GATE ME 2019 Set 2 — Question 41
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Strength of Materials → Beams & Columns → Deflection of Beams
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Question
A prismatic, straight, elastic, cantilever beam is subjected to a linearly distributed transverse load as shown below. If the beam length is , Young's modulus , and area moment of inertia , the magnitude of the maximum deflection is
Correct answer
(B) (qL⁴)/(30EI)
Solution
For a cantilever beam fixed at and free at , with a triangular load (maximum load at the fixed end and zero at the free end), the governing differential equation is:Integrating four times and applying boundary conditions ( at the fixed end and at the free end), the deflection at the free end () is found to be:Thus, option (B) is correct.
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