![]() Moment of Inertia of a Rectangle Subsection 10.4.2 Structural Steel Sections Note that when using the parallel axis theorem, area is always positive, and the MOI of the hole \(I_2\) is subtracted from \(I_1\) to get the MOI of the combined shape. Moments of inertia are always calculated relative to a specific axis, so the moments of inertia of all the sub shapes must be calculated with respect to this same axis, which will usually involve applying the parallel axis theorem. Subsection 10.4.1 Composite Area Methodįor a composite shape made up of \(n\) subparts, the moment of inertia of the whole shape is the sum of the moments of inertia of the individual parts, however the moment of inertia of any holes are subtracted from the total of the positive areas. The procedure is to divide the complex shape into its sub shapes and then use the centroidal moment of inertia formulas from Subsection 10.3.2, along with the parallel axis theorem (10.3.1) to calculate the moments of inertia of parts, and finally combine them to find the moment of inertia of the original shape. In this section we will find the moment of inertia of shapes formed by combining simple shapes like rectangles, triangles and circles much the same way we did to find centroids in Section 7.5. When do you need to apply the parallel axis theorem?Ībout which point do you find the smallest area moments of inertia? What is it about this point that is so special? Where do the common shape area moment of inertia equations come from? Section 10.4 Moment of Inertia of Composite Shapes Key Questions Relation Between Loading, Shear and Moment.** Search this PAGE ONLY, click on Maginifying Glass **Īll calculators require a java enabled browser.\newcommand Section Properties Radius of Gyration Cases 35 - 37.Section Properties Radius of Gyration Cases 32 - 34. ![]() Section Properties Radius of Gyration Cases 28 - 31.Section Properties Radius of Gyration Cases 23 - 27.Section Properties Radius of Gyration Cases 17 - 22. ![]() Section Properties Radius of Gyration Cases 11 - 16.Section Properties Radius of Gyration Cases 1 - 10. ![]()
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