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 3.3.14P
The steel axle of a large winch on an ocean liner is subjected to a torque of 1.65 kN · m (see figure).
- What is the minimum required diameter dminif the allowable shear stress is 48 M Pa and the allowable rate of twist is 0.75º/m? (Assume that the shear modulus of elasticity is 80 G Pa.)
- Repeat part (a) if the shaft is now hollow with an inner diameter of 5d/8, Compare dminvalues to corresponding values from part (a)
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12.
Figure Q12 shows a prospective design for a conveyor roller system, for transferring
crates, one at a time. The system is made up of two parallel rectangular steel
beams, built-in at one end and simply supported at the other, with closely spaced
rollers mounted in-between, for the crate to pass over.
a) Using Macaulay notation, carry out an analysis of the problem and calculate
the deflection of the mid-length point of the beams when the crate is
centrally located, midway between A and B. State any important
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
Weight of one crate = 800 N
[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
A
Figure Q11
P
a) Show that the total strain energy of the ring due to the applied forces is:
U =
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2EI
[12 marks]
b) Find the maximum bending stress produced if forces of P = 8 N are applied.
[6 marks]
c) What minimum force P would cause the material in the ring to yield and at
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E for the ring material = 75 GPa
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[7 marks]
Q2(15 Marks): From Fig. 2, Determine
(a) mass equivalent in term x2, (b)
stiffness equivalent in term x2, and (c) the
natural frequency for the system in term
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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