$1.$ Consider a W$12$X$87$ column of $A36(F_y=36$ksi$)$ steel with $L_{tz}=20ft,L_{ty}=14ft.$

a$.$ Show that this is a nonslender element cross section

b$.$ Determine which direction govems flexural buckling using the three methods presented in class

c$.$ Calculate the effective slendemess ratio

d$.$ Calculate the available strength of this column using AISC Specification equations $($there are no

strength tables for A$36$ columns in the AISC Manual$).$

$2.$ Consider a column subject to the following conditions. Select the lightest W$10$ section for each case using

$L_{cx}=L_{sy}=16ft.$ Note that in all three cases, $P_D+P_L=545$kips. Discuss results.

a$.P_D=65$kips,$P_L=480$kips

b$.P_D=480$kips,$P_L=65$kips

c$.P_D=530$kips,$P_L=15$kips

$3.$ Select the lightest W $12$ section for a column with $P_u=795$kips with $L_{tz}=24ft,L_{ty}=14ft.$