Question

2. Determine if Column A (W12X190) below is adequately sized for the applied load Pu. If not, select an new W12 that satisfies the design strength required. . Assume in plane all girder to to column connections are moment connections. o Assume columns are A992 steel have their strong axis (lx) oriented in the frame direction. Assume Out plane that there is bracing at the top, bottom, and mid-height of the column. . Assume out plane that simple connections connect to the column. (Ky - 1.0) Pu- 2250k 26-0" 30'-0 26-0 W16X89 W16X89 W16X89 W16X89 W16X89 W16X89 W16x89 W16X89 W16X89 LA

Answer 1

MOMENTS OF INERTIA Columns w12x190 = 1890 in w12×190 1890 in = Beams/ Girders 1300 in 1300 in 12 W16X89 - W16X89 - W12X190 W16X89 W16X89 W12X190 12 1890 1890 12 x 12 12 x 12 26 30 1300 1300 26 x 12 30 x 12 3.38 10 From alignement chart, for sway not prevented, 2.4 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 12x190 56 in2 rx5.82 in r3.25 in Restraints Along x direction Unsupported Lengths of column, 12 ft Along y direction Unsupported Lengths of column, ads Factored Axial Load P" = 2250 kips CALCULATIONS Yield stress of steel Modulus of Elasticity of steel Effective length factors 50 ksi E29000 ksi 2.4 K.L 2.4 x ( 12 x 12 in )/ 5.82 = 59.381 K,L 1 x 6 x 12 in 3.25 = 22.154 Since K,L/rx > KyLyfryKxLx/rx controls 2 K L 1 0.7851.5 Note 1.5, F -(0.658F For 1.5,F0.877 Therefore, critical stress, Fr 38.633 ksi Hence,

Design axial strength of column, 0.9 x 38.6 x 56 1947 kips2250 kips NOT SAFE Hence

Therefore, critical stress Fcr= 39,137 ksi Hence, Design axial strength of column, = 0.9 x 39.1 x 67.7 2385 kips2250 kips P SAFE Hence, W12x210 W12x230 2161 kips 2385 kips NOT OK OK