# Stress

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

Tags: Equations for Strain and Stress Equations for Soil Equations for Hoop Stress