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)

164 Reinforced concrete beams-the serviceability limit states
Uncracked section
(a)
Equivalent section
(b)
Fig. 5.2-6
(5.2-14)
where stresses are compressive when X; is measured into the compression
zone, and tensile when x; is measured into the tension zone. The curvature
is given by
1 = __M_ (5.2-15)
r Eclu
which can be derived in the same manner as eqn (5.2-11).
Case 3: The partially cracked section
The partially cracked section is a device introduced by CP 110 in 1972 and
retained in BS 8110: Part 2: Clause 3.6. Figure 5.2-7 shows a beam section
in which, as usual, strains are assumed to be linearly distributed. However,
in the tension zone (that is, below the neutral axis) some concrete tension
still exists as represented by the triangular stress distribution in Fig.
5.2-7(c), in which the concrete tensile stress has a specified value let at the
level of the tension reinforcement. Note particularly that the concrete
stresses above the neutral axis (but not those below it) and the
reinforcement stresses are related to the strains in Fig. 5.2-7(b) by the
usual equations:
lc = EcEc; ~~ = Est:~; Is= Esfs (5.2-16)
Below the neutral axis, however, the concrete tensile stresses are not to be
determined from the strain diagram, but from the specified value let· For
example, at the tension face or soffit of the beam, the concrete stress is
h-x
concrete stress at tension face = -d--Iet
(5.2-17)
-x