Beam Loads

The amount by which a uniform beam deflects under a load is a function of the position along the beam. For example, a 2x4 piece of wood that is supported between two sawhorses will deflect more in the middle of the sawhorses than it will close to its ends. In this example, the beam is sagging under its own weight, which we may think of as being a uniform load .

In general, the deflection of a beam depends on the distribution of its load. In theory, a load may have virtually any shape. For this document, however, we will only consider loads whose weight distribution can be modeled by simple mathematical functions.

In the exposition that follows, we will let L be the total length of the beam and we let x measure the position along the beam (with x=0 being the left-hand endpoint of the beam.)

Simple Loads
More Complicated Loads

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The Geometry Center Calculus Development Team