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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