Betonarme çerçeve sistemlerin lineer olmayan hesabı ve dolgu duvarların modellenmesi
Non-linear analysis of reinforced concrete frame systems and modelling of masonry infill walls
- Tez No: 142808
- Danışmanlar: PROF. DR. SUMRU PALA
- Tez Türü: Yüksek Lisans
- Konular: İnşaat Mühendisliği, Civil Engineering
- Anahtar Kelimeler: Belirtilmemiş.
- Yıl: 2003
- Dil: Türkçe
- Üniversite: İstanbul Teknik Üniversitesi
- Enstitü: Fen Bilimleri Enstitüsü
- Ana Bilim Dalı: Yapı Analizi ve Boyutlandırma Bilim Dalı
- Bilim Dalı: Belirtilmemiş.
- Sayfa Sayısı: 98
Özet
ÖZET Yüksek lisans tezi olarak sunulan bu çalışmada, betonarme çerçeve sistemlerin dış yükler altındaki yük parametresi - yerdeğiştirme ilişkileri elde edilerek lineer olmayan davranışlarının incelenmesi ve yapılardaki mevcut dolgu duvarların yapı davranışına sistem rijitliği, dayanımı ve sünekliği gibi kavramlar bakımından etkisinin araştırılması amaçlanmıştır. İncelenen betonarme düzlem çerçeve sistemlerin bir kısmı için deneysel çalışmaların yapılmış olması kuramsal sonuçlarla deneysel sonuçların karşılaştırılmasına ve kuramsal çözümlerin gerçek davranışa ne kadar yakın olduğunun öğrenilmesine olanak sağlamıştır. Birinci bölümde, yapı sistemlerinin hesap esasları ve dış yükler altındaki lineer olmayan davranışları anlatılmış ve çalışmanın amacı ve kapsamı hakkında bilgi verilmiştir. İkinci bölümde betonarme çubukların lineer olmayan davranışı incelenmiştir. Betonarme çubuklar için iç kuvvet - şekildeğiştirme bağıntıları hakkında bilgi verilmiştir. Yapı malzemelerinin şekildeğiştirme özellikleri için yapılan varsayımlar, kullanılan malzeme modelleri verilmiştir. Kesitlerde moment - eğrilik bağıntılarının, karşılıklı etki diyagramlarının elde edilmesi ve bu bağıntıların nasıl idealleştirildiği anlatılmıştır. Üçüncü bölümde dolgu duvarların yapı davranışına etkisi, göçme şekilleri ve yapı çözümlemesinde modellenmesi hakkında bilgi verilmiştir. Dolgu duvarların eşdeğer sanal çubuk modeliyle yapı sisteminde temsil edilmesi anlatılmıştır. Bu modelin uygulanabilmesi için çeşitli araştırmacılar tarafından önerilen bağıntılara yer verilmiş ve bu çalışmada dolgu duvarların modellenmesi için kullanılan eşdeğer sanal çubuk parametreleri açıklanmıştır. Dördüncü bölümde yapı sistemlerinin malzeme özellikleri bakımından lineer olmayan davranışlarının incelenmesi için kullanılan plastik mafsal teorisi hakkında bilgi verilmiştir. Lineer olmayan statik çözümlemede kullanılan plastik mafsal türleri ve şekildeğiştirme sınır durumları açıklanmış, çözümlemede kullanılan program için hesapta izlenen yol anlatılmıştır. Beşinci bölüm sayısal incelemelere ayrılmıştır. Ele alman betonarme düzlem çerçeveler için lineer olmayan statik çözümlemeyle yatay yük parametresi- yerdeğiştirme ilişkileri elde edilmiştir. Aynı çerçeveler, yapı sisteminde dolgu duvarlar da yer alacak şekilde modellenmiştir. Çıplak çerçeveler için elde edilen sonuçlar dolgu duvarlı örneklerde elde edilen sonuçlarla karşılaştmlmıştır, dolgu duvarların sistem davranışına etkisi irdelenmiştir. Ayrıca elde edilen kuramsal sonuçlar tekrarlı yatay yükler altında deneysel olarak test edilmiş çerçeve sonuçlarıyla karşılaştınlmıştır.
