Çift yönlü çok modlu doğrusal olmayan itme analizinin betonarme bir binada karşılaştırmalı incelenmesi
A comparative study of bi-directional multi-mode nonlinear pushover analysis in a reinforced concrete building
Yazar: HAKAN MACUN
Danışman: DOÇ. DR. BEYZA TAŞKIN AKGÜL
İstanbul Teknik Üniversitesi / Fen Bilimleri Enstitüsü / İnşaat Mühendisliği Ana Bilim Dalı / Yapı Mühendisliği Bilim Dalı
Derece: Yüksek Lisans, 2014
Konu: İnşaat Mühendisliği = Civil Engineering

Özet:
Bu tez çalışması kapsamında literatürde son yıllarda yer almış çift yönlü, çok modlu, doğrusal olmayan itme analizinin, tek yönlü uygulamalara göre yapısal davranışı ne ölçüde temsil ettiği araştırılmıştır. Bu amaçla ele alınan betonarme çok katlı bir bina, ilk aşamada tek yönlü ve çok modlu itme analizine tabi tutularak her iki bina doğrultusu için ayrı ayrı incelenmiştir. Daha sonra aynı binada, aynı sayıda mod bileşeni dikkate alınmak suretiyle iki yönlü modal itme analizi uygulanmıştır. Sonuçlar gerçek çözüm olarak kabul edilen doğrusal olmayan dinamik analiz bulgularıyla karşılaştırılmış ve tartışmaya açılmıştır.
Dört bölümden oluşan bu çalışmanın birinci bölümünde; konuya giriş yapılmış ve binaların deprem performansının değerlendirilmesi konusunun hangi koşullardan ötürü ortaya çıktığı açıklanmıştır.
Çalışmanın ikinci bölümünde; betonarme yapı sistemlerinin deprem performansına göre belirlenmesinde betonarmeyi oluşturan malzeme özellikleri, tasarım ve modelleri, plastik mafsal hipotezi ve süneklik kavramları irdelenmiştir. Günümüzde yürürlükte olan "2007 Deprem Bölgelerinde Yapılacak Binalar Hakkında Yönetmelik" içeriğinde olan mevcut binaların değerlendirilmesi ile ilgili genel kurallar da bu bölümde özetlenmiştir.
Üçüncü bölümde; 20 katlı betonarme bir binaya ait tasarım boyutları üzerinden tek ve çift yönlü olmak üzere çok modlu itme analizi uygulamaları yapılmıştır. Doğrusal olmayan bu çok modlu sistem yapının deprem yükleri altındaki iç kuvvet ve şekildeğiştirme isteminin ve dolayısıyla kesit hasarlarının bulunmasında kullanılabilir. Bu verilerin karşılaştırılması amacıyla bir deprem kaydı kullanılarak zaman tanım alanında hesap yöntemiyle iç kuvvet ve şekildeğiştirme talepleri doğrusal olmayan dinamik analizle hesaplanmıştır.
Bulgular tezin dördüncü bölümünü oluşturan sonuçlar kısmında tartışılmıştır.

Abstract:
In this investigation; structural responses of bi-directional, multi-modal, non-linear pushover analysis procedure which has taken place in the literature in the recent years are compared with the structural responses of uni-directional ones. For this purpose, a reinforced concrete multi-storey building is subjected to uni-directional and multi-modal non-linear pushover analysis in first phase and examined separately for each direction of the building. Later, considering the same number of mode components is performed bi-directional non-linear modal pushover analysis for the same building. Results are comparatively evaluated with the non-linear dynamic analysis findings, which is accepted as exact solution and discussions are carried out.
Nonlinear behaviours of the structural materials in the buildings, which are designed with the current force-based code method are specifically described in the current seismic codes. Structures that are designed with the linear "Capacity Design" methods can also demonstrate the expected nonlinear behaviours. In general; in these methods which are used in structures that exhibit linear-elastic characteristics under seismic effects, seismic load reduction factor is used in order to take into account the structural material behaviours beyond the elastic limits. Elastic earthquake forces are decreased with this reduction factor. Therefore, the behaviour of the structure depends on that coefficient which is calculated during the linear elastic analysis. In the nonlinear analysis methods, different behaviour factors are concerned for each element represent inelastic attitude rather than a single coefficient. Performance based evaluation methods are especially needed in the evaluation of existing structures.
