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

p8.63 A downward concentrated load P = 42 kN acts on wall
BC of the box beam shown in Figure 8.63a. The load acts at a distance
a = 35 mm below the z centroidal axis. The box has dimensions
b = 80 mm, d = 120 mm, and t = 8 mm, as shown in Figure
8.63b. Determine the normal stress
(a) at corner A.
(b) at corner D.
D
z
C
P
FIGURE p8.63a
x
a
y
B
p8.64 The cantilever beam shown in Figure P8.64a is subjected
to load magnitudes P z = 2.8 kips and P y = 8.3 kips. The flanged
cross section shown in Figure P8.64b has dimensions b f = 8.0 in.,
t f = 0.62 in., d = 10.0 in., and t w = 0.35 in. Using L = 84 in., determine
(a) the bending stress at point A.
(b) the bending stress at point B.
(c) the angle β that the neutral axis makes with the +z axis. Note
that positive β angles rotate clockwise from the +z axis.
A
t
(typ)
D
z
b
y
P
b – t
2
FIGURE p8.63b
B
C
a
d
bending stress is 150 MPa, and the allowable compressive bending
stress is 80 MPa. What is the largest bending moment M z that can
be applied as shown to this cross section?
A
d
y'
θ
z
z'
D
FIGURE p8.65
y
p8.66 The moment acting on the cross section of the zee shape
shown in figure P8.66 has a magnitude of M z = 5,600 lb ⋅ ft and is
oriented at an angle θ = 24°. The dimensions of the cross section are
b f = 3.0 in., t f = 0.35 in., d = 7.0 in., and t w = 0.20 in. Determine
(a) the moments of inertia I y′ and I z′ .
(b) the product of inertia I y′z′ .
(c) the principal moments of inertia and the angle from the +z′
axis to the axis of the maximum moment of inertia.
(d) the bending stress at points A and C.
(e) the angle β that the neutral axis makes with the +z axis. Note
that positive β angles rotate clockwise from the +z axis.
B
b
t
(typ)
C
M z
L
z
A
A
y
B
C
b f
y
B
t f
z
z'
M z
D
y
A
b f
y'
θ
B
t w
C
t f
d
x
P z
z
d
FIGURE p8.66
P y
t w
FIGURE p8.64a
FIGURE p8.64b
p8.65 The U-shaped cross section is oriented at an angle θ =
35° as shown in Figure P8.65. The dimensions of the cross section
are b = 80 mm, d = 65 mm, and t = 5 mm. The allowable tensile
D
C
p8.67 A beam cross section is fabricated by rigidly attaching
two lumber boards together as shown in Figure P8.67. The dimensions
of the cross section are b 1 = 7.25 in., b 2 = 9.25 in., and t = 1.50 in.
The moment acting on the cross section is M z = 930 lb ⋅ ft. Determine
(a) the moments of inertia I y and I z .
(b) the product of inertia I yz .
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