RC Design To BS 8110 A. Allen

 

REINFORCED CONCRETE DESIGN TO BS8110 Simply explained

 

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Design of Prestressed Concrete   R.I. Gilbert and N.C. Mickleborough Design of Structural Elements   Concrete, steelwork, masonry and timber design to  British Standards and Eurocodes  C. Arya Durability of Concrete Structures: Investigation,   Repair and Protection Edited by G.C. Mays Examples of the Design of Reinforced Concrete   Buildings to BS 8110 C.E. Reynolds and J.C. Steedman

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REINFORCED CONCRETE DESIGN TO BS8110 Simply explained  A. H. A L L E N MA, BSc, CEng, FICE. FIStructE   Formerly Head of Design Department   Training Division  Cement and Concrete Association

CRC Press

Taylor &Francis Gr Group oup Boca Raton London New York

CRC Press is an imprint of the Taylor & Francis Group, an informa business

A TAYLOR & FRANCIS BOOK 

 

First Published by Taylor and Francis  2 Park Square, Milton Park, Abingdon, Oxon, 0X14 4RN  711 Third Avenue, New York, NY 10017 First issued in hardback 2017 First edition 1988 Taylor & Francis is an imprint of d/e Taylor & Francis Group 

©

1988 1988 Taylor and Francis

Typeset in 10/12pt Photina by Cotswold Typesetting Ltd., Gloucester 

Apart from fair as dealing for the purposes of Copyright research orDesigns private and study, or     criticism or any review, permitted under the UK Patents Act, 1988, this publication publication may may not be reproduced, stored, or transmitted, transmitted, in  any form or by any means, without the prior permission in writing of the    publishers, or in the case o f reprographic reproduction only in accordance wi with th  the terms of the licences issued by the Copyright Licensing Agency in the UK, or in accordance with the terms of licences issued by the appropriate   Reproduction Rights Organization outside the UK. Enquiries concerning   reproduction outside the terms stated here should be sent to the publishers at the  London address printed on this page. The publisher makes no representation, express or implied, with regard to the   accuracy of the information contained in this book and cannot accept any legal  responsibility or liability for any errors or omissions that may be made. A Catalogue record for this book is available from the British Library Library of Congress Data  Allen, A.H. (Arthur Cataloging-in-Publication Horace) Reinforced concrete design to BS8110: simply explain/A.H. Allen.  p. cm. Includes index. ISBN 0-419-14550-8 (pbk.) 1. Reinforced concrete constniction-Standards-Great Britain. I. Tide. TA683.24.A36 1988 624.r8314-dcl9 88-9702 CIP

ISBN 13: 978-1-138-41401-3 (hbk)  ISBN 13: 978-0-419-14550-9 (pbk)

 

CONTENTS

Preface  Notat  No tatio ionn

1 Limit state sta te principles princip les 1.1 1.1 1.2 1.3 1.4 1.5 1.6 1.7

Characteristic streng th of materials Concrete Reinforcemen Reinforcementt Characteri Characteristic stic loads Des Design ign strengths strength s of materials Design loads Lim Limit it state requireme nts

2 Robustness Robustn ess 2.1 2.2 2.3 2.4

Compliance Compliance with the Building Building Regulations 1985 Requirements Recommendations Offic fficee proced pro cedure ure

3 Analysis Analysis of structur stru ctures es 3.1 3.2 3.3 3.4

Braced frame, i.e i.e.. frame not no t providing lateral stability Unbraced frame, i.e i.e.. frame providing lateral latera l stability Redistribution Redistribution of mom ents - clause 3.2.2 Summary

ix xi

1 3 4 5 5 6 8 13

16 16 16 17 21

22 22 25 26 40

4 Cover

41

4.1 4.2 4.3 4.4 4.5 4.6 4.7

41 41 42 42 42 43 44

Nominal Bar size size cover Aggregate si size ze Uneven surfaces Cover Cover against agains t corrosion Cover as fire fire protec tion Select Selection ion of appropriate cover

5 Strength of sections sections - ultimate limit limit state 5.1 Desig Designn ch charts arts 5.2 Desig Designn formulae 5.3 Strain compatibility

6 Serviceability Serviceabili limitrt conditions state sta te of deflection deflect iongula r sections 6.1 Span andtysupport suppo for rectan sections 6.2 Percentage of tension reinforcement and service service stress stress

45 46 48 55

58 60 60 v

 

vi CONTENTS

6.3 Percentage of compression compression reinforcement 6.4 Other factors 6.5 Flanged beams

60 61 61

7 Serviceability Serviceability limit state sta te of crack cra cking ing

63

8 Bond Bond and anchorage anchorag e

67

8.1 Minimum distance between bars

67

8.2 8.3 8.4 8.5 8.6 8.7 8.8 8.9

67 68 68 69 72 73 75 78

Minimum percentages of reinforcement in beams and sla slabs bs Maximum percentages of reinforcement in beams and sla slabs bs Ancho rage bond Curtailment of bars Lapping of reinforcem ent Anchorage Ancho rage lengths of hooks and bends Bearing stresses inside bend, clause 22 .8. .8.25 25 Simplified Simplified rules for detailing deta iling

9 Shear

80

9.1 Bent-up bars

88

10 Corbe Corbels ls,, bearings bear ings an andd nibs

90

10.1 Corbels 10.2 Bearings 10.3 Continuous concrete nibs

90 94 95

11 Columns

99

11.1 11.2 11.3 11.4

104 104 106 106

Slenderness ratios Moments and force forcess in columns Short columns Slender Slender columns

12 Solid Solid slabs

122

12.1 One-way spann ing slabs slabs 12.2 Two-way spanning span ning

122 127

12.3 Loads Loads on supporting beams 12.4 Shear 12.5 Deflection

131 132 132

13 Ribbed slabs (solid (solid or hollow blocks or voids) voids) 13.1 13.2 13.3 13.4 13.5 13.66 13. 13.7

Definitions Definitions Hollow or soli solidd blocks blocks and formers Thickness of topping Fire Fire requirements Hollow clay floor floor blocks Edges Edges Analysis

14 Flat construction constru 14.1 slab Defini Definitions tions ction 14.2

Notation

133 133 134 134 135 136 136 137

141 141 141

 

