Question

Four L3 3 릊 n. angles are welded to a rolled w section as shown. Determine the moments of inertia and the radii of gyration of the combined section with respect to the centro dal x and y axes if a = 6 in. (Round the final answers to one decimal place.) 1.3 x 3 3 11,8 x 31 in' in. int in. The moment of inertia with respect to the x axis is The radius of gyration with respect to the x axis is The radius of gyration with respect to the y axis is

Answer 1

Given that, four L_3 times 3 times 1/4 in angles are welded to a rolled w section. The above diagram is given in the question. Now, we have to calculate the total area, A = A_w + 4.A_angle - (1) \r\n Here, A_w is the area of the web and A_angle is the area of the angle. Obtain the areas A_angle and A_w for the shapes L_3 times 3 times 1/2 and W_8 times 31 from Appendix B properties of the rolled-steel shapes A_angle = 1.44 in^2 A_w = 9.12 in^2 Now, substitute 1.44 in^2 for A_angle and 9.12 in^2 for A_w in eq^n(1) A = 4(1.44) + (9.12) A = 14.88 in^2 Calculate the moment of inertia of the angle about x-axis by the parallel axis theorem. (I_x)_angle = I_x + A_angle(d)^2 - (2) Here, I_x is the centroidal moment of inertia about x-axis and d is the central distance from x-axis. \r\n Now, obtain the values of x, y and I_x for angle