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The flexural rigidity (EI) of a cantilever beam is assumed to be constant over the length of the beam shown in figure. If a load P and bending moment PL/2 are applied at the free end of the beam then the value of the slope at the free end is

1. PL² / 2EI
2. PL² / EI
3. 3PL² / 2EI
4. 5PL² / 2EI

Correct answer: PL² / EI

Solution

A tip load P gives end slope PL^2/(2EI). A tip moment M = PL/2 gives end slope ML/EI = PL^2/(2EI). Superposing, total slope = PL^2/(2EI) + PL^2/(2EI) = PL^2/EI, the second option.

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