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

z
A
y
FIGURE p6.42/43
L 1
(1)
T B
B
p6.43 The compound shaft shown in Figure P6.42/43 consists of
a solid aluminum segment (1) and a hollow brass segment (2) that
are connected at flange B and securely attached to rigid supports at
A and C. Aluminum segment (1) has a diameter of 0.875 in., a length
L 1 = 45 in., a shear modulus of 3,800 ksi, and an allowable shear
stress of 6 ksi. Brass segment (2) has an outside diameter of 0.68 in.,
a wall thickness of 0.09 in., a length L 2 = 30 in., a shear modulus of
6,400 ksi, and an allowable shear stress of 8 ksi. Determine
(a) the allowable torque T B that can be applied to the compound
shaft at flange B.
(b) the magnitudes of the internal torques in segments (1) and (2).
(c) the rotation angle of flange B that is produced by the
allowable torque T B .
p6.44 In Figure P6.44, shafts (1) and (2) are identical solid 1.25 in.
diameter steel [G = 11,500 ksi] shafts. Shaft (1) is fixed to a rigid
support at A and shaft (2) is fixed to a rigid support at C. Shaft (1)
has a length L 1 = 4.25 ft, and shaft (2) has a length L 2 = 2.75 ft. The
allowable shear stress of the steel is 8,000 psi. The number of teeth
on gears B and D is N B = 72 teeth and N D = 54 teeth, respectively.
Determine the allowable magnitude of the torque T E .
L 2
(2)
C
x
(a) the maximum magnitude of T 0 that may be applied to the
assembly.
(b) the maximum shear stress magnitude in aluminum segments
(1) and (3).
(c) the maximum shear stress magnitude in bronze segment (2).
z
y
A
L 1
(1)
FIGURE p6.45
B
2T 0
(2)
L 2
p6.46 The torsional assembly shown in Figure P6.46 consists of
a hollow aluminum alloy [G = 28 GPa] segment (2) and two brass
[G = 44 GPa] tube segments (1) and (3). The brass segments have
an outside diameter of 114.3 mm, a wall thickness of 6.1 mm, and
lengths L 1 = L 3 = 2,400 mm. The aluminum segment (2) has an
outside diameter of 63.5 mm, a wall thickness of 3.2 mm, and a
length L 2 = 4,200 mm. If concentrated torques T B = 4 kN · m and
T C = 7 kN · m are applied in the directions shown, determine
(a) the maximum shear stress magnitude in brass tube segments
(1) and (3).
(b) the maximum shear stress magnitude in aluminum
segment (2).
(c) the rotation angle of joint C.
C
T 0
L 3
(3)
D
x
y
L 1
A
T E
E
(1)
L 1
N B
B
L 2
(2)
C
z
A
(1)
B
T B
(2)
L 2
T C
C
L 3
(3)
D
x
FIGURE p6.44
N D
p6.45 The torsional assembly shown in Figure P6.45 consists of
solid 2.50 in. diameter aluminum [G = 4,000 ksi] segments (1) and
(3) and a central solid 3.00 in. diameter bronze [G = 6,500 ksi] segment
(2). The segment lengths are L 1 = L 3 = 36 in. and L 2 = 54 in.
Concentrated torques T B = 2T 0 and T C = T 0 are applied to the
assembly at B and C, respectively. If the rotation angle at joint B
must not exceed 3°, determine
D
FIGURE p6.46
p6.47 The gear assembly shown in Figure P6.47 is subjected to
a torque T C = 300 N ⋅ m. Shafts (1) and (2) are solid 30 mm diameter
steel [G = 80 GPa] shafts, and shaft (3) is a solid 35 mm diameter steel
shaft. The shaft lengths are L 1 = L 3 = 1,250 mm and L 2 = 850 mm.
The number of teeth on gears B and E is N B = 60 teeth and N E =
108 teeth, respectively. Determine
(a) the maximum shear stress magnitude in shaft (1).
(b) the maximum shear stress magnitude in shaft (3).
(c) the rotation angle of gear E.
(d) the rotation angle of gear C.
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