Analysis of two box beams-joint systems under in-plane bending and axial loads by one-dimensional higher-order beam theory

If two thin-walled box beams meet at a joint, significant flexibilities that cannot be dealt with by the classical Euler or Timoshenko beam theory are observed. Especially under in-plane bending and axial loads, the deformation of the two box beams-joint system near the joint region is so complicated that no theoretical one-dimensional approach that interprets its mechanical behavior correctly has yet been proposed. To establish an effective higher-order beam theory, we introduce a new additional bending distortion degree representing anticlastic curvature effects and also redefine the section-shape functions of the bending warping and bending distortion degrees. In box beams-joint systems, it is crucial to find the matching conditions among field variables at the joint, but no exact conditions applicable for the systems under in-plane bending and axial loads are available. In this paper, we newly derive the explicit form of the transformation matrix relating six field variables of two box beams at a joint-axial displacement, transverse displacement, in-plane bending/shear rotation, bending warping, and two bending distortions. The accuracy and validity of the developed higher-order beam theory and the exact matching conditions are checked by comparing the present beam based results and ABAQUS shell analysis results for various box beams with different joint angles.