Perde-çerçeve betonarme sistemlerde deprem etkisi altında doğrusal olmayan davranışın incelenmesi
Nonlinear behavior of reinforced concrete dual structural systems subjected to earthquake excitation
Yazar: MEHMET BURAK YILMAZ
Danışman: PROF. DR. ZEKAİ CELEP
İstanbul Teknik Üniversitesi / Fen Bilimleri Enstitüsü / İnşaat Mühendisliği Ana Bilim Dalı / Deprem Mühendisliği Bilim Dalı
Derece: Doktora, 2014
Konu: Deprem Mühendisliği = Earthquake Engineering

Özet:
Betonarme perdeler gerek deprem kuvvetlerinin karşılanması, gerekse yatay yer değiştirmenin sınırlanması amacıyla depremselliğin yüksek olduğu bölgelerdeki betonarme binaların taşıyıcı sistemlerinin düzenlenmesinde sıkça kullanılan yapı elemanlarıdır. Betonarme perdelerin analizi ve boyutlandırılması bir takım kurallar çerçevesinde yapılır. Kuvvet esaslı tasarımda, deprem yükü azaltma katsayısının dikkate alınması sebebiyle analiz sonucu bulunan kesit tesirleri betonarme boyutlandırılmasında doğrudan kullanılamaz. Bu noktada kapasite tasarım kuralları uygulanır ve analizden elde edilen kesit tesirleri çeşitli işlemler sonucu dikkate alınır. Analiz sonucu bulanan perde taban momenti, kritik perde yüksekliği ve moment zarfı tanımları dikkate alınarak boyutlandırma için kullanılacak tasarım moment değerine çevrilir. 
Modern deprem yönetmeliklerinde, analizden elde edilen kesme kuvveti de tasarımda doğrudan kullanılamamaktadır. Perde tasarım kesme kuvvetini elde etmek için, perdenin moment kapasitesinin tasarım moment değerine oranı olan moment dayanım fazlalığı miktarında artırım yapmanın çoğu zaman yeterli olmadığını daha önce yapılan çalışmalar göstermiştir. Bunun birincil sebebi, depremin perdelerde oluşturduğu kesme kuvveti dağılımının, perdenin tabanında oluşan eğilme mafsalı sebebiyle değişmesidir. Perde kesme kuvvetindeki bu değişim kesme kuvveti dinamik büyütmesi olarak tanımlanır. 
Perdelerde oluşan kesme kuvvetindeki dinamik büyütme, zaman tanım alanında doğrusal olmayan analiz ya da her itme adımında oluşan mafsallarla uyumlu mod şekillerini kullanan itme analizi yöntemleri uygulanarak dikkate alınabilmektedir. Ayrıca bu olgu, perdeler üzerinde yapılan dinamik deneylerde de izlenmiştir. Kesme kuvvetindeki bu büyütme, Deprem Bölgelerinde Yapılacak Binalar Hakkındaki Yönetmelik (2007), Eurocode 8, Yeni Zelanda Deprem Yönetmeliği ve Kanada Deprem Yönetmeliği gibi yönetmeliklerde farklı yaklaşımlarla dikkate alınmaktadır. 
Deprem yönetmeliklerinde bulunan perde kesme kuvvetindeki dinamik büyütme katsayıları, konsol perdeler üzerinde yapılan parametrik çalışmalar sonucu ortaya atılmıştır. Bu tez kapsamında, konsol perdelerde yapılan parametrik çalışmalar perde-çerçeve sistemler için genişletilmiş ve konu ile ilgili öneriler yapılmıştır. Ayrıca, konsol perdeler ile ilgili yeni çalışmalar da eklenmiş olup hem konsol perdeler üzerine yeni bulgular elde edilmiş hem de perde-çerçeve sistemler ile yapılan çalışmaların sonuçları konsol perde sonuçlarıyla karşılaştırılmıştır. İlave olarak, bağ kirişli perdelerde de kesme kuvvetinde dinamik büyütme etkisi farklı bağ kirişi katkı oranlarına göre incelenmiştir. Çalışmada, parametrik çalışmanın müsaade ettiği ölçüde, literatürde kabul gören perde modelleriyle çalışılmıştır. Bu perde modellerinin mevcut deney sonuçlarıyla karşılaştırması yapılarak çalışma için uygunluğu gösterilmiştir.

Abstract:
In the design of structural systems under earthquake loads, seismic load reduction factor or the so-called behavior factor is employed to take into account nonlinear behavior of the structural system globally as indicated in various seismic codes and guidelines used in high seismicity areas. This modification makes it possible to adopt linear analysis, avoiding the sophisticated nonlinear analysis. The seismic load reduction factor used in the modification of the seismic forces also includes the over-strength of the structural system due to the use of design strengths of materials instead of the actual strengths. The capacity design principle together with the load reduction factor is employed to avoid brittle failures in case of seismic effects of strong ground motions. 
