GATE Papers >> Mechanical >> 2017 >> Question No 109

Question No. 109 Mechanical | GATE 2017

A 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 : (A) P2L36EI

Solution of Question No 109 of GATE 2017 Mechanical Paper

M = P.x

Strain energy $ \begin{array}{l}=\int\limits_0^\mathrm L\frac{\mathrm M^2\mathrm{dx}}{2\mathrm{EI}}=\int\limits_0^\mathrm L\frac{\mathrm P^2\mathrm x^2\mathrm{dc}}{2\in\mathrm I}=\frac{\mathrm P^2}{2\mathrm{EI}}\left(\frac{\mathrm x^3}3\right)_0^\mathrm L\\\end{array} $

Strain energy $ \begin{array}{l}=\frac{\mathrm P^2\mathrm L^3}{6\mathrm{EI}}\\\end{array} $

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