Question

3. Calculate the moment of inertia with respect to both centroidal axes for the area a, b, c, d (30 points) Y (b) Y 10" 5 X X X 2" 15" 15" 6" 2" 6" T. (c) (d)

Answer 1

Y ," (2 1011 X 17 اع il -6" v @ Area of post o Ai= 2x 14 in 2 Centroid, from base y, of part 0 Area of part 2 A2 = 10x2 in 2 centroid from base of baste 42=2+1 = 7" Aly, & A2 Ya AltA2 2X14X1 + 10X2X7 2x14 +10x2 ỹ = 3.5 in moment of Inertia about horiontal Centroidal axis Ixx Ixent A1 (5-4,)2 + Ix2 + Az 19-42)2 4x14x23 + 14X2X(3.5-112+ +,x2x103 +2x10X ( 3.5-7) Fax: 5% int moment af. Inertia about vertical Centoidal Axis Iyy = Iy, of Iya + x 28148 + tex 10x 23 Iyy 12 2 = = 464 in4

7 Area 2 in2 U 10 2 .X A2 = {x10x10 ina ya upiny Az= 10² m2 Yg = 10 = sin lo 10 15" 22 -84, y Centroid from you anes - 10) = -24.in in 11 2 X10X10 + І 2 moment of Inesha about vertical Centoidal Axej, Centreid Hom bere A, EX10X10 Y = 1 in (3) Centooid forum beese ý = Alyt A2 % + A3Y3 2,= 65- AITA2 TA3 72 = 45+1) = 3x10x10x + 2x10 XlOx + 102x5 x10x10 + 10² Ý = 4.166666667) moment of Inertia about horizontal Centooidal Ares Inge = Ixt Al 19-9,)2 + Izet Az 19-Y₂)² + 58+ A3 (9-73)² 4, X 108/03 +1x10x10x (4.166666-1972 Bo X10X10% + Źx10x10x(4./66666-52 + x 104 +10° x 14.86666,5)2 Igex = 1527.77178 in 4 Iyy = Iy, + A, xx, 2 & lyg & Az X X2² + Iya Že X16X103 +3 x 10 xlox ( - 3.92 + 36 of Śc X10X102 + 4x10x10x(39) 36 2 4 + 10 72 Iyy = 8333.3333 in 4