The ratio of the stress induced by a suddenly applied axial load to that induced by the same load applied gradually is:
Try it first: pick an option, then read the explanation.
Correct answer: C. 2
Asked in SSC JE 23/09/2019 (Evening); SSC JE 02/03/2017 (Morning)
Detailed Explanation
Compare the work done by the load with the strain energy stored in the bar.
Gradual: work \(= \tfrac12 P\delta\) = strain energy \(\tfrac12 \sigma A \delta \Rightarrow \sigma = P/A\).
Sudden: work \(= P\delta\) (full load acts through the whole extension) \(= \tfrac12\sigma A\delta \Rightarrow \sigma = 2P/A\).
Why “2” Is Correct
A suddenly applied load produces twice the stress of the same load applied gradually.
Why the Other Options Are Wrong
- A. 1.5: 1.5 does not come from the energy balance.
- B. 2.5: 2.5 does not come from the energy balance.
- D. 3: 3 does not come from the energy balance.
Key Point
Suddenly applied load: σ = 2P/A (twice the static stress).
Key Concepts for Students
- Impact (falling) load: σ = (P/A)[1 + √(1 + 2AEh/PL)].
- With h = 0, the impact formula gives the sudden-load result 2P/A.
- Strain energy U = σ²V/2E.
Practice more: this is question 18 in Stress and Strain MCQs – Part 2. Try the whole set and check every answer instantly.