Üçgen konsol plakların incelenmesi yapı sistemlerinin hesap yöntemlerinin karşılaştırılması

Abstract

Bu çalışma iki ana bölümden oluşmaktadır : Üçgen Konsol Plakların İncelenmesi ve Yapı Sistemlerinin Hesap Yöntemlerinin Karşılaştırılması. Birinci kısımda üçgen Konsol Plak, ızgara sistem ortamın da idealleştirerek; çeşitli geometrik özellikleri, farklı yükleme durumları ve boşta olan kenarlarda çeşitli rijitliklerdeki kenar kirişlerin bulunması halleri için hesapları yapılmış ve sonuçlar mühendislik kullanımı için tablolaştırılmıştır. Hesaplar "SAP 90" procrramı ile yapılmış, ayrıca bölüm içinde bazı çıkış diyagramları verilmiştir. ikinci kısımda Yapı Sistemlerinin Hesap Yöntemleri, seçilen üç açıklıklı düzlem çerçevede çeşitli yükleme durumları için farklı hesap yöntemleri kullanılarak karşılaştırılmış ve sistemin betonarme hesapları yapılmıştır. Çerçevenin açı yöntemine göre ön boyutlandırması yapılmıştır. Daha sonra sırayla? sabit yükler için Matris Kuvvet Yöntemi, P, ve P2 ilave yükleri için Cross Yöntemi, W (Deprem) yükü için Açı Yöntemi, düzgün sıcaklık değişmesi için Matris Deplasman Yöntemi, mesnet çökmeleri için de Cross Yöntemi kullanılarak kesit tesirleri hesaplanmıştır. Ayrıca, Endirekt Deplasman Yöntemine göre de iki kesitte M, N, T tesir çizgileri çizilmiştir.

In structural engineering, both safety and economic factors are considered in the design of structures. Because, as it is known, these two basic factors considerably effect each other. Before the use of computer technology in structural engineering, safety factor was the most important aspect in the design of structures because of the indeterminacy of the real behavior of the structures. Due to the development of structural analysis methods and computer technology, the behaviour of structures is determined more precisely. Therefore, the problem of economical design becomes more important. For this reason, structural engineers use the design methods which consider both material and geometrical non-linearities. This master thesis consists of two parts. In the first part of the thesis, triangular plates with one edge clamped and two edges free, in the second part of the thesis, Comparison of Methods of Structural Analysis, are investigated. ? In engineering applications, triangular cantilever plates are sometimes used in entrance eaves and balconies of buildings. In such cases, the plate is rigidly clamped along one edge and is free along the other edges. In this study, these types of plates are analyzed for various geometrical dimensions and different loading conditions. The triangular cantilever plates, stiffened with edge beams along free edges are also investigated. The numerical results are given in tabular form so that they can be easily used in practical applications. VI The plate is idealized as an equivalent grid system and analyzed by Matrix Displacement Method. In this method, the unknowns are vertical displacement and two rotations at each joint. These unknowns are determined through the equilibrium equations of the joints, i.e. vertical equilibrium equation and two moment equilibrium equations. The computer program SAP 90 is used for numerical study. In order to select the most proper grid system, the calculations are repeated for different grid patterns. It is observed that sufficiently accurate results can be obtained when the longer side of the triangle is divided into twenty elements. The results are also compared with those obtained through finite element analysis. After selecting the properly equivalent grid system, the plate is analyzed for different e = Lx/Ly values varying from 0.25 to 2.00, under uniformly distrxbuted load and concentrated load acting on the free corner. The coefficients for bending moments and vertical displacement are given in tables. A simple formula is also presented for determining the bending moment of triangular cantilever plates subjected to uniformly distributed load. By means of these tables, the triangular plates with one edge clamped and supported on the opposite corner, can be analyzed under uniformly distributed laod. This is accomplished by the Force Method considering the triangular cantilever plate as a subsystem. Especially in entrance eaves and balconies, there exist paraphet beams along the free edges of the plate. In order to investigate the effect of these edge beams on the behavior of plate, the plate with dimensions of e= Lx/Ly= 0.50 and subjected to uniformly distributed load is analyzed for different values of edge beam stiffness. The numerical results are presented in a table. As a limiting case, the triangular cantilever plate with edge beams whose bending and torsional rigidities are infinite is analyzed. The results are compared with known values of bending moments for triangular plates with clamped edges. The comparison has shown a good agreement. vn In the second part, the analysis of a three-span reinforced concrete plane frame subjected to various external effects is presented. Different analysis methods have been used for each external loading. Thus, the application and comparison of these methods have been illustrated. The preliminary cross-sectional dimensions of frame have been determined through the utilization of the Slope- Deflection Method. At the end of this chapter, a sufficient result can be obtained in predesigning of the structural system by decreasing the characteristic strengths of material in some proportion while only the dead weight and live loads are considered. In the second chapter of the second part, the structure is analysed by the Matrix Force Method for dead weight acting on the structure. The unknowns are the forces acting at the ends of the members which have formed the structure. In this method, first, a number of forces released which are equal to number of unknowns (the degree of indeterminacy). Each release can be made by the removal of either support reactions or internal forces. Due to this property, analysis can be made with lesser unknowns for the systems having more members in a frame. In addition, it is possible to obtain equations in which the band width is kept small and system equation is stable, by means of the freedom in choosing unknowns. These equations, however, are written systematically even they can be derived automatically. In the third chapter of this part, the structure is analysed by the Cross Method for live loads P, and ?2' As it's known, the analysis of statically indeterminate structures, generally, requires the solution of linear simultaneous equations. In the Cross Method, the unknowns are rotations and translations of the joints. In this method, a part the simultaneous equations are solved by using successive iterations. In the fourth chapter, the structure subjected to lateral load is analysed by the Slope - Deflection Method. The unknowns, in this method, are rotations of joints and independent translations of the members ends, as in the Cross Method. The linear simultaneous equations are obtained automatically. Vlll In the fifth chapter, the uniform temperature changes have been taken into account as an external effect on the structure. Uniform temperature change is the temperature change at centerline of the members. Because of this effect, some internal forces acting on the cross-sections of statically indeterminate structure occur. To determine these forces the structure is analysed by the matrix Displacement Method. In the Matrix Displacement Method the unknowns are the joint translations and rotations. This method is more useful for the systems having hige degrees of statically indeterminacy. In other words, if systems having more members meeting at joints of the systems, this method supply to operate with lesser unknowns. Although, the band width of simultaneous equation is limited and there is no elasticity in choosing the unknowns, generation of the stiffness matrix is usually not difficult because of localized effect, so a displacement of a joint effects only the members meeting at the given joint. Thus, it is easy to formulate the Matrix Displacement Method and this method is more suitable for computer programming. The last analysis method to determine the structure subjected to different support settlements is Cross Method. At the end of these calculations, the dimensions of the critical cross-sections obtained from the preliminary analysis are checked under the most unsuitable loading conditions. These loading conditions are some combinations which consider different external effects action in certain proportions according to Turkish Design Code. In this study, it is observed that the most unsuitable loading condition is obtained from the following combination : 1.4*G + 1.6*P IX Where G : Dead weight P : Live load In the sixth chapter of the second part, finally, the influence lines for bending moment, axial force and shear force of two given sections are obtained by means of the Indirect Displacement Method which is an efficient and reliable method.