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 short-term and long-term deflections (BS 8110) 177
Loading on beam Curvature diagram
(a)
I· ·I
Triangular
(b) (r----~~
Rectangular
Uniform distribution
Sinusoidal distribution
(d) .,~-.....,:mccnCCI":iCI' lllaOII~a
leJ(~tc=J{
- ·a-;- a2 T '2
Trapezoidal T
Fig. 5.5-1 Curvature diagrams for various loadings
(c)
a = (~LL)[(~)(L)J = _1 1z(_l_)
32rm 8 2 9.6 rm
Note: Useful properties of the parabola are given in books on structural
mechanics, e.g. Reference 15. See also Problem 4.1 at the end of Chapter
4.
(d) As an exercise, the reader should verify that
a= ~~z(t)
(e) Referring to the deflected shape in Fig. 5.5-1(e), the reader should
work out the solution in the following steps:
(1) Determine the deflection a 2 . This is the moment of the entire
curvature diagram about the right support.
(2) 0 1 = a 21
l.
(3) Determine the deflection a 3 . This is the moment of the left half
of the curvature diagram taken about midspan.
(4) Then