$6-7.$ Several building columns are to be designed using A$992$ steel and the AISC Specification. Select the lightest available W sections and state the LRFD design strength, ${}_c{P}_n$ and the ASD allowable strength, $\frac{P_n}{{}_c},$ for these columns that are described as follows:

a$.P_D=90$ kips and $P_L=160$kips,$L_c=20ft,$ pinned end supports, W$14.($Ans$.$ W$14\backslash$times $61,$ LRFD ${}_c{P}_n=399k>P_u=364k$;$W1461,$ ASD $($:$\frac{P_n}{{}_c}=266k>P_a=250k$

ANSWER PARTS A$,$B$,$ C$,$ and D