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

p8.86 The curved tee shape shown in Figure P8.86 has crosssectional
dimensions b 1 = 1.25 in., d 1 = 0.25 in., b 2 = 0.25 in., and
d 2 = 1.00 in. The radial distance from the center of curvature, O, to
A is r i = 2.00 in. Determine the stresses at A and B for an applied
load P = 560 lb.
a
P
P
b 2
B
A
r i
O
b 1
d 2
d
B
FIGURE p8.86
A
r i
p8.87 The curved bar shown in Figure P8.87 has a trapezoidal
cross section with dimensions b 1 = 75 mm, b 2 = 30 mm, and d =
100 mm. The radial distance from the center of curvature, O, to A
is r i = 120 mm. Determine
(a) the radial distance r c − r n between the centroid and the neutral
axis.
(b) the largest value of M if the allowable normal stress is 200 MPa.
O
r i
b 1
O
d 1
FIGURE p8.88
p8.89 The curved bar shown in Figure P8.89 has an elliptical
cross section with dimensions a = 0.9 in. and b = 0.4 in. The inner
radius of the curved bar is r i = 1.50 in. For an applied moment M =
1,700 lb ⋅ in., determine
(a) the radial distance r c − r n between the centroid and the neutral
axis.
(b) the maximum compressive stress.
M
r i
O
r i
b 2
2b
b 2
M
2a
B
A
O
M
r i
b 1
O
d
FIGURE p8.89
p8.90 The curved bar shown in Figure P8.90 has a triangular
cross section with dimensions b = 1.5 in. and d = 1.2 in. The inner
radius of the curved bar is r i = 3.8 in. For an applied load P = 70 lb,
determine the stresses at A and B.
FIGURE p8.87
b
d
p8.88 The curved bar shown in Figure P8.88 has a trapezoidal
cross section with dimensions b 1 = 0.75 in., b 2 = 1.50 in., and d =
2.00 in. The radial distance from O to A is r i = 1.50 in. A load P =
1,400 lb acts on the bar. If the allowable stress is 18 ksi, what is the
largest permissible distance a?
B
A
FIGURE p8.90
P
O
r i
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