Question

how to solve 9.32

For the shaded are showo, determine the polar moment of inertia with respect to point D. knowing that the polar moments of inertia with respect to points A and B are, respectively, J. = 4000 in and ), = 6240 in, and that dy = 8 in. and d, = in. 9.31 and 9.32 Determine the moments of inertia 7, and ī, of the area shown with respect to centroidal axes respectively parallel and perpendicular to the side AB. a Fig. P9.29 and P9.30 -180 in 4 in I in. 60 60 10 in Dimensions in mm Fig. P9.31 Flg. Pg. De

Answer 1

y 1 180 * Et 29292Y 80 - mm 4 Go - bort 60 .about Y- ari's y - Bomm = 90 mm 2 it is Symmelriced A4, + A242 Y = section - 1 .600*2256000omast 4800mm² by 69,00 12 A = bxd = 60x80 Kia Y-Y,= 36-40- 36mm. 40mm P P P P P P P P Section 2 (199) (40 960000mm 180x40 = 7200mm? Inter -л, съх loomm K2 = %-Y = 100-76= 24 mm Y = 80+ euro 192000 + 720000 A14, tA₂ML У (4300)(40) + (7200) Clou) - 1 2000 Aita 4800 +7200 Ý = 76mm a- nomm Ixa (Iany + A, k, 2) + (Inxa + A2K ² _K2) (2560000 +(4300) (309)+ (2960000+ o+(1200) (24)² (1200) (243) Ixx = 23 80700+ 960oot 1.38×10² mmt Inn (40)(180) dobis (80)660)3 Iuy Iny, + Iuy2 12 Tuy 144000+ 1.94% 1037 2.08x107mmt