Yüksek dayanımlı çok katlı çelik çerçevelerin göçme güvenlikleri yapı sistemlerinin hesap yöntemlerinin karşılaştırılması

Abstract

Yüksek Lisans tezi olarak sunulan bu çalxşma iki ana bölümden oluşmaktadır. "Yüksek Dayanimlx Çelikten Yapılmış Çok Katlı Düzlem Çerçevelerin Gerçek Göçme Güven likleri" ve "Yapı Sistemlerinin Hesap Yöntemlerinin Karşı laştırılması". Birinci bölümde, çok katlı çelik yapıların deprem kuvvetleri altında gerçek göçme güvenliklerinin belirlen mesi amacıyla yürütülen ve seçilen çok katlı çelik yapı sistemlerinin dış yükler altındaki II. mertebe, elasto- plastik davranışını esas alan bir çalışmanın esasları açıklanmış ve sayısal uygulamalar verilmiştir. Sayısal uygulamalar için seçilen modellerden biri yirmi katlı, yüksek dayanımlı çelikten yapılmış düzlem çerçeve, diğeri ise yirmi katlı, genişliği yapı yüksekliği boyunca değiş ken düzlem çerçevedir. Her iki yapı modelinin önce ülke mizde yürürlükte bulunan hesap yönetmeliklerine göre bo- yutlandırılmaları yapılmıştır. Ardından sırasıyla sabit düşey, artan yatay yükler ve orantılı olarak artan düşey ve yatay yükler altında II. mertebe elastoplastik hesap lar yapılmış ve bu hesaplara ait sayısal sonuçlar veri lerek değerlendirilmiştir. İkinci bölümde, yapı sistemlerinin hesap yöntemle ri, seçilen üç açıklıklı bir düzlem çerçeve üzerinde çe şitli yükleme durumları için farklı hesap yöntemleri kul lanılarak karşılaştırılmıştır. önce Açı Yöntemine göre yapının ön boyutlandırılması yapılmıştır. Daha sonra sırasıyla sabit yükler için Matris Deplasman Yöntemi, P,, P_ ve P- ilave yükleri için Cross Yöntemi, W (Deprem) yükü için Rölaksasyon Yöntemi, düzgün sıcaklık değişmesi için Matris Kuvvet Yöntemi ve mesnet çökmeleri için de Açı Yöntemi kullanılarak iç kuvvetler hesap edilmiştir. En elverişsiz iç kuvvetler, düzenlenen bir süperpozisyon tablosu yardımı ile bulunmuş, kritik kesitlerde betonarme kesit hesapları yapılmış ve enkesit donatı krokileri çi zilmiştir. Ayrıca, Endirekt Deplasman Yöntemi ile, seçi len iki kesitte M, N, T tesir çizgileri çizilmiştir.

This study which is submitted as Master Thesis, consists of two parts: 1. The Collapse Safety of High-Strength Steel Multistory Plane Frames, 2. Comparison of Methods of Structural Analysis In the first part of this thesis, the elastic- plastic behavior and collapse safety of high-strength 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 design and construction of tall buildings became more popular in our country, 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 plane structures enable engineers to reach more realistic and economical solutions. Further, by the use of these methods the behavior and collapse safety of building 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" has been started under the sponsorship of Turkish Scientific and Technical Research Council. This study which is carried out parallel to the research project aims: a. to investigate the collapse safety and the elastic-plastic, second-order behavior of two sample frames designed according to the provisions of the Turkish codes for steel design, vi b. based on the numerical results obtained through the non-linear analyses of sample frames, to discuss the current steel design codes with special emphasis on seismic safety and economical design of multistory steel frames. The procedure followed in the study has following steps: a. Selection of two sample structures commonly encountered in practice. These are, a twenty story, two bay, high-strength steel frame and a twenty story, plane steel frame with set-back. b. Design of sample frames according to the provisions of Turkish elastic code for steel design (TS 648). c. Analyses of frames according to the second-order, elastic-plastic theory under constant gravity and increasing lateral loads and proportinally 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 critical sections where the internal forces reach the limiting 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 while the remaining part of the structure is elastic. 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 as "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 PL2 through the loss of vii 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 for the determination of collapse loads of structural systems 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 the 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 multistory plane frames according to Turkish code for steel structures, (TS 648). The computer program consists of successive analysis and design steps. The design is based on the results of gravity and lateral load analyses. When the number 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 of the first part, the numerical results of the detailed second-order, elastic- plastic analyses of two sample frames are presented. The results of analyses of twenty-story, high- strength steel plane frame have shown that the seismic viii safety under factored gravity loads (GLF= 1.50) is 2.21 while a collapse safety of 1.79 is attained under proportionally increasing gravity and seismic loads. The use of high-strength steel in multistory building frames causes marginal increases the second- order effects. The results of analyses of twenty-story, steel plane frame with set-back have shown that the seismic safety under factored gravity loads is 1.68 while a collapse safety of 1.60 is attained under proportionally increasing gravity and seismic loads. When a multistory frame has a set-back in lower stories, the slenderness ratio of overall structure decreases. Besides, substantial bending moment redistribution among lower story columns occur. These two factors result in higher collapse load. In the second part of the thesis, 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. In the preliminary design of the structural system, realistic member sizes can be obtained by decreasing the characteristic strengths of materials 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 unkonwns 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. In chapter 2.4.2. of this part, the structure is analyzed by the Moment Distribution (Cross) Method for live live loads P,,P" and P,i As itis known, the analysis of xx statically indeterminate structures generally requires the solution of linear simultaneous equations. In the Moment Distribution Method, the unknowns are rotations and translations of the joints. 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 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. In 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 settlement. The unknowns is 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. x 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