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.
x_{i} | A_{i} | x_{i}A_{i} | |
---|---|---|---|
Region 1 | x-distance for Region 1 | Area of Region 1 | Product of x_{i} and A_{i} |
TOTALS | ----------------- | Sum of all A_{i} rows | Sum of all x_{i}A_{i} 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: