Question

For the following section: 12 A- 13 (1- 30 mm A- 30 mm 14 70 mm (1 A- 140 mm Fo 30 mm 30 mm 170 mm 4- The moment of inertia (I^) about the x axis (10'mm4) is: A- 154 B- 124 C- 254 D- 224 5- The moment of inertia (7y) about the y axis (10°mm4) is: A- 51.3 B-91.3 C-81.3 D- 101.3 6- The value of y is: A- 70 7 R- 90.7 C- 80.7 D- 51.7 7- The moment of inertia (I) about the horizontal centroid axis x' (10 mm2) is А- 87 6 В- 77.6 С-97.6 D- 67.6 8- The value of x is: A- 61.6 B-81.6 C-51.6 D- 91.6 9- The moment of inertia (1.,) about the vertical centroid axis y' (10 mm4) is: A- 81.2 B- 71.2 C-41.2 D- 31.2 15 A- 16 А- 17 A- For the following section: 50 mm 50 mm 250 mm 50 mm 350 mm 10- The value ofy is: A- 91.7 B- 81.7 C- 617 D- 51.7 11- The moment of inertia (I,) about the horizontal centroid axis x (10 mm4) is: А- 226 В-206 С-216 D- 236

Answer 1

mm 30 mm 3, 7--.- --- 140 2 1 - mm - - - - -- IA - - - - - iust 30 I Toi 30 m - ry, he - 76 k 170- > 30 mm in mit Area of paot 0 Air 30 mmx (30+170) mm = 6000 mm2 centroid of part o forom $•x axis yo = 30 = 15mm Centroid oy part O from y asis Yz: X = (30 7170) 31= Loomm Area cf part @ A2 = 140mmx30mm = 4200 mm Centroid of past @ from xe axis y2 = 30+ lyo - 100 mm centroid of part ② from y anis LE32= 20 = 15 mm

Area of part ☺ A3 = 30x130+70) mm2 A2- 3000 mm Centroid og part from se Qris Yg = 30+140 + Y = 185 mm centroid of part ☺ forom yources olz = (30+70), 50 mm moment of Inertia of part D about its own horizontal Centroidal Avis, Tixe = * *(30+70)x 303 = 450000 mm 4 moment of Inerta of poot o about its own veutical Centoid aris Tryc = 5 x 30x (30+70)3 = 2x107 mm 4 moment of Inertia of past @ about its own horizontel Centroido Aviso Taxc = 5x30x1403 = 6860000 mm 4 moment of Inestia ay part about its own vertical centroidal Ases Izyc = 72 x 140X303 - 315000 mmy moment of Inertia of past about els own horizontal Centroidol Axis I3xc = x 30+70) x 303 = 225000 mm?

moment of Inertia of port ( about its own vesticeul Centroidal Aris, Izyc = +2 x 30 x(30+70)3 = 25x105 mm Quest© moment of Inestia (Ix) about the x arus (using parallel Axis theorem) Ixe = (Iixe+ A, 42)+(Inxe + A2 y 2) + ( 13xc+ Azy =1450000+6000x152) +(6860000 +4200 x 100%) +225000*1852X3000) = 153560000 mm = 153.56 X106 mm 4 TTx 154 x 106 mm 4 Answer o obton Question ☺ moment of Inertia (Iy) about the y axis luoing parallel Axis theorem) Iy = (Ilyc ta, x, 2) + ( Il y ct A2 44²) +(I3yc +A223²) = (2x107 + 6000X100%) + ( 315000+ 4200X152) +(25x105 + 3000x502) = 91.26 X106 Ty913 x 106 mmt) So option ® 913 is correct

Question © - Aly + A 2 Y₂ + A3Yz A, TA2 TA3 = 6000x15+ 4200 X 100 + 3000 * 185 6000 +4200 + 3000 ỹ - 80.6818 mm [s x 80,7 mm) So Phan ©80.7 mm is correct Question moment of Inertia about honzontal Centroidal aris Ixl Ixel = Ix-(A, +AztA3) . 92 = 153.56 X106– (6000 +4200+3000) X 80.6812 = .. 67. 633 X106 mmt so obton 0 676 is corect Question ® ă = 4 A, TA2 +A = 6000x100 + 4200 XIS + 3000x50 6000 +4200 + 3000 DE = 61.5909 mm a = 6106 mm. Option A 61.6 10 correct + ( LA X + Xa

Question 9 moment of Thertia (ly) about vertical Centroidal Ano Ty' = Jy - (AltA2+A2) 52 = 91.26 X106 -717,0 (6000+4200 +3000)X 61.5909 = 46.1866 X106 mmt Iy 1 ~41, 2 x 106 mmt so option © 41.2 is coreet