Civil Engineering Reference
In-Depth Information
which gives
Wab
L
which is the result we would have obtained by calculating the moment of
R
C
(
M
B
=
=
Wa
/
L
from Ex. 15.1) about B.
E
XAMPLE
15.3
Determine the force in the member AB in the truss shown in
Fig. 15.9(a).
C
30 kN
C
C
C
4m
a
B
v,B
10 kN
D
a
B
B
D
4m
E
A
A
E
F
IGURE
15.9
Determination of
the internal force in
a member of a truss
using virtual work
3m
(a)
(b)
We are required to calculate the force in the member AB, so that again we need to
relate this internal force to the externally applied loads without involving the internal
forces in the remaining members of the truss. We therefore impose a virtual extension,
v,B
, at B in the member AB, such that Bmoves to B
. If we assume that the remaining
members are rigid, the forces in them will do no work. Further, the triangle BCD will
rotate as a rigid body about D to B
C
D as shown in Fig. 15.9(b). The horizontal
displacement of C,
C
, is then given by
C
=
4
α
while
v,B
=
3
α
