model code 2010 - institution of structural engineers · this draft of the fib model code 2010 was...

Model Code 2010 First complete draft

Volume 2

April 2010

Subject to priorities defined by the Technical Council and the Presidium, the results of fibs work in Commissions and Task Groups are published in a series of technical publications called 'Bulletins'.

category minimum approval procedure required prior to publication Technical Report approved by a Task Group and the Chairpersons of the Commission State-of-Art Report approved by a Commission Manual, Guide (to good practice) or Recommendation

approved by the Technical Council of fib

Model Code approved by the General Assembly of fib

Any publication not having met the above requirements will be clearly identified as a preliminary draft. This Bulletin 56 is a draft Model Code; it has not yet been approved by the General Assembly of fib.

This draft of the fib Model Code 2010 was prepared by fib Special Activity Group 5, New Model Code:

Walraven (Convener; Delft University of Technology, The Netherlands) Bigaj-van Vliet (Technical Secretary; TNO-Built Environment and Geosciences, The Netherlands) Balazs (Budapest Univ. of Technology and Economics, Hungary), Cairns (Heriot-Watt University, UK), Cervenka (Cervenka Consulting, Czech Republic), Corres (FHECOR, Spain), Cosenza (Universita di Napoli Federico II, Italy), Eligehausen (Univ. Stuttgart, Germany), Falkner (Technische Univ. Braunschweig, Germany), Fardis (Univ. of Patras, Greece), Foster (Univ. of New South Wales, Australia), Ganz (VSL International, Switzerland), Helland (Skanska Norge AS, Norway), Hj (HOJ Consulting GmbH, Switzerland), van der Horst (Delft University of Technology, The Netherlands), Keuser (Univ. der Bundeswehr Mnchen, Germany), Klein (T ingenierie SA, Switzerland), Kollegger (Technische Univ. Wien, Austria), Mancini (Politecnico Torino, Italy), Marti (ETH Zurich, Switzerland), Matthews (BRE, United Kingdom), Menegotto (Univ. di Roma La Sapienza, Italy), Mller (Univ. Karlsruhe, Germany), Pinto (Univ. di Roma La Sapienza, Italy), di Prisco (Univ. of Milano, Italy), Randl (FHS Technikum Krnten, Austria), Rostam (Denmark), Sakai (Kagawa Univ., Japan), Schiessl (Technische Univ. Mnchen, Germany), Sigrist (TU Hamburg-Harburg, Germany), Taerwe (Ghent Univ., Belgium), Ueda (Hokkaido Univ., Japan), Wight (Univ. of Michigan, USA), Yamazaki (Nihon Univ., Japan) Invited experts who contributed substantially to the text: Bentz (Univ. of Toronto, Canada), Burkart (Univ. Karlsruhe, Germany), Cervenka (Cervenka Consulting, Czech Republic), Creton (ATS/BN Acier, France), Curbach (Technische Univ. Dresden, Germany), Demont (Trefileurope, Belgium), Dehn (MFPA Leipzig GmbH, Germany), Fernandez Ruiz (EPF Lausanne, Switzerland), Gehlen (Technische Univ. Mnchen, Germany), Glavind (Danish Technological Institute, Denmark), Matthys (Ghent Univ., Belgium), Mechtcherine (Technische Univ. Dresden, Germany), Muttoni (EPF Lausanne, Switzerland), Plizzari (Univ. Brescia, Italy), Reinhardt (Univ. Stuttgart, Germany), Triantafillou (Univ. of Patras, Greece), Vandewalle (Katholieke Univ. Leuven, Belgium), Vrouwenvelder (TNO-Built Environment and Geosciences, The Netherlands) Cover image: Grand Rapids Art Museum, Michigan, USA; one of the Special Mention recipients in the 2010

fib Awards for Outstanding Concrete Structures, Buildings Category. Kulapat Yantrasast, design architect; Anton Nelson, structural engineer. Photo credit: Steve Hall, Hedrich Blessing

fdration internationale du bton (fib), 2010 Although the International Federation for Structural Concrete fib fdration internationale du bton does its best to ensure that any information given is accurate, no liability or responsibility of any kind (including liability for negligence) is accepted in this respect by the organisation, its members, servants or agents. All rights reserved. No part of this publication may be reproduced, modified, translated, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without prior written permission from fib. First published in 2010 by the International Federation for Structural Concrete (fib) Postal address: Case Postale 88, CH-1015 Lausanne, Switzerland Street address: Federal Institute of Technology Lausanne - EPFL, Section Gnie Civil Tel +41 21 693 2747 Fax +41 21 693 6245 [email protected] www.fib-international.org ISSN 1562-3610 ISBN 978-2-88394-096-3 Printed by DCC Document Competence Center Siegmar Kstl e.K., Germany

fib Bulletin 56: Model Code 2010, First complete draft Volume 2 iii

Contents Notations vii

PART III: DESIGN

7 Design 1 7.1 Conceptual design 1

7.1.1 General 1 7.1.2 Methodology 1 7.1.3 Structural concept and basis for design 5

7.2 Structural analysis and dimensioning 6 7.2.1 General 6 7.2.2 Structural modelling 7 7.2.3 Dimensioning values 16

7.3 Verification of structural safety (ULS) for predominantly static loading 27 7.3.1 General 27 7.3.2 Bending with and without axial force 27 7.3.3 Shear 30 7.3.4 Torsion 43 7.3.5 Punching 45 7.3.6 Design with stress fields and strut and tie models 53 7.3.7 Compression members 59 7.3.8 Lateral instability of beams 64 7.3.9 3D Solids 65

7.4 Verification of structural safety (ULS) for non-static loading 68 7.4.1 Fatigue design 68 7.4.2 Impact and explosion 76 7.4.3 Seismic design 85

7.5 Verification of structural safety (ULS) for extreme thermal conditions 108 7.5.1 Fire design 108 7.5.2 Cryogenic design 125

7.6 Verification of serviceability (SLS) of RC and PC structures 129 7.6.1 Requirements 129 7.6.2 Design criteria 129 7.6.3 Stress limitation 130 7.6.4 Limit state of cracking 132 7.6.5 Limit states of deformation 148 7.6.6 Vibrations 155

7.7 Verification of safety and serviceability of FRC structures 157 7.7.1 Classification 157 7.7.2 Design principles 157 7.7.3 Verification of safety (ULS) 159 7.7.4 Serviceability Limit State (SLS) 165

7.8 Verification of limit states associated with durability 167 7.8.1 General 167 7.8.2 Carbonation induced corrosion uncracked concrete 169 7.8.3 Chloride induced corrosion uncracked concrete 174 7.8.4 Influence of cracks upon reinforcement corrosion 177

Copyright fib, all rights reserved. This PDF copy of fib Bulletin 56 is intended for use and/or distribution only within National Member Groups of fib.

iv fib Bulletin 56: Model Code 2010, First complete draft Volume 2

7.8.5 Risk of depassivation with respect to pre-stressed steel 178 7.8.6 Freeze/thaw attack 178 7.8.7 Chemical attack 182 7.8.8 Alkali-aggregate reactions 184

7.9 Verification of robustness 186 7.9.1 General 186 7.9.2 Specific methods to improve robustness by structural measures 188

7.10 Verification of sustainability 190 7.10.1 Impact on environment 190 7.10.2 Impact on society 191 7.10.3 Aesthetics 192

7.11 Verification assisted by numerical simulations 193 7.11.1 Purpose 193 7.11.2 Methods of numerical simulation 193 7.11.3 Safety formats for non-linear analysis 196 7.11.4 Resistance parameter identification 200

7.12 Verification assisted by testing 202 7.12.1 Scope 202 7.12.2 Definition 203 7.12.3 Aims of verification assisted by testing 204 7.12.4 Requirements 205 7.12.5 Planning 205 7.12.6 Testing conditions and measurements 207 7.12.7 Laboratory report 208 7.12.8 Statistical analysis of test results 209 7.12.9 Verification procedure 210

7.13 Detailing 213 7.13.1 Basic principles 213 7.13.2 Positioning of reinforcement 213 7.13.3 Prestressed structures 221 7.13.4 Bearings and joints 222 7.13.5 Structural members 223 7.13.6 Special aspects of precast concrete elements and composite structural members 229