14.3 Column heads 14.4 14 .4 Divi Division sion of panels 14.5 Thickness of panels 14.6 Defle Deflection ction 14.7 Crac Crackk control 14.8 Analysi Analysiss 14.9 Shear 14.10 Arrangemen t of reinf reinforcemen orcementt

15 Staircases 15.1 15.2 15.3 15.4 15.5

142 143 143 144 145 145 148 158

159

General requiremen requirements ts Transverse spans Longitudinal spans Flig Flights hts or landings built into wall wallss Stair Stairss with quarter qu arter landings

16 Bases

159 160 161 163 167

169

16.1 Pad foot footings ings 16.2 Pil Pilee caps

170 187

17 Torsion

193

17.1 17.2 17.3 17.4 17.5

196 198 20 0 201 202

Membrane analogy Derivati Derivation on of Co Code de equations fo forr rectan gula r secti sections ons Te Tee, e, Ell and an d I beams Bo Boxx sections Shear centre

Appendixes Appendix Appendix Appendix Appendix Index

212 1 2 3 4

Calculation for deflec deflection tion Calculation for crack wid widths ths Radii of bends to limit bearin bearingg stresses Tables of shear sh ear resistan resistance ce for links

212 224 22 4 230 23 0 235 237

vii c o n t e n t s

 

PREFACE

At the request of ma ny practising design engineers the au tho r has updated up dated his previous previous Reinforce orced d Concrete Design Design to CPI 10 - Simply Explained  (Cement and Concrete  boo k Reinf  book Association, London, 1974). With the knowledge gained from writing that book and lecturing on design courses presented by the Cement and Concre Concrete te Association Association he was invited to join the drafting panel to revise Section 3, Reinforced Concrete, of CPI 10. Dr Matthews has said in the Foreword of BS8110 that there are no major changes in  principl  prin ciple, e, b ut the th e text te xt ha s be been en largely larg ely re rew w ri ritte tte n w ith alt alter erat atio ions ns in th thee order ord er an andd arrangement of topics. This is very true, but in the alterations new material has also  beenn in  bee intro trodu duced ced.. One of the inhe i nhe rent problems problems in upda ting a Code Code of Practice is is tha t the th e members of the Committee are familiar with the existing Code. They are aware of the ideas and  princip  pri nciples les involve inv olvedd w he n it wa s w ri ritt tten en and an d as assu sume me th a t en engi ginee neers rs us usin ingg th thee revised revis ed version will will also also be familiar with the background. This is is not always the th e case, case, an d in the th e first chapter of this new book the author has repeated some of the material from the  previo  pre vious us book boo k to en ensu sure re th a t you y ou ng engi en ginee neers rs do no n o t for forget get the t he basic basi c princi pr inciple pless of limit state design. A criticism criticism of the ea rlier Code Code of Practice CPI 14 was t ha t it a ppeared to co ncentrate on the strength strengt h criterion, even th ough ou gh permissi permissible ble stresse stressess at w orking conditions were involved. invol ved. A feature of the new n ew design m ethod w as th at n ot only did it involve involve strength (ultimate limit state), but also deflection and cracking (serviceability limit states) were taken more seriously. With the passage of time the emphasis on serviceability appears to be diminishing. Minor calculations still still have to be carried out a nd in P art 2 of the Code there is a great deal of information; b ut will the majority of engineers read P art 2? For many man y of what wh at are referred referred to as ‘no ‘norm rm al’ building struc tures they will not need to do this, and some of of the basic understanding of what they are doing in Part 1 will be overlooked. As with the previous Code Code,, a Handbook Han dbook ha s been produced which gives gives background information, but mainly in the form of references*. Many design engineers are still seeking seeki ng guidance in using the th e Code Code itse itself lf and it is the hope of the a uth or tha t ha t this book will be found to be as useful as the previous one. Design examples and design aids are given and these should prove to be of use to new and experienced engineers. For those engineers familiar familiar with CPI 10 the terminology should not n ot be a proble problem, m,  b  buu t th they ey will have ha ve to get us used ed to lookin loo kingg in a different differ ent place pla ce for th thee in infor form m ati ation on th they ey need and, in several cases, a slightly different approach. The change is obviously not as great as when engineers had to convert from CPI 14 to CPI 10. The notation is essentially the same as that of CPI 10, but in the revision it was decided deci ded that the th e nota tion rele vant to each topic should be included at the beginning of that topic. This means that symbols are often repeated and the reader has to make certain that the same symbol means the same thing every time. *H *Hand andboo book k to British Standard BS811 BS 8110: 0: 19 1985 85 Structural Structu ral use of Concret Concrete, e, Rowe, R. E. et al   (1987).

 

 X 

PREFACE

It is expected expected that th at as reference reference to clauses is is made the read er will will have at h an andd a copy copy of the Code, thus avoiding the constant repetition of many clauses. Although Althou gh this book has been prepared prepared from the au th or ’s own lecture notes he would like like ttoo acknowledge contributions contribu tions m ade by his colleagues in the Cement and Concrete Concrete Association Associ ation.. These contributions have been in the form of comments, (he (helpf lpful) ul) critici criticism sm and discussions. He thanks, in alphabetical order, Andrew Beeby, lohn Clarke, Ray Rogers and Tony Threlfall, and also Susan Munday who typed it all. Extracts from Extracts from BS8110: P arts 1, 2 and 3 :1 9 8 5 are reproduced by permission permission of BSI. Complete copies can be obtained from them at Linford Wood, Milton Keynes, MK14 6LE.

