Design Method Of Second-order Effect Of Reinforced Concrete Bent Frames

This dissertation talks about one aspect of the research on remaining problems of second-order effect design method in the book Code for design of concrete structures GB50010-2010,mainly aimed at providing reference to the new revision of bent frames second-order effect design method in the book Code for design of concrete structures.This paper makes further exploration which is based on the previous study of the second-order effect of reinforced concrete bent frames of our team,the focus of attention is focused on the following two aspects:Firstly,it is recognized that there are some defects in the ?-l0 method of the existing standard in the bent frames,so we strive to improve the traditional ?-l0 method which is based on investigating the law of second-order effect of reinforced concrete bent frames in practical engineering.Secondly,the second-order effect of bent frames should been solved in structural analysis,but the analysis process is very complicated because of the influence of the material nonlinearity,so the idea of the current specification is to consider the second-order effect of bent frames in the section design,which is an expedient measure based on current analytical means.With the idea of the American ACI318,the elastic second-order analysis method employing stiffness reduction will be the fundamental way to solve the second-order effect problems of bent frames.Currently,the values of the stiffness reduction factor of columns are mainly based on the analysis results of some frame structures,therefore,in a sense,it can only be regarded as the stiffness reduction factor of frame columns.In this paper,the stiffness reduction factor of bent columns is studied to verify the effectiveness of the reduction stiffness method which is applied to the bent frames.The progress of research work mainly includes the following aspects:(1)The simplified rules of basic load combination has been removed in the book Load code for the design of building structures GB50009-2012.Under this premise,we found out more than 20 most unfavorable load combinations from more than 1000 possible load combinations of bent frames,and summarized the second-order effect rules and influence factors of bent frames.(2)According to the "separation bar method" which is used to derive the calculated length of frame columns,the upper and lower columns of the bent frames are independent as the mutually constrained components.By defining the critical instability state of the bent columns,the calculated length l0 of bent columns is obtained by matching the moment magnification factor ?,and then put forward the ?-l0 method which is correct in concept.(3)The original nonlinear analysis of bent frames mainly used the PMM automatic coupling hinge model in SAP2000.The PMM automatic coupling hinge model based on the FEMA356 permissibility criterion is a rigid-plastic hinge which simulates the plastic deformation properties after yield of structures and can't simulate the plastic deformation due to the tensile cracking of concrete and the bond slip of reinforced concrete before yield.However,the PMM fiber hinge model which is based on the uniaxial constitutive model of material and the strain flat section assumption can be used to calculate the axial force-to-axial strain and the moment-curvature relationship in two orthogonal directions,thus effectively considering the stiffness loss caused by the tensile cracking of concrete.Therefore,in this paper the PMM fiber hinge based on the material model in S AP2000 is used in the nonlinear analysis of the bent frame structures.Through the simulation analysis of the experiment,the PMM fiber hinge model can achieve better accuracy than the PMM automatic coupling hinge model.(4)We complete elastic second-order analysis and nonlinear second-order analysis on 68 single and double span equal height bent frames by using the improved nonlinear analysis method,and the stiffness reduction factor is introduced to consider the material nonlinearity.Then the reasonable stiffness reduction factor is calculated by making use of the equivalent principle of second-order effect of overall structure.Finally,we suggest that the proper stiffness reduction factor ? for single and double span bent frames should be 0.75.(5)In this paper we introduce the elastic second-order analysis method considering stiffness reduction factor into the analysis of the unequal-height bent frames,and propose the elastic stiffness reduction factor of the bent columns under the bearing capacity limit state.