PART IV: CONSTRUCTION

8 Construction 237 8.1 General 237 8.2 Execution management 237

8.2.1 Assumptions 237 8.2.2 Documentation 238 8.2.3 Quality management 238

8.3 Reinforcing steel works 239 8.3.1 Transportation and storage 240 8.3.2 Identification 240 8.3.3 Cutting and bending 240 8.3.4 Welding 242 8.3.5 Joints 244 8.3.6 Assembly and placing of the reinforcement 244 8.3.7 Construction documents reinforcement 245


fib Bulletin 56: Model Code 2010, First complete draft Volume 2 v

8.4 Prestressing works 245 8.4.1 General 245 8.4.2 Packaging, transportation, storage and handling of materials and components 246 8.4.3 Prestressing works for post-tensioning tendons 247 8.4.4 Prestressing works for pretensioning tendons 252 8.4.5 Replacement of tendons 254 8.4.6 Construction documents prestressing 255

8.5 Falsework and formwork 255 8.6 Concreting 255

8.6.1 Specification of concrete 255 8.6.2 Placing and compaction 256 8.6.3 Curing 257 8.6.4 Execution with precast concrete elements 257 8.6.5 Geometrical tolerances 258

PART IV: CONSERVATION AND DISMANTLEMENT

9 Conservation 259 9.1 Conservation objectives 259 9.2 Conservation strategies and tactics 260

9.2.1 General 260 9.2.2 Strategy using proactive conservation measures 261 9.2.3 Strategy using reactive conservation measures 263 9.2.4 Situations where conservation measures are not feasible 264

9.3 Conservation management 264 9.3.1 Through-life conservation process 264 9.3.2 Conservation Plan 268

9.4 Condition survey 269 9.4.1 Condition survey and monitoring activities 269 9.4.2 Locations for surveys and monitoring activities 271 9.4.3 Tools and techniques for surveys and monitoring 271 9.4.4 Gathering data for Condition Control purposes 272 9.4.5 General flow of condition survey process 275

9.5 Condition assessment 277 9.5.1 Identification of deterioration mechanisms and prediction of damage 277 9.5.2 Identification of deterioration mechanism 277 9.5.3 Factors influencing deterioration 278 9.5.4 Determination of deterioration level and rate 278

9.6 Condition evaluation and decision-making 278 9.6.1 General 278 9.6.2 Threshold levels for deterioration of material and / or structural performance 279 9.6.3 Judgment criteria 279 9.6.4 Selection of interventions 280

9.7 Interventions 281 9.7.1 Maintenance interventions 282 9.7.2 Preventative interventions 282 9.7.3 Remedial interventions 283 9.7.4 Rebuild, reconstruction and replacement 283


vi fib Bulletin 56: Model Code 2010, First complete draft Volume 2

9.7.5 Strengthening or upgrading interventions 284 9.7.6 Other activities and measures 285 9.7.7 Execution of interventions 286

9.8 Recording 287

10 Dismantlement, recycle and reuse 288 10.1 General 288 10.2 Dismantlement and removal 288

10.2.1 General 288 10.2.2 Consideration at design stage 288

10.3 Recycle and reuse 288


fib Bulletin 56: Model Code 2010, First complete draft Volume 2 vii

Notations

Meaning of Roman capital letters A area B (void) C torsional moment of inertia D fatigue damage factor; diffusion coefficient E modulus of elasticity; earthquake action F action in general; local loading G permanent action; shear modulus H horizontal component of a force I second moment of a plane area J creep function K (permeability) coefficient L can be used for 'span; length of an element' in place of I M bending moment; coefficient of water absorption N axial force O (void) P force Q variable action R strength (resisting load effect); reaction at a support; resultant S load effect (M, N, I', T); static moment of a plane area T torsional moment; temperature U (void) V shear force, volume W modulus of inertia X reaction or force in general, parallel to x-axis Y reaction or force in general, parallel to y-axis Z reaction or force in general, parallel to z-axis

NOTE: Roman capital letters can be used to denote types of material, e.g. C for concrete, LC for lightweight concrete, S for steel, Z for cement.

Meaning of Roman lower case letters a deflection; distance; acceleration b width c concrete cover d effective height; diameter (see also h) e eccentricity f strength of a material g distributed permanent load; acceleration due to gravity h total height or diameter of a section; thickness i radius of gyration j number of days k all coefficients with dimension 1 span; length of an element m bending moment per unit length or width; mass; average value of a sample n normal (longitudinal, axial) force per unit length or width o (void) p prestressing q distributed variable load r radius s spacing; standard deviation of a sample t time; torsional moment per unit length or width; thickness of thin elements u perimeter


viii fib Bulletin 56: Model Code 2010, First complete draft Volume 2

v velocity; shear force per unit length or width w width of a crack x co-ordinate; height of compression zone Y co-ordinate; height of rectangular diagram co-ordinate; lever arm

Use of Greek lower case letters alpha angle; ratio; coefficient beta angle; ratio; coefficient gamma safety factor; density; shear strain (angular strain) delta coefficient of variation; coefficient epsilon strain zeta coefficient eta coefficient theta rotation iota (void) kappa (to be avoided as far as possible) lambda slenderness ratio; coefficient mu relative bending moment; coefficient of friction; mean value of a whole

population nu relative axial force; Poisson's ratio xi coefficient; ratio omicron o (void) pi (mathematical use only) rho geometrical percentage of reinforcement; bulk density sigma axial stress; standard deviation of a whole population tau shear stress upsilon (void) phi creep coefficient chi (to be avoided as far as possible) psi coefficient; ratio omega mechanical percentage of reinforcement

Mathematical symbols and special symbols S sum difference; increment (enlargement) diameter of a reinforcing bar or of a cable (apostrophe) compression (only in a geometrical or locational sense) e base of Naperian logarithms exp power of the number e ratio of the circumference of a circle to its diameter n number of ... w/c water/cement ratio not greater than: indicates the upper bound in a formula * not smaller than: indicates the lower bound in a formula * < smaller than > greater than *: These symbols placed at the end of an expression indicate that where the result to which it leads is higher

(or lower) than the limit given, then the values given should be taken into account and not the result obtained from the formula.


fib Bulletin 56: Model Code 2010, First complete draft Volume 2 ix

General subscripts a support settlement; additional; accidental load b bond; bar; beam c concrete; compression; column d design value e elastic limit of a material f forces and other actions; beam flange; bending; friction g permanent load h horizontal; hook i initial j number of days k characteristic value 1 longitudinal m mean value; material; bending moment n axial force o zero p prestressing steel q variable load r cracking s ordinary steel; snow; slab t tension;* torsion;* transverse u ultimate (limit state) v shear; vertical w wind; web; wire; wall x linear co-ordinate y linear co-ordinate z linear co-ordinate 1, 2, 3 particular values of quantities cc conventional asymptotic value

NOTE: * When confusion is possible between tension and torsion, the subscripts tn (tension) and tr (torsion) should be used.

