Question

A simply supported beam of span Land flexural rigidity El, carries a unit point load at its centre. The strain energy in the beam due to bending is

• A. $\frac{L^3}{48EI}$
• B. $\frac{L^3}{192EI}$
• C. $\frac{L^3}{96EI}$
• D. $\frac{L^3}{16EI}$

Answer 1

The correct option is C $\frac{L^3}{96EI}$

Strain energy due to bending

$=\int \frac{M_x^{2}dx}{2EI}=\frac{1}{2}W\delta$

The deflection under the load,

$\delta =\frac{W{L}^3}{48EI}=\frac{L^3}{48EI}$

$\therefore$Strain energy due to unit load

=$\frac{1}{2}\times 1\times \frac{L^3}{48EI}=\frac{L^3}{96EI}$