 

NOTATION

BS8110 now provides a list of symbols at the beginning of each section defining the symbols used in that section rather than a general list at the start of the Code. An attempt has been made here to give a general list of symbols relating to reinforced concrete. In a num ber of cases cases the list appears to conta in ambiguities, ambiguities, but bu t as this book is meant to be read in conjunction with the Code, the reader should find that no ambiguities actually occur in use. Ac 

Acc Ah As  Asb Asc A's 

^s ^s.P .Prov ^Lprov Asreq Ast Asv a  a'  ah

acr acr af au au auaav av  b   b  b''   b  bcc   be   b  btt   bv  b  bw w

c

Area of concrete Area of concret con cretee in compres com pression sion Area of steel required requir ed to resist horizontal horizon tal shea r  Area of tension reinforcement A re a of b e n t -u p b a r s Area of compressio compressionn reinforcement, reinforcem ent, or, in columns, columns , the area of reinforce ment Area of compression compression reinforcement Area Are a of tensio ten sionn reinfor rein forcem cement ent provided at midspa mid spann (at suppo sup port rt for a cantilever) Area of comp compress ression ion reinforc rein forcem ement ent provided Area of tens tension ion reinforc reinforcemen ementt required requir ed at midspan midsp an to resist the momen mo mentt due to design ultimate loads (at support for a cantilever) Area of trans tra nsve verse rse steel in a flange Area of shear reinforcement, or area of two legs of a link  Deflection Distance Distance from the compression fa face ce to the point at which the crack width is  being  bei ng ca calcu lculat lated ed Centre-to-centre distance between bars (or groups of bars) perpendicular to the plane of bend Distance from the crack considered to the surface of the nea rest longitudinal longi tudinal  bar   ba r  Angle of intern int ernal al friction betw een the faces faces of the joint Deflecti Deflection on of column colu mn at ultim ate limit state Average Av erage deflection of all column colu mnss at a given level at ult ultim imate ate limit state stat e Length of that part of a member traversed by shear failure plane Width (breadth) (bread th) or eff effect ective ive widt widthh of section Effe Effect ctive ive section dimension dimen sion of a colu column mn perpendicula perpen dicularr to the y  axis Breadth of the compression   face of a beam measured midway between restraintss (or the bre adth of the compression face restraint face of a cantilever) cantilever) Breadth of effecti effective ve mo mome me nt transfer trans fer strip (of flat slab) Width of section at the centroid of tension ste steel el Width (breadth) of section used to calculate the shear stress Breadth or effective breadth of the rib of a beam Width of column xi

 

xii

cmjn

 NOTATI  NOT ATION ON

cx, cy  d 

d'  dh  dn  Ec  Ecq Ect  En  Es  Et  Eu E0  e  ea  ex exl  ex2 F 

Fb Fbt Fs Ft / f hs  / bu fc  / cu f s  f t  fy

/ G Gk H h  hf   hagg 

hc h{

hmax

hmin 

I K  

Minimu Min imum m cover cove r to th thee tensio ten sionn steel Plan dimensions of column, parallel to longer and shorte r side side of base respectively Ef Effe fecti ctive ve depth dept h of section or, for sections entirely in compression, distance distan ce from most highly stressed face of section to the centroid of the layer of reinforcement furthest from that face Depth to the compression reinforcement Depth of the head (o (off a column) Depth to the centroid of the compression zone Static Static modulus modulu s of elasticity elasticity of concrete Dynamic modulus mo dulus of eelastic lasticity ity of concrete concrete Static modulu mo duluss of elasticity of concrete conc rete at age t  Effective ^static) modulus of elasticity of concrete Nominal earth load Modulus of elasticity of reinforcement reinforce ment Modulus of elasticity of concrete concret e at the age of loading t Modulus of elasticity of concrete at age of unloading Initial modulu mod uluss of elasticity at zero stress Eccentri Ecce ntricity city,, or the base of Napierian logarithms Additional eccentricity due to deflections deflections Resultant eccentricity of load at right angles to the plane of the wall Resultant Resultan t eccentricity eccentricity calculated at the top of a wall Resultant eccentricity calculated at the bottom of a wall Total design ultim ate load on a beam or strip of slab Des Design ign for orcce in a bar us used ed in th thee cal calcu cula lati tion on of anchor anchorage age bo bond nd st strress sses es Tensile force force due to ultim ate loads in a bar or group grou p of bars in con tact at the start of a bend Force in a bar or grou groupp of bars Basic force used in defining tie forces Stre St ress ss Bond stress Design ultim ate ancho anc horag ragee bond bon d stress Maximum compressive compressive stress stress in the concrete und er service service loads Characte Characteristic ristic streng stre ngth th of concrete Estimated Estimated design service service stress in the tension reinforcement Maxim um design principal tensile stress Characteristic strength of reinforcement Characteristi Characteristicc streng th of she ar or link reinforcement Shear modulus modu lus C h a r a c t e r i s t i c d e a d lo a d Storey height heig ht Overall Overall depth of the cross-secti cross-section on measured measu red in the plane und er consider ation Ef Effe fect ctive ive section dimension dimens ion in a direction perpend perp endicula icularr to the x axis Maximum si size ze of the coarse aggregate Ef Effe fect ctive ive diam eter of a column colu mn or colu mn head Depth (thickness) of flange Larger dimension dimen sion of a rec tangu tan gular lar section Smaller dimension of a recta ngu lar section Second Second momen mo mentt of area of the section section Coefficie Coefficient, nt, as approp app ropriat riatee

 

