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FIGURE P3.2
A bar structure. Each bar has the same modulus of elasticity and cross-sectional area.
3.3 Solve Problem 3.1 using the principle of stationary potential energy.
3.4 Solve Problem 3.1 using Castigliano's theorem, part I.
3.5 Determine the vertical displacement
V
at point
a
of the truss shown. The cross-
sectional area of each member is
A
.
cos
2
Answer:
V
=
P
/(
KE
)
, where
K
=
(
2
A
/
L
)
α
+
A
/(
L
cos
α)
Hint:
The strain in bars
ab
and
ad
is
V
cos
α/
L
and the strain in
ac
is
V
/(
L
cos
α).
FIGURE P3.5
Castigliano's Theorem, Part II
3.6 For a cantilevered beam of length
L
with a load
P
applied at the free end, find the
deflection at the point where the load is applied.
w
=
PL
3
/(
)
Answer:
3
EI
x
=
L
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