Multiple choice

U1 and U2 are the strain energies stored in a prismatic bar due to axial tensile forces P1 and P2 respectively. The strain energy stored in the same bar due to combined action of P1 and P2 will be

  1. U = U1 + U2

  2. U = U1 U2

  3. U < U1 + U2

  4. U > U1 + U2
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D Correct answer
Explanation

Strain energy is proportional to the square of the force (U = P^2L/2AE). When two forces act simultaneously, the total energy is U = (P1+P2)^2 * L/2AE = (P1^2 + P2^2 + 2P1P2) * L/2AE = U1 + U2 + (2P1P2 * L/2AE). Since P1 and P2 are positive, the term 2P1P2 is positive, making U > U1 + U2.

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