Research On Analytic Calculation Method Of Overall Stability Of Frame And Shear Wall-frame Structure

The critical force(or calculated length factor)is still an important parameter required in engineering design calculation.The critical force is the upper limit of the bearing capacity of the component or structure,which can be used to evaluate the bearing capacity;The critical force can be used to approximate the second-order effect bending moment.The calculation methods in the current specifications(such as Code for design of steel structures and Code for design of concrete structures)are still based on first-order elastic analysis,and the second-order effect is calculated through the amplification factor,which requires the critical force of the component.Therefore,the specification also provides some corresponding charts and formulas for determining the calculated length coefficient.The method is simple and practical,but it also has the following disadvantages:(1)does not consider the mutual support between the same layer columns;(2)does not consider the mutual support between different layers;(3)Shear wall-frame structure does not take into account the lateral support provided by the shear wall;(4)does not consider the stiffness reduction due to plasticity;These shortcomings can cause the calculated critical force to be too large(unsafe)or too small(conservative)in some cases.The research obtained in this paper can make up for the deficiencies mentioned above.Now the overall stability of the structure solved through the finite element software is becoming more and more,and how to test the results of finite element calculation is an unavoidable problem.Code for design of steel structures gives calculation tables for calculating the effective length factor of non-sideways frame columns braced with strong bracing system and free sideways unbraced frame columns,but for frame columns with elastic lateral displacement between the two,the current specification lacks the corresponding calculation formula s and tables and can not consider the mutual support between the same layer columns and the inter-story interaction.Based on the fact that the rocking column needs to be attached to other structures to maintain its own stability,the basic calculation model of the spring-rocking column is created,and the concepts of the internal stiffness and the external stiffness are defined.According to the principle that the stiffness of structures is weakened to zero by the external stiffness of structures,the simple and practical calculation formula for directly calculating the overall elastic stability of the side-shifting frame and the shear wall-frame structure is further derived.By analyzing current numerical and simplification methods,the theoretical calculation method is adopted to determine the section bearing capacity of the reinforced concrete by using strain to calculate internal force.These methods are accurate for using the whole constitutive relationships of reinforcement and concrete without simplification as well as no iterative and convergence error for the analytical algorithms.Through the test of eccentrically compressed columns of reinforced concrete,the variation rules of stiffness is analyzed and the equivalent bending stiffness calculation formula of the compression column is obtained.In order to verify these calculation formulas and calculation methods,it is judged by comparison with the current specification method,the finite element ansys method and the test results,etc.(1)The spring in the spring-rocking column model is replaced by three spring compression columns of simulating various lateral displacement type compression columns.According to the principle that when the column is in the critical steady state,the stiffness of compression columns is weakened to zero by the external stiffness,the calculation formulas of the internal and external stiffness ratio coefficients of various lateral displacement type s of compression columns are derived.According to these coefficients,calculation formulas for determining the critical bearing capacity and the effective length factor of compressed columns are derived.The method determines the effective length factor of compressed columns is quick and convenient,which is suitable for weak braced frame columns with elastic lateral displacement.(2)The deflection method can convert the solution of the critical force of frames into the lateral displacement of frames,which greatly simplifies the solution of the critical force.This paper deduces the calculation formula of the critical force for single-layer and multi-layer frames of single-span using the deflection method.These formulas can consider the mutual support between the same layer columns and the inter-story interaction,which can make up for the deficiency of the standardized calculation length coefficient method.(3)The spring in the spring-rocking column model is replaced by the side shift frame.According to the principle that when the structure is in the critical steady state,the stiffness of frames is weakened to zero by the external stiffness,the stability of the side shift frame is transformed into the lateral stiffness of frames,and the simple and practical calculation formula for calculating the critical bearing capacity of frames is derived.This formula avoids the inconvenience of the effective length factor method for checking one-by-one column,and can well consider the mutual support between the same layer columns and the inter-story interaction.(4)The spring in the spring-rocking column model is replaced by shear wall-frame structures.According to the principle that when the structure is in the critical steady state,the stiffness of shear wall-frame structures is weakened to zero by the external stiffness,the stability of shear wall-frame structures is transformed into the lateral stiffness of shear wall-frame structures,and the simple and practical calculation formula for calculating the critical bearing capacity of shear wall-frame structures is derived,which can make up for the deficiency of the standardized method for determining stability of shear wall-frame structures.(5)By referring to Eurocode 2,all the possible strain distributions at the ultimate limit state of the RC cross-section are obtained for Chinese condition.In this paper these strains are used as independent variables to derive the formula for calculating the internal force of reinforced concrete rectangular section,which can avoid complex solutions to many parameters of the standardized method.The relation of the axial force-moment is drawn into some nomograms,which can be used for bearing capacity and reinforcement design and consider the second-order effect of the section.(6)Through the test of nine eccentric compression columns,the variation rulers of the stiffness of reinforced concrete compression columns is summarized,and the equivalent reduction stiffness calculation formula of the compression columns is obtained.Based on the second-order elastic global analysis method of reduced stiffness,the calculation method of elastoplastic overall stability bearing capacity of reinforced concrete structures is proposed.