GATE ME 2017 Set 2 — Question 9
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Strength of Materials → Beams & Columns → Energy Methods & Castigliano
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Question
A cantilever beam of length and flexural modulus is subjected to a point load at the free end. The elastic strain energy stored in the beam due to bending (neglecting transverse shear) is
Correct answer
(A) (P² L³)/(6EI)
Solution
The elastic strain energy due to bending is given by:For a cantilever beam with a point load at the free end, the bending moment at a distance from the free end is:Substituting this into the strain energy formula:Thus, the correct option is (A).
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