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Newton's Second Law: Rotatory Version

A prismatic, ...

Question

A prismatic, straight, elastic, cantilever beam is subjected to a linearly distributed transverse load as shown below. If the beam length is L,Young's modulus E and area moment of inertia I, the magnitude of the maximum deflection is

A

\frac{q L^{4}}{10 E I}

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B

\frac{q L^{4}}{60 E I}

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C

\frac{q L^{4}}{15 E I}

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D

\frac{q L^{4}}{30 E I}

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Solution

The correct option is D $\frac{q L^{4}}{30 E I}$

By using moment area IInd theorem
$Y_{B} - Y_{A}$ $= A ¯ ¯¯¯ ¯ X o f \frac{M}{E I}$ diagram between B and A
$Y_{m a x} - 0 = (\frac{1}{4}) (\frac{q L^{2}}{6 E I}) (L) (\frac{4 L}{5})$
$Y_{m a x} = \frac{q L^{4}}{30 E I} (↓)$

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