REINFORCED CONCRETE DESIGN
142
SERVICEABILITY, DURABILITY AND STABILITY REQUIREMENTS 143
tensile stress caused by bond between the steel and concrete exceeds the concrete tensile strength, Ihll.t is
concrete strain) x crack spacing with the maximum width corresponding to the maximum spacing of small
fbSr.us;;' [lAc
Wmax = (E,sh
where
where fb '" average bond stress s '" development length along a bar For a round bar 411'~
_
A-
~
,
~ II A '
Est. = shrinkage strain
In practice, variations in restraints cause large variations withln members and between otherwise similar members, with 'full' restraint seldom occurring. The behaviour depends considerably on this and temperatures at the time of casting. Guidance concerning possible 'restraint factors' is given in Part 2 of as 8110.
1·leoee. since 1:.11 '"
(6.14)
0I:c = coeffi cient of thermal expansion of concrete - taken as 0.5 x the value for mature concrete, to aUow for creep effects
_ 4
1J'4)2 -
t eull) .I'mu
T = fall in tem perature from hydration peak
E u s '" sum of perimete rs of reinforcement. Us
+ To:( -
for similar bars
,
then
Example 6.5 CoJculo/ion o/Shrinkoge and Thermal Cmck Widths ~
~U
,
_ 4rA c -<I>-
flIP 4rtb
The maximum crack spacing is twice this value immediately prior to the formation of a new crack , when the developmen t length on both sides is Smin. that is S
'"
mu
f,ifJ 2rfb
\
A fully restrained :>ection of reinforced concrete wall is 150 mm thick, and drying! shrinkage strain of 50 microstrain (esh) is anticipated together with a temperature 1\ drop (n of 20°C after setting. Determ ine the minimum horizontal reinforcement to control cracking and estimate maximum crack widths and average spacing for a suitable reinforcement arrangement. Three-day ultimate tensile strength of concrete (It) = ultimate average bond stress (Ib) = 1.5 N/ mm1
-
and thus
s ;;.
,I,!
(6.13)'
Crack spacing and hence width, therefore. is governed both by the reinforcement size and quantity for ratios above the critical value, which should be taken as a minimum requirement for controlled cracking. Empirical values for general use are given in section 6.1.
Modulus of elasticity of concrete (Ee) = 10 kN/ mm 2 Coefficient of thermal expansion for mature concrete (etc) = 12 microstrainrC Characteristic yield strength of reinforcement (ly) = 460 N/ mm 2 Modulus of elasticity of reinforcement (E, ) = 200 kN/mm 2 Critical steel ratio 'cUt =
II = ~ '" 0 .33 per cent from equation 6.12 I, 460
= 0 .33
6.5.1 Crack Width CoJculo/ion The expressions for crack spacing assume that the total thermal and shrinkage strains are sufficien t to cause cracking, although in practice it is found that pre· dicted cracks may not always occur. It is possible to estimate however the maxi· mum crack width likely to occur by considering total concrete contraction in conjunction with the maximum likely crack spacing. For steel ratios greater than the critical value , and when the total contraction exceeds the ultimate tensile strain fo r the concre te (eult), the tensile stress in the concrete increases from zero at a crack to a maximum value at mid·distance between cracks. Hence the mean tensile strain in the uncracked length is euJ .l2 when a new crack Is just about to form . The crack width Is thus given by crick width · (total unit movement -
x 150 x 1000
100
=495 mml/m This could be convenien tl y provided as 10 mm bars at 300 mm centres in each face of the member (524 mml/rn). For this reinforcement, the ll1u,umum crack spacing is given by equation 6.13 as smax
=
{,<J) 2 ~ Ib
A(
• __I::;,S,:;':-:cl0,;-;2)( S24 ~~
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