Question
Download Solution PDFA cantilever beam of length L and flexural modulus EI is subjected to a point load P at the free end. The elastic strain energy stored in the beam due to bending (neglecting transverse shear) is
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
\({M_{x - x}} = P \cdot x\)
\(Strain\;energy = \mathop \smallint \limits_0^L \frac{{{{\left( {{M_{x - x}}} \right)}^2}dx}}{{2EI}}\)
\({U_{X - X}} = \mathop \smallint \limits_0^L \frac{{{{\left( {Px} \right)}^2}}}{{2EI}}dx = \frac{{{P^2}}}{{2EI}}\mathop \smallint \limits_0^L {x^2}dx\)
\( = \frac{{{P^2}}}{{2EI}}\left| {\frac{{{x^3}}}{3}} \right|_0^L = \frac{{{P^2} \cdot {L^3}}}{{2EI \times 3}} = \frac{{{P^2}{L^3}}}{{6EI}}\)
Last updated on Apr 16, 2025
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