Problem $7-$ Stability $-10$ points

A$500$ steel grade $C$ with a yield stress of $50$ksi. and simple $($pinned$)$ supports. $E=29{10}^3$ksi. Use AISC

methods.

a$)$ Find $r$ the radius of gyration.

b$)$ Find the maximum load, in kips, limited by yield $($length $=0),$ Use a factor of safety of $1\mathrm{.}67.$

c$)$ If $L=8ft(96$ inches$),$ what is the allowable load in kips?

d$)$ If $L=18ft,$ what is the allowable load in kips?

e$)$ If we chose an aluminum tube of equal weight with $L=8ft,$ what now is the allowable load in

kips? Compensating for density gives an area $=7\mathrm{.}32i{n}^2.$ One potential solution is a $5\mathrm{.}55\mathrm{.}5\frac{3}{8}$

$A=6\mathrm{.}88i{n}^2,I=29\mathrm{.}7i{n}^4,r=2\mathrm{.}08in.$ Use $2014-$T$6$ with a yield stress of $28$ksi.