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

120 N/mm
40 kN/m
A
B C
100 mm 65 mm 65 mm
D
100 mm
E
A
3 m
B
2 m
C
FIGURE p17.70/71
FIGURE p17.73
p17.71 Figure P17.70/71 shows a compound steel [E = 200 GPa]
rod with 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, calculate the deflection of the compound rod at C, using
Castigliano’s second theorem.
p17.72 Figure P17.72 shows a simply supported beam. Assume
that EI = 15 × 10 6 kip·in. 2 for the beam. Use Castigliano’s second
theorem to determine
(a) the deflection at A.
(b) the slope at C.
A
p17.73 A cantilever beam is loaded as shown in Figure P17.73.
Assume that EI = 74 × 10 3 kN · m 2 for the beam, and employ Castigliano’s
second theorem to find
(a) the slope at C.
(b) the deflection at C.
B
3.5 kips/ft
8 ft 20 ft
FIGURE p17.72
C
p17.74 Compute the minimum moment of inertia I required for
the beam in Figure P17.74 if the maximum beam deflection must not
exceed 35 mm. Assuming that E = 200 GPa, employ Castigliano’s
second theorem.
A
FIGURE p17.74
p17.75 In Figure P17.75, if the maximum beam deflection must
not exceed 0.5 in., what is the minimum moment of inertia I
required for the beam? Utilize Castigliano’s second theorem, and
assume that E = 29,000 ksi.
A
FIGURE p17.75
125 kN
B
125 kN
4 m 4 m 4 m
1.5 kips/ft
15 ft
C
B
D
75 kip·ft
789