L I 

4 

2b l lh2 4  4  lex, ley

4

4 

Ir 4

lx, lx,  4  4 

4

12 M 

M,dd Mi A/I, max My 

A4, M! M2 msx, msy

 N  N  Nbbal  N  Ndd  N  Nuuz n  n0 nw

Qk R r   r ps l/ rb l / r cs l/rx

Ss  sb

Span of member or, in the case of a cantilever, length Span or effe effect ctive ive span of member, or anch orage length Clear horizontal distance between supporting members Breadth of supp orting ortin g mem ber at one end or 1.8 m, whichev whi chever er is the smaller  Breadth of supporting supportin g member at the th e other end or 1.8 m, whiche ver is is tthe he smaller  Dimension related to columns (variously defined) Effective height of a column or wall Effective height in respect of the major or minor axis respectively Effe Effecti ctive ve dimension dimen sion of a head (of colum n) Clear height of column or wall between end restraints Distance between betw een centres of columns, column s, frames or walls supportin sup portingg any two adjacentt floor adjacen floor spans Floor-to-ceil Floor-to-ceiling ing height heig ht Length of side sidess of a slab panel pane l or base Distance between point of zero moment Panel length parallel parallel to span, measured from centres of columns Panel width, measured from centres of columns Design Design ultimate resistance mom ent Addi Additi tion onal al desi design gn ult ultimat imatee moment moment in induc duced ed by de defl flec ecti tion on of be beam am Initial design ultim ate mome mo me nt in a column colu mn befor beforee allowance allowan ce for additional addition al design moments Design mo mome ment nt transferred trans ferred between betw een slab and column colu mn Maximum Maxim um design mo ment me nt transferred transf erred between betwe en slab and colum n Design Des ign mom ent of resistance of the section section Design Design ultimate mom ents abou t the x and y axis respectively Effe Effect ctiv ivee uniax ial design ultim ate mom ents about abo ut the x  and y  axis respectively Smaller initial end mo ment me nt due to design ultim ate loads La Larrger in i ti al end end m om om ent ent d ue to de des ig n ult ult i m at at e lo loads Maximum design ultimate moments either over supports or at midspan on strips of unit width and span lx or 4  respectively Design axi axial al force Design axi axial al load loa d capaci cap acity ty of a ba bala lanc nced ed section sec tion Numb Nu mber er of dis d isco cont ntin inuo uous us edges (0 ^ 4) Design ultim ul tim at atee capac cap acity ity of a sectio sec tionn w he n subjec sub jected ted to axial axi al load loa d only onl y Des Design ign ultimate load per un it are a, or num ber of columns resisting sides sidesway at a given level or storey (in clause 3.8.1.1)  Num  Nu m be berr of store st oreys ys in a st stru ruct ctuu re Design ultimate axial load C h a r a c t e r i s t i c i m p o se d l o a d Restraint factor (against early therm al contrac tion cracking) cracking) Internal Intern al radius of bend Radius of cur vatu re Curva Curvatu ture re at mi mids dspa pann or or, ffor or ca cant ntil ilev ever ers, s, at at tthe he su supp ppor ortt se sect ctiion Shrinkage curv ature C u rv atu re a t x First First mom ent of area of reinforcement abou t the centroid of the cracked or gross section Spacing Spaci ng of bent-up bars

xiii  NOTATION  NOTAT ION

 

xiv

Sv

 NOTATION  NOTAT ION

T tc

if  u Wo

V v, Vc Vco

Kr  K. K  V Vc Vc' Vc' ^max

Vs*’ s*’ ^ vt ^t.min

Vtu Wk  X

*1 y0 i/po

hi i

a a c,2

^c.min ae a si/ /? Tf  Tm

At e £cc «cs £c.l £m

6sh

Spacing of links links along member  Torsional moment due to ultimate loads Effective thickness of a slab for fire resistance assessment Thickness of non-combustible finish (for fire resistance) Length (or effective length) of the outer perimeter of the zone considered Effective length of the perimeter which touches a loaded area Shear force due to design ultimate loads, or design ultimate value of a concentrated load load Design shear resistance of bent-up bars Design ultimate shear resistance of the concrete Design ultimate shear resistance of a section uncracked in flexure Design Des ign ultimate shea r resistance of a section cracked in flexure Design effective shear force in a flat slab Design Des ign shea r force force transferred to colum n Design shear stress Design shear stress in the concrete Design concrete shear stress corrected to allow for axial forces Maximum design shear stress Design end shear on strips of unit width and span lx or ly respectively and considered to act over the middle three-quarters of the edge Torsional shear stress Minimum torsional shear stress, above which reinforcement is required Maximum combined shear stress (shear plus torsion) Characteristic wind load  N  Neu eutra tra l aaxis xis dep d epth, th, or dime di mens nsio ionn of o f a shea sh ea r pperi erime meter ter pa paral rallel lel to th thee axis of  bendin  ben dingg Smaller centre-to-centre dimension of a rectangular link  Half the side of the end block  Half the side of the loaded area Larger centre-to-centre dimension of a rectangular link  Lever arm Coefficient of exp xpan ansi sion on,, oorr angle ngle be bettween ween sh shea earr rei einf nfor orce ceme ment nt an andd the the  pl  plan anee of beam b eam or slab Ratio of the sum of the column stiffness to the sum of the beam stiffness at the lower or upper end of a column respectively Ctl and a c 2 Lesser of a Ctl Modular ratio ( E JE eff) Bending mom ent coeffic coefficien ients ts for slabs spanning spann ing in two directions directions a t right angles, simply supported on four sides Coefficient, variously defined, as appropriate Partial safety factor for load Partial safety safety factor for for strength streng th of materials Difference in temperature Strain Final (30 year) creep strain in concrete Free shrinkage strain Strain in concrete at maximum stress Average strain at the level where the cracking is being considered Thermal strain assumed to be accommodated by cracks Shrinkage of plain concrete

 

Strain at th e level considered, calculated calculate d ignoring ign oring the stiffening effe effect ct of the concrete in the tension zone Coefficie Coef ficient nt of friction frictio n Proportion of so solid lid material per un it w idth of slab slab Area of steel relative to area of concrete Creep coefficient, or diameter Effective bar size

xv  NOTATI ON

 

LIMIT STATE PRINCIPLES

Codes of Practice hhave Codes ave developed considerably since the first attem pt in 1934. 193 4. The way in which they have done so is outlined in Table in  Table 1.1. From Table From  Table 1.1 it can be seen seen tha t working stresses have gradually increased and the load factor or factor of safety has decreased. This has arisen m ainly from the satisfactory  perfo  pe rform rmanc ancee of str s truu ctur ct ures es and an d the th e ge gene neral ral im pr prov ovem emen entt in co cons nstr truc ucti tion on stand sta ndar ards ds.. Qualityy control of concrete took a large jump forward in the 1965 edition of CPI 14, Qualit 14, when statistical control was introduced and the allowable compressive stress in  bend  be ndin ingg wa wass in incre crease asedd if ther th eree wa wass a design des ign mix. Subs Su bsta tant ntia iall progre pro gress ss ha d also been made in the philosophica p hilosophicall approach appro ach to stru ctura l design, design, mainly due to the w ork of the intern int ernatio atio nal na l committees. One of these, the t he Comité Européen du Béton (CE (CEB), published fo r an Internatio Intern ational nal Code Code of Practice fo r Reinforced Reinforced Concrete, in 1963 its Recommendations for generally known as the Blue Book, and later, in conjunction with the Fédération Internationale de la Précontrainte (FIP), a complementary report dealing with  prestr  pre stress essed ed co conc ncret rete. e. F ur urth ther er to these th ese ther th eree w as publi pu blish shed ed in 19 7 0 th thee International  Recommendations for the Design and Construction of Concrete Structures   giving the Principles and Recommendations and generally known as the Red Book. When the drafting committees for CPI 14 and 115 were reconvened in 1964, they agreed to adopt the CEB report as a guide in the preparation of the new British Codes with the proviso that the new recommendations should not change unduly the Table 1.1 1.1 Development of Co Codes des of Practice Practi ce since since 193 19344 Code