Subscripts for actions and action effects a(A) support settlement; accidental action cc creep of concrete cd delayed elasticity of concrete cf delayed plasticity of concrete cs shrinkage of concrete ep earth pressure eg(E) earthquake; seismic ex explosion; blast eq (E) forces and other actions g(G) permanent load im impact lp liquid pressure m(M) bending moment n(N) axial force p(P) prestress q(Q) variable load s(S) snow load t(T) torsion; temperature v(V) shear w(W) wind load


x fib Bulletin 56: Model Code 2010, First complete draft Volume 2

Subscripts obtained by abbreviation abs absolute act acting adm admissible, permissible cal calculated, design crit (or cr) critical ef effective el (or e) elastic est estimated exc exceptional est external fat fatigue inf inferior int internal lat lateral lim limit max maximum min minimum nec necessary net net nom nominal obs observed pl plastic prov (or pr) provisional (stage of construction), provided red reduced rel relative, relaxation rep representative req required res resisting, resistant ser serviceability, service sup superior tot total var variable

Notation list

Roman lower case letters

1 / r curvature of a section of an element 1 /r(g) curvature due to g 1 /r(g+q) curvature due to g and q 1 /r0 (g+9) instantaneous (initial) curvature due to g and q 1 /r1 curvature of an uncracked concrete section (state I) 1 /r1 r curvature in state I under cracking moment 1 /r2 curvature of a cracked concrete section (state II) 1 /r2r curvature in state II under cracking moment 1 /rts tension stiffening correction for curvature a deflection ac elastic deflection (calculated with rigidity Ec Ie) b breadth of compression zone or flange bred reduced breadth of web bx smaller side dimension of a rectangular section by greater side dimension of a rectangular section bw breadth of web c concrete cover, concentration of a substance in a volume element cl column dimension parallel to the eccentricity of the load


fib Bulletin 56: Model Code 2010, First complete draft Volume 2 xi

c2 column dimension perpendicular to the eccentricity of the load c m i n minimum concrete cover c n o m nominal value of concrete cover (= c m i n + tolerance) d effective depth to main tension reinforcement d effective depth to compression reinforcement d m a x maximum aggregate size e load eccentricity e0 first order eccentricity (= MSd / Nsd) e01 smaller value of the first order eccentricity at one end of the considered element e02 greater value of the first order eccentricity at one end of the considered element etot total eccentricity fbd design value of bond stress fc cylinder compressive strength of concrete fc* cylinder compressive strength of concrete under triaxial loading (confined strength),

reduced concrete strength due to transverse tension fcc cylinder compressive strength of concrete under uniaxial stress fcd* design compressive strength of concrete under triaxial loading (confined strength),

reduced design concrete strength due to transverse tension fcd design value of fc fcd1 average design strength value in an uncracked compression zone fcd2 average design strength value in a cracked compression zone fcd,fat design fatigue reference strength of concrete under compression fck characteristic value of fc fck,cf value of fck of confined concrete fck.cube characteristic value of cube compressive strength of concrete fck,fat fatigue reference compressive strength fcm mean value of compressive strength fc at an age of 28 days fct axial tensile strength of concrete (determined according to R1LEM CPC 7) fctd design value of fct fctk characteristic value of fct fctm mean axial tensile strength fct,fl mean flexural tensile strength (at T = 20C) fct,sp mean splitting tensile strength fd design value of strength fp0,1 0,1 % proof stress of prestressing reinforcement Fp0,2 0,2% proof stress of prestressing reinforcement fp0,1k characteristic 0,1% proof stress fp0,2k characteristic 0,2% proof stress fpt tensile strength of prestressing reinforcement fptd design tensile strength of prestressing reinforcement fptk characteristic tensile strength of prestressing reinforcement


xii fib Bulletin 56: Model Code 2010, First complete draft Volume 2

fpy tension yield stress of prestressing reinforcement fpyd design value of tension yield stress of prestressing reinforcement fpyk characteristic value of tension yield stress of prestressing reinforcement fR relative (or projected) rib area ft tensile strength of non- prestressing reinforcement ftk characteristic value of tensile strength of non- prestressing reinforcement fy tension yield stress of non- prestressing reinforcement fyc strength of steel in compression fycd design strength of steel in compression fyd design value of tension yield stress of non- prestressing reinforcement fyk characteristic value of tension yield stress of non- prestressing reinforcement gd design value of distributed permanent load h overall depth of member, total height; notional size of a member (2 Ac/u; u: perimeter

in contact with the atmosphere) hb depth of beam hf depth of flange hw height of water column i radius of gyration l design span, effective span, length of an element, thickness of a penetrated section l measured elongation between two measuring points 10 design lap length, effective length (of columns); distance between measuring points lb basic anchorage length lbp basic anchorage length of pretensioned reinforcement lbpd design anchorage length of pretensioned reinforcement lbpt transmission length of pretensioned reinforcement lb,min minimum anchorage length lb,net design anchorage length lch characteristic length (fracture parameter) lp development length for prestressing reinforcement lpl plastic length (region in which tensile strain is larger than yield strain) lpl residual elongation after unloading lp,max length over which the slip between prestressing steel and concrete occurs ls,max length over which the slip between steel and concrete occurs lt transmission length m moment per unit width (out-of-plane loading); mass of substance flowing: degree

of hydration n number of bars, number of load cycles; force per unit width (in-plane-loading) nRi number of cycles leading to failure at stress levels Si,min and Si,max, respectively nSi number of cycles applied at constant minimum and maximum stress levels Si,min

and Si,max, respectively p local gas pressure


fib Bulletin 56: Model Code 2010, First complete draft Volume 2 xiii

q distributed variable load qd design value of distributed variable load r radius s slip (relative displacement of steel and concrete cross-sections), shear slip (at

interfaces); spacing of bars smax maximum bar spacing sr distance between cracks; radial spacing of layers of shear reinforcement sr,m mean spacing between cracks t time, age, duration; thickness of thin elements t0 age at loading ts concrete age at the beginning of shrinkage or swelling tT effective concrete age u length of a perimeter; component of displacement of a point u0 length of the periphery of the column or load ul length of the control perimeter for punching uef length of the perimeter of Aef un length of the control perimeter for punching outside a slab zone with shear

reinforcement v shear force per unit width (out-of-plane loading), component of displacement of a

point w crack width; component of displacement of a point wc crack width for ct = 0 wk calculated characteristic crack width wlim nominal limit value of crack width x depth of compression zone, distance z internal lever arm

Greek lower case letters

coefficient, reduction factor e modular ratio (Es / Ec) e ,p modular ratio (Ep / Ec) e ,sec secant modular ratio (Es,sec / Ec,sec) ST coefficient of thermal expansion for steel T coefficient of thermal expansion in general coefficient characterizing the bond quality of reinforcing bars c(t,t0) coefficient to describe the development of creep with time after loading safety factor c partial safety factor for concrete material properties c,fat partial safety factor for concrete material properties under fatigue loading F partial safety factor for actions G partial safety factor for permanent actions Q partial safety factor for variable actions s partial safety factor for the material properties of reinforcement and prestressing steel


xiv fib Bulletin 56: Model Code 2010, First complete draft Volume 2

s,fat partial safety factor for the material properties of reinforcement and prestressing steel under fatigue loading

jj node displacement strain c concrete compression strain c* concrete compression strain under triaxial stress cm average concrete strain within ls,max c0 concrete strain at peak stress m compression cc(t) concrete creep strain at concrete age t > t0 ci(t0) stress dependent initial strain at the time of stress application cn(t) total stress independent strain at a concrete age t (= cs(t) + cT(t,T) ) cs(t,ts) total shrinkage or swelling strain at concrete age t (t in days) c(t) total stress dependent strain at a concrete age t (= ci(t0) + cc(t) ) ct concrete tensile strain cT(t,T) thermal strain at a concrete age t cu ultimate strain of concrete in compression d0 strain of prestressed reinforcement corresponding to Pd0 pu total elongation of prestressing reinforcement at maximum load r strain at the onset of cracking s steel strain s1 steel strain in uncracked concrete s2 steel strain in the crack sm mean steel strain sr increase of steel strain in cracking state sr1 steel strain at the point of zero slip under cracking forces sr2 steel strain in the crack under cracking forces (ct reaching fctm) sT thermal strain of steel su strain of non-prestressing reinforcement at maximum load ts increase of strain by the effect of tension stiffening u total elongation of reinforcing steel at maximum load uk characteristic total elongation of reinforcing steel at maximum load yd design yield strain of non - prestressing reinforcement (= fyd / Es) transverse contraction ratio of bond strength of prestressing steel and high-bond reinforcing steel viscosity of gas angle between web compression and the axis of a member; rotation f angle between inclined compression in a flange and the axis of the member slenderness ratio (= l0 / i) coefficient of friction, relative bending moment relative axial force c Poisson's ratio of concrete s Poisson's ratio of steel sd relative design axial force (= NSd / Ac fcd) ratio of (longitudinal) tension reinforcement (= As/bd) s,ef effective reinforcement ratio (= As/Ac,ef) t relaxation after t hours w ratio of web reinforcement (= Asw/bws sin) stress


fib Bulletin 56: Model Code 2010, First complete draft Volume 2 xv

1 , 2 , 3 principal stresses c concrete compression stress cd design concrete compression stress ct concrete tensile stress c,ef compression stress of confined concrete c,max maximum compressive stress c , m i n minimum compressive stress p0(x) initial stress in prestressing reinforcement at a distance x from anchorage device p0,max. maximum tensile force in prestressing reinforcement at tensioning pcs tendon stress due to prestress after all losses (due to creep and shrinkage) pd tendon stress under design load Rsk(n) stress range relevant to n cycles obtained from a characteristic fatigue strength function s steel stress s 2 steel stress in the crack sE steel stress at the point of zero slip s r 2 steel stress in the crack under crack loading (ct reaching f c t m) S s steel stress range under the acting loads b local bond stress b m mean bond stress f u , d ultimate design shear friction capacity m a x maximum value of bond stress R d resistance to shear stress (design value) S d applied shear stress (design value) (t,t0) relaxation coefficient mechanical reinforcement ratio s w mechanical ratio of stirrup reinforcement v volumetric ratio of confining reinforcement w volumetric mechanical ratio of confining reinforcement wd design volumetric mechanical ratio of confining reinforcement

