Page 161 - Shigley's Mechanical Engineering Design

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136 Mechanical Engineering Design
spring rate. Compare these with a single strip of cross section 30 mm by 4 mm. Solve the prob-
lem two ways: (a) using Eqs. (3–40) and (3–41), and (b) using Eq. (3–47). Compare and discuss
your results
2 mm
4 mm
Problem 3–56
T
30 mm

3–57 Using a maximum allowable shear stress of 70 MPa, find the shaft diameter needed to transmit
40 kW when
(a) The shaft speed is 2500 rev/min.
(b) The shaft speed is 250 rev/min.
3–58 Repeat Prob. 3–57 with an allowable shear stress of 20 kpsi and a power of 50 hp.
3–59 Using an allowable shear stress of 50 MPa, determine the power that can be transmitted at 2000 rpm
through a shaft with a 30-mm diameter.
3–60 A 20-mm-diameter steel bar is to be used as a torsion spring. If the torsional stress in the bar is
not to exceed 110 MPa when one end is twisted through an angle of 15°, what must be the length
of the bar?
3
3–61 A 2-ft-long steel bar with a -in diameter is to be used as a torsion spring. If the torsional stress
4
in the bar is not to exceed 30 kpsi, what is the maximum angle of twist of the bar?
3–62 A 40-mm-diameter solid steel shaft, used as a torque transmitter, is replaced with a hollow
shaft having a 40-mm OD and a 36-mm ID. If both materials have the same strength, what is
the percentage reduction in torque transmission? What is the percentage reduction in shaft
weight?
3–63 Generalize Prob. 3–62 for a solid shaft of diameter d replaced with a hollow shaft of the same
material with an outside diameter d, and an inside diameter that is a fraction of the outside diam-
eter, x × d, where x is any fraction between zero and one. Obtain expressions for percentage
reduction in torque transmission and percentage reduction in weight in terms of only x. Notice
that the length and diameter of the shaft, and the material, are not needed for this comparison.
Plot both results on the same axis for the range 0 < x < 1. From the plot, what is the approxi-
mate value of x to obtain the greatest difference between the percent decrease in weight and the
percent decrease in torque?
3–64 A hollow steel shaft is to transmit 4200 N · m of torque and is to be sized so that the torsional
stress does not exceed 120 MPa.
(a) If the inside diameter is 70 percent of the outside diameter, what size shaft should be used?
Use preferred sizes.
(b) What is the stress on the inside of the shaft when full torque is applied?
3–65 The figure shows an endless-belt conveyor drive roll. The roll has a diameter 120 mm and is
driven at 10 rev/min by a geared-motor source rated at 1.5 kW. Determine a suitable shaft diam-
eter d C for an allowable torsional stress of 80 MPa.
(a) What would be the stress in the shaft you have sized if the motor starting torque is twice the
running torque?
(b) Is bending stress likely to be a problem? What is the effect of different roll lengths B on
bending?