# 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.

## 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.

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.