Topic: Strength of Materials
$\frac{PL³}{3EI}$ 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. $\frac{P^2L^3}{3EI}$
- B. $\frac{P^2L^3}{6EI}$
- C. $\frac{P^2L^3}{4EI}$
- D. $\frac{P^2L^3}{48EI}$
Answer: B. $\frac{P^2L^3}{6EI}$
Explanation: The strain energy ($U$) due to bending in a cantilever beam subjected to a point load P at the free end is defined by $U = \int_{0}^{L} \frac{M² dx}{2EI}$. Given the bending moment $M = Px$, substituting this provides $U = \int_{0}^{L} \frac{(Px)^2 dx}{2EI} = \frac{P²}{2EI} \left[\frac{x³}{3}\right]_{0}^{L} = \frac{P^2L^3}{6EI}$.