Beams: Symbols

 

Notation and symbols commonly used in Euler-Bernoulli beam theory are summarized below:
Independent Parameters
Quantity Symbol Object Units
  elastic modulus   E scalar N/m2
  area moment of inertia   I scalar m4
  line pressure load   p scalar N/m
  concentrated force load   P scalar N
  location along beam   x scalar m
  height above neutral surface   y scalar m

Dependent Parameters
Quantity Symbol Object Units
  transverse displacement   w scalar m
  slope of neutral surface   q scalar radian
  rotation of beam cross section   c scalar radian
  moment resultant   M scalar N-m
  shear resultant   V scalar N
  stress   s scalar N/m2
  strain   e scalar 1
 
Neutral Plane - Plane in the beam where all bending stresses are zero. It is the reference point for the integral defining the Area Moment of Inertia, I.

Line Pressure Load - Out of convenience, beam theory defines the units for a pressure load as [N/m], as opposed to real pressure units [N/m2]. To convert a real pressure to this line pressure for beams, multiply the true pressure by the beam width,

 

 

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