Jeodezik kubbe formlu bir taşıyıcı sistemin AISC 360-10 yönetmeliği kullanılarak mafsallı ve ankastre düğüm noktası tiplerine göre karşılaştırmalı analizi
Comparative structural analysis of hinged jointed and fixed jointed geodesic domes with respect to AISC 360-10 specificatons
Yazar: MİTHAT KUZULU
Danışman: YRD. DOÇ. DR. BARLAS ÖZDEN ÇAĞLAYAN
İstanbul Teknik Üniversitesi / Fen Bilimleri Enstitüsü / İnşaat Mühendisliği Ana Bilim Dalı / Yapı Mühendisliği Bilim Dalı
Derece: Yüksek Lisans, 2015
Konu: İnşaat Mühendisliği = Civil Engineering

Özet:
Antik çağlardan günümüze, yapı ve yapısal eleman tasarım doktrinleri sıklıkla değişmiştir. Tüm değişikliklerin ortak yönü ise, tasarımı iyileştirmek ve güncel taleplere daha iyi cevap vermek adına yapılmış olmalarıdır. Strüktürün ve malzemenin doğasına uygun tasarım yapmak, maliyetler ve tasarım bütünlüğü açısından büyük önem taşımaktadır. Yapısal elemanların bir araya getirilerek optimum tasarımlı bir yapının inşa edilmesinde, tasarımın mümkün olduğunca doğaya uyumlu olması büyük avantaj yaratmaktadır. Tarihte, formun doğaya uygun hale getirilmesi denince akla ilk olarak kemer ve kubbe taşıyıcılar gelmektedir. Bu tip taşıyıcıların ortak özelliği, doğada var olan formlardan esinlenilmiş olması ve malzemenin mekanik özelliklerine uygun davranış sergileyecek şekilde düzenlenmesidir. Doğaya ve doğal formlara uygunluk kıstasının yenilikçi ve belki en ileri formlarından birisi , jeodezik kubbelerdir. Jeodezik kubbeler, bilim adamlarının doğadaki moleküler formlardan veya doğal strüktürlerden faydalanarak ortaya çıkardığı ideal bir taşıyıcı sistem tipidir. Modern jeodezik kubbe formunu ilk olarak Buckminster Fuller tanımlamış, ortaya attığı teoriler ve bilim dünyasına kazandırdığı patentler ile günümüze ışık tutmuştur. Yapısal elemanların, uygun geometri ile üretildiği takdirde, bileşenlerinin ne kadar uyumlu çalışacağını belirgin bir şekilde ortaya koyan jeodezik kubbeler sayesinde, geniş açıklıkları en ekonomik şekilde geçmek mümkün olmaktadır. Bu tez çalışmasında, jeodezik kubbe yapılar hakkında genel tanımlar yapılarak konuya giriş yapılmıştır. Jeodezik formlarda frekans kavramı ve jeodezik formları modelleme esasları anlatılmıştır. Jeodezik kubbelerde normalizasyon kavramına giriş yapılmıştır. Yapısal analiz bölümünde, belirli bir frekansta, çapta ve yükseklikte bir jeodezik kubbe formu ele alınarak, AISC 360-10 (Amerikan çelik yapı şartnamesi), DBYHBY 2007 (Deprem bölgelerinde yapılacak binalar hakkında yönetmelik) ve ASCE 7-10 (Binalar ve diğer yapılar için minimum tasarım yükleri) ışığında; tanım, modelleme, yükleme ve analiz aşamalarından geçirilmiştir. Yapı, analiz edilirken düğüm noktaları ankastre ve mafsallı olarak tanımlanmış iki ayrı model hazırlanmıştır. Analiz verileri ışığında; yapı stabiliteleri, yapının burkulma performansları ve yapısal elemanlar için kesit tahkikleri yapılmıştır. Mafsallı ve ankastre düğüm noktalı olarak tasarlanan ve analiz edilen edilen yapılar, bu bağlamlarda karşılaştırılmıştır. Mafsallı düğüm noktası için bir düğüm noktası tipi belirlenerek gerilme tahkikleri yapılmış ve çalışma sonlandırılmıştır.

Abstract:
Since the ancient times, doctrines of structural design and structural member design have changed frequently. These changes have in common in the aspect of their aim. All changes have been made in order to improve the design and to fulfill the recent requirements of the design trends.
Designing harmoniously with the structure and with the nature of the structural material is crucial to get the integrality in the design. Compatibility of the design with the nature also enables to get an optimum design in the aspect of building costs.
