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How to design concrete structures using Eurocode 2
3. SlabsIntroductionThis to be redrafted as appropriate in
each country.
This publication is part of the series ofguides entitled How to design concretestructures using Eurocode 2.Their aimis to make the transition to Eurocode 2:
Design of concrete structuresas easyas possible by drawing together in one
place key information and commentary
required for the design of typical
concrete elements.
Designing to Eurocode 2
This guide covers the analysis and design of slabs to Eurocode 21.
Eurocode 2 does not contain the derived formulae or specific guidanceon 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, highlighted the key differences
between Eurocode 2 and the national codes, including terminology. A
separate guide in this series covers the design of flat slabs3.
Where NDPs occur in the text in this publication, recommended values
in 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 the
figures and charts. (Derivations can be found at www.eurocode2.info.)A list of symbols related to slab design is given at the end of this guide.
Design procedure
A procedure for carrying out the detailed design of 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, actions, material properties, methods of
analysis, minimum concrete cover for durability and control of crack
widths can be found in the accompanying guide How to design concretestructures using Eurocode 2: Getting started
4.
Fire resistance
Eurocode 2, Part 12: Structural fire design5, 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 slabs. There are, however, some
restrictions which should be adhered to. Further guidance on the
advanced and simplified methods 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 themain reinforcing bar to the surface of the member. It is a nominal
(not minimum) dimension, so the designer should ensure thata cnom + link + bar /2. The requirements for various types of slab aregiven in Table 2.
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Figure 1Procedure for determining flexual reinforcement
Flexure
The design procedure for flexural design is given in
Figure 1; this includes derived formulae based on the
simplified rectangular stress block from Eurocode 2.
Where appropriate, Table 3 may be used todetermine
bending moments and shear forces for slabs. Further
information for the design of two-way, ribbed or waffle
slabs is given in the appropriate sections on pages 5
and 6.
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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
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).
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 to design concrete structuresusing Eurocode 2: Deflection
6.
The span-to-depth ratios should ensure that deflection islimited to span/250 and this is the procedure presented in
Figure 3.
Note
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Design for shear
It is not usual for a slab to contain shear reinforcement,
therefore it is only necessary to ensure that the concrete
shear stress capacity without shear reinforcement
(vRd,c see Table 7 is more than applied shear stress(vEd = VEd/(bd)). Where shear reinforcement is required,e.g. for ribs in a ribbed slab, refer to How to designconcrete structures using Eurocode 2: Beams
7.
Two-way slabs
There is no specific guidance given in Eurocode 2 on how
to determine the bending moments for a two-way slab.
The assessment of the bending moment can be carried
out using any suitable method from Section 5 of the Code.
However, co-efficients may be obtained from Table 8 ( to
determine bending moments per unit width (Msx and Msy)where:
Msx = sxwlx2
Msy = sywlx2
Where sx and sy are coefficients, lx is the shorter span
and w(load per unit area) is the STR ultimate limit statecombination. For more information on combinations refer
to How to design concrete structures using Eurocode 2:Introduction to Eurocodes
2.
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Ribbed or waffle slabs
Current practices for determining forces in ribbed and waffle
slabs may also be used for designs to Eurocode 2. Where a
waffle slab is treated as a two-way slab refer to previous
section, but note that their torsional stiffness is significantly
less than for a two-way slab and the bending moment
co-efficients may not be applicable. Where it is treated as a
flat slab reference may be made to How to design concrete
structures to Eurocode 2: Flat slabs3
The position of the neutral axis in the rib should be
determined, and then the area of reinforcement can be
calculated depending on whether it lies in the flange or web
(see flow chart in Figure 6. Where a slab is formed with
permanent blocks or a with a topping thickness less than 50
mm and one-tenth of the clear distance between ribs it is
recommended that a longitudinal shear check is carried out
to determine whether additional transverse reinforcement
isrequired (see EN 199211,Cl 6.2.4).
Figure 6Procedure for determining flexural capacity of flanged ribs
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Rules for spacing andquantity ofreinforcement
Minimum area of principal reinforcementThe minimum area of principal reinforcement in the main
direction is As,min = 0.26 fctmbtd/fyk but not less than0.0013btd, where bt is the mean width of the tension zone(see Table 6). For a T-beam with the flange in compression,
only the width of the web is taken into accountin calculatingthe value ofbt.
Minimum area of secondary reinforcementThe minimum area of secondary transverse reinforcement is
20% As,min. In areas near supports, transverse reinforcementis not necessary where there is no transverse bending
moment.
Maximum area of reinforcementOutside lap locations, the maximum area of tension or
compression reinforcement should not exceed
As,max = 0.04 Ac
Minimum spacing of reinforcementThe minimum clear distance between bars should be the
greater of:
1.0 xBar diameter
Aggregate size plus 5 mm
20 mm
Maximum spacing of reinforcementFor slabs less than 200 mm thick the following maximum
spacing rules apply:
For the principal reinforcement: 3hbut not more than400 mmn
For the secondary reinforcement: 3.5hbut not more than
450 mm
The exception is in areas with concentrated loads or areas
of maximum moment where the following applies: For the principal reinforcement: 2hbut not more than
250 mm
For the secondary reinforcement: 3hbut not more than400 mm
Where his the depth of the slab.
For slabs 200 mm thick or greater crack control might limit the
spacing and reference should also be made to section 7.3.3
of the Code orHow to design concrete structures using
Eurocode 2: Getting started5
.
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References1 Eurocode 2: Design of concrete structures Part 11 General rules and rules for buildings. EN 199211:2004.
2 NARAYANAN, R S & BROOKER, O. How to design concrete structures using Eurocode 2: Introduction to Eurocodes.
The Concrete Centre, 2005.
3 MOSS, R M & BROOKER, O. How to design concrete structures using Eurocode 2: Flat slabs. The Concrete Centre, 2006.
4 BROOKER, O. How to design concrete structures using Eurocode 2: Getting started. The Concrete Centre, 2005.
5 EN 199212, Eurocode 2: Design of concrete structures. General rules structural fire design, BSI 2004.
6 WEBSTER, R & BROOKER, O. How to design concrete structures using Eurocode 2: Deflection calculations. The Concrete
Centre, 2006.
7 MOSS, R M & BROOKER, O. How to design concrete structures using Eurocode 2: Beams. The Concrete Centre,2006.
Acknowledgements
This guide was originally published by BCA and The Concrete Centre in the UK. The authors of the original publication wereR M Moss BSc, PhD, Ceng, MICE, MIStructE and O Brooker BEng, 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