Üç boyutlu düzensiz bir yapı sisteminin deprem performansının irdelenmesi
Seismic performance analysis of a three dimensional irregular structure
Yazar: ERKAN ŞENOL
Danışman: DOÇ. DR. ERCAN YÜKSEL
İstanbul Teknik Üniversitesi / Fen Bilimleri Enstitüsü / İnşaat Mühendisliği Ana Bilim Dalı / Yapı Mühendisliği Bilim Dalı
Derece: Yüksek Lisans, 2012
Konu: İnşaat Mühendisliği = Civil Engineering
Dizin: Doğrusal olmayan analiz = Nonlinear analysis ; Perdeli sistemler = Shear wall systems ; Performans analizi = Performance analysis ; Pushover analiz = Pushover analysis

Özet:
Bu tez kapsamında, üç boyutlu düzensiz bir yapı sisteminin doğrusal ve doğrusal olmayan analizleri DOC3B yapı analiz programı ile gerçekleştirilmiştir. Analizi için tasarlanmış olan yapıda kat planının sadece üst köşe elemanlarında birer perde eleman bulunmaktadır. Bu tip bir perde yerleşim seçimi ile yapı örneğine burulma düzensizliği kazandırılmıştır.Gerçek yapıyı doğru bir şekilde modellemek, doğru sonuçlar elde edebilmek için oldukça büyük önem taşımaktadır. Bu sebepten ötürü her bir yapı elemanı da hassas bir şekilde modellenmek zorundadır. Modelleme sırasında kirişler ve kolonlar çubuk eleman olarak modellenmektedirler, perdeler ise levha eleman kabul edilirler. Alternatif olarak ise perde elemanlar bazı basitleştirmeler sonucu çeşitli tekniklerle modellenebilmektedirler.Perdelerin modellenmesi için pek çok metot geliştirilmiştir. En bilinen modelleme metodu, geniş orta dikme kolon modelidir. Rijit kirişler ise, perdenin bulunduğu bölüm boyunca devam eder ve orta kolonun üst ucunda birleşirler. Bir diğer model, geniş orta dikme kolon modeline benzeyen gergili çerçeve modeldir. Orta dikme modelde bulunan elemanlara ek olarak yerleştirilmiş, uçlarında dönme serbestliği olduğu kabul edilen iki çapraz eleman perde alanının bir ucundan diğer ucuna kadar devam ederler. Bir başka modelde ise, perdenin her iki ucuna perde rijitliğinin yarısına sahip iki kolon eleman yerleştirilmesi ve perdenin kaldırılmasından ibarettir. Kolon elemanları üst noktalarından birbirine rijit bir kiriş bağlamaktadır. Bu tez kapsamında gerek perdelerin şekil yapısından ötürü, gerekse çerçeve sistemine uygunluğundan ötürü geniş orta dikme kolon modeli kullanılmıştır.Yapının modelleme metoduna karar verdikten sonra DOC3B programının sonuçlarının doğruluğu irdelenmiştir. Bunun için, hesap sonuçlarına güvenilen bir paket program, SAP2000 kullanılmıştır. Doğrulama için her iki programda örnekler oluşturulmuş, hem statik hem de dinamik analiz sonuçları karşılaştırılmıştır. Oluşturulan örnek modellerden ilki tek katlı tek açıklıklı bir yapı, diğeri ise tez sırasında irdelenen düzensiz perdeli betonarme yapıdır. Statik analizler sonucunda kesit tesir değerleri ve deplasman değerleri, dinamik analizler sonucunda ise modlara ait titreşim periyotları yeter derecede yakın sonuçlar vermiştir.Program doğrulaması tamamlandıktan sonra yapı sistemi üç ayrı yapı modeli olarak tasarlanmış ve her bir modele sabit tek modlu itme analizi uygulanmıştır. Oluşturulan yapı modelleri, perdeye komşu olan kiriş ve döşemelerin farklı varyasyonlarından oluşmaktadır. Yapı modelleri hem x hem de y doğrultularında itme analizine tabitutulmuş, simetrik olmayan doğrultularda her iki yönde itme analizi yapılmıştır. İtme analizleri sonucunda perde çevresinde meydana gelen döşeme boşluklarının, kat planındaki düzensizliklerin ve döşeme boşluğunu çevreleyen kirişlerin tasarımının yapıya olan etkileri incelenmiş, sonuçlar irdelenmiştir.

