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

(a) the normal stress in each material at point H, which is located
a distance a = 1.75 in. above the z centroidal axis.
(b) the normal strain in each material at point H.
(c) the maximum bending stress in each material.
p8.39 A composite
y
beam consists of a bronze
[E = 105 GPa] bar (2) attached
rigidly to an alu-
z
d
(2)
minum alloy [E = 70 GPa]
bar (1) as shown in Figure
(1)
P8.39. The dimensions of
b
the cross section are b 1 =
2 b 1
60 mm, b 2 = 25 mm, and FIGURE p8.39
d = 40 mm. The allowable
stress of the aluminum alloy is 165 MPa, and the allowable stress of
the bronze is 210 MPa. What is the magnitude of the allowable bending
moment M z that may be applied to the composite cross section?
p8.40 Two aluminum alloy
plates (2) are attached to the
b2
b2
sides of a wooden beam (1) as a
shown in Figure P8.40. The dimensions
of the composite cross
y
section are b 1 = 80 mm, d 1 = d 2 z
240 mm, b 2 = 10 mm, d 2 =
120 mm, and a = 60 mm. Determine
(2)
(2)
the maximum bending a
(1)
stresses produced in both the
wooden beam and the aluminum
b 1
plates if a bending moment FIGURE p8.40
M z = +6,000 N ⋅ m is applied
about the z axis. Assume that E 1 = 12.5 GPa and E 2 = 70 GPa.
p8.41 A wooden beam (1) is reinforced
with steel plates (2) rigidly attached to its
top and bottom surfaces, as shown in Figure
P8.40. The dimensions of the cross section
are b 1 = 6 in., d 1 = 12 in., b 2 = 4 in., and d 2 =
0.5 in. The elastic moduli of the wood and
steel are E 1 = 1,250 ksi and E 2 = 30,000 ksi,
respectively. The allowable bending
stresses of the wood and steel are 1,200 psi
and 20,000 psi, respectively. Determine the
largest concentrated vertical load that can
be applied at midspan if a simply supported
beam with this cross section spans 18 ft.
p8.42 A bronze [E = 15,200 ksi] bar is rigidly attached to a
stainless steel [E = 27,500 ksi] bar to form a composite beam.
The composite beam is subjected to a bending moment
M = 6,400 lb ⋅ ft about the z axis (Figure P8.42a/43a). The dimensions
of the beam cross section are b = 4.5 in., d B = 2.25 in., and
d S = 1.00 in. (Figure P8.42b/8.43b). Determine
(a) the maximum bending stresses in the bronze and stainless
steel bars.
(b) the normal stress in each bar at the surface where they contact
each other.
(1)
z
(2)
b 1
y
(2)
b 2
FIGURE p8.41
d 2
d 1
d 2
d 1
M
Bronze
Stainless
steel
FIGURE p8.42a/43a
FIGURE p8.42b/43b
p8.43 A bronze [E = 100 GPa] bar is rigidly attached to a stainless
steel [E = 190 GPa] bar to form a composite beam. The allowable
bending stresses for the bronze and stainless steel bars are
180 MPa and 225 MPa, respectively. Determine the allowable
bending moment M (Figure P8.42a/43a) that can be applied to the
composite beam if the dimensions of the beam cross section are
b = 150 mm, d B = 85 mm, and d S = 40 mm (Figure P8.42b/8.43b).
p8.44 A wooden beam (1) is
reinforced on its lower surface by
a steel plate (2) as shown in Figure
P8.44. The dimensions of the cross
section are b 1 = 220 mm, d =
380 mm, b 2 = 160 mm, and t =
20 mm. The elastic moduli of the
wood and steel are E 1 = 12.5 GPa
and E 2 = 200 GPa, respectively.
The allowable bending stresses of
the wood and steel are 7.5 MPa and
150 MPa, respectively. This cross
z
y
section is used for a simply supported beam that spans 9 m. What is
the largest uniformly distributed load that can be applied to the beam?
p8.45 A composite beam consists of a concrete slab (1) that is
rigidly attached to the top flange of a W16 × 40 standard steel shape
(2). The cross section of the beam is shown in Figure P8.45. The
slab has a width b = 48 in., a thickness t = 4 in., and an elastic
modulus of 3,500 ksi. The elastic modulus of the steel shape is
30,000 ksi, and the cross-sectional dimensions are presented in
Appendix B. For a bending moment of M z = +150 kip ⋅ ft, determine
(a) the location of the centroid for the transformed section,
measured upward from point K.
(b) the normal stress at H in the concrete slab.
(c) the normal stress at K in the steel shape.
H
Concrete slab (1)
z
Steel shape (2)
FIGURE p8.45
K
y
b
M
x
Bronze
z
y
Stainless steel
Steel
plate (2)
b
Cross section
Wooden
beam (1)
z
FIGURE p8.44
d
b 1
y
b 2
t
d B
d S
d
t
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