Study On The Calculation Method Of The Second-order Effect Of Reinforced Concrete Columns

The stability calculation of reinforced concrete columns considering the second-order effect involves nonlinear factors,such as material nonlinearity and geometric nonlinearity,which makes analysis and ca lculation difficult.Although China’s "GB 50010-2010 Design Specification for Concrete Structures" provides a "magnification factor method" for calculating eccentric compression members,this method simplifies nonlinear factors and the formulas obtained al so have shortcomings.Therefore,this paper sorts out the simplified calculation process from three aspects: structural level,component level and section level,optimizes the unreasonable part,and on the basis of learning some traditional methods,we car ried out in-depth Research,and finally put forward four different levels of practical calculation methods to solve practical engineering problems.(1)Based on the actual stress distribution diagram,using the method of calculating internal force from str ain,and using strain as an intermediate variable,the calculation formulas for the bearing capacity of normal section of reinforced concrete rectangular,circular and ring members are derived respectively.Furthermore,the data is calculated from all the strains in the limit state of the cross-section bearing capacity,and a dimensionless nomogram that can reflect the relationship between the axial force,bending moment and rebar rate is drawn.This nomogram is combined with the "Increase coefficient metho d" can be used for the design and strength check calculation of reinforced concrete short columns and slender columns.(2)First,the axial force-bending moment-curvature of the section is accuratel y calculated from the strain based on the actual stress di stribution diagram at the section level.Then,the numerical integration method of successive approximation(conjugate beam method)is used to calculate the second-order deflection at the member level.Finally,computer programming is used to establish a s econd-order elastoplastic accurate algorithm for reinforced concrete columns.(3)A more accurate simplified calculation model of limit curvature is proposed at the cross-section level,then the second-order deflection is calculated by the model column method at the component level,and the simplified second-order equilibrium equation is obtained.Finally,computer programming is used to establish Second-order elastoplastic approximation algorithm for reinforced concrete columns.(4)By constructing a paral lel coordinate system,all possible solutions of the second-order equilibrium equation are drawn into a nomogram.Only three parameters need to be calculated,and four auxiliary lines are made in the figure to manually calculate the reinforcement design an d strength check of the reinforced concrete column considering the second-order effect,which provides designers with a simple and practical calculation tool.