Abstract:
In this M.Sc. thesis, a three dimensional and irregular structure analysed in linear and nonlinear manner by using a developed structural analysing programme DOC3B (Nonlinear analysis of orthogonal three dimensional structural systems). An irregular floor plan which includes two shear wall located at the top corners designed for analysis. Location of the shear walls decided which causes buckling irregularity.Creating an accurate structural model has a significant importance due to obtain convergent results with real structure. Therefore every member of structure have to be modelled with high accuracy and versatility. Beams and columns can be considered as frame sections nonetheless shear walls should be designed as area sections. Alternatively shear walls can be simplified by making some adjustments so that they can be defined as frame models.There are lots of methods for modelling shear walls. The well - known method is wide column frame model. It is described as a frame model at the middle surface of the shear wall and two rigid horizontal element connect that frame member from the top point. This method can be desired because of adopting it into developed analysing programmes easily and provide saving time by reducing analysing procedure. On the other hand, this acceptance cause much more rolative errors when comparing to other methods. Users always should be aware of this rolative errors cannot be ignored.Second method,the braced frame model, have common properties with wide column frame model. In this method, frame also includes horizontally rigid arms and braces, but the central column of the previous frame is omitted and replaced by a column on one vertical edge and a hinged link on the other. The results compare in accuracy with simple rectangular plane stress finite elements [Stafford Smith, Amal Girgis]. The braced frame model is more efficient than the braced wide column and it is also more consistent and accurate. The real issue of this method rigidity of braces.Third method uses two column which has half of the bending rigidity of shear wall and located at starting and ending points of this element. These two column connected to each other by a beam that has a significant bending rigidity (about infinite). This method uses systems' own nodal points. Therefore it can be used easily at the simplified frame analysing programmes. Disadvantage of this method, locating of colums cause moments return into axial forces at columns. Moreover, obtained bending moments values are lower than true values.In this thesis wide column method selected for shear wall solutions due to shape of shear wall (L shape). Therefore central column turns compatible with the system frames. Furthermore, decreasing alaysing steps provide saving important time. These model the fastest method for solving shear wall problems.There dimensional structures only defined by using two dimensional sub - systems in DOC3B. DOC3B firstly create rigidity and force matrices of two dimensional sub - systems. Then programme combines these matrixes into three dimensional rigidity and force matrices. Because of defining sub - systems, beams' horizontal and vertical rigidity values; columns and shear walls' every rigidity values at every vertical sub - system defined seperately. Material properties defined at a different file and assigned every member at the sub - systems. These provides user with calculate true capacity behavior during analysis procedure.After selecting solution method, it is have to shown that DOC3B gives high accurate results with a programme that analysis results are proved. Because of this reason, a worldwide known programme, SAP2000 used in this thesis for comparison. Verifications made on two models that one of a simply frame model and other one is main model used in thesis. Besides two new specifications of DOC3B tested first time at this step. The first specification is defining uniform distributed load on frame elements. The second is set of equations at the direction of 'z'. Moreover second specification also provide that assign loads at any direction.Firstly, vertical loads assigned frame members of models and a horizontal point load assigned just one point to cause torsion at the simple model. Bending moments, shear and axial forces and nodal points displacements compared after static analysis. These control parameters have nearly same values and displacement values proved occuring of torsion. Free vibration modes compared at the dynamic analysis step. According to analysis results first three mode found as 1.873, 1.368 and 0.502s by using DOC3B and 1.880, 1.372 and 0.505s by using SAP2000. These results proved DOC3B gives accurate results.After linear analysis and proving DOC3B, nonlinear analysis is made for determining performance capacity of structure. Structural performance is defined by damages of structural members. General acceptance in performance based design provide life safety performance level after earthquakes that has a probability of exceedance of 10%/50 years. Nonlinear push-over analysis apllied to the structural model for determining performance level. Turkish Seismic Code 2007 includes several nonlinear analysis procedures. These are "incremental equivalant earthquake load method", "incremental mode combining method" and "nonlinear time history analysis". Structural model pushed by using "incremental equivalant earthquake load method" in this study due to DOC3B has not coded for changable modes and nonlinear time history analysis yet.Nonlinear incremental push over analysis can be subjected to structures by using several methods. The simplest push over method is constant single mode push over. Force applied to the structural modal according to dominant mode. Until structure reaches the collapse mode, it is pushed. The other method is flexible single mode push over analysis. This method accepts building modes change after every pushing step. Pushing step increases when a structural member reach its own capacity. Therefore the force vector applied to the structural model has to be calculated at any pushing step.Because of structural model has irregularity, firstly it should be decided that which direction structural model pushed along. Because of that base shear forces and top displacements compared to each other at both directions ( x and y ). Comparisons showed, although pushig only one direction is enough at the direction of symmetry, structural model should be pushed at any direction at the non-symmetrical direction.Three different structural model created by making some changes in floor plan. First model has no changes in floor plan. The second model has floor gaps next to the shear walls. The third model, capacity of beams, which around the floor gaps, increase by using more wide dimensions. Incremental push over analysis performed on every model. After that performance analysis is made for structural elements chosen randomly.Results showed that floor gaps cause an incremantation at top displacement nevertheless when beam around the gaps changes with much more rigid elements this incrementation can be prevented. Modal capacity diagrams are the proof of this situation. Strains of structural elements have very small values so that when comparing the hazard levels there is no differences between three model. However when comparing the strain values instead of hazard levels, floor gaps cause an incremantation up to 100%. This situation cause beams around the gaps reaches their capacities much more earlier and make shear walls independent members from whole structure. This situation shows that if there are floor gaps, beams around them should be more rigid to prevent torsion and also reaching structure's capacity.DOC3B, the programme used in this whole study, is still in development process. DOC3B able to cope with lineer and nonlineer analysis, push over analysis and can calculate strain and stress values at any cross - section. This provide user with making performance analysis easier and faster.The reasons of development of DOC3B is produce a programme that has specifications listed below;?Capable with nonlinear analysis much more easily?User friendly?Local producement?Can be rival to the other structural analysis programmes.However DOC3B still have some disadvantages like listed below;?it is not possible making time domain analysis?Only three degree of freedom can be defined at nodal points?Data inputting takes important time and it is highly possible making mistakes.