Question

Determine the moments of Inertia of the shaded area shown with respect to the x and y-axes. Given a = 82 mm. 125 mm - 250 mm 125 mm The moment of inertia with respect to the x-axis is 106 mm The moment of inertia with respect to the y-axis is 106 mm4

Answer 1

Moment of Inertia I = I - IL 3 where I BD 12 + AY 1.12642.50° +631260 x 03) 9,- Jy = 0 IN. A and Centroida) Axis Corinside se atis. > 1627 60 416.7 mot wNt TT Dt + de 52 12.3 1647 +0=1773 4780 mont 128 I, I = 145005636. 7 mont 1145.00 563 x 100 mm x 100 mmt 12 .N to y Axis 6 I with respect I A = 31250 mmt A₂ = 10562.0mm 62.5mm 1,92 I = 47= 4182 47 4182 - 34.80mme 31 31

Now Neutral Aris lies, J = A, I, - Az Y (31250 x 62.5) - (0362 362.03% 34.80) 31250 10562.03 9 = 76.6 4mo Novo Moment of Inertia Ij Let J HI ca col 76.64 - 62.5= 14.14mm J - ₂ = 76.64 -34.8 = 41.84 mm DB 12 2 50x125 ² + (31250x 11 12 46938216.67 mmt 177 178 1647 + (10562 16 562.03X 41.84" I DA + A T 128 4 = 362 4 4 5 25.5 mm m4 11 Iy, - Iye 10693691-17 mm Ig 110.6936 X106 mmt Thank you. All the Best.