| The second-order effect of structure has great influence on the internal force and deformation of structure,so it is necessary to understand its basic law and take corresponding engineering measures in structural analysis or section design.It has been more than 100 years since Leonhard Euler first put forward relevant concepts,This field has gradually developed and matured.With the progress of modern economy,the building structure is also developing towards a higher and more complex direction,and the applicability of the second-order effect theory of structure is challenged.For example,in order to adapt to the complex mountainous conditions,the problem of the second-order effect of the dropped stories frame structure is rarely involved in the previous research.In order to meet the needs of engineering practice,this paper extends the team’s previous research on the second-order effect theory and practical engineering methods of regular structure to the dropped stories frame structure,exploring the second-order effect law of the dropped stories frame structure and demonstrate the applicability of the design scheme considering the second-order effect of structure in the current “Code for Design of Concrete Structures ”(GB50010-2010),and also providing a reference for the compilation of the second-order effect part of the dropped stories frame structure in the “Design Standard for Mountain Architectural structures”.Based on the team’s previous research on the second-order effect of regular structure,according to the characteristics of the dropped stories frame structures with or without pull beam,and by adjusting the stiffness ratio of different upper and lower grounding ends in the overall structure,this paper sets a series of different examples to analyze the second-order effect law and practical engineering methods,and obtains the following research results with certain engineering significance :(1)In view of the current concrete code that the restrained part of the bottom anti lateral force component is on the same horizontal plane and the regular frame structure with shear deformation as the main part is an effective simplified method when considering the structural P-△effect,but whether it can be extended to the mountainous dropped stories frame structure with two or more embedded ends not on the same horizontal plane remains to be verified.In this paper,based on the deformation characteristics of the structure,the lateral deformation components of the structure are screened,and the applicability and limitations of the story augmenting factor method are verified by theoretical analysis and comparison of calculation examples.(2)Because of the natural irregularity,the story augmenting factor method is limited.For the frame structure with pull beam,the upper structure is similar to the regular frame structure due to the constraint of pull beam,which is dominated by shear deformation and the "layer effect" is very obvious,so the story augmenting factor method for the upper structure is still applicable;for the frame structure without pull beam,due to the lack of the constraint of pull beam and the upper grounding terminal,however,due to the constraints of the upper structure beams,the other upper structures are still suitable to consider the second-order effect of this part of the structure with the story augmenting factor method.(3)The dropped part of the dropped stories frame structure will be affected by the interaction of the upper and lower grounding terminals,which is natural and irregular.The concept of "layer effect" has been fuzzy,so the story augmenting factor method cannot be used to consider its P-△effect.However,through theoretical analysis and comparison of calculation examples,it is found that the finite element iterative method based on the equivalent horizontal force can simulate well after one iteration,Because of the influence of the structure P-△effect on the internal force and deformation of the dropped stories frame structure.The analysis method of one-time iteration considering the P-△effect of the dropped stories frame structure is quick and convenient,with high efficiency and accuracy meeting the actual requirements of the project.(4)The elastic second-order analysis method considering the reduction of stiffness is a practical method which can consider both the geometric nonlinearity and the material nonlinearity.That is to say,the elastic second-order analysis is used to simulate the geometric nonlinearity of the structure considering the influence of the P-△effect,while the material nonlinearity such as the concrete cracking,the bond slip between the steel bar and the concrete is based on the stiffness of each structural member When the elastic second-order analysis method considering the stiffness reduction is used to simulate and calculate the geometric nonlinearity and material nonlinearity of the frame structure,because its accuracy depends on the value of the stiffness reduction coefficient to a great extent,we take the second-order effect of the whole structure as the condition,and compare the Pushover nonlinear analysis result with the elastic second-order analysis considering the stiffness reduction.The comparison of the results verifies the applicability of the stiffness reduction coefficient of regular frame in the“Code for Design of Concrete Structures”(GB50010-2010)in the dropped stories frame structure.(5)In this paper,an improved iterative method is used to analyze the first-order elastic analysis of the frame structure with different variables,and the results are compared with those of the second-order elastic analysis.It is proposed that the first-order elastic analysis considering the reduction of stiffness can complete the transition from the first-order elastic analysis to the second-order elastic analysis,that is,through the reduction of stiffness The coefficient and the improved iterative method can realize the first-order elastic analysis,which directly considers the material nonlinearity and geometric nonlinearity of the frame structure.A simplified practical method is proposed to consider the effect of the frame structure. |
