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

p6.15 Figure P6.15 shows a cutaway view of an assembly in
which a solid bronze [G = 6,500 ksi] rod (1) is fitted inside of an
aluminum alloy [G = 4,000 ksi] tube (2). The tube is attached to a
fixed plate at C, and both the rod and the tube are welded to a rigid
end plate at A. The rod diameter is d 1 = 1.75 in. The outside diameter
of the tube is D 2 = 3.00 in., and its wall thickness is t 2 = 0.125 in.
Overall dimensions of the assembly are a = 40 in. and b = 8 in. The
allowable shear stresses for the bronze and aluminum materials are
10,000 psi and 8,000 psi, respectively. Further, the rotation angle of
end B must be limited to a magnitude of 5°. On the basis of these
constraints, what is the maximum torque T B that can be applied at
end B?
D 2
End
plate
A
FIGURE p6.15
Fixed
t 2 plate
d 1
Tube (2)
a
Rod (1)
C
b
T B
B
p6.17 The copper pipe shown in Figure P6.17 has an outside
diameter of 70 mm and a wall thickness of 5 mm. The pipe is subjected
to a uniformly distributed torque t = 500 N ⋅ m/m along its
entire length. Using a = 1.0 m, b = 1.6 m, and c = 3.2 m, calculate
(a) the shear stress at A on the outer surface of the pipe.
(b) the shear stress at B on the outer surface of the pipe.
a
y
T B
FIGURE p6.16
b
C
B
x
A
(2)
T C
(1)
L 2
L 1
z
p6.16 A compound shaft (Figure P6.16) consists of a titanium alloy
[G = 6,200 ksi] tube (1) and a solid stainless steel [G = 11,500 ksi]
shaft (2). Tube (1) has a length L 1 = 40 in., an outside diameter D 1 =
1.75 in., and a wall thickness t 1 = 0.125 in. Shaft (2) has a length
L 2 = 50 in. and a diameter d 2 = 1.25 in. If an external torque T B =
580 lb ⋅ ft acts at pulley B in the direction shown, calculate the
torque T C required at pulley C so that the rotation angle of pulley C
relative to A is zero.
A
FIGURE p6.17
B
t
c
C
x
6.7 Gears in Torsion Assemblies
154
Gears are a fundamental component found in many types of mechanisms and devices—
particularly those devices which are driven by motors or engines. Gears are used for many
purposes, such as
• transmitting torque from one shaft to another,
• increasing or decreasing torque in a shaft,
• increasing or decreasing the rate of rotation of a shaft,
• changing the rotation direction of two shafts, and
• changing rotational motion from one orientation to another—for instance, changing
rotation about a horizontal axis to rotation about a vertical axis.