1/11/2024 0 Comments Centroid and moment of inertia![]() ![]() ![]() 2.2 Centroid of a curve L,anareaA, and a volume V The centroid of an area A,Fig.2. It is a mathematical property of a section concerned with a surface area and how that area is distributed about the reference axis (axis of interest). 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. It is always considered with respect to a reference axis such as X-X or Y-Y. Sol: The given plate is symmetrical about the y-y axis, therefore \ = 150 mm. The moment of inertia is defined as the product of mass of section and the square of the distance between the reference axis and the centroid of the section. 76 2 Centroids and Moments of Inertia z y O x C C A L V dL dA dV r Fig. The Moment of Inertia (I) is a term used to describe the capacity of a cross-section to resist bending. To find \, we have to divide the whole Figure into standard areas.Įxample: Find the moment of inertia of a plate with a circular hole about its centroidal x axis as shown in Fig.8. Sol: The given I-section is symmetrical about the y-y axis, therefore, ![]() = + Įxample: Determine the moment of inertia about the horizontal axis passing through the centroid of the section as shown in Fig.7. ![]()
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