specific site. In the absence of site specific restrictions, maximum panel sizes are usually in the order of 12m  3.5m and not more than 20 tonnes. However, to establish site specific bounds on panel sizes and weights, it is usually essential that the designers consider the construction sequence and crane locations early in the design development. This may require early contractor consultation. Further reading: guidance on craneage

7.2

Precast construction

Off-site fabrication Advantages of off-site fabrication over in situ construction can include less site labour, faster construction and better quality control. Longer lead in times, greater need for standardisation and additional contracted party interfaces in the design and/or construction are three common disadvantages. A more extensive, but still not exhaustive, list of pros and cons is given in Figure 7.1.

The following texts are recommended as a source of further guidance on craneage: – BS 7121-1: 2006: Code of practice for safe use of cranes – Part 1: General. London: BSI, 2006 – Skinner, H. et al. Tower crane stability. CIRIA C654. London: CIRIA, 2006 Characteristics of jointed systems Joints are a key part to any off-site fabricated system. While large areas of the panels can behave in a similar manner to monolithic walls, joints will often have a significant impact on the design. These usually

Pros

Cons

– – – –

– Less inherent robustness – Poor joint details can be points of structural weakness and can have a detrimental effect on fire resistance, thermal and acoustic insulation and waterproofing – Panels require built-in erection tolerances and long-term joint locking mechanisms – Less opportunity for flexural continuity leading to structural performance inefficiencies – Erection logistical challenges: transportation, delivery, storage craneage and temporary propping – Longer lead-in period

Faster site construction Less wet trades on-site Less skilled labour on-site Safer working conditions: less work at height, better safety controls – Better control of component quality – Greater opportunity for architectural finishes (e.g. cast surface patterns and/or colour pigments in concrete panels) – Greater component precision, allowing refined designs (e.g. reduced permissible concrete cover to reinforcement)

Figure 7.1 Typical pros and cons of off-site prefabrication, stated relative to in situ construction 40

The Institution of Structural Engineers Stability of buildings Part 3

Non-monolithic shear wall construction

Figure 7.2 Buildings with exposed prefabricated elements introduce components that may have vastly different properties to those of the panels; they can also cause high stress concentrations where the joints are discrete. These features will often add to the potential failure mechanisms and can impact on the overall robustness of a structure (Box 7.1).

(including robustness forces). The joints tend to be located at or close to slab levels (the exact position varies by material construction). This ensures the necessary out-of-plane restraint close to the joint but also allows the construction to proceed a storey at a time with a high degree of repetition.

Most precast wall systems contain both vertical and horizontal joints between panels. Neither of these joints tends to provide significant minor axis bending resistance and panels will normally be designed to span one-way between points of lateral support. This may be horizontally between return walls but is more often vertically between floor slabs.

Vertical joints primarily transfer vertical shear between panels to resist the deformation shown in Fig. 2.5c. Their placement is largely dependent on the specific wall geometry together with limitations on fabrication, transportation and craneage. Openings should be considered when deciding on their layout. Whether an opening can be housed within a single panel will often depend on the panel and opening dimensions and whether the panel can sustain the temporary stresses during lifting.

Where panels span vertically, horizontal joints (i.e. those between panels stacked one above another) transfer horizontal shear, compression and tension Box 7.1

Robustness

Actions through both lintels and vertical joints can be reduced significantly in the completed structure by staggering openings and joints from floor to floor (Figure 7.3). While efficient, this is rarely practical and tends not to be favoured by the architect and/or services engineer. Joints will often contain steel connection components. These may be reinforcing bars with couplers or grout ducts in concrete systems; nails, screws and wall ties in timber platform construction; or bolts with or without gusset plates in CLT construction. Both the connector and its anchorages into the panel must be sufficient to transfer the design and minimum robustness forces.

Vertical joint The direct failure of a single loadbearing precast wall panel caused by a domestic gas explosion led to the partial collapse of Ronan Point, a 22-storey apartment building in London. This event publically highlighted the need for robustness criteria7.2, 7.3. Although the failure did not result in a loss of global stability, the scale of the failure – which extended through the four floors above the explosion and to all 17 floors below – was deemed disproportionate to the cause. Failure was concluded to have been ‘progressive’, with the failure of each wall panel leading to the overloading and/or loss of restraint to its neighbour. The failure prompted a review of UK Building Regulations, the findings of which established design philosophies for robustness which are used universally adopted in modern codes of practice.

 Openings  ‘framed’ by   wall and  lintel panels     Openings  contained   within  single panels   

‘Deep beam’ spanning opening below

Horizontal joint Figure 7.3 Joints around openings The Institution of Structural Engineers Stability of buildings Part 3

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7.2

7.3

Non-monolithic shear wall construction Joint details must provide sufficient tolerance to allow erection to proceed. Where this initial tolerance invalidates a load path that is later relied upon, a locking mechanism is needed. This might be mechanical with an insert or locking nut, or chemical with grout or resin. How it is fixed or installed must be considered when planning the joint and can impact the setting out, access requirements and load capacity of the connection. In many instances the dimensions and requirements of a joint can govern the thickness of a panel. Joint slip Joint slip is movement within a joint that is not representative of the wall panels. It can result from either tolerance between components or from elastic or plastic deformation within the highly stressed region of the joint. It is most pronounced where: – The joint’s stiffness is significantly less than the panel stiffness – Discrete joints cause significant stress concentrations in either the connector or the panel – Multiple joints have a cumulative effect on the global stiffness of a system (e.g. where the jointed panels are narrow relative to the overall dimension of a wall) – Joints are positioned in areas of high stress (e.g. around openings) Slip resulting within a joint should be considered in the overall stability model where it is significant to the global behaviour of the system (Box 7.2). Slip can be critical where it causes a change in global stiffness that has a significant impact on: – The distribution of forces between walls in a multiwalled structure – The magnitude of PD effects – The serviceability sway deflection Design responsibility and programme Off-site fabricated elements follow a procurement model similar to structural steelwork. While site Box 7.2

erection is usually fast, it is preceded by a significant lead-in period during which the material order, factory work and site delivery take place. Approvals, reviews and any necessary dialogue between the consulting engineer and the subcontractor/supplier must also occur and be programmed for in this period. Finalised design information must be issued ‘For Construction’ and provided to the subcontractor in advance of the lead-in period. It must include all details for the end product: reinforcement, cast-ins, cut-outs, connectors and fixings, etc. To produce this level of detail, the design of the building services must be well progressed with all penetrations known; the architect must have finalised all setting out information; and the subcontractor must have erection, fixing and/or in situ pour sequences developed sufficiently to locate cast-ins for temporary props. The level of detail provided by the consulting engineer can vary between projects, with detailed design responsibility often split between the consultant and the subcontractor/supplier. Without exception, the consulting engineer must, however, maintain responsibility for the global behaviour of the completed structure. As a minimum, they must develop a credible scheme that presents feasible outline designs and performance requirements for the panels and principal joints upon which the design can be detailed. Whether the design consultant then goes on to detail the panels and the joints will be dependent on the supply chain and contractual arrangements.

