Mevcut bir demiryolu köprüsünün deprem performansının doğrusal olmayan yöntemlerle incelenmesi
Seismic performance evaluation of existing railway bridge by nonlinear analysis methods
Yazar: OGÜN ERBAY ONAY
Danışman: DOÇ. DR. ABDULLAH NECMETTİN GÜNDÜZ
İstanbul Teknik Üniversitesi / Fen Bilimleri Enstitüsü / İnşaat Mühendisliği Ana Bilim Dalı / Yapı Mühendisliği Bilim Dalı
Derece: Yüksek Lisans, 2016
Konu: İnşaat Mühendisliği = Civil Engineering

Özet:
Yapılarda oluşan hasarın düzeyinin belirlenmesinde elastik (doğrusal) hesap yöntemlerinin yetersiz kalması performansa dayalı hesap yöntemlerine başvurulmasını gerekli kılmaktadır. Bu hesap yöntemlerinden en gerçekçi ve doğru sonuçlar veren yöntemlerden biri ise şekil değiştirmeye bağlı olarak performans değerlendirmesidir. Bu yoldan hareketle, tez çalışmasına konu olan "Konya-Mersin Demiryolu Projesi Km: 298+040 – 299+040" arasında yapılması planlanan öngerilmeli betonarme demiryolu köprüsünün doğrusal olmayan yöntemlerle deprem performansı incelenmiştir.
Doğrusal olmayan performansın değerlendirilmesinde "plastik mafsal" hipotezinden yararlanılmıştır. Plastik mafsal boyunun belirlenmesinde Caltrans V.1.7'deki ifadelerden yararlanılmıştır. Deprem hesapları ile ilgili olarak AASHTO ve FEMA356 yönetmelikleri esas alınmıştır. Spektrum eğrisinin oluşturulmasında FEMA 356 kriterleri esas alınarak, "DLH Kıyı ve Liman Yapıları, Demiryolları,Hava Meydanları İnşaatlarına İlişkin Deprem Teknik Yönetmeliği"  EK-B kısmında bulunan enlem ve boylam değerlerine ait spektral ivme katsayıları belirlenmiştir.
İlk olarak tez çalışmasına konu olan demiryolu köprüsünün özellikleri hakkında bilgiler verilmiştir. Köprü alt yapı ve üst yapı elemanlarıyla birlikte tanıtılmıştır. Matematiksel model kurulması ile ilgili esaslar 3. bölümde açıklanmıştır. Köprünün sonlu elemanlar modeli SAP2000 programıyla kurulmuştur. Köprünün tüm elemanlarının gerçek boyutlarında ve kütlelerinde modellenmelerine dikkat edilmiştir. Yapının modal analizinde, üst yapının kabuk eleman modeli ve çubuk eleman modelleriyle kurulan iki modeli incelenmiş olup, bu iki modele ait sonuçlar karşılaştırılmıştır.
Doğrusal olmayan analiz aşamasında önce yapının itme analizi gerçekleştirilmiştir. Düşey taşıyıcı elemanlara (ayaklar) ait moment – eğrilik ve moment-dönme ilişkilerinin belirlenmesinde XTRACT programından yararlanılmıştır.1.mod ve 2. mod şekilleri ile orantılı olarak birim yükleme şekli köprüye etkitilerek analiz yapılmıştır. 50 yılda aşılma olasılığı %50 olan S1 depremi (kullanım depremi) ile 50 yılda aşılma olasılığı %2 olan S2 depremi (minimum hasar) altında plastik mafsallarda oluşan dönmeler ve beton, donatı çeliği birim şekil değiştirmeleri incelenmiştir.
Demiryolu köprüsünün doğrusal olmayan analizinde diğer bir yöntem olarak "Zaman Tanım Alanında Hesap" yöntemi kullanılmıştır. Köprünün bulunduğu konumun zemin karakteristikleriyle uyumlu olarak ölçeklenen deprem kayıtları altında analiz yapılmıştır.
Yapılan analizler sonucunda elde edilen hesaplar karşılaştırılarak mevcut köprünün deprem performansı hakkında yorum yapılmıştır.

Abstract:
The bridges are key structures in transportation for a long time. Due to this situation, the safety and serviceabiality of them is an important topic. The performance evaluation of bridges in seismic regions like as Turkey, must be investigated correctly. After the siginificant eartquakes in 1980's and 1990's (1989 Loma Prieta, 1994 Northridge, 1995 Kobe, 1999 Chi-Chi, 1999 İzmit), the forced based performance evaluations were not seemed sufficient. Due to insufficiency of elastic methods about investigating the damage in structures, displacement based performanced-based design method must be used. Displacement-based performanced design is used because of its realistic and reliable results.  This attitude considered in "AASHTO 2009: LRFD Bridge Design Specifiations" for the first time. Nonlinear pushover analysis and time history analysis methods were involved in guide for determining capacity of bridges. The guide specifications also recognize that the inelastic demand calculated by elastic response spectrum analysis with cracked section properties for concrete columns may not represent the realistic inelastic behavior of bridges under strong motion. The AASHTO guide specifications define the structural displacement capacity as the displacement, at which the first column reaches its inelastic capacity. However, the guide specifications use the acceleration (force) spectrum for the response spectrum analysis, and the displacement demand is still estimated based on the equal-displacement approximation with a modification for short period structures. Using this approach, it is possible, in some cases (Suarez and Kowalsky,2006), that calculated demands will not be in good agreement with results obtained from nonlinear time history analysis. This is due to fact that the column cracked section stifness distribution at yield in the response spectrum analysis different from stiffness distribution at the maximum demand response.  To overcome this problem, several researchers (Dwairi, Suarez, Kowalsky, Priestley) have recommended using the direct displacement-based design (DDBD) method. Instead of using an acceleration spectrum and the equal-displacement approximation, DDBD uses the displacement spectrum at the design level of ground motion to obtain the inelastic structural period. Depending on the importance of a bridge, the bridge can be designed for a certain level of performance in terms of target displacement, strain or ductility.
