Structural Masonry Designers’ ManualW. G. Curtin, G. Shaw, J. K. Beck

and W. A. Bray

Third Edition revised by

David Easterbrook

BlackwellScience

Structural Masonry Designers’ Manual

Structural Masonry Designers’ ManualW. G. Curtin, G. Shaw, J. K. Beck

and W. A. Bray

Third Edition revised by

David Easterbrook

BlackwellScience

© 2006 Estate of W.G. Curtin, G. Shaw, J.K. Beck, W.A. Bray and D. Easterbrook

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First published in Great Britain byGrananda Publishing Ltd 1982

Reprinted 1982Second edition published by

Blackwell Scientific Publications 1987Reprinted 1989, 1991Second edition (revised) published by

Blackwell Science 1995Reprinted 1997, 1999

ISBN-10: 0-632-05612-6ISBN-13: 978-0-632-05612-5

Library of Congress Cataloging-in-Publication Data

Structural masonry designers’ manual / W.G. Curtin . . . [et al.].— 3rd ed. / rev. by David Easterbrook.p. cm.

Includes index.ISBN-13: 978-0-632-05612-5 (hardback : alk. paper)ISBN-10: 0-632-05612-6 (hardback : alk. paper) 1. Masonry—Handbooks, manuals, etc. 2. Structural

design—Handbooks, manuals, etc. I. Curtin, W. G. (William George) II. Easterbrook, David.

TA670.S725 2006693′.1—dc22

2005024960

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Preface to the Third Edition x

Acknowledgements xi

The Authors xii

Notation xiii

1 Introduction 11.1 Present structural forms 11.2 Examples of structural layout suiting

masonry 21.3 Reinforced and post-tensioned

masonry 21.4 Arches and vaults 21.5 The robustness of masonry structures 21.6 Prefabrication 31.7 Future tradesmen 31.8 Engineering education 3

2 Advantages and disadvantages of structural masonry 42.1 Advantages 4

2.1.1 Cost 42.1.2 Speed of erection 42.1.3 Aesthetics 42.1.4 Durability 52.1.5 Sound insulation 52.1.6 Thermal insulation 52.1.7 Fire resistance and accidental

damage 52.1.8 Capital and current energy

requirements 62.1.9 Resistance to movement 62.1.10 Repair and maintenance 62.1.11 Ease of combination with other

materials 72.1.12 Availability of materials and

labour 72.1.13 Recyclability 7

2.2 Disadvantages 72.2.1 Lack of education in masonry 72.2.2 Increase in obstructed area over

steel and reinforced concrete 72.2.3 Problems with some isolated

details 72.2.4 Foundations 82.2.5 Large openings 82.2.6 Beams and slabs 82.2.7 Control joints 82.2.8 Health and safety considerations 8

3 Design philosophy 103.1 Strength of material 103.2 Exploitation of cross-section 103.3 Exploitation of essential building elements 13

4 Limit state design 16

5 Basis of design (1): Vertical loading 185.1 Compressive strength of masonry 185.2 Characteristic strength and

characteristic load 185.3 Partial safety factors for loads, γf 205.4 Characteristic compressive strength

of masonry, fk 205.4.1 Brickwork 225.4.2 Blockwork 235.4.3 Natural stone masonry

and random rubble masonry 255.4.4 Alternative construction

techniques 265.5 Partial safety factors for material

strength, γm 275.5.1 Manufacturing control (BS 5628,

clause 27.2.1) 275.5.2 Construction control 27

5.6 Slenderness ratio 285.7 Horizontal and vertical lateral supports 28

5.7.1 Methods of compliance: Walls – horizontal lateral supports 29

5.7.2 Methods of compliance: Walls – vertical lateral supports 32

5.8 Effective height or length: Walls 325.9 Effective thickness of walls 34

5.9.1 Solid walls 345.9.2 Cavity walls 34

5.10 Loadbearing capacity reduction factor, β 355.11 Design compressive strength of a wall 365.12 Columns 36

5.12.1 Slenderness ratio: Columns 365.12.2 Columns formed by openings 375.12.3 Design strength 385.12.4 Columns or walls of small

