Statics

While all Statics problems represent the reality of 3D, many can be analyzed in 2D. 

Any three-dimensional structure that is symmetric (in terms of both geometry and loading) can be condensed to a 2D problem.

When the geometry requires a 3D approach, such as the whimsical childrens' play structure shown in the photo, we have a few analysis options to pursue.

• If the problem is relatively simple, we may decide to conduct three planar two-dimensional analyses (the xy plane, xz plane, and yz plane). For simple problems, this approach is recommended.

• If the problem is more complex, we may apply the mathematical rigor of vector notation. We will learn to apply these fundamentals by hand.

Rest assured that when you are confronted with any degree of complexity (e.g. the playground in the photograph), you will not be doing these calculations by hand. That would waste time, and the likelihood of errors is high. Instead, you would use software (finite element analysis) in your calculations.

The problems we solve in this class do not require linear algebra or matrix solution methods. Instead, we will use simple algebra (substitution and elimination methods to solve systems of equations). If you'd like to learn more about solving a system of linear equations, check out this link.

uAB = a unit vector (meaning that it has a unit length) that defines the inclination of the line of action from Point A to Point B

rAB = a position vector that goes from Point A to Point B

F = a force vector (perhaps a load vector or a reaction vector)

M = a moment vector (yes, moment is a vector, that will be explained a little later)