Yığma demiryolu köprülerinin sonlu elemanlar programları ile modellenmesi
Modeling of masonry railway bridges with finite element programs
Yazar: UĞUR BURAK BAĞCI
Danışman: DOÇ. DR. KADİR ÖZAKGÜL ; PROF. DR. ELİŞAN FİLİZ PİROĞLU ; DR. ÖĞR. ÜYESİ MELTEM ŞAHİN
İstanbul Teknik Üniversitesi / Fen Bilimleri Enstitüsü / İnşaat Mühendisliği Ana Bilim Dalı / Yapı Mühendisliği Bilim Dalı
Derece: Yüksek Lisans, 2018
Konu: İnşaat Mühendisliği = Civil Engineering
Dizin: Demir yolları = Railways ; Köprüler = Bridges ; Modelleme = Modelling ; Paket programlar = Packaged softwares ; Sonlu elemanlar yöntemi = Finite element method ; Yapısal analiz = Structural analysis ; Yığma yapılar = Masonry buildings

Özet:
Kültürel mirasımız olan yığma köprülerimizi korumak gelecek nesillere karşı görevimizdir. Ülkemizin dört bir yanında yer alan tarihi eserlerimizin pek çoğu bugün bile görevlerine devam etmektedirler. Bu eserlerimizin mevcut durumunun tespiti ve gerekli bakım ve restorasyonların yapılabilmesi için yapıların davranışının doğru anlaşılabilmesi çok önemlidir. 
Birinci bölümde konu hakkında genel bilgi verilmiş, çalışmanın amacı anlatılmıştır.
İkinci bölümde yığma yapılar hakkında bilgi verilmiş, bu yapım tarzında kullanılan malzemelere değinilmiştir. Yığma köprülere geçiş yapılarak, bu eserlerin tarihsel gelişimi üzerinde durulmuştur. Kullanım amacına ve geçtiği açıklıklara göre kullanılan farklı kemer tiplerinden bahsedilmiştir. Kemer köprülerin çalışma mekanizması, avantaj ve dezavantajları, zaman içerisinde maruz kaldığı etkiler ve bu etkiler sonucu meydana gelen deformasyonlar incelenmiştir. 
Üçüncü bölümde yığma yapıların bilgisayar programlarında modellenmesi ve analizi hakkında bilgiler verilmiştir. Analiz programlarının kullandığı yöntemler ve kritik analiz yaklaşımlarından bahsedilmiş, kullanılan eleman tipleri anlatılmıştır. Kullanılan dinamik analiz metotları anlatılmış ve yapı elemanlarının doğrusal olmayan davranışı ve davranışın değerlendirilme sebepleri incelenmiştir. Yığma yapıların modellenmesinde homojenleştirme teknikleri üzerinde durulmuş, farklı problemler için önerilen modellenmesi yöntemleri anlatılmıştır.
Dördüncü bölümde ise çalışmada davranışı incelenen demiryolu kemer köprülerinin mimari, geometrik ve malzeme özellikleri verilmiştir. Daha sonrasında ise modelleme aşamasına geçilmiştir. İncelenen iki adet köprünün her biri için dört adet olmak üzere toplam sekiz adet model oluşturulmuştur. Modelleme aşamasında yapılan kabüller, modellerin çalışabilmesi için yapılan idealleştirmeler ve kullanılan analiz opsiyonları anlatılmıştır. Kullanılan malzeme değerleri ve grafikleri bu bölümde yer almaktadır. Modelleme tamamlandıktan sonra, modellerin karşılaştırma için uygun olup olmadığı adım adım kontrol edilmiştir. Uygunluk görüldükten sonra zaman tanım alanında dinamik analizlere geçilmiştir. Analizler için 53 adet farklı deprem kaydı kullanılmıştır. Modellerden elde edilen sonuçlar, geometrik ve malzeme ikinci mertebe etkileri ayrı ayrı değerlendirilerek taban kesme kuvveti, deplasman, hız ve ivme değerleri üzerinden grafikler yardımı ile karşılaştırılmıştır. 
Beşinci ve son bölümde ise yapılan işlemler kısaca özetlenmiştir. Elde edilen sonuçlar sırasıyla önceki bölümde verilen grafik ve tablolar yardımıyla sunulmuştur.

Abstract:
Protecting masonry bridges which are cultural heritage is our duty to future generations. Many of our historical monuments, which are located all around our country, continue their mission even today. It is very important to understand the behavior of structures in order to determine the current situation of these monuments and to carry out necessary maintenance and restoration.
