Civil Engineering Reference
In-Depth Information
Using a spreadsheet program, obtain the following:
a. A plot of the stress-strain relationship. Label the axes and show
units.
b. A plot of the linear portion of the stress-strain relationship. De-
termine modulus of elasticity using the best fit approach.
c. Proportional limit.
d. Yield stress at an offset strain of 0.002 in/in.
e. Initial tangent modulus:
1. If the specimen is loaded to 3200 lb only and then unloaded,
what is the permanent change in gage length?
2. When the applied load was 1239 lb, the diameter was mea-
sured as 0.249814 inches. Determine Poisson's ratio.
4.7
An aluminum alloy rod has a circular cross section with a diameter
of 8 millimeters. This rod is subjected to a tensile load of 4 kN. As-
sume
a. What will be the lateral strain if Poisson's ratio is 0.33?
b. What will be the diameter after load application?
E
=
69 GPa.
4.8
A 3003-H14 aluminum alloy rod with 0.5 in. diameter is subjected to
2000-lb tensile load. Calculate the resulting diameter of the rod. If
the rod is subjected to a compressive load of 2000 lb, what will be
the diameter of the rod? Assume that the modulus of elasticity is
10,000 ksi, Poisson's ratio is 0.33, and the yield strength is 21 ksi.
4.9
The stress-strain relation of an aluminum alloy bar having a length
of 2 m and a diameter of 10 mm is expressed by the equation
b
9
d
s
70,000
3
7
s
270
e =
c
1
+
a
where is in MPa. If the rod is axially loaded by a tensile force of 20
kN and then unloaded, what is the permanent deformation of the bar?
4.10 A tension test was performed on an aluminum alloy specimen to frac-
ture. The original diameter of the specimen is 0.5 in. and the gage
length is 2.0 in. The information obtained from this experiment
consists of applied tensile load (
P
) and increase in length The
results are tabulated in Table P4.10. Using a spreadsheet program, com-
plete the table by calculating engineering stress
s
1
¢L
2
.
1
s
2
and engineering
strain
1
e
2
.
Determine the toughness of the material
1
u
t
2
by calculating
the area under the stress-strain curve, namely,
e
f
u
t
=
3
s de
0
where is the strain at fracture. The preceding integral can be ap-
proximated numerically using a trapezoidal integration technique:
e
f
n
n
1
2
u
t
=
a
u
i
=
a
1
s
i
+ s
i - 1
21
e
i
- e
i - 1
2
i = 1
i = 1
Search WWH ::
Custom Search