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SHM expression

The expressio...

Question

The expression of the elastic curve at the free end of a cantilever beam of span 'L', flexural rigidity 'EI' and subjected to uniformly distributed load intensity 'w' is -

A

$w L^{2} / (2 E I)$

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B

$w L^{3} / (3 E I)$

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C

w L^{4} / (8 E I)

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D

w L^{3} / (6 E I)

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Solution

The correct option is C $w L^{4} / (8 E I)$
(c)

The expression of elastic curve at free-end, i.e., the deflection at free end.
$δ_{A} = \frac{w L^{4}}{8 E I}$

$N o t e : R o t a t i o n a t A, θ_{A} = \frac{w L^{3}}{6 E I}$

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