Steel stress ( working load)

Load Load facto factor  r 

19 3 4 DSIR 

(1 400.N4 /5m/ym 2)

2.2

1 948 CPI 14 1957 CPI 14

0 .5 /, (1 8 9 N /m m 2)

2 .0

0 .5 / y (2 (2 1 0 N /m m 2)

2.0

1965 CP116\ CP I14 / 1972 CPI 10

0-55fy (230N/mm2) 0 - 5 8 /y (267N/mm2)* (without redistribution)

Deflection

Cracking

Comments

 Nothing  Nothin g

Concrete n o m in a l -

W a r n in g

Nothing

 proporti ons.  proportions. Beams Bea ms - straight line theory Ditto

Warning + s p a n / d e p th

 Nothingg  Nothin

 Nothing  Noth ing

Warning + expanded 1.8 span/depth 1.6 *-1.8 Span/effective depth ratios

W ar arning Bar   spacing rules

Concrete nominal or strength Concrete statistical control for quality Ditto

*I *Itt should be noted tha t these values are included as an indication to show tthe he trend; sp spec ecific ific values are not given in the Code.

 

2 LIMIT STATE P R IN C IP L E S

 pr  prop opor ortio tions ns of o f st stru ruct ctur ures es com pa pared red w it ithh ttho hose se desi d esign gned ed to t o th e reco re com m mend me ndati ation onss of the current codes. The main consequence of this decision was that limit state design was acceptedd as th e basis for accepte for the prep aration of the n ew drafts. drafts. Later, Later, these tw o committees in conjun ction w ith the drafting committee for CPI 16 agreed to the unification of the three codes into a single document, which would rationalize design and coordinate detailed interpretation, for concrete construction. The Code for Water Retaining Structures w as not included and an d alth oug h th at Code Code (now BS8007) relies relies very heavily heavily on the building structures document it has retained its independence. In drafting CPI 10 it was decided to go right back to square one and establish the engin eer’ eer’ss intentions and problems. The purpose of design may, perhaps perh aps oversimp oversimply, ly, be stated as the provision of a structure complying with the client’s and the user’s requirements. In design appropriate attention must be paid to overall economy, the safety, serviceability and aesthetics of the structure. In most cases the design process entails finding the cheapest solution capable of satisfying the appropriate safety, serviceabi servi ceability lity and aesthetic considerations. The design of a structure for a specific function is usually a two-stage process, involving firs firstt the selection selection of an appropriate type or form of struc ture and secondly secondly the detailed detail ed design of the various parts p arts of the chosen structure. In selecting selecting the type or form of structure the question of the relative costs of different types of structures and of dif differ ferent ent methods of construction of the same str uctu re will be of great im portance. In this selection selection the designer must rely to a large extent on his exper experience ience,, judgem ent and intuition. A preliminary study of several types of structure may be necessary. Having selected the type of structure the designer then has to proceed with the detailed design of the chosen one, always bearing in mind the factors of safety considerations and cost. In most cases the aesthetic requirements will have been substantially met in the selection of the type of structure and will now be completely satisfied by the specification of surface finishes, colour, etc. Fundamentally, then, the design process consists of finding and detailing the most economical structure consistent with the safety and serviceability requirements. In design the following points have to be taken into consideration: 1. variations in materials in the structu structure re and in test spe specimens cimens 2. variations in loading 3. constructional inaccuracies 4. accuracy design calculations calculations 5. safety andofserviceability. For (1) (1) we know th at th e cube test is a reliable reliable guide as regards regard s quality of concrete concre te from the mixer but does not no t gua rantee rant ee th at the concrete con crete in the structu re is the same. If we get get consistent cube results of the required strength this means that the potential of the concrete in the stru cture is higher. This is why wh y we took a highe r proportion of the cube streng stre ngth th as a permissible st stress ress whe n we have hav e quality control, con trol, i.e. a design mix. There is, however, still still no gu aran arantee tee th at the th e concrete in the struc ture is of the same consistent strength and properties, as has been shown from tests that have been performed. The same applies applies to reinforcement, as tests are carried ou outt on small samples which m ay or may not be truly representative of the whole. For (2) we must enquire how near the truth is the loading given in BS6399, Part 1. Constructional inaccuracies (3) are  proba  pro bably bly accid acc ident ental. al. For (4) des design igners ers ca cann an andd do m ak akee mi mista stakes kes in ca calcu lculat latio ions ns bu butt very often in analysis they assume a structure will behave in a certain way or that certain conditions con ditions exist. exist. Item (5) is dealt with quite arbitrarily in previous codes codes - if the structure does not collapse it is deemed to be satisfactory.

 

