Discussion Of Strength And Stability Problems Considering The Second-order Effect In Reinforced Concrete Building Structure

In building structure design, the strength and stability problems considering the second-order effect are the key issues in the performance control of bar as well as the overall structure under the action of axial force, bending moment and shear force at the same time. Because of the complexity of the second-order effect and stability, there are still several key problems to be solved. Correct understanding the concepts associated with the second-order effect and stability problems like geometric nonlinearity, buckling, and, effective length, and understanding the correct application method for engineering design have important guiding significance.In recent years, with the rapid development of domestic infrastructure construction and real estate industry, more and more complex forms, shapes and diverse architectural structures emerge. Compared with late last century, not only the structural height is further increased, and often for the requires of the use function, multiple-layer mega columns and surrounding frame columns with high-strength concrete and reinforced bar, heavier burdened load, and the considerable slenderness ratio, or other strut-type components which are mainly bear high pressure under the horizontal load are used in the structures(such as the multiple-layer mega columns of Shanghai center, the main structure mega columns of Guangzhou East tower, the baroclinic member of diamond lattice frame tube of Guangzhou West Tower as well as the multiple-layer frame columns which are frequently encountered in other high-rise buildings, etc.). For these components, structural designers have reason to be concerned about whether there exists stability risks, and hope to get an effective method to check their stability. But China’s “Code for design of Concrete Structures”(GB50010-2010)[1] and “Technical specification for concrete structures of tall building”(JGJ3-2010)[2] are similar to specifications of other countries, they don’t give the appropriate provisions due to conventional concrete structures don’t have stability problems, thereby there is room to make up for the shortfall. On the other hand, from the domestic academic journals in which the second-order effect and stability article of reinforced concrete structure, especially design methods for the stability-demand structural members are discussed in recent years, we can clearly see, notwithstanding some articles have made an effective further clarification about these related conceptual issues, but there have been some interpretation and use which are not necessarily accurate about the concepts related to second-order effect, laws and analysis methods of second-order effect in structures, history background of effective length and the effectiveness of various identification methods for stability critical state exposed in many articles, it can only add more confusion for structure design field in which it is unable to find a system and pertinent explanation of these issues from the relevant books and literature; and the practices that structural designers directly copy the design methods which may be questionable suggested in some literatures when they do not find other effective methods, is bound to be a security risk in the completed structural design work.Because the author’s academic team are the responsible organization which has been involved in or participated in the revision of the second-order effect provisions of China’s “Code for design of Concrete Structures” since the late 1970 s, it is necessary to make efforts to clarify the concept of the above mentioned problems, and for the shortfall in code about the stability design of reinforced concrete members under the action of axial force, shear and moment which have a variety of side constraints.Therefore, this paper intends to complete the study by the following tasks under the recommendation of the academic team:① Briefly describe the law of two types of second-order effect, that is P- ? effect and P-δ effect, which has been relatively accurately identified so far through structural analysis; deduce, explain and give a conclusion about the problem which is controversial in engineering field about "whether the second-order effect increase the shear force in frame beams and columns under horizontal load or not"; give an introduction about the “layer increase coefficient method” for shear type structure and “overall increase coefficient method” for flexural type structure or shear-flexural type structure in “Code for design of Concrete Structures” and “Technical specification for concrete structures of tall building” which are used to calculate the structural P- ? effects, geometric nonlinearity theory and geometric stiffness based finite element method(virtual column method) that is used to calculate the second-order effect in SATWE, ETABS, SAP2000 and other structural analysis softwares. Hope this work can help structural designers have a more intuitive, accurate understanding of the law of internal force amplifying effect and deformation of various types of structures under the action of second-order effect.② Briefly describe the ideas and methods used to solve the strength and deformation problems considering the second-order effect in various versions of China’s “Code for design of Concrete Structures” so far.③ Briefly describe the issues related to structural stability theory. Calculation methods of stability capacity and buckling modes for Euler single column and the overall structure are introduced; discuss the differences and relations of strength, buckling and second-order effect; give a stability design idea for reinforced concrete structures. Whereby conclude two important understandings: 1. From a macro perspective, up to now there are two ideas for solving the structure’s stability problem, one is the effective length method based on the concept of elastic bifurcated point instability, which transforms the non-elastic instability issues of overall structure into the stability checking of each component of the structure, although it will be somewhat complicated to understand the concept of the transformation process, but this transformation makes the stability design process more simplified, and more in line with the structural designers’ component-level design habit, so until today, this stability design method based on the effective length is still widely used in structural design field; the second is advanced analysis method based on the concept of elastic asymptotic instability or inelastic extreme point instability, the method directly fully takes the initial imperfections, geometric nonlinearity, material non-elastic effects and various types of factors which influences the stability of structure and components into account in the analysis process, it considers the strength failure process and the stability failure process under the influence of second-order effect as two specific periods in the whole inelastic second-order deformation process under load, it completes the strength and stability design based on the structural reliability level; 2. In the modes of elastic asymptotic instability and inelastic extreme point instability which are ubiquitous in actual projects, it can be considered that the ultimate state of the development of second-order effect is instability, from this point of view, the strength and stability problems considering the second-order effect have good agreement in the law of second-order effect.④ Discuss the effective length, indicate some specific differences between the effective length used in the past which belongs to the category of second-order effect and the effective length which belongs to the category of stability and the consistency foundation of the overall trend they express; highlight the various types of proposals given in the literatures for the effective length determining methods which have been discussed from the perspective of elastic bifurcated point instability so far, analyse the deficiencies of these proposals, and give a recommendation of the author for the compression strut’s effective length determining method which is more in line with the actual mechanical behavior compared to the all kinds of old methods, and explain their application conditions.⑤ Briefly introduce the overall structural strength and stability checking method— — “Advanced Analysis Method”, which has been proposed currently in the international steel structure field, and can better consider all types of component initial imperfections, second-order effect(geometric nonlinearity) and non-elastic properties of the material.This paper hopes to propose a new practical method for determining the effective length of the single compression strut which may have the risk of instability in structure on the basis of combing, summarizing, clarifying the law of second-order effect and the related conceptual issues of strength and stability considering second-order effect, and on the premise of using existing methods specified to ensure the overall stability of the structure. This method can be only regarded as the first critical step of the entire methodology to solve inelastic extreme point instability problems of single strut with arbitrary constraints. After the reasonable determination of effective length, it is necessary to conclude a specific method which is convenient for engineering application and suitable for nonlinear inelastic extreme point instability checking of reinforced concrete eccentric compressive bar, through the nonlinear finite element analysis of all kinds of compressive bar with different end constraints, different proportions of the end moment, and the consideration of reliability requirements. This paper only gives a general idea about this method; the specific work is expected to be arranged for the follow-up graduate students.