Question

A simply supported beam of span I and flexual rigidity EI carries at unit load at its mid -span. The strain energy at this condition in the beam due to bending is

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

Answer 1

The correct option is B $\frac{I^3}{96EI}$



$M_x=\frac{Px}{2}$

$\therefore$ SE stored in the beam =
$2\underset{0}{\overset{1/2}{\int }}\frac{M_x^{2}dx}{2EI}=2\underset{0}{\overset{1/2}{\int }}\frac{(Px/2{)}^{2}dx}{2EI}=\frac{P^2{l}^3}{96EI}$

For unit load P = 1

$SE=\frac{l^3}{96EI}$