Higher-order in-plane bending analysis of box beams connected at an angled joint considering cross-sectional bending warping and distortion

By using existing beam theories alone, it is not possible to correctly predict the structural behavior of thin-walled closed beams connected at an angled joint that is under in-plane bending. Sectional deformations occurring near a joint cannot be estimated by using the Euler/Timoshenko beam elements, but they significantly increase the overall flexibility of a beam structure. Following a recent development of a higher-order beam analysis for joined box beams at an arbitrary angle under out-of-plane bending and torsion, a higher-order analysis suitable for box beams connected at an angled joint under in-plane bending is newly developed and implemented in finite element formulation. For the analysis, two sectional deformation degrees of freedom accounting for bending distortion and warping are included in addition to the standard degrees of freedom of extension, bending deflection and bending/shear rotation. The employed sectional deformation function for bending distortion is the same as that for a curved box beam, but the function for bending warping is newly developed. Then, a procedure to match the five one-dimensional field variables from extension to bending warping at an angled joint is presented. The validity and effectiveness of the developed analysis are confirmed by comparing the present beam results with those obtained by shell finite elements.