Literature Overview of Higher Order Beam Theories taking into account In-Plane and Out-of-Plane Deformation
Evangelos J. Sapountzakis*, Amalia K. Argyridi
Institute of Structural Analysis and Antiseismic Research, School of Civil Engineering, National Technical University of Athens, Athens, 15780, Greece.
The fundamental beam theories are Euler-Bernoulli and Timoshenko beam theories where the cross-section is considered undeformable either in-plane or out-of-plane. These theories provided the inspiration to the researchers in order to develop higher order beam theories, i.e. tools to reliably analyze beam members using a minimum number of equations instead of 3D or shell models. The analysis of a member employing a beam theory consists of two parts. In the first part, a cross-sectional analysis is conducted calculating the geometric constants of the cross-section of the beam. In the second part, the aforementioned geometric constants are substituted in the global equilibrium equations of the beam to calculate the response of the member under any kind of loading. The main difference among higher order beam theories and Euler-Bernoulli, Timoshenko ones is that in the first case higher order degrees of freedom are added to the model to capture warping and distortional phenomena leading to the appearance of respective higher order geometric constants. In this paper, a brief literature overview is presented regarding the major beam theories taking account out-of plane (warping) and in-plane (distortional) deformation.
Key words: Beam theories, Distortion, In-plane deformation, Warping, Out-of-plane deformation.