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)

Energy dissipation for a rigid region 313
o(mlq)
oan
... = 0
Example 8.5-3
If the triangular slab in Example 8.5-2 is orthotropically reinforced, as
indicated by the values for moment axes in Fig. 8.5-5(a), calculate the
energy dissipation per unit deflection at point d, for a = 25°, 30°, 35°, 40°
and 45°. Plot a graph of a against energy dissipation.
(a) Determine the worst position of the yield line and the corresponding
collapse load q.
(b) Can your solution be used as evidence that your minimum collapse
load is the lowest possible load for any collapse mode?
(c) Does your answer in (a) above provide a good basis for design
purpose?
SOLUTION
(a)
For a general value of a, if we consider unit deflection at d, then
the energy dissipations ( U) are given by eqn (8.5-7):
U(Region A) = m[ad)m[BA]m + 0.75m[ad)o.7sm[8A)o.75m
m
I --
o~5m
Fig. 8.5-5
= m(de)(Jf) + 0.75m(ae)(Jg)
f
II
~II II
,.., •
6J".
c· I
,.o.
~
•
~0 •
"'~-t>
{a)
2·8m
2·7m
2·6m
u 2·5
2·4
2· 3m ........ +-:--~--+-:::---+::---+-"7""
25. 30. 35. 40. 45.
a
{b)