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

pRoBLEmS
p10.17 For the beam and loading shown in Figure P10.17, use
discontinuity functions to compute the deflection of the beam at D.
Assume a constant value of EI = 1,750 kip ⋅ ft 2 for the beam.
A
B
C
D
E
A
v
p10.18 The solid 30 mm diameter steel [E = 200 GPa] shaft
shown in Figure P10.18 supports two pulleys. For the loading
shown, use discontinuity functions to compute
(a) the deflection of the shaft at pulley B.
(b) the deflection of the shaft at pulley C.
p10.19 For the beam and loading shown in Figure P10.19, use
discontinuity functions to compute
(a) the slope of the beam at C.
(b) the deflection of the beam at C.
Assume a constant value of EI = 560 × 10 6 N ⋅ mm 2 for the beam.
p10.20 The solid 30 mm diameter steel [E = 200 GPa] shaft
shown in Figure P10.20 supports two belt pulleys. Assume that the
bearing at A can be idealized as a pin support and that the bearing
at E can be idealized as a roller support. For the loading shown, use
discontinuity functions to compute
(a) the deflection of the shaft at pulley B.
(b) the deflection of the shaft at point C.
5 kips 3 kips
B
4 ft 6 ft
3 ft
A
FIGURE p10.17
B
C
250 mm 350 mm
800 N
FIGURE p10.18
A
v
210 N.m
500 N
B C D
200 mm 150 mm 250 mm
100 mm
FIGURE p10.19
1,400 N
C
x
E
D
x
p10.21 The cantilever beam shown in Figure P10.21 consists
of a W530 × 74 structural steel wide-flange shape [E = 200 GPa;
I = 410 × 10 6 mm 4 ]. Use discontinuity functions to compute the
deflection of the beam at C for the loading shown.
v
300 mm 200 mm
30 kN/m
A B C
3 m 2 m
FIGURE p10.21
p10.22 The cantilever beam shown in Figure P10.22 consists of
a W21 × 50 structural steel wide-flange shape [E = 29,000 ksi;
I = 984 in. 4 ]. Use discontinuity functions to compute the deflection
of the beam at D for the loading shown.
p10.23 The simply supported beam shown in Figure P10.23
consists of a W410 × 85 structural steel wide-flange shape
[E = 200 GPa; I = 316 × 10 6 mm 4 ]. For the loading shown, use
discontinuity functions to compute
(a) the slope of the beam at A.
(b) the deflection of the beam at midspan.
v
FIGURE p10.20
v
9 kips
600 N
300 mm 200 mm
800 N
A B C D
4 ft 3 ft
9 ft
FIGURE p10.22
40 kN
4 kips/ft
75 kN/m 75 kN/m
A B C
D
2.5 m
FIGURE p10.23
3.0 m
2.5 m
x
x
x
421