Advantages of shear walls in structural systems of buildings have long been recognized especially in earthquake prone regions. Because they have large lateral load capacity to increase the structural capacity of the structural system and large lateral rigidity to keep seismic damages in a minimum level. In the design of shear walls, wall base moment obtained from the structural analysis is used; then, design moment envelope is obtained by using the critical wall height definition. This concept proposes a linear envelope for the seismic bending moment demand, which is obtained by shifting vertically the moment demand of the linear analysis by the horizontal length of the wall. The main aim of design moment envelope is to limit the location of plastic deformations to the base region, while keeping the other parts of the wall elastic.
On the other hand, for shear forces, a different capacity design concept is adopted which takes into account the flexural overstrength to increase the design shear by considering the results of the linear analysis. However, it is shown that, this increase in the design shear force is not enough to ensure ductile failure in case of seismic forces higher than the design ones, because nonlinear dynamic response changes patterns of lateral inertial forces. In other words, dominant mode shape changes with the formation of the base hinge that shifts the location of the resultant lateral forces downward. This phenomenon is called dynamic shear amplification or shear magnification and it is taken into account in the regular design globally by increasing the design shear forces, where flexural overstrength is considered separately as well.
The study focuses on seismic shear force, bending moment and displacement demands on ductile cantilever walls and dual wall structures assuming that nonlinear deformations take place. In the first chapter literature review on the shear wall models and dynamic shear force amplification effect of shear walls are presented. 
In the second chapter, verification of the analysis results of shear wall models, which are used in the analyses, with shear wall experiment results of the other researchers is carried out. Concrete and steel material models and fiber element model are presented. It is verified that the models are capable to simulate results of the monotonic and the cyclic wall tests with acceptable accuracy. The plastic deformations are included to the analysis in addition to elastic parts, by assuming fiber model. It is shown that the presented fiber modeling of RC walls provides an adequate representation of stiffness and strength behavior of the walls, which had been tested by previous researchers. Moreover, due to easy applicability of the presented fiber modeling, it can be used by engineers in practice as well as in detailed analysis. Constitutive material laws with hysteretic rules are implemented for concrete and steel fibers. 
In the third chapter, nonlinear behavior of the cantilever shear walls are studied. In order to investigate the nonlinear behavior of reinforced concrete shear walls subjected to seismic loads and the extent of the related code requirements, an extensive parametric study is carried out. Shear walls having a height of 5, 10, 20 and 30 story and rectangular cross section are analyzed by considering four ductility levels and ten earthquake records having different levels of acceleration and frequency content. Variation of shear amplification depending on different values of the period and the ductility of the shear walls are investigated. As in most of the previous studies by others, nonlinear time-history analyses are performed for a constant flexural capacity along the entire height of the wall. Moreover, in the present study structural systems are analyzed where flexural capacity is assumed to vary with elevations along the height of the wall in order to make comparison between the variable flexural capacity and the constant flexural capacity along the height of the walls by adopting nonlinear dynamic analysis. Large number of numerical results obtained from the dynamic analyses indicate that for tall ductile shear walls in which the flexural capacity decrease along its height (as usual in everyday design practice) plastic hinges form above the base region of the shear walls. It is observed that the base shear force and the shear force profile on the shear wall do not change dramatically for the different capacity variations of the shear walls. Furthermore, existing top displacement-base curvature relationships which are used in displacement-based design are investigated. It is found that, contribution of the elastic displacement to the total top displacement is significantly higher than expected and should not be neglected.
In the fourth chapter, shear demand of reinforced concrete walls in dual structural systems is investigated. Behavior of the dual wall-frame system under lateral load is different from a single cantilever shear wall and a sway frame system as well. Dual systems combine the advantages of the shear walls and the frame systems. Under the action of lateral forces, frame will deform primarily in a shear mode as a result of flexural deformation, whereas a wall will behave like a vertical cantilever with primary flexural deformations. Due to the compatibility of deformations, the resultant behavior is that of an interaction of the wall and the frame. In the chapter three, it is pointed out that moment and shear force distributions in shear walls, obtained by using nonlinear dynamic analysis, display a variation different from the distribution used in the design procedure. Due to this difference, the maximum shear demand in the shear walls during an earthquake is generally higher than that computed by using linear dynamic and static analysis. In this chapter, the nonlinear behavior of the wall-frame system has been examined by using nonlinear analysis to observe the dynamic amplification of shear force in shear walls. Large numbers of numerical analyses are carried out on structural systems consisting of various combinations of walls and frames. Relationships between the shear amplification with the period and the displacement ductility have been studied depending on the contributing of the shear walls. Numerical results are presented in figures for comparison and steps of the performance evaluation methods are critically discussed. For this purpose, 5, 10, 20 and 30 story planar dual RC structural systems are designed. Later, these buildings are analyzed using the nonlinear dynamic analysis by assuming that they are subjected to ten earthquake records of far-field earthquakes that are scaled based on the elastic code spectra. The numerical results including the relation between the coefficient of dynamic amplification of shear forces in shear walls and the period and the load reduction factor of the structural systems are presented.In the fifth chapter, the results of the presented study are summarized and recommendations for future studies are underlined.