Question

Statics

3. For the following composite area shown below. Shaded regions have material while white regions are empty. Include proper units. a. Find the location of the centroid measured from the shown X and Y axes. b. Calculate the moment of inertia and radius of gyration about the indicated axes Yc centroidal Ixe = bh?/12 and lyc = hb?/12 h Xc b Yc centroidal Ixe = r4/4 and Iye = 1r4/4 Xc ka nga X- Y- 8" (5 points) (5 points) (5 points) (5 points) 1,- X K- (5 points)

Answer 1

3 TX 3 10x1 12 =0.8333 Ily 18103 . 83.333 12 centroid of I Xi 1002 5" 5,- ₂- 8.5" / 2 63 +8 Inac 6x83 2561 Izy = 144 12 12 Х. - 2 + 6/2 -S" 8/ 34" (3 ( it is deduction so tve Isoc= I - 7 x 14. T 14 17 A 7) 34 4 4 4 X 11 2+3=5" Y 1 = 3 Al area Az area 10x1=10 8x6 = 48 1 Az area 6 TIX/² = T (deduction) overall centroid x = A, SCI+ A2-A3X3 AH A2-A3 х 10 X5 +48 X 5-7X5 10 +48-7 T: AYITALY, -A3Y3 AtAz - Az 4-82 10x 8.5+ 48x4-7x4 10+48 - IT 2 +A6² IDC Fix I where his distance Ilse + A,9² from centroid to x ocas = 0.8333;+ 10 X 8.52 Izx= Izol+Ag2 256 + 48x42 Izx = Isset Aziz 774 + 718425 = 723.333 1024 51.05 (deduction) IX Iix + Izt Izt 1696-28 = 83.33+10x5? 144+ 48857 333.33 1344 "I ly = I ly + A, xc,? Izy + A24² Izyt Az x3² = 7/4+TT X 5² Iy = Tiy + Izy Izy - - 79.325 (deduction) + Izy -I3y 1598-008 |_x j Ix - А. 1696.28 10148-T 5.56

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