U1 and U2 are the strain energies stored in a prismatic bar due to axial tensile forces P1 and P2
respectively. The strain energy U stored in the same bar due to combined action of P1 and P2
will be-
-
A.
U < U1+U2
-
B.
U=U1U2
-
C.
U=U1+U2
-
D.
U > U1+U2
Correct Answer:
D. U > U1+U2
Explanation:
When a prismatic bar is subjected to multiple axial loads, the total strain energy is not simply the sum of the individual strain energies because strain energy is a function of the square of the applied force. The total strain energy U for combined forces P1 and P2 is proportional to (P1 + P2)^2, which expands to P1^2 + P2^2 + 2*P1*P2. Since U1 is proportional to P1^2 and U2 is proportional to P2^2, the additional term 2*P1*P2 makes the total strain energy U greater than the sum of U1 and U2. Therefore, U > U1 + U2.
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