In this study, finite element analysis programs SAP2000 and ANSYS were compared from different points. For comparison base shear forces, displacement, velocity and acceleration values were used. Also ease of modelling, analysis time were considered. To obtain numerical values two masonry railway bridged were used.
In the first part, general information is given about the topic, the aim of the study is explained.
In the second part, there is information about masonry structure types. The historical development of masonry bridges was also emphasized. Different types materials are used in masonry structures. Material properties affect the strength and durability of the structure. Also in railway bridges, specific materials like tracks, ballast are used. Different types of archs due to bridges purpose and length was listed. There are many masonry bridges built in the past. Probable problems are identified by examining the deformations of these bridges. The working mechanism of the bridge, advantages and disadvantages, the effects that it has been exposed over time and the deformations from these effects have been investigated.
In the third part, information about computer aided modeling and analysis of masonry structures were given. Finite elements method is commonly used for these structures analyses. By finite element method, masonry bridges or different systems can be modelled and analysed. In this method, the element to be inspected is divided into small pieces and each small piece being analyzed separately. So that the behavior of the entire system is understood. The methods used by these softwares and critical approaches were mentioned and the effect of the type of element used on the analysis results was mentioned. The dynamic analysis methods were explained and the nonlinear behavior of the structural elements and also the reasons of the behavior were investigated. In this work geometric and material nonlinear analyses were made. P-δ and P-Δ effects were considered in geometric nonlinear analyses. In material nonlinear analyses, nonlinear behaviour of material was considered. To do this stress-strain graphs for each material defined. Because of there is not any data from bridges, these values have taken from the similar works.
Modelling of masonry structures is different and harder than steel or reinforced concrete structures due to their material properties. To facilitate this problem homogenization methods were suggested. The appropriate method should be chosen according to the problem type. In this work macro modelling method was chosen because of all system will be examined. 
In order to obtain numerical values, two masonry railway bridge were investigated. It was desired to see the effect of mass and length of bridges difference by working with two bridges. In the fourth section, the architectural, geometric and material properties of the railway arch bridges were given. Solid elements are used in the models. Because the SAP2000 program can not analyze material nonlinearity with solid elements, new models with shell elements were produced. In structural modelling section a total of eight models including four for each of the two bridges examined were created. So that material nonlinear analysys and material and geometric nonlinear analyses can be made separately. But due to solid and shell element there is a difference between analyses results of SAP2000 solid and shell modals. These differences were shown in this section. To improve accuracy some assumptions made during the modeling phase, the idealizations made for the operation of the models and the analysis options used were explained. In analyses partional damping was used. Damping coefficients were calculated by modal analyses results. Hilber-Hughes and Taylor's method was chosen as time integration method. Also time step was calculated according to user manual for every record. 
Once the modeling is complete, it is checked step by step to see if the models are suitable for comparison. To show the equivalence of the models, firstly the masses of the models are compared. After the equilibrium of the masses, modal analysis was performed. The rigidity of the models was checked by modal analysis. With modal analysys, mode shapes and period values were compared and found to be similar. Lasty analysys are performed under dead loads and deformations are compared. Then it is seen that these values are equal, time history analyses are carried out.
After compliance time history analyses are started. 53 different earthquake records were used for analyses to improve the consistency of the results. The earthquake records were obtained from The Pacific Earthquake Engineering Research Center (PEER). Analyses made for eight different modals with two programs. To compare base shear force, displacement, velocity and acceleration values were used. To obtain displacement, velocity and acceleration values, two points were picked on bridges which one is in the middle of the bridge and the other one is on the support. It is seen in the graphs calculated with these values, graphs are corresponding but there is a difference between peak points. These differences are relatively few in base shear force, displacement and velocity values but difference in acceleration are bigger. To see this difference in percent, the maximum value of every analysis were obtained and graphics were created. Also with these maximum values, geometric and material nonlinear analyses effect were seen. By taking average values for all earthquake records gave deviation amounts. These values are given with charts for different cases.  
By this work it is seen these programs gives same results in modal analysys and dead load scenarios. Base shear force, displacement, velocity and acceleration graphs are similar between two programs. If maximum values of every earthquake records, base shear force, displacement, velocity gave similar values, there is difference between acceleration values. Also difference percentage is increasing with bridges mass increase. This shows us, if base shear force, displacement or velocity values are needed, that using one of this finite element analysis program would be enough. But acceleration values are needed, using this two programs would be appropriate. Also modelling SAP2000 is easier than ANSYS, and SAP2000 completes analyses quicker for these bridges. In the fifth and last section, the operations are briefly summarized and these results were presented respectively.