Equivalent Bending Moment Factors for Out-of-Plane Stability Calculation Considering Sway-Frame Buckling

An analysis was conducted to determine the equivalent bending moment factor for out-of-plane flexural-torsional buckling of frame columns in multi-story buildings with reinforced concrete floor slabs. These columns are characterized by permitted lateral sway but zero twist angles at both ends. The equilibrium differential equations and boundary conditions were derived based on the exact total potential energy principle. The model accounted for the lateral out-of-plane displacement stiffness at the column top， with its elastic energy included in the total potential energy. The derivation showed that the simply-supported ends and zero-twist-angle boundary conditions necessitated zero lateral displacement at the column top. Consequently， the sway spring term was eliminated from the simplified total potential energy expression， confirming that lateral sway stiffness does not affect the out-of-plane stability of columns under pure bending. With a three-term sine series as the trial function， the simplified total potential energy was solved to obtain the equivalent bending moment factor， and the corresponding buckling modes were also presented. The result indicated that this factor was identical to that for frame columns in a non-sway buckling scenario. The conclusion was further validated by finite element buckling analysis and supported by discussions referencing earlier research findings presented in the paper.