So, having the purpose of design which, as previously stated, consists of finding and dealing with the most economical structure associated with safety and serviceability requirements, a nd conscious that th at variability exist existss between construction m aterials and the construction process itself, if we now list the various criteria required to define the serviceability or usefulness of any structure we should be able to state a design  philo  ph iloso soph phyy to cope w ith it h thes th esee in a ra rati tion on al m anne an ne r. The various criteria required to define define the serviceabi serviceability lity or usefulness of any structure structu re can be described under the following headlines. The effects listed may lead to the struc ture being considered ‘unfit ‘unfit for use’. 1. Collapse: failure of one or more critical sections; overturning or buckling. 2. Deflection: the deflecti deflection on of the stru structur ctur e or o r any par t of the struc ture adversely adversely affe affect ctss the appearance or efficiency of the structure. 3. Cracking:  cracking of the concrete which may adversely affect the appearance or efficiency of the structure. 4. Vibration : vibration from forces due to wind or machinery may cause discomfort or alarm, damage the structure or interfere with its proper function. 5. Durability: porosity of concrete. 6. Fatigue:   where loading is predominantly cyclic in character the effects have to be considered. 7. Fire resistance:  insufficient resistance to fire leading to 1, 2 and 3 above. Whe n any an y s tructu re is rendered unfit un fit for for use for for iits ts designed designed function by one or more of the above causes, it is said said to have entered a limit state.  The Code defines defines the limit states as: 1. Ultimate limit state:  the ultimate limit state is preferred to collapse. 2. Serviceability limit states:  deflection, cracking, vibration, durability, fatigue, fire resistance and lightning. The purpose of design, then, is to ensure that the structure being designed will not  become  beco me unfit un fit for tthe he us usee for wh ic ichh it is requir req uired, ed, i.e. th at it will no t rrea each ch a limit limi t sstat tate. e. The essential basis basis of the design method, therefore, therefore, is to consider each limit state and to  provid  pro videe a su suita itable ble m ar argi ginn of safety. sa fety. To obta ob tain in value val uess for thi thiss m ar argi ginn of safety sa fety it was  propos  pro posed ed t h a t prob p robabi abilit lityy cons co nsid idera eratio tions ns shou sh ould ld be uuse sedd and an d tthe he design des ign process pro cess sh shou ould ld aim at providing acceptable probabilit probabilities ies so that the th e struc ture would not become unfit for use throughout its specified life. Accepting Accepti ng the fact tha t the streng s trengths ths of constructional constructio nal materials vary, as do also also the loads on the structure, two partial safety factors will now be used. One will be for materials and is designated ym; the other, for loading, is termed yf. These factors will vary for the various limit states and different materials. As new knowledge on either materials or loading becomes available the factors can be amended quite easily easily wit withou houtt the complicated procedures to amend one overall factor used in previous Codes.

1.1 1.1 Characteristic strength streng th of materials For  bo  both th co conc nc ret retee  and reinforcement the Code uses the term   ‘characteristic strength’ instead of 28-day works cube strength and yield stress, although it is still related to these. The characteristic strength st rength for all  materials has h as the th e notatio n / kand is define definedd as th thee value valu e of the cube st stren rength gth of concr concrete ete ((/c /cuu), the yield or proof stress of reinforcem ent

3 CHARACTER ISTIC STRENGTH OF MATERIALS

 

4 LIMIT STATE

(/y), below which 5% of all possible test results would be expected to fall. The value therefore is /k=/„-1.64s

P R IN C IP L E S

where f m is the mean strength of actual test results determined in accordance with a standard procedure, s is the standard deviation, and 1.64 is the value of the constant required to comply with 5% of the test results falling below below the characteristic strength, as indicated in Fig. 1.1. Frequency of resulhs

FIG. 1.1 Characteristic strengt stre ngth. h.

1.2 Concrete This is is dealt with in Section 6 of the Code, Code, bu t BS5328 BS5 328:: Methods for Specifying Concrete  Including Ready-Mixed Concrete give  givess a m uch fuller fuller treatm ent of the subject. subject. Durability Durability is given more importance in BS8110 th than an it was in C PI 10 an d we shall therefore concentrate on how this requirement affects the designer, as given in Section 3. The strength streng th of concrete for design design purposes will will be based on tests made on cubes at an age of 28 days unless there is satisfactory satisfactory evidence evidence tha t a particula p articula r testing regime is is capable of of predicting the 28-da y stren gth a t an earlier age. age. These 28-day cha racteristic strengths determine the grade of the concrete and it is important to select the correct grade appropriate for use. The concrete has to provide the durability for the environmental conditions as well as adequate strength for the loading requirements. For example, example, clause 33.1.7.2 .1.7.2 says tha t for reinforced reinforced concrete the lowest grade should  be C2 5 for conc co ncret retee made ma de w it ithh nor n orm m al al-w -w ei eigh ghtt aggr ag greg egat ates. es. Referenc Ref erencee to Table Tabl e 3. 3.44 of th thee Code, however, does not reveal a grade lower than C30. It is only by reading clause 3.3.5.2 3.3.5 .2 th that at it can be found tha t uunde nde r certain speci specifi ficc conditions a Grade Grade C30 can be classed as Grade C2 5. As As compliance with wi th these th ese conditions con ditions is not easy to achieve this will will not be expanded upon up on (a concrete concre te technolog techn ologist ist is best consulted). We shall deal deal with the normal approach. In selecting an appropriate grade of concrete, the designer has to determine the environment and exposure conditions to which the members of the structure will be subjected. These are given in Table 3.2 of the Code, and it is is probable that th at there t here will be more th an one condition of exposure. Moving Moving then th en to Table Table 3.4 of the Code Code will will give the

 

lowest grade of concrete to meet the durability requirements for nominal cover to all reinforcement. For a severe severe exposure the lowest grade is C40 and a no nominal minal cover of 40 mm is required. The same grade of concret concretee can be used for a mil mildd exposure when the nominal cover is 20 mm. The subject of cover to reinforcement will be discussed more fully later, but at this stage it is important for the designer to realize that a grade of concrete is selected for durability as well as for for strength. Having chosen a grade, the concrete con crete supplier will will then have to add the value of 1.64 times the standard deviation to obtain the target mean strength. In general the minimum cement content given in Table 3.4 of the Code will be exceeded but the maximum free water/cement ratio should not be exceeded. It should also be noted that the age allowance for concrete increasing in strength with age has now been deleted.

1.3 Reinforcement The reinforcement should comply with BS4449, BS4461 or BS4483, all of which specify the tests for compliance to obtain the characteristic strength. Section 7 of the Code Code dea deals ls with spec specifi ificati cation on an d workm anship. The designation of the reinforcement with its specified characteristic strength is shown in Table 1.2. Table 1.2 Designation of reinforcement reinfo rcement Specified characteristic  strength (fy) Designation

Hot-rolled mild steel High-yield steel (hot rolled or cold worked)

Nominal sizes

(N/mm2)

All sizes All sizes

250 4 60

From the table it can be seen that the characteristic strength of high-yield bars is indepen ind ependen dentt of wh eth ether er they a re hot-rolled or cold-rolled cold-rolled worked. A subdivision is made later in the Code to determine the bond characteristics which depend on the surface shape of the bar.

