Question

Determine the most economical W14 for member AB shown below in a multistory braced frame. The axial compressive load is 400 kips dead load and 1100 kips live load. Assume that bracing is only provided at the column base and at the connection with the beams. Use A992 steel. W18x143 W18x192 10ft W14x176 W18x143 W18x192 B 10ft A 25ft 35ft

Answer 1

GIVEN DATA Grade of steel Service dead load, Service live load, Po= A 992 400 kips 1100 kips PL = Restraints Along x direction Unsupported Length of column, Bottom End Top end Lx = 10 ft : pinned (assumed for preliminary design) : fixed Along y direction Unsupported Length of column, Bottom End Top end Ly = 10 ft : pinned : pinned CALCULATIONS Yield stress of steel Modulus of Elasticity of steel Fy = 50 ksi E = 29000 ksi Factored Design Load, Pu = 1.2 Po + 1.6 PL 2240 kips Effective length factors, Ky = 2 Ky = 1 Assuming Kl/ry 40 F KL ace ry 2 E 0.529 < 1.5 Note: For î, <1.5, F = (0.658+?. DF, 0.877 2 > 1.5, For 2 Therefore, critical stress, For = 44.47 ksi Therefore, required area of cross-section, Ag = P_/OFF 2240 / 0.9 x 44.47

55.97 in? Select W 14x193 CHECK CAPACITY Properties of Steel section Column Section Gross area of cross section, Radii of gyration, W 14x193 2 56.8 in Ag = 6.5 in ry = Kx = Ky = 4.05 in 2.14 Effective length factors, 1 KL r 2.14 x ( 10 x 12 in )/ 6.50 39.51 KL, 1x ( 10 x 12 in)/ 4.05 ry 29.63 Since KxLx/rx > KyLy/ry , KxLx/rx controls. K,L, F 2c = ry πΕ 0.522 < 1.5 Note: For 2. <1.5, Fo = (0.658442 )F, 0.877 2 > 1.5, For = F, 2 Therefore, critical stress, For= 44.61 ksi Hence, Design axial strength of column, 44.61 Pn= 6F, 0.9 x 2280 kips SAFE X 56.8 2240 kips = Pu Hence, Thus, the member size is OK

MOMENTS OF INERTIA Columns W14x176 = 2140 in 2400 in 4 W 14x193 Beams/ Girders W18x143 2750 in W14x176 10 W18x192 = 3870 in W18x143 18x1024 W18x192 W 14x193 10 GA = EI/L. [13/L3 2140 10 x 12 + 2400 10 x 12 25 35 2750 25 x 12 3870 35 x 12 2.06 = EI/L. Elf/LB 10 From alignement chart, for sway not prevented, Kx = 2.14 [for unbraced frame] Ky = 1 [for pinned ends]