Practice Question: Minimize Shear Force on an Overhanging Beam

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Solution

Answer: A) 79 Kip

The main idea for this question is that point load P acting at the end of the beam overhang will cause compression on support b and uplift on support a. The greater the value of load P is, the greater the value of uplift on point a will be.

Consider the reaction at support a to be zero:

\[F_{ya} = 0\]

Accordingly, we calculate force P that will achieve equilibrium.

Sum of Moments at point b:

\[3 \ klf \times 25 \ ft \times \frac{25 \ ft}{2}-3 \ klf \times 10 \ ft \times \frac{10 \ ft}{2}-P \times 10 \ ft=0 \\\]

 

\[P = 78.75\ kip\\\]
 

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