Stress

This section does not explain the feeling you get before your due to take your finite elements final.

A stress is a quantitative measure of the internal forces acting within a deformable body (see plasticity for more info). Lets try to explain it through a few examples. If you have two different sized wooden beams, a 6"x6" and a 12"x12", both spanning 10'-0", it should be obvious through observation that the 12"x12" is much stronger than the 6"x6". Now place 2,000 lbs at the center of each beam. If the force acting on both beams is 2,000 lbs, how can you quantitatively show that the 12"x12" is in fact the stronger of the two? That is where the internal forces (i.e. the beams stresses) acting on the beams comes into play.

Types of Stress:

Although there are many names given to stress, there are only two fundamental types of stress. They differ in the orientation of the loaded area. They are the normal stress (the area of the force is perpendicular to the force carried), and shear force (the area is parallel to the force).

The normal and shear forces can be further broken down into:

• Axial Stress
  • Can be broken down further into compression stress and tensile stress
• Bending Stress (aka Flexural Stress)
• Shear Stress
• Bearing Stress?
• Yield Stress?
• Ultimate Stress?

How do you calculate the various stresses?

Stress is most commonly calculated as force per unit area, F/A. Although different shapes and materials will calculate stress differently (which can make things quite tedious).

Here are a few common methods of calculating stress, if you are looking for a specific case I highly recommend you read our pages which relate to specific materials (for example, concrete will rarely use stress calculations, since most concrete is non-homogenous it makes it difficult to use non-subjective reasoning)

Axial Stress

f_a = \frac{F}{A}

where:

Bending Stress

f_b = \frac{F}{S}

where:

Note: Bending Stress is unique because it will place the lower portion of a beam into tensile stress and put the upper part of a beam into compressive stress (this is also true with bending in a truss). This is why rebar will often be placed on the bottom of a concrete beam (to handle the tensile forces)). You can see this visually when an object is in bending, the lower portion will be expanding in length while the upper portion contracting in length.

Shear Stress

f_v = \frac{F}{A}

where:

Bearing Stress

f_{be} = \frac{F}{A}

where:

Yield Stress