Question

Find the lightest W12 Section to support the service compression loads listed below. The column is 30 ft long with the end connections as shown. The column is braced at mid-height but only in the strong axis. Steel is ASTM A572 Grade 50. Use the ASD method only.

oku W2! IMIDTH SUPPORT CONDITION LOADS I DEAD = 1 2look TT LIVE = 1564

Answer 1

Gr 50 GIVEN DATA Grade of steel Service Dead Load, Service Live Load, PO = PL = A 572 200 kips 150 kips Restraints Along x direction Unsupported Length of column, Bottom End Top end Lx = 15 ft : pinned : pinned Along y direction Unsupported Length of column, Bottom End Top end Ly = 30 ft : fixed : pinned CALCULATIONS Yield stress of steel Modulus of Elasticity of steel Fy = E = 50 ksi 29000 ksi Design Load, P D = = + L 350 kips Effective length factors, KX = K = 1 0.8 Assuming KI/Ty = 95 CE 2'E = 107.00 > 95.00 Note: [ (KL/r)? For < F-1 20 5 3(KL/r) (KL/r) 3' 8C 8C 127 E KL >0. F. - 23(KL/P). Therefore, allowable stress, Fo= 15.84 ksi Therefore, required area of cross-section, Ag = P/F = 350 / = 22.1 in? 15.84

Select W 12x79 CHECK CAPACITY Properties of Steel section Column Section Gross area of cross section, Radii of gyration, A, - W 12x79 23.2 in? 5.34 in 3.05 in Ty = = 1x 15 x 12 in )/5.34 = 33.708 Ayly = 0.8 x 30 x 12 in)/3.05 = 94.426 C = 27'E = 107.00 > 94.43 Note: For KT <C, [_(KL/r)?] [ 20 " F, = 5 3(KL/r) (KL/P) 3 8C 8C KI >C. F. = 23(KL/r) Therefore, allowable stress, Fo= 15.97 ksi Hence, Nominal axial strength of column, P = = = F,4, 15.97 X 370.5 kips SAFE 23.2 > 350 > = P. Hence,