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Transcript of L7 Flat Slabs
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HHOOWW TTOO DDEESSIIGGNN
CCOONNCCRREETTEESSTTRRUUCCTTUURREESS
Flat Slabs
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Instructions for the Members of BIBM, CEMBUREAU, EFCA and ERMCO:
It is the responsibility of the Members (national associations) of BIBM, CEMBUREAU, EFCA and ERMCOto translate and/or adapt this publication within their national framework, to publish it under their ownname and to disseminate it to their contacts at national level.
Copyright: Name of National MemberAcknowledgements to the European Concrete Platform
EMBARGO: 31 March 2007
The Members of BIBM, CEMBUREAU EFCA and ERMCO are not allowed to publish this brochure before31 March 2007.
Copyright: European Concrete Platform (when legal body is established), March 2007.
All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in
any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior written
permission of the European Concrete Platform: BIBM (International Bureau for Precast Concrete);
CEMBUREAU, The European Cement Association; EFCA (European Federation of Concrete Admixtures
Associations); ERMCO (European Ready Mixed Concrete Organisation).
Published by the European Concrete PlatformEditor: Jean-Pierre Jacobs8 rue Volta1050 Brussels
Layout & Printing byThe European Concrete Platform
All information in this document is deemed to be accurate by the European Concrete Platform at the time ofgoing into press. It is given in good faith.
Information on European Concrete Platform document does not create any liability forBIBM, CEMBUREAU,EFCA and ERMCO. While the goal is to keep this information timely and accurate, the European ConcretePlatform cannot guarantee either. If errors are brought to its attention, they will be corrected.
The opinions reflected in this document are those of the authors and BIBM, CEMBUREAU, EFCA and ERMCOcannot be held liable for any view expressed therein.
All advice or information from the European Concrete Platform is intended for those who will evaluate thesignificance and limitations of its contents and take responsibility for its use and application. No liability (includingfor negligence) for any loss resulting from such advice or information is accepted.
Readers should note that all European Concrete Platform publications are subject to revision from time to timeand therefore ensure that they are in possession of the latest version.
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How to design concrete structures using Eurocode 2
7. Flat slabs
IntroductionThis should be redrafted as appropriatein a country
Designing to Eurocode 2This guide covers the analysis and design of concrete flat slabs to
Eurocode 21. Eurocode 2 does not contain the derived formulae or
specific guidance on determining moments and shear forces. This has
arisen because it has been European practice to give principles in the
codes and for the detailed application to be presented in other sources
such as textbooks.
The first guide in this series, How to design concrete structures usingEurocode 2: Introduction to Eurocodes
2, provides an overview of
Eurocodes including terminology.
Where NDPs occur in the text in this publication, recommended valuesin EN 1992 are used and highlighted in yellow. The UK values havebeen used for NDPs embedded in figures and charts and the relevantNDPs are scheduled separately to assist other users in adapting thefigures and charts.(derivations can be found at www.eurocode2.info). Alist of symbols related to flat slab design is given at the end of this guide.
Analysis
The following methods may be used:
Equivalent frame method
Finite element analysis
Yield line analysis
Grillage analogy
The Eurocode gives further advice on the equivalent frame method in
Annex I. Once the bending moments and shear forces have been
determined, the following guidance can be used for the design of flat
slabs.
Design procedure
A procedure for carrying out the detailed design of flat slabs is shown in
Table 1. This assumes that the slab thickness has previously been
determined during conceptual design. More detailed advice on
determining design life, loading, material properties, methods of
analysis, minimum concrete cover for durability and bond, and control of
crack widths can be found in another guide in this series, How to designconcrete structures using Eurocode 2: Getting started
3.
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Fire resistance
Eurocode 2, Part 12: Structural fire design4, gives a
choice of advanced, simplified or tabular methods for
determining the fire resistance. Using tables is the
fastest method for determining the minimum
dimensions and cover for flat slabs. There are,
however, some restrictions and if these apply further
guidance can be obtained from specialist literature.
Rather than giving a minimum cover, the tabular
method is based on nominal axis distance, a. This is
the distance from the centre of the reinforcing bar to
the surface of the member.
It is a nominal (not minimum) dimension, so the
designer should ensure that a cnom + link + bar/2
The requirements for flat slabs are given in Table 2
Flexure
The design procedure for flexural design is given in
Figure 1; this includes derived formulae based on thesimplified rectangular stress block from Eurocode 2.
Where appropriate Table 3 may be used to determine
bending moments for flat slabs.
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Whichever method of analysis is used, Cl. 9.4.1 requires
the designer to concentrate the reinforcement over the
columns. Annex I of the Eurocode gives
recommendations for the equivalent frame method on
how to apportion the total bending moment across a bay
width into column and middle strips to comply with Cl.
9.4.1. Designers using grillage, finite element or yield
line methods may also choose to follow the advice in
Annex I to meet this requirement.
Eurocode 2 offers various methods for determining the
stress-strain relationship of concrete. For simplicity the
method presented here is the simplified rectangular
stress block (see Figure 2).
The Eurocode gives recommendations for the design of
concrete up to class C90/105. However, for concrete
strength greater than class C50/60, the stress block is
modified. It is important to note that concrete strength is
based on the cylinder strength and not the cube strength
(i.e. for class C28/35 the cylinder strength is 28 MPa,
whereas the cube strength is 35 MPa).
