Use $1400$ psi for bending $175$ psi for shear and $1700$ ksi for modulus $($E$).$

Design spacing And choose most economical use either $2$ x $4$ or $2$ x $6$ southern pine given info:

$$ L$/240$ deflection limit

$$ Wall load $50$ psf

$$ pin$-$roller end connections

$$ Wall $8\text{'}$ high by $20\text{'}$ wide

$2$X$4=$$$3$ per $8\text{'}$ length

$2$X$6=$ $$5\mathrm{.}15$ per $8\text{'}$ length