A steel column (E = 200 GPa) that is fixed at the base and free at the top is constructed of a HE 180B wide-flange member (see figure). The column is 3 m long. The force P acting at the top of the...

A steel column (E = 200 GPa) that is fixed at the base and free at the top is constructed of a HE 180B wide-flange member (see figure). The column is 3 m long. The force P acting at the top of the column has an eccentricity e = 32 mm.

(a) If P = 180 kN, what is the maximum compressive stress in the column?

(b) If the yield stress is 240 MPa and the required factor of safety with respect to yielding is 2.1, what is the allowable load P_allow?