Engineering Mechanics: Statics & Dynamics (14th Edition)

Published by Pearson
ISBN 10: 0133915425
ISBN 13: 978-0-13391-542-6

Chapter 10 - Moments of Inertia - Section 10.4 - Moments of Inertia for Composite Areas - Problems - Page 547: 51



Work Step by Step

We can find the required moment of inertia as follows: $I_x^{\prime}=\Sigma (I+Ad^2_y)$ We plug in the known values to obtain: $I_x^{\prime}=\frac{(100+100)(2\cdot 25+2\cdot 200 sin 45^{\circ})^3}{36}+4(\frac{200 cos 45^{\circ}(200 sin 45^{\circ})^3}{36})+200 cos 45^{\circ}200 sin 45^{\circ}\cdot \frac{200 sin45 }{3^2}-2(\frac{(200)^4(\frac{\pi}{4}-\frac{sin 45}{2})}{4})$ This simplifies to: $I_x^{\prime}=520(10^6)mm^4$
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