7.3

Precast reinforced concrete wall construction

Precast reinforced concrete wall construction has been common since the middle of the last century.

Modelling joint slip with 1- and 2-dimensional elements

Joint slip may be difficult to predict accurately in analysis and a sensitivity study is often useful to determine the significance of joint flexibility. At preliminary stages, slip can be modelled approximately by varying the stiffnesses of the panels above and below the theoretical design value, or by imposing non-elastic deformations between nodes of the model. Some element and connection forces will be amplified by increased stiffness, while others are amplified by decreased stiffness. Where the joint slip proves to have significant impact on the stiffness (say by altering the stress distribution by more than 10%), physical testing may be required to determine refined bounds on the design parameters. These parameters are often non-linear and should make allowance for any time-based softening, friction loss and creep. Joint slip can be modelled in either a grillage or 2-dimensional FE model. In a grillage model, it is best achieved by joining elements with translational springs in the axis of the joint. In 2-dimensional FE models, a similar outcome is best achieved by having a continuous or broken line of ‘soft’ elements of reduced in-plane shear stiffness coinciding with the joint plane.

Stub element with high flexural stiffness/low axial stiffness

Low stiffness elements

Vertical joints

Panelised wall 42

The Institution of Structural Engineers Stability of buildings Part 3

1-D element model

2-D element model

Non-monolithic shear wall construction

Vertical joint

. Min m m 75

. Min m m 0 15

7.4

Steel plate

Oversized washers Pier Elevation Anchor bolts into cast-in ferrules

Spandrel panel Plan

Figure 7.6 Vertical joint (shown between planar panels; corner details similar)

Figure 7.4 Minimum wall thicknesses Out of favour in the UK following the Ronan Point failure (Box 7.1), it has seen a steady revival fuelled by the advantages of off-site production. These drivers, together with innovations across the global industry, have made the technique popular for low- to medium-rise structures. Form Precast structural walls are usually upward of 150mm thick, with either one or two layers of reinforcement. Thinner shear-resistant spandrel panels as little as 75mm are possible but only in conjunction with integral piers (Figure 7.4). Panel design Away from the joints, individual panels act as monolithic reinforced concrete elements and can be designed largely in accordance with generic guidance for reinforced concrete. The internal stress field in the permanent state will be dependent on both the direct loads acting on the panel and the nature of the actions transferred via any joints. Temporary (handling) load cases may need to be considered in addition to those for the permanent state. These must take account of the lifting points which, where necessary, should be specified by the designer. Joints It is normal practice to use vertical dowel bars housed within cast-in corrugated sleeves for horizontal joints (Figure 7.5). Once assembled, the

Precast wall

Bleed hole

Centrally placed corrugated grout sleeve 25mm

Grout feed

Slab poured once wall installed

Dowel bar anchored into founding structure

Figure 7.5 Horizontal dowelled joint (shown to a foundation)

sleeves are grouted enabling the dowel to transfer shear and tension. Compression is transferred away from the dowels via a combination of any local shims and the gross contact area of grout. Shims will usually be pre-loaded by the self-weight of the structure before the grout is installed and this load is unlikely to be redistributed in the permanent state. The position, contact area and material of shims may therefore be critical and should be defined. Ensuring shims have adequate edge distance so that they are away from the cover zone is essential. Vertical joints tend to use discrete steel plates, channels or angles bolted to adjacent panels across the joint (Figure 7.6). Bolts can fix into cast-in threaded anchors (sometimes known as ‘ferrules’), usually positioned to +5mm. Alternatively they can pass through a sleeve in the wall (to be grouted once the bolt is installed) and fixed on the far wall face. As these pieces of steelwork are exposed, fire proofing and corrosion protection are often needed and must be specified by the designer. Further reading: precast reinforced concrete wall construction The following texts are recommended sources of further guidance on precast reinforced concrete wall construction: – Elliott, K.S. Precast concrete structures. Oxford: Butterworth-Heinemann, 2002 – Southcott, M.F. and Tovey, A.K. Tilt-up concrete buildings: design and construction guide: a comprehensive guide to the benefits, economics and practicalities of tilt-up design and construction in the UK. Crowthorne: BCA, 1998

7.4

Hybrid precast in situ reinforced concrete wall construction

Hybrid reinforced concrete walls, sometimes referred to as ‘twin wall’ construction, comprise of precast cassettes stitched together on-site with loose reinforcement and filled with in situ concrete to form solid walls. They are intended as a replacement to traditional in situ reinforced concrete walls, offering improved finish quality, reduced formwork and faster construction (Box 7.3). Their use is increasingly common on low- to mediumrise developments and, like precast reinforced The Institution of Structural Engineers Stability of buildings Part 3

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7.4

Non-monolithic shear wall construction Box 7.3

Hybrid precast in situ reinforced concrete wall construction to the Francis Crick Institute, London

The Francis Crick Institute is approximately 150  70m on plan with four independently stabilised blocks. Each block is stabilised by shear walls, the majority of which are of hybrid construction. These were constructed with the columns one floor at a time7.4. This photograph taken during construction shows a hybrid wall alongside a traditionally formed in situ wall. This side-byside comparison illustrates the props necessary to the hybrid walls but also the lack of formwork.

