Question

304 4 in. 3 in.

For the rectangular region,

1) determine the moment of inertia about the u-axis

2) determine the product of inertia about the u-v axes

3) determine the moment of inertia about the v-axis

4) determine the principal moments of inertia and the principal directions at the centroid C (Imax, Imin, angle about the x-axis)

Answer 1

D 9 (d) 4 m 9 in (b) For the eactangular region In = bd 3x43 = 16 in 12 469 12 4x3 12 9 in Lu= Intly, sine 20 2 19 Eny = funt by = 16+9 = 25 int ③ Moment of inertia about u- omis (in-Ly case + Luy 167,9 + 16 = ?) as 2x30 + 25 si 2x 12.5 + 3.5% + 2 + 25x / 35.9 in4 Ans @ Product of wertia about Sun = -( Ix - y) sin 20+ Suy 432 -(1679) * Sun 28 30 + 25 us 2x 30 3.03 7 12.50 9.47 in Ans u v anes

11 1.75 - 21.65 ③ Moment of inertia about re- asia's Sv= (5x+ly) - (x - y) ces 20-say sin 20 (16ĘT)- (1679) Cs 2x 30 - 25*5w2x30 12.5-3.5*4 - 25 X 1 12.5- = 1-10.9uy Aus. 6 Principal moment of inertia, 11,2 = 1x+dy I vitezky**(ny) 1679 I v 0523°4251 12.5 | 25-24 fi 12.5 + 25-24 = 37.74 in so, Iman 37.74 in 1 Ans 12 12.5-25.24 -12.74 Sw, gun -12.74 in Has Principal direction about the controll tausop 52 2x25 16-9 = 7.14 2 fug Ix-by 202 = tail (5:14) ВР, 41-01° = 82.03 , 2012 = 1807 A2.03 = 262-03

2 Op2 - 262.03 : 131° 2 Hence, Pornepal direction op, = 41 6P2 = 131 fm- Summary ty Moment of werlia ractangle of d → Lx In = bd b Fy= db 12