Çok katlı diyagonalli düzlem çelik çerçevelerin göçme güvenlikleri yapı sistemlerinin hesap yöntemlerinin karşılaştırılması /
Yazar: HÜSEYİN UZUNER
Danışman: PROF.DR. ERKAN ÖZER
İstanbul Teknik Üniversitesi / Fen Bilimleri Enstitüsü
Derece: Yüksek Lisans, 1993
Konu: İnşaat Mühendisliği = Civil Engineering
Dizin: Diyagonal düzlem = Diagonal plane ; Yapı sistemleri = Structure systems ; Çelik-metal = Steel-metal ; Çerçeve = Frame

Özet:
ÖZET Yüksek Lisans tezi olarak sunulan bu çalışma iki ana bölümden oluşmaktadır. "Çok Katlı Diyagonalli Düzlem Çelik Çerçevelerin Gerçek Göçme Güvenlikleri" ve "Yapı Sistemlerinin Hesap Yöntemlerinin Karşılaştırılması". Birinci bölümde, çok katlı çelik yapıların deprem kuvvetleri altındaki gerçek göçme güvenliklerinin belir lenmesi amacıyla yürütülen ve seçilen çok katlı çelik yapı sistemlerinin dış yükler altındaki elastoplastik davranış larını esas alan bir çalışmanın esasları açıklanmış ve sa yısal uygulamalarına ait sonuçlar verilmiştir. Sayısal uygulama için seçilen taşıyıcı sistem modeli yirmi katlı, üç açıklıklı diyagonalli düzlem çelik çerçeve sistemidir. Bu yapı modelinin önce ülkemizde yürürlükte bulunan elas tik hesap yönetmeliklerine göre boyutlandırılması yapıl mıştır. Ardından sırasıyla sabit düşey, artan yatay yük ler ve orantılı olarak artan düşey ve yatay yükler altında II. mertebe elastoplastik hesapları yapılmış ve bu hesap lara ait sayısal sonuçlar verilerek değerlendirilmiştir. İkinci bölümde, yapı sistemlerinin hesap yöntemleri, seçilen iki açıklıklı bir düzlem çerçeve üzerinde çeşitli yükleme durumları için farklı hesap yöntemleri kullanıla rak karşılaştırılmıştır. önce Açı Yöntemi 'ne göre yapının önboyutlandırılması yapılmıştır. Daha sonra sırasıyla, yapı yükleri için Matris Deplasman Yöntemi, p^, P2 ilave yükleri için Cross Yöntemi, W (Deprem) yükü için Rölaksas- yon Yöntemi, düzgün sıcaklık değişmesi için Matris Kuvvet Yöntemi ve mesnet çökmeleri için de Açı Yöntemi kullanıla rak iç kuvvetler hesaplanmıştır. En elverişsiz iç kuvvet ler, düzenlenen bir süperpozisyon tablosu yardımı ile bu lunmuş, kritik kesitlerde betonarme kesit hesapları yapıl mış ve kesit krokileri çizilmiştir. Ayrıca, Endirekt Dep lasman Yöntemi ile, seçilen iki kesite ait M, N, T tesir çizgileri çizilmiştir. v

Abstract:
THE COLLAPSE SAFETY OF BRACED MULTISTORY STEEL FRAMES COMPARISON OF METHODS OF STRUCTURAL ANALYSIS SUMMARY In structural engineering, both safety and economical factors are considered in the design of a structure. 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 structures. Due to the development of structural analysis methods and computer technology, the behavior of structures can be determined more precisely. Therefore, the problem of economical design becomes more important. For this reason, structural engineers use the advanced analysis and design methods which predict the actual behavior of structures. This study which is submitted as Master Thesis, consists of two parts: 1. The Collapse Safety of Braced Multistory Plane Steel Frames 2. Comparison of Methods of Structural Analysis In the first part of this thesis, the elastic- plastic behavior and collapse safety of braced multistory plane steel frames subjected to gravity and lateral loads are investigated and the numerical results obtained in the course of the study are presented. In the first chapter of the first part, the scope and aim of the study are introduced. In the last decade, the number of tall buildings in our country increased rapidly, especially in major cities. Although most of the tall buildings are designed as reinforced concrete structures, it is believed that, in the near future the use of structural steel in tall buildings will gain much importance due to several practical and economical reasons. The recent developments in the non-linear analysis methods of structural systems enable engineers to reach more realistic and economical solutions. Further, by the use of these methods the behavior and collapse safety of vibuilding structures designed by the current allowable- stress design method can be studied in detail. By considering the facts above, a research project on the "Determination of Collapse Safety of Multistory Steel Frames Under Seismic Loads and Earthquake Resistant Structural Design" is being carried out under the sponsorship of Turkish Scientific and Technical Research Council. This study which is a part of this research project aims: a- to investigate the collapse safety and the elastic-plastic, second order behavior of a sample frame designed according to the provisions of the Turkish codes for steel design, b- based on the numerical results obtained through the non-linear analysis of the sample frame, to discuss the current steel design codes with special emphasis on seismic safety and economical design of multistory steel frames. The procedure followed in this study has the following steps: a- Selection of a sample structure commonly encountered in practice. The steel structure studied here is a twenty story-three bay braced plane frame. b- Design of the sample frame according to the provisions of Turkish Code for Steel Design (TS 648). c- Analyses of frame according to the second-order theory under constant gravity and increasing lateral loads as well as proportionally increasing gravity and lateral loads by using effective computer programs developed for the practical applications of the non-linear theory. d- Discussion of the numerical results obtained in the analyses. In the second chapter, the second-order, elastic- plastic behavior of structural systems subjected to gravity and lateral loads is discussed. The non-linear behavior of structures is caused by two reasons such as geometrical and material non- linearities. Material non-linearity represents the load carrying capacity of material beyond the proportional limit. As the gravity and lateral loads are increased starting from the initial state, plastic deformations develop at sections where the internal forces reach the viilimiting values corresponding the proportional limit. In the case of structures made of ductile material such as steel, the plastic deformations are assumed to be accumulated at certain sections which are defined as plastic sections. This assumption is called as "Plastic Hinge Hypothesis". Geometrical non-linearity represents the effect of geometrical changes on the