Timothy A. Philpot - Mechanics of materials _ an integrated learning system-John Wiley (2017)

p17.63 The truss shown in Figure P17.62/63 is subjected to
concentrated loads P = 200 kN and Q = 40 kN. Members AB, BC,
DE, and EF each have a cross-sectional area A = 2,700 mm 2 . All
other members each have a cross-sectional area A = 1,060 mm 2 . All
members are made of steel [E = 200 GPa]. For the given loads,
utilize Castigliano’s second theorem to determine the horizontal
displacement of joint B.
p17.64 The truss shown in Figure P17.64 is subjected to concentrated
loads P = 130 kN and 2P = 260 kN. All members are
made of steel [E = 200 GPa], and each member has a crosssectional
area A = 4,200 mm 2 . Use Castigliano’s second theorem to
determine
(a) the horizontal displacement of joint A.
(b) the vertical displacement of joint D.
P 2P 2P 2P P
A
C E G H
p17.67 Calculate the slope and the deflection of the beam at B
for the loading shown in Figure P17.67. Use Castigliano’s second
theorem, and assume that EI is constant over the length of the
beam.
A
FIGURE p17.67
w 0
L
p17.68 Apply Castigliano’s second theorem to compute the
slope and deflection of the beam at C for the loading shown in
Figure P17.68. Assume that EI is constant over the length of the
beam.
B
6 m
P
B D F
8 m 8 m 8 m
FIGURE p17.64
8 m
A B C
p17.65 Employing Castigliano’s second theorem, calculate the
slope of the beam at A for the loading shown in Figure P17.65.
Assume that EI is constant over the length of the beam.
FIGURE p17.68
L
L
2
M 0
A
L
B
p17.69 What is the deflection of the compound rod at C for the
loading shown in Figure P17.69? Between A and B, the rod’s diameter
is 35 mm, and between B and C, its diameter is 20 mm. Assume
that E = 200 GPa for both segments of the compound rod, and use
Castigliano’s second theorem.
FIGURE p17.65
p17.66 Determine the deflection of the beam at A for the loading
shown in Figure P17.66, utilizing Castigliano’s second theorem.
Assume that EI is constant over the length of the beam.
500 N
P
A
640 mm 320 mm
B
C
FIGURE p17.69
A
x
a
FIGURE p17.66
B
L
b
C
p17.70 The compound steel [E = 200 GPa] rod shown in Figure
P17.70/71 has a diameter of 20 mm in each of segments AB and
DE, and a diameter of 35 mm in each of segments BC and CD. For
the given loading, employ Castigliano’s second theorem to find the
slope of the compound rod at A.
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