Tiêu đề 7 Centroids and Moment of Inertia.pdf ✅

PSAD 7: Centroids and Moment of Inertia This module shows the formulas for the centroids and moments of inertia of common shapes and how these are used in composite shapes. For the basic concepts, refer to MSTC 79: Centroids and MSTC 80: Moment of Inertia. 1. Centroid 1.1. Calculator Technique Limitation: It is not applicable to sections with hollow portions. Step 1: Enter statistics mode in the calculator. If both x and y are needed, then use the 2-variable/Linear/A+Bx function (Table should show x, y, f). If only one of x and y is needed, then use the single variable function (Table should show x, f). Step 2: Fill up the table. The variables x and y in the table represents x and y while “FREQ”, short for frequency, represents the AREA. Step 3: Compute the required values. Enter “S-Var” In the calculator, n represents the total area of the section while x and y are the coordinates of the centroid. 2. Moment of Inertia 2.1. Parallel Axis Theorem The Parallel Axis Theorem is helpful in computing for the moment of inertia of a composite section. I = ∑(I + Ad 2 ) Where ∑ Ad 2 is called the transfer formula. A is the area of each segment while d is the distance from the reference axis and the centroid of the composite section.