Roman capital letters

A total area of a section or part of a section (enclosed within the outer circumference) A1 section area in state I (taking into account the reinforcement) Ac area of concrete cross section or concrete compression chord Ac,ef effective area of concrete in tension Acore effectively confined area of cross-section in compression Aef area enclosed by the centre-lines of a shell resisting torsion Ap area of prestressing reinforcement As area of reinforcement As' area of compressed reinforcement Ash area of hoop reinforcement for torsion Asl area of longitudinal reinforcement Ast area of transverse reinforcement Asw area of shear reinforcement As,cal calculated area of reinforcement required by design As,ef area of reinforcement provided As,min minimum reinforcement area D fatigue damage, diffusion coefficient


xvi fib Bulletin 56: Model Code 2010, First complete draft Volume 2

Dlim limiting fatigue damage E modulus of elasticity Ec reduced modulus of elasticity for concrete Ec(t0) modulus of elasticity at the time of loading t0 Eci tangent modulus of elasticity at a stress i (at T = 20C) Ec,sec secant modulus of elasticity at failure for uniaxial compression

(Ec,sec= fcm / |c0| ) EP modulus of elasticity of prestressing steel Es modulus of elasticity of steel Es,sec secant modulus of elasticity of steel F force, applied load or load effect Fb bond force transmitted along the transmission length Fc strut force (compression force) Fd design value of action Fpt tensile load of prestressed reinforcement Fp0,1 characteristic 0,1 % proof -load FSd,ef effective concentric load (punching load enhanced to allow for the effects of moments) Ft tie force (tension force) Fud ultimate dowel force G permanent action GF fracture energy of concrete GF0 base value of fracture energy (depending on maximum aggregate size) Ginf favourable part of permanent action Gsup unfavourable part of permanent action H horizontal force, horizontal component of a force I second moment of area I 1 second moment of area in state I (including the reinforcement) I2 second moment of area in state II (including the reinforcement) Ic second moment of area of the uncracked concrete cross-section (state I) J(t,t0) creep function or creep compliance representing the total stress dependent strain per

unit stress Kg coefficient of gas permeability Kw coefficient of water permeability L span, length of an element M bending moment; maturity of concrete Mr cracking moment MRd design value of resistant moment MSd design value of applied moment Mu ultimate moment My yielding moment N axial force, number of cycles to failure (fatigue loading) Nr axial cracking force NRd design value of resistance to axial force NSd design value of applied axial force Pd0 design value of prestressing force (initial force) Pk,inf lower characteristic value of prestressing force Pk,sup upper characteristic value of prestressing force Pm mean value of prestressing force


fib Bulletin 56: Model Code 2010, First complete draft Volume 2 xvii

Q variable single action; volume of a transported substance (gas or liquid) R resistance (strength); bending radius; universal gas constant Rd design resistance RH ambient relative humidity RH0 100% relative humidity S load effect (M, N, V, T); absorption coefficieni Scd stress range under fatigue loading Scd,max design value of maximum compressive stress level (fatigue loading) Scd,min design value of minimum compressive stress level (fatigue loading) Sc,max maximum compressive stress level (fatigue loading) Sc,min minimum compressive stress level (fatigue loading) Sd design load effect (M, N, V, T) T temperature, torsional moment T temperature change TRd design value of resistance to torsional moment TSd design value of applied torsional moment TSd,eff effective design value of applied torsional moment V shear force; volume of gas or liquid VRd design value of resistance to shear force VSd design value of applied shear force Vu ultimate shear force W1 section modulus in state I (including the reinforcement) W2 section modulus in state II (including the reinforcement) Wc section modulus of the uncracked concrete cross-section (state I) Wc,cf volume of confined concrete We external work Wi internal work Ws,trans volume of closed stirrups or cross-ties

Others

nominal diameter of steel bar n equivalent diameter of bundles containing n bars p diameter of prestressing steel (for bundles equivalent diameter) (t,t0) creep coefficient 0 notional creep coefficient pl plastic rotation capacity U total perimeter of rebars

Statistical symbols

Roman lower case letters

fx(x) probability density function (of normal distribution) fr(r) probability density function (of log-normal distribution) fR(r) probability density function of resistance fS(s) probability density function of action k normalised variable or fractile factor mx mean (same meaning as x ) mR mean of resistance


xviii fib Bulletin 56: Model Code 2010, First complete draft Volume 2

mS mean of action pf failure probability x! median x modal value x mean (same meaning as mx) xp p-%-fractile

Greek lower case letters:

sensitivity factor reliability index (partial) safety factor x2 scattering or variance x standard deviation R standard deviation of resistance S standard deviation of action

Roman capital letters:

Fr(r) probability distribution function (of log-normal distribution) Fx(x) probability distribution function (of normal distribution) R resistance S action Vx coefficient of variation Z safety zone (difference of R and S)

Others

(k) normalized function


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Man

y i

tera

tion

s of

the

des

ign

pro

cess

are

com

monly

req

uir

ed t

o r

efin

e th

e

des

ign c

once

pts

to

acc

ord

wit

h t

he

fun

ctio

nal

req

uir

emen

ts a

nd a

ssoci

ated

finan

cial

/ o

ther

co

nst

rain

ts.

The

anal

yti

c to

ols

appli

ed a

t th

is s

tage

to t

he

inves

tigat

ion of

the

pro

ble

m

and

ev

alu

atio

n

of

pote

nti

al opti

ons

may

be

rela

tivel

y c

rude.

T

he

bas

ic ap

pro

ach

to

d

esig

n re

lies

o

n d

eco

mp

osi

tio

n an

d in

tegra

tio

n.

Sin

ce d

esig

n p

roble

ms

are

larg

e an

d c

om

ple

x,

they

hav

e to

be

dec

om

po

sed

into

su

b-p

roble

ms

that

ar

e sm

all

eno

ugh

to

so

lve.

T

her

e ar

e n

um

ero

us

alte

rnat

ive

way

s to

dec

om

po

se d

esig

n p

roble

ms,

su

ch a

s d

eco

mp

osi

tio

n b

y

funct

ions

of

the

faci

lity

, b

y s

pat

ial

loca

tio

ns

of

its

par

ts,

or

by l

inks

am

on

g

var

ious

funct

ions

or

par

ts.

So

luti

ons

to s

ub

-pro

ble

ms

mu

st b

e in

tegra

ted

into

an o

ver

all

solu

tio

n.

Th

e in

tegra

tio

n a

nd

rat

ion

alis

atio

n p

roce

ss o

ften

cre

ates

conce

ptu

al c

onfl

icts

whic

h m

ust

be

iden

tifi

ed a

nd

res

olv

ed.

Var

ious

idea

s fo

r so

lvin

g t

he

pro

ble

m u

nd

er s

tud

y a

re p

rod

uce

d d

uri

ng t

he

conce

ptu

al d

esig

n s

tage,

wit

h o

ne

that

co

mp

lies

in

an

op

tim

al m

ann

er w

ith

the

spec

ifie

d r

equir

emen

ts.

