A brass cube of 48 mm on each edge is comp ressed in two perpendicular directions by forces P = 160 kN (see figure).
(a) Calculate the change ...IV in the volume of the cube and the strain energy U stored in the cube. assuming E = 100 GPa and i’ = 0.34.
(b) Repeat part (a) if the cube is made of an alumim um alloy with E = 73 GPa and v = 0.33.
(a)
The change
Answer to Problem 7.5.10P
The change
The strain energy
Explanation of Solution
Given information:
Forces acting on the cube in the perpendicular directions is
Figure (1)
Write the expression for the volumetric strain.
Here, the change in the volume of the cube is
Write the expression for the strain energy stored in the cube.
Here, the strain energy stored in the cube is
Write the expression for the stresses.
Write the expression for the stresses along x-direction and y-direction.
Here, the stress along x-axis is
Write the expression for the strain along x-direction.
Here the Poisson’s ratio is
Write the expression for the strain along y-direction.
Write the expression for the strain along z-direction.
Calculation:
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Conclusion:
The change
The strain energy
(b)
The change
Answer to Problem 7.5.10P
The change
The strain energy
Explanation of Solution
Given information:
Modulus of elasticity is
Calculation:
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Conclusion:
The change
The strain energy
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Chapter 7 Solutions
Mechanics of Materials (MindTap Course List)
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