If $2$x$6$ studs, $3000$ mm long are used to build the frame system of a house and the studs are nailed to the wall plates so that the column is stable in its weak direction determine if the stud is capable of carrying a perfectly axial load of $21$ kN$.$

Design for occupancy load, dry conditions, mild temperature.

Assume Fc$=900$ psi$=6\mathrm{.}20$ MPa, E$=1,400,000$ psi$=9650$ MPa, Emin$=500,000$ psi$=3445$ MPa.