Th

ese

idea

s, e

ven

th

ou

gh

lac

kin

g i

n d

etai

l, m

ust

des

crib

e th

e so

luti

on

fr

om

th

e p

oin

ts

of

vie

w

of

fun

ctio

nal

ity

, st

ruct

ura

l

bea

ring c

apac

ity,

const

ruct

ion

an

d e

con

om

y.

Th

is p

has

e sh

ould

id

enti

fy t

he

more

cri

tica

l as

pec

ts w

hic

h n

eed

to

be

mo

re t

horo

ugh

ly d

evel

op

ed i

n t

he

foll

ow

ing s

tages

of

the

des

ign

pro

cess

.

7.1

.2

Met

ho

do

log

y

Conce

ptu

al d

esig

n i

s a

crea

tive

act

for

whic

h i

t is

not

easy

to

est

abli

sh a

met

hodolo

gy.

Fig

ure

7

.1-1

il

lust

rate

s a

pro

cess

w

hic

h m

ay p

rovid

e so

me

insi

ght

and b

e of

assi

stan

ce w

ith

th

is a

ctiv

ity.


7

Des

ign

2

Fig

ure

7.1

-1:

Met

ho

dolo

gic

al

flo

wch

art

for

conce

ptu

al

des

ign

7.1

.2.1

In

pu

t

Init

ial

info

rmat

ion

mu

st b

e es

tab

lish

ed w

ith

reg

ard

to

:

bas

ic e

xte

rnal

in

pu

t dat

a,

serv

ice

crit

eria

,

per

form

ance

req

uir

emen

ts.


fib

Bu

llet

in 5

6:

Mod

el C

od

e 20

10

, F

irst

co

mp

lete

dra

ft

Volu

me

2

3

Basi

c ex

tern

al

inp

ut

data

If t

he

bas

ic e

xte

rnal

in

pu

t d

ata

is n

ot

avai

lable

to t

he

des

igner

, a

pro

cess

wil

l nee

d t

o b

e es

tab

lish

ed s

o t

hat

it

can b

e obta

ined

eit

her

fro

m t

he

ow

ner

,

the

arch

itec

t, th

e au

thori

ties

or

som

e o

ther

so

urc

e, or

via

an

ap

pro

pri

ate

pro

cess

inst

igat

ed b

y t

he

des

ign

er.

Bas

ic d

ata

shal

l be

clea

rly s

pec

ifie

d i

n t

he

Ser

vic

e C

rite

ria

Agre

emen

t, s

ee s

ub

clau

se 3

.5.2

.2.5

.

bas

ic d

ata

appli

cab

le,

incl

ud

ing t

hir

d p

arty

inte

ract

ion

s (g

eote

chnic

al

dat

a, m

eto

cean

d

ata,

to

pogra

ph

ical

an

d b

ath

ym

etri

cal

dat

a, cl

imat

o-

logic

al

dat

a,

envir

on

men

tal

dat

a (e

arth

qu

ake,

h

urr

ican

es),

m

ater

ial

pro

per

ties

, ac

cess

ibil

ity

and

tr

ansp

ort

fa

cili

ties

, lo

cal

const

ruct

ion

rule

s, e

tc.)

Ser

vice

cri

teri

a

The

serv

ice

crit

eria

sh

all

be

dis

cuss

ed a

nd e

stab

lish

ed w

ith t

he

ow

ner

or

the

arch

itec

t; i

t sh

all

be

app

roved

by a

ll a

nd

shal

l be

clea

rly s

pec

ifie

d i

n t

he

Ser

vic

e C

rite

ria

Agre

emen

t, s

ee s

ub

clau

se 3

.5.2

.2.5

.

gen

eral

aim

s fo

r th

e u

se o

f th

e co

nst

ruct

ion

wo

rks

(eff

icie

ncy

, co

mfo

rt,

safe

ty,

etc.

),

oper

atio

nal

an

d m

ainte

nan

ce r

equ

irem

ents

(ef

fici

ency

, ec

on

om

y,

etc.

),

spec

ial

req

uir

emen

ts o

f th

e st

akeh

old

ers

(up

gra

din

g,

rep

lace

men

t, e

tc.)

,

obje

ctiv

es o

f pro

tect

ion a

nd s

pec

ial

risk

s,

load

ings

and

lo

adin

g c

om

bin

atio

ns,

envir

onm

enta

l co

ndit

ions

codes

and r

egu

lato

ry r

equ

irem

ents

.

Per

form

ance

req

uir

emen

ts

The

per

form

ance

re

qu

irem

ents

sh

all

be

esta

bli

shed

, pro

pose

d

and

expla

ined

by t

he

des

ign

er,

in c

onju

nct

ion

wit

h t

he

ow

ner

, an

d s

hal

l be

clea

rly

spec

ifie

d i

n t

he

Ser

vic

e C

rite

ria

Agre

emen

t, s

ee s

ubcl

ause

3.5

.2.2

.5.

per

form

ance

cri

teri

a fo

r se

rvic

eabil

ity a

nd

saf

ety (

incl

ud

ing d

ura

bil

ity

and r

obust

nes

s),

serv

ice

life

co

nst

rain

ts (

tem

po

rary

, re

pla

ceab

le,

evo

luti

ve,

lo

ng t

erm

),

reli

abil

ity c

onst

rain

ts,

per

form

ance

req

uir

emen

ts f

or

sust

ain

abil

ity.

7.1

.2.2

A

ctiv

itie

s

In g

ener

al,

acti

vit

ies

per

form

ed d

uri

ng t

he

stag

e of

conce

ptu

al d

esig

n o

f

const

ruct

ion w

ork

s ar

e re

late

d t

o:

T

he

conce

ptu

al d

esig

n p

roce

ss c

an b

e ch

arac

teri

zed

by a

ser

ies

of

inte

r-

acti

ve

acti

vit

ies,

des

crib

ed a

s fo

llo

ws:

const

rain

t an

alysi

s an

d c

lass

ific

atio

n,

envir

onm

ent

anal

ysi

s (i

ncl

ud

ing l

oca

l poli

tics

and l

oca

l tr

adit

ions)

,

form

ula

tio

n,

whic

h r

efer

s to

th

e d

efin

itio

n o

r d

escr

ipti

on

of

a d

esig

n

pro

ble

m

in

bro

ad

term

s,

thro

ugh

th

e sy

nth

esis

o

f id

eas

des

crib

ing

alte

rnat

ive

con

cep

ts,


7

Des

ign

4

gen

eral

co

nce

pti

on

,

choic

e of

mat

eria

ls (

con

sider

ing e

con

om

y a

nd e

ner

gy c

onsu

mpti

on f

or

pro

duct

ion

and

eli

min

atio

n),

stru

ctura

l co

nce

pt

(str

uct

ura

l lo

gic

, d

imen

sions)

,

inte

gra

tion

an

d

aest

het

ics

(leg

ibil

ity,

sim

pli

city

, pro

port

ions,

equil

ibri

um

, sh

apes

, det

ail

ph

ilo

sop

hy),

const

ruct

ion

met

ho

d (

seq

uen

ces)

,

rough c

ost

est

imat

e,

com

par

ison

of

alte

rnat

ives

,

succ

essi

ve

pre

sen

tati

on

, ex

pla

nat

ion

and d

iscu

ssio

ns

wit

h t

he

ow

ner

(arc

hit

ect)

,

afte

r ac

cep

tan

ce b

y th

e ow

ner

-

pre

par

atio

n of

the

bas

is f

or

des

ign

(dra

win

gs,

no

tes,

rep

ort

s).

anal

ysi

s,

wh

ich

re

fin

es

the

pro

ble

m

def

init

ion

or

des

crip

tio

n

by

separ

atin

g

imp

ort

ant

from

p

erip

her

al

info

rmat

ion

and

b

y

pu

llin

g

toget

her

th

e es

sen

tial

det

ail.

