A timber $E=1600$ksi beam is loaded and supported as shown. The cross section of the timber beam is $b=4in.$ wide and $h=13$ in$.$ deep. The beam is supported at $B$ by a $0\mathrm{.}625$ in$.-$diameter steel rod, which has no load before the distributed load is applied to the beam. After a distributed load of $w=980l\frac{b}{f}t$ is applied to the beam, determine:

$($a$)$ the force $F$ carried by the steel rod.

$($b$)$ the maximum bending stress ${}_{\text{m}\text{a}\text{x}}$ in the timber beam.

$($c$)$ the deflection $v_B$ of the beam at $B.$

Assume $L=18ft,L_1=19ft.$

Answers:

$($a$)F=lb.$

$($b$){}_{\text{m}\text{a}\text{x}}=$ psi.

$($c$)v_B=$ in$.$