• Is a slender structure in which the length is isgnificantly larger than the other two dimensions. A beam element is a one-dimensional line or curve that represents the neutral axis of the beam.
  • The stress in the direction of the beam element (the bending stress) is considered significantly greater than other stresses.
  • Allowed to only deform in the transverse direction
  • The loads applied are specified as shear forces and bending moments
  • 2 degrees of freedom per node: transverse (normal) displacement and rotation about the neutral axis. The rotation is the derivative of transverse displacement

  • Different with pin-jointed elements. PJE has only nodal displacement as degree of freedom. PJE can only stretch or compress along the line of the element.



Two assumptions for the beam thickness:

  1. Thin beam elements (Euler-Bernoulli formulations): shear deformations are ignored plane cross sections remain perpendicular after deformation
  2. Thick beam element (Timoshenko formulations): sear deformations are allowed, cross-section may not remain normal


  • The external force vector contains the shear loads and the bending moment

  • Theta is the slope of the transverse displacement at the nodal point
  • To model continous beam structure, theta must be continue from one beam element to another. So, displacement must be at least cubic interpolation


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