CVE 220 Mechanics of Material Lecture No. 9 S. 2002

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CVE 220 Mechanics of MaterialLecture No. 9 (S.
2002)

• Gere Section 3.6-3.8
• James Hu

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Reading

• pp. 220-231

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Maximum Normal Strain (review)
normal strain in the 45o direction
from geometry (section 3-6)
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Law of Cosine
g
b
a
a
b
c
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Derivation of emax g/2
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Relationship Between E, G, and n
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Circular Shafts
Circular shafts to transmit mechanical power
from one device to
another
W Work
W T y
y Angle of rotation in radian
T torque exerted on the shaft
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Power
Power the rate at which work is done
f frequency in Hz.
(revolutions per second)
n rpm (revolutions per minute)
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Units for Power
1 watt one joule (N-m) per second
U.S. engineering practice horsepower (hp)
1 horsepower 550 ft-lb/s
1 horsepower 746 watts
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Example 3-8
Find maximum shear stress tmax in the shaft
the angle of twist between A and C, fAC
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Example 3-8 solution
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Example 3-8 solution (contd.)
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Statically Determinate/Indeterminate (review)

• Statically determinate reactions and internal
  forces can be determined solely from the
  free-body diagram.
• Statically indeterminate reactions and internal
  forces cannot be determined by statics alone. The
  calculation of the structural deformation is an
  essential ingredient in the analysis

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Equation of Compatibility (review)
statically determinate
statically indeterminate
equation of equilibrium
equation of compatibility
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Analysis statically indeterminate bar (review)
force-displacement relationship
dAB dAC dCB 0
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Analysis statically indeterminate bar (review)
(static equation)
(geometric equation)
force-displacement relation
(constitutive relations)
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Example 2-5 (review)
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Example 2-5 (contd.) (review)
equation of equilibrium
equation of compatibility
ds dc
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Statically Indeterminate Torsional Members
Equation of equilibrium
Equation of compatibility
Torque-displacement relations
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Example 3-9
Textbook did not use the concept of internal
forces
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Results of Two Scenarios
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Homework Assignment 5

• Problem 3.7-4 (page 261)
• Problem 3.7-8 (page 261)
• Problem 3.8-5 (page 263)
• Problem 3.8-11 (page 264)

Due 2/28/2002
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Problem 3.8-5
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Problem 3.8-11