Pearson eText for Materials for Civil and Construction Engineers -- Instant Access (Pearson+)
4th Edition
ISBN: 9780137505586
Author: Michael Mamlouk, John Zaniewski
Publisher: PEARSON+
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Textbook Question
Chapter 1, Problem 1.50QP
Briefly discuss the concept behind each of the following measuring devices:
a. LVDT
b. strain gauge
c. proving ring
d. load cell
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A tensile test was performed on a metal specimen having a circular cross section with a diameter of 0.510 inch. For each increment of load applied, the strain was directly determined by means of a strain gage attached to the specimen. The results are shown in Table 1.1.a. Prepare a table of stress and strainb. Plot these data to obtain a stress-strain curve. Do not connect the data points; draw a best-fit straight line through them.c. Determine the modulus of elasticity as the slope of the best-fit lineLoad (Ib)Strain × 106 (in./in.)0025037.150070.31000129.11500230.12000259.42500372.43000457.73500586.5
1.5-7
The data shown in the table were obtained from a tensile test of a metal specimen with
a rectangular cross section of 0.2 in.² in area and a gage length (the length over which
the elongation is measured) of 2.000 inches.
a. Generate a table of stress and strain values.
b. Plot these values and draw a best-fit line to obtain a stress-strain curve.
c. Determine the modulus of elasticity from the slope of the linear portion of the curve.
Load
(kips)
0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
5.5
50
6.0
6.5
Elongation × 10³
(in.)
0
0.160
0.352
0.706
1.012
1.434
1.712
1.986
2.286
2.612
2.938
3.274
3.632
3.976
Load
(kips)
7.0
7.5
8.0
8.5
9.0
9.5
10.0
10.5
11.0
11.5
12.0
12.5
13
Elongation × 10³
(in.)
4.386
4.640
4.988
5.432
5.862
6.362
7.304
8.072
9.044
11.310
14.120
20.044
29.106
A tensile test specimen having a diameter of 10 mm and a gage length of 50 mm was tested to fracture. The stress-strain curve from the tension test is shown below. The lower plot is the expanded region OAB and associated with the strain values given in the lower scale. Showing your points and construction on graphs and the associated calculations, determine the following quantities.
Proportional limit: _____
Rupture stress: _____
Secant modulus at stress level of 420 MPa: _____
Tangent modulus at stress level of 420 MPa: _____
Determine the plastic strain at stress level of 420 MPa: _____
If the shear modulus of the material is 55GPa, determine the Poisson’s ratio assuming the material is isotropic. _____
Determine the axial force acting on the specimen when it is extended by 0.2 mm. _____
Chapter 1 Solutions
Pearson eText for Materials for Civil and Construction Engineers -- Instant Access (Pearson+)
Ch. 1 - State three examples of a static load application...Ch. 1 - A material has the stressstrain behavior shown in...Ch. 1 - A tensile load of 50.000 lb is applied to a metal...Ch. 1 - A tensile load of 190 kN is applied to a round...Ch. 1 - A cylinder with a 6.0 in. diameter and 12.0 in....Ch. 1 - A metal rod with 0.5 inch diameter is subjected to...Ch. 1 - A rectangular block of aluminum 30 mm 60 mm 90...Ch. 1 - A plastic cube with a 4 in. 4 in. 4 in. is...Ch. 1 - A material has a stressstrain relationship that...Ch. 1 - On a graph, show the stressstrain relationship...
