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

From Equation (17.40), the beam deflection at C can now be determined:
3 3
5,223.868 kN⋅m 5,223.868 kN⋅m
∆ C =
=
5 2
EI 3.4 × 10 kN⋅m
-3 ∴D = 15.3643 × 10 m = 15.36 mm ↓
Ans.
C
pRoBLEmS
p17.56 Use Castigliano’s second theorem to determine the vertical
displacement of joint B for the truss shown in Figure P17.56/57.
Assume that each member has a cross-sectional area A = 0.85 in. 2
and an elastic modulus E = 10,000 ksi. The loads acting on the truss
are P = 17 kips and Q = 9 kips.
y
x
Q
P
B
4.5 ft
p17.59 In Figure P17.58/59, use Castigliano’s second theorem
to find the horizontal displacement of joint D for the truss. The
assumptions are that each member has a cross-sectional area A =
2.25 in. 2 and an elastic modulus E = 29,000 ksi and that the loads
acting on the truss are P = 13 kips and Q = 25 kips.
p17.60 Employ Castigliano’s second theorem to calculate the
horizontal displacement of joint A for the truss shown in Figure
P17.60/61. Make the assumption that each member has a crosssectional
area A = 1,600 mm 2 and an elastic modulus E = 200 GPa.
C
E
A
C
7.5 m
6.5 ft
5 ft
FIGURE p17.56/57
p17.57 Applying Castigliano’s second theorem, find the horizontal
displacement of joint B for the truss shown in Figure
P17.56/57. Assume that each member has a cross-sectional area A =
0.85 in. 2 and an elastic modulus E = 10,000 ksi, and that the loads
acting on the truss are P = 17 kips and Q = 9 kips.
p17.58 Compute the vertical displacement of joint D for the truss
shown in Figure P17.58/59. Assume that each member has a crosssectional
area A = 2.25 in. 2 and an elastic modulus E = 29,000 ksi.
The loads acting on the truss are P = 13 kips and Q = 25 kips.
Employ Castigliano’s second theorem.
18 ft
A
P
12 ft 18 ft
B
18 ft
FIGURE p17.58/59
C
y
P
x
D
Q
A B D
52 kN 85 kN
FIGURE p17.60/61
6 m 10.5 m
p17.61 In Figure P17.60/61, use Castigliano’s second theorem
to compute the vertical displacement of joint B for the truss.
Each member is assumed to have a cross-sectional area A =
1,600 mm 2 and an elastic modulus
E = 200 GPa.
p17.62 In Figure P17.62/63,
the truss is subjected to concentrated
loads P = 200 kN and Q =
40 kN. Members AB, BC, DE,
and EF each have a crosssectional
area A = 2,700 mm 2 ,
and 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, calculate
the horizontal displacement of
joint F by applying Castigliano’s
second theorem.
C
B
A
P
9 m
FIGURE p17.62/63
P
F
E
D
y
6 m
6 m
x
Q
Q
787