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

z
FIGURE p8.8
p8.9 An aluminum alloy [E =
10,300 ksi] tee-shaped bar is
c
used as a beam. The cross section
of the tee shape, shown in
y
Figure P8.9, has a total depth of Strain gage
d
d = 7.5 in. The centroidal z axis
z
of this cross section is located
2.36 in. above point H. The H
beam spans in the x direction FIGURE p8.9
and it bends about the z centroidal
axis. A strain gage is affixed to the side of the tee stem at a
distance c = 1.25 in. below the top surface of the tee shape. After
loads are applied to the beam, a normal strain of ε x = −810 mε is
measured by the strain gage. What is the bending stress at point H?
p8.10 The cross-sectional dimensions
of the beam shown in
Figure P8.10 are d = 17 in., b f =
10 in., t f = 1.0 in., t w = 0.60 in., and
a = 3.5 in.
(a) If the bending stress at point
K is 5.4 ksi (C), what is the
bending stress at point H?
State whether the normal
stress at H is tension or
compression.
(b) If the allowable bending
stress is 30 ksi, what is the
magnitude of the maximum
bending moment M z that can
be supported by the beam?
p8.11 The cross-sectional dimensions
of the beam shown in Figure
P8.11 are r o = 115 mm and r i =
95 mm. Given M z = 16 kN ⋅ m, α =
30°, and β = 55°, what are the bending
stresses at points H and K?
b
t
(typ.)
p8.12 The cross-sectional dimensions of the beam shown in
Figure P8.12 are a = 5.0 in., b = 6.0 in., d = 4.0 in., and t = 0.5 in.
The internal bending moment about the z centroidal axis is M z =
−4.25 kip ⋅ ft. Determine
(a) the maximum tensile bending stress in the beam.
(b) the maximum compressive bending stress in the beam.
y
H
FIGURE p8.10
z
z
K
y
b f
β
K
t w
r i
y
FIGURE p8.11
d
r o
α
t f
a
H
d
p8.13 Two uniformly distributed loads w = 3,600 lb/ft act on the
simply supported beam shown in Figure P8.13a. The beam spans are
a = 8 ft and L = 16 ft. The beam cross section shown in Figure P8.13b
has dimensions of b 1 = 16 in., d 1 = 6 in., b 2 = 10 in., and
d 2 = 10 in. Calculate the maximum tensile and compressive bending
stresses produced in segment BC of the beam.
A
a
FIGURE p8.12
FIGURE p8.13a
b
p8.14 An extruded polymer beam is subjected to a bending
moment M as shown in Figure P8.14a. The length of the beam
is L = 800 mm. The cross-sectional dimensions (Figure P8.14b)
of the beam are b 1 = 34 mm, d 1 = 100 mm, b 2 = 20 mm, d 2 =
20 mm, and a = 7 mm. For this material, the allowable tensile
bending stress is 16 MPa and the allowable compressive bending
stress is 12 MPa. Determine the largest moment M that can
be applied as shown to the beam.
M
A
w
a
y
L
FIGURE p8.14a
z
B
d 1
y
L
d 2
b 2
t
(typ.)
C
FIGURE p8.13b
B
z
b 1
y
d 2
a
a
a
w
a
z
b 2
y
b 1
FIGURE p8.14b
d
D
a
x
d 1
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