the central void and connects the skins of a single cassette. It acts to maintain the form of the cassette in the temporary state and to resist bursting pressures during placement of the in situ concrete. It also acts as shear reinforcement. Total wall thicknesses are usually upwards of 200mm but thicknesses less than 250mm are difficult to achieve7.5. Joints Stitch bars transfer shear and tension between cassettes. They are fitted in situ once the cassettes are positioned, often as a pre-formed cage for easy handling. These are positioned in the void between precast skins and have reduced effective depth relative to bars cast in the precast cassettes. This has no impact on pure tension but means that joints tend to have less flexural capacity than the parent panels. Stitch bars will usually have restricted lap lengths owing to the geometrical conflict imposed by the cast in lattice reinforcement (Figure 7.8). This incomplete development has a detrimental impact on a joint’s strength and also its ductility. It affects the pure tension, flexure and shear capacities.

concrete wall construction, they are most suited to buildings with repetitive wall arrangements consisting of planar elements that are consistent from storey to storey. Form The cassettes are made up of two skins of precast concrete, each typically 50–80mm thick, with cast in main vertical and horizontal reinforcement (Figure 7.7). Lattice reinforcement, usually welded to the main bars to form ‘lattice girders’, is cast in during the prefabrication. This reinforcement spans

Wall reinforcement within precast shims

Lattice reinforcement across cassette

25mm tolerance gap packed level with shims

Loose bars to joint

Full lap

Timber chocks

In situ slab

Precast projects into slab cover zone

Full lap

In situ core

Precast cassette Figure 7.7 Hybrid wall cross-section showing a typical junction to an in situ slab 44

The Institution of Structural Engineers Stability of buildings Part 3

In-plane panel shear Shear between the precast and in situ faces of a single panel must be considered as this is the load path transferring forces from the main bars within the precast skin to the stitch bars across the in situ joints. Shear must transfer between concrete cast at different times, and guidance on this is given in BS EN 1992 Part 1-1 Clause 6.2.57.6. In most situations, the shear stress will be small owing to the very large area over which the shear acts. However, the stress becomes more significant as the shear force increases; typically when the main reinforcement bar size and wall thickness are large. This tends to set an effective upper thickness limit on hybrid walls at about 400mm. Both the concrete interface and the lattice reinforcement can contribute to the overall shear resistance. Lattice reinforcement must be anchored into the precast skins to make an effective contribution. This anchorage is often via welds to the main bars and supplementary requirements for welded steel reinforcement must be adhered to; for designs to Eurocodes, see BS EN 100807.7. The roughness of the internal surfaces to the precast skins has the most significant influence on the concrete surface shear interlock. These surfaces are normally unformed during casting and can be of varying roughness. Further considerations Challenging details include slabs at different levels, double height walls with horizontal joints that are unrestrained, and panels supporting down-stand beams. Although it is usual to have panels terminating above and below floor slabs (Fig. 7.7), pull out reinforcement, couplers or ferrules can be cast in to accommodate slabs butting into the side of a panel. These can be fixed to the form when casting the precast skin to achieve good accuracy (+5mm typically). Where a panel is to support a down-stand beam, the effects of end moments, local crushing, wall buckling

Non-monolithic shear wall construction

7.5

Cage lowered from above Prefabricated reinforcement cage Lattice reinforcement to the cassettes Prefabricated cage

Lattice reinforcement

Restricted lap length Figure 7.8 Stitch detail at vertical joints

and instability should be considered. It is not uncommon for such joints to dictate the width of the in situ portion of the wall and hence the overall wall thickness. Where this has significant impact, it may be advantageous to have an in situ column between panels, possibly protruding from the plane of the wall (Figure 7.9).

In situ Precast

Panels should be sized to allow erection on shims, leaving a gap of approximately 25mm at the base (Fig. 7.7). This allows tolerance on the set out, but also provides the principal means of checking whether the in situ concrete reaches the base of the pour. At the top, internal panels should either project a small amount (typically the slab cover depth) into the slab soffit where the slab is in situ, otherwise they should terminate short of precast floor units allowing room for shims and grouting. Meanwhile a shadow gap can be incorporated where the slab uses precast biscuit units as permanent formwork (Figure 7.10). At perimeter walls, it is typical to extend the outer precast skin to the slab finish level, using it as formwork to the slab (Fig. 7.10).

In situ column between wall cassettes Figure 7.9 Down-stand beam connections

In specifying a hybrid wall system, the detailed design engineer must specify a rise limit rate to be adopted by the contractor during concreting. This limit will be dependent on capacity of each of the lattice reinforcement and precast skins to resist the pressure of the wet concrete and can be as low as 1m/hr7.5. Where the wall is narrow, pokering the in situ concrete can be near on impossible and the in situ concrete should be specified as a workable or self-compacting mix with plasticisers and/or maximum 10mm aggregate.

7.5

Timber and light gauge steel ‘platform’ frame construction

‘Platform’ frame construction is suitable for low-rise cellular buildings, practical up to a maximum of six storeys7.8. The walls are hollow, comprising an

External skin acts as formwork to the slab

Precast biscuit slab

Shadow gap Precast wall cassette

Note Reinforcement within the precast wall cassettes and slab biscuit is omitted for clarity. Figure 7.10 Perimeter wall detail with shadow gap to biscuit slab The Institution of Structural Engineers Stability of buildings Part 3

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7.5

Non-monolithic shear wall construction

Figure 7.11 Platform frames undergoing construction

internal stud frame with face-fixed sheathing board (Figure 7.11). Studs can be either timber or light gauge steel, while the sheathing is usually either a wood-based product (typically plywood or orientated strand board) or plasterboard.

provide buckling restraint to the sheathing (resulting in tension in the fixings) as well as transfer in-plane shear (Figure 7.12).

Walls are typically installed a storey at a time, followed at each turn by the floor structure which creates a platform off which the next level is fixed. The floor structures are usually of similar lightweight timber construction to the walls, detailed to act as horizontal diaphragms. Being lightweight, wind uplift and overturning are often critical and both the components and their connections will often need to resist anchorage tension. Robustness tie forces must also be considered.

Shear buckling can be avoided by limiting the diaphragm slenderness, measured as the distance between stud fixings divided by the thickness of the sheathing. BS EN 1995 Part 1-1 Clause 9.2.4.3.2(7)7.9 states that shear buckling of wood-based products can be disregarded when the slenderness ratio is less than or equal to 100. This generally defines limits on the spacing of the studs (varying with the sheathing thickness). However, 400 or 600mm centres are typical in the UK7.10. Both spacings are suited to standard 2.9  1.2m sheathing board and catered for with standard cavity insulation.

