Question

Statics problem

Problem 09.036 - Moment of inertia of complex composite Determine the moments of inertia of the shaded area shown with respect to the x and y-axes. Given a = 80 mm. 125 mm 250 mm 125 mm The moment of inertia with respect to the x-axis is * 106 mm 4 The moment of inertia with respect to the y-axis is Х 106 mm4.

Answer 1

We used the equation of moment of inertia of rectangular block, semicircle and parallel axis theorem to find out the moment of inertia of shaded part about x and y axis. The detailed handwritten solution attached here.
d > 9 b data for this case Form the given & a=gon d = 250 mm mm 6 = 125 mm inertia of of block The about moment yo egn axis are by green reb 3 db I y B = Ite 3. bd 12 & bo

of inertia of with The moment respect to semicircle gineen C. Yo by & Iyo T an Ixc 8 8 Now thedrem we use parallel axis the above ean of block C semicircle to find out the moment of inertia of shaded part about e Y anis. About x - aais distance ca alb are both xc The olj axis کہ کی So from the moment away x-axis. inertia is x -axis abuut given by egh 3 2 I bd Area of + * ( & Block 1 2 २ of T a Area er ㅏ klo cemicircle 2 4 2 3 d Tian bd d 7 a + lo 12 3 125*250 (1954 J + 125 250 250 a * (So)" TT (80) f 2 (250" = 651.061 * 10' 173.16 * 106

Ix 4 477.881 * 106 mm About Y- ancis from Gocis The axis awcy distance Y age oly of moment & Axis Yc a Ч are parallel So given eque by is inertia about Y axis 3 db )” - Iy Area of Block + 1 2 4 Tah g 3 bd + db 12 els Elu 2 3 25 T* 8o - 125 250*125 * 2 50 + 4 8 162.76 *10 106, 16.086 #10 106 146. 676 Iy mms *106