In the history of the structural design and the structural member design, mankind has always pursued to get more effective and more natural behaved structures. The first form of this pursuit can be claimed to be the arch concept. With the accumulation of the knowledge obtained from the arch designs, a more complex form, "dome structures" showed up in the scene. As the dome designs had been elaborated, structurally more efficient types of the domes were formed. Speaking of structurally more efficient dome forms, the geodesic dome types appeared. Geodesic forms and geodesic dome structures are formed with the inspiration of molecular forms of the materials, the atomic forms, honeycombs, crystal structures, etc. 
The modern types of the geodesic forms and especially geodesic domes have been derived from the early studies and works of Sir Buckminster Fuller in 1950's. He has many patents and projections about geodesic forms and this visionary man's contribution to this knowledge have been enlightening the related studies, even today.
In this study, the idea of geodesic forms is explained. The frequency concept which determines the spherical features and the stability behavior of the dome structure is defined. Examples of well known geodesic dome structures in the world and related to this, examples of their joint connection types are given.
This thesis is prepared to explain the geodesic dome concept, define the natural behavior of the geodesic structure, explain the method of forming a geodesic structure and make a comparison between two analysis outputs of alternative geodesic structural analysis models with same polyhedron frequencies, load definitions, load application approaches, geometry and with different connection types.
In this study, two similar "12V frequency" geodesic domes which have "50m" in diameter and "15.2m" in height formed and modeled with the "Geodesica" software. The output file from the software was imported firstly to AutoCAD software and then to SAP2000 analysis software. With this procedure, the geometry of the analysis models are obtained. In addition to this, manually modeling & normalizing the geodesic forms are explained using diverse frequency models. Forming the geometry is explained step by step.
In the load definitions process, "snow, wind" loads are obtained from ASCE 7-10 (Minimum design loads for buildings and other structures).
For determining the seismic loads, DBYBHY 2007 (Specification for structures to be built in disaster areas) is used.
For temperature difference loads (self straining loads) an assumption is made.
The load combinations are taken from the combination tables of ASCE 7-10 (Minimum design loads for buildings and other structures) and derived to bring in compliance with the analysis model. Applications of loads to points, areas and joints are monitored to clarify the procedure. All loads are applied to the joints of the analysis model except for the self straining forces (loads from temperature differences) 
In the analysis part; response spectrum analysis, modal analysis and buckling analysis are performed for both models. Regarding to the outputs of these analysis, the frame sections are optimized. As the sections are optimized, the results are collected to be used in the calculations. 
For the analysis model with hinged joints (M2-2 and M3-3 released), the calculations of stress checks are made with respect to AISC 360-10 (Specification for structural steel buildings) and allowable stress design (ASD) criteria. Frames are calculated in two stress conditions. Which are axial pressure and tensile.
Modal frequencies and buckling behavior outputs are collected to be used in the results section.
For the analysis model with fixed joints (with no moment releases), the calculations of stress checks are made with the stress check module of SAP2000 analysis software. Besides, "all load related" and "structural characteristics" of the model is made with respect to ASCE 7-10 (Minimum design loads for buildings and other structures) and AISC 360-10 (Specification for structural steel buildings), stress check modules are compiled and the stress analysis & checks worked properly.
After determining the stress values of the structural members for both analysis models, a sample hinged connection design is given in order to monitor the design criteria of AISC 360-10 (Specification for structural steel buildings) for joints and welds.
After all process is completed, a clear result emerged.
The geodesic dome with the hinged connection members work properly and distribute loads, forces and stresses between the structural members with a high performance. The seismic performance and structural stability is solid. However, with many hinges in the connections, the buckling analysis showed that the structure is slightly vulnerable to the buckling loads. In order to increase the buckling factor of the structure, greater cross sections for the frames are selected. The increased sections are located on the lower/bottom elevations of the structure. Due to this increase in the cross sections, the weight of steel structure also increased and the capacity/stress ratios declined which makes the system members work with a lower capacity ratio due to the specified loads.
The geodesic dome with fixed connection members work properly and distribute loads, forces and stresses between the structural members with a high performance as well as the analysis model with the hinged jointed frames.
The seismic performance and structural stability is solid. In the buckling analysis, great numbers for factor values are obtained. This system is compiled with frame sections with lower cross sections.
Analysis model with fixed joints gives an output of total material weight significantly lower when compared to the analysis model with hinged joints. However, producing and mounting the fixed connections in a geodesic dome is a really big challenge. The production and erection processes of this type of structure should be performed with a really high precision in order to get a structural behavior as simulated in the analysis model.
Selecting