In the light of these approach, the nonlinear analysis of the railway bridge is done which is located in the Konya-Mersin Railway Project at 298+945 kilometer. The bridge has three span, 95m length and 12 meter superstructure width. There are two rail lines supported with ballast, for high speed train transportation. The loads acting on the superstructure are carried by the composite section which is composed of prestressed girders and reinforced concrete deck. The structural system of the bridge is simple beam, the girders supported with elastomeric bearings on the substructures parts in every span. The movement of supports in transverse direction of bridge are restrained by shear keys and some of them restrained in the longitudinal direction for decreasing the displacements from the vibrating train motion. Two piers have 46 meter length in first span and 45 meter length in second span. The dimensions of piers 3 meter in longitudinal direction bridge and 8 meter in cross direction of bridge. Section type of piers are hollow section. Soil profile of the location of bridge is rock, corresponded to B class according to DLH seismic code for bridges.  Calculations and drawings of railway bridge are obtained from the project company.
AASHTO and FEMA356 seismic codes are used in seismic performance evaluation. Spectral acceleration-time curves of the bridge are formed in view of this codes by using spectral factors at DLH Seismic code. Spectral acceleration factors are determined from the lattitude and longitude of the bridge location. Plastic hinge hypothesis is used for nonlinear performance evaluation. According to this hypothesis, the nonlinear behaviour (plastic rotation) is located at some special parts of system. Plastic rotation occurs when the current moment is more than the yielding moment in the section. In this project, the plastic hinge regions are expected the bottom sections of columns. The expression of plastic hinge length in Caltrans Seismic Design Criteria V.1.7 is used for determining the plastic hinge length of columns. The plastic hinges are assigned the mid of this lengths. The moment-rotation relation of hinges are defined according to FEMA 356 seismic code criterias. In the nonlinear analysis of bridges the cracked section properties are used to observe deformations and displacements correctly.
Firstly, the railway bridge is introduced with its substructure and superstructure parts. The mathematical model of bridge is established in SAP2000 finite element analysis program. All of elements are modelled with their real mass and rigidity.  There are two types of finite element model in modal analysis of bridges, one of them established with shell elements and the other one established with frame elements.  The results of this models are compared.
In the first step of nonlinear analysis of bridge, pushover analysis is performed. Moment-curvature and moment-rotation relations of columns are formed by using XTRACT section analysis program.  The unit loading proportional with first and second mode of bridge is acted to bridge step by step analysis. After forming the pushover curves in the x and y direction, the target displacements are determined by intersecting the capacity-curve with spectral accelaration-displacement curve. Rotations of plastic hinges and unit deformations of concrete and steel are evaluated under, %50 probability of exceeding occurance in 50 years as defined S1 and %2 probability exceeding occurance in 50 years as defined S2 in the static pushover analysis. At S1 level in longitudinal direction, the rigidity increasing occurs because of the exceeding the distance between the girders and abutment. In this situation, abutment has large rigidity therefore the system can not overcome this rigidity. Because of the sum of rigidities, abutments start to take forces and the base force of system increase. In cross direction, the target displacement is lower than the distance between the shear keys and girders so no crashing occurs. At S2 level in longitudinal direction, the system can not push to target displacement and the system are more hardened with regard to S1 level. The moments and base forces increase proportionally with this hardening. In cross direction, target displacement is higher than the distance so the girders crash the shear keys. After that, the movement comes out with new rigidity of system. In addition, the deformations of elastomeric bearings are observed. Especially, the abutment bearings don't satisfy the conditions at S1 and S2 level. For this reason, elastomeric bearings should be replaced by new ones then the eartquake calculations must be done again. 
The second method in the nonlinear analysis of railway birdge is "Nonlinear Time-History Analysis" Three earthquake records which are Kobe, Kocaeli and Erzincan, are scaled by using SEISMOMATCH 2016 program according to S1 and S2 spectral curves. At S1 earthquake level, in longitudinal direction no plastic hinge occurs. The forces, displacements and concrete and steel strains are lower than pushover analysis. In cross direction, due to exceeding the distance between girders and shear keys the forces and concrete and steel strains are higher than pushover analysis. Despite this situation, plastic hinge formation at columns does not occur. At S2 eartquake level, in longitudinal direction no plastic hinge occurs. The forces, displacements and concrete and steel strains are lower than pushover analysis like as S1 earthquake level. In cross direction, the rigidity increase with crashing the shear keys and the railway bridge tends to make displacements after this situation. The forces and concrete and steel strains are generally at the same level with S2 earthquake level. There are some bearings not satisfied the conditions at S1 and S2 level. Therefore, elastomeric bearings should be replaced by new ones then the eartquake calculations must be done again.
After the completion of two types of nonlinear analysis of railway bridge, the results are compared. At S1 eartquake level in longitudinal direction,  pushover results are higher than time history analysis results. In cross direction, the time history results are higher than pushover results because the girders crash the shear keys. At S2 earthquake level in longitudinal direction, pushover results are higher than time history analysis results. In cross direction, the results are close for two analysis type. The number of elastomeric bearings not satisfied the displacement conditions are high at S1 and S2 levels so they should be replaced with new elastomeric bearings. The seismic performance of bridge is investigated in the light of this results. As a conclusion, the bridge fulfill the safety conditions at S1 and S2 level in all nonlinear analysis.