Question

Determine the inertial properties of the region shown. About the centroid

3.5 in. - X B 2 in. 7.5 in.

Answer 1

Complete solution is given below.

Assume referent reference axis as shown below. - 3.5 2 A3 A2 Al 1.5 T. S 17 Areas of different region" ( A, a 7.5x1.5 - 11.25 in? Az = TLX 3.5* 19.24 in² 6.28 in² Az = . TL x 2 ay Controidal distance with respect to reference sais x = t = 3.75 in 8.985 in 4.5+ (425) 23 = 7.5+ ( x ) 8.35 in

71 = 1.5 2 0.75 in . Y 2 = 3.5 in 3.5 in 73 = sy moment of Inertia of individual asseas Ix 7.5*1.53 2.11 in4 12 Iny 52.73 1.5X 7.33 12 58,93 Iza 10 Tx 3.54 Izy 0.11 x 3.54 = 16.51 6.28 TL x 24 I 3x 8 I ay Ooll x 24 * 24- 1. 76 4) īs (11.25x 3.45) +19.24*8.985)-46.26*8.35) 11.25+ 19.24 6.28 162.62/ 24.21 X z = 6.717 in

y = (16.25x0.75)+(19.24x 3.5) -(6.28 * 3.5) LA.21 g 2.22 in 57 moment ģf Inertia with respect to centroid Ix = doll + (11.25) (0.75 -2.22) + 58.93 + (19.24)(3.5-2.22)2 – (6.28)(3.5-2:22) 6.28 I 26.42 + 90.45 16.57 Ix 1003 in 4 • Iy 3 52.73 + (16.25)( 6.717 - 3.75) ? + 16251 + (19.24) (6.717 - 8.985)? (6.28) (6.714 – 8.35) ? - 1.76 151.76 + 115.4.8 18.51 Ly Iy = 248,73 in 4