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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Problem 3
•
Compute the coefficient matrix and the right-hand side of the n-parameter Ritz approximation of the
equation
d
du
(1+x)·
= 0 for 0 < x < 1
dx
dx
u (0)
=
0, u(1) = 1
Use algebraic polynomials for the approximation functions. Specialize your result for n = 2 and compute the
Ritz coefficients.
Chapter 3 Solutions
Mechanics of Materials (MindTap Course List)
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