1. Introduction

This book presents an advanced beam theory for accurate and efficient analyses of thin-walled beam structures, focusing primarily on thin-walled closed beams but including other types. Beam members exhibit non-negligible sectional deformations such as warping and distortion if they consist of thin-walled sections. Because classical beam theories, such as the Euler and Timoshenko beam theories [see, e.g., Gere and Timoshenko (1997)], use only six degrees of freedom (DOFs) representing three rigid-body translations and three rigid-body rotations of a beam cross-section, the aforementioned non-rigid sectional deformations cannot be depicted at all by them. Therefore, additional DOFs corresponding to non-rigid sectional deformations must be incorporated for an accurate analysis of a thin-walled beam, even when a beam theory is used. However, it is difficult to derive the sectional deformations systematically, and it is much more difficult to establish matching conditions among the corresponding degrees of freedom at a joint of multiply-connected thin-walled beams. It may be apparent that the standard field matching conditions established for classical beam theories are no longer useful if the field variables include DOFs representing non-rigid sectional deformations in addition to conventional six DOFs. In this case, therefore, an alternative field matching approach for these field variables should be established for an analysis of a thin-walled beam-joint structure.