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

m6.21 A composite torsion member consists of two solid shafts
joined at flange B. Shafts (1) and (2) are attached to rigid supports
at A and C, respectively. Using the allowable shear stresses indicated
on the sketch, determine the maximum torque T that may be
applied to flange B in the direction shown. Determine the maximum
shear stress in each shaft and the rotation angle of flange B at
the maximum torque.
FIGURE m6.21
pRoBLEmS
p6.39 A hollow circular cold-rolled stainless steel [G 1 =
12,500 ksi] tube (1) with an outside diameter of 2.25 in. and an
inside diameter of 2.00 in. is securely shrink fitted to a solid 2.00 in.
diameter cold-rolled bronze [G 2 = 6,500 ksi] core (2) as shown in
Figure P6.39/40. The length of the assembly is L = 20 in. The allowable
shear stress of tube (1) is 60 ksi, and the allowable shear
stress of core (2) is 25 ksi. Determine
(a) the allowable torque T that can be applied to the tube-andcore
assembly.
(b) the corresponding torques produced in tube (1) and core (2).
(c) the angle of twist produced in the assembly by the allowable
torque T.
T
A
(1)
FIGURE p6.39/40
p6.40 The composite shaft shown in Figure P6.39/40 consists of
an aluminum alloy tube (1) securely bonded to an inner brass core
(2). The aluminum tube has an outside diameter of 60 mm, an
inside diameter of 50 mm, and a shear modulus G 1 = 26 GPa. The
solid brass core has a diameter of 50 mm and a shear modulus G 2 =
44 GPa. The length of the assembly is L = 600 mm. If the composite
shaft is subjected to a torque T = 5.0 kN ⋅ m, determine
(a) the maximum shear stresses in the aluminum tube and the
brass core.
(b) the rotation angle of end B relative to end A.
(2)
L
p6.41 A solid 2.50 in. diameter cold-rolled brass [G = 6,400 ksi]
shaft that is L 1 + L 2 = 115 in. long extends through and is completely
bonded to a hollow aluminum [G = 3,800] tube, as shown in
Figure P6.41. The aluminum tube (1) has an outside diameter of
3.50 in., an inside diameter of 2.50 in., and a length L 1 = 70 in. Both
B
T
the brass shaft and the aluminum tube are securely attached to the
wall support at A. External torques in the directions shown are
applied at B and C. The torque magnitudes are T B = 6.0 kip ⋅ ft and
T C = 2.5 kip ⋅ ft, respectively. After T B and T C are applied to the
composite shaft, determine
(a) the maximum shear stress magnitude in aluminum tube (1).
(b) the maximum shear stress magnitude in brass shaft segment (2).
(c) the maximum shear stress magnitude in brass shaft segment (3).
(d) the rotation angle of joint B.
(e) the rotation angle of end C.
z
L 1
A
y
FIGURE p6.41
p6.42 The compound shaft shown in Figure P6.42/43 consists
of two pipes that are connected at flange B and securely attached
to rigid walls at A and C. Pipe (1) is made of an aluminum alloy
[G = 26 GPa]. It has an outside diameter of 140 mm, a wall thickness
of 7 mm, and a length L 1 = 9.0 m. Pipe (2) is made of steel
[G = 80 GPa]. It has an outside diameter of 100 mm, a wall thickness
of 6 mm, and a length L 2 = 7.5 m. If a concentrated torque of 15
kN ⋅ m is applied to flange B, determine
(a) the maximum shear stress magnitudes in pipes (1) and (2).
(b) the rotation angle of flange B relative to support A.
(1)
(2)
L 3
B
T B
(3)
C
T C
x
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