Stress

Written by Jerry Ratzlaff on . Posted in Classical Mechanics

stressStress, 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

 

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