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 formula

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

Where:

 Units English Metric $$\large{ \sigma }$$  (Greek symbol sigma) = stress $$\large{\frac{lbf}{in^2}}$$ $$\large{MPa}$$ $$\large{ A_c }$$ = 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 Stress 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