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Deflection
Eurocode 2 has two alternative methods of designing for
deflection; either by limiting span-to-depth ratio or by
assessing the theoretical deflection using the
Expressions given in the Eurocode. The latter is dealt
with in detail in another guide in this series, How todesign concrete structures using Eurocode 2: Deflectioncalculations
5.
The span-to-depth ratios should ensure that deflection is
limited to span/250 and this is the procedure presented
in Figure 3. The span-to-depth ratios are
appropriate where the structure remains propped during
construction or until the concrete attains sufficient strength
to support the construction loads. It can generally be
assumed that early striking of formwork will not significantly
affect the deflection after installing the cladding and/or
partitions6.
Punching shear
The design value of the punching shear force, VEd, willusually be the support reaction at the ultimate limit state.
Standard factors for edge and corner columns that allow
for moment transfer () are greater in Eurocode 2.
However, can be calculated directly from Expressions
(6.38) to (6.46) of the Eurocode to give more efficient
designs.
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In Eurocode 2 the maximum value of shear at the
column face depends on the concrete strength
used.
The control perimeters for rectangular columns in
Eurocode 2 have rounded corners.
Where shear reinforcement is required the
procedure in Eurocode 2 is simple; the point at
which no shear reinforcement is required can be
calculated directly and then used to determine the
extent of the area over which shear reinforcement isrequired.
It is assumed that the reinforcement will be in a
radial arrangement. However, the reinforcement
can be laid on a grid provided the spacing rules are
followed.
The procedure for determining the punching shear
requirements is shown in Figure 6.
As an alternative to using shear links, proprietary shear studrails may be used. Eurocode 2 (Figure 6.22) allows them tobe laid out in a radial or cruciform pattern and gives spacingrequirements for both. Other techniques are available forincreasing punching shear resistance and these arecovered in a best practice guide.
Figure 6Procedure for determining punching shear capacity
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Rules for spacing and quantity ofreinforcement
Minimum area of reinforcement
The minimum area of longitudinal reinforcement in the main
direction is As,min = 0.26 fctmbtd/fyk but not less than0.0013bd(see Table 6).
The minimum area of a link leg for vertical punching shear
reinforcement is
1.5Asw,min /(sr.st) 0.08(fck)/fyk.
which can be rearranged as
Asw,min (sr.st)/Fwhere
sr = the spacing of the links in the radial direction
st = the spacing of the links in the tangential directionFcan be obtained from Table 10
Maximum area of reinforcement
Outside lap locations, the maximum area of tension or
compression reinforcement should not exceed
As,max = 0.4 Ac
Minimum spacing of reinforcementThe minimum spacing of bars should be the greater of:
1 x Bar diameter
Aggregate size plus 5 mm
20 mm
Maximum spacing of main reinforcementFor slabs less than 200 mm thick the following maximum
spacing rules apply:
For the principal reinforcement: 3h but not more than
400 mm
For the secondary reinforcement: 3.5h but not more
than 450 mm
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The exception is in areas with concentrated loads or areas of
maximum moment where the following applies:
For the principal reinforcement: 2hbut not more than250 mm
For the secondary reinforcement: 3hbut not more than400 mm, where his the depth of the slab.
For slabs 200 mm thick or greater reference should be made
to Section 7.3.3 of the Eurocode orHow to design concrete
structures using Eurocode 2: Getting started
3
.
Spacing of punching shear reinforcementWhere punching shear reinforcement is required the
following rules should be observed.
It should be provided between the face of the column
and kdinside the outer perimeter where shear
reinforcement is no longer required. kis 1.5, unless theperimeter at which reinforcement is no longer required
is less than 3dfrom the face of the column. In this casethe reinforcement should be placed in the zone 0.3dto1.5dfrom the face of the column.
There should be at least two perimeters of shear links.
The radial spacing of the links should not exceed 0.75d
(see Figure 9). The tangential spacing of the links should not exceed
1.5dwithin 2dof the column face. The tangential spacing of the links should not exceed
2dfor any other perimeter. The distance between the face of the column and the
nearest shear reinforcement should be less than 0.5d.
Note
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References1 EN 199211, Eurocode 2: Design of concrete structures General rules and rules for buildings.2 NARAYANAN, R S & BROOKER, O. How to design concrete structures using Eurocode 2: Introduction to
Eurocodes. The Concrete Centre, 2005.3 BROOKER, O. How to design concrete structures using Eurocode 2: Getting started. The Concrete Centre, 2005.4 EN 199212, Eurocode 2: Design of concrete structures. General rules structural fire design.5 WEBSTER, R & BROOKER, O. How to design concrete structures using Eurocode 2: Deflection calculations. The
Concrete Centre, 2006.
6 PALLETT, P. Guide to flat slab formwork and falsework. Construct, 2003.
AcknowledgementsThis guide was originally published by BCA and The Concrete Centre in the UK. The authors of the original publication
were R MossBSc, PhD, DIC, CEng, MICE, MIStructE and O BrookerBEng, CEng, MICE, MIStructE
Europeanised versions of Concise EC2 and How To LeafletsConvention used in the text
1. Nationally determined parameters that occur in the text have been highlighted yellow
2. Text is highlighted in pink indicates that some action is required on the part of thecountry adapting the documents for its use