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P
zb
1
L
b
a
4
x
2
z
5
L
L
3
P
xc
c
d
P
zc
(a) 5-bar truss
x
u
xa
a
θ
u
xb
u
za
z
b
u
zb
FIGURE 3.2
Truss.
(b) Elongation of the
j
th bar
Use (1), (2), and (3), to form the total strain energy
1
2
V
1
+
V
1
2
V
3
2
+
−
EA
L
1
2
(
1
2
V
3
+
1
2
√
2
V
2
√
2
1
2
√
2
V
4
2
U
i
=
V
2
−
V
4
)
+
+
√
2
(4)
From Eq. (8) of Example 3.3
2
U
i
∂
V
k
=
K
kh
(5)
∂
V
h
∂
Thus, for example,
√
2
4
1
2
U
i
∂
EA
L
K
11
=
V
1
=
+
∂
V
1
∂
(6)
√
2
4
2
U
i
∂
EA
L
K
12
=
V
1
=
∂
V
2
∂
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