Design of Structural Elements
120
5.2.8 Steel Reinforcement Modulus of Elasticity: Es (Clause 2.4.2.3)
The modulus of elasticity of reinforcement is equal to tanθ, where θ is the angle of the
linear section of the stress-strain curve given in Figure 2.2 of the code. This should be
taken as 200 kN/mm2 as indicated in Figure 5.12.
5.2.9 Material Partial Safety Factors: γm (Clause 2.4.4.1)
As indicated in Section 2.4 when using limit state design:
Design strength =
Characteristic strength
γm
The appropriate values of γm for concrete and reinforcement are given in Table 2.2 of
Clause 2.4.4.1 as:
γm =
=
=
=
≥
1.5
1.25
1.4
1.05
1.5
for concrete in flexure or axial load,
for concrete shear strength without reinforcement,
for bond strength between the reinforcement and the concrete,
for reinforcement,
for other conditions e.g. bearing stresses.
5.2.10 Durability (Clauses 2.2.4 and 3.1.5)
The integrity of reinforced concrete depends on its ability to prevent corrosion of the
reinforcement when exposed to a wide range of environmental conditions, e.g. ranging
from ‘mild exposure’ such as concrete surfaces protected against weather or aggressive
conditions to ‘most severe’ or ‘abrasive’ conditions in which concrete surfaces may be
frequently exposed to sea water spray, de-icing salts or the abrasive actions of machinery.
The classification of exposure conditions in terms of ‘moderate’, ‘severe’, ‘very
severe’, ‘most severe’ and ‘abrasive’ is defined in Table 3.2 of the code.
In addition to protection against corrosion of the steel (Table 3.3), fire resistance
requirements (Table 3.4) are also necessary to allow sufficient time to evacuate a building
and prevent premature failure, spalling of the concrete must be avoided and adequate bond
forces must develop between the reinforcement and the concrete.
The essential elements of design which ensure adequate durability are the structural
form/detailing and the amount of concrete cover provided to protect the steel, as illustrated
in Figure 5.13.
cover
cover
cover
cover
Figure 5.13
Design of Reinforced Concrete Elements
121
Concrete cover is defined as the thickness of concrete between the outer surface of the
steel reinforcement and the nearest concrete surface. The actual concrete cover provided
varies due to a number of factors such as:
♦ construction tolerances inherent in building the formwork (i.e. the mould into
which the concrete is cast),
♦ variations in dimensions of the reinforcement resulting from the cutting and
bending of the steel, and
♦ errors occurring during the fixing of the steel in the formwork.
The limiting values of cover given in Tables 3.3 and 3.4 of the code which ensure
adequate provision to satisfy durability and fire protection are specified in terms of
‘nominal’ cover to all reinforcement including the links. As indicated in Clause 3.3.1.1,
the nominal cover is: ‘… the dimension used in design and indicated on the drawings. The
actual cover to all reinforcement should never be less than the nominal cover minus
5 mm …’
There a number of criteria to be considered when determining the nominal cover. They
are:
♦ Bar size (Clause 3.3.1.2)
Single bars: nominal cover ≥ main bar diameter d1
diameter d1
Figure 5.14(a)
nominal cover
nominal cover
Paired bars:
nominal cover ≥
2 d1
where d1 is the main bar diameter
diameter d1
Figure 5.14(b)
nominal cover
nominal cover
Bundled bars: nominal cover ≥ 2
Aequivalent
π
where Aequivalent is the cross-sectional area equal to the sum of the
cross-sectional areas of the bars in the bundle

 2 
 e.g. In Figure 5.14(c) Aequivalent = 4 ×  πd1  


 4 

diameter d1
-
Figure 5.14(c)
nominal cover
nominal cover
122
Design of Structural Elements
♦ Nominal maximum aggregate size (Clause 3.3.1.3)
Nominal cover
≥ nominal maximum size of aggregate
minimum thickness of concrete section
i.e. normally ≤
4
In most cases, 20 mm aggregate is suitable.
