Study on Reasonable Linear Stiffness Ratio in Frame Structure Based on Lagrange Multiplier Method

Frame structure is a common structure of multi-story and high-rise buildings; research on columnpsilas reasonable linear stiffness ratio is an important aspect on frame structure optimization design. The thesis researches on reasonable linear stiffness ratio when the frame beam-columnpsilas lateral displacement stiffness reaches its maximum value based on Lagrange multiplier method structure optimization theory and on the premise that total material quantity of framework beam-column is definite. Different from traditional estimation methods and trial calculation on section dimension of beam-column, the reasonable section dimension of beam-column can be calculated by the derived formulas on preliminary design stage. This method is not only used as basis for the frame beam-columnpsilas section dimension confirmation on preliminary design stage, but also taken as reference for research on beam-columnpsilas reasonable linear stiffness ratio for similar structure. In addition, adjusted frame beam-column´s section dimension based on the method reduces the columnpsilas axial compression ratio, shear compression ratio and improve the structural ductility.