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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

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