F. K. Kong MA, MSc, PhD, CEng, FICE, FIStructE, R. H. Evans CBE, DSc, D ès Sc, DTech, PhD, CEng, FICE, FIMechE, FIStructE (auth.)-Reinforced and Prestressed Concrete-Springer US (1987)

188 Reinforced concrete beams-the serviceability limit states
easel
Directly over a bar, the distance acr is equal to the concrete cover Cmin, and
eqn (5.6-1) reduces to
width over a bar = 3cminEm (5.6-4)
Case2
When the distance acr is large, eqn (5.6-1) approaches the following limit:
width away from a bar = l.5(h - x)Em (5.6-5)
For a given member, Em is a maximum at the tension face; if (h - x) is
sufficiently small for the crack width at the tension face not to exceed the
permissible limit of 0.3 mm, it will not exceed that limit anywhere. This
explains why excessive crack widths rarely occur in slabs under service
loading, provided the thickness does not exceed about 200 mm.
Example 5.6-l
Referring to the midspan section of the beam in Example 5.2-1 and Fig.
5.2-5, calculate the design surface crack width:
(a) directly under a bar on the tension face;
(b) at a bottom corner of the beam;
(c) at a point on the tension face midway between two bars; and
(d) at a point on a side face 250 mm below the neutral axis.
SOLUTION
(a)
(b)
Directly under a bar on tension face. Equation (5.6-4) applies. From
Fig. 5.6-1(a),
acr = Cmin = 40 mm
From Example 5.2-1(b),
x = 303.6 mm
and E1 (designated Eh then) = 0.00176.
Substituting into eqn (5.6-2),
( 450)(750-303.6)(750-303.6)
Em = 0·00176 - 3{200){1cP){3769){690-303.6)
= 0.001657
Using eqn (5.6-4),
crack width = {3){ 40){0.001657)
= 0.20 mm
Bottom corner. From Fig. 5.6-1{b),
ij = (acr + 20) = ~(60Z + 60 2 )
Therefore
acr = 64.85 mm