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

y
w
a
A
a
x
L
FIGURE p9.7a Simply supported wooden beam.
B
x
p9.9 The wooden beam shown in Figure P9.9a supports loads
w = 470 lb/ft and P = 1,000 lb on span lengths L AB = 10 ft, L BC = 5 ft,
and L CD = 5 ft. The beam cross section shown in Figure P9.9b has
dimensions b 1 = 1.5 in., d 1 = 6.0 in., b 2 = 5.0 in., and d 2 = 16.0 in.
Determine the magnitude and location of
(a) the maximum horizontal shear stress in the beam.
(b) the maximum tensile bending stress in the beam.
d
z
y
H
y H
A
y
w
B
C
P
D
x
K
y K
LAB
LBC
LCD
FIGURE p9.9a Simply supported wooden beam.
b
FIGURE p9.7b Cross-sectional
dimensions.
y
p9.8 The simply supported wooden beam shown in Figure P9.8a
carries a uniformly distributed load w = 780 lb/ft, as shown in
Figure P9.8a, where L AB = 8 ft and L BC = 16 ft. The cross-sectional
dimensions of the beam, as shown in Figure P9.8b, are b = 6 in.,
d = 20 in., y H = 5 in., and y K = 7 in. Section a–a is located at x = 4 ft
from A.
d 1
z
d 2
(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 150 psi, what is
the largest distributed load w that can be supported by the
beam?
A
y
x
a
a
B
w
C
x
b 1
b2
b1
P
FIGURE p9.9b Crosssectional
dimensions.
p9.10 For the wooden beam shown in Figure P9.10a, assume
that L = 1.2 m and P = 12 kN. The beam cross section shown in
Figure P9.10b has dimensions b = 50 mm and d = 250 mm.
(a) Determine the maximum horizontal shear stress in the beam.
(b) If the allowable shear stress for the wood is 850 kPa, what is
the minimum width b that is acceptable for this beam?
2P
LAB
LBC
A
B
C
D
FIGURE p9.8a Simply supported wooden beam.
y H
y K
H
K
z
y
b
d
FIGURE p9.8b Cross-sectional
dimensions.
z
L
2
L
2
L
2
FIGURE p9.10a Simply supported
wooden beam.
y
b
d
FIGURE p9.10b Cross-sectional
dimensions.
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