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GATE 2020 CE (CE2) – Question 38

Solid Mechanics · Simple stress and strain relationships · 2 marks · Multiple choice

A prismatic linear elastic bar of length L, area A and Young’s modulus E stores energies $U_1,U_2$ under axial tensile loads $P_1,P_2$ respectively. If U is its energy under $P_1+P_2$, which is correct?

  1. $U=U_1+U_2$
  2. $U=U_1-U_2$
  3. $U<U_1+U_2$
  4. $U>U_1+U_2$

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Correct answer: (D) $U>U_1+U_2$

Explanation

Axial strain energy is $U=P^2L/(2AE)$. Expansion at $P=P_1+P_2$ gives $U=U_1+U_2+P_1P_2L/(AE)$. Both loads are tensile, so the extra term is positive: **$U>U_1+U_2$, D**.