Question

Use Code: Steel Construction Manual, 15th Edition, American Institute of Steel Construction

Problem 3 Solve for ® Pn for the W8x40 columns below for two cases and assuming Pu = 450 kip. a) Use elastic G b) Use inelastic G W12x50 Assume no I WAB SAB 10 ft is in plame Cable bracing shown. K 16 ft >

Answer 1

GIVEN DATA Properties of Steel section Grade of steel Column Section Gross area of cross section, Radii of gyration, A 992 W 8x40 11.7 in? 3.53 in 2.04 in Factored Design Load, 450 kips CALCULATIONS Yield stress of steel Modulus of Elasticity of steel Fy = E = 50 ksi 29000 ksi Effective length factors, (from frame analysis) K = Ky = 1.8 1 AXE 1.8 x 10 X 12 in )/3.53 = 61.19 y = 1x 10 x 12 in )/2.04 = 58.82 Since K, Ly/1x > Kyly/ry, KxLx/rx controls. 2.KL, F, = 0.809 1.5 Note: For À<1.5, F, = (0.658°)F, 4. »1.5. Fe=[1087?) Therefore, critical stress, For= 38.02 ksi Hence, Design axial strength of column, 6.P. - ,F,A, = 0.9 x = 400 kips NOT SAFE 38.02 x 11.7 < 450 kips = PU Hence, Thus, the member size is OK

MOMENTS OF INERTIA Columns W8x40 = 146 in Beams/ Girders W12x50 = 391 in -W12x50 W8x40 GASIL 13/L3 146 10 x 12 16 391 16 x 12 0.60 G3 = 31/L IzL; 10 = From alignment chart, for sway not prevented, KX = 1.8 [for unbraced frame] 1 [for pinned ends]

GIVEN DATA Properties of Steel section Grade of steel Column Section Gross area of cross section, Radii of gyration, A 992 W 8x40 11.7 in 3.53 in 2.04 in Factored Design Load, = 450 kips CALCULATIONS Yield stress of steel Modulus of Elasticity of steel Fy = E = 50 ksi 29000 ksi Effective length factors, (from frame analysis) Kx = Ky = 1.75 1 K4 = 1.75 x 1 10 x 12 in )/3.53 = 59.49 Ayly 1x 10 X 12 in )/2.04 = 58.82 Since KxLx/rx > K, Ly/ry KxLx/rx controls. 2 - KL, F, = 0.786 1.5 Note: For 2. <1.5, F, = (0.6584)F, 1>1.5, F = Therefore, critical stress, Fo= 38.61 ksi Hence, Design axial strength of column, P., = = F,4, 0.9 x 407 kips 38.61 x 11.7 < 450 kips = P.

Hence, NOT SAFE Thus, the member size is OK

MOMENTS OF INERTIA Columns W8x40 = 146 in Beams/ Girders W12x50 = 391 in -W12x50 W8x40 GA - IL Ig/L3 146 10 x 12 16 391 16 x 12 0.60 G5 = EI.IL 1,/L3 10 P. = 1 0927 (0.658 i = 0.30 Therefore, GA melastic = GB inelastie = 0.22 10.00 From alignement chart, for sway not prevented, Kx = 1.75 [for unbraced frame] Ky = 1 {for pinned ends]