Özet (Çeviri)
SUMMARY Structures should be adequate enough to provide the required performance criteria in terms of concepts such as stiffness, strength and ductility. These factors should be taken into consideration in the design phase in addition to the fact that an economical design should be achieved. It's possible to make more reliable and realistic design by examining the structure behaviour under external loads till the collapse mechanism occurs. Collapse mechanisms in structures occur by buckling of the system by the second order effects or by reaching the load capacity in the system sections. Frame sections usually reach their ultimate load with deformations exceeding linear - elastic limits, hence structure behaviour in collapse mechanism can be studied more realistically by using non-linear theory. In this study titled as“ Non-Linear Analysis of Reinforced Concrete Frame Systems and Modelling of Masonry Infill Walls ”, non-linear behaviour of structures in case of material properties is examined. Non-linear static procedure (Pushover Analysis) is applied in the analysis of reinforced concrete frame systems. Non-linear analysis of the reinforced concrete frame systems consists of two main parts including the bare frame system analysis and following this, the masonry infilled frame system analysis. The infill influence on the behaviour of the system subjected to external loads is examined and load parameter (base shear)-top displacement relations obtained from the bare frame and masonry infilled frame results were compared. Being tested of the analysed concrete frame systems experimentally under monotonously increasing lateral forces, provided the comparison of the theoretical results by experimental results and investigations of the how realistic the theoretical results are. The system followed in the study is given below: a) Concrete and reinforcing steel properties were assumed such as. Concrete compression strength and strain corresponding to this stress.. Reinforcement bars yielding strength and strain.. Reinforcement bars tensile strength and strain. b) The internal force-deformation relationships for reinforced concrete frame elements were evaluated. c) For representing the infill wall effects in the frame system equivalent strut model was formed and parameters necessary for the model were evaluated.d) Frame systems were analysed by non-linear static procedure and lateral load parameter - top displacement relations were obtained. e) Theoretical results were compared with the results obtained from experimental studies. f) Theoretical results relating to bare frame and masonry infilled frame systems were compared and the results were interpreted. The second chapter covers the detailed investigation of non-linear bahaviour of reinforced concrete members. Basic assumptions made for reinforced concrete are given below:. Plane sections remain plane after bending. Full bond exists between concrete and reinforcing steel. Tensile strength of concrete is negligible Moment-curvature relatonships and yielding surfaces of reinforced concrete sections were obtained by a computer program. Confinement in concrete is taken into consideration in the concrete model, thus concrete allowable strain value can take higher values than 0,003. The amount, shape, strength, interval of transverse bars determine the confinement quantity in the section. The related confined concrete strength is also incresed. In the steel material model there is a linear relation between stress and strain values till yielding strength is reached. After yielding of the reinforcement bar, hardening of the steel is considered in the model by a second line. The moment - curvature relations were idealized by three linear equation. First part is up to cracking. Then there is a decrease in the section rijidity. Second part ends with the forming of plastic deformations in the sections. At that time the section carries the yielding moment. Usually this limit state is reached by yielding of the tensile reinforcement. At the end of the last part, section reaches the ultimate strength. Axial force-bending moment interaction diagrams were also idealized by lines connecting the points that are located on the diagram. The bare frames in the structures are filled with brick masonry walls for architectural and functional requirements. Since they are normally considered as architectural elements, their influence is usually ignored in the structural anaysis phase. In fact, when the structure is subjected to earthquake loads that interact with the surrounding frame. This interaction has an effect on the system behaviour. Such an interaction may or may not be beneficial for the system behaviour. Infilled walls affect the structure behaviour in terms of system stiffness, strength and ductility. It's known that infill walls are brittle elements so that they decrease the system ductility till the peak load. They can carry compression forces and increase the lateral load carrying capacity of the system and also increase the initial stiffness of the system. XIBehaviour of infilled frame systems have been searched by many researchers. Different approaches by the information gained from experimentally studies and the real earthquake effects on structures were presented. Infill wall properties are based on different properties such as frame element stiffness, length, thickness of the wall, brick masonry and mortar type, their compression strength, etc. Because of the complexity of the problem, the effect of masonry infill walls is often neglected in the design of structures except considering their weight in calculating the estimated earthquake force. Different failure modes for the masonry-infilled frames were defined. These are : 1) The corner crushing mode represents crushing of the infill at least around one of its loaded corners. 