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# Chapter 11. Finding the Centers of Objects and Regions

In Chapter 10, I describe how to find the resultant (combined) force of a variety of distributed loads by simply determining the areas under the load diagram. This calculation provides you with two of the three pieces of information required to fully define a force vector — namely, the magnitude (the vector's length) and the sense (the vector's direction). However, you also need to determine a force vector's point of application in order to properly define the vector. (Check out Chapter 4 for details on these vector properties.)

For concentrated loads (single loads applied at a point — see Chapter 9), you can determine the point of application almost by inspection. If a small object hits a wall, a concentrated force from the ball is located at the point of impact. However, distributed loads (loads spread over a line or area — see Chapter 10) are different.

To find the point of application of a resultant of a distributed load, you have to calculate the center of area or the centers of mass and gravity for the load or object. In this chapter, I show you how to perform these calculations.

# Defining Location for Distributed Loads

Depending on the type of distributed loads you encounter along your statics journeys, the resultant force of each of those loads must ...

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