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Note 3 Level 2
Technical Technical Guidance Note
TheStructuralEngineer March 2013
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Designing a concrete slab Introduction
The subject of this guide is the design of one way spanning concrete slabs to BS EN 1992-1-1 – Eurocode 2: Design of Concrete Structures – Part 1-1: General Rules for Buildings. The design of such elements is very simple to carry out and thus acts as a good introduction to the concept of reinforced concrete.
ICON LEGEND
Principles of W concrete slab design W Applied practice
W Worked example
W Further reading
W Web resources
Principles of concrete slab design Reinforced concrete is a composite material. The strengths of both the concrete and the steel reinforcement cast within it are what make it work as a structural element. Concrete is excellent in compression while steel’s strength lies in its ability to withstand tension. In very simple terms, if either component were removed then the structural performance of the remaining component would be significantly reduced. It is this basic tenet that must be remembered and enforced whenever designing a reinforced concrete element. Figure 3.5 of BS EN 1992-1-1 Eurocode 2: Design of Concrete Structures – Part 1-1: General Rules for Buildings defines the area of reinforcement As required in a concrete element that is to resist tension due to bending. From this figure it is possible to derive the following equation that can be used to calculate the area of reinforcement, which will resist tension:
M A s = 0.87f z yk Where: M is the applied design bending moment fyk is the tensile capacity of the steel reinforcement z is the lever arm distance between the tension and compression stresses within the element
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The lever arm can be calculated using the following quadratic equation:
z = d 70.5 + (0.25 - K/1.134)A Where: d is the effective depth of reinforcement K is defined as
M bd 2 fck fck is the characteristic cylinder strength of concrete at 28 days The value of z can be no higher than 0.95d.
Material properties and detailing requirements
Reinforcement bars come in a range of sizes, from 6mm to 50mm in diameter. For reinforced concrete slabs it is common to place 10, 12, 16 and 20mm diameter bars that are spaced between 125mm and 250mm apart. If the bars need to be larger than this, then it may be prudent to thicken the slab as otherwise the reinforcement in the slab becomes difficult to construct. The minimum area of steel in a slab should not be less than 0.0013bd and the maximum spacing between bars is explained in Clause 7.3.3 of BS EN 1992-1-1. It is dependent upon the stress in the reinforcement, with the trend being the higher the magnitude of stress, the closer the spacing between them.
The tensile capacity of reinforcement is taken to be 500 N/mm2 and in the Shear in concrete slabs Eurocodes the concrete strength is based A concrete slab is defined as an element on the cylinder crushing strength at the 28 whose width is more than 5 times its depth. days curing period. This can range from In all other instances the element is a beam 12 N/mm2 through to 90 N/mm2. In the UK, and therefore must be treated as such. Slabs concrete strength is classified in terms of typically have lower magnitudes of shear cube crushing strength, which is slightly applied to them than beams. It is for this greater than cylinder strength. It is for this reason that it is possible to have no shear reason that concrete strength classifications reinforcement within a one way spanning are labelled with both cylinder and cube slab which has a continuous line support via strength, e.g. C28/35, with the second a beam or a wall. number being the cube strength. These are described in Table 3.1 of BS EN 1992-1-1, EN The design shear resistance for concrete 206 Concrete - Specification, performance, slabs VRd,c is defined in Clause 6.2.1 of production and conformity and BS 8500 BS EN 1992-1-1. Concrete - Complementary British V Rd,c = 6C Rd,c k (100t 1 fck) 1/3 + k 1 v cp@ b w d Standard to BS EN 206-1.
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TheStructuralEngineer March 2013
Where: CRd,c is defined as
can be used instead, to determine the shear and bending moments in a slab. Provided the geometry of the slab spans are within 15% of each other and the dead and imposed loads are similar on all spans, then the coefficients described in Table 1 can be used. In addition, the imposed load must be less than or equal to the dead load in order for these coefficients to remain valid.
0.18 cc which for permanent conditions γc is 1.5 while in accidental conditions it is 1.2. k is defined as
200 d
1+
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Serviceability
with d being the effective depth of reinforcement in mm ρ1 is the reinforcement ratio for longitudinal reinforcement and is defined as
A sl bw d with Asl being the area of tension steel and bw the width of the slab, typically taken to be 1m k1 is the coefficient applied to compressive stress and is defined as 0.15 in the UK σcp is the compressive stress in the concrete due to direct loading or prestressing and is defined as
N Ed Ac where NEd is the axial force in the cross section of the slab and Ac is the cross sectional area of the concrete The value of the resistance to shear stress is compared against the applied shear stress, which is defined as
V Ed bd
As a composite material, it is quite difficult to ascertain the magnitude of deflection for reinforced concrete. It is for this reason that the concept of allowable span/depth ratios has been developed, which reduces the need to carry out complex calculations. Clause 7.4.2 describes how modification factors can be applied to this base limit of span/depth. These factors are based on the amount of stress the tension and compression reinforcement are subjected to due to loading. In the UK they are defined in the National Annex in Table NA.5. The expression used to determine the modification factors is dependent upon the ratio of tension reinforcement ρ compared to the reference reinforcement ratio ρ0
t0 l ; a d = K 11 + 1.5 fck t + 3.2 fuk
where VEd is the applied shear.
t0 l 1 ; d = K 11 + 1.5 fck t - t' + 12
Analysis of concrete slabs
Thankfully there are a set of coefficients that
Where: l/d is the span to depth ratio limit to which the slab must comply K is the factor that takes into account different structural forms, e.g. cantilever slab vs. continuous slab and is read from Table NA.5
Table 1: Bending moment and shear coefficients for slabs with uniform loading and spans Support type
Pinned
Continuous
Location
End support
End span
End support
End span
First interior support
Interior spans
Interior supports
Bending moment
0
0.086Fl
-0.04Fl
0.075Fl
-0.086Fl
0.063Fl
-0.063Fl
Shear
0.4F
0
0.46F
-
0.6F
-
0.5F
Note: ‘F’ is the total ultimate load and ‘l’ is the span of the slab
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span and supports, which is defined as
As bw d This ratio must be less than ρ0.
