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

p8.71 The notched bar shown in Figure P8.71/72 is subjected to
a bending moment M = 300 N ⋅ m. The major bar width is D = 75 mm,
the minor bar width at the notches is d = 50 mm, and the radius of
each notch is r = 10 mm. If the maximum bending stress in the bar
must not exceed 90 MPa, determine the minimum required bar
thickness b.
b
p8.74 The machine shaft shown in Figure P8.74/75 is made of
1020 cold-rolled steel. (See Appendix D for properties.) The major
shaft diameter is D = 1.000 in., the minor shaft diameter is d =
0.625 in., and the radius of the fillet between the major and minor
diameter sections is r = 0.0625 in. The fillets are located at x = 4 in.
from C. If a load P = 125 lb is applied at C, determine the factor of
safety in the fillet at B.
D
d
M
x
D
d
Radius r
P
FIGURE p8.71/72
Radius r
p8.72 The machine part shown in Figure P8.71/72 is made of
cold-rolled 18-8 stainless steel. (See Appendix D for properties.)
The major bar width is D = 1.50 in., the minor bar width at the
notches is d = 1.00 in., the radius of each notch is r = 0.125 in., and
the bar thickness is b = 0.25 in. Determine the maximum safe moment
M that may be applied to the bar if a factor of safety of 2.5 with
respect to failure by yield is specified.
p8.73 The C86100 bronze (see Appendix D for properties) shaft
shown in Figure P8.73 is supported at each end by self-aligning bearings.
The major shaft diameter is D = 40 mm, the minor shaft diameter
is d = 25 mm, and the radius of the fillet between the major and minor
diameter sections is r = 5 mm. The shaft length is L = 500 mm and the
fillets are located at x = 150 mm. Determine the maximum load P that
may be applied to the shaft if a factor of safety of 3.0 is specified.
A
FIGURE p8.74/75
B
p8.75 The machine shaft shown in Figure P8.74/75 is made of
1020 cold-rolled steel. (See Appendix D for properties.) The major
shaft diameter is D = 30 mm, the minor shaft diameter is d = 20 mm,
and the radius of the fillet between the major and minor diameter
sections is r = 3 mm. The fillets are located at x = 90 mm from C.
Determine the maximum load P that can be applied to the shaft at
C if a factor of safety of 1.5 is specified.
p8.76 The grooved shaft shown in Figure P8.76 is made of
C86100 bronze. (See Appendix D for properties.) The major shaft
diameter is D = 50 mm, the minor shaft diameter at the groove is d =
34 mm, and the radius of the groove is r = 4 mm. Determine the
maximum allowable moment M that may be applied to the shaft if
a factor of safety of 1.5 with respect to failure by yield is specified.
x
C
P
x
Radius r
M
M
D
d
D
d
FIGURE p8.73
L / 2
L / 2
FIGURE p8.76
Radius r
8.10 Bending of curved Bars
Consider an unstressed curved bar (Figure 8.21a) of uniform cross section with a vertical
axis of symmetry (Figure 8.21b). The outer and inner fibers of the beam are located at radial
distances r o and r i from the center of curvature, O, respectively. The radius of curvature
of the centroidal axis is denoted by r c . We will focus our attention on a small portion of the
bar located between cross sections a–c–e and b–d–f that are separated from each other by
a small central angle θ.
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