FIB 52: Structural Concrete Textbook on behaviour, design and performance, Second edition Volume 2: Basis of design

347 Pages·2010·40.592 MB·English

Structural Concrete
Textbook
on behaviour, design and performance

Second edition
Volume 2

January 2010
Subject to priorities defined by the Technical Council and the Presidium, the results of fib’s work in
Commissions and Task Groups are published in a continuously numbered series of technical publications
called 'Bulletins'. The following categories are used:
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) approved by the Technical Council of fib
or Recommendation
Model Code approved by the General Assembly of fib
Any publication not having met the above requirements will be clearly identified as preliminary draft.
This Bulletin N° 52 was approved as an fib Manual by the Technical Council in June 2009.
This second volume of the Structural Concrete Textbook was drafted by the following authors:
György L. Balázs* (Budapest Univ. of Technology and Economics, Hungary) Editor, Convener; Section 4.3.2
Andrew Beeby* (United Kingdom) Sections 4.3.1 and 4.3.3
Agnieszka Bigaj-van Vliet* (TNO, The Netherlands) Section 4.5
Mario A. Chiorino (Politecnico di Torino, Italy) Section 4.1.6
Josef Eibl* (Germany) Sections 4.1.1 – 4.1.5
Rolf Eligehausen* (Univ. Stuttgart, Germany) Section 4.5
Gert König (Univ. Leipzig, Germany) Sections 4.2 and 4.4.3
Marco Menegotto (Univ. of Rome, Italy) Section 4.4.2
Paul Regan* (United Kingdom) Section 4.4.1
Mario Sassone (Politecnico di Torino, Italy) Section 4.1.6
Kurt Schäfer (Germany) Section 4.4.4
Nguyen Viet Tue* (TU Graz, Austria) Sections 4.2 and 4.4.3

* member of Special Activity Group 2, “Dissemination of knowledge”, Working Group “Textbook”.

Full address details of Commission/Task Group members may be found in the fib Directory or through the
online services on fib's website, www.fib-international.org.

Cover image: Wadi Abdoun Bridge, Jordan, one of the winners of the 2010 fib Awards for Outstanding
Concrete Structures [photo courtesy of Dar Al-Handasah (Shair & Partners)].

© fédération internationale du béton (fib), 2010

Although the International Federation for Structural Concrete fib - fédération internationale du béton - does its
best to ensure that any information given is accurate, no liability or responsibility of any kind (including liability
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All rights reserved. No part of this publication may be reproduced, modified, translated, stored in a retrieval
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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 Génie Civil
Tel [phone] • Fax [phone]
[email protected] • www.fib-international.org

