# Stress

Written by Jerry Ratzlaff on . Posted in Classical Mechanics

Stress, abbreviated as $$\sigma$$ (Greek symbol sigma), is the force per unit area of cross-section.  The maximum stress of a material before it breaks is called breaking stress or ultimate tensial stress.

## Stress Types

• Fatigue stress  -  Failure or weakening of a material due to repetition and load cycling.
• Flow stress  -  When a mass of flowing fluid indicates a dynamic pressure on a conduit wall.
• Pressure stress  -  Stresses induced in vessels containing pressurized materials.
• Residual stress  -  Stresses caused by manufacturing processes in a solid material after the origional cause has been removed.
• Structural stress  -  Stresses produced in structural members because of the weight they support.
• Thermal stress  -  Whenever temperature gradients are present in a material.

## Stress Patterns

• Compressive stress  -  The opposite of tensile stress.
• Shear stress  -  Tends to deform the material by breaking rather than stretching without changing the volume by restraining the object.
• Tensile stress  -  A stress in which the two sections of material on either side of a stress plane tend to pull apart or elongate.

## stress formula

 $$\large{ \sigma = \frac{F}{A_c} }$$

### Where:

 Units English Metric $$\large{ \sigma }$$  (Greek symbol sigma) = stress $$\large{\frac{lbf}{in^2}}$$ $$\large{Pa}$$ $$\large{ A_c }$$ = area cross-section $$\large{ ft^2}$$ $$\large{ m^2}$$ $$\large{ F }$$ = force $$\large{ lbf }$$ $$\large{N}$$

### Solve For:

 $$\large{ A_c = \frac{ F }{ \sigma } }$$ $$\large{ F = \sigma \; a_c }$$

## Related formulas

 $$\large{ \sigma = \lambda \; \epsilon }$$ (elastic modulus) $$\large{ \sigma = E \; \epsilon }$$ (Young's modulus)

### Where:

$$\large{ \sigma }$$  (Greek symbol sigma) = stress

$$\large{ \lambda }$$  (Greek symbol lambda) = elastic modulus

$$\large{ \epsilon }$$  (Greek symbol epsilon) = strain

$$\large{ E }$$ = Young's modulus