Stress

Written by Jerry Ratzlaff on . Posted in Classical Mechanics

stressStress, 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

 

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