Master's Thesis in Civil Engineering, Structural Design
February 2011
Abstract:
In optimal civil engineering structure construction have been significantly developed for static loadings. However, in the optimization for seismic loads, many problems appear, such as the dependence of constraints on time, the variability of the design space in time, and gradient calculations. In order to optimize against earthquakes, in this research, the spectral dynamic analysis method has been used, which has acceptable accuracy and is not involved with the above-mentioned problems. For this purpose, short, medium and long steel frames have been optimized against earthquakes. The results of optimization using the classical method (gradient-based methods) have been compared with the results of discrete optimization of the genetic algorithm, to ensure that the overall optimal plan is obtained. In the classical method, progressive finite difference method is used to calculate gradients and sensitivity analysis. Using finite element analysis, static analysis has been performed and considering the mass of the structure in a consistent way, the simplifying assumption of the shear frame has been avoided. Considering the geometric stiffness, secondary effects have been applied in the static analysis. In order to perform seismic analysis, by calculating the elastic response spectrum of an arbitrary earthquake, the dynamic analysis of the response spectrum of the structure has been done.
In this thesis, the ability of the methods presented by solving several problems of optimizing braced and unbraced steel frames and complying with the technical regulations and regulations of permissible stress in topic 10 of the National Building Regulations has been presented. The results are compared with each other and the most economical structural system against the height has been determined. Chapter 1 Introduction Introduction 1-1-Research Field The meaning of optimization in civil engineering is to find a design for the structure that meets the technical criteria and has the minimum economic cost. Building frames are the most common civil engineering structures. Therefore, optimizing these types of structures will be a great help from an economic point of view. Optimal design of building frames widely in the decade. 60 AD was studied; Because finding the optimal answer analytically is only possible for simple and regular frames. Since the 1980s, with the rapid development of computer technology, many methods and computer programs have been presented in the field of optimization of real structures, under the constraints of practical design[2] [1]. Since there is no unique method to optimally solve all optimization problems, therefore, several methods have been developed to solve optimization problems [2]. In general, the optimization methods used in engineering can be divided into two distinct categories: a) gradient[3]
b) heuristic[4]
Among the most famous gradient optimization methods are linear programming (LP) [5], second-order programming (QP)[6] and Non-Linear Programming (NLP)[7], and among the exploratory methods, genetic algorithm (GA) [8], simulation annealing (SA) [9], particle swarm optimization (PSO) [10] and fuzzy optimization (FO) [11] can be mentioned. In gradient optimization, obtaining the optimal solution requires the calculation of gradients and sensitivity analysis [12]. The methods of sensitivity analysis are given in Figure 1-1.
(Images can be seen in the main file)
In addition to the problems in the field of choosing the optimization method and the method of sensitivity analysis, the way of applying the seismic load is also one of the important factors in the optimization problem. In general, the load caused by an earthquake can be applied to the structure in three ways:
A. Equivalent Statics (ESL)[13]
b. Response Spectrum Analysis (RSA)[14]
P. Time history analysis (THA) [15]
In this research, frame optimization is used. Braced and unbraced steel structures, under gravity and seismic loads, have been studied using SQP [16] and Genetic Algorithm (GA). The load caused by the earthquake is directly applied to the structure using the response spectrum analysis (RSA) method.At the end, the results of applying these methods on 4, 10 and 18 story braced and unbraced steel frames have been compared with each other and the necessary discussions and investigations have been made.
Exploration of the effects of soil and structure interaction
2D extraction of frames from the entire structure
Exploration of seismic design criteria and details of connections
1-3-Research is necessary
In seismic areas like our country, Iran, there is an urgent need for optimal design of earthquake-resistant structures. May The optimal design of these structures plays a significant role in reducing the statistics of damages and casualties caused by earthquakes. In most of the researches that will be mentioned in the next chapter, many simplifying assumptions have been used, among them shear frame [17], strong column-weak beam [18], etc. In addition to these assumptions, the aim of many researches in recent years has been to compare optimization methods with each other and to reduce the convergence time of the results. Therefore, the necessity of a research in which the optimization using the design restrictions found in topic 10 of the National Building Regulations of Iran (1387) and standard 2800 (3rd edition) and the application of actual earthquake loading is strongly felt. The design regulations are the response spectrum analysis (RSA) method. In this method, the responses of the structure are in the linear elastic range and unlike the time history analysis method, the time variable is removed from the response [4]. To perform this method, first, modal analysis [19] should be performed and the natural frequencies of the structure should be calculated. Then, using the plot spectrum, in which all possible frequencies are plotted against the maximum responses, and using the method Statistics of complete quadratic composition (CQC) [20], the responses of the maximum structure are calculated. Therefore, a function has been written in the MATLAB environment to generate the elastic response spectrum, which calculates the spectrum of displacement (Sd) [21], pseudo-velocity (Spv) [22] and pseudo-acceleration (Spa) [23] of the desired earthquake using the numerical solution of Newmark's linear method, for the range of periodicity and desired damping.
Instead of using ready-made commercial programs, a program has been written in the MATLAB environment that is able to perform Static, P-Delta and dynamic analysis of the response spectrum. This program is written based on the Finite Element Method (FEM) [24], to create a user-friendly environment, program inputs are introduced to the program in an Excel attachment. In this file, the coordinates of the nodes, the number of the elements and their beginning and end nodes, the degree of freedom of each node, the static concentrated loads in each node, the uniform loads on each element, the specifications of each element that include the modulus of elasticity and specific mass, and at the end the desired earthquake accelerometer and the constant damping of the structure should be entered. Figure 1-2 shows the flowchart of the written program.
The method of doing the work is described in detail in the third chapter. In short, the work steps are as follows:
Calculation of the elastic response spectrum.
To reduce the number of unknown design variables, one can express the characteristics of the section such as the moment of inertia [1] and the base of the section [2] (for example, y) in terms of the cross-sectional area x, or use the spatial spline interpolation method based on the cross-sectional area.
Application of the initial design variable. Calculating the mass matrix and stiffness matrix of the elements and then, taking into account the degrees of freedom of the nodes, assembling and forming the mass and stiffness matrix of the entire structure and as a result calculating the displacements, support reaction and internal forces of the members. Applying the geometric stiffness matrix[3] and P-Delta analysis.
Calculating the mass of the structure based on the load, solving the characteristic equation[4] and calculating Vectors[5] and eigenvalues[6] (Modi shapes[7] and frequencies).
Analysis of the response spectrum according to the elastic response spectrum calculated in step (1) and calculation of the maximum responses of the structure using the CQC statistical method. Determining the sign of the responses resulting from the response spectrum analysis, according to the dominant mode of the structure.