♦ Uneven surfaces (Clause 3.3.1.4)
When concrete is cast on uneven surfaces (e.g. earth or blinding, which is finely
crushed aggregate rolled on the top of compacted fill such as hardcore) additional
cover to that indicated in Table 3.3 should be provided as shown in Figure 5.15.
nominal cover > 75 mm
uneven earth surface
Concrete cast directly on the earth – nominal cover from average soil level
nominal cover > 40 mm
blinding layer
hardcore
Concrete cast on an adequate blinding layer (e.g. 50 mm thick)
Figure 5.15
♦ Ends of straight bars (Clause 3.3.2)
Normally 40 mm cover is provided at the ends of straight bars, as shown in
Figure 5.16, however as indicated in this clause where the end of a floor or roof
unit is not exposed to the weather or to condensation, cover is not mandatory.
nominal cover
Figure 5.16
In Clause 7.3 of the code recommendations are given to ensure that the reinforcement is
properly placed and the required cover obtained. This is achieved during construction by
inserting spacer blocks and chairs in the formwork, on the reinforcement as indicated in
Design of Reinforced Concrete Elements
123
Figures 5.17 and 5.18. The spacers must be designed such that they are durable and will
not lead to corrosion of the reinforcement or to spalling of the concrete. The use of spacer
blocks constructed on site from concrete is not permitted.
Concrete spacer
Plastic spacer
Spacer for vertical application
Figure 5.17
Single and continuous high wire chairs for top steel – particularly in cantilevers
Figure 5.18
5.2.10.1 Minimum Dimensions (Clause 3.3.6 and Figure 3.2)
In addition to nominal cover requirements, the code also specifies minimum dimensions
(i.e. beam widths, rib widths, floor and wall thicknesses, and column widths) for some
structural elements to provide adequate fire resistance. The dimensions are given to ensure
minimum periods of fire resistance ranging from 0.5 hours to 4 hours and relate
specifically to the covers given in Table 3.4.
5.2.11 Example 5.1: Nominal Cover 1
A rectangular reinforced concrete beam inside a building is simply supported and is
required to support precast concrete units as shown in Figure 5.19. Using the data given,
determine:
(i)
(ii)
the nominal cover required to the underside of the beam, and
the minimum width of beam required.
Data:
Exposure condition
Characteristic strength of concrete
Nominal maximum aggregate size
Diameter of main tension steel
Diameter of shear links
Minimum required fire resistance
(fcu)
(hagg)
mild
40 N/mm2
20 mm
25 mm
8 mm
1.5 hours
Design of Structural Elements
124
main steel
b
Figure 5.19
Solution:
(i)
Clause 3.3.1.2
Nominal cover ≥ (main bar diameter − link diameter)
≥ (25 − 8) = 17 mm
Clause 3.3.1.3
Nominal cover ≥ nominal maximum aggregate size > 20 mm
Clause 3.3.3
Exposure condition is mild
Grade of concrete is C40
Table 3.3
Nominal cover ≥ 20 mm*
Clause 3.3.6
Minimum fire resistance = 1.5 hr
The beam is simply supported
Table 3.4
Nominal cover ≥ 20 mm*
The required nominal cover = 20 mm
*Note: Under these conditions this value can be reduced to 15 mm when the maximum
aggregate size does not exceed 15 mm.
(ii)
Clause 3.3.6
Figure 3.2
The minimum beam width b to satisfy the required 1.5 hours.
fire resistance = 200 mm
5.2.12 Example 5.2: Nominal Cover 2
A continuous, ribbed floor slab covering a car parking area is exposed on the underside
and protected on the topside as shown in Figure 5.20. Using the data given determine:
(i)
(ii)
(iii)
the nominal cover required to the underside of the rib,
the nominal cover required to the topside of the floor, and
the minimum floor thickness and width of rib required.
