Abstract
This chapter introduces first the theory to derive the elemental stiffness matrix of Euler–Bernoulli beam elements. Then, the principal finite element equation of such beams and their arrangements as plane frame structures are briefly covered. Furthermore, a combination of Euler–Bernoulli beam and rod element is introduced as a generalized beam and frame element. Comments on the computer implementation of the corresponding Maxima modules are provided. The chapter includes detailed Maxima examples which allow an easy transfer to other problems.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
Note that the equivalent expression ‘thin beam’ is used in many references.
- 2.
Depending on the bending plane, i.e. x-y or x-z, \(I_z(x)\) or \(I_y(x)\) should be used. Note that x is always along the longitudinal beam axis in our derivations.
- 3.
All elements aligned along the same axis (x), which implies that no rotation is required.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Öchsner, A., Makvandi, R. (2019). Euler–Bernoulli Beams and Frames. In: Finite Elements Using Maxima. Springer, Cham. https://doi.org/10.1007/978-3-030-17199-5_4
Download citation
DOI: https://doi.org/10.1007/978-3-030-17199-5_4
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-17198-8
Online ISBN: 978-3-030-17199-5
eBook Packages: EngineeringEngineering (R0)