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Impact versus gradual loading: compare induced stresses in a linear elastic member A body (within elastic range) is loaded suddenly versus the same load applied gradually (static). How do the resulting stresses compare? Choose the correct relation.

Difficulty: Easy

equal to
one-half
twice
four times

Correct Answer: twice

Explanation:

ConceptFor a suddenly applied load (no initial velocity, no damping), the maximum strain/stress in a linear elastic member is twice the value produced by the same load applied gradually.

Derivation sketchGradual loading: σ = P/A.Sudden loading: strain energy ½ k δ² equals work P δ; solving gives δ = 2(P/k) and σ = 2(P/A).

Final Answertwice

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