1.4 Characteristic Character istic loads For loading we use the th e ‘cha ‘cha racte ristic’ rist ic’ load (Fk (Fk) as the basis. Ideally Ideally this should sho uld be determined from the mean load and its standard deviation from the mean, and using the same probability as fo forr the materials we should shou ld say th that at Fk= Fm+ 1.64s. The characteristic load would be that value of loading such that not more than 5% of the spectrum of loading throu th rougho gho ut the li life fe of the structu st ructu re will li liee above the value of the characteristic load (see (see  Fig. 1.2 1.2). ). Although several surveys have been carried out, we are not yet able to give a statistical interpre tation and reasoning reaso ning to them . The surveys do do imply imply that, in general, the overall o verall imposed loads to be considered in design oonn floor floorss are well above the loading that occurs most of the time, although in individual areas the loading may well be above that th at for which the floors floors have been designed. designed. For characteristic loads we shall use those given and defined in BS6399: Part 1 for dead and imposed loads and CP3:

5

CHARACTER ISTIC LOADS

 

6

Frequency of  result’ss result’

Mean

Char acter isNc

LIMIT STATE P R IN C IP L E S

FIG . 1.2

Characteristic load load..

Chapter V: Pa rt 2 for wind loads loads,, altho ugh the t he loading conditions during erection and an d construction constru ction should be considered considered in design design and should n ot be such th at the subsequent sub sequent compliance of the structure with the limit state requirements is impaired. The characteristic dead, imposed and wind loads have the notation Gk, Qk, Wk  respectiv respe ctively, ely, where the upper-case letters letters denote th e to tal load on a span. Lower-case Lower-case letters denote uniform load per square metre, although in design examples for beams the lower-case letters letters hav e been used for a uniformly distributed load, so tha t Gk= gj .

1.5 Design Design strength stre ngthss of materials materi als We obtain the design strengths of the materials by dividing the characteristic streng strengths ths  by the th e pa rt rtia iall safety safe ty facto fac torr ym, ym, i.e. design des ign st stre reng ng th = f j y m. ymtakes acco unt of possi possible ble dif differ ferenc ences es between the th e materia l in the th e ac tual structu s tructu re and th e stren gth derive d erivedd from from test specimens specimens.. In concrete, this th is would cover such item itemss as insufficient compaction, differences in curing, etc. For reinforcement it would cover such items the dif differ between assumed actual cross-sectional cross-se ctional caused  by r olling roll ing tolera tolaseranc nces, es, ference corros corence rosion ion, , etc. The Th e valu va lues esanofdym for each material mat erial willareas be different differ ent for the different limit states by virtue of the different probabilities that can be accepted. Table 1.3 sets out these values, and it should be noted th at ultim ate limit state values values only are given in Part 1 of the Code. For serviceability, clause 2.4.6.1 refers to 3.2 in Pa rt 2 of the Code, Code, but the t he values given in the table below are tak en from the Handbook (see Preface). Table 1.3 Values of ym for concrete and steel at different limit states Values of ym Limit state

Ultimate Deflection Cracking

Concrete

Steel

1.5 1.0 1.3

1.15 1.0 1.0

 

For both materials, the factor for the ultimate limit state is higher than the others  becau  bec ause se n o t onl o nlyy m us t tthe he probabi prob ability lity of failure failu re be decr d ecreas eased ed bu t failur fa iluree ssho hould uld also be localized. The ymfactor therefore also contains an allowance for this; as a compressive failure fail ure in concrete is is sudden and w ithout ithou t warn ing th e factor for for concrete is higher th an for reinforcement. Deflection is related to the whole member and the factor for both materials is 1.0. For cracking only parts of the member are affect affected ed and a factor between 1.0 and 1.5 fo forr concrete has been sel select ected, ed, but kept at 1.0 for reinforcement. reinforcement. W hen one o ne is analysing any cross-section within the structure the properties of the materials should be assumed to be those associated with their design strengths strength s appropriate app ropriate to the limit state  being  bei ng conside con sidered. red. The short-term design stress-strain curve for concrete is shown in Fig. 1.3 1.3.. By  putt  pu ttin ingg in i n th e re le leva vant nt valu v aluee of ymdep ymdepen endin dingg on the th e llimit imit sta s tate te being b eing consid con sidere eredd we can c an obtain the th e appropriate design stress-strain curve. Two things here h ere are worthy worth y of note.

F IG . 1.3 1.3 Short-term Short-te rm design design stress-strai stress -strainn relation for normal norm al weight concrete (/cu (/cuin N/m N/ m m 2).

First, design strength has been defined as characteristic strength divided by ym, and yet the th e m axim um stress value valu e is given as 0.6 7/cu 7/cu/ym. /ym. The reason reas on for this is th at the characteristic streng th has been derived derived from tests tests on cubes. cubes. It is wel welll established established from tests that the m aximu m compressive compressive stress stress at failure in a member of the same concrete as a cube h as a value in the region of 0.8/ cu. This is a peak value and as an additional safety factor ag again ainst st compressive failure this vvalue alue ha s been reduced red uced to 0.6 0 .6 7/c 7/cuu, which agrees with the design methods using ultimate load. If one were using cylinders in determining the th e characteristic strength s trength the factor would be of the order of 0.85, 0.85 , as the cylinder strength is nearer th thee actual actu al behaviou b ehaviou r and is approximately approximately 0.8 x cube strength. Secondly, it is suggested in the Code that for the serviceability limit states the short term elastic modulus may be taken from a table in the Code Code,, i.e. i.e. a linear stress-strain stress -strain relationship is assumed with a specified value for Ec depending on /cu. The initial ta ng ent en t modulus modu lus for servi serviceability ceability limit limit states will seldom seldom be used unless a rigorous analysis is being carried out. Where sustained loading is being considered, however, allowance for shrinkage shrinkag e an andd creep should be made. For the serviceabilit serviceabilityy limit states Poisson’s ratio may be taken as 0.2. short-term stress-strain  relationship is shown in Fig. 1.4. For reinforcement the short-term 1.4. This  This dif diffe fers rs quite considerably considerably from CPI 10 in ttha ha t th e relationship is now bilinear fo for  r 

7 DESIGN STRENGTHS OF MATERIALS

 

8 LIMIT STATE PRINCIPLES

FIG. 1.4 Short-term design design stressstress-strain strain relation for for reinforcement (/ in N/m m 2).

reinforcement and also the maximum design stress in compression is the same as in tension. The elastic modulus remains at 200 kN/mm2. It iiss importan t to point out at this stage that th at in the majority of design design calculations this is the last time that the partial safety factors for materials will be referred to. They are  built  bui lt in to for formu mulae lae and an d design des ign char ch arts ts so th a t a de desig signer ner will us usua ually lly refer to the characteristic strengths, stren gths, i. i.e. e. / cu and /y / y.