plan area 395.13 Eccentric loading 395.14 Combined effect of slenderness and

eccentricity of load 405.14.1 Walls 405.14.2 Columns 41

5.15 Concentrated loads 43

Contents

vi Contents

6 Basis of design (2): Lateral loading – tensile and shear strength 476.1 Direct tensile stress 486.2 Characteristic flexural strength (tensile)

of masonry, fkx 486.2.1 Orthogonal ratio 49

6.3 Moments of resistance: General 516.3.1 Moments of resistance:

uncracked sections 516.3.2 Moments of resistance:

Cracked sections 536.4 Cavity Walls 54

6.4.1 Vertical twist ties 556.4.2 Double-triangle and wire

butterfly ties 566.4.3 Selection of ties 566.4.4 Double-lead (collar-jointed) walls 576.4.5 Grouted cavity walls 576.4.6 Differing orthogonal ratios 57

6.5 Effective eccentricity method of design 576.6 Arch method of design 58

6.6.1 Vertical arching 586.6.2 Vertical arching: Return walls 606.6.3 Horizontal arching 60

6.7 Free-standing walls 626.7.1 General 626.7.2 Design bending moments 626.7.3 Design moment of resistance 63

6.8 Retaining walls 636.9 Panel walls 63

6.9.1 Limiting dimensions 636.9.2 Design methods 646.9.3 Design bending moment 646.9.4 Design moments of resistance 686.9.5 Design of ties 68

6.10 Propped cantilever wall design 696.10.1 Geometric and other sections in

shear 706.11 Eccentricity of loading in plane of wall 70

6.11.1 Design of walls loaded eccentrically in the plane of the wall 71

6.12 Walls subjected to shear forces 716.12.1 Characteristic and design

shear strength 716.12.2 Resistance to shear 72

7 Strapping, propping and tying of loadbearing masonry 737.1 Structural action 747.2 Horizontal movement 767.3 Shear keying between wall and floors 777.4 Holding down roofs subject to

upward forces 777.5 Areas of concern 777.6 Other factors influencing the details

of connections 787.7 Illustrated examples of strapping and tying 807.8 Design examples: Straps and ties for

a three-storey masonry building 89

8 Stability, accidental damage and progressive collapse 948.1 Progressive collapse 948.2 Stability 968.3 Accidental forces (BS 5628, clause 20) 988.4 During construction 998.5 Extent of damage 998.6 Design for accidental damage 100

8.6.1 Partial safety factors 1008.6.2 Methods (options) of checking 1018.6.3 Loadbearing elements 1018.6.4 Protected member 1038.6.5 General notes 109

9 Structural elements and forms 1109.1 Structural elements 110

9.1.1 Single-leaf walls 1109.1.2 Double-leaf collar-jointed walls 1109.1.3 Double-leaf cavity walls 1109.1.4 Double-leaf grouted cavity walls 1109.1.5 Faced walls 1119.1.6 Veneered walls 1119.1.7 Walls with improved section

modulus 1119.1.8 Reinforced walls 1139.1.9 Post-tensioned walls 1149.1.10 Columns 1149.1.11 Arches 1159.1.12 Circular and elliptical tube

construction 1169.1.13 Composite construction 1169.1.14 Horizontally reinforced masonry 116

9.2 Structural forms 1169.2.1 Chimneys 1169.2.2 Crosswall construction 1189.2.3 Cellular construction 1199.2.4 Column and plate floor

construction 1199.2.5 Combined forms of construction 1209.2.6 Diaphragm wall and plate roof

construction 1219.2.7 Fin wall and plate roof

construction 1219.2.8 Miscellaneous wall and plate

roof construction 1219.2.9 Spine wall construction 1219.2.10 Arch and buttressed construction 1229.2.11 Compression tube construction 123