To act as shear walls, the sheathing must act as vertical diaphragms connected via the stud frame to the applied horizontal actions. Fasteners connecting the sheathings to the studs must be adequate to

Where a sheathed wall panel is subject to significant out-of-plane forces (e.g. a wind pressure on a fac¸ade), minor axis flexure may also influence the stud spacing or section. The sheathing may or

Figure 7.12 Shear forces in a sample of fixings caused by in- and out-of-plane actions 46

The Institution of Structural Engineers Stability of buildings Part 3

Non-monolithic shear wall construction

Plane sections remain plane

Discontinuous strains between sections

ε

ε

Composite

Non-composite

Figure 7.13 Composite and non-composite flexural behaviour may not be designed to act compositely with the stud frame (Figure 7.13). Where it is to act compositely, it must be continuous between supports (typically the floors) or fully lapped, and must have adequate fixings to transfer longitudinal (flexural-borne) shear stresses to the stud. This construction is commonly referred to as ‘stressed skin’ construction. While the stud frame will support the sheathing, it is normal that the sheathing provides essential local restraint to the stud frame (both lateral torsional and in-plane Euler buckling restraint). In this way, the sheathing and stud frame are generally co-dependent (with neither being sufficient to withstand loads independently). Both wood-based products and plasterboard have unfavourable characteristics that limit their adequacy as primary structural elements: – Wood-based products are combustible and their thin nature means they have limited fire resistance. Where critical, they generally require additional fire protection, usually in the form of plasterboard. – Plasterboard loses integrity when exposed to moisture. Moisture-resistant products are available, however these only contain water repellent additives that delay the loss of performance; they do not completely eradicate it. – Plasterboard is widely recognised as a nonstructural material that is often removed unwittingly when buildings are remodelled.

Further reading: platform frame construction The following texts are recommended sources of further guidance on platform frame construction: – Institution of Structural Engineers and TRADA. Manual for the design of timber building structures to Eurocode 5. London: IStructE, 2007 – Grubb, P.J. et al. Building design using cold formed steel sections: light steel framing in residential construction. SCI Publication 301. Ascot: SCI, 2001

7.6

Mass timber

Cross laminated timber (CLT) and glued laminated (glulam) timber are both solid engineered products available in dimensions far exceeding those of sawn timber7.12. As examples of ‘mass timber’, both are well suited to solid wall construction and can achieve far greater capacity than is possible from sheathed stud systems (Figure 7.14).

On balance, wood-based products (with plasterboard fireproofing) are recommended for structural sheathing in preference to plasterboard. Note that although plasterboard may provide fire protection to wood-based sheathing, a wall containing both materials should only rely on the resistance provided by the wood-based product. This, and further design recommendations for sheathed partitions, is contained in the British document PD 6693 Part 1, cited in the UK National Annex to BS EN 1995 Part 1-1. This document7.11 gives non-contradictory complementary information to BS EN 1995 Part 1-17.9.

Figure 7.14 CLT walls under construction The Institution of Structural Engineers Stability of buildings Part 3

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7.6

7.6

Non-monolithic shear wall construction Box 7.4

Mass timber construction to The Forte´, Melbourne

Completed in 2012, ‘The Forte´’ (pictured) is Australia’s first CLT building7.13. It is a ten storey residential block, of cellular layout with 128mm thick CLT shear walls. All CLT panels (485 tonnes in total, with the largest measuring 16.5  3m) were imported to Melbourne from a production centre in Europe. At the time, this was favourable due to a strong Australian Dollar7.14. Another noteworthy all-timber residential building is that at 24 Murray Grove, London7.15. This project was widely publicised for completing the construction of eight of the nine floors in 27 days by a team of four people7.16.

Form The bending and shear stiffness of timber are comparatively low. Hence deflection is often critical – with shear lag, in particular, of greater impact in timber systems than in those of steel or concrete. Where a concrete wall may easily have a height to length aspect ratio L/b ¼ 8, a timber wall should target 3 or 4 to efficiently achieve the necessary stiffness. This may ultimately limit a building’s height on any given site, and puts greater pressure on the plan layout to achieve an efficient wall arrangement. Wall thicknesses are available up to 400mm as a single section7.19 but nothing close to this has been used on projects to date. Acoustic and fire performance can each increase the thickness beyond that which is needed for strength or stiffness. Plasterboard can be used as an effective means of fire protection avoiding a sacrificial char thickness. Meanwhile, dual wall systems with two panels sandwiching a narrow air gap or acoustically absorbent spacer can be favourable when acoustic requirements govern. Penetrations can be incorporated into timber walls by either taking cut-outs from a single solid panel, or by joining two independent panels with a lintel (usually a glulam beam). Where a cut-out is made, the significant stress concentrations at the corners of the opening will often govern the entire wall panel design. This can be overcome by bolting additional sections across the highly stressed regions (Figure 7.15). The performance of such bolstering is highly dependent on the strength and stiffness of the fixings. The effect of eccentricity should also be considered where elements lap out-of-plane.

Recent investment and developments in CLT and glulam have enabled low- and medium-rise timber structures that would traditionally have been constructed using masonry, steel or concrete (Box 7.4). One driving force for this has been the sustainability agenda, discussed in the Institution’s publication Building for a sustainable future: an engineer’s guide7.17. Other drivers include the favourable characteristics of timber as a workable material, and the abundant/discounted supply of timber in some geographic regions7.18.