1.6 Design loads We obtain the design load by multiplying the characteristic load by the other partial safety factor y(; this factor yf  is introduced to take account of: 1. possibl possiblee un usual usu al increases in the load beyond those in deriving the characteristic load 2. ina inaccu ccu rate assessm ent of eff effec ects ts of of loading 3. variations in dimensional accuracy achieved in construction 4. the im portance of the limit limit state being considere considered. d. y{varies for

different dif ferent limit limit states and also for ddiffere ifferent nt combinati com binations ons of loading. As with the design strengths strength s of materials, Pa rt 1 of the Code gives gives num erical values a t ultimate limit state but the reader is referred to Part 2 to assess values at serviceability limit states. The effect of the load is now classed as adverse or beneficial. Values of yf for ultimate limit state are given in Table 1.4. Table 1.4 Values of yf at ultim ultimate ate limit state Load type Dead Load combination 1. Dead and imposed 

(and earth and water  pressure)  pressur e) 2. Dead and wind (and earth and water  pressure) 3. Dead and wind and imposed (and earth and water pressure) pressure)

Imposed

Adverse

Beneficial

Adverse

1.4

1.0

1.6

1.4

1.0

1.2

1.2

1.2

Beneficial

0

1.2

Earth  and water  pressure

Wind

1.4

 — 

1.4

1.4

1.2

1.2

 

The arra nge me nt of loads loads should shou ld be such as to cause the most severe effe effect cts, s, i.e. i.e. the most severe stresse stresses. s. The ‘adverse’ partial factor is is applied applied to any loads tha t tend to  pr  produ oduce ce a more mo re critica crit icall desig d esignn con c ondit dition ion.. Th Thee ‘benefici bene ficial’ al’ factor facto r is appli a pplied ed to t o loads load s tthh at tend to produce a less critical condition. So, in a normal building structure with dead and imposed loads, the maximum design load on a span from lload oad combination (1) is 1.4Gk 1.4Gk+ + 1 .6 Qk. The minimu min imum m design load is 1.0Gk. Under combination which be some a stability theremost criti critical cal case caload se may arise whe n(2), mo moments ments will due generally to 1.4Gkon parts condition, of the sstructu tructu are additive addit ive to the w ind mom ents (using 1.4 Wk) and mom ents due to 1.0Gkon 1.0Gkon o ther parts of the structure form the restoring moment. For load combination (3) a factor of 1.2 is used throughout the structure, with no variations for loaded and unloaded spans. However,, w hen consideri However considering ng load combinations (2) and (3) the horizontal wind load load should not be les lesss tha n the notio nal horizontal load as given given in clause 3.1.4.2 and will  be dealt de alt w ith w he n consid con sideri ering ng ro robu bustn stness ess.. In addition add ition to the above factors we m ay have h ave to consider the th e effect effectss of excessive excessive loads. loads. In this case the y{factor should be taken as 1.05 on the defined defined loads loads and only those loads likely to be acting simultaneously need be considered. Also, if a structure can sustain locali localized zed damage, to ma intain intai n continued stability stability the yf yffactor is is again 1.05 and is applied to loads In which are likely likel to occur before befor tempo rary or temp pe rmerature an anen entt remedial measures arealltaken. general, the yef effe fect cts s of creep, cre ep, eshrinkag e and wi will ll not  be con consid sidere eredd for ul ulti tim m at atee limit lim it state. sta te. For serviceability limit states, clause 3.3 in Part 2 says that the loading assumed in these calculations will depend depend on wh ethe r the aim is to produce a best estimate of the likely behaviour of the structure or to comply with a serviceability limit state requirement. It does go on to say, however, that for limit state calculations the characteristic values will be used generally. This implies a partial factor of 1.0. The design loads for the serviceability limit states apply when estimating the immediate immedia te deflections deflections of a stru cture ctu re but b ut in most m ost cases it will be necessary to estim ate the additional time-dependent deflection deflectionss due to creep, creep, shrinkage shrinkag e and an d ttemperatu emperature. re. It will also be necessary to assess how much of the live load is permanent and how much is transitory.

EXAMPLE 1.1 A five-storey building of the cross-section shown has the following characteristic loads on the frame: Roof: Roof:

Dead 22 kN/m kN/ m Imposed 7 kN/m kN/ m Parapet 1 m high - point load load 12 kN

Floors: Floor s: Dead 20 kN/m kN /m Imposed 25 kN/m Cladding Claddi ng - point load 15 kN Wind: 7 kN/m.

 

10m

10 LIMIT STATE

30 m

P R IN C IP L E S

30m

30 m

30 m

50m

^ ________ 7-5 m_________ ^^^ 2-5

|

Calculate the maximum ultimate design load for the left-hand column and check if tension can occur (ignore the self load of the columns). The structure can be simplified as follows:

180m

50 m

R  7-5 m

Characteristic loads: Dead load (# (#k)(< kN/m Impose Imposed d load ( v101 kN

' 143 kN/m

'1 0 2 kN/m 72 kN r

wlOI kN

9-8 kN/m 9-8 kN/m

—► L

 

( 1)

_R 

 _ L

 

( 2)

_ R 

 

12

Moments about R 

LIMIT STATE

(1 (1)) 7.5L= 72 x 7.5 7.5 + 102 x 7.52 7.52/2 /2 - 143 x 2.52/2 2.52/2 - 101 x 2 .5 -9 .8 x 182/2 182/2 = 1122 L — 150 150 kN. (2) (2) 7.5L = 101 x 7.5 + 143 x 7.52 7.52/2 /2 44- 9.8 x 182/2 182/2 -1 0 2 x 2.52/2 2.52/2 - 72 x 2.5 = 5868 L= 782 kN. kN.

P R IN C IP L E S

Load combination (3) Design loads: UD load = 1.2 gk+  1.2