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

p9.17 The extruded plastic shape shown in Figure P9.17 will be
subjected to an internal shear force V = 300 lb. The dimensions of the
cross section are b = 1.5 in., d = 3.0 in., c = 2.0 in., and t = 0.15 in.
Determine
(a) the horizontal shear stress at points A and B.
(b) the horizontal shear stress at point C, which is located at a
distance y C = 1.0 in. below the z centroidal axis.
(c) the maximum horizontal shear stress in the extrusion.
d = 410 mm, t w = 12 mm, b = 120 mm, and t = 8.0 mm. If the beam
will be subjected to a shear force V = 165 kN, determine
(a) the shear stress at point H, located at y H = 160 mm above the
z centroidal axis.
(b) the shear stress at point K, located at y K = 70 mm below the
z centroidal axis.
b
z
y C
A
B
C
y
V
t
(typ.)
c
d
z
H
K
y
V
x
Square tube
t
z
y H
y K
H
y
K
t w
Web
plate
b
d
p9.18 The extruded plastic shape
shown in Figure P9.18 has dimensions
D = 30 mm, d = 24 mm, a = 85 mm, and
t = 7 mm.
(a) Determine the horizontal shear
stress at point A for a shear force V
= 320 N.
(b) If the allowable shear stress for the
plastic material is 1,100 kPa, what
is the maximum shear force V that
can be applied to the extrusion?
b
FIGURE p9.17
t
FIGURE p9.18
p9.19 The internal shear force at a certain section of a steel
beam is V = 9 kN. The beam cross section, shown in Figure P9.19,
has dimensions b = 150 mm, c = 30 mm, d = 70 mm, and t = 6 mm.
Determine
(a) the shear stress at point H.
(b) the shear stress at point K.
(c) the maximum horizontal shear stress in the cross section.
d
c
H
z
y
b
V
p9.20 The beam cross section shown in Figure P9.20a has been
proposed for a short pedestrian bridge. The cross section will consist
of two square tubes that are welded to a rectangular web plate.
The dimensions of the cross section, as shown in Figure P9.20b, are
K
c
D
t
(typ)
d
z
y
V
A
FIGURE p9.19
a
FIGURE p9.20a Beam
segment.
p9.21 The cantilever beam shown in Figure P9.21a/22a is subjected
to a concentrated load P. The cross-sectional dimensions of
the rectangular tube shape shown in Figure P9.21b/22b are b =
6 in., d = 10 in., and t = 0.375 in.
(a) Compute the value of Q that is associated with point H, which is
located to the right of the vertical centroidal axis at z H = 1.50 in.
(b) If the allowable shear stress for the rectangular tube shape is
16 ksi, determine the maximum concentrated load P that can
be applied as shown to the cantilever beam.
z
y
P
FIGURE p9.21a/22a
Beam segment.
Square tube
FIGURE p9.20b Crosssectional
dimensions.
p9.22 The cantilever beam shown in Figure P9.21a/22a is subjected
to a concentrated load P = 25 kips. The cross-sectional dimensions
of the rectangular tube shape shown in Figure P9.21b/22b
are b = 5 in., d = 9 in., and t = 0.25 in. Determine
(a) the shear stress at point K, which is located to the left of the
vertical centroidal axis at z K = 1.00 in.
(b) the maximum horizontal shear stress in the rectangular tube
shape.
x
t
(typ.)
z
z K
K
b
z H
H
FIGURE p9.21b/22b
Cross-sectional
dimensions.
y
b
d
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