Performance based evaluation studies have been accelerated with Vision 2000 (1995), ATC-40 (1996) and FEMA 273,274 (1997). The objective of Vision 2000 has been defined as creating the necessary procedures for the determination of predictive seismic performance of structures. FEMA 273 and FEMA 274 documents that were published by Building Seismic Safety Council were followed by the publishing of ATC-40 in 1996 by Applied Technology Council.
In Turkey, seismic performance of structures can be determined with two different approaches described in the "Specification For Buildings To Be Built In Seismic Zones" (2007) (Turkish Seismic Code). The first approach is determining the seismic performance of building with linear elastic analysis methods. Equivalent seismic load
or mode superposition methods can be used for calculating the earthquake loads. The second approach is determining the seismic performance of building with deformation-based nonlinear analysis methods. Defined in Turkish Seismic Code; any of the incremental pushover analysis, modal pushover analysis or nonlinear dynamic time history analysis methods can be used for performance evaluation with certain conditions. 
Nonlinear behaviour of the structure must be determined in performance-based design and evaluation of the structure under the seismic loads. The methods used for this purpose; nonlinear static pushover analysis and nonlinear dynamic analysis are specified in two classification of the methods. Nonlinear behaviour of structure under the seismic loads can be obtained in a manner very close to actual values with the nonlinear dynamic analysis methods. This dynamic analysis method which is also described as time history analysis, has several disadvantages in practical usage about being highly complex and time-consuming. Because of this case, the nonlinear static pushover analysis methods become even more important. In this method; lateral loads which represent the strength of the structure under seismic loads act on the structure at floor levels. Lateral loads are increased with a certain rate and the base shear force and the top displacement relationship is determined until it reaches a certain displacement or collapsing status.
In general, nonlinear pushover analysis methods are simplier than the other ones about acquisition and evaluation of the base shear and displacement relationship. This method also creates an intermediate section between deficiencies of linear elastic analysis methods and complexities of the nonlinear dynamic analysis methods. In this thesis, both of the methods are investigated and comparatively evaluated. Based on structural dynamics theory, the modal pushover analysis procedure (MPA) retains the conceptual simplicity of current procedures with invariant force distribution, now common in structural engineering practice. The MPA procedure for estimating seismic demands is extended to unsymmetric-plan buildings. In the MPA procedure, the seismic demand due to individual terms in the modal expansion of the effective earthquake forces is determined by nonlinear static analysis using the inertia force distribution for each mode, which for unsymmetric buildings includes two lateral forces and torque at each floor level. These "modal" demands due to the first few terms of the modal expansion are then combined by the CQC rule to obtain an estimate of the total seismic demand for inelastic systems.
In the first section of this four chaptered thesis; the topic has been started with the introduction and proceeded with the explanation for what purpose the idea of assessment of the buildings' earthquake performance has emerged.
In the second part of this study; characteristics, design and models of the structural materials, plastic hinge hypothesis and ductility concept subjects have been investigated in the evaluation of reinforced concrete building systems according to their expected earthquake performances. General rules and code conditions related to the  consideration  of  existing  structures,  which  take  place in the operative code
 "Specification For Buildings To Be Built In Seismic Zones" (2007) also has been summarized in the second section.
At the third chapter; uni-directional and bi-directional multi-mode non-linear pushover analysis have been applied to the 20-storey building which has been designed according to the 2007 Turkish Seismic Code. This multi-modal non-linear system can be used in the determination of the internal forces, deformation demands and damage in the structure under the earthquake loads. In order to compare these datas, an earthquake record has been used for the nonlinear dynamic analysis  in terms of obtaining the internal forces which are assumed to be the 'exact' responses
of the structure.
The numerical findings obtained by nonlinear static and dynamic analysis are comparatively discussed in the fourth chapter. It is shown in this chapter that results of nonlinear modal pushover analysis and nonlinear dynamic analysis are approximately the same. However, with the usage of the combination rules, final numerical values are diverging. Therefore, modal pushover analysis method results does not coincide with exact values completely.