Question

4. A column is made by lacing together two structural-steel C200x17.1 channels, as shown. If the column is 7 m long, fixed at one end and pinned at the other irn both planes, calculate the maximum slenderness ratio. The lacing joining the two channels does not affect its moment of inertia, but does make the channels act as one member. IIO 5. Two structural-steel L 127x89x12.7 angles are fastened back to back, as shown to form a column 3 m long. If the ends are fixed in both planes, find the maximum slenderness ratio.

Answer 1

Maximum slenderness ratio, lambda = effective length of column(L_e)/Minimum radius of Gyration (r_min) r_min = squareroot I_min/A For, C 200 times 17.1 (From steel tables) c = 14.5mm A = 2170 mm^2 I_11 = 13.5 times 10^6 mm^4 I_22 = 0.545 times 10^6 mm^4 I_xx = 2 times I_11 = 2 times 13.5 times 10^6 mm^4 = 27 times 10^6 mm^4 I_yy = 2 times [I_22 + A.(y)^2] = times [0.545 times 10^6 + 2170 times (69.5)^2] = 22.0532 times 10^6 mm^4 so, I_yy is minimum among both centroidal axes. so, r_min = squareroot 22.0532 times 10^6/2 times 2170 0 2 sections = 71.2839 mm so, lambda_max = L_e/r_min L_e for one end fixed and other end pinned is = L times 1/squareroot 2 = 7 times 1/squareroot 2 = 4.949m = > lambda_max = 4950 mm/71.2839 lambda_max = 69.437