Question

7:00 morgan.blackboard.com Module 10: Chapter 10-Moments of Inertia 6. Determine the moment of inertia for the shaded area about the axis 7. Determine the moment of inertia I of the shaded area about the x axis 150 mm 8. Determine the product of inertia for the beam's cross-sectional area with respect to the u and waxes. 20 mm

Answer 1

Moment of inertia of strip about y - axis: - dI_y = (2x)3 dy/12 (The strip is rectangular) OR dI_y = 8x^3 dy/12 Put y = 1/50 x^2 OR X = squareroot 50 y therefore dI_y = 8 (squareroot 50 y)^3 dy/12 OR dI_y = 8 times 50 squareroot 50 y^3/2 dy/12 integrating w.r.t y I_y = integral d I_y = 8 times 50 squareroot 50/12 integral^y = 200 mm_y = 0 y^3/2 dy OR I_y = 400 squareroot 50/12 [y^5/2/5/2]^200_0 OR I_y = 400 squareroot 50/12 times 2/5 [200^5/2 - 0^5/2] I_y = 400 squareroot 50/12 times 2/5 times 200^2 squareroot 200 OR I_y = 80 squareroot 50/6 times (200)^2 (squareroot 50 times 4) OR I_y = 160000000/3 mm^4 Ans OR I_y = 53333333.333 mm^3