Question

5. A built-up section consists of two MC18 x 42.27 identical channels placed back to back and two plates PL % x 16 as shown in Fig. Q5. The section is subjected to axial loads P= 100 k and P check. Properties of each channel is as follows: A= 12.6 in2, d = 18.00 in, I,= 554 in*, I 14.3in, = 0.877 in. Use steel with F,= 50 ksi. 300 k. Is this section satisfactory for the given loads? Use LRFD method to (25%) MC 18 x 42.27 2 in 2 in 20 ft -PL 3/4 x 16 PL 3/4 x 16 MC 18 x 42.27 Fig. Q5

Answer 1

GIVEN DATA Properties of Steel section in 2 Gross area of cross section, 49.2 Radii of gyration, r = 7.166 in 6,708 in r = Restraints Along x direction L = Unsupported Length of column, 20 ft Bottom End : fixed : fixed Top end Along y direction Unsupported Length of column, 20 ft Bottom End fixed : fixed Top end CALCULATIONS Yield stress of steel Fy= 50 ksi Modulus of Elasticity of steel 29000 ksi E = ку 3 Effective length factors, 0.65 Ку - 0.65 к. L, 0.65 x ( 20х 12 in 7.17 21.769 к.L, 12 in 6.71 0.65 x( 20 x - =23.256 Since K, L/r < KyLy/ry, KyLy/ry controls VE r 0.307 < 1.5 Note: For à <1.5, F =(0.658 )F, 0.877 F r Therefore, critical stress, 48.066 ksi Hence Design axial strength of column, Ф.Р, 3 ф.F., А, 0,9 x 48.07 x 49.2

2128 kips Py1.2 P +1.6 P = 1.2 x 1001.6 x 300 Design load, 570 kips Since design strength is greater than design load, the column is safe.