$(30$ points$)$ The wooden inverted T$-$beam is made from two $1-$in$.$ thick boards. Knowing

that the allowable normal stress of the wood in tension is ${}_{\text{a}\text{l}\text{l}}=+4\mathrm{.}0$ksi, the allowable

normal stress in compression is ${}_{\text{a}\text{l}\text{l}}=-9\mathrm{.}0$ksi, and the allowable shear stress is ${}_{\text{a}\text{l}\text{l}}=2\mathrm{.}5$

ksi:

i$)$ Determine the maximum concentrated load $P$ that the beam can safely support.

ii$)$ If each load $P$ is set equal to $P=2\mathrm{.}0k,$ specify the minimum spacing of nails needed

to hold the two boards together if each nail can safely resist $500lb$ in shear.