Use E $=2910^6$ psi. A column of $22-$ft effective length is made by welding two $90\mathrm{.}5-$in$.$ plates to a W$835$ as shown. Determine

a$)$ The magnitude of the area of the built$-$up column cross$-$section is $\_\_\_\_\_$in$^2.$

b$)$ The magnitude of the area moment of inertia of the column about the centroidal x$-$axis is $\_\_\_\_\_$in$^4.(6$ sig figs$)$

c$)$ The magnitude of the area moment of inertia of the column about the centroidal y$-$axis is $\_\_\_\_\_$in$^4.(6$ sig figs$)$

d$)$ The magnitude of the critical axial compressive force for the column based upon buckling about the centroidal x$-$axis is $\_\_\_\_\_$lb$.(6$ sig figs$)$

e$)$ The magnitude of the critical axial compressive force for the column based upon buckling about the centroidal y$-$axis is $\_\_\_\_\_$lb$.(6$ sig figs$)$

f$)$ The magnitude of the critical axial compressive force for the column based upon buckling is $\_\_\_\_\_$lb$.(6$ sig figs$)$

g$)$ The magnitude of the allowable axial compressive force for the column based upon buckling is $\_\_\_\_\_$lb$.(6$ sig figs$)$

h$)$ For this problem ONLY, assume the column is braced such that buckling will not occur about the weak$-$axis of the Built$-$Up member.$($The column remains a "built$-$up column", composed of $3$ pieces.$)$

The magnitude of the allowable axial compressive force for the column based upon buckling is $\_\_\_\_\_$lb$.(6$ sig figs$)$

i$)$ When the column is loaded to the allowable axial compressive force, the magnitude of the compressive normal stress is $\_\_\_\_\_$ksi.

j$)$ If the column were made from A$36$ steel, the yield strength of the material is $\_\_\_\_\_$ksi.

k$)$ Assume:

the column is made from A$36$ steel

the column is loaded to the allowable axial compressive force

The magnitude of the ratio of the compressive normal stress to the yield strength is $\_\_\_\_\_.$

l$)$ If the column has "fixed$-$fixed" end conditions, the actual length of the column is $\_\_\_\_\_$ft$.$

m$)$ If the column has "fixed$-$pinned" end conditions, the actual length of the column is $\_\_\_\_\_$ft$.$

n$)$ If the column has "pinned$-$pinned" end conditions, the actual length of the column is $\_\_\_\_\_$ft$.$

o$)$ If the column has "fixed$-$free" end conditions, the actual length of the column is $\_\_\_\_\_$ft$.$