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Pascal's Law

The figure sh...

Question

The figure shows a simply supported beam PQ of uniform flexural rigidity EI carrying two moments M and 2M

The slope at P will be

A

0

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B

M L / (9 E I)

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C

M L / (6 E I)

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D

M L / (3 E I)

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Solution

The correct option is C $M L / (6 E I)$

$R l - \frac{M l}{6 E I} \times (\frac{2 l}{3} + \frac{l}{9}) - \frac{M l}{6 E I} (\frac{l}{3} + \frac{l}{9}) + \frac{M l}{6 E I} (\frac{l}{3} - \frac{l}{9}) = 0$
$R l = \frac{M}{18 E I} [2 l + \frac{1}{3} + l + \frac{l}{3} - l + \frac{l}{3}]$
$R = \frac{M}{18 E I} [3 l] = \frac{M l}{6 E I} = \frac{M l}{6 E I}$

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