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

pRoBLEmS
p6.1 A solid circular steel shaft having an outside diameter d =
60 mm is subjected to a pure torque T = 2,400 N ⋅ m. What is the
maximum shear stress in the shaft?
p6.2 A hollow stainless steel shaft with an outside diameter of
42 mm and a wall thickness of 4 mm has an allowable shear stress
of 100 MPa. Determine the maximum torque T that may be applied
to the shaft.
p6.3 What is the minimum diameter required for a solid steel
shaft to transmit a torque of 20,000 lb ⋅ ft if the maximum shear
stress in the shaft must not exceed 8,000 psi?
p6.4 The compound shaft shown in Figure P6.4 consists of two
steel [G = 80 GPa] pipe segments. The shaft is subjected to external
torques T B and T C that act in the directions shown. Segment (1) has
an outside diameter of 206 mm and a wall thickness of 10 mm. Segment
(2) has an outside diameter of 138 mm and a wall thickness of
14 mm. The torque is known to have a magnitude of T C = 22 kN ⋅ m.
The shear strain in segment (1) is measured as 500 mrad. Determine
the magnitude of the external torque T B .
A
y
(1)
FIGURE p6.4
T B
p6.5 A solid constant-diameter circular shaft is subjected to
torques T A = 420 lb ⋅ ft, T B = 1,040 lb ⋅ ft, T C = 850 lb ⋅ ft, and T D =
230 lb ⋅ ft, acting in the directions shown in Figure 6.5. The bearings
shown allow the shaft to turn freely.
(a) Plot a torque diagram showing the internal torque in
segments (1), (2), and (3) of the shaft. Use the sign
convention presented in Section 6.6.
(b) If the allowable shear stress in the shaft is 6,000 psi, what is
the minimum acceptable diameter for the shaft?
B
(2)
T C
C
x
p6.6 The nut on a bolt is tightened by applying a force P = 16 lb
to the end of a wrench at a distance a = 6 in. from the axis of the
bolt, as shown in Figure P6.6. The body of the bolt has an outside
diameter d = 0.375 in. What is the maximum torsional shear stress
in the body of the bolt?
d
FIGURE p6.6
p6.7 A solid circular bronze [G = 6,500 ksi] shaft 5 ft long and
1.375 in. in diameter carries a torque of 80 lb ⋅ ft. For this shaft,
determine
(a) the maximum shear stress.
(b) the magnitude of the angle of twist.
p6.8 A solid titanium alloy [G = 114 GPa] shaft that is 900 mm
long will be subjected to a pure torque T = 160 N ⋅ m. Determine the
minimum diameter required if the shear stress must not exceed
165 MPa and the angle of twist must not exceed 5°. Report both the
maximum shear stress τ and the angle of twist φ at this minimum
diameter.
p6.9 A compound shaft (Figure P6.9) consists of two segments.
Segment (1) is a solid bronze [G = 45 GPa] shaft with an outside
diameter of 80 mm, a length L 1 = 780 mm, and an allowable shear
stress of 65 MPa. Segment (2) is a solid aluminum alloy [G =
26 GPa ksi] shaft with an outside diameter of 95 mm, a length L 2 =
620 mm, and an allowable shear stress of 40 MPa. The maximum
rotation angle at the free end of the compound shaft must be limited
to φ A ≤ 2.5°. Determine the magnitude of the largest torque T A that
may be applied at A.
a
P
y
y
T B
T A
z
T D
x
D
FIGURE p6.5
(3)
C
T C
(2)
B
(1)
A
T A
x
A
FIGURE p6.9
(1)
L 1
B
(2)
L 2
C
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