■ Thin-Walled Structures

Deviation of Sectional Deformation for Thin-Walled Box Beams

The explicit relations are useful to interpret the physical significance of the generalized forces and can be critical in deriving explicit equilibrium conditions among the generalized forces at a joint of multiple thin-walled beams, a theory allowing the explicit relations needs to be developed. We newly propose a higher-order Vlasov torsion theory that not only includes as many torsion-related modes as desired but also provides the explicit F-U and 𝝈-F relations that are fully consistent with those by the Vlasov theory.

Matching Conditions for Joints in Thin-Walled Box Beams

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. 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. 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.

Sectional Deformation and Matching Conditions
for Plate Box Beams with General Sectional Shapes

Expanding upon previous research endeavors, this study achieves a hierarchical derivation of orthogonal cross-section modes for thin-walled beams with arbitrary sections. Leveraging the freedom in sectional deformations obtained from these modes, the investigation extends to deducing matching conditions for joint structures composed of general plate-box beams. Subsequently, the successful application of these derived conditions enables accurate 1D analysis of frame structures consisting of plate-box beams with diverse cross-sections, achieving a level of precision comparable to shell analysis. This breakthrough contributes significantly to the advancement of structural engineering, particularly in the efficient analysis and design of complex frame systems.