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Note 3 Level 2
Technical
Technical Guidance Note
TheStructuralEngineer
March 2013
29
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
TSE15_29-31.indd 29
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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Note 3 Level 2
30
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+
Technical
Technical Guidance Note
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
TSE15_29-31.indd 30
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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31
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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