Analysis of Three Thin-Walled Box Beams Connected at a Joint under Out-of-Plane Bending Loads

Abstract

When thin-walled box beams meet at an angled joint, the joint region exhibits significant flexibilities that cannot be modeled by the Timoshenko or Euler beam theory especially at a joint of multiple box beams. Conventionally, the flexibilities are represented by artificial spring elements when the Timoshenko beam theory is used. On the other hand, this investigation presents a higher-order beam analysis applicable to three thin-walled box beams connected at a joint under out-of-plane bending loads; no artificial spring element will be used. Because the higher-order theory includes the sectional distortion and warping degrees of freedom, it accurately predicts the structural behavior of thin-walled straight box beams. The main issue in joint analysis is how to match all field variables of bending displacement, bending rotation, warping, and distortion at the joint—no investigation applicable to the analysis of a joint of three box beams has been reported so far. The difficulties result from the fact that the standard vector transformation useful for the Timoshenko beam is not applicable, because the higher-order beam theory involves variables producing zero resultant. In this work, a three-beam joint-matching condition using the Lagrange multipliers is proposed where the three-dimensional displacements calculated by the higher-order beam theory are imposed to be continuous along shared edges of interfacing beams. The validity of the developed matching approach is tested with several numerical examples. A special consideration is also discussed to deal with the case when joint angles between two of the three beams are unequal.