What is the vertical displacement at the point C of the structure shown in the figure given below ?

\frac{9 P a^{3}}{2 E I}

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\frac{27 P a^{3}}{2 E I}

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\frac{27 P a^{3}}{8 E I}

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\frac{3 P a^{3}}{8 E I}

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Solution

The correct option is A $\frac{9 P a^{3}}{2 E I}$
(a) The vertical displacement at C will be due to deflection of point B. The beam AB is subjected to a moment Pa and axial force P. So the deflection of point C will be
$\frac{P a (3 a)^{2}}{2 E I} = \frac{9 P a^{3}}{2 E I} i n t h e v e r t i c a l l y u p w a r d d i r e c t i o n .$

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