Answered: Are the composite areas divided into…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Are the composite areas divided into several parts having simpler shapes?

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Step 1

The properties of composite areas are generally solved or analyzed by dividing them into simpler shapes. For instance, I-section or T-section can be divided into simpler shapes like rectangles. Dividing the composite areas into simples shapes helps in solving the properties of the composite area by just plugging in properties of simpler areas that are already known.

Some of the problems where a composite area is divided into simpler shapes are,

(i) While finding the centroid of the composite the following expression is used,

$x = \frac{Σ x_{i} A_{i}}{Σ A_{i}} y = \frac{Σ y_{i} A_{i}}{Σ A_{i}} z = \frac{Σ z_{i} A_{i}}{Σ A_{i}}$

Where $(x, y, z)$ is the coordinate of the centroid of the composite area and $(x_{i}, y_{i}, z_{i})$ are the centroids of the simpler areas A_i.

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