Question

The strain energy due to bending in the cantilever beam shown in the figure is _____

• A. $\frac{P^2{L}^3}{12EI}$
• B. $\frac{P^2{L}^3}{6EI}$
• C. $\frac{P^2{L}^3}{24EI}$
• D. $\frac{P^2{L}^3}{48EI}$

Answer 1

The correct option is D $\frac{P^2{L}^3}{48EI}$

$U=\underset{0}{\overset{l}{\int }}\frac{M_x^{2}dx}{2EI}=\underset{0}{\overset{\frac{L}{2}}{\int }}\frac{{\left(Px\right)}^{2}dx}{2EI}$

$=\frac{P^2}{2EI}\frac{L^3}{8\times 3}=\frac{P^2{L}^3}{48EI}$