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

pulley is a belt having tensions F 1 = 120 lb and F 2 = 480 lb. If the
shaft turns at 180 rpm, calculate
(a) the horsepower being transmitted by the shaft.
(b) the maximum shear stress in the shaft.
p6.31 A conveyor belt is driven by a 20 kW motor turning at 9 Hz.
Through a series of gears that reduce the speed, the motor drives the
belt drum shaft at a speed of 0.5 Hz. If the allowable shear stress is
70 MPa and both shafts are solid, calculate
(a) the required diameter of the motor shaft.
(b) the required diameter of the belt drum shaft.
p6.32 A motor at A supplies 25 hp to the system shown in Figure
P6.32/33. Sixty percent of the power supplied by the motor is
taken off by gear C, and the remaining 40 percent of the power is
taken off by gear D. Power shaft segments (1) and (2) are hollow
steel tubes with an outside diameter of 1.50 in. and a wall thickness
of 0.1875 in. The diameters of pulleys A and B are D A = 4 in. and
D B = 14 in., respectively. If the allowable shear stress for the steel
tubes is 8,000 psi, what is the slowest permissible rotation speed for
the motor?
D B
B
F 2
F 1
D
FIGURE p6.30
(1)
C
FIGURE p6.32/33
D A
A
Shaft
Pulley
p6.33 A motor supplies sufficient power to the system shown in
Figure P6.32/33 so that gears C and D provide torques T C = 2.6 kN ⋅ m
and T D = 1.2 kN ⋅ m, respectively, to machinery in a factory. Power
shaft segments (1) and (2) consist of a hollow steel tube with an
T C
(2)
D
d
T D
outside diameter of 90 mm and a wall thickness of 8 mm. The diameters
of pulleys A and B are D A = 100 mm and D B = 360 mm,
respectively. If the power shaft [i.e., segments (1) and (2)] rotates at
160 rpm, determine
(a) the maximum shear stress in power shaft segments (1) and (2).
(b) the power (in kW) that must be provided by the motor.
(c) the rotation speed (in rpm).
(d) the torque applied to pulley A by the motor.
p6.34 In Figure P6.34/35, the motor at A produces 30 kW of
power while turning at 8.0 Hz. The gears at A and B connecting the
motor to line shaft BCDE have N A = 30 teeth and N B = 96 teeth,
respectively. On the line shaft, gear C takes off P C = 50% of the
power, gear D removes P D = 30%, and gear E removes the remainder.
The line shaft will be solid, all segments will have the same
diameter, and the shaft will be made of steel [G = 80 GPa]. The
lengths of the segments are L 1 = 4.6 m, L 2 = 2.3 m, and L 3 = 2.3 m,
and the bearings shown permit free rotation of the shaft. Determine
the minimum diameter required for line shaft BCDE for an allowable
shear stress of 65 MPa and an allowable rotation angle of 10°
of gear E relative to gear B.
N B
N A
B
A
(1)
L 1
FIGURE p6.34/35
C
p6.35 In Figure P6.34/35, the motor at A produces 25 hp while
turning at 2,600 rpm. The gears at A and B connecting the motor to
line shaft BCDE have N A = 30 teeth and N B = 140 teeth, respectively.
On the shaft, gear C takes off P C = 40% of the power, gear D
removes P D = 40%, and gear E removes the remainder. Line shaft
BCDE is a solid 1.25 in. diameter shaft made of an aluminum alloy
that has a shear modulus of 3,800 ksi. The lengths of the segments
are L 1 = 80 in., L 2 = 42 in., and L 3 = 36 in. The bearings shown
permit free rotation of the line shaft. Calculate
(a) the magnitude of the maximum shear stress in each shaft
segment.
(b) the rotation angle of gear E with respect to gear B.
P C
p6.36 The motor at A is required to provide 40 hp of power to
line shaft BCDE shown in Figure P6.36/37, turning gears B and E
at 900 rpm. Gear B removes 70% of the power from the line shaft,
and gear E removes 30%. Shafts (1) and (2) are solid aluminum
alloy shafts with an outside diameter of 1.25 in. and a shear modulus
of 3,800 ksi. Shaft (3) is a solid steel shaft that has an outside
diameter of 0.75 in. and a shear modulus of 11,600 ksi.
The shaft lengths are L 1 = 8.25 ft, L 2 = 4.25 ft, and L 3 = 7.0 ft.
The diameters of pulleys A and C are D A = 2 in. and D C = 10 in.,
L 2
D
P D
(2) (3)
L 3
PE
E
x
165