# Simple Beam Loads

## Concentrated Load

A concentrated load is an idealized
simplification of a load whose extent is very small compared to the
length of the beam. For example, if a mass *m * is hung by a rope and the
rope is tied around a long beam at some location *x=A * along
the beam, then the load is well-approximated by a concentrated force
of magnitude *mg * (where *g * is the acceleration due to
the earth's gravity).
One of the simulations in the interactive portion of this lab is the bending
of a cantilevered beam (i.e. a beam clamped at one end as
pictured below) with a concentrated load placed at *x=L * (the end of
the beam.)

## Uniform Load

A uniform load is a load that exerts equal force along each point of
the beam's length. If the total mass of the load is *m *,
then the force per unit length that the beam feels is
*q *(*x *) = *q0 * where *q0 * = *mg */*L *

## Triangular Loads

A triangular load is a load whose force varies linearly along the
beam's length and which is zero at one of the beam's ends. If the
total mass of the load is *m *, then the force that the beam
feels at *x * is *q *(*x *)* = q0 * (*1-x/L *)
for a "left-handed" triangular load or *q *(*x *) *= q0
x/L * for a "right-handed" triangular load where *q0 =
2mg/L *.

## Parabolic Loads

A parabolic load is a load whose force varies quadratically along the
beam's length and which is zero at one of the beam's ends. For the
purpose of this lab, we assume that if the
total mass of the load is *m *, then the force that the beam
feels at *x * is *q *(*x *)* = q0
*(*1- *(*x/L *)^{2}) for a "left-handed" parabolic load
or *q *(*x *)* = q0 *(*1- *(*x/L-1 *)^{2}) for a "right-handed" parabolic
load where *q0 = 3mg/ *(*2L *).

**Return to: **Beam Loads

**Next: **More Complicated Beam Loads

**Up: **Outline

The Geometry Center Calculus Development Team
Copyright © 1996 by The Geometry Center.
Last modified: Fri Apr 12 15:50:26 1996