Question

PROBLEM 3 3 in 16 in. 8.92 in. Using the parallel-axis theorem, determine the product of inertia of the area shown with respect to the centroidal x and y axes. 2 in 0.61 in. 4 in с 2 16,5 in

Answer 1

Title - Moment of Inertia

Solution Step 1: Divide the whole geometry into parts of regular shape & number them , & 3 с By Parallel Anis Theorem, Moment of Inertia about 2- quis, Ixx : Ixx biod, Arhi? [bidz ² + A3 h3 A2-h2² + b2.da² 12 + + + 12 12 Ixx (12x2) x (4:39) + 12.6239 *[*(186)2(137] 15. (42% (154) x (1.39)+7 + [4X (10.94 (4 X16.5) * (2.363 Ixx = 470-5304 + 1959 26 2037.2286

2 4 .. Ixx = 2703.685 in Now, Moment of Inertia about y-anis, Iyy debes Aich, Iyy di.biz 12 [d3b3 + A 3 h3² A2h2² + + + + 12 :. Туу 2 x (12) + 12 + 4x (15)3 (15x4) x (4:42)27 + 2x3) * (2-7397 (4.428] * {1*** (*)*, C6836) (500"] 12 Iyy 492.6336 7 229 7.184 7 1998.33 04 E Iyy 4788.148 in 4 Now, product of Inertia Ixx. Iyy Product of Inertia. = 2703.685 x 4788: 148 6 8 Product of Inertia = 12.9456 X 100 in

Summary - Parallel axis theorem is used to find the moment of inertia about x and y axes. According to parallel axis theorem, we need to distribute the whole geometry into small regular shapes and then use the theorem.