(a)
The work done in expanding a
(a)
Answer to Problem 2.81P
The work done in expanding a
Explanation of Solution
Given:
Thickness of shell is
Initial diameter is
Final diameter is
The stress for material is
Concept used:
Write the expression for true strain for shell.
Here,
Write the expression for specific energy for balanced biaxial plane stress condition.
Substitute
Here,
Write the expression for work done.
Here,
Substitute
Simplify above expression.
Write the expression for stress for material.
The true strain is obtained by integrating the above expression.
After integration simplify above expression.
Calculation:
Substitute
Substitute
Substitute
Conclusion:
Thus, the work done in expanding a
(b)
Explain the dependency of answer on yield criterion.
(b)
Explanation of Solution
In this case, the amount of tension applied on biaxial stress plane is equal in magnitude and in biaxial plane with equal stresses the yield criterion for both maximum shear stress theory and distortion energy gives same result.
Thus, the answer is not dependent on any yield criterion.
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Chapter 2 Solutions
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