Unified Higher-Order Beam Analysis for Multiply-Connected Thin-Walled Box Beams

Abstract

Both the consideration of significant higher-order deformation degrees and the derivation of exact matching conditions among field variables at a joint are required to establish a one-dimensional beam model applicable to thin-walled box beam systems. Especially when three or more box beams are multiply-connected at a joint, significantly flexible behavior is observed near the joint that dominates the structural responses of the entire system. Moreover, the flexibility of the joint varies considerably depending on the number of beam members connected at the joint and the joint angles among the members. Because of the difficulties, no one-dimensional beam analysis method has yet been proposed that can capture the structural responses of the box beams-joint systems accurately. With this background, this study proposes a unified one-dimensional higher-order beam analysis approach for the first time that is applicable to the multiply-connected box beams-joint systems under both out-of-plane loads and in-plane loads. It is worth mentioning that the concept of so-called edge resultants as well as conventional (sectional) resultants are employed to derive physically correct equilibrium conditions at a joint and that the exact joint matching conditions are theoretically derived by applying an energy method to the equilibrium conditions. The derived matching conditions are valid even when any number of beams meet at any angle. In addition, higher-order deformation degrees (e.g. bending warping, bending distortion, and etc.) are newly introduced or redefined that are essential to represent the exact joint flexibility of considered systems. The accuracy and validity of the proposed analysis method are checked by comparing the present approach based results and the shell analysis results for various box beams-joint systems.