Face-fixed strengthening to the lintel

Material properties Material properties can vary somewhat from native sawn timber and may be taken from manufacturer data with reference to codes of practice or standardised test measures. Both CLT and glulam can contain a mix of stress grades, with higher grades used at the extremities responding to the flexural stress distribution. Timber is not a linear elastic material, nor is it isotropic; both of these characteristics should be appreciated when setting up and justifying the accuracy of an analysis model. In the case of CLT, the behaviour depends on the orientation and build-up of

Lintel beam

Opening cut out of single panel

Discrete wall panels

Figure 7.15 Openings and lintel strengthening 48

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7.7

the laminates. Most CLT has a symmetrical profile with outer laminates in the same orientation. Joints Horizontal joints in solid timber construction are best located immediately above the floor bearing, with walls butt connected. This avoids axial loads passing through the cross-grain of floor elements. Slabs may be supported off steel angle bearers face-fixed to the wall panels (Figure 7.16). Vertical panel-to-panel joints are normally lapped where the panels are co-planar, or butt jointed where panels are orthogonal. In both instances it is common to have two lines of screws positioned as shown in Figure 7.17. Both details must have screws adhering to minimum edge distances and spacing as defined in codes of practice. Additionally, where using the butt connection, screws must anchor into the vertical laminates only, not the horizontal end grain.

Floor Joint in wall immediately above floor slab Moment from eccentric floor bearing taken by wall below

Steel bearing angle with fixings for robustness

Wall

Figure 7.16 Floor to wall joint

in a range of sizes, usually larger than bricks and a multiple of a standard brick module including mortar (i.e. 225  75mm). They are also available in a range of densities that correlate to the strength. Brick and block sizes vary internationally and sizes should always be used that are appropriate to the region. This should be something the project architect is mindful of, but the sizes will likely influence structural details (e.g. the setting out of supporting beams and/or strip foundations).

Figure 7.17 Vertical joints between co-planar and orthogonal panels

7.7

Loadbearing masonry

Loadbearing masonry is a traditional approach to wall construction that remains popular in many regions. Clay bricks, concrete blocks and natural stone may be used as constituent ‘units’. The size of the units is critical in differentiating masonry from the precast systems discussed in previous sections. Qualities of masonry include its reasonable compressive strength, durability, fire resistance, ability to insulate, aesthetic quality, and ease of handling during erection. A disadvantage is the labourintensive in situ construction process which is a wet trade susceptible to weather conditions. Further disadvantages of traditional unreinforced masonry include its brittle nature and limited tensile capacity. These latter characteristics tend to make unreinforced masonry highly sensitive to movement and also prone to sudden failure. These characteristics can, however, be lessened with the use of reinforcement. Masonry units and mortar Manufactured clay bricks and concrete blocks are most widely used and are much cheaper than natural stone. Both are available in standard sizes. In the UK, standard bricks are 215  65  102.5mm and are used with a 10mm mortar joint. Blocks are available

The weight and ease of handling should also be considered when choosing a block size. CIRIA guide C662 recommends blocks weighing over 20kg should be avoided where manual handling is intended7.20. Mortar is used in all but ‘dry stone wall’ construction to provide nominal tensile and shear adhesion between adjacent units. Most modern construction uses cement-based mortar, although lime-based mortar remains necessary for the repair and/or adaption of many historic buildings where it was used in the original construction. Lime-based mortar can generally accommodate a greater degree of movement than cement mortar but both are ultimately brittle. Form A wall may be made up of a single or multiple ‘skins’, each skin being a solid arrangement of the brick or block units. The packing arrangement within a skin is often referred to as the ‘bond’. Most skins are a single brick or block unit thick and use a stretcher bond (Figure 7.18). This leads to a macro

Figure 7.18 Masonry stretcher bond The Institution of Structural Engineers Stability of buildings Part 3

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Fire protection to surfaces including the steel connection pieces

7.7

Non-monolithic shear wall construction on the floor bearing detail; guidance is given in Section 5.3.6 of the Institution’s Manual for the design of plain masonry in building structures to Eurocode 67.21.

behaviour that tends to be non-isotropic with differing horizontal (bed joint) and vertical characteristics. Skins can be standalone or form part of a cavity wall system in which two skins are spaced apart and tied at regular intervals. Cavity wall construction can be favourable for insulation and acoustic isolation. Wall ties should always be used in cavity construction to improve robustness. They also act to enhance the buckling capacity of a wall, increasing the axial load carrying capacity above the sum of the component skins. Reinforced masonry uses steel bars or wire placed horizontally and/or vertically in one of the configurations shown in Figure 7.19. Bed-joint reinforcement is generally restricted to bars or wire (up to 6mm diameter). Meanwhile, reinforcement within the cores of hollow units or the cavity of a cavity wall can be standard reinforcement as used for reinforced concrete. The limiting bar size is generally governed by the compressive strength of the masonry unit. It should be noted that any reinforcement within hollow cores or a cavity must be grouted to be effective. Design Axial compression in loadbearing masonry walls enhances both the shear and bending capacities by providing a pre-compression. This makes up for the lack of tensile strength. However, it also makes walls vulnerable to buckling and out-of-plane failure is often critical. As such, out-of-plane actions at the ultimate limit state tend to dominate the design of shear walls. This is true even where the out-of-plane actions are several orders of magnitude less than the in-plane actions. Minor axis slenderness is generally used as a governing parameter in the design of unreinforced walls (Section 2.8). This is a function of the wall’s effective thickness, height and/or horizontal span. An axial load eccentricity should be considered additional to all lateral actions to determine the critical design case. This eccentricity is dependent

Provided the ultimate limit state is satisfied, serviceability checks of individual panels are seldom needed and are largely omitted from design guidance. A common check is to limit overall inter-storey sway. The Institution’s Manual for the design of building structures to Eurocode 17.22 recommends that both total sway and inter-storey drift should not exceed height/500. Movement Bricks and blocks both exhibit dimensional instability that can continue over a number of years. This is often best accommodated with the inclusion of vertical movement joints. The spacing of joints is dependent on the nature of the unit and mortar but spacing of 12–15m for clay bricks and 6–8m for concrete blocks is typical. It should be noted that fired clay bricks tend to expand while concrete blocks tend to shrink; both by as much as 0.5mm/m7.21. Cavity walls with an external brick/internal block skin configuration should have joints staggered to minimise the stresses developing in the cavity ties. Damp proof course External masonry walls often require a damp proof course or membrane positioned in a bedjoint close to ground level. Such membranes impede the passage of moisture up into the wall but can have variable structural characteristics. In particular, they can cause a slip plane that has a detrimental impact on the shear capacity of a wall. Little guidance is given in BS EN 1996 Part 1-17.23 on the friction, interlock and/or adhesion that can be assumed, and specific product data should generally be sought from the manufacturer. Robustness Walls should be tied to adjacent structural elements in order to avoid collapse. Guidance is given in the Institution’s Practical guide to structural robustness and disproportionate collapse in buildings7.2.

