Exact matching at a joint of multiply-connected box beams under out-of-plane bending and torsion

Accurate analysis of thin-walled box beams meeting at a joint requires not only consideration of higher-order deformation degrees (such as warping and distortion) but also exact matching conditions at the joint. Especially when more than two box beams are connected at a joint, the deformation of the beam-joint system is so complicated that no one-dimensional beam analysis has yet predicted its structural behavior correctly. Since a beam theory incorporating higher-order deformations is available, the main difficulty is determining the exact matching conditions at the joint. In this paper, we derive the exact matching conditions for five field variables-bending deflection, bending/torsional rotations, warping, and distortion-of multiply connected box beams under out-of-plane bending and torsional loads. The derived relations are valid irrespective of the number of beams and angles. We introduced a new concept called "edge resultants" besides conventional (sectional) resultants, and demonstrated its effectiveness for exact derivation and physical interpretations of the derived equations. The accuracy and validity of the proposed theory are checked by comparing the predicted results with those of shell finite element analysis.