Tesir çizgilerinin hesabında endirekt Müller-Breslau prensibi ve bazı uygulamaları
Indirect Müller-Breslau principle for construction of influence lines and some applications
Yazar: TURGAY TAHTACİ
Danışman: PROF. DR. ENGİN ORAKDÖĞEN
İstanbul Teknik Üniversitesi / Lisansüstü Eğitim Enstitüsü / İnşaat Mühendisliği Ana Bilim Dalı / Yapı Mühendisliği Bilim Dalı
Derece: Yüksek Lisans, 2023
Konu: İnşaat Mühendisliği = Civil Engineering
Dizin: Müller biçki sistemi = Muller cutting system ; Tesir kesiti = Cross section ; İzostatik pres = Isostatic press

Özet:
Bu çalışmada tesir çizgilerinin hazır bir yapı analizi yazılımı ile belirlenmesinde Müller-Breslau Prensibi'nin uygulanabilirliği araştırılmıştır. Müller-Breslau Prensibi'ne göre, sistem üzerindeki herhangi bir kesite yapılacak rölatif yerdeğiştirme  yüklemesi, mesnetlere uygulanacak yerdeğiştirme yüklemesi dışında kolaylıkla yapılamamaktadır. Bu sebeple söz konusu yerdeğiştirmeyi oluşturan kuvvetin sisteme uygulandığı Endirekt Müller-Breslau Prensibi adında alternatif bir yöntem sunulmuştur. Bu alternatif yöntemde, hazır yazılım kullanılarak aynı koordinatlara sahip ancak farklı sınır koşullarına sahip iki ayrı düğüm noktasına iki ayrı yükleme yapılması mümkün olmaktadır. Endirekt Müller-Breslau Prensibi, çalışma kapsamında farklı yapı sistemleri üzerinde denenmiş ve yöntemin çeşitli sistemler üzerinde geçerli ve uygulanabilir olduğu görülmüştür. Çalışma beş bölüm halinde sunulmuş ve birinci bölümünde çalışmanın amacı, kapsamı ve literatürdeki çalışmalar ile ilgili bilgiler verilmiştir. 
İkinci bölümde yapı sistemlerine etkiyen yükler hakkında genel bilgi verilerek bu yüklerin sınıflandırması yapılmıştır.
Çalışmanın üçüncü bölümünde tesir çizgisi kavramının tanımı yapılarak genel özelliklerinden bahsedilmiştir. İzostatik sistemlerin tesir çizgilerinin hesaplanması anlatılarak örnek bir basit mesnetli kiriş için tesir çizgisi fonksiyonları
oluşturulmuştur. Yine bu bölümde hiperstatik sistemlerin tesir çizgilerinin özelliklerinden bahsedilerek tesir çizgilerinin hesaplanmasında kuvvet yöntemi detaylı bir şekilde anlatılarak bu yöntem ile örnek bir hiperstatik çerçeve sisteminin tesir çizgisi hesaplanmıştır.
Çalışmanın dördüncü bölümünde Endirekt Müller-Breslau Prensibi detaylı bir şekilde anlatılarak yöntemin SAP2000 programında nasıl uygulanacağından bahsedilmiştir. Bu kısımda düzlem kafes, sürekli kiriş, izostatik çerçeve, eğri eksenli çubuklu çerçeve, çubuk elemanlardan oluşan kare ızgara, yine çubuk elemanlardan oluşan L şeklinde ızgara gibi sistemler SAP2000 programında modellenerek, eğilme momenti, kesme kuvveti, mesnet tepkisi, plastik dönme, burulma momenti gibi tesir çizgileri Endirekt Müller-Breslau Prensibi ile elde edilmiştir. Endirek Müller-Breslau Prensibi ile elde edilen tesir çizgileri, yapı sistemlerine birim yüklemeler yapılarak elde edilen sonuçlar ile karşılaştırılmıştır. Yapılan karşılaştırmalarda Endirek Müller-Breslau Prensibi'nin doğruluğu ispatlanmıştır. Çalışma kapsamında literatürde kullanılan bazı sayısal örneklere ait tesir çizgileri Endirek Müller-Breslau Prensibi ile elde edilmiştir.
Son bölümde çalışmada elde edilen sonuçlar ile ilgili düşüncelere yer verilerek, Endirekt Müller-Breslau Prensibi'nin kullanılabileceği çalışmalardan bahsedilmiştir.

