Çok katlı düzlem ve uzay çelik çerçevelerin gerçek göçme güvenlikleri yapı sistemlerin hesap yöntemlerinin karşılaştırılması
The Collapse safety of multistoroy plane and space steel frames-comparison of methods of structural analysis
- Tez No: 39184
- Danışmanlar: PROF.DR. ERKAN ÖZER
- Tez Türü: Yüksek Lisans
- Konular: İnşaat Mühendisliği, Civil Engineering
- Anahtar Kelimeler: Belirtilmemiş.
- Yıl: 1993
- Dil: Türkçe
- Üniversite: İstanbul Teknik Üniversitesi
- Enstitü: Fen Bilimleri Enstitüsü
- Ana Bilim Dalı: Belirtilmemiş.
- Bilim Dalı: Belirtilmemiş.
- Sayfa Sayısı: 107
Özet
ÖZET Yüksek lisans tezi olarak sunulan bu çalışma iki ana bölümden oluşmakta dır.“ Çok Katlı Düzlem ve Uzay Çelik Çerçevelerin Gerçek Göçme Güven likleri ”ve“ Yapı Sistemlerinin Hesap Yöntemlerinin Karşılaştırılması ”. Birinci bölümde, çok katlı çelik yapıların deprem kuvvetleri altında gerçek göçme güvenliklerinin belirlenmesi amacıyla yürütülen ve seçilen çok katlı çelik yapı sistemlerinin dış yükler altındaki elastoplastik davranışım esas alan bir çalışmanın esasları açıklanmış ve sayısal uygulamaları verilmiştir. Sayısal uygulamalar için seçilen taşıyıcı modellerinden biri otuz katlı iki a- çıklıklı düzlem çerçeve, diğeri ise on katlı, planda düzensiz bir uzay yapı sistemidir. Her iki yapı modelinin önce ülkemizde mevcut bulunan elastik hesap yönetmeliklerine göre boyutlandırılmaları yapılmıştır. Ardından sıra sıyla sabit düşey, artan yatay yükler ve orantılı olarak artan düşey ve yatay yükler altında II. mertebe elastoplastik hesapları yapılmış ve bu he saplara ait sayısal sonuçlar verilerek değerlendirilmiştir. İkinci bölümde, yapı sistemlerinin hesap yöntemleri, seçilen dört açıklıklı bir düzlem çerçeve üzerinde çeşitli yükleme durumları için farklı hesap yöntemleri kullanılarak karşılaştırılmıştır. Önce Açı Yöntemi'ne göre yapı nın ön boyutlandırılması yapılmıştır. Daha sonra sırasıyla, yapı yükleri i- çin Matris Kuvvet Yöntemi, plf p2, p3 ilave yükleri için Açı Yöntemi, W (Deprem) yükü için Rölaksasyon Yöntemi, düzgün sıcaklık değişmesi için Matris Deplasman Yöntemi ve mesnet çökmeleri için de Cross Yöntemi kul lanılarak iç kuvvetler hesaplanmıştır. En elverişsiz iç kuvvetler, düzenle nen bir süperpozisyon tablosu yardımı île bulunmuş, kritik kesitlerde beto narme kesit hesapları yapılmış ve kesit krokileri çizilmiştir. Ayrıca, Endi- rekt Deplasman Yöntemi ile, seçilen iki kesite ait M, N, T tesir çizgileri çi zilmiştir.
Özet (Çeviri)
THE COLLAPSE SAFETY OF MULTISTORY PLANE AND SPACE STEEL FRAMES- COMPARISON OF METHODS OF STRUCTURAL ANALYSIS SUMMARY This study which is submitted as Master Thesis, consists of two parts: 1- The Collapse Safety of Multistory Plane and Space Steel Frames 2- Comparison of Methods of Structural Analysis In the first part of this thesis, the elastic-plastic behavior and collapse safety of multistory plane and space 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 be lieved 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 and space 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 de sign 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. viThis study which is a part of this 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, 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 this study has following steps: a- Selection of two sample structures commonly encountered in practice. These are, a thirty story, two-bay plane frame and ten-story space frame with asymmetric shape in plan. b- Design of sample frames according to the provisions of Turkish elastic code for steel design (TS648). c- Analysis of frames according to the second-order, elastic-plastic theory under constant gravity and increasing lateral loads as well as pro portionally 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 struc tural 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 be yond the proportional limit. As the gravity and lateral loads are increased starting from the initial state, plastic deformations develop ât sections where the internal forces reach the limiting values correspond 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. The assumption is called as“ Plastic Hinge Hypothesis ”. viiGeometrical 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 ^^ 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 for the determination of collapse loads of plane and space frames 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 sec tion 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 and space frames according to Turkish code for steel structures, (TS648). A computer program developed for automated design of multistory steel plane frames has been used for the design of thirty-story building frame. viiiThe computer program consists of successive analysis and design steps. The design is based on the results of gravity and lateral load analyses. When 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 con straints into the design. The design of ten-story space frame has been carried out by the use of in dependent analysis and design computer programs. 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 thirty-story plane frame have shown that the seismic safety under factored gravity loads (GLF=1.50) is 1.67 while a col lapse safety of 1.55 is attained under proportionally gravity and seismic loads. The redistribution between components of ten-story space frame results in higher collapse safety factors: 2.^7 under non-proportional loading and 2.00 under proportional gravity and seismic loads. In the second part of the thesis, the analysis of a four-span reinforced con crete plane frame subjected to various external effects is presented. Dif ferent 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 deter mined through the utilization of the Slope-Deflection Method. In the pre liminary design of the structural system, realistic member sizes can be ob tained by decreasing the characteristics strengths of material in some pro portion 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 Force Method for dead weight acting on the structure. ixThe unknowns are the end forces of members which forms the structure. In this method, first, a number of forces which are equal to 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 hav ing 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 2.4.2. of this part, the structure is analyzed by the Slope-De flection Method for live loads pj, p2 and pa. The unknowns, in this method, are rotations of joints and independent relative displacements of members. The linear simultaneous equations can be obtained automati cally. 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-Deflec tion 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 struc ture. Uniform temperature change is the temperature change at the cen- terline of members. Due to this effect, internal forces occur in statically indeterminate structures. In order to determine these forces the structure is analyzed by Matrix Displacement Method. In the Matrix Displacement Method, the unknowns are the joint transla tions 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 equa tions is limited and there is no elasticity in choosing the unknowns, gen eration of the stiffness matrix is usually practical because of localized ef fect, i.e., a displacement of a joint effects only the members meeting at the given joint. Thus, the formulation of the Matrix Displacement Method is easier and this method is more suitable for computer programming. In chapter numbered 2.4.5., the structure is analyzed by the Moment Dis tribution (Cross) Method for different support settlements.As it is known, the analysis of statically indeterminate structures generally requires the solution of linear simultaneous equations. In this method however, a part of the simultaneous equations which correspond to the joint rotations are solved by using successive iterations. At the end of these calculations, the dimensions of the critical cross-sec tions obtained from the preliminary analysis are checked under the most unsuitable loading conditions. These loading conditions are several combi nations which consider different external effects acting in certain propor tions 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 ob tained by means of the 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
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