Eksenel doğrultuda fonksiyonel olarak değişen üniform olmayan kirişlerde açı yöntemi
Slope deflecti̇on method in non-uniform beams withfunctional changes in axis
Yazar: SİMGE CERRAH
Danışman: PROF. DR. REHA ARTAN
İstanbul Teknik Üniversitesi / Fen Bilimleri Enstitüsü / İnşaat Mühendisliği Ana Bilim Dalı / Yapı Mühendisliği Bilim Dalı
Derece: Yüksek Lisans, 2019
Konu: İnşaat Mühendisliği = Civil Engineering

Özet:
Bu tez kapsamında değişken kesitlerde açı yöntemi hesabı için formüller geliştirilmiştir. Bu formüller bulunurken başlangıç  değerleri yönteminden faydalanarak hesaplar yapılmıştır. Temel denklemler matris olarak yazılıp başlangıç değerleri metodu ile kompakt bir hale getirilmiştir. Başlangıç değer problemi çözümü için bir taşıma matrisi bulundu. Bulunan taşıma matrisi iki katlı integrallere sahip bir formda olduğu için yapılan hesabı kolaylaştırmak amacıyla Cauchy ardışık integrallerinden daha sade bir forma getirildi. Bundan sonra problemin bilinmeyenlerine ulaşıldı. Geliştirilen formüller, her tip kiriş için geçerli formüller olup, kesitlerin atalet momenti fonksiyonu formüllerde yerleştirip ilgili birim deplasman sabitleri, uç momenti gibi değerlere direkt olarak ulaşıldı. Başlangıç değerleri yöntemiyle düzgün yayılı yük altındaki sabit kesitli ankastre kirişin moment ve kesme kuvvetine, düzgün yayılı yük altındaki sabit kesitli basit kirişin dönme ve çökme değerleri bulundu. Açı yönteminde kullanılacak olan birim deplasman sabitleri ve uç moment formülleri elde edildi.Geliştirilen formüllerle çeşitli örnekler çözüldü.

Abstract:
In this study, the slope-deflection method for variable rods along the axis of inertia moment and elasticity modulus is discussed in detail and an effective method is presented. The unkowns used in the slope-deflection method in the variable cross-sections are calculated with the help of the initial values method are given as analytical expressions. In this thesis, firstly, general information about the analysis of structures was given. A structure refers to a system of connected parts used to support a load. To analyze a structure properly, certain idealizations must be made as to how the members are supported and connected together. The loadings are determined from codes and local specifications, and the forces in the members and their displacements are found using the theory of structural analysis. Formulas developed for calculating slope-deflection method of variable sections were developed. While calculating these formulas, calculations were made by using the initial values method. Differential equations are an important topic in calculus, engineering, and the sciences. A lot of the equations that you work with in science and engineering are derived from a specific type of differential equation called an initial value problem. The basic equations mentioned in the second chapter were written as matrix and compacted by the initial values method. A transport matrix was found to solve the initial value problem. Since the transport matrix was in a form with double integrals, it was brought to a simpler form than the Cauchy sequential integrals to facilitate the calculation. After that, unknowns of the problem were reached. The formulas developed are valid formulas for each type of beam and the moment of inertia of the sections is placed in the formulas and the related unit displacement constants and end moments are directly reached. 
Using the initial values method, the moment and shear force of the fixed section built-in beam under uniformly distributed load, and the rotation and collapse values of simple sectioned fixed beam under uniformly distributed load were found.The formulas found with the initial values were applied to a built-in beam loaded with arbitrary distributed load and the fix-end moments formulas were reached.Various examples were solved with the formulas developed.