Moment Amplification Factors Of Columns In Frame-Flexural Bracing Systems And The Overall Elastic Stability

In multi-story buildings, bracing systems are often used to improve the lateral stiffness of the whole structures. Frame-bracing structure is a type of dual systems, among which the bracing system may be shear wall, reinforced concrete core, vertical truss, etc. The lateral displacements of bracing systems are composed of flexural and shear deformation in practical structures. If the shear deformation is considered to be small (e.g., concrete core) the bracing is regarded as the flexural system, which is a widely used type. Under lateral load, considering the P — Δ effect, the moment in columns will be enlarged, and the magnified coefficient should be researched in design.The moment amplification factor in a vertical column with variable cross section is first investigated, and combining the factor in pure frame the formula in frame—shear wall structure are proposed. In this paper two idealized models are used to study the analytic solution of the moment amplification factor in frame columns. A two-story frame shear wall structure with two strides, on the base of slope deflection method by the equilibrium equation involving second-order effect, the analytic expression is obtained. The other model is the continuous beam, by solving the equilibrium equation the factor is obtained. The proposed formula is consistent the result of the analytic solution. Then an advanced formula with respect the individual -story height is suggested. More ANSYS examples about cantilever and multi-story frame shear wall structures indicate the advanced formula is much better in practical designs.Meanwhile, this paper researches the overall stability of the frame-flexural bracing system, by regarding shear wall as flexural cantilever, frame as shear cantilever, solving equilibrium equation considering second order effect, the critical load is obtained, which is simplified as summation of the critical load of the frame plus that of the bracing. Also, the buckling mode and critical load isinvestigated by FEM analysis, the comparison with FEM shows the analytic solution is accurate and may be used in practice.