Abstract:
In this thesis, the applicability of the Müller-Breslau Principle was investigated in determining the influence lines with a structure analysis program. Müller-Breslau Principle is one of the effective method for construction of influence lines. On the other side, commercial computer codes are effective tools for analysis and design of structures such as SAP2000 and these packages may also be used for construction of influence lines according to Müller-Breslau Principle. However, analysis of the structure for displacement applied to the system in accordance with the Müller-Breslau 
Principle is not an easy task, except in special cases corresponding to support settlements. For this reason, an alternative method called Indirect Müller-Breslau Principle, in which the force corresponds to unit displacement is applied to the system, is presented. Indirect Müller-Breslau Principle has applied to different structral systems within the scope of the study and it has been seen that the method is valid and applicable on various systems. The study is presented in five parts and in the first part, information on subject of the study and studies in the literature are given. In the second part, general information about the live loads acting on the structural systems is given and the classification of these loads is made. In the third part of the study, the definition of the influence line is given and its general characteristics are mentioned. By explaining the finding of the influence lines of staticly determinate structures, influence line functions are created on a sample simply supported beam. Again in this section, the characteristics of the influence lines of statically undeterminate structures are mentioned and the force method in the 
construction of the influence lines is presented in detail and illustrated with a numerical example. In the fourth part of the study, the Indirect Müller-Breslau Principle is explained in detail and how the method will be applied in the SAP2000 program is mentioned. In this section, systems such as truss, continuous beam, staticly determinate frame, frame 
with arch, square and L shaped grillages are modeled in the SAP2000 program and such as bending moment, shear force, support force, plastic rotation, torsion moment influence lines were obtained by the Indirect Müller-Breslau Principle. The influence line ordinates obtained by using Indirect Müller-Breslau Principle were compared by applying unit loadings to the structural systems. In the comparisons made, it was observed that the constructed influence lines by using Indirect Müller-Breslau Principle were correct. In order to make the method comparable, numerical examples that have been used before in the literature are also included in the study. Flow chart in the construction of influence lines with Indirect Müller-Breslau Principle is as follows:
1- Initially the structural system is modeled in the SAP2000 program, the nodal 
point (joint) on the cross section which influence line is investigated is disconnected 
by the joint disconnection feature of SAP2000.
2- After the nodal joint disconnection, two nodal points will be formed on the 
said cross- section. The coordinates of these two nodes are the same. In addition, more 
points may occur on this cross-section, depending on the number of connected 
elements on this cross-section. The nodal points of other elements except the element 
whose influence line is calculated are merged. Finally at this cross-section two nodal 
points must be remain. This situation is explained in more detail in the truss, frame 
with arch, square and L shaped grillages examples used in the study.
According to Müller-Breslau Principle, the internal force component which influence 
line constructed is eliminated first by cutting at the direction of internal force and an 
unit displacement is applied at inverse direction. The elastic curve of the structure due 
to this displacement yields to the influence line of related internal force. In the 
construction of influence lines by the Indirect Müller-Breslau Principle, a unit force
couple or a unit moment couple will be applied to these two joints at the beginning.
The reason for the joint disconnection is to apply unit loads in opposite directions on 
the same section.
3- These two nodes will be free in all directions after joint disconnection. A 
constraint is assigned to these two points in such a way that the eliminates the internal 
force component which influence line constructed and their all other displacements are 
equal.
4- After this process, unit force or unit moment couple is applied to these two 
points according to the internal force component of constructed ifluence line and 
system analysis is made. As a result of the analysis, the displacements in the direction 
of this internal force component are read at these two points. Using these 
displacements and Betti's Reciprocal Theorem, a constant coefficient is calculated.
5- The influence line is obtained by multiplying this constant coefficient with 
the elastic curve obtained as a result of unit loading. This process is equivalent to 
multiplying the displacement values obtained as a result of the unit loading apply in 
the SAP2000 program and the mentioned constant number.
By using the method, the influence lines of plastic rotations can also be constructed 
easily. If the rotational influence line ordinates of the potential plastic hinges on the 
structure, obtained by the method proposed in the study, are collected in a database, 
the database can be used in the nonlinear analysis of the system or in the structural 
health monitoring algorithm. Thus, these influence lines are very useful for structural 
monitoring since the plastic rotations can be calculated by other tools after an 
earthquake or an impact loading. Plastic hinge rotations which come from structural 
health monitoring system can be used to evaluate the structure for new internal force 
distribution.
The Indirect Müller-Breslau Principle can also be used to obtain the influence line 
ordinates of the plates if the plates are idealized as a grid frame system and appropriate 
transformations are made.
In the last section, conclusions on comparisons of the results from SAP2000 and the 
other methods.