Consistent higher-order beam theory for thin-walled box beams using recursive analysis: Edge-bending deformation under doubly symmetric loads

Thin-walled box beams generally exhibit complex sectional deformations that are not significant in solid beams. Accordingly, a higher-order beam theory suitable for the analysis of thin-walled box beams should include degrees of freedom representing sectional deformations. In a recent study, a recursive analysis method to systematically derive sectional membrane deformations has been proposed to establish a consistent higher-order beam theory. In this study, another recursive analysis method is proposed that is suitable for the closed-form derivation of new sectional bending deformations representing the bending of edges (or walls) of the cross-section shown in a box beam under doubly symmetric loads. A consistent 1D higher-order beam theory appropriate to include these additional deformation modes as beam degrees of freedom is also established. The proposed theory provides explicit formulas that relate stresses to generalized forces including self-equilibrated forces such as bimoments. Furthermore, sectional modes are hierarchically derived so that the level of solution accuracy can be effectively and systematically controlled. Thus, the accuracy for static displacement/stress calculations and eigenfrequencies can be adjusted to be fully comparable with plate/shell results. When general doubly symmetric loads are applied to a box beam, the edge membrane modes derived in an earlier study can also be used as additional degrees of freedom besides the edge-bending modes derived in this study. The validity of the proposed beam approach is verified through the analyses of static displacements and stresses as well as eigenfrequencies for free vibration problems.