ISSN 1562-3610
ISBN 978-2-88394-092-5

Printed by DCC Document Competence Center Siegmar Kästl e.K., Germany
.
Contents
4 Basis of design 1
4.1 Structural analysis 1
4.1.1 Introduction 1
4.1.2 Elastic and time dependent analysis of linear members 1
(Basis of the theory – Time-dependent behaviour)
4.1.3 Elasto-plastic analysis of linear members 13
(Remarks on the strut-and-tie method – Slabs)
4.1.4 Nonlinear analysis 25
(Basic equations - linear members – Constitutive laws for plane biaxial
reinforced concrete structures within a FE-code)
4.1.5 Selected comments 38
(Variable inclination of compression diagonals in shear design – Linear
elastic computer codes for two-dimensional reinforced concrete members –
Evaluation of the prestressing state in T-beams – Nonlinear stress ranges
within in plane loaded plates – Rough estimation of creep – Torsional
stiffness of statically indeterminate structures – Modelling of reinforced
concrete for a nonlinear calculation)
4.1.6 Further considerations and updates on time dependent analysis of
concrete structures 43
(Introduction – General considerations on structural effects of creep and
shrinkage – Limit states – Evaluation of time dependent effects in concrete
structures in the serviceability domain; statistical nature of the problem –
Prediction models for creep and shrinkage and database for their
calibration – The structural analysis problem: the linear aging viscoelastic
approach – Constitutive laws in linear aging viscoelasticity: integral-type
creep and relaxation laws for uniaxial stress and strains – Linear aging
viscoelastic solutions for effective homogeneous structures of averaged
rheological properties – Linear aging viscoelastic solutions for effective
homogeneous structures of averaged rheological properties with elastic
(steel) redundant restraints of structural elements – Heterogeneous
structures – Methods of solving the linear aging viscoelastic problem –
Accurate numerical solutions as a sequence of elasticity problems with
initial strains – Conversion to algebraic expressions: Age-Adjusted
Effective Modulus (AAEM) method – Guidelines for design – Design aids)
4.2 Design format 70
4.2.1 Definition of limit states 70
fib Bulletin 52: Structural Concrete – Textbook on behaviour, design and performance, vol. 2 iii
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4.2.2 Safety concept 71
(Theoretical background – Frequently used distribution functions – Failure
probability and reliability index – Relation between reliability index and
safety factors – Determination of failure probability – Determination of
partial safety factors)
4.2.3 Design format 85
(General – Design format for ultimate limit state – Design format for
serviceability limit state)
4.3 Serviceability Limit States principles 90
4.3.1 General 90
4.3.2 Crack control 97
4.3.3 Deformation 133
(Introduction – Criteria for deflection control – Basic equations for the
calculation of deflections – Calculation of deflection by numerical
integration – Calculation of the defection of indeterminate beams by
numerical integration – Long term deflections – Accuracy of deflection
calculations – Simplifications to the calculation of deflections – Span/depth
ratios – Deformations and stresses due to temperature change)
4.4 Ultimate Limit State principles 171
4.4.1 Basic design for moment, shear and torsion 171
(Purpose and place of ultimate limit state design – Structural modelling –
Limiting stresses for static design – Axial load and flexure – Combined
shear and flexure – Torsion – Plates and slabs)
4.4.2 ULS of buckling 250
(Introduction – Reduction of capacity – Effects of prestressing – Effects of
restraints – Slenderness limits – Analysis – Safety – Detailing)
4.4.3 Fatigue 266
(Problem statement – Fatigue verification in CEB-FIP Model Code 1990 –
Stress calculations under cyclic loads – Fatigue resistance of steel and
concrete – Application example)
4.4.4 Nodes 281
(Introduction to the design of nodes – Principles for the verification of
singular nodes and anchorage – Typical nodes – References and indication
of numerical examples)
4.5 Anchorage and detailing principles 301
4.5.1 Reasons and background for detailing rules 301
iv fib Bulletin 52: Structural Concrete – Textbook on behaviour, design and performance, vol. 2
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4.5.2 Arrangement of reinforcement 301
(Minimum concrete cover – Spacers – Single bar spacing – Bundled bars
spacing – Skin reinforcement for large concrete covers and thick or
bundled bars – Allowable mandrel diameter – Minimum reinforcement
ratio)
4.5.3 Anchorage regions 306
(Anchorage of reinforcing steel – Anchorage of prestressing reinforcement
– Anchoring devices)
4.5.4 Detailing of tensile bending reinforcement 312
(Envelope line of the tensile force and the load balancing mechanism in
members subjected to bending and shear – Anchorage out of support –
Anchorage over support – Distribution of the reinforcement in the cross-
section of box girders or T-beams)
4.5.5 Splices in structural members 314
(Lap splices in tension – Lap splices in compression – Lap splices of
welded fabrics – Splices by welding – Splices by mechanical devices – Lap
splices of bundled bars)
4.5.6 Detailing of shear reinforcement 326
(Efficiency of anchorage of shear reinforcement – Distribution of shear
reinforcement)
4.5.7 Industrialisation of reinforcement 328
Annex: List of notations 331
fibBulletin 52: Structural Concrete – Textbook on behaviour, design and performance, vol. 2 v
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4 Basis of design
4.1 Structural analysis
by Josef Eibl
4.1.1 Introduction
The aim of structural analysis is to quantify the consequence of external or internal
actions on structural members or systems. This is done by mapping real structures onto
idealised mechanical models (see e.g. Section 4.1.4), which are then analysed using the tools
of mechanics and mathematics.
The mechanical basis for the analysis of statically loaded structural systems is the theory
of continuum mechanics, predominantly:
 equilibrium conditions
 kinematic relations (compatibility equations) and
 constitutive laws.
As the first two sets of equations are given in any textbook on structural analysis the main
problem is the modelling of reinforced concrete behaviour, which is rather complicated.
In the following mainly the behaviour of beams is treated because an exhaustive
instruction on the relevant structural analysis in general would exceed the frame of this
chapter.
4.1.2 Elastic and time dependent analysis of linear members
(1) Basis of the theory
In case of the theory of elasticity we may start with the equilibrium conditions:
dN
 q
H
dx
(4.1-1) (4.1-1)
2
dM d M dV
 V    q
dx , dx2 dx V
where
q local horizontal force and
H
q local vertical force,
v
and the kinematic relationships (Fig. 4.1-1):
dw
(4.1-2)
u  u (x)  z  u(x)  z (4.1-2)
0 0
dx
fib Bulletin 52: Structural Concrete – Textbook on behaviour design and performance, vol. 2 1
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du du0 d2w 1
(x)    z    z (4.1-3) (4.1-3)
0
dx dx dx2 r
where u and w are displacement components of a point.
 du 
0
 
