Topic: Strength of Materials
$\frac{PL^{3}}{3EI}$ is the deflection under the load P of a cantilever beam (length L, modulus of elasticity E, moment of inertia I). The strain energy due to bending is
- A. $\frac{P^{2}L^{3}}{3EI}$
- B. $\frac{P^{2}L^{3}}{6EI}$
- C. $\frac{P^{2}L^{3}}{4EI}$
- D. $\frac{P^{2}L^{3}}{48EI}$
Answer: B. $\frac{P^{2}L^{3}}{6EI}$
Explanation: Given Deflection ($\delta$) = $\frac{PL^{3}}{3EI}$. Strain energy = $\frac{1}{2} \times P \times \delta = \frac{1}{2} \times \text{load} \times \text{Deflection} = \frac{1}{2} \times P \times \frac{PL^{3}}{3EI} = \frac{P^{2}L^{3}}{6EI}$.