Strain Energy of a Truss: Problem 12.25 Solution

________________________________________________________________________
PROBLEM (12.25) A truss ABC consisting of two members supports a vertical load P at joint B as
shown in Fig. P12.25. Each member has axial rigidity AE. Determine the strain energy of the truss.
SOLUTION
Apply the method of joints at pin B. Use cos60 3 2
o= and sin60 1 2 o=
32
0: 0,
23
yBC BC
FFPF=−=
∑=
P
11
0: 23
xBCABAB
FFFF== =
∑
B
P
2L
We have
AB BC
LLL
=
=
Therefore
222
1()
22AB AB BC BC
FL
UF L
AE AE
== +
∑FL
22
14
[() (2)
23 3
PP
LL
AE
=+
]
or 2
1.5 PL U
AE
=
F
A
B
FBC
60o
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