Question

Find I, and ly for the composite area shown. Show complete solution with formulae as needed. - 3 in. -10.5 in

Answer 1

the centroids of Solution: At first we need to find composite area. k 3.5 in MY 13.5/2= 6.75in 3 in 340.5 -1.5in IS 10.5 in 4.5 16.5 2 +3 Bin = 8.25 Bin 317 I 10.5 5-145 เซ 2 = 5.25 10.5m We divided the whole artem into 3 parts. fore part 1; A = 3x 10.5 = 31.5 in2 2 = 5.25m 2,= 105 in for part 2: A₂ = 1.5x10.5=15.75in2 N2 = 4.5 in 2 = 8.25 in Az = 3x13.5= 40.5 int X3 = 6.75 in 23 = 15 in for part 3;

so = I xi (31.5x5-25)+(1575*4.5) ZAD + (40.5x6.75) (31-5+ 15.75 + 40.5) on n = 5.808 in also, - IDEAL (31-5*1-5)+(1575*8.25) + (40.5*15) = 2 Ai (31.5 + 15.754 Difference on, 5= 8.942 in Now we com find the centroids using parallel oon's theorem: between centroids of We know Ix = (x) et Aidni Individual o CArea and main Individual parts M.O.I ly=(Iyout Aidxe along in ani's Carreal ancis Individual part's M.OI. about bornig Difference between Note Fore Rectangle, and centroids of Individual and main body alona x bd3 anis No Tz bodry about x 1 dl kx + d. 3 72 *. M. o. I = Moment of Inertia.

Ix For 4 for Calculation: Part 1; A = 31.5 in 2 (1x) = 10.5 x 3 12 doi= (5-4,2 on ay = (8.942-10572 on, da = (7.442)2 in2 Post 2; A= 15.75in . (I) = 1.5x 10.53 ans 2 12 druh = (5 – 2 or deze - (8.942 – 8.252 r do 2 = (0.692) 2 in2 Part 3; Az= 40.5 in? (Ixo = 13.5*33.4 For dyz = (563)2 or; da?= (8-942-15, 2 or dag ² = (-6.058) ² (6.058) in

There force; x = [ (IX)o, + Ady, " + [(Iy). + A, dy 2] + [(1x)og+ Az dy'] 09 Ix = 10.5 x 3² + 31.5x (7.442) 2 + 105x10-5} + 15.754 (0.69232 1315x33 - 40.5x (6.058) 2 12 or or I For Ix = 3437.145 int x 3437 inh calculation Part 1; A. = 31.5 in? (ty)o, = 3x10.53 de = (x-2,2 dx² = (5808- 5.2502 dzi 2 (0.558) 2 in2 Part 2; A = 15.75in? (ty) o. = 10.581.53 4 0212 For

dx2 - (n_n) 2 daz² = (5.808 - 4.52 da 2 2 = (1.30872 in2 For Part 3; Az = 40.5 in 2 (Ig) o = 3x13.53 ist daze = (in – x3)2 daz² = (5.808 – 6.752 deze = (-0.942) ² (0.942 in2 Therefore; tya [(Tylo, & A, de 1+ [ (Tydo, + A, dx2] + [ (ty) oz + Az drez] on ay = 3x10.58 + 31.5*(0.55882 + 10.5x1.53 + 15.75*(1.308)2 + 3x13.53 + 40.5*(0.942)? on, Iy = 980.145 int or, ty ~ 980 int 12 T2 (Answer)