Problem $4.$

See the framing elevation 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$).$ Assume this column is pinned$-$pinned. The column is a W$10$x$33.$

a$)$ What is $rx$ and ry for the given section?

b$)$ Calculate $k\frac{L}{r}x$ and $k\frac{L}{r}y.$

c$)$ What is the critical buckling stress $($with safety factor $$ applied$),FFcr$ for the column?

d$)$ What is $Pn?$

e$)$ Is the column sufficient for the applied loads? What is the DCR $($Demand$-$Capacity Ratio$)?$