# Stress

Written by Jerry Ratzlaff on . Posted in Classical Mechanics Stress, abbreviated as $$\sigma$$ (Greek symbol sigma), also called normal stress, 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

• Bulk Stress (Volume Stress)  -  The volume of the body changes due to the stress.
• Compressive Stress  -  The opposite of tensile stress.
• Fatigue Stress  -  Failure or weakening of a material due to repetition and load cycling.
• Hoop Stress  -  The circumferential and perpendicular stress to the axis imposed on a cylinder wall when exposed to an internal pressure load.
• Hydraulic Stress  -  The internal force per unit area when the force is applied by the fluid on the body.
• Longitudinal Stress  - When the length of the body changes its length by normal stress that is applied.
• Pressure Stress  -  Stresses induced in vessels containing pressurized materials.
• Radial Stress  -  The stress towards or away from the central axis of a curved member.
• Residual Stress  -  Stresses caused by manufacturing processes in a solid material after the origional cause has been removed.
• Shear Stress (Tangential Stress)  -  Tends to deform the material by breaking rather than stretching without changing the volume by restraining the object.
• Structural Stress  -  Stresses produced in structural members because of the weight they support.
• 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 