Reinforcement

Bed-joint reinforcement

Figure 7.19 Reinforced masonry 50

The Institution of Structural Engineers Stability of buildings Part 3

Vertical and/or horizontal reinforcement in hollow units

Cavity wall ties

Cavity wall reinforcement

Non-monolithic shear wall construction Further reading: introduction to masonry The following guides provide a more extensive introduction to masonry wall construction and are additional to the sources referenced within the main text: – ‘Introduction to masonry. Technical Guidance Note’. The Structural Engineer, 91(6), June 2013, pp24-26 – Curtin, W.G. et al. Structural masonry designers’ manual. 3rd ed. Oxford: Blackwell, 2006 – Roberts, J.J. and Brooker, O. How to design masonry structures using Eurocode 6 Part 2. TCC/03/36. Revision 2. London: The Concrete Centre, 2013. Available at: http:// www.eurocode6.org/Published%20support%20material.htm [Accessed: 13 January 2015]

7.8

Box 7.6

Composite steel plate diaphragm walls to China World Trade Centre, Beijing

Composite steel-reinforced concrete walls extend through the basement to the 16th floor of this 74 storey (330m) tower providing greater robustness, ductility and stiffness than is achievable with either traditional reinforced concrete or steel plate shear walls. Each wall has a web plate, welded to boundary elements (steel beams and columns). These steel assemblies, complete with shear studs attached to the plate, were encased within in situ reinforced concrete forming a ‘composite special plate wall’7.26.

Steel plate diaphragm walls in steel framed buildings

Steel plate diaphragms are suited to medium- and high-rise structures where they have been proven to match or outperform more conventional braced frames and reinforced concrete shear walls. The plates, together with the surrounding frame, are often lighter than equivalent reinforced concrete walls and this can lead to reduced foundation loads. They are also relatively thin (typically 5–12mm) and can minimise the loss of lettable floor area. These are advantages that led to the system being used for Jinta Tower, Tianjin7.24. To their detriment, the steel plates require almost continuous fixing to the surrounding frame elements. This generally necessitates either a large number of bolts or site welds. Despite some use in the UK (Box 7.5), steel plate diaphragms have been most widely used in China, Japan, and North America, in both new developments and as seismic retrofits to existing structures. The American standard AISC 341-107.26 and Canadian standard CSA S16-147.27 are the most widely used sources of guidance; both give specific criteria for the design of these systems where subject to dominant seismic loads. Box 7.5

In very tall buildings, each of the following must be carefully considered: stiffness of the plate, axial shortening and stiffness of the frame elements, fatigue due to cyclic oscillation, and buckling at service loads. The flexural stiffness of the bounding frame elements must be such that in-plane forces along the elements do not cause significant deflection so as to impact the load path through the plate. Minimum stiffnesses for each of the columns and beams are defined in both the American and Canadian codes. Finally, steel plates can be cast within reinforced concrete walls to produce composite sections that outperform traditional reinforced walls. This system was used within the China World Trade Centre, Beijing7.28 (Box 7.6).

Steel plate diaphragm walls to Embankment Place, London

This over-site development positioned above the platforms to Charing Cross Station has much of the superstructure hung to ensure a column free space at platform level. This concentrates a large percentage of the equivalent horizontal force (referred to as ‘notional horizontal force’ at the time of the design) at the top of the cantilevering stability cores. To cater for this force and provide sufficient stiffness so that PD effects are not overwhelming, a welded steel plate shear wall is incorporated through the upper storeys of the superstructure7.25.

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7.9

Non-monolithic shear wall construction

7.9

References

7.1

Corus. Bi-Steel design and construction guide. Scunthorpe: British Steel, 1999

7.2

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

7.3

7.18

Fast, P. Unusual hybrid timber-steel structures [webinar]. 19 May 2010. Available at: https://istructe. adobeconnect.com/_a848983388/p83578900 [Accessed: 13 January 2015]

7.19

Sutton, A. et al. Cross-laminated timber: an introduction to low-impact building materials. BRE Information Paper IP 17/11. Watford: IHS BRE Press, 2011

Elliott, K.S. and Jolly, C.K. Multi-storey precast concrete framed structures. 2nd ed. Chichester: Wiley-Blackwell, 2013

7.20

Ove Arup & Partners and Gilbertson, A. CDM2007 – Construction work sector guidance for designers. CIRIA C662. 3rd ed. London: CIRIA, 2007

7.4

Partridge, R. et al. ‘The Francis Crick Institute’. The Structural Engineer, 92(3), March 2014, pp10-19

7.21

Institution of Structural Engineers. Manual for the design of plain masonry in building structures to Eurocode 6. London: IStructE, 2008

7.5

Whittle, R. and Taylor, H. Design of hybrid concrete buildings: a guide to the design of buildings combining in-situ and precast concrete. CCIP-030. Camberley: The Concrete Centre, 2009

7.22

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

7.23

BS EN 1996-1-1: 2005 þ A1: 2012: Eurocode 6 – Design of masonry structures – Part 1-1: General rules for reinforced and unreinforced masonry structures. London: BSI, 2012

7.24

Sarkisian, M. et al. ‘World’s tallest steel shear walled building’. CTBUH Journal, 1, 2011, pp28-33. Available at: http://ctbuh.org/LinkClick.aspx?fileticket=e2KgCTBu8 yw%3D&tabid=3096&language=en-US/&_sm_au_= iVVR0qQLjsLrMLsN [Accessed: 13 January 2015]

7.25

Barrie, M. and Weston, G. ‘Embankment Place: building over Charing Cross Station’. The Structural Engineer, 70(23/24), 8 December 1992, pp405-411

7.26

AISC 341-10: Seismic provisions for structural steel buildings. Chicago, Il: AISC, 2010. Available at: www.aisc.org/2010sp [Accessed: 13 January 2015]

7.27

CSA S16-14: Design of steel structures. Toronto, Ontario: Canadian Standards Association, 2014

7.28

China World Tower. Available at: http://www. skyscrapercenter.com/beijing/china-world-tower/379/ [Accessed: 13 January 2015]

