The centroid or center of area of a geometric region is the geometric center of an object's shape. Centroid calculations are very common in statics, whether you're calculating the location of a distributed load's resultant or determining an object's center of mass. To compute the center of area of a region (or distributed load), you can compute the x-coordinate (and the other coordinates similarly) from the following equations:
For discrete regions: You can break discrete regions into simple shapes such as triangles, rectangles, circles, and so on.
For discrete shapes, creating a simple table such as the one that follows for each coordinate can be useful. You can create as many rows as you need for as many regions as you have.
| xi | Ai | xiAi | |
|---|---|---|---|
| Region 1 | x-distance for Region 1 | Area of Region 1 | Product of xi and Ai |
| TOTALS | ----------------- | Sum of all Ai rows | Sum of all xiAi rows |
For continuous regions: Continuous regions are usually defined by more complex boundaries, so you must define them with mathematical equations such as the one that follows:
