
Concept explainers
The elastic portion of the tension stress-strain diagram for an aluminum alloy is shown in the figure. The specimen used for the test has a gage length of 2 in. and a diameter of 0.5 in. When the applied load is 9 kip, the new diameter of the specimen is 0.49935 in. Calculate the shear modulus Gal for the aluminum.

The shear modulus for an aluminum alloy
Answer to Problem 3.1RP
The shear modulus for an aluminum alloy is
Explanation of Solution
Given information:
Gage length is
The diameter of the specimen is
The axial load acts on the specimen is
The new diameter of the specimen is
Calculation:
Calculate the modulus of elasticity for aluminum
Here, the stress is
Refer the stress-strain diagram.
The value of stress is 70 ksi and the value of strain is
Substitute 70 ksi for
The expression to find the cross-sectional area of the specimen
Here, the diameter of the specimen is
Substitute
Find the value of stress when the specimen is loaded with a 9 kip load using the relation:
Here, the load is P.
Substitute 9 kip for P and
The expression to find the strain in the longitudinal or axial direction
Here, the Young’s modulus of the aluminum is
Substitute
Find the strain in lateral direction
Here, the new diameter is
Substitute
Find the Poisson’s ratio
Substitute
Calculate the modulus of rigidity for the specimen
Substitute
Therefore, the shear modulus for an aluminum alloy is
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