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

p12.5 An extruded polymer flexural member is subjected to an
internal axial force P = 580 lb, an internal shear force V = 420 lb,
and an internal bending moment M = 6,400 lb ⋅ in., acting in the
directions shown in Figure P12.5a. The cross-sectional dimensions
(Figure P12.5b) of the extrusion are b 1 = 2.0 in., t 1 = 0.6 in., b 2 =
4.0 in., t 2 = 0.4 in., d = 4.5 in., and t w = 0.4 in. Determine the normal
and shear stresses acting on horizontal and vertical planes
(a) at point H, which is located at a distance y H = 0.8 in. above
the z centroidal axis.
(b) at point K, which is located at a distance y K = 1.1 in. below
the z centroidal axis.
Show the stresses on a stress element for each point.
z
H
K
y
FIGURE p12.5a
V
M
P
p12.6 The machine component shown in Figure P12.6 is subjected
to a load P = 450 lb that acts at an angle β = 25°. The dimensions
of the component are a = 4.0 in., b = 0.625 in., c = 2.0 in., and
d = 2.5 in. Determine the normal and shear stresses acting on horizontal
and vertical planes
(a) at point H, which is located at a distance y H = 0.5 in. above
the z centroidal axis.
(b) at point K, which is located at a distance y K = 0.75 in. below
the z centroidal axis.
Show the stresses on a stress element for each point
c
P
β
y
FIGURE p12.6
x
y H
y K
p12.7 A load P = 900 N exerted at an angle β = 30° acts on the
machine part shown in Figure P12.7a. The dimensions of the part
are a = 180 mm, b = 60 mm, c = 100 mm, d = 40 mm, and e = 10 mm.
a
x
z
y H
y K
z
H
K
b 1
y
t w
FIGURE p12.5b
H
K
Cross section
y
b
t 1
b 2
t 2
d
H
K
d
The part has a uniform thickness of 8 mm (i.e., it is 8 mm thick in
the z direction). Determine the normal and shear stresses acting on
horizontal and vertical planes at points H and K, which are shown
in detail in Figure P12.7b. For each point, show these stresses on a
stress element.
d
e
P
C
β
c
H
FIGURE p12.7a
H
b
FIGURE p12.7b Detail at pin B.
p12.8 A hollow aluminum pipe is subjected to a vertical force
P x = 1,500 N, a horizontal force P y = 2,400 N, and a concentrated
torque T = 80 N ⋅ m, acting as shown in Figure P12.8. The outside
and inside diameters of the pipe are 64 mm and 56 mm, respectively.
Assume that a = 90 mm. Determine the normal and shear
stresses on horizontal and vertical planes at (a) point H and
(b) point K. For each point, show these stresses on a stress element.
z
e
K
H K
T
x
FIGURE p12.8
P x
b
A
d
B
y
K
B
y
P y
a
b
a
y
x
b
x
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