You built a new ${12}^{\text{'}}{22}^{\text{'}}$ deck. The building official wants to see a lateral load calculation on the deck for a live$-$load of $50psf(l\frac{b}{s}f)$ to check your hold$-$down size. Using the free$-$body diagram below, calculate the maximum hold$-$down force $($tension force$)$ and shear force per unit length.

Notes:

a$)$ For simplicity we can assume one hold down will be in compression and one will be in tension.

b$)$ For simplicity don't factor the live load or try to estimate dead load.

c$)$ Shear per unit length is the shear force divided by the length over which it acts.

d$)$ The lateral force can be taken as $10\%$ the vertical live$-$load and is applied through the center of mass of the deck.

$F_{LL}=$Area$(f{t}^2)**LL(\frac{lb}{sf})$