Question
Download Solution PDFIf elastic strength increases 3 times, then Proof Resilience:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
Proof Resilience is the strain energy stored per unit volume when a material is deformed up to its elastic limit. It depends on the square of the elastic strength (proof stress).
Given:
- Initial elastic strength = \(\sigma_e\)
- Elastic strength increases by 3 times → New elastic strength = \(3\sigma_e\)
- Young's modulus (E) remains constant
Step 1: Recall Proof Resilience formula
\( U = \frac{\sigma_e^2}{2E} \)
Step 2: Calculate new Proof Resilience
With new elastic strength \(3\sigma_e\):
\( U_{\text{new}} = \frac{(3\sigma_e)^2}{2E} = \frac{9\sigma_e^2}{2E} = 9U \)
Conclusion:
When elastic strength increases 3 times, Proof Resilience increases by 9 times because it is proportional to the square of the elastic strength.
Last updated on Jun 7, 2025
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