Question:
A simply supported beam is loaded with a uniformly distributed load (UDL). Which statements about strain energy are TRUE?
A simply supported beam is loaded with a uniformly distributed load (UDL). Which statements about strain energy are TRUE?
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Strain energy in beams always depends on load intensity, length, Young’s modulus, and moment of inertia.
Updated On: Dec 2, 2025
- It increases with increase in UDL
- It increases with increase in cross-sectional area of the beam
- It is independent of the length of the beam
- It is dependent on Young’s modulus of elasticity
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The Correct Option is A, D
Solution and Explanation
For a simply supported beam with UDL $w$, the strain energy is:
\[ U = \int_0^L \frac{M(x)^2}{2EI}\,dx. \]
From this expression:
- Increasing UDL increases the bending moment $M(x)$, so the strain energy increases. Hence (A) is true.
- Increasing cross-sectional area increases $I$, which reduces strain energy, not increases it. Thus (B) is false.
- The length $L$ appears directly in the integral, so strain energy clearly depends on $L$. Hence (C) is false.
- Young’s modulus $E$ appears in the denominator, proving strain energy depends on $E$. Thus (D) is true.
\[ U = \int_0^L \frac{M(x)^2}{2EI}\,dx. \]
From this expression:
- Increasing UDL increases the bending moment $M(x)$, so the strain energy increases. Hence (A) is true.
- Increasing cross-sectional area increases $I$, which reduces strain energy, not increases it. Thus (B) is false.
- The length $L$ appears directly in the integral, so strain energy clearly depends on $L$. Hence (C) is false.
- Young’s modulus $E$ appears in the denominator, proving strain energy depends on $E$. Thus (D) is true.
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