Concept explainers
Solve the preceding problem for an aluminum plate with h = 10 in.. i = 0.75 in., E = 10,600 ksi, v = 0.33. P = 96 kips. Pt,. = 24 kips. and V =18 kips.
For part (b) of Problem 7.5-12, assume that the required strain energy stored is 640 in.-lb. In part (c). the change in volume cannot exceed 0.05%.
(a)
The change
The strain energy
Answer to Problem 7.5.13P
The change
The strain energy
Explanation of Solution
Given information:
The normal force acting on the x-direction is
Figure (1)
Write the expression for the volumetric strain.
Here, the change in the volume of the plate is
Write the expression for the strain energy stored in the plate.
Here, the strain energy stored in the plate is
Write the expression of the original volume of plate
Here, the width of the plate is
Write the expression for the stress along x-direction.
Here the normal force along x-direction is
Write the expression for the stress along y-direction.
Here the normal force along y-direction is
Write the expression for the area of the plate.
Write the expression for the shear modulus.
Write the expression of the volumetric strain.
In the following plate the area of the shear stress for the both side of the plate is
Write the expression of the shear stress.
Calculation:
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Conclusion:
The change
The strain energy
(b)
The maximum permissible thickness of the plate.
Answer to Problem 7.5.13P
The maximum permissible thickness of the plate is.
Explanation of Solution
Given information:
The strain energy
Write the expression of the strain energy stored in the plate.
Calculation:
Substitute
Conclusion:
The maximum permissible thickness of the plate is
(c)
The minimum width
Answer to Problem 7.5.13P
The minimum width
Explanation of Solution
Given information:
The change in the volume is
Write the expression of the condition of the change in the length.
Calculation:
Substitute
Substitute
Substitute
Conclusion:
The minimum width
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Chapter 7 Solutions
Mechanics of Materials (MindTap Course List)
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