A Beam—Just a Beam in Linear Plane Bending

  • Reinhold KienzlerEmail author
  • Patrick Schneider
Part of the Advanced Structured Materials book series (STRUCTMAT, volume 110)


Starting from the equations of the linear, three-dimensional theory of elasticity, the displacements are expanded into power series in the width- and height-coordinates. By invoking the uniform-approximation method in combination with the pseudo-reduction technique, a hierarchy of beam theories of different orders of approximation is established. The first-order approximation coincides with the classical Euler-Bernoulli beam theory, whereas the second-order approximation delivers a Timoshenko-type of shear-deformable beam theory. Differences and implications are discussed.


Taylor-series expansion Consistent beam theories Uniform approximation Pseudo reduction Euler-Bernoulli beam Timoshenko beam 


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Bremen Institute for Mechanical Engineering (Bime)University of BremenBremenGermany
  2. 2.Technische Universität Darmstadt, Institute for Lightweight Construction and Design (KLuB)DarmstadtGermany

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