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)

180 Reinforced concrete beams-the serviceability limit states
2.5-6; Ec values for long-term loading will be discussed later under the
heading of creep. The second moment of area I is significantly affected by
the cracking of the concrete. Consider the simply supported beam in Fig.
5.5-3. In the region A, the bottom-fibre tensile stresses are sufficiently low
for the concrete to remain uncracked; hence the second moment of area
for this region would be that for an uncracked section (eqn 5.2-13). In
region B, the situation is more complicated: at a section containing a crack,
the I value for a cracked section (eqn 5.2-9) is appropriate. However, in
between cracks the tensile forces in the concrete are not completely lost
and neither I for an uncracked section nor that for a cracked section is
appropriate. Clearly, in deflection calculations it is the sum effect of the EI
values that is important, and BS 8110 recommends that the properties
associated with the partially cracked section in Section 5.2 should be used
for the entire beam, and that the values of the tensile stress fct in Figs 5.2-7
and 5.2-8 should be taken as 1 N/mm 2 for short-term loading and 0.55
N/mm 2 for long-term loading.
Creep
BS 8110: Part 2: Clause 3.6 recommends that, in calculating the curvatures
due to long-term loading, the effective or long-term modulus of elasticity
Eerr should be taken as
E _ Ec(Table 2.5-6)
eff - 1 + q,
where if' is called the creep coefficient, which is defined by
_ creep strain
if' - elastic strain
(5.5-3)
(5.5-4)
Values of q, are given in BS 8110: Part 2: Clause 7.3. (See also the
prediction of creep strains in Section 2.5(b), which can be used to obtain an
approximate estimate of the creep coefficient if'.)
Shrinkage
A plain concrete member undergoing a uniform shrinkage would shorten
without warping. However, in a reinforced concrete beam, the reinforcement
resists the shrinkage and produces a curvature. Consider the beam
section in Fig. 5.5-4. A unit length of the beam is shown in Fig. 5.5-5. In
Fig. 5.5-5, Ecs represents the concrete shrinkage and is the uniform
shortening which would occur over the unit length, had the beam been
Fig. 5.5-3