Üçgen enkesitli uzay kafes sistemlerde stabilite incelemesi yapı sistemlerinin hesap yöntemlerinin karşılaştırılması

Abstract

Bu çalışma iki ana bölümden oluşmaktadır, üçgen Enkesitli Uzay Kafes Sistemlerde Stabilite İncelemesi ve Yapı Sistemlerinin Hesap Yöntemlerinin Karşılaştırılması. Çalışmanın birinci bölümünde üçgen enkesitli uzay kafes sistemlerin değişik parametrelere bağlı olarak burkulma yükleri belirlenmiş, sistem geometrisinin ve enkesit karakteristiklerinin burkulma yüklerini hangi yönde ve ne şekilde etkiledikleri incelenmiştir. Elde edilen sayısal sonuçlardan ve dolu gövdeli sistemler için verilen yanal burkulma formüllerinden yararlanarak, üçgen enkesitli uzay kafes sistemler için yaklaşık bir bağıntı önerilmiş ve sistemin kesin hesabı sonucunda bulunan burkulma yükleri ile önerilen bağıntıdan bulunan burkulma yüklerinin karşılaştırılması da yapılmıştır. Yapı sistemlerinin hesap yöntemlerinin karşılaştırılması bölümünde, düzlemi içerisinde çeşitli yükler etkisinde bulunan üç açıklıklı bir düzlem çerçeve seçilmiş ve değişik yükleme durumları için farklı hesap yöntemleri kullanılarak statik hesapları yapılmıştır. Çerçeve açı yöntemi kullanılarak yaklaşık olarak boyutlandırılmıştır. Daha sonra sırasıyla sabit yükler için Matris Deplasman Yöntemi, Pi, P2 ilave yükleri için Açı Yöntemi, W (deprem) yükü için Cross Yöntemi, Düzgün Sıcaklık Değişmesi için Matris Kuvvet Yöntemi ve son olarak mesnet çökmeleri için Cross yöntemi kullanılarak kesit tesirleri hesaplanmıştır. Ayrıca, elde edilen kesit tesirlerinin en elverişsiz kombine - zonlarına göre kesitler donatılmış ve Endirekt Deplasman Metodundan yararlanılarak iki kesite ait M,N,T tesir çizgileri çizilmiştir.

This study which is presented as Master Thesis is composed of two parts: 1- Stability of triangulated space trusses, 2- Comparison of methods of structural analysis. The first part consists of six chapters. In the first chapter the subject is introduced and the aim of the study is presented. The triangulated space trusses are common structural systems in engineering applications. The purlins, girts and roof trusses of industrial buildings, the girders of portal cranes may be given as examples. In these structural systems the compression forces occur in either upper chord or lower chord members depending on the position of the system and the direction of external loads. In the following figure a triangulated space truss subjected to vertical loads is shown. When the external loads reach to a critical value the system buckles due to compression forces in the upper chord. However, the critical load is very much affected by the resisting PA forces occured in the Lower chord. Therefore the buckling load is a function of system geometry i.e. b/h ratio. i L- 1- » VI The aim of the study to investigate the second-order behavior of triangulated space trusses and to determine the buckling loads. By the use of the numerical results, it is also aimed to propose an approximate formula for calculating the buckling loads. In the second chapter a method of successive approximation is presented for the second-order analysis of structural systems. At each step of the iteration the equilibrium equation are written on the deformed structure. The methods for the determination of buckling loads are also given. The analysis of the space trusses is performed by means of a computer program which is based on the Matrix Displacement Method. The third chapter outlines the principles of this method. In the fourth chapter the results of numerical investigations are given in detail. The variation of buckling loads due to the following parameters are examined: a- geometry of the cross-section (b/h ratio), b- boundary conditions, c- cross-sectional characteristics of members, d- Loading conditions, The most important result drawn from the nemerical investigations that, the system does not buckle when b/h ratio is equal or exceeds unity. Even if the b/h ratio is smaller, the effective length obtained through the system buckling load does not exceed the individual member length considerably. It is also observed that the first buckling mode of the structure is symmetrical. The fifth chapter is devoted to the determination of the equivalent cross-sectional characteristics of the system. Approximate formulae are given for the lateral flexural stiffness and the torsinal stiffness of the triangular cross-section of the truss. The effect of diagonal member forces on the shear stiffness of the cross-section is considered. The determination of shear center is also explained. In the sixth chapter the following approximate formula is proposed for the buckling load of triangulated space trusses subjected to axial forces corresponding to constant bending moment, (M0>. TT V^V^t t**> "T ' ' " '" -1. ill ' L / 1--^- vii where, b : width of triangular cross-section, h : height of triangular cross-section, L : span of truss, EI : effective lateral flexural stiffness, GJ£: effective torsinal stiffness, (M ) : critical bending moment (=upper chord compression ° cr force x h) The comparison of results obtained through the numerical investigations and the approximate formula is also given. The results of comparison have indicated a close approximation. In the second part of the study 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 the 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 the preliminary design of the structural system by decreasing the characteristic strengths of material in some proportion since only the dead weight and live loads are considered. In the second chapter of this part, the structure is analysed by the Matrix Displacement Method for dead weight acting on the structure. In the Matrix Displacement Method the unknowns are the joint translations and rotations. This method is more useful for the systems having high degrees of statical 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 simulateneous equations 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. In the third chapter of the second part, the structure is analysed by the Slope-Deflection Method for live Loads P, and P2. The unknowns, in this method, are rotation of joints and independent displacements of the member ends. The Linear simultaneous equations are obtained automatically and solved by computer. viii In the forth chapter of this part, the structure is analysed by the Moment Distribution (Cross) Method for lateral Loads. As it is known, the analysis of statically indeterminate structures, generally, requires the solution of linear simultaneous equations. In the Moment Distribu tion (Cross) Method, the unknowns are rotations and translations of the joints. In this method, a part the simultaneous equations which correspond to the joint rotations are solved by using successive iterations. In the fifth part, 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 Force Method. In the Matrix Force Method, 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. The last analysis method to determine the structure subjected to different support settlements is Moment Distribution (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 acting 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: IX 1,4 x G + 1,6 x P where G : Dead Weight P : Live Load In the sixth part 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.