Subject : Structural Analysis 1

Topic : General Principles

Difficulty : Low

Strain Energy:

$U=\int_{}^{} \frac{M^{2}}{2EI}dx$

$\Rightarrow U=\frac{1}{2EI}\int_{0}^{L} \left(\frac{wx^{2}}{2}\right)^{2}dx$

$=\frac{1}{2EI}\int_{0}^{L} \frac{w^{2}x^{4}}{4}dx$

$=\frac{1}{2EI}\left[\frac{w^{2}x^{5}}{20}\right]_0^L=\frac{1}{2EI}\times\frac{w^{2}L^{5}}{20}$

$U=\frac{w^{2}L^{2}}{40EI}$