equilibrium equations. As it is known, the theory which considers the geometrical non- linearity is called "Second-Order Theory". When both non-linearities are considered in the analysis of a structural system, the collapse of structure occurs at a load parameter of P _ through the loss of stability. This load parameter value is referred to as the "Second-Order Limit Load". In some cases, the structure may be considered as being collapsed due to the excessive deflections and plastic deformations or the rupture of critical sections. In the third chapter, the method of load increments which is applied to the determination of collapse loads braced plane steel frame is outlined. In the application of the method, the structure is analyzed for successive load increments. A given load increment is terminated when the internal forces at any potential plastic section location reach the limiting values defined by the yield condition, i.e., when a plastic section forms. After the formation of each plastic section, the plastic rotation at this section is introduced as a new unknown. Besides, an equation is added to system of equations to express the incremental yield condition. Since the system of equations corresponding to the previous load increment have already been solved, the solution for the current load increment is obtained simply by the elimination of the new unknown. As it is clearly seen from the above discussion that, the determination of the second-order limit load of a structure ' is reduced to the determination of an extended system of linear equations and the solution of this system and its subsystems. The fourth chapter is devoted to the computer design of braced multistory steel plane frames according to Turkish Code for Steel Structures, (TS 648). The computer program used in this study consists of successive analysis and design steps. The design is based on the results of gravity and lateral load analyses. viiiWhen the member sizes obtained in two successive steps are the same, the iteration is terminated. The effective lengths of columns are determined either by the analytical method or by the use of approximate charts. The computer program enables designer to add various structural constraints into the design. In the fifth chapter, the numerical results of the detailed second order, elastic-plastic analyses of the sample frame are presented. The results of analyses of twenty-story braced plane steel frame have shown that the seismic safety under factored gravity loads (GLF= 1.50) is 2.01 while a collapse safety of 1.87 is attained under proportionally gravity and seismic loads. The results of the investigation have indicated that the collapse loads of steel braced frames have higher values as compared with those of unbraced frames. This is due to the relatively small second-order effects developed in the braced frames. In the second part of the thesis, the analysis of a two-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. In the preliminary design of the structural system, realistic member sizes can be obtained by decreasing the characteristic strengths of material in some proportion since only the dead loads and live loads are considered. In the chapter numbered 2.4.1. of this part, the structure is analyzed 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 convenient for those systems having high degree of statical indeterminacy. In other words, for systems having more members meeting at joints, this method enables designer to deal with less unknowns. Although the band width of simultaneous equations is limited and there is no elasticity in choosing the unknowns, generation of the stiffness matrix is usually practical because of localized effect, i.e., 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. ixIn chapter 2.4.2. of this part, the structure is analyzed by the Moment Distribution (Cross) Method for live loads P, and P_. As it is known, the analysis of statically indeterminate structures generally requires the solution of linear simultaneous equations. In the Moment Distribution Method, the unknowns are rotations and translations of the joint. In this method, a part of the simultaneous equations which correspond to the joint rotations are solved by means of successive iterations. In chapter 2.4.3., the structure subjected to lateral loads is analyzed by the Relaxation Method. The unknowns and the equations in this method are same as those of the Slope-Deflection Method. The linear simultaneous equations are obtained automatically and solved by Relaxation Method. The only difference between the Relaxation Method and the Slope Deflection Method is the solution technique of the linear simultaneous equations. In the chapter numbered 2.4.4. of this 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 the centerline of members. Due to this effect, internal forces occur in statically indeterminate structures. lu order to determine these forces the structure has been analyzed by Matrix Force Method. In the Matrix Force Method, the unknowns are the end forces of members which forms the structure. In this method, first, a number of forces which are equal to the number of unknowns (the degree of indeterminacy) are released. Each release can be made by the removal of either support reactions or internal forces. In this method, analysis can be made with lesser unknowns for the systems having more members in a frame. Further, it is possible to obtain equations with sufficient stability and with narrower band width by means of the freedom in choosing unknowns. In chapter numbered 2.4.5., the structure is analyzed by the Slope-Deflection Method for different support settlements. The unknowns in this method are rotations of joints and independent relative displacements of members. The linear simultaneous equations can be obtained automatically. At the end of analysis 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 several 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: 1.4G + 1.6P where G : Dead Weight P : Live Load Finally, in the chapter numbered 2.5. of this part, the influence lines for bending moment, axial force and shear force of two given sections are obtained by means of Indirect Displacement Method which is an efficient and reliable method. In the third part of this thesis, the results obtained in the first and second parts of the study are given. XI