Answered: Determine the following for the figure…

Determine the following for the figure shown, a. Centroidal Moment of Inertia about the x-axis b. Moment of inertia about the y-axis

Engineering Fundamentals: An Introduction to Engineering (MindTap Course List)

5th Edition

ISBN:9781305084766

Author:Saeed Moaveni

Publisher:Saeed Moaveni

Chapter9: Mass And Mass-related Variables In Engineering

Section: Chapter Questions

Problem 33P

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Concept explainers

Moments

There are various practical applications of the concept of moments, like a rotation of the crank due to linear motion of the piston, the moment of inertia and its use in designing beams and columns, bending moment concept, torque, twisting moment, etc.

Question

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Determine the following for the figure shown,
a. Centroidal Moment of Inertia about the x-axis
b. Moment of inertia about the y-axis

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First of all, I already ask the first Tutor in Bartleby to solve the 3 questions which are the 1.) Total Area AT 2.) Centroid about the x-axis ȳ (y-bar) 3.) Centroid about the y – axis x̄ (x-bar). This is his computations: A1= 3400, A2=800, A3=706.85834, A4=176.71458 Y1=42.5, Y2=26.666, Y3=52.7324, Y4= 62.5 X1=20, X2=53.333, X3=52.7324, X4=17.5 Total Area: 4730.14376 ȳ=40.604 x̄ (x-bar) = 30.6224 Please, I want you to solve the: 4.) Moment of Inertia About the x-axis Ix 5.) Moment of Inertia About the y – axis Iy 6.) Polar Moment of Inertia about the axes Jo 7.) Moment of Inertia About the centroidal x-axis Ix note: In locating the centroid of the entire section, Varignon's Theorem. Varignon's Theorem locates the centroid of a composite body. I hope you will use the formulas I will be giving.
Load(N) Deflection (mm) 0 0 18.97653 0.000237 32.77441 0.001098 51.461163 0.001594 76.185582 0.001849 87.863388 0.002257 105.729758 0.002586 126.469914 0.003218 143.448229 0.003437 162.779096 0.003581 181.543668 0.004574 195.541246 0.004563 217.83033 0.005191 244.968433 0.005753 253.314036 0.006191 268.431367 0.006538 292.33781 0.006976 316.690668 0.007269 331.577837 0.008005 352.21158 0.008481 373.106153 0.008909 393.808677 0.009246 409.857991 0.009922 429.378258 0.010108 449.377721 0.010512 469.233361 0.010947 489.128391 0.011398 510.003982 0.011648 526.693131 0.012103 549.488784 0.012722 568.293636 0.013062 587.17942 0.01341 608.291451 0.013959 626.355518 0.014182 638.624416 0.014722 662.308826 0.015088 675.839531 0.015494 707.505477 0.016118 729.367369 0.016579 749.521008 0.016853 735.919806 0.016815 759.436614 0.017338 783.326777 0.017777 802.632402 0.018384 819.026737 0.018615 843.967335…
Given: A1= 3400, A2=800, A3=706.85834, A4=176.71458 Y1=42.5, Y2=26.666, Y3=52.7324, Y4= 62.5 X1=20, X2=53.333, X3=52.7324, X4=17.5 Total Area: 4730.14376 ȳ=40.604 x̄ (x-bar) = 30.6224 Please, I want you to solve the: 4.) Moment of Inertia About the x-axis Ix 5.) Moment of Inertia About the y – axis Iy 6.) Polar Moment of Inertia about the axes Jo 7.) Moment of Inertia About the centroidal x-axis Ix note: In locating the centroid of the entire section, Varignon's Theorem. Varignon's Theorem locates the centroid of a composite body. I hope you will use the formulas I will be giving.
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