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

D
M
r i
O
A
B
p8.83 The curved tee shape shown in Figure P8.83 is subjected
to a bending moment M = 2,700 N ⋅ m. The dimensions of the cross
section are b 1 = 15 mm, d 1 = 70 mm, b 2 = 50 mm, and d 2 = 20 mm.
The radial distance from the center of curvature, O, to A is r i =
85 mm. Determine
(a) the radial distance from O to the neutral axis.
(b) the stresses at points A and B.
d
M
O
FIGURE p8.80
M
r i
A
M
r i
b 2
A
d 2
p8.81 Determine the stresses acting at points A and B for the
curved solid rod shown in Figure P8.81. The diameter of the curved
solid rod shown in Figure P8.81 d = 0.875 in. The inner radius of
the bend in the rod is r i = 1.5 in. A load P = 90 lb is applied at a
distance a = 5 in. from the center of curvature, O. Determine the
stresses acting at points A and B.
B
FIGURE p8.83
B
b 1
d 1
B
d
A
B
A
r i
O
a
P
p8.84 The curved flanged shape shown in Figure P8.84/85 is
subjected to a bending moment M = 4,300 N ⋅ m. Dimensions of the
cross section are b 1 = 75 mm, d 1 = 15 mm, b 2 = 15 mm, d 2 = 55 mm,
b 3 = 35 mm, and d 3 = 15 mm. The radial distance from the center of
curvature, O, to A is r i = 175 mm. Determine the stresses at points
A and B.
FIGURE p8.81
a
P
B
b 2
b 3
d 3
d 2
p8.82 A solid circular rod of diameter d is bent into a semicircle
as shown in Figure P8.82. The radial distance to the centroid of
the rod is to be r c = 3d, and the curved rod is to support a load
P = 5,000 N. If the allowable stress must be limited to 135 MPa,
what is the smallest diameter d that may be used for the rod?
M
r i
A
M
r i
b 1
d 1
B
O
FIGURE p8.84/85
O
P
r i
A
O
r c
P
p8.85 The curved flanged shape shown in Figure P8.84/85 has
cross-sectional dimensions b 1 = 45 mm, d 1 = 9 mm, b 2 = 9 mm,
d 2 = 36 mm, b 3 = 18 mm, and d 3 = 9 mm. The radial distance from
the center of curvature, O, to A is r i = 140 mm. Determine
d
FIGURE p8.82
(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 250 MPa.
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