Problem $4.$

See the framing plan below. At floor $3,$ a total of $120$ kips is loaded into the column by the beams. At floor $2,$ a total of $150$ kips is loaded into the column. At floor $3$ beams frame into the column both directions. At floor $2,$ beams frame into the column in the plane of the page but there is no beam framing into the column into$/$out of the page. The column cross section is as shown in section A$-$A $($hint: pay attention to the orientation$)$

The Young$$s Modulus of Steel is $29,000$ ksi.

a$)$ Calculate the area of the column cross$-$section.

b$)$ Calculate the moment of inertia of the column about Axis X$-$X and Axis Y$-$Y$.$

c$)$ Calculate the normal stress of the column at the base.

d$)$ Calculate the total shortening of the column.

e$)$ Calculate the critical buckling load of the column about Axis X$-$X$.$

f$)$ Calculate the critical buckling load of the column about Axis Y$-$Y$.$

g$)$ Given the answers to e$)$ and f$),$ what is the critical buckling load of the column.

h$)$ Given the total load on the column, is the critical buckling load exceeded?ELEVATION

OCL I IUIN M$-$M