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)

162 Reinforced concrete beams-the serviceability limit states
n T
I· b=45o ·I
h -r--·--·-r--'--·--·
Jl
750 d
6190 • • •
As= 3-4Qmm
(a)
(b)
Fig. 5.2-5
ae = 200/28 = 7.14
(3769)
aee = (7.14)(450)(690) = 0.087
From Figs 5.2-3 and 5.2-4,
xld = 0.35; Iclbd 3 = 0.054
therefore
x = (0.35)(690) = 241.5 mm
Ic = (0.054)(450)(690 3 ) = (7982)(10 6 ) mm 4
From eqn (5.2-7),
f = ae M (d - x)
s Es fc
(7.14) (694)(10 6 )
= (200)(103) (7982)(106) (690 - 24 1. 5 )
= 0.00139
(This is also the concrete strain at the level of the tension steel.)
From Fig. 5.2-5(b), the concrete strain at the tension face is
h - X (750 - 241.5)
fh = d _ X f 5 = 690 _ 241.5 (0.00139) = 0.00157
At 250 mm below the neutral axis, the concrete strain is
c(250) = ( 690 :_5~4 1. 5 )(0.00139) = 0.00077
(b) Long-term strains due to service loading
Ec = (!)(28) kN/mm 2 = 14 kN/mm 2