10 Design of masonry elements (1): Vertically loaded 12410.1 Principle of design 12410.2 Estimation of element size required 12410.3 Sequence of design 12410.4 Design of solid walls 12410.5 Design of cavity walls 130

10.5.1 Ungrouted cavity walls 13010.5.2 Grouted cavity walls 13210.5.3 Double-leaf (or collar-jointed)

walls 134

Contents vii

10.6 Design of walls with stiffening piers 13410.7 Masonry columns 13610.8 Diaphragm walls 13810.9 Concentrated loads 140

11 Design of masonry elements (2): Combined bending and axial loading 14211.1 Method of design 142

12 Design of single-storey buildings 17312.1 Design considerations 17312.2 Design procedure 177

13 Fin and diaphragm walls in tall single-storey buildings 17813.1 Comparison of fin and diaphragm

walls 17913.2 Design and construction details 18013.3 Architectural design and detailing 181

13.3.1 Services 18213.3.2 Sound and thermal insulation 18313.3.3 Damp proof courses and

membranes 18313.3.4 Cavity cleaning 183

13.4 Structural detailing 18313.4.1 Foundations 18413.4.2 Joints 18413.4.3 Wall openings 18513.4.4 Construction of capping beam 18513.4.5 Temporary propping and

scaffolding 18513.5 Structural design: General 186

13.5.1 Design principles: Propped cantilever 186

13.5.2 Calculate design loadings 18713.5.3 Consider levels of critical

stresses 18813.5.4 Design bending moments 18813.5.5 Stability moment of resistance,

MRs 19013.5.6 Shear lag 19013.5.7 Principal tensile stress 190

13.6 Design symbols: Fin and diaphragm walls 191

13.7 Fin walls: Structural design considerations 19113.7.1 Interaction between leaves 19113.7.2 Spacing of fins 19113.7.3 Size of fins 19213.7.4 Effective section and trial

section 19213.8 Example 1: Fin wall 193

13.8.1 Design problem 19313.8.2 Design approach 19413.8.3 Characteristic loads 19413.8.4 Design loads 19413.8.5 Design cases (as shown in

Figure 13.42) 19413.8.6 Deflection of roof wind girder 19413.8.7 Effective flange width for

T profile 196

13.8.8 Spacing of fins 19613.8.9 Trial section 19613.8.10 Consider propped

cantilever action 19713.8.11 Stability moment of resistance 19713.8.12 Allowable flexural compressive

stresses, pubc, taking into account slenderness, β, and material, γm 197

13.8.13 Calculate MRs and compare with Mb 199

13.8.14 Bending moment diagrams 20013.8.15 Consider stresses at level of Mw 20013.8.16 Design flexural stress at

Mw levels 20113.8.17 Consider fins and deflected

roof prop 20213.9 Diaphragm wall: Structural design

considerations 20213.9.1 Determination of rib centres, Br 20213.9.2 Depth of diaphragm wall and

properties of sections 20413.9.3 Shear stress coefficient, K1 20513.9.4 Trial section coefficients,

K2 and Z 20613.10 Example 2: Diaphragm wall 207

13.10.1 Design problem 20713.10.2 Characteristic and design loads 20713.10.3 Select trial section 20813.10.4 Determine wind and

moment MRs at base 20813.10.5 Consider stress at level Mw 20913.10.6 Consider diaphragm with

deflected roof prop 21013.10.7 Calculate shear stress 21113.10.8 Stability of transverse shear

walls 21113.10.9 Summary 211

13.11 Other applications 211

14 Design of multi-storey structures 21414.1 Structural forms 214

14.1.1 Stability 21514.1.2 External walls 21514.1.3 Provision for services 21614.1.4 Movement joints 21614.1.5 Vertical alignment of

loadbearing walls 21714.1.6 Foundations 21814.1.7 Flexibility 21814.1.8 Concrete roof slab/Loadbearing

wall connections 21814.1.9 Accidental damage 21814.1.10 Choice of brick, block and

