The W12 * 50 is made of A992 steel and is used as a column that has a length of 20 ft. If its ends are assumed pin supported, and it is subjected to an axial load of 150 kip, determine the factor of safety with respect to buckling.

Problem 13-7The W12 x 50 is made of A992 steel and is used as a column that has a length of 20 ft. If itsends are assumed pin supported, and it is subjected to an axial load of 150 kip, determinethe factor of safety with respect to buckling. Step-by-step solution Step 1 of 4 ^Obtain the properties of W12 x 50 from the table Appendix B “Geometri1properties of structuralshapes”. 2 Area, A = 14.7inMoment of inertia, l = 56.3in 4 yCalculate the critical load using the following formula. 2 ElPcr 2 (KL)Here, E is the modulus of elasticity of the A992 steel, l is the moment of inertia, L is the length ofthe column, and K is the effective length factor.Substitute 29 x 10 ksi for E, 56.3in for l y1 for K which is pinned at both ends, and 20 ft for L. 2P = El 2 cr (KL) 2 3 (29 x 10 )(56.3) = 2 (1 x 10 x 12) = 279.759 kip