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 3.8.7P
A stepped shaft ACE is held against rotation at ends A and B and subjected to a torque T0acting at section C(see figure). The two segments of the shaft (AC and CB) have diameters dAand dg, respectively, and polar moments of inertia IpAand IpBrespectively. The shaft has length L and segment AC has length a.
- For what ratio a/L will the maximum shear stresses be the same in both segments of the shaft?
- For what ratio a/L will the internal torques be the same in both segments of the shaft?
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12.
Figure Q12 shows a prospective design for a conveyor roller system, for transferring
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beams, built-in at one end and simply supported at the other, with closely spaced
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a) Using Macaulay notation, carry out an analysis of the problem and calculate
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assumptions used in your analysis.
[20 marks]
b) Comment briefly whether this would be the maximum deflection of the beams
when the crate is centrally located.
2 m
8 m
A
Direction of travel
Figure Q12 (side view, only one beam visible)
Useful information
I for each separate beam = 12 ×10 m²
E for both beams = 210 GPa
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[5 marks]
B
11.
A ring (side view shown in Figure Q11) has a circular solid cross-section of 5 mm
diameter. The ring itself has a radius of R = 100 mm and a very narrow gap at point
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○
P
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Figure Q11
P
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U =
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2EI
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[6 marks]
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Q2(15 Marks): From Fig. 2, Determine
(a) mass equivalent in term x2, (b)
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x2. Note: (1) J Cylinder =
mcr?
J link
(2)
2
3
Pulley, mass moment of
inertia J
Rigid link 1 (mass m₁),
rotates with pulley.
about O
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Adherence to the symbols as in the question
152 153
xx(1)
Fig. (2)
m
k₁
nimmunizmu
Rigid link 2 (mass m₂)
Chapter 3 Solutions
Mechanics of Materials (MindTap Course List)
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