Distributed Forces

A distributed force is any force where the point of application of the force is an area or a volume. This means that the "point of application" is not really a point at all. Though distributed forces are more difficult to analyze than point forces, distributed forces are quite common in real world systems so it is important to understand how to model them.

Distributed forces can be broken down into surface forces and body forces. Surface forces are distributed forces where the point of application is an area (a surface on the body). Body forces are forces where the point of application is a volume (the force is exerted on all molecules throughout the body). Below are some examples of surface and body forces.

The Hoover Dam by Curimedia [CC-BY-2.0 (http://creativecommons.org/licenses/by/2.0)], via Wikimedia Commons
The water pressure pushing on the surface of this dam is an example of a surface force.
The gravitational force on this airplane is distributed over the entire volume of the airplane, and is an example of a body force.

Representing Distributed Forces:

Distributed forces are represented as a field of vectors. This is drawn as a number of discrete vectors along a line, over a surface, or over a volume, that are connected with a line or a surface as shown below.

Force Distributed over a Line
This is a representation of a surface force in a 2D problem (A force distributed over a line). The magnitude is given in units of force per unit distance.
Force Distributed over a surface
This is a representation of a surface force in a 3D problem (a force distributed over an area). The magnitude is given in units of force per unit area (also called a pressure).

Though these representations show a discrete number of individual vectors, there is actually a magnitude and direction at all points along the line, surface, or body. The individual vectors represent a sampling of these magnitudes and directions.

It is also important to realize that the magnitudes of distributed forces are given in force per unit distance, area, or volume. We must integrate the distributed force over it's entire range to convert the force into the usual units of force.

Analysis of Distributed Forces:

Because distributed forces can vary in magnitude and direction with position, they cannot be simply added or subtracted like point forces. Instead much of the analysis relies on calculus, which is needed to find the overall magnitude and direction the force exerts over a given area and the overall moment the distributed force exerts about a given point. This calculus based approach is needed to analyze internal loads, but if we are only interested in external forces (such as in statics and dynamics), then the simplest option is to convert these distributed loads to their equivalent point loads. The equivalent point load is a point force that would cause the same reaction forces and moments as the original distributed force. Once the distributed force has been converted to it's equivalent point load, it can be used in analysis just as a point force would.