Civil Engineering Reference
In-Depth Information
W
B
C
A
L
/2
L
/2
(a)
3
WL
/16
Elastic bending moment diagram
ve
ve
5
WL
/32
(b)
Collapse mechanism
W
U
C
A
B
(c)
M
P
Bending moment diagram at collapse
ve
ve
F
IGURE
18.11
Plastic hinges in a
propped cantilever
M
P
(d)
plastic hinge forms. Thus this redistribution of moments tends to increase the ultimate
strength of statically indeterminate structures since failure at one section leads to other
portions of the structure supporting additional load.
Having located the positions of the plastic hinges and using the fact that the moment
at these hinges is
M
P
, we may determine the ultimate load,
W
U
, by statics. Therefore
taking moments about A we have
L
2
−
M
P
=
W
U
R
C
L
(18.17)
where
R
C
is the vertical reaction at the support C. Now considering the equilibrium
of the length BC we obtain
R
C
L
2
=
M
P
(18.18)
