A beam spanning $15m,$ fixed at one end and pinned at the other end, has a cross section of a W$460384$ and made of $345W$ steel. The beam carries a factored point load of $P{f}_f$ located at $7\mathrm{.}7m$ from the fixed supported and a factored uniformly distributed load of $20k\frac{N}{m}.$ Compute the maximum factored point load, $P_f,$ that the member can resist. The beam is braced at the ends and at $6m$ from the fixed support. Please be sure to include a diagram $115$ m$......$ Case $(1),17$

$V_f=\frac{wl}{2}+\frac{P{a}^2}{l^3}(a+3b)$

$M_f=\frac{w{l}^2}{8}+\frac{P{a}^{2}b}{l^2}$

${}_{\text{m}\text{a}\text{x}\text{e}}=\frac{5w{l}^4}{384EI}+\frac{2P{a}^3{b}^2}{3EI(3a+b{)}^2}$