Fully Coupled 10-Degree-of-Freedom Beam Theory for Piecewise Straight Thin-Walled Beams with General Quadrilateral Cross Sections

Abstract

A fully coupled 10-degree-of-freedom (DOF) beam theory is developed for the analysis of thin-walled closed piecewise straight beams of general quadrilateral cross sections. The developed beam theory can predict the structural response of arbitrarily shaped thin-walled quadrilateral sectioned beams that are curved or connected to each other through a number of angled joints. For accurate prediction, the local effects by four beam sectional deformations such as torsional warping, torsional distortion, bending warping, and bending distortion must be taken into account in addition to the structural responses by standard six translational and rotational DOFs of the Timoshenko beam theory. When two straight beams of general quadrilateral sections meet at an angle, all 10 DOF deformations become fully coupled. Furthermore, it is not easy to derive the exact interface conditions at the angled joint because 10 DOFs have different physical behavior. For the analysis of the beam system in consideration, the section deformation patterns corresponding to all of the 10 DOFs are presented. In particular, the cross-sectional shape functions for bending distortion and bending warping for general quadrilateral sections are derived for the first time. Then, a systematic method to match 10 DOFs of two straight quadrilateral beams meeting at a joint of an arbitrary angle is developed. Several numerical case studies are considered to check the validity of the developed beam analysis.