Data:
Characteristic strength of concrete
Nominal maximum aggregate size
Diameter of main tension steel
Diameter of shear links
Minimum required fire resistance
35 N/mm2
20 mm
32 mm
10 mm
2.0 hours
(fcu)
(hagg)
h
rib width b
Figure 5.20
Design of Reinforced Concrete Elements
125
Solution:
(i)
Clause 3.3.1.2
Nominal cover ≥ (main bar diameter − link diameter)
≥ (32 − 10) = 22 mm
Clause 3.3.1.3
Nominal cover ≥ nominal maximum aggregate size
≥ 20 mm
Table 3.2
Exposure condition is moderate
Grade of concrete is C35
Table 3.3
Nominal cover ≥ 35 mm
Clause 3.3.6
Minimum fire resistance = 2.0 h
The rib is continuous
Table 3.4
Nominal cover ≥ 35 mm*
The required nominal cover to the underside of the ribs = 35 mm
(ii)
The topside of the slab is protected and hence the exposure condition is mild:
Table 3.3
Nominal cover ≥ 20 mm
Clause 3.3.6
Minimum fire resistance = 2.0 h
The floor is continuous
Table 3.4
Nominal cover ≥ 25 mm
The required nominal cover to the topside of the floor
= 25 mm
(iii)
Clause 3.3.6
Figure 3.2
The minimum rib width b to satisfy the required 2.0 hours
fire resistance = 125 mm
This can be achieved if the bars are placed vertically, as shown.
The minimum width b required to accommodate the bars and the
cover = (35 + 10 +32 + 10 + 35) = 122 mm < 125 mm
If the bars are placed horizontally, assuming a gap of 25 mm
(i.e. [hagg + 5 mm], see Clause 3.12.11.1), the minimum width
required = [2 × (35 + 10 + 32) + 25] ≈ 180 mm > 125 mm
Clause 3.3.6
Figure 3.2
The minimum floor thickness h to satisfy the required
2.0 hours fire resistance = 125 mm
*Note: In the case of the cover exceeding 40 mm for dense or 50 mm for lightweight
aggregate concrete there is a danger of spalling. If the ribbed slab were simply
supported then Note 2 in Table 3.4 indicates that additional measures would be
necessary to reduce the risks of spalling, as indicated in section 4 of
BS 8110:Part 2:1985.
Possible measures include an applied finish by hand or spray of plaster, the
provision of a false ceiling as a fire barrier, the use of lightweight aggregates, the
use of sacrificial tensile steel, or the provision of supplementary reinforcement in
the form of welded steel fabric placed within the cover at 20 mm from the
concrete face.
Design of Structural Elements
126
5.2.13 Example 5.3: Nominal Cover 3
A ground floor slab in a warehouse building is constructed on a blinded, compacted layer
of hardcore as shown in Figure 5.21. Using the data given, determine the nominal cover
required to the underside of the slab.
Data:
Characteristic strength of concrete (fcu)
Nominal maximum aggregate size (hagg)
Diameter of main tension steel
35 N/mm2
20 mm
20 mm
ground floor slab
blinding
cover
hardcore
Figure 5.21
Solution:
(i)
Clause 3.3.1.2
Nominal cover ≥ main bar diameter
≥ 20 mm
Clause 3.3.1.3
Nominal cover ≥ nominal maximum aggregate size
≥ 20 mm
Clause 3.3.3
Exposure condition is mild
Grade of concrete is C35
Table 3.3
Nominal cover ≥ 20 mm
Clause 3.3.1.4
Since this slab is cast against an adequate blinding
Table 3.4
Nominal cover ≥ 40 mm
The required nominal cover = 40 mm
5.3 Flexural Strength of Sections
The flexural strength (i.e. the ultimate moment of resistance of a cross-section) is
determined assuming the following conditions as given in Clause 3.4.4.1, BS8110:Part 1.
♦ Plane sections remain plane, i.e.
surface A
surface A
before deformation
after deformation
The surface of any cross-section does not distort out-of-plane during deformation.
Figure 5.22