Mechanics of Materials (MindTap Course List)
9th Edition
ISBN: 9781337093347
Author: Barry J. Goodno, James M. Gere
Publisher: Cengage Learning
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Textbook Question
Chapter 3, Problem 3.9.12P
A heavy flywheel rotating at n revolutions per minute is rigidly attached to the end of a shaft of diameter d (see figure). If the bearing at A suddenly freezes, what will be the maximum angle of twist <£of the shaft? What is the corresponding maximum shear stress in the shaft?
(Let L = length of the shaft, G = shear modulus of elasticity, and / = mass moment of inertia of the flywheel about the axis of the shaft. Also, disregard friction in the bearings at Sand Cand disregard the mass of the shaft.)
Hint: Equate the kinetic energy of the rotating flywheel to the strain energy of the shaft.
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Students have asked these similar questions
1. A maintenance engineer is dimensioning a motor that will drive a shaft at 12 Hz and
provide 20 kW of power (see figure). Determine:
(a) If the shaft has a diameter d of 30 mm, what is the maximum shear stress Tmax in
the shaft?
(b) If the maximum allowable shear stress is 40 MPa, what diameter d is needed for
the shaft?
c) What is the effect of the maximum shear stress on the system?
(d) What is the ratio of the diameter and the tension in the system?
For items a and b, justify your answer
20 kW
12 Hz
1. A maintenance engineer is dimensioning a motor that will drive a shaft at 12 Hz and
provide 20 kW of power (see figure). Determine:
(a) If the shaft has a diameter d of 30 mm, what is the maximum shear stress Tmax in
the shaft?
(b) If the maximum allowable shear stress is 40 MPa, what diameter d is needed for
the shaft?
c) What is the effect of the maximum shear stress on the system?
(d) What is the ratio of the diameter and the voltage in the system?
For items a and b, justify your answer
20 kW
12 Hz
4 kN
3 kN
375 mm
B
375 mm
750 mm
As shown in the figure, the shaft is supported by bearings A and B and is subjected
to a concentrated load.
Material A-36 steel
Diameter: 50 mm
Find the maximum displacement and maximum stress.
1) Determine the theoretical stress value using the stress formula due to bending load.
2) Model with a solid model to obtain stress values and displacements at
Creosimulate.
3) Model with Beam model to obtain stress values and displacements at Creosimulate.
Chapter 3 Solutions
Mechanics of Materials (MindTap Course List)
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