In

terp

reta

tio

n a

nd

pre

dic

tio

n a

re u

sual

ly

requir

ed a

s p

art

of

the

anal

ysi

s,

sear

ch,

whic

h

invo

lves

gat

her

ing

a se

t o

f po

ten

tial

so

luti

on

s fo

r

per

form

ing

the

spec

ifie

d

funct

ion

s an

d

sati

sfyin

g

the

use

r

requir

emen

ts,

dec

isio

n,

wh

ich

mea

ns

that

eac

h o

f th

e p

ote

nti

al s

olu

tio

ns

is e

val

uat

ed

and c

om

par

ed t

o t

he

alte

rnat

ives

unti

l th

e b

est

solu

tio

n i

s o

bta

ined

,

spec

ific

atio

n,

wh

ich

is

to d

escr

ibe

the

cho

sen

solu

tio

n i

n a

form

wh

ich

conta

ins

eno

ugh

det

ail

for

imp

lem

enta

tio

n,

modif

icat

ion

, w

hic

h r

efer

s to

the

chan

ge

in t

he

solu

tion

or

re-d

esig

n i

f

the

solu

tion

is

foun

d t

o b

e w

anti

ng o

r if

new

info

rmat

ion

is

dis

cover

ed

in t

he

pro

cess

of

des

ign

.

7.1

.2.3

T

he

role

of

exp

erti

se, in

sigh

t an

d t

ools

Att

ribute

s an

d t

oo

ls s

uch

as

the

foll

ow

ing m

ay b

e em

plo

yed

duri

ng t

he

conce

ptu

al d

esig

n s

tage:

exper

ience

, plu

s in

sigh

t fr

om

bac

kgro

und,

feed

bac

k,

dat

abas

e so

urc

es,

intu

itio

n, fe

elin

g, se

nsi

tivit

y f

or

the

circ

um

stan

ces,

crea

tivit

y, im

agin

atio

n,

c

apac

ity o

f si

mu

ltan

eou

s an

alysi

s an

d i

nte

gra

tion o

f d

iver

se c

rite

ria

and c

onst

rain

ts t

akin

g i

nto

acc

ou

nt

thei

r re

lati

ve

wei

ghts

,

quic

k p

re-d

esig

n m

eth

od

s,

dev

elopm

ent

of

idea

s,

con

cepts

an

d

des

ign

det

ails

by

sket

chin

g

(ran

gin

g f

rom

ro

ugh

fre

ehan

d s

ket

ches

to a

ccura

te d

raw

ings)

,

vis

ual

izat

ion

to

ols

.

T

he

conce

ptu

al d

esig

n p

roce

ss a

ims

to f

ind

acc

epta

ble

solu

tio

ns

for

the

def

ined

req

uir

emen

ts,

const

rain

ts a

nd

th

e as

soci

ated

op

po

rtu

nit

ies

pro

vid

ed

by t

he

circ

um

stan

ces.

Th

e p

roce

ss i

s gu

ided

by t

he

exp

erie

nce

gat

her

ed i

n

com

par

able

const

ruct

ion

wo

rks,

alo

ng w

ith

in

sigh

t an

d i

ntu

itio

n o

bta

ined

in

oth

er r

elev

ant

circ

um

stan

ces.

A v

arie

ty o

f to

ols

an

d a

ids

may b

e u

sed

to

ass

ist

the

pro

cess

, in

clu

din

g

tho

se

for

vis

ual

isat

ion

of

can

did

ate

sch

emes

an

d

alte

rnat

ive

opti

on

s, b

asic

dim

ensi

on

ing o

f el

emen

ts,

pre

lim

inar

y e

val

uat

ion

of

econom

ic o

utc

om

es,

etc.


fib

Bu

llet

in 5

6:

Mod

el C

od

e 20

10

, F

irst

co

mp

lete

dra

ft

Volu

me

2

5

7.1

.3

Str

uct

ura

l C

on

cep

t a

nd

Ba

sis

for

Des

ign

The

Str

uct

ura

l C

once

pt

der

ived

fro

m t

he

conce

ptu

al d

esig

n i

ncl

ud

es:

the

chose

n s

tru

ctura

l sy

stem

,

info

rmat

ion

on

the

mo

st i

mp

ort

ant

dim

ensi

on

s, c

onst

ruct

ion

mat

eria

l

pro

per

ties

an

d c

on

stru

ctio

n d

etai

ls,

com

men

ts o

n t

he

envis

aged

met

ho

ds

of

con

stru

ctio

n.

The

Str

uct

ura

l C

on

cept

der

ived

fr

om

th

e co

nce

ptu

al

des

ign

sh

all

be

des

crib

ed i

n t

he

Bas

is o

f D

esig

n,

incl

ud

ing t

he

bas

es a

nd

req

uir

emen

ts f

or

the

subse

quen

t des

ign

, ex

ecu

tio

n,

use

an

d c

on

serv

atio

n.

The

Bas

is f

or

Des

ign

des

crib

es:

The

exte

nt

and

co

nte

nt

of

the

bas

is of

des

ign sh

all

be

adap

ted to

th

e

import

ance

of

the

con

stru

ctio

n

wo

rks

and

the

asso

ciat

ed

haz

ards

and

envir

onm

enta

l ri

sks,

bu

t it

mu

st a

lway

s ex

ist

no m

atte

r h

ow

min

or

the

pro

ject

mig

ht

be

consi

der

ed t

o b

e.

the

des

ign

wo

rkin

g l

ife,

the

serv

ice

situ

atio

ns

con

sid

ered

,

the

haz

ard

sce

nar

ios

con

sider

ed,

the

requir

emen

ts

of

stru

ctu

ral

safe

ty,

serv

icea

bil

ity

and

du

rab

ilit

y

toget

her

w

ith

th

e m

easu

res

nee

ded

to

gu

aran

tee

them

, in

clu

din

g

div

isio

n

of

resp

on

sibil

itie

s,

pro

cess

es,

contr

ols

an

d

corr

ecti

ve

mec

han

ism

s,

the

assu

med

gro

un

d c

ond

itio

ns,

the

import

ant

assu

mp

tio

ns

in t

he

stru

ctu

ral

and

anal

yti

cal

mo

del

s,

the

acce

pte

d r

isks,

oth

er c

ond

itio

ns

rele

van

t to

th

e des

ign

.


7

Des

ign

6

7.2

S

tru

ctu

ral

an

aly

sis

an

d d

imen

sio

nin

g

7.2

.1

Gen

era

l

In s

om

e ca

ses,

this

mo

del

may b

e b

ased

on e

xper

imen

tal

test

s m

ade

for

the

par

ticu

lar

des

ign

o

r o

n

a co

mb

inat

ion

of

test

ing

and

anal

yti

cal

calc

ula

tions.

S

truct

ura

l an

alysi

s co

mp

rise

s th

e d

eter

min

atio

n o

f act

ion

eff

ects

su

ch a

s

inte

rnal

forc

es a

nd

mo

men

ts,

sup

port

rea

ctio

ns

and d

efo

rmat

ion

s ca

rrie

d o

ut

on t

he

bas

is o

f a

stru

ctu

ral

mo

del

. T

o t

hat

aim

th

e st

ruct

ure

can

be

sub

div

ided

into

com

ponen

ts,

like

bea

ms,

sla

bs,

wal

ls a

nd

sh

ells

and

co

nn

ecti

ng a

reas

.

Anal

yse

s sh

all

be

carr

ied

ou

t u

sin

g i

dea

lisa

tion

s o

f b

oth

th

e geo

met

ry a

nd

the

beh

avio

ur

of

the

stru

ctu

re.

Th

e id

eali

zati

on

s sh

all

be

appro

pri

ate

to t

he

case

consi

der

ed.

The

effe

ct

of

geo

met

ry

and

th

e p

rop

erti

es

of

the

stru

cture

an

d

its

beh

avio

ur

at e

ach

sta

ge

of

con

stru

ctio

n a

nd s

ervic

e sh

all

be

con

sid

ered

in

des

ign.

Sec

ond o

rder

eff

ects

shal

l b

e ta

ken

in

to a

cco

unt

wher

e th

ey a

re l

ikel

y t

o

affe

ct t

he

over

all

stab

ilit

y o

f a

stru

cture

sig

nif

ican

tly a

nd

for

the

atta

inm

ent

of

the

ult

imat

e li

mit

sta

te a

t cr

itic

al s

ecti

on

s

Impose

d

def

orm

atio

ns

can

re

sult

fr

om

dif

fere

nti

al

sett

lem

ents

,

tem

per

ature

gra

die

nts

or

dif

fere

nce

s in

hu

mid

ity o

r fr

om

sei

smic

act

ions.