 
1 0  0   dx 
(xz)     (4.1-4)
1
0 z    d2w 
 r  z 
 dx2 
They are the result of the Bernoulli-Navier assumption, postulating a linear strain
distribution over the cross-section after loading (Fig. 4.1-1).
Fig. 4.1-1: Definitions
The basis for the theory of elasticity is a very simple linear-elastic constitutive law,
which has nothing in common with the real behaviour of steel and concrete in the cracked
state (Fig. 4.1-2)
(4.1-5)
  E
This is explained by the historical development of mechanics where one started with the
simplest assumption to describe material behaviour. Otherwise the resulting analytical
problems could not have been overcome in the past.
With the equivalence relationships
 N   dA 
 i   (4.1-6)
   
M  zdA
i A
regarding eqs. (4.1-3) and (4.1-4) one finds:
2 4 Basis of design
.
 du 
 A 0 
N 
 i  dx  (4.1-7)
 E
M   d2w 
 i
I 
 dx2 
where
A area of cross section
I moment of inertia of cross section.
Fig. 4.1-2: Ideal-elastic constitutive law Fig. 4.-3: System –II. order theory
This equation may be written in an alternative from if one considers the last expression in
eq. (4.1-1)
 du 
A 0
q   dx 
 H   (4.1-8)
qV   d2 Id2w
dx2  dx2 
Eqs. (4.1-7) and (4.1-8) are the classical differential equations of the elastic beam and the
basis of all the well known formulas of structural beam analysis. Due to eqs. (4.1-3), (4.1-5)
and (4.1-6) the normal force N = f(u ) and the moment M = g(w") are decoupled. Therefore
0
in the case of Fig. 4.1-3 a we have the following moment equilibrium condition for the
undeformed bar with EI = const.
EIw" = -M (x)
q
I. Order Theory (4.1-9 a)
internal external
Here M characterizes the external moment at the undeformed bar. However if we take
q
the existing deformations exactly into account and write the equilibrium condition for the
deformed system we have according to Fig. 4.1-3 b.
EIw" = – (M +N·w)
q
II. Order Theory
internal external
fib Bulletin 52: Structural Concrete – Textbook on behaviour design and performance, vol. 2 3