mortar strengths 21914.2 Crosswall construction 219

14.2.1 Stability 21914.2.2 External cladding panel walls 22014.2.3 Design for wind 22114.2.4 Openings in walls 22214.2.5 Typical applications 222

viii Contents

14.2.6 Elevational treatment of crosswall structures 224

14.2.7 Podiums 22414.3 Spine construction 224

14.3.1 Lateral stability 22514.3.2 Accidental damage 226

14.4 Cellular construction 22614.4.1 Comparison with crosswall

construction 22714.4.2 Envelope (cladding) area 22714.4.3 Robustness 22714.4.4 Flexibility 22714.4.5 Height of structure 22714.4.6 Masonry stresses 22714.4.7 Foundations 228

14.5 Column structures 22814.5.1 Advantages 22814.5.2 Cross-sectional shape 22814.5.3 Size 229

14.6 Design procedure 22914.7 Example 1: Hotel bedrooms, six floors 229

14.7.1 Characteristic loads 22914.7.2 Design of internal crosswalls 23114.7.3 Partial safety factor for material

strength (Table 4, BS 5628 – see Table 5.11) 232

14.7.4 Choice of brick in the two design cases, at ground floor level 232

14.7.5 Choice of brick in the two design cases, at third flood level 232

14.7.6 Design of gable cavity walls to resist lateral loads due to wind 232

14.7.7 Uplift on roof 23214.7.8 Design of wall 23214.7.9 Calculation of design wall

moment 23314.7.10 Resistance moment of wall

(Figure 14.46) 23314.7.11 Overall stability check 23314.7.12 Eccentricity of loading 23514.7.13 Accidental damage 235

14.8 Example 2: Four-storey school building 23614.8.1 Characteristic loads 23714.8.2 Design of wall at ground

floor level 23714.9 Example 3: Four-storey office block 238

14.9.1 Column structure for four-storey office block 238

14.9.2 Characteristic loads 23914.9.3 Design of brick columns 23914.9.4 Loading on column P 239

15 Reinforced and post-tensioned masonry 24315.1 General 244

15.1.1 Design theory 24415.1.2 Comparison with concrete 24415.1.3 Applications 245

15.1.4 Prestressing 24615.1.5 Methods of reinforcing walls 24615.1.6 Composite construction 24715.1.7 Economics 24715.1.8 Corrosion of reinforcement

and prestressing steel 24715.1.9 Cover to reinforcement and

prestressing steel 24815.1.10 Cover 248

15.2 Choice of system 24915.3 Design of reinforced brickwork 250

15.3.1 Partial factors of safety 25015.3.2 Strength of materials 25115.3.3 Design for bending:

Reinforced masonry 25115.3.4 Lateral stability of beams 25115.3.5 Design formula for bending:

Moments of resistance for reinforced masonry 252

15.3.6 Design formula: Shear stress 25515.3.7 Shear reinforcement 25515.3.8 Design formula: Local bond 25615.3.9 Characteristic anchorage

bond strength, fb 25615.3.10 Design for axial loading 256

15.4 Example 1: Design of reinforced brick beam 257

15.5 Example 2: Alternative design for reinforced brick beam 259

15.6 Example 3: Reinforced brick retaining wall 261

15.7 Example 4: Column design 26215.8 Design of post-tensioned brickwork 263

15.8.1 General 26315.8.2 Post-tensioned masonry:

Design for flexure 26515.8.3 Design strengths 26615.8.4 Steel stresses 26715.8.5 Asymmetrical sections 26715.8.6 Losses of post-tensioning

force 26815.8.7 Bearing stresses 26915.8.8 Deflection 26915.8.9 Partial safety factor on

post-tensioning force 26915.9 Example 5: High cavity wall with

wind loading 26915.9.1 Capacity reduction factor, β 27015.9.2 Characteristic strengths 27015.9.3 Design strengths (after losses) 27115.9.4 Section modulus of wall 27115.9.5 Design method 27115.9.6 Calculation of required

post-tensioning force 27115.9.7 Consider compressive stresses:

