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Structures study material for the A.R.E. -Architectural Registration Exam.


A push or pull exerted on an object.

A Force includes:

Magnitude, Direction and a Point of Application

Forces are measure in units of:

Weight. Usually Kips or Pounds.

One Kip

1,000 pounds.

External Force or a "Load"

A force applied to a body.

The resistance of a body to the load is called:

an internal force or a "stress."

Line of Action

Is a line parallel to and in line with the force. The force may be considered as acting anywhere along its line of action.


Lines of action of severa forces pass through a common point.


Lines of action that do not pass through a common point.


one force that will produce the same effect on a body as two or more other forces. If the forces have the same line of action, they may be added directly for the resultant.

Can Concurrent forces be added directly.

No. They must be added vectorially.

Force Polygon

A diagram that adds forces by mapping or drawing them out.

What do you need to keep in mind when determining resultants?

1. Order of drawing forces makes no difference.
2. Resultant is directed "away" from the origin or starting point.
3. The resultant is concurrent with the original forces. (their lines of action pass through a common point.)


A force equal in magnitude to the resultant, but opposite in direction.

Resolving Forces

Replacing one force with two or more forces that will produce the same effect on a body as the original force. These forces are called components.

Resolving Forces can be done in two ways:

1. Graphic resolution.
2. Analytical resolution.

Right Triangle Formulas

1. Sin Theta = A/C
2. Cos Theta = B/C
3. Tan Theta = A/B
4. A = C sin theta
5. B = C cos theta
6. CC = the square root of AA + B*B
these basic rules may easily be used to determine the vertical and horizontal components of a force.

Vertical and Horizontal components must be:

added together by x or by y axis.

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