T

he

inte

rnal

forc

es a

nd

mo

men

ts i

n a

str

uct

ure

foll

ow

fro

m a

syst

em o

f

load

s or

from

im

po

sed

def

orm

atio

ns

or

fro

m a

co

mb

inat

ion

of

bo

th.

Wit

h

regar

d to

th

e th

eory

o

f pla

stic

ity

both

th

e upper

an

d

the

low

er

theo

rem

of

pla

stic

ity c

an b

e ap

pli

ed.

The

appli

cati

on

o

f th

e lo

wer

th

eore

m of

pla

stic

ity im

pli

es th

at a

safe

bea

ring m

ode

is f

ou

nd

, if

a s

tati

call

y a

dm

issi

ble

bea

ring s

yst

em a

ppli

es i

n

whic

h,

under

th

e ac

tio

ns

def

ined

, th

e ad

mis

sible

st

ress

es

are

now

her

e

exce

eded

. E

xam

ple

s o

f su

ch s

yst

ems

are

stru

t an

d t

ie m

odel

s an

d t

he

stri

p

met

hod,

use

d f

or

the

des

ign

of

slab

s. T

he

solu

tions

found c

an b

e m

ore

or

less

econo

mic

, but

rep

rese

nt

a lo

wer

bo

und

for

the

bea

ring c

apac

ity.

The

appli

cati

on

of

the

up

per

th

eore

m o

f pla

stic

ity r

equir

es t

he

adopti

on o

f

a pat

tern

of

yie

ld l

ines

, gen

erat

ing a

kin

emat

ic m

echan

ism

. T

he

pat

tern

that

fail

s at

th

e lo

wes

t lo

ad

rep

rese

nts

th

e b

eari

ng

capac

ity.

This

m

ethod

is

par

ticu

larl

y v

aluab

le f

or

find

ing t

he

bea

rin

g c

apac

ity o

f ex

isti

ng s

truct

ure

s.

In

tern

al

forc

es,

mo

men

ts

and

d

eform

atio

ns

in

stat

ical

ly

ind

eter

min

ate

stru

cture

s m

ay b

e d

eter

min

ed b

ased

on:

theo

ry o

f li

nea

r el

asti

city

,

theo

ry o

f li

nea

r el

asti

city

wit

h l

imit

ed r

edis

trib

uti

on

,

theo

ry o

f pla

stic

ity,

nonli

nea

r m

eth

od

s.


fib

Bu

llet

in 5

6:

Mod

el C

od

e 20

10

, F

irst

co

mp

lete

dra

ft

Volu

me

2

7

The

effe

ct

of

cree

p

and

sh

rin

kag

e o

f co

ncr

ete

and

re

lax

atio

n

of

pre

stre

ssin

g

stee

l gen

eral

ly

hav

e to

b

e ta

ken

in

to

acco

unt

in

ver

ifyin

g

serv

icea

bil

ity.

Typic

al

of

D-r

egio

ns

are

the

area

s w

her

e st

ruct

ura

l co

mponen

ts

are

connec

ted (

e.g.

bea

m c

olu

mn

, lo

ad i

ntr

od

uct

ion a

reas

and s

upport

s).

In

ord

er t

o c

arry

ou

t d

imen

sio

nin

g,

the

stru

cture

an

d i

ts c

om

po

nen

ts c

an

be

subdiv

ided

into

B-

and

D-

regio

ns.

In

B-r

egio

ns

the

forc

es a

nd

mo

men

ts

var

y g

radual

ly.

In D

-regio

ns

the

forc

es a

nd

mo

men

ts v

ary d

isti

nct

ly.

Exce

pt

for

tho

se

due

to

the

seis

mic

ac

tio

n,

the

effe

ct

of

imp

ose

d

def

orm

atio

ns

may

be

negle

cted

in

ver

ifyin

g s

tru

ctu

ral

safe

ty i

f an

adeq

uat

e

def

orm

atio

n c

apac

ity i

s en

sure

d f

or

all

par

ts o

f th

e st

ruct

ure

.

If d

etai

led i

nves

tigat

ion

s ar

e n

eces

sary

for

the

det

erm

inat

ion

of

forc

es a

nd

mo

men

ts i

n t

he

serv

icea

bil

ity l

imit

sta

te,

an a

nal

ysi

s ca

n b

e ca

rrie

d o

ut

wit

h

adeq

uat

ely r

educe

d s

tiff

nes

s o

f st

ruct

ura

l ar

eas

du

e to

cra

ckin

g.

7.2

.2

Str

uct

ura

l m

od

elli

ng

7.2

.2.1

G

enera

l

The

stat

ic a

nd g

eom

etri

cal

bo

un

dar

y c

on

dit

ions

as w

ell

as t

he

tran

smis

sio

n

of

support

re

acti

on

s sh

all

be

taken

in

to

acco

unt

wh

en

idea

lisi

ng

and

del

imit

ing t

he

syst

em.

Soil

str

uct

ure

inte

ract

ion

shal

l b

e co

nsi

der

ed a

pp

ropri

atel

y.

7.2

.2.2

G

eom

etri

c im

per

fecti

on

s

Dev

iati

ons

in c

ross

-sec

tio

nal

dim

ensi

ons

are

norm

ally

tak

en i

nto

acc

ount

in

the

mat

eria

l sa

fety

fa

cto

rs.

Thes

e nee

d

ther

efore

not

be

incl

uded

in

stru

ctura

l an

alysi

s.

T

he

unfa

voura

ble

eff

ects

of

po

ssib

le d

evia

tio

ns

in t

he

geo

met

ry o

f th

e

stru

cture

an

d t

he

po

siti

on o

f th

e lo

ads

shal

l b

e ta

ken

in

to ac

cou

nt

in th

e

anal

ysi

s of

mem

ber

s an

d s

tru

cture

s.

Imper

fect

ions

shal

l b

e ta

ken

in

to

acco

unt

for

the

ver

ific

atio

n

of

the

ult

imat

e li

mit

sta

te f

or

per

sist

ent

and

acc

iden

tal

des

ign

sit

uat

ion

s. I

n t

he

case

of

slen

der

com

pre

ssio

n m

em

ber

s, t

he

seco

nd

ord

er e

ffec

ts a

nd

th

e in

flu

ence

s

of

cree

p o

f co

ncr

ete

shal

l be

taken

in

to a

cco

un

t (s

ub

clau

se 7

.3.7

).

Imper

fect

ions

nee

d

no

t b

e co

nsi

der

ed

for

the

ver

ific

atio

n

of

the

serv

icea

bil

ity l

imit

sta

te.


7

Des

ign

8

In

the

case

o

f b

rid

ge

pie

rs

or

hig

hly

st

ress

ed

buil

din

g

colu

mns,

th

e

incl

inat

ion re

sult

ing fr

om

th

e b

ase

rota

tio

n ca

n be

of

import

ance

fo

r th

e

dim

ensi

onin

g o

f th

e b

raci

ng s

tru

ctura

l m

em

ber

s (e

.g.

floor

slab

s, b

raci

ngs

of

bu

ildin

gs,

bri

dge

bea

rin

gs)

. T

he

effe

ct o

f th

e m

isal

ignm

ent

shal

l be

esti

mat

ed

and i

f nec

essa

ry t

aken

in

to c

on

sid

erat

ion

in

th

e ca

lcula

tions.

U

nle

ss s

pec

ifie

d o

ther

wis

e in

th

e b

asis

of

des

ign

, th

e u

nin

tend

ed b

ase

rota

tion o

f ver

tica

l co

mp

ress

ion

mem

ber

s am

ou

nts

to

1

200

i

0.0

1 l

1

300

(l

in

m)

(7.2

-1)

wher

e:

l den

ote

s th

e h

eigh

t o

f th

e co

mp

ress

ion

m

em

ber

o

r co

mp

ress

ion

mem

ber

s st

and

ing o

n t

op

of

on

e an

oth

er.

