$5\mathrm{.}15-6.$ The truss shown in Figure P$5\mathrm{.}15-6$ is part of a roof system supporting a total gravity load of $40psf$ of roof surface, half dead load and half snow. Trusses are spaced at $10$ feet on centers. Assume that wind load is not a factor and investigate the adequacy of a W$612$ of A$992$ steel for use as a purlin. No sag rods are used, so lateral support is at the ends only. Manual Table $6-2$ may be used.

a$.$ Use LRFD$.$

b$.$ Use ASD.

Figure P$5\mathrm{.}15$