Textile membranes are typically fixed to circular hollow sections (CHS) via cables attached to multiple welded steel brackets. In these bracket joints, each level along the supporting CHS has usually two brackets, which generate overlapped local stresses. Therefore, the capacity of such joints is not well-defined in international standards. This study investigates the stress distribution around the welded double-bracket joint. The membrane structure of a newly constructed stadium in Egypt’s New Capital serves as the primary motivation for this research. The verified numerical finite element model is used to analyze the stresses and deformations in these joints. The study examines various parameters, including the spacing of brackets in the longitudinal and transverse directions, bracket thickness, and the diameter-to-thickness ratio of CHS columns. A proposed simplified design formula is introduced to account for these factors. Finally, the case study for stadium façade column supporting membrane is presented in comparison with the studied cases. This research analyzes the behavior of steel connections supporting membrane structures as part of a case study on the Olympic Stadium façade in Egypt’s new Capital.