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Euler-Bernoulli Beams and Frames

In: Computational Statics and Dynamics

Author

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  • Andreas Öchsner

    (Esslingen University of Applied Sciences)

Abstract

This chapter starts with the analytical description of beam members. Based on the three basic equations of continuum mechanics, i.e., the kinematics relationship, the constitutive law and the equilibrium equation, the partial differential equation, which describes the physical problem, is derived. The weighted residual method is then used to derive the principal finite element equation for beam elements. Assembly of elements and the consideration of boundary conditions is treated in detail as well as the post-computation of some quantities. Furthermore, the classical beam element is generalized by the superposition of a beam and rod element. The chapter concludes with the spatialFrame structure arrangements of generalized beam elements in a plane to form frame structures.

Suggested Citation

  • Andreas Öchsner, 2023. "Euler-Bernoulli Beams and Frames," Springer Books, in: Computational Statics and Dynamics, edition 3, chapter 0, pages 103-226, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-09673-0_3
    DOI: 10.1007/978-3-031-09673-0_3
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