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

Experimental and numerical research on out-of-plane flexural property of plates reinforced SHS X-joints

“…Chen et al [9] studied the mechanical performance of reinforced concrete beam-thin-wall joints under out-of-plane bending moments. Jang et al [10] investigated a higher-order beam analysis applicable to three thin-walled box beams connected at a joint under out-of-plane bending. Soh et al [11] investigated the behavior of completely overlapped tubular joints under out-of-plane bending used in the eccentrically braced offshore jackets.…”

Topology optimization of thin‐walled box beam structures based on the higher‐order beam theory

“…When multiple beams are connected at a joint, as required in the ground beam model, one may use a matching method developed by [14] in which three-dimensional displacements are matched on the shared edges of beams meeting at a joint. In order to employ HoBT [13,14] for topology optimization, the key issue is how to parameterize joint connectivity in terms of design variables of the beams connected to a joint. However, there occurs some difficulty in the parameterization because the method by [14] can be used only if a joint connectivity type is known.…”

“…In order to employ HoBT [13,14] for topology optimization, the key issue is how to parameterize joint connectivity in terms of design variables of the beams connected to a joint. However, there occurs some difficulty in the parameterization because the method by [14] can be used only if a joint connectivity type is known. To see the reason for the difficulty, note that a density design variable is assigned to each thin-walled box beam to parameterize its material property ( Figure 1) for topology optimization.…”

“…Because the connectivity of a joint should be determined by the beams connected to the joint, the joint connectivity type varies as the values of the design variables of the beams are varied. For this reason, one cannot know the joint type in advance, so the method by [14] cannot be directly used, and therefore, a new method describing the joint types suitable for topology optimization should be developed for the higher-order beam-based topology optimization. To facilitate the representation of various joint types, the notion of the so-called joint element derived by static condensation is proposed.…”

“…If the HoBT is used, however, this is not the case because cross-sectional deformations do not have resultants; force or moment resultants of warping and distortion are zero. To express the joint matching condition for the higher-order beam elements, Jang et al [14] considered the continuity of three-dimensional displacements. For example, three-dimensional displacements on the centerline of the shared edges, edge 1 and edge 3, are imposed to be continuous to derive the matching conditions for the joint in Figure 3 connecting two thin-walled beams.…”