Question

Problem#2 A W12 x58, A992 column is pinned at the top and fixed at the bottom as shown. Lateral bracing is provided to assist with weak-axis buckling strength 12.5 ft from the ground level. For the condition where the column only supports axial load, determine the design strength of the column. K 1.0 7.5 ft K- 0.8 20 ft K = 0.8 | 12.5 ft

Answer 1

given column of any end condition so axial load axing on the column M_x = -Pxy [EI d^2 y/dx^2] = -Py from the Bending Moment Equation M/I = 5/y d^2 y/dx^2 + Py/ = 0 the solution for the above equation (ii) is y = C_1 cos (x squareroot P/EI) + C_2 sin (x squareroot P/EI) apply boundary conditions at x = 0, y = 0 rightwardsdoublearrow 0 = C_1 times 1 + C_2 times 0 C_1 = 0 at x = L, y = 0 0 = 0 + C_2 sin L squareroot P/EI rightwardsdoublearrow sin (2 squareroot P/EI) = 0 C_2 notequalto 0 (L squareroot P/EI) = n pi but given factor for one end is fixed & other end is hinged is 0.8. so effective length is = 0.8 times L 0.8 times L times squareroot P/EI = n pi \r\n P = n^2 pi^2 EI/(0.8 L)^2 so the critical (81) design load is P_cr = pi^2 EI/(0.8 L)^2