Homework: Slender Columns Template

The $15\text{'}15$ in$.$ column shown below must extend from footing level to the second floor of a braced frame structure with an unsupported length of $20\mathrm{.}5$ ft $.$ Exterior exposure requires $2in.$ clear cover for the outermost steel. Analysis indicates that the critical loading corresponds with the following service loads: $($a$)$ from dead loads, $P=180$kips,$M_{\text{t}\text{o}\text{p}}=30ft-$kips, $M_{\text{b}\text{o}\text{t}}=15ft$ kips; $($b$)$ from live loads, $P=110$kips,$M_{\text{t}\text{o}\text{p}}=60ft-$kips, $M_{\text{b}\text{o}\text{t}}=30$ ft $-$kips, with the column bent in double curvature as shown. The effective length factor $k$ determined using Fig. $10\mathrm{.}13$a is $0\mathrm{.}90.$ Material strengths are $-4000$ psi and $-60000$ pisi. Using the ACI moment magnifier method, determine whether the column is adequate to resist these loads. $(20$pt$)$