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A cantilever beam of length, L, and flexural rigidity, EI, is subjected to an end moment, M, as shown in the figure. The deflection of the beam at x = L/2 is

1. M L² / (8 E I)
2. M L² / (16 E I)
3. M L² / (24 E I)
4. M L² / (32 E I)

Correct answer: M L² / (8 E I)

Solution

A cantilever with an end moment M has deflection y(x) = M x^2/(2EI). At x = L/2, y = M(L/2)^2/(2EI) = M L^2/(8EI). Stored M L^2/(16EI) is wrong.

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