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)

Calculation of crack widths (BS 8110) 187
5.6 Calculation of crack widths (BS 8110: Part 2)
(Note: In day-to-day design, crack control is exercised by the straightforward
application of simple detailing rules-see Section 5.4)
Much research has been done on cracks in concrete [17-20]. As the load
on a beam increases, the number of cracks, and hence the crack spacing,
rapidly reach a nearly constant value which does not change appreciably
with further increase in the load. For a beam in such a condition, Beeby
and his colleagues [17) have concluded that, directly over a reinforcement
bar, the crack width increases with the concrete cover and with the average
strain at the level at which cracking is being considered; with increasing
distance from the bar, the crack width increases with the height to which
the crack penetrates, i.e. the width increases with (h - x) where h is the
overall beam depth and x the neutral axis depth. Their research forms the
basis of the following crack width formula in BS 8110:
design surface crack width ~ [""•'m l
1 + 2 acr - Cmin
h-x
(5.6-1)
where acr = the distance from the point considered to the surface of the
nearest longitudinal bar;
l:m = the average strain at the level where cracking is being
considered, calculated allowing for the stiffening effect of the
concrete in the tension zone, and is obtained from eqn
(5.6-2);
Cmin = the minimum cover to the tension steel;
h = the overall depth of the member; and
x = the neutral axis depth calculated on the assumption of a
cracked section, i.e. using eqn (5.2-4) (or Fig. 5.2-3); this
value of x is then used to obtain the strain l:m in following the
equation:
bt(h - x)(a' - x)
l:m = ~:, - 3EsAs(d - x) (5.6-2)
where ~: 1 (see eqn 5.6-3) is the strain at the level considered, calculated on
the assumption of a cracked section, with the concrete modulus Ec taken as
half the value in Table 2.5-6 (to allow for creep effects), bt is the width of
the section at the centroid of the tension steel, a' is the distance from the
compression face to the point at which the crack width is being calculated
and As is the area of tension reinforcement. Using (-!Ec) with eqn
(5.2-5(a)),
(5.6-3)
where x 1 is the distance, measured from the neutral axis, to the point at
which the strain ~: 1 is sought.
A negative value for em indicates that the section is uncracked. There
are two special cases.