EBK MATERIALS FOR CIVIL AND CONSTRUCTIO
4th Edition
ISBN: 8220102719569
Author: ZANIEWSKI
Publisher: PEARSON
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Textbook Question
Chapter 4, Problem 4.7QP
An aluminum alloy bar with a rectangular cross section that has a width of 12.5 mm, thickness of 6.25 mm, and a gauge length of 50 mm was tested in tension to fracture according to ASTM E-8 method. The load and deformation data were as shown in Table P4.7. 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. Determine the modulus of elasticity using the best fit approach.
c. Proportional limit.
d. Yield stress at an offset strain of 0.002 m/m.
e. Tangent modulus at a stress of 450 MPa.
f. Secant modulus at a stress of 450 MPa.
TABLE P4.7
Load (kN) | ∆L (mm) | Load (kN) | ∆L (mm) |
0 | 0 | 33.5 | 1.486 |
3.3 | 0.025 | 35.3 | 2.189 |
14.0 | 0.115 | 37.8 | 3.390 |
25.0 | 0.220 | 39.8 | 4.829 |
29.0 | 0.406 | 40.8 | 5.961 |
30.6 | 0.705 | 41.6 | 7.386 |
31.7 | 0.981 | 41.2 | 8.047 |
32.7 | 1.245 |
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An aluminum alloy bar with a rectangular cross section that has a width of
12.5 mm, thickness of 6.25 mm, and a gauge length of 50 mm was tested in
tension to fracture according to ASTM E-8 method. The load and deformation
data were as shown in Table P4.6.
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. Determine
the modulus of elasticity using the best fit approach.
c. Proportional limit.
d. Yield stress at an offset strain of 0.002 m/m.
e. Tangent modulus at a stress of 450 MPa.
f. Secant modulus at a stress of 450 MPa.
TABLE P4.6
Load (kN)
AL (mm)
Load (kN)
AL (mm)
33.5
1.486
3.3
0.025
35.3
2.189
14.0
0.115
37.8
3.390
25.0
0.220
39.8
4.829
29.0
0.406
40.8
5.961
30.6
0.705
41.6
7.386
31.7
0.981
41.2
8.047
32.7
1.245
A round aluminum alloy bar with a 0.25-in. diameter and a 1-in. gauge length was tested in tension to fracture according to ASTM E-8 method. The load and deformation data were as shown in Table P4.8.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. Determine 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. f. If the specimen is loaded to 3200 lb only and then unloaded, what is the permanent change in gauge length? g. When the applied load was 1239 lb, the diameter was measured as 0.249814 in. Determine Poisson’s ratio.
A 19-mm reinforcing steel bar and a gauge length of 75 mm was subjected to ten-
sion, with the results shown in Table P3.27. Using a computer spreadsheet pro-
gram, plot the stress-strain relationship. From the graph, determine the Young's
modulus of the steel and the deformation corresponding to a 150-kN load.
TABLE P3.27
Load, kN
Deformation, mm
54
0.084
163
0.168
284
0.336
330
1.428
366
3.360
Chapter 4 Solutions
EBK MATERIALS FOR CIVIL AND CONSTRUCTIO
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