# More Complicated Beam Loads

## Exponential Loads

An exponential load is a load whose force varies exponentially along the
beam's length. In this document, we assume a force distribution
of the form
*q *(*x *)* = q0 *exp(*-x/L *) for a "left-handed"
distribution, or *q *(*x *)* = q0
*exp(-(*L-x *)*/L *) for a "right-handed"
distribution. If the total mass of the load is *m *, we leave
the computation of *q0 * as an exercise for the reader.

## Sine Load

A load whose force at the point *x *
is *q (x) = q0 *sin(Pi x/L ) will be called a sine load.
If the total mass of the load is *m *, a short computation shows that
*q0 = mg Pi/ *(*2L *).

## Cosine Load

A load whose force at the point *x *
is *q (x) = q0 *cos*(Pi x/(2L)) * will be
called a cosine load.
If the total mass of the load is *m *, then
*q0 = mg Pi/(2L) *.

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The Geometry Center Calculus Development Team
Copyright © 1996 by The Geometry Center.
Last modified: Fri Apr 12 15:50:01 1996