2) The sliding shear failure represents horizontal sliding of the masonry infill by exceeding the shear stress mat the infill can resist. 3) The diagonal compression mode represents the diagonal crushing of the infill within its central region. 4) The diagonal cracking mode is forming of the cracks in the infill in the diagonal direction connecting two loaded corners. Sometimes it is not a failure mode because the infill can still carry loads after cracking. 5) In the frame failure mode, the damage is formed in the frame members before the infill fails. This situation occurs in the frames with weak members and strong infill elements. As the lateral forces increase acting on an infilled frame system, separation between frame and the infill wall occurs on the tension diagonal and a diagonal compression zone is formed that carries load. In designing phase the compression zone is defined by a equivalent strut, as shown in Figure 1. JTL --t- J, I h Figurel Forming of Compression Zone in Infill Frame XllThe infill thickness (t) is considered as to be the thickness of equivalent strut. The effective width of the equivalent strut (w) is a parametric value and several equations were given for this value. Previous studies indicate that this value depends on relative stiffness of boundary frame and infill, modulus of elasticity of the infill, ratio of infill height to length and thickness of the infill. The modulus of elasticity of the infill can be obtained by the parametric equations depending on the properties of brick members and mortar such as brick compression strength, mortar compression strength, etc. More sufficient way to obtain the modulus of elasticity of the infill is testing the masonry prisms experimentaly and evaluating the stress - strain relationships. Load carrying capacity of infill wall is defined by some researchers. For non-lineer anaysis the internal force-deformation relationship should also be defined for the equivalent strut. The main idea is that the equivalent strut loses its strength after reaching the ultimate load because brick masonry is a brittle material. The only internal force that the strut carries is the axial force in compression. Tensile strength of the equivalent strut is negligable. Force - deformation relationship used for defining the equivalent strut properties is given in Figure 2. Force Deformation Au Figure 2 Equivalent Strut Force - Deformation Relationship. R : Ultimate axial load capacity of the strut (kN). Ay : Axial deformation of the strut corresponding to ultimate load (m). Au : Final axial deformation of the strut (m) As seen in the figure there is a linear increase in the strut axial load capacity till the ultimate capacity is reached, then the capacity starts to decrease. In this study, ultimate strain of the equivalent strut was taken as 0.01 and Au value was obtained multiplying this strain value by the strut length. In the anaysis phase, a nonlinear static procedure (pushover analysis) based on the plastic hinge hypothesis is applied. Frame systems are analysed under constant vertical loads and monotonous increased lateral forces. Deformation controlled Xlllanalysis was used and the system was subjected to monotonous increased lateral forces until it collapses. Plastic hinge locations were determined on the geometric model and hinge properties were defined. Three kinds of plastic hinge properties were used in the analysis. P hinges were used to determine load-deformation relations for equivalent struts, M3 hinges were used to determine moment - rotation relations for beam and column sections and PMM hinges were used to determine axial force- bending moment interaction surfaces for column sections. The steps given below were followed throughout the non-linear static analysis procedure.. Formation of the system geometry.. Assignment of frame sections.. Definition of plastic hinge properties.. Assignment of plastic hinges to the locations on the frame members.. Definition of the load patterns.. Definition of pushover cases.. Solution. At the end of the anaysis, the lateral load parameter - displacement values are obtained for several steps formed by the program and a diagram is given. Plastic hinge locations, their deformation cases, internal forces of the system members can also be obtained for each step. XIV
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