7.6

7.7

BS EN 1992-1-1: 2004: Eurocode 2: Design of concrete structures – Part 1-1: General rules and rules for buildings. London: BSI, 2004 BS EN 10080: 2005: Steel for the reinforcement of concrete – Weldable reinforcing steel – General. London: BSI, 2005

7.8

UK Timber Frame Association. ‘Timber Engineering Notebook series. No. 3: Timber frame structures – platform frame construction (Part 1)’. The Structural Engineer, 91(5), May 2013, pp26-32

7.9

BS EN 1995-1-1: 2004 þ A1: 2008: Eurocode 5: Design of timber structures – Part 1-1: General – Common rules and rules for buildings. London: BSI, 2009

7.10

Institution of Structural Engineers and TRADA. Manual for the design of timber building structures to Eurocode 5. London: IStructE, 2007

7.11

PD 6693-1:2012: Recommendations for the design of timber structures to Eurocode 5: Design of timber structures – Part 1: General – Common rules and rules for buildings. London: BSI, 2012

7.12

UK Timber Frame Association. ‘Timber Engineering Notebook series. No. 2: Engineered wood products and an introduction to timber structural systems’. The Structural Engineer, 91(4), April 2013, pp42-48

7.13

Powney, S. Melbourne marvel. Timber & sustainable building. 2012. Available at: http://www.timberbuilding.com/features/melbourne-marvel/ [Accessed: 13 January 2015]

7.14

XE Currency Charts (AUD/EUR). Available at: http:// www.xe.com/currencycharts/?from ¼ AUD&to ¼ EUR& view ¼ 10Y [Accessed: 13 January 2015]

7.15

MGB Architecture and Design. The Case for tall wood buildings. 2013. Available at: www.nzwood.co.nz/ canterbury-rebuild/news-post-tag-test/ [Accessed: 13 January 2015]

7.16

KLH UK. Murray Grove – Timelapse sequence. 2009. Available at: http://www.klhuk.com/news/stadthaustimelapse.aspx [Accessed: 13 January 2015]

7.17

Institution of Structural Engineers. Building for a sustainable future: an engineer’s guide. London: IStructE, 2014

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The Institution of Structural Engineers Stability of buildings Part 3

8

Shear infill panels

8.1

Introduction

This chapter gives a brief introduction to systems that provide stability without contributing to the vertical load resistance. These systems are typically made up of discrete elements and used almost exclusively in framed buildings. The focus is on common considerations that are not specific to any particular panel or frame material. However, some specific commentary on masonry infill panels is included which supplements the guidance given in Section 7.7.

8.2

Common characteristics of infill systems

Both the frame and the infill can be of any suitable material (timber, masonry, concrete, steel, composites or glass). Consequently there can be huge variation in the specifics of the design. However, common points to be considered include: – The interfaces and load paths between the frame and the infill elements – Any eccentricity between the centrelines of the frame and that of the infill – The strain compatibility of the different materials/ components (including both elastic and non-elastic strains, considering the orientation of non-isotropic materials where applicable) – The chemical compatibility of the different materials (e.g. bi-metallic corrosion) considering the materials of the frame, the infill and the fixings – The capacity and stiffness of the fixings and their anchorage into the frame/infill – The tolerance and sensitivity to workmanship and/ or initial dimensional deviations – The temporary stability of the frame in advance of the infill installation – The long-term durability and design life of the infill, and requirement for maintenance – The long-term safety of the structure and the heightened risk of ill-planned alterations (Box 8.1). These are in addition to the more standard attributes Box 8.1

Safety of structural shear infill panels

The use of elements that are traditionally considered ‘secondary’ or ‘non-structural’ for primary stability systems is not without serious risk. Where used, the designer must make clear the importance of these elements and ensure that this information is adequately recorded and available to guide future refurbishment and remodelling. In the UK, such notices should be included on construction drawings and in the building safety file under the terms of the CDM Regulations8.1. It is recommended that structural walls are labelled as such on the architect’s drawings. This is in addition to the wall’s disposition being specified on the structural engineer’s drawings.

including: – The panel aspect ratio – The disposition of openings – The robustness of the system It should be noted that ‘non-elastic strains’ include creep and shrinkage, and dimensional variation caused by thermal loads and/or moisture content. Load paths To provide resistance, an infill panel must form part of a load path that locks together elements of a frame. Connections must be stiff, strong and without risk of premature brittle failure (Box 8.2).

Box 8.2

Non-structural partitions and cladding

When detailing non-structural partitions and cladding, engineers must appreciate that it is stiffness and not strength that defines the distribution of forces within an elastic system. To avoid failure, any components that lock two points must have either strength or ductility that is adequate for the anticipated strains. These properties are seldom achievable in partitions and cladding. Indeed, the majority of modern buildings of three or more storeys adopt non-structural cladding and partitions installed, with connections that allow movement deliberately to prevent unintentional load paths forming. This approach allows these elements to be of low strength and does not unduly penalise brittle materials such as glass, terracotta or stone. Removed from the load paths, engineers must not assume that any resistance to the global system is contributed by these elements. Mechanical fixings between the panel and the frame are always recommended and are often essential to achieve robustness requirements for new or altered structures. However, a traditional means of achieving a load path was to create an infill panel that was tightly packed between columns without fixings. This approach provides no robustness and is particularly vulnerable in extreme loading events8.2. With or without fixings, panels will usually bear on the slab or beam below and include a deflection head to accommodate vertical differential movement of the floor structure above (the latter to ensure the infill does not attract vertical load). Thus, a gap at the top of an existing wall is not in itself an indicator that a wall panel is non-structural. Geometrical compatibility of the infill and frame materials, together with relative stiffnesses and tolerance, are critical. The thermal and chemical characteristics of both the frame and the infill can be important in this regard. For porous or curing materials (including clay bricks, concrete and timber) the designer must appreciate the time-based differential movement that can occur, and the impact this may have on the performance. The Institution of Structural Engineers Stability of buildings Part 3

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8.3

Shear infill panels and/or replacement strategy. This should accompany the design data and be explicitly communicated to, and accepted by, the client and building manager.

