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

pRoBLEmS
p8.26 A small aluminum alloy [E = 70 GPa] tee shape is used as
a simply supported beam as shown in Figure P8.26a. For this beam,
a = 160 mm. The cross-sectional dimensions (Figure P8.26b) of the
tee shape are b = 20 mm, d = 30 mm, and t = 6 mm. After loads are
applied to the beam at B, C, and D, a compressive normal strain of
440 mε is measured from a strain gage located at c = 8 mm below
the topmost edge of the tee stem at section 1–1. What is the applied
load P?
A
w 0
2L
3
FIGURE p8.28a/29a
B
L
3
C
y
P P 3P
A
a
B
FIGURE p8.26a
a
Strain gage
H
c
z
C
FIGURE p8.26b
p8.27 A solid steel shaft supports loads P A = 250 N and P C =
620 N as shown in Figure P8.27. Assume that a = 500 mm, b =
700 mm, and c = 600 mm. The bearing at B can be idealized as a
roller support, and the bearing at D can be idealized as a pin
support. If the allowable bending stress is 105 MPa, determine the
minimum diameter that can be used for the shaft.
t
y
b
a
2
A B C D
1
1
a
2
t
D
d
a
E
x
p8.29 A simply supported wooden beam (Figure P8.28a/29a)
with a span of L = 24 ft supports a uniformly distributed load w 0 =
450 lb/ft. The allowable bending stress of the wood is 1,200 psi. If
the aspect ratio of the solid rectangular wood beam is specified as
h/b = 3.0 (Figure P8.28b/29b), calculate the minimum width b that
can be used for the beam.
p8.30 A cantilever timber beam (Figure P8.30a/31a) with a
span of L = 4.25 m supports a linearly distributed load with maximum
intensity of w 0 = 5.5 kN/m. The allowable bending stress of
the wood is 7.0 MPa. If the aspect ratio of the solid rectangular
timber is specified as h/b = 0.67 (Figure P8.30b/31b), determine the
minimum width b that can be used for the beam.
w 0
A
L
FIGURE p8.30a/31a
b
h
FIGURE p8.28b/29b
B
b
h
FIGURE p8.30b/31b
PA
FIGURE p8.27
a b c
p8.28 A simply supported wooden beam (Figure P8.28a/29a)
with a span of L = 6 m supports a uniformly distributed load w 0 .
The beam width is b = 120 mm and the beam height is h = 300 mm
(Figure P8.28b/29b). The allowable bending stress of the wood is
8.0 MPa. Calculate the magnitude of the maximum load w 0 that
may be carried by the beam.
PC
p8.31 A cantilever timber beam (Figure P8.30a/31a) with a
span of L = 14 ft supports a linearly distributed load with maximum
intensity of w 0 . The beam width is b = 15 in. and the beam height is
h = 10 in. (Figure P8.30b/31b). The allowable bending stress of the
wood is 1,000 psi. Calculate the magnitude of the maximum load
w 0 that may be carried by the beam.
p8.32 The lever shown in Figure P8.32 must exert a force of
P = 2,700 lb at B, as shown. The lever lengths are a = 10.5 in. and b =
46.0 in. The allowable bending stress for the lever is 12,000 psi. If the
height h of the lever is to be three times the thickness t (i.e., h/t = 3),
what is the minimum thickness t that can be used for the lever?
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