Mechanics of Materials (MindTap Course List)
9th Edition
ISBN: 9781337093347
Author: Barry J. Goodno, James M. Gere
Publisher: Cengage Learning
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Chapter 3, Problem 3.3.18P
A vertical pole of solid, circular cross section is twisted by horizontal forces P = 5kN acting at the ends of a rigid horizontal arm AB (see figure part a). The distance from the outside of the pole to the line of action of each force is c = 125 mm (sec figure part b) and the pole height L = 350 mm.
(a)
If the allowable shear stress in the pole is 30 MPa, what is the minimum required diameter dminof the pole?
(b)
What is the torsional stiffness of the pole (kN · m/rad)? Assume that G = 28 GPa.
(c) If two translation al springs, each with stiffness k =2550 kN/m, are added at 2c/5 from A and B (see figure part c), repeat part (a) to find dmin.
Hint: Consider the pole and pair of springs as "springs in parallel."
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A thin uniform rod of mass m and length 2r rests in a smooth hemispherical bowl of radius r. A
moment M
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HINT: It will help you to find the length l of that portion of the rod that remains outside the
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M
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a) How many degrees of freedom does this system have?
b) Write an equation for the virtual work in terms of the angle 0 and the motion of the
center of mass (TF)
c) Derive an equation for the variation in the position of the center of mass (i.e., Sŕƒ)
a. HINT: Use the center of the bowl as the coordinate system origin for the problem.
d) In the case of no applied moment (i.e., M = 0), derive an equation that can be used to
solve for the equilibrium angle of the rod. DO NOT solve the equation
e) In the case of an applied moment (i.e., M:
=
mgr
4
-) derive an equation that can be used to
solve for the equilibrium angle of the rod. DO NOT solve the equation.
f) Can the angle 0 and…
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Chapter 3 Solutions
Mechanics of Materials (MindTap Course List)
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