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

p9.3 The beam segment shown in Figure P9.3a/4a is subjected
to internal bending moments M A = -9.2 kN ⋅ m and M B = -34.6
kN ⋅ m. The segment length is Dx = 300 mm. Consider area (1)
shown in Figure P9.3b/4b, and use cross-sectional dimensions of
b 1 = 250 mm, d 1 = 15 mm, b 2 = 10 mm, d 2 = 370 mm, b 3 = 150 mm,
and d 3 = 15 mm.
M A
A
z
Δx
B
y
M B
FIGURE p9.3a/4a Beam segment.
x
The cantilever beam has a length L = 6 ft and supports a concentrated
load P = 3,800 lb.
(a) Calculate the horizontal shear stress at points A, B, C, and D.
(b) From your results in (a), plot a graph showing the distribution
of shear stresses from top to bottom of the beam.
p9.6 A 6 m long simply supported wooden beam carries a 36 kN
concentrated load at B, as shown in Figure P9.6a. The crosssectional
dimensions of the beam, as shown in Figure P9.6b, are
b = 150 mm, d = 400 mm, a = 90 mm, and c = 30 mm. Section a–a
is located at x = 0.8 m from B. Determine
(a) the magnitude of the shear stress in the beam at point H in
section a–a.
(b) the magnitude of the shear stress in the beam at point K in
section a–a.
(c) the maximum horizontal shear stress that occurs in the beam
at any location within its entire span.
(d) the maximum tensile bending stress that occurs in the beam at
any location within its entire length.
(1)
d 1
y
P
a
z
(2)
(3)
b 1
b 2
y
d 2
d 3
A
x
a
L
3
B
2L
3
C
x
b 3
FIGURE p9.3b/4b Cross section.
FIGURE p9.6a Simply supported wooden beam.
p9.4 The beam segment shown in Figure P9.3a/4a is subjected
to internal bending moments M A = -45.0 kip ⋅ ft and M B = −26.0
kip ⋅ ft. The segment length is Dx = 9 in. Consider area (3) shown in
Figure P9.3b/4b, and use cross-sectional dimensions of b 1 = 6.6 in.,
d 1 = 0.6 in., b 2 = 0.4 in., d 2 = 10.8 in., b 3 = 4.2 in., and d 3 = 0.6 in.
p9.5 A cantilever wooden beam (Figure P9.5a) consists of eight
2 in. thick planks glued together to form a cross section that is 16 in.
deep, as shown in Figure P9.5b. Each plank has a width b = 5.5 in.
a
z
c
H
K
y
b
d
FIGURE p9.6b Cross-sectional
dimensions.
y
P
2 in. (typ)
z
y
A
B
C
D
p9.7 A 6 m long simply supported wooden beam carries a uniformly
distributed load of 14 kN/m, as shown in Figure P9.7a. The
cross-sectional dimensions of the beam, as shown in Figure P9.7b,
are b = 200 mm, d = 480 mm, y H = 80 mm, and y K = 160 mm. Section
a–a is located at x = 1.2 m from B.
L
FIGURE p9.5a Cantilever
beam.
x
FIGURE p9.5b Crosssectional
dimensions.
b
16 in.
(a) Determine the magnitude of the shear stress in the beam at
point H in section a–a.
(b) Determine the magnitude of the shear stress in the beam at
point K in section a–a.
(c) If the allowable shear stress for the wood is 950 kPa, what is
the largest distributed load w that can be supported by the
beam?
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