Question

A simply supported beam of span L is subjected to a concentrated load W at midpsan. The strain energy due to bending in the beam would be

• A. $\frac{W^2{L}^3}{48EI}$
• B. $\frac{W^2{L}^3}{96EI}$
• C. $\frac{W^2{L}^3}{24EI}$
• D. $\frac{W{L}^3}{96EI}$

Answer 1

The correct option is B $\frac{W^2{L}^3}{96EI}$



The strain energy due to bending in beam is given as

$E=2\times {\int }_0^{L/2}\frac{M_x^{2}dx}{2EI}$

where, $M_x=\frac{w}{2}x$

$\Rightarrow E=\frac{1}{EI}{\int }_0^{L/2}{\left(\frac{W}{2}x\right)}^{2}dx=\frac{w^2}{4EI}{\int }_0^{L/2}{x}^{2}dx$

$\frac{w^2}{4EI}{\left[\frac{x^3}{3}\right]}_0^{L/2}=\frac{w^2{L}^3}{96EI}$