Name:
Practice Problem Assignment #1
E MCH 315 Summer 2018
Instructions:
1. Complete each problem to the best of your ability. The assignments are meant to help you
prepare for the exam, so effort put into understanding the practice problems will pay dividends
on the exams.
2. Work neatly. Use extra paper if necessary. Unclear or illegible work cannot be given credit.
3. Write your name on each page.
4. Show all of the steps that led your solution.
5. Include all units, e.g. Pa or psi for pressure, meters or feet for length, etc.
6. Circle your final answer.
Questions/Concerns:
1. Refer to the three course textbooks:
a. Mechanical Response of Engineering Materials by Queeney & Segall is the primary
textbook and will be extremely useful for the practice problem assignments.
b. Mechanics of Materials by Hibbeler is an excellent resource for reviewing stress, strain,
Hooke’s law, Mohr’s circle, and other strength of materials topics.
c. Mechanical Behavior of Materials by Dowling is an additional reference for yielding,
fatigue, fracture mechanics, viscoelasticity, and creep.
2. Contact one of the teaching assistants or Professor Passmore during office hours or by email
with questions.
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Name:
4.1)
A standard specimen that is 0.505 inches in diameter with gage length of 2 inches was used for a
tensile test. The following data was recorded for this aluminum alloy with fracture occurring at
an elongation of 0.018 inches:
Load
(lb.)
0
1000
2100
3200
4200
5200
6200
Elongation
(in.)
0
0.001
0.002
0.003
0.004
0.005
0.006
Load
(lb.)
7200
8000
8300
8600
8700
8750
8800
Elongation
(in.)
0.007
0.008
0.009
0.010
0.012
0.014
0.018
Plot the stress-strain diagram and determine:
(a)
(b)
(c)
(d)
(e)
(f)
The approximate proportional limit
The yield strength based on the 0.2% offset method
The modulus of elasticity
The modulus of resilience
The tensile strength
The percent elongation
Note: it may be advisable to plot two graphs: one to emphasize the elastic and near-yield region and the
other showing the full response over the entire strain range.
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Name:
3
Name:
4.3)
Shown below is the stress-strain response curve for cartridge brass (70% Cu, 30% Zn, or UNS alloy
C26000) in the HO1 temper.
More refined data in the elastic and near-yield regime are given as:
Stress (psi)
13072
26144
39200
44120
47390
Strain
0.00108
0.00217
0.0033
0.0055
0.013
Using this data, calculate the following:
(a) Modulus of Elasticity
(b) Proportional Limit
(c) 0.2% Offset Yield Strength
(d) Ultimate Tensile Strength
(e) Modulus of Resilience
(f) Toughness
(g) Percent Elongation
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5
Name:
4.4) For the aluminum alloy 5052, in the - 0 temper state shown below, find:
(a) Tensile strength
(b) Percent elongation
(c) Toughness
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Name:
4.6)
A member made of cold-worked columbium is 15 in. long, and has a rectangular cross-section ¼
in. by ¾ in. For a tensile load of 5000 lb., determine the total change in:
(a) Length
(b) Cross-sectional dimensions
(c) Volume
For the analysis, assume elastic behavior with E = 22.7 x 106 psi and  = 0.28.
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Name:
4.8)
Using the following data for rubber, construct a stress-strain diagram and determine:
(a) Secant modulus and the tangent modulus at a service stress of 200 psi
(b) Resilience
(c) Hysteresis loss per cycle in in.-lb. / in.3
LOADING
Stress (psi)
0
60
120
180
240
300
UNLOADING
Strain (in./in.)
0.00
0.40
1.25
2.42
3.55
4.25
Stress (psi)
300
240
130
120
100
60
0
Strain (in./in.)
4.25
4.15
3.90
3.13
2.00
.070
0.00
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Name:
4.13)
Experiments show that for ductile metals, there is no volume change in the plastic range of
straining. Neglecting the small elastic volume change that would occur from the total strain,
compute the value of Poisson’s ratio for zero volume change. Subtle hint: do a thought
experiment wherein you apply an axial strain of your choice, observe a transverse strain,
calculate the before-and-after volumes, and demand the change to be zero!
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