Problem #$1$:

Design $($bending and shear$)$ a roof beam to support $14psf$ dead load and a $20psf$ roof live load. The ${13}^{\text{'}}-6"$ long simply supported beams, which are placed $16"$ on center, are attached to plywood sheathing that provides them with an adequate lateral support. The material is No $1.$ Douglas FirLarch $($DF$-$L$)$ with an $MC19\%$ and normal temperature conditions apply.