In

buil

din

gs,

th

e av

erag

e m

isal

ign

men

t

im

of

a gro

up

o

f ver

tica

l

com

pre

ssio

n m

em

ber

s ca

n b

e es

tim

ated

wit

h t

he

equ

atio

n

1.0

0.5

(1.0

)im

im

(7

.2-2

)

wher

e:

m

den

ote

s th

e n

um

ber

o

f co

mp

ress

ion

m

emb

ers

wh

ich

h

ave

to b

e

incl

uded

in

det

erm

inin

g t

he

effe

ct o

f th

e m

isal

ign

men

t, s

ee F

igu

re

7.2

-1.

Fig

ure

7.2

-1:

Geo

met

rica

l im

per

fect

ion

s


fib

Bu

llet

in 5

6:

Mod

el C

od

e 20

10

, F

irst

co

mp

lete

dra

ft

Volu

me

2

9

7.2

.2.3

S

tru

ctu

ral

geo

met

ry

For

the

stru

ctura

l an

alysi

s, t

he

stru

ctu

re s

hal

l b

e id

eali

sed

usi

ng s

uit

able

model

s;

exam

ple

s ar

e p

lan

e o

r sp

ace

fram

es

and

B

- an

d

D-r

egio

ns

of

stru

ctura

l co

mpon

ents

.

In t

he

case

of

T-b

eam

s, t

he

effe

ctiv

e sl

ab w

idth

dep

end

s o

n t

he

web

and

the

flan

ge

dim

ensi

on

s, t

he

typ

e o

f ac

tio

n,

the

span

, th

e su

pp

ort

co

ndit

ion

s an

d

the

tran

sver

se r

ein

forc

emen

t. T

he

effe

ctiv

e s

lab

wid

th m

ay b

e es

tim

ated

wit

h

the

equat

ion (

see

Fig

ure

7.2

-2):

bb

bb

wi

eff

eff

,

(7.2

-3)

wher

e

bef

f,i

0.2

b i

0.1

l 0

0.2

l 0

(7.2

-4)

The

dis

tance

l0 b

etw

een

th

e p

oin

ts o

f ze

ro m

om

ent

may b

e d

eter

min

ed f

or

usu

al c

ases

acc

ord

ing t

o F

igu

re 7

.2-3

, b

ased

on

th

e f

oll

ow

ing a

ssu

mp

tio

ns:

- th

e ca

nti

lever

len

gth

is

smal

ler

than

hal

f th

e ad

jace

nt

span

,

- th

e ra

tio b

etw

een

adja

cen

t sp

ans

is b

etw

een

1 a

nd

1.5

.

Fig

ure

7.2

-2:

Eff

ecti

ve s

lab

wid

th


7

Des

ign

10

Fig

ure

7.2

-3:

Rel

eva

nt

dis

tan

ces

l 0

for

the

det

erm

inati

on

of

the

effe

ctiv

e sl

ab

wid

th

7.2

.2.4

C

alc

ula

tion

meth

od

s

7.2

.2.4

.1

Anal

ysi

s bas

ed o

n l

inea

r el

asti

city

This

appro

ach

im

pli

es t

hat

th

e r

esp

on

se r

elat

ionsh

ip

is l

inea

r, a

nd t

he

assu

mpti

on o

f re

ver

sib

le d

efo

rmat

ion

s is

ret

ained

. T

he

resu

lts

are

real

isti

c

on

ly u

nder

that

act

ion

s ar

e lo

w a

nd

mem

ber

s ar

e uncr

acked

.

A

nal

ysi

s of

elem

ents

bas

ed o

n t

he

theo

ry o

f li

nea

r el

asti

city

may b

e u

sed

for

both

the

serv

icea

bil

ity a

nd

th

e u

ltim

ate

lim

it s

tate

s.

For

UL

S v

erif

icat

ions

exis

tin

g p

ract

ice

allo

ws

the

use

of

linea

r el

asti

c

anal

ysi

s w

ithout

dir

ect

ver

ific

atio

n o

f su

ffic

ient

duct

ilit

y.

This

is

bas

ed o

n t

he

assu

mpti

on t

hat

th

ere

is d

uct

ilit

y e

no

ugh

to

bal

ance

the

lack

of

com

pat

ibil

ity.

The

met

hod i

s norm

ally

use

d w

ith

th

e gro

ss-s

ecti

on o

f co

ncr

ete

mem

ber

s;

ther

efore

it

re

quir

es

def

init

ion

of

geo

met

ry

of

the

stru

cture

, but

not

nec

essa

rily

of

the

rein

forc

emen

t.

F

or

the

det

erm

inat

ion

of

the

acti

on

eff

ects

, li

nea

r el

asti

c an

alysi

s m

ay b

e

carr

ied o

ut

assu

min

g:

uncr

acked

cro

ss s

ecti

ons,

linea

r st

ress

-str

ain r

elat

ion

ship

s,

the

mea

n v

alu

e of

the

mo

du

lus

of

elas

tici

ty.

Cra

cked

cro

ss-s

ecti

on

s m

ay,

ho

wev

er,

be

use

d i

f in

the

lim

it s

tate

under

consi

der

atio

n a

fu

lly d

evel

op

ed c

rack

pat

tern

can

be

expec

ted.

The

resu

lts

of

a li

nea

r an

alysi

s ar

e al

so u

sed

in

th

e ver

ific

atio

n f

or

the

serv

icea

bil

ity l

imit

stat

e.

F

or

det

erm

inin

g t

he

effe

ct o

f im

po

sed

def

orm

atio

ns

at t

he

ult

imat

e li

mit

stat

e a

reduce

d s

tiff

nes

s co

rres

po

ndin

g t

o c

rack

ed s

ecti

ons

may

be

assu

med

.

For

the

serv

icea

bil

ity l

imit

sta

te a

gra

dual

evo

luti

on

of

crac

kin

g s

ho

uld

be

consi

der

ed.

7.2

.2.4

.2

Anal

ysi

s ac

cord

ing t

o l

inea

r el

asti

city

wit

h l

imit

ed

redis

trib

uti

on

Lin

ear

anal

ysi

s w

ith

lim

ited

red

istr

ibu

tio

n m

ay b

e ap

pli

ed t

o t

he

anal

ysi

s

of

stru

ctura

l m

em

ber

s fo

r th

e ver

ific

atio

n a

t th

e U

LS

.


fib

Bu

llet

in 5

6:

Mod

el C

od

e 20

10

, F

irst

co

mp

lete

dra

ft

Volu

me

2

11

If r

edis

trib

uti

on

of

mo

men

ts i

s ap

pli

ed i

n d

eter

min

ing t

he

rein

forc

emen

t

this

may

hav

e an

in

fluen

ce o

n d

efle

ctio

n a

nd

cra

ck w

idth

.

T

he

infl

uen

ce o

f an

y r

edis

trib

uti

on

of

mo

men

ts o

n o

ther

asp

ects

of

des

ign

shal

l be

consi

der

ed.

The

mo

men

ts a

t th

e U

LS

cal

cula

ted

usi

ng a

lin

ear

elas

tic

anal

ysi

s m

ay b

e

redis

trib

ute

d,

pro

vid

ed t

hat

th

e re

sult

ing d

istr

ibuti

on

of

mo

men

ts r

emai

ns

in

equil

ibri

um

wit

h t

he

appli

ed l

oad

s.

Red

istr

ibuti

on o

f b

endin

g m

om

ents

wit

ho

ut

exp

lici

t ch

eck o

n t

he

rota

tio

n

capac

ity i

s al

low

ed f

or

con

tinu

ou

s b

eam

s o

r sl

abs

wh

ich

are

pre

do

min

antl

y

subje

cted

to f

lex

ure

an

d h

ave

a ra

tio

of

the

len

gth

s o

f ad

jace

nt

span

s in

the

range

of

0.5

to 2

. In

th

is c

ase

the

foll

ow

ing r

elat

ion

s sh

ou

ld a

pp

ly:

dx

kk

u/

21

fo

r M

Pa

f ck

50

(7.2

-5)

dx

kk

u/

43

fo

r M

Pa

f ck

50

(7.2

-6)

and

5k

wher

e C

lass

B,

Cla

ss C

or

model code 2010 - institution of structural engineers · this draft of the fib model code 2010 was...

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