Determine the largest force $P$ that can be applied to the beam if the allowable

bending stress is ${}_{\text{a}\text{l}\text{l}\text{o}\text{w}}=38$ksi and the allowable shear stress is

${}_{\text{a}\text{l}\text{l}\text{o}\text{w}}=29$ ksi. Assume the reactions at the supports at A and $B$ are vertical.

Take $a=6$ in$.$

Hints:

Find the reactions and hence, the shear and moment diagrams in terms of $P.$

Notice that the stress in the beam cannot exceed the allowable stress.