Ch. 1 - The rectangular block shown in Figure P1.11 is...Ch. 1 - The rectangular metal block shown in Figure P1.11...Ch. 1 - A cylindrical rod with a length of 380 mm and a...Ch. 1 - A cylindrical rod with a radius of 0.3 in. and a...Ch. 1 - A cylindrical rod with a diameter of 15.24 mm and...Ch. 1 - The stressstrain relationship shown in Figure...Ch. 1 - A tension test performed on a metal specimen to...Ch. 1 - An alloy has a yield strength of 41 ksi, a tensile...Ch. 1 - Prob. 1.21QPCh. 1 - Figure P1.22 shows (i) elasticperfectly plastic...Ch. 1 - An elastoplastic material with strain hardening...Ch. 1 - A brace alloy rod having a cross sectional area of...Ch. 1 - A brass alloy rod having a cross sectional area of...Ch. 1 - A copper rod with a diameter of 19 mm, modulus of...Ch. 1 - A copper rod with a diameter of 0.5 in., modulus...Ch. 1 - Define the following material behavior and provide...Ch. 1 - An asphalt concrete cylindrical specimen with a...Ch. 1 - What are the differences between modulus of...Ch. 1 - Prob. 1.33QPCh. 1 - A metal rod having a diameter of 10 mm is...Ch. 1 - What is the factor of safety? On what basis is its...Ch. 1 - Prob. 1.36QPCh. 1 - Prob. 1.37QPCh. 1 - A steel rod, which is free to move, has a length...Ch. 1 - In Problem 1.38, if the rod is snugly fitted...Ch. 1 - A 4-m-long steel plate with a rectangular cross...Ch. 1 - Estimate the tensile strength required to prevent...Ch. 1 - Prob. 1.42QPCh. 1 - Briefly discuss the variability of construction...Ch. 1 - In order to evaluate the properties of a material,...Ch. 1 - A contractor claims that the mean compressive...Ch. 1 - A contractor claims that the mean compressive...Ch. 1 - Prob. 1.47QPCh. 1 - Prob. 1.48QPCh. 1 - Prob. 1.49QPCh. 1 - Briefly discuss the concept behind each of the...Ch. 1 - Referring to the dial gauge shown in Figure P1.51,...Ch. 1 - Repeat Problem 1.51 using the dial gauge shown in...Ch. 1 - Measurements should be reported to the nearest...Ch. 1 - During calibration of an LVDT, the data shown in...Ch. 1 - During calibration of an LVDT, the data shown in...
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- Question No.1 : A 32-mm rebar with a gauge length of 200 mm was subjected to tension to fracture according to ASTM E-8 method. The load and deformation data were as shown in table below. Using calculations and diagram 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. e. Ultimate strength. f. Modulus of resilience and toughness. g. If the rebar is loaded to 390 kN only and then unloaded, what is the permanent change in length? Load (kN) Displacement (mm) Load (kN) Displacement (mm) 472.9 8.4 62.2 0.1 487.1 9.7 188.9 0.2 496.4 11.1 329.8 0.4 505.7 12.4 383.4 1.7 512.8 13.7 426.0 4.0 522.6 15.3 447.3 5.9 532.4 18.5 462.5 7.2 525.9 22.4arrow_forwardA round steel bar with a diameter of 12mm and a gauge length of 0.5 mm was subjected to tension to rupture following ASTM E-8 test procedure. The load and deformation data were as shown in Table. Using a spreadsheet program obtain the following: A plot of the stress–strain relationship. Label the axes and show units. A plot of the linear portion of the stress–strain relationship. Determine modulus of elasticity using the best fit approach. Proportional limit. Yield stress. Ultimate strength. When the applied load was 18kN, the diameter was measured as12.7mm Determine Poisson’s ratio. After the rod was broken, the two parts were put together and the diameter at the neck was measured as 10.6 mm. What is the true stress value at fracture? Is the true stress at fracture larger or smaller than the engineering stress at fracture? Why? Do you expect the true strain at fracture to be larger or smaller than the engineering strain at fracture? Why?arrow_forward2. A steel bar, whose cross section is 0.55 inch by 4.05 inches, was tested in tension. An axial load of P = 30,500 lb. produced a deformation of 0.105 inch over a gauge length of 2.05 inches and a decrease of 0.0075 inch in the 0.55-inch thickness of the bar. Determine the lateral strain. * Your answer Determine the axial strain. Your answer Determine the Poisson's ratio v. * Your answer Determine the decrease in the 4.05-in. cross-sectional dimension (in inches). * Your answerarrow_forward
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