Problem $4$

A W$14$x$120$ beam as shown is laterally braced at the vertical supports $($A$,$ C and D$)$ and at point $B,$ which is the midspan of $AC$ and an intermediate hinge. A concentrated factored load $V$ kips is applied at point $B,$ and a concentrated factored moment $4V$ kip$-$ft is applied at point $D$ as shown.

a$)$ Draw the bending moment diagram of the entire beam for the factored loads.

b$)$ What is the maximum value of $V$ for which the beam can resist the applied loads? Which of the three unbraced segments determine $V?$

Assume that the beam is compact and neglect self$-$weight. Use design charts for this problem. $F_y=50$ksi.