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

pRoBLEmS
p12.1 A compound shaft consists of segment (1), which has a
diameter of 1.25 in., and segment (2), which has a diameter of 1.75 in.
The shaft is subjected to a tensile axial load P = 9 kips and torques
T A = 7 kip ⋅ in. and T B = 28 kip ⋅ in., which act in the directions
shown in Figure P12.1. Determine the normal and shear stresses at
(a) point H and (b) point K. For each point, show the stresses on a
stress element.
T B
z
y
(a) at point H, which is located at a distance y H = 120 mm above
the z centroidal axis.
(b) at point K, which is located at a distance y K = 80 mm below
the z centroidal axis.
Show the stresses on a stress element for each point.
H
y
V
M
z
d
y H
y K
H
y
t
h
T A
P
x
A
FIGURE p12.1
H
(1) B (2)
K
C
z
K
FIGURE p12.3a
P
x
K
FIGURE p12.3b
p12.2 The flanged member shown in Figure P12.2a is subjected
to an internal axial force P = 6,300 lb, an internal shear force V =
5,500 lb, and an internal bending moment M = 77,000 lb ⋅ ft, acting
in the directions shown. The dimensions of the cross section are
b f = 10.00 in., t f = 0.68 in., d = 12.00 in., and t w = 0.32 in. (Figure
12.2b). Determine the normal and shear stresses at point H, where
a = 2.50 in.
P
M
p12.4 A hat-shaped flexural member is subjected to an internal
axial force P = 7,200 N, an internal shear force V = 6,000 N, and an
internal bending moment M = 1,300 N ⋅ m, acting as shown in Figure
P12.4a. The dimensions of the cross section (Figure P12.4b)
are a = 20 mm, b = 100 mm, d = 55 mm, and t = 4 mm. Determine
the stresses acting on horizontal and vertical planes
(a) at point H, which is located at a distance y H = 20 mm above
the z centroidal axis.
(b) at point K, which is located at a distance y K = 12 mm below
the z centroidal axis.
Show the stresses on a stress element for each point.
H
a
x
V
d
y
y
t w
M
z
FIGURE p12.2a
y
H a
t z
f
FIGURE p12.2b
t f
b f
H
z
K
FIGURE p12.4a
V
P
x
p12.3 Figure 12.3a shows a doubly-symmetric beam whose
cross section is shown in Figure P12.3b. The beam has been proposed
for a short footbridge. The cross section will consist of two
identical steel pipes that are securely welded to a steel web plate
that has a thickness t = 9.5 mm. Each pipe has an outside diameter
d = 70 mm and a wall thickness of 5 mm. The distance between the
centers of the two pipes is h = 370 mm. Internal forces P = 13 kN,
V = 25 kN, and M = 9 kN ⋅ m act in the directions shown in Figure
P12.3a. Determine the stresses acting on horizontal and vertical
planes
y H
y K
a
H
z
K
FIGURE p12.4b
y
b
t
(typ)
a
d
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