Figure 8.1 Indicative frame reactions showing the impact of infill panels on a regular column grid

Failure mechanisms All failure mechanisms shown in Fig. 2.5 apply locally to the individual panels and their interfaces with the frame. Forces will tend to transfer through a panel via diagonal compression struts and/or tension ties. The compatibility of these should be considered, as any strain in one diagonal will tend to cause an opposite strain in the other. Diagonal compression in the panel cannot be transferred to the frame by direct bearing where there is a deflection head. Instead, shear fixings are generally needed to maintain vertical equilibrium. These fixings, together with the surrounding panel and frame, should each be checked for combined shear with compression. Usually the same fixings will also need to accommodate shear with tension under load reversal. Beyond the fixings, the frame elements that surround the panels will be subject to forces resulting from the stiffness of the panels. These forces are similar in nature to those seen when using eccentric bracing and it is essential they are not overlooked. Ultimately they must be tacked down through the frame and subsequently the foundations (Figure 8.1). Durability and maintenance Structural infill panels should be designed for the same design life and probabilities of failure as the elements that make up the structural frame. Where this is impractical it may be acceptable to devise a clear and implementable maintenance

In determining the design life, the risk of degradation should be assessed using a structured risk assessment approach. This should consider all potential triggers and/or accelerators specific to the project. Human behaviour may need to be considered here and accidental, malicious and uninformed/negligent actions can heighten certain risks. Such an assessment is not unique to infill panels. However, these risks can become pronounced as the material can be easily damaged without heavy tools or significant force. Thus the risks are generally higher with lightweight infill systems. Other triggers can include an isolated event such as a flood. Meanwhile environmental conditions (temperature, humidity, chloride exposure, etc.) can act as accelerators. Construction Structural infill panel systems can have significant impact on the construction programme and temporary bracing to the frame is often essential ahead of the panels being installed. Although the design of the temporary works may not be the responsibility of the design engineer, the designer must make it clear to the contractor that the frame will be compromised or inadequate before the panels are installed. This may not be immediately clear to the contractor who may interpret the frame to be a moment frame. As a rule, the designer must always state which elements are providing stability, and the dependencies of the different systems. They may also need to advise the contractor of temporary loads and/or detail permanent works with connections for temporary elements. A design risk assessment can formalise and assist this process, helping the designer to identify and manage construction risks.

8.3

Masonry infill panels

Masonry infill panels are common in low- and medium-rise framed buildings of the last century (Figure 8.2). As a consequence they are a common feature of buildings undergoing remodelling.

Figure 8.2 Masonry infill panels within reinforced concrete frames (masonry panels to car park are creatively decorated to be disguised in building’s elevation) 54

The Institution of Structural Engineers Stability of buildings Part 3

Shear infill panels

Forces on the frame can cause bending and shear in the frame elements

Separation of frame from wall

                 

Figure 8.3 Infill panels under load

When a masonry infill is loaded in shear, separation of the infill from the frame tends to occur to all but the compression corner regions (Figure 8.3). The infill subsequently acts as a diagonal compression strut preventing sway deformation of the frame. Stafford-Smith and Riddington8.3 define the effective area of the strut Astrut as that given in Equation 8.1: Astrut ¼ 0.1Ld t

8.3

Panels with openings: require load path into the beams and generally cannot have a deflection head

Solid panel with vertical shear connections to the columns can have a movement joint (a deflection head) to the beam above

. . .Eqn 8.1

Reactions transfer down through the frame

where: Ld is the diagonal length of panel t is the thickness of the panel Figure 8.4 Masonry panel struts The direction of the strut in a given panel will depend on the direction of the shear, which is usually reversible under lateral loads. Hence all four corners and each of the two diagonals should be detailed to provide an adequate load path. Doors and other openings can be accommodated provided that adequate compression struts can still form. However, these openings will often change the strut angles, decreasing the strut area and increasing the stress within the panel. The revised strut pattern may also change the forces acting on the frame elements (Figure 8.4). Dominant failure modes for infill panels include shear along the bedding planes, or crushing at the compression corners. Out-of-plane buckling is typically avoided by adhering to maximum slenderness ratios (Section 7.7). Note that masonry infill panels are not subject to the pre-compression that gives loadbearing masonry much of its flexural and shear strength. Figure 8.5 Confined masonry construction It should also be noted that masonry infill panels that do not carry vertical load differ in construction and behaviour from confined masonry walls that do. These systems can be similar in appearance (Figures 8.2 and 8.5). The notable difference is the order of construction: confined masonry has the frame constructed after the wall is built while an infill is built to fit a pre-formed frame (Figure 8.6).

The wall is constructed after the frame

Frame (cast in situ ) completed after the wall panel is built

Confined masonry has been omitted from this Guide; for more information on confined masonry walls refer to the EERI Seismic design guide for low-rise confined masonry buildings8.4.

Infill panel

Confined masonry

Figure 8.6 Infill panels and confined masonry The Institution of Structural Engineers Stability of buildings Part 3

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8.4

Shear infill panels Further reading: masonry infill panels The following text is recommended as a source of further guidance on masonry infill panels: – Elliott, K.S. and Jolly, C.K. Multi-storey precast concrete framed structures. 2nd ed. Chichester: Wiley-Blackwell, 2013 It should be noted that this book provides guidance on both masonry (brickwork) and precast concrete shear infill panels; the latter is not discussed herein.

8.4

References

8.1

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

8.2

Taucer, F. et al. The 2007 August 15 magnitude 7.9 earthquake near the coast of Central Peru: EEFIT field mission, 5-12 September 2007/Final report. Available at: http://www.istructe.org/webtest/files/e3/e39c4dd50f03-446b-8ad2-bf9cbf796ee4.pdf [Accessed: 13 January 2015]

8.3

Stafford-Smith, B. and Riddington, J.R. ‘The Design of masonry infilled steel frames for bracing structures’. The Structural Engineer, 56B(1), March 1978, pp1-7

8.4

Meli, R. et al. Seismic design guide for low-rise confined masonry buildings. Oakland, CA: EERI, 2011. Available at: http://www.world-housing.net/wp-content/ uploads/2011/08/ConfinedMasonryDesignGuide82011. pdf [Accessed: 13 January 2015]

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The Institution of Structural Engineers Stability of buildings Part 3