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Strength of Materials

Double Integration -Cantilever - Standard Cases

A straight ca...

Question

A straight cantilever of uniform cross-section carries a total load W distributed evenly over its entire length. If the free end of the cantilever is now propped upto the level of the fixed end, the vertical force required at the prop is

A

\frac{3}{8} W

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B

\frac{5}{8} W

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C

\frac{3}{4} W

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D

W

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Solution

The correct option is A $\frac{3}{8} W$
Vertical downward deflection due to UDL = Upward deflection due to reaction at prop

$\frac{w L^{4}}{8 E I} = \frac{R_{B} L^{3}}{3 E I}$

$R_{B} = \frac{3}{8} w L = \frac{3}{8} W$

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