After losses 27215.9.8 Consider compressive stresses:

Before losses 27415.9.9 Design of post-tensioning

rods 274

Contents ix

15.10 Example 6: Post-tensioned fin wall 27515.10.1 Design procedure 27515.10.2 Design post-tensioning force

and eccentricity 27615.10.3 Characteristic strengths 27715.10.4 Loadings 27715.10.5 Design bending moments 27815.10.6 Theoretical flexural tensile

stresses 27815.10.7 Calculations of P and e 27815.10.8 Spread of post-tensioning

force 27915.10.9 Characteristic post-tensioning

force Pk 27915.10.10 Capacity reduction factors, β 27915.10.11 Check combined compressive

stresses 27915.10.12 Design flexural compressive

strengths of wall: After losses 28215.10.13 Check overall stability

of wall 28215.10.14 Design of post-tensioning

Rods 28415.11 Example 7: Post-tensioned brick

diaphragm retaining wall 28415.11.1 Design procedure 28415.11.2 Design loads 28515.11.3 Trial section 28615.11.4 Calculate theoretical flexural

tensile stresses 28915.11.5 Minimum required post-

tensioning force based on bending stresses 289

15.11.6 Characteristic post-tensioning force, Pk 289

15.11.7 Capacity reduction factors 28915.11.8 Check combined compressive

stresses 29015.11.9 Check shear between leaf

and cross-rib 29115.11.10 Design of post-tensioning

rods 293

16 Arches 29416.1 General design 294

16.1.1 Linear arch 29516.1.2 Trial sections 29616.1.3 Mathematical analysis 297

16.2 Design procedures 29916.3 Design examples 299

16.3.1 Example 1: Footbridge arch 29916.3.2 Example 2: Segmental arch

carrying traffic loading 301

16.3.3 Example 3: Repeat Example 2 using a pointed arch 304

Appendix 1 Materials 307A1.0 Introduction 307A1.1 Clay masonry units (clay bricks) 307

A1.1.1 Sizes 307A1.1.2 Classification 307A1.1.3 Strength and durability 308A1.1.4 Testing 309

A1.2 Calcium silicate units (bricks) 309A1.3 Concrete bricks 310A1.4 Stone units (stonework) 310A1.5 Concrete units (blocks and bricks) 310

A1.5.1 Sizes 310A1.5.2 Classification 310A1.5.3 Density 310A1.5.4 Form 310A1.5.5 Strength 310A1.5.6 Durability 310

A1.6 Mortars 311A1.6.1 Constituents 311A1.6.2 Choice of mortar 312A1.6.3 Proportioning and mixing 312A1.6.4 Testing 312

Appendix 2 Components 314A2.1 Wall ties 314A2.2 Damp proof courses 314A2.3 Fixings 314A2.4 Brick bonds 315

Appendix 3 Movement joints 317A3.1 Movement due to thermal expansion

and contraction 318A3.2 Movement due to moisture 318

A3.2.1 Fired clay units 318A3.2.2 Concrete and calcium

silicate units 319A3.3 Movement due to chemical interaction

of materials (sulphate attack) 320A3.4 Differential movement with dissimilar

materials and members 320A3.5 Foundation settlement 321A3.6 Movement of joints and

accommodation of movement 322A3.7 Jointing materials and typical details 323A3.8 Mortars in assisting movement

control 323

Appendix 4 Provision for services 324

Index 327

The original Structural Masonry Designers’ Manual wasviewed by many in the industry as a seminal reference for structural engineers designing masonry structures. Theauthors were founding members and directors of CurtinsConsulting Engineers, a civil engineering consultancy prac-tice, which was synonymous with the innovative and cre-ative use of structural masonry in the latter part of the lastcentury (1970s onwards). Both Bill Curtin and Gerry Shawwere educated in the old way which consisted of workingby day and studying by night. This engendered a passionfor their subject, which is evident in the previous editions ofthis book.

