GATE ME 2021 Set 1 — Question 27
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Strength of Materials → Beams & Columns → Deflection of Beams
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Question
A cantilever beam of length, , and flexural rigidity, , is subjected to an end moment, , as shown in the figure. The deflection of the beam at is
Correct answer
(C) (ML²)/(8EI)
Solution
For a cantilever beam with an end moment , the bending moment is constant throughout the length: .
Using the differential equation for deflection:Integrating once with respect to :At the fixed end (), slope .
Integrating again:At the fixed end (), deflection .
So, the deflection equation is:At :
Using the differential equation for deflection:Integrating once with respect to :At the fixed end (), slope .
Integrating again:At the fixed end (), deflection .
So, the deflection equation is:At :
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