Problem $5\mathrm{.}4.$A No$.1$ grade of Douglas fir$-$larch is to be used for a series of floor beams $6$ ft on center, spanning $14$ ft $.$ If the total uniformly distributed load on each beam, including the beam weight, is $3200$ lb $,$ select the section with the least cross$-$sectional area based on bending stress.

Problem $5\mathrm{.}4.$B A simple beam of Hem Fir, select structural grade, has a span of $18$ ft with two concentrated loads of $4$ kips each placed at the third points of the span. Neglecting its own weight, determine the size of the beam with the least cross$-$sectional area based on bending stress.

Problem $5\mathrm{.}4\mathrm{.}6$ Rafters are to be used on $24-$in$.$ centers for a roof span of $16$ ft $.$ Live load is $20$ psf $($without snow$)$ and the dead load is $15$ psf $,$ including the weight of the rafters. Find the rafter size required for Douglas fir$-$larch of $($a$)$ No$.1$ grade and $($b$)$ No$.2$ grade, based on bending stress.