ρ' is the ratio of compression reinforcement at mid span and supports, which is defined as
As ' bw d ρ0 is the reference reinforcement ratio and is defined as
10 -3 fck There are two further factors that can be applied to the span/depth ratio. The first considers the effect of flange width for beams. If the ratio of flange width to beam width is greater than 3, then the span/depth ratio is multiplied by 0.8. This does not apply to slabs as they do not have a flange and are therefore not considered. The second factor concerns long spanning slabs that exceed 7m. In such instances the span/depth ratio should be multiplied by 7/leff, with leff being the effective span in m.
Corrosion and fire protection Expression 7.16.a in BS EN 1992-1-1 applies if ρ ≤ ρ0.
Expression 7.17.a in BS EN 1992-1-1 applies if ρ >ρ0.
While single span slabs are relatively straight forward to analyse, the same cannot be said for continuous slabs. They are, by their very nature, statically indeterminate and therefore more complex analysis techniques such as moment distribution are needed.
ρ is the ratio of tension reinforcement at mid
Before any design can be carried out, some 3 parameters concerning the 2 t0 k E exposure conditions of the 1 t concrete element must be established. This is controlled by establishing the amount of concrete cover that is t' E assumed to be in place with fck t 0 respect to the reinforcement within the element. Clause 4.4.1 of BS EN 1992-1-1 explains how the minimum concrete cover is determined. The nominal cover to reinforcement cnom is defined as:
c nom = c min + Dc dev Where: cmin is the minimum cover to the reinforcement that allows bond forces to be transmitted, prevents the reinforcement from corroding and provides adequate fire resistance Δcdev is an allowance for deviation from design due to tolerance and is taken to be 10mm The value of cmin is defined as the higher value of two dimensions. The first is the minimum cover due to bond cmin,b , which
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relates to how the reinforcement is interacting with the concrete. This can be found from Table 4.2 in BS EN 1992-1-1. The second cmin,dur is the minimum cover required in order to protect the reinforcement from moisture ingress and is affected by environmental conditions. The value of cmin,dur is based on the projected environmental conditions the concrete element is going to be exposed to, which is based on the structural classification of the element. The exposure class is defined in Table 4.1 of BS EN 1992-1-1 and this is cross referenced to the structural classification of concrete elements which is found in Table A.4 of BS 8500: 2006 Concrete Complementary British Standard to BS EN 206-1 – Part 1: Method of specifying
and guidance for the specifier. This only applies to the UK where it is recommended within the National Annex to BS EN 1992-1-1, that this table is used. Fire protection is dependent upon the overall thickness of the element as well as the cover of concrete to the reinforcement. The cover in terms of fire protection is defined as the distance from the centre of the group of bars (or bar) to the outer surface of the concrete element. Table 5.8 of BS EN 1992-1-2 Eurocode 2: Design of concrete structures – Part 1-2: General rules – Structural fire design provides data which can be used to determine the thickness and cover requirement for concrete elements. This is plotted against the overall fire rating of the structure that is being designed.
Worked example A one way, simply supported single span roof slab to a one storey building spans 6m. Check to see if a 225mm thick concrete slab made from C30/37 concrete with H12 bars at 200mm c/s the ultimate bending / can support pp p g moment of 47 kNm/m / and a fire rating a n o of 1 h hour. hour u Th The c concrete n t iis n nott directly e l e exposed p s d tto wa water. water r
Eurocode 0.
Applied practice BS EN 1992-1-1 Eurocode 2: Design of Concrete Structures – Part 1-1: General Rules for Buildings BS EN 1992-1-1 UK National Annex to Eurocode 2: Design of Concrete Structures – Part 1-1: General Rules for Buildings BS EN 1992-1-2 Eurocode 2: Design of concrete structures – Part 1-2: General rules – Structural Fire Design BS 8500: 2006 - Concrete Complementary British Standard to BS EN 206-1 – Part 1: Method of specifying and guidance for the specifier
Glossary and further reading Cover – Concrete cover to reinforcement. One way span – A slab that sits between a pair of perpendicular supports. Further Reading The Institution of Structural Engineers (2006) Manual for the design of concrete building structures to Eurocode 2 London: The Institution of Structural Engineers The Concrete Centre (2009) Worked Examples to Eurocode 2: Volume 1 [Online] Available at: www.concretecentre.com/ pdf/Worked_Example_Extract_Slabs.pdf (Accessed: February 2013) Mosley W., Bungey J. and Hulse R. (2007) Reinforced Concrete Design to Eurocode 2 (6th ed.) Basingstoke, UK: Palgrave Macmillan Reynolds C.E., Steedman J.C. and Threlfall A.J. (2007) Reynolds’s Reinforced Concrete Designer’s Handbook (11th ed.) Oxford, UK: Taylor & Francis The Institution of Structural Engineers (2012) Technical Guidance Notes 1-5 and 17 (Level 1) The Structural Engineer 90 (1-3, 10) Eurocode 0.
Web resources The Concrete Centre: www.concretecentre.com/ The Institution of Structural Engineers library: www.istructe.org/resources-centre/library
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