Gerry Shaw was until his tragic death a Visiting Professorin The Principles of Engineering Design at the University ofPlymouth. The updated manual takes nothing away fromthe enthusiastic approach to masonry design evidenced bythe Curtins’ authors in the previous editions. Their prag-matic and practical approach to masonry design is retainedin its fullness.

The new revision reflects changes in the industry withrespect to health and safety, as well as Building Regulationrequirements for heat loss, noise transmission and dis-proportionate collapse rules. The recent amendments to BS5628 Parts 1, 2 and 3 are also included.

One major change is the transition from British specifica-tions for materials to European Standard specifications.European specifications are based on performance criteriarather than prescriptive criteria and this will require struc-tural engineers to be more aware of the materials that theyspecify.

Many changes have taken place in masonry constructionsince the last edition of the book was published. Many ofthese changes are quite rightly related to health and safetyissues, which now appear to influence both the structuralform and the choice of material. The current shortage ofskilled labour within the construction industry furtheraffects the design decisions made by structural engineers.However, innovative work in the use of structural masonryis still in evidence in structural engineering design.

The format of the book has remained unchanged since it ismeant to be a discussion of process, both theoretical andpractical, rather than a series of calculation sheets withoutexplanation. The drawings have been updated, but havealso been produced in an illustrative format rather than atechnical drawing format. This is intended to aid the readerin the understanding of the principles.

Preface to the Third Edition

We appreciate the help given by many friends in the con-struction industry, design professions and organisations.We learnt much from discussions (and sometimes, argu-ments) on site, in design team meetings and in the drawingoffice. To list all who helped would be impossible – to listnone would be churlish. Below, in alphabetical order, aresome of the organisations and individuals to whom we owethanks:

Brick Development AssociationBritish Standards InstitutionBuilding Research EstablishmentCement and Concrete Association

Professor Heyman for permission to quote from his book,Equilibrium of Shell Structures.

Mr J. Korff, Deputy Structural Engineer, GLC, for advice onaccidental damage.

Mr W. Sharp, County Structural Engineer, LandcashireCounty Council, for particular help on strapping and tying.

Acknowledgements are also due to the BCRA for permis-sion to quote from their SP93 ‘Strapping & Tying’, whichwas largely based on information supplied by LancashireCounty Council’s structural engineer and W. G. Curtin andPartners.

Extracts from BS 5628 1985 and 1992 are reproduced by per-mission of BSI. Complete copies can be obtained from themat Linford Wood, Milton Keynes MK14 6LE.

Finally, the authors are grateful to the Institution ofStructural Engineers for giving their permission to repro-duce extracts from the Profile of Dr Bill Curtin, the originaland full version of which was published in The StructuralEngineer, 69 (21), 1991.

Acknowledgements

forgeneralassistance

54647

W. G. Curtin was the founder of Curtins ConsultingEngineers plc, a highly respected civil and structural engi-neering consultancy. He was a member of the Institution ofStructural Engineers Science and Research Committee, of numerous CIRIA committees and the Code of PracticeCommittee for Structural Masonry, and of the StructuralEngineering and Building Board of the Institution of CivilEngineers. His experience embraced over 50 years ofdesigning, building, supervising and researching includingmasonry structures. For this he was awarded the HenryAdams Bronze Medal (twice) and the Oscar Faber Diplomaby the Institution of Structural Engineers.

G. Shaw was a director of Curtins with around 40 years’experience in the building industry including more than 30 years as a consulting engineer. He was continuouslyinvolved with innovative developments in structuralmasonry with direct responsibility for numerous importantmasonry structures, including the world’s first prestressedmasonry box girder footbridges. He was also involved inresearch working closely with the University of Plymouthand the Building Research Establishment and was a mem-ber of EPSRC Built Environment College. He was co-authorof a number of design notes and major text books includingStructural Foundation Designers’ Manual and StructuralMasonry Detailing.

J. K. Beck, a former director of Curtins, is an engineer with many years’ experience at home and abroad. Amongthe many structural masonry projects he has designed and supervised is, probably, the tallest slender crosswallstructure in Europe. He served on the Institution ofStructural Engineers ad hoc committee on Design ofMasonry Structures and was co-author of StructuralMasonry Detailing.

W. A. Bray joined Curtins in 1977. He was a group leader responsible for the design and supervision of many masonry structures including the world’s first post-tensioned diaphragm wall structure. He later left the prac-tice to follow another career path, via contracting.

Dave Easterbrook is a chartered engineer who has workedin local authority and consultancy for 13 years before join-ing The School of Civil and Structural Engineering at theUniversity of Plymouth in 1991. He lectures in structuraldesign and his research is focused on structural masonry.He worked in conjunction with the late Gerry Shaw ofCurtins on the construction of the first prestressed masonryflat arch structures built at Tring, Herts, and alongsideGerry in his role as a Professor in the principles of engineer-ing design at Plymouth. He is a member of The Institutionof Structural Engineers’ Codes Panel.

The Authors

A cross-sectional areaAs cross-sectional area of primary reinforcing steelAsc area of compressive reinforcementAsv area of shear reinforcementa depth of stress block or shear spanav shear span (distance from support to concentrated

load)B width of bearing under a concentrated loadBr centre-to-centre of cross-ribs in diaphragm wallBM bending momentb width of sectionbc breadth of compression facebr clear dimension between diaphragm cross-ribsC compressive forceCc total compressive forceCs compressive force in reinforcementCpe wind, external pressure coefficientCpi wind, internal pressure coefficientD overall depth of diaphragm wall section or depth

of archDia diameter of reinforcing bard effective depth to tensile reinforcement and depth

of cavity (void) in diaphragm walldn depth to neutral axisd2 depth to compression reinforcementE Young’s modulus of elasticityEm modulus of elasticity of masonryEu nominal earth and water loade eccentricityea additional eccentricity due to deflection in walleef effective eccentricityem the larger of ex and etemax maximum eccentricity that can be practically

accommodated in sectionet total design eccentricity at approximately mid-

height of wallex eccentricity at top of wallFk characteristic loadFm average of the maximum loads carried by two test

panelsFt tie forceFb, fb characteristic anchorage bond strengthfbs characteristic local bond strengthfc design axial stress due to minimum vertical loadfk characteristic compressive strength of masonryfki characteristic compressive strength of masonry at

age when post-tensioning force is appliedfkx characteristic flexural strength (tensile) of masonryfkxpar value of fkx when plane of failure is parallel to bed

joints

fkxperp value of fkx when plane of failure is perpendicularto bed joints

ft theoretical flexural tensile stress or flange thicknessfuac design axial compressive stressfubc flexural compressive stress at design loadfubt flexural tensile stress at design loadfv characteristic shear strength of masonryfw flange widthfy characteristic tensile strength of steelGk characteristic dead loadgA design vertical load per unit areagB design load per unit area due to loads acting at

right angles to the bed jointsgd design vertical dead load per unit areaHz thrust at crown of archh clear height of wall or column between lateral

supportsha clear height of wall between concrete surfaces or

other construction capable of providing adequateresistance to rotation across the full thickness ofthe wall

hef effective height or length of wall or columnhL clear height of wall to point of application of lateral

loadI second moment of area/moment of inertiaIna second moment of area about neutral axisK stiffness coefficientKa constant term relating design strengths of steel and

masonryK1 shear stress coefficient for diaphragm wallsK2 trial section stability moment coefficient for

diaphragm wallsk multiplication factor for lateral strength of axially

loaded walls

k1

from Rankine’s formula for retained

materialsL lengthLa a span in accidental damage designLef, lef effective lengthLf spacing of fins, centre-to-centrela lever armM, MA applied design bending momentMa design bending moment at base of wallMd design moment of resistanceMR moment of resistanceMRs stability moment of resistanceMrb moment of resistance of a balanced sectionMrs moment of tensile resistanceMw design bending moment in height of wall

1 − sin θ1 + sin θ

Notation