Investigating modal pushover and axial displacement analyzes to estimate the capacity of two-dimensional reinforced concrete frames

Master's Thesis in Civil-Structural Engineering

Abstract

In order to estimate the capacity of buildings, it will be much easier and less expensive to use static methods instead of incremental dynamic methods. Although the incremental dynamic method gives more accurate and closer answers to the real behavior of the structure, its high cost and time-consuming nature have increased the desire to use static methods to estimate the capacity. In non-linear static analysis methods, the basis of the method is based on the fact that the behavior of the structure is controlled by the first mode and the shape of the structure remains constant after yielding. Past research indicates that this method provides better results compared to other methods including FEMA-440 methods. Another non-linear static analysis method is the displacement-axis method (DPA), which is based on the assumption of loading by displacement. Due to the use of higher modes in the region after yielding, this method has a good overlap with the incremental dynamic method.

The aim of this research is to evaluate the accuracy of the MPA and DPA methods in estimating the seismic capacity of regular structures and compare the results with the values ??obtained from nonlinear incremental dynamic analysis. For this purpose, a number of regular concrete frames were subjected to equivalent non-linear static analysis (MPA) and (DPA) and incremental dynamic analysis. During these analyses, the general and local responses of the structures obtained from the equivalent non-linear static analysis and incremental dynamic analysis are compared. The answers include the displacement of the roof, the relative displacement of the floors, the cut of the base, the location of the plastic joint and the frame damage index. After performing the analysis, categorizing and presenting the statistical results for different parameters of the response of the structures, controlling the conformity or non-conformity of the answer of the analyzes and analyzing the results are among the tasks that have been done to reach the conclusion. According to the responses of each of the methods, it can be concluded that the modal method has higher accuracy and correlation in displacement responses, while the displacement-axis method has more favorable results in force responses. Both methods are associated with significant errors in determining the amount of damage and damage to the frame. Chapter 1: An overview of nonlinear analysis methods and a review of the research done According to the earthquake load, non-linear analysis is mainly used to estimate the behavior of the structure due to the application of possible earthquake force in the future. In nonlinear analysis, two main problems; How to model the structure and how to apply the earthquake load to the structure model are very important. According to the conditions and importance of the structure as well as the purpose of the analysis, accounting engineers are faced with these issues.

Nonlinear analyzes are divided into dynamic and static categories according to the characteristics of the materials that make up the structural members and the method of applying the earthquake load, and according to the degrees of freedom of the structure model, they are divided into models with many degrees of freedom, several degrees of freedom, and one degree of freedom. It is very clear, if we have a model that considers the nonlinear characteristics of its members and the earthquake load is applied without change and dynamically, and also the maximum possible degrees of freedom are considered in the modeling of the structure, the results of the analysis will be the most accurate, and the more the assumptions of the analysis are simplified, the less accurate the results will be. But there are some problems that force designers to use less dynamic nonlinear methods for analysis. The complexity, time-consuming and high cost of this type of analysis, and in addition to the problems that may appear in the justification and interpretation of the results, limits the application of this type of analysis to research projects and special cases. Therefore, the methods of designing structures resistant to earthquake loads have been changing and revised in recent years, and researchers have been trying to find an alternative method that is reliable, accurate, and simple at the same time. Most of the activities have been in the direction of non-linear static analysis methods, and so far various methods have been presented that are able to estimate the responses of the structure well.Among these methods, non-linear static analysis methods that have been introduced in new regulations such as FEMA ATC can be mentioned. Or the methods provided by researchers such as Elnashai [1], Aschhei [2], etc. Of course, each of these methods has strengths and weaknesses. Nevertheless, research in this field is being carried out extensively.

One of the research fields related to nonlinear analysis are issues related to the analysis of irregular structures. Research has shown that most non-linear static analysis methods are not accurate enough in estimating the results of regular structures. Therefore, investigating new methods in relation to regular structures can be considered as one of the research paths.

Past studies show that Chopra's Modal Pushover Analysis [3] method, which is one of the recent non-linear static analysis methods, provides very good results for regular frames. Thus, the purpose of this research is to examine this method in predicting the responses of irregular bending frames.

In this text, it has been tried to include the materials related to the research path in a suitable way. For this purpose, in the rest of this chapter, generalities related to the nonlinear analysis of structures and its types are stated. In the next chapter, we will have an overview of past researches on nonlinear static analysis and analysis of regular structures. In the third chapter, the generalities of nonlinear static analysis and its types of methods are examined. To get familiar with the studied models and the characteristics of selected earthquakes, we have included them in the fourth chapter.

1-2-Overview of non-linear analysis methods of structures

The design approach in the last two decades is changing from design based on resistance due to the problems that exist in this type of design to design based on performance (PBD). Currently, this method is mostly used in the improvement and reconstruction of existing buildings and structures.

Among the problems of the design method based on resistance, the following can be mentioned:

Using strength reduction coefficients or ductility coefficients in the design of structures leads to non-uniform risk or vulnerability in them. Therefore, ductility will be a weak characteristic to show the damage potential. To put it more clearly, if two different buildings are designed based on the same regulations and with the same force reduction coefficients or ductility coefficients, under the effect of certain earthquakes, different levels of damage may occur in them. In addition to the issue of uncertainty in determining the final displacements, this issue will also increase the complexity of the design because it turns the design process into a repetitive process.

The issue of damage to the instrumental and non-instrumental members depends on the strain and relative displacement. It is clear that in the design based on force, there are no links between the existing resistance and the damage corresponding to it.

Non-linear analysis methods are the most used for designing structures, evaluating and improving existing structures based on the PBD method [5,4]. The purpose of this analysis is to predict the response of the structure under earthquake shaking that will occur in the future. This problem has gained great importance and value in design based on performance, as a method for seismic design and evaluation. In the PBD method, it uses the prediction of the structure's performance in an earthquake to decide on its safety in an earthquake. For this purpose, PBD expresses the primary performance characteristics as predicted damages in structural and non-structural members. Structural damage is the reason for inelastic behavior, so the traditional analysis and design methods that use linear elastic methods are only able to implicitly predict the behavior of the structure, on the other hand, the aim of nonlinear analysis methods of structures under the effect of earthquake forces is to directly estimate the amount of inelastic deformations. The typical process of inelastic analysis is similar to the common linear methods in which the structural model is subjected to a number of earthquakes, Figure (1-1).

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The results of the analysis are the estimation of engineering demand responses from the structural model, and these results are subsequently used in comparison with acceptable criteria to determine the performance of the structure.