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)

168 Reinforced concrete beams-the serviceability limit states
(b) Instantaneous curvatures 11 ru and 11 r;p
ae = 200/28 = 7.14
628
aee = (7.14)(185)(340) = 0.071
From Figs 5.2-3 and 5.2-4,
xld = 0.32 /jbd 3 = 0.045
whence
x = 108.8 mm
From eqn (5.2-20),
M.(net) = (48)(106)- H18lj~65--1~~~sf)3}(1)
= (48)(106) - (5.03)(106) = (42.97)(106) Nmm
Mp(net) = (36)(106) - (5.03)(106) = (30.97)(106) Nmm
Using eqn (5.2-23), the instantaneous curvatures llri 1 and 1/rip• due
respectively to the total and the permanent load, are
1 (42.97)(10 6 ) -6 -1
rit = (28)(103)(327)(106) = (4·69)(10 ) mm
1 (30.97)(106) mm- 1 ( )( _ 6) _ 1
rip = (28)(103)(327)(106) = 3.39 10 mm
(c) Difference in instantaneous curvatures .
.l - ..l = (4.69)(10-6) - (3.39)(10-6) = (1.30)(10-6) mm- 1
rit rip
An examination of the calculations in (b) above shows that the
difference in instantaneous curvatures may be obtained directly as
1 1 _ Mt- MP
rit - rip - Ecfc
(5.2-24)
Note that M 1 - Mf! = M 1(net) - Mp(net); that is the terms involving
let in eqn (5.2-20) cancel out.
5.3 Deflection control in design (BS 8110)
Excessive deflections may lead to sagging floors, to roofs that do not drain
properly, to damaged partitions and finishes, and to other associated