Question

find the magnitude and orientation of the principle moment of inertia of the given shape, 60 mm 40 mm 40 mm

Answer 1

I_x = 3.2 times 10^6 mm^4 I_y = 7.2 times 10^6 mm^4 I_xy = 2.7 times 10^6 mm^4 Principal axis, tan 2 theta_p = 2I_xy/I_x.I_y 2 theta_p = tan^-1(2 times 24 times 10^6/3.2 - 7.2 times 10^6 = -50.194 degree theta_p = -25.097 degree & 64.903 degree Principal MOI, I_1, 2 = I_x + I_y/2 plusminus squareroot (I_x - I_y/2)^2 + I_xy^2 = 5.2 times 10^6 plusminus 3.124 times 10^6 I_1 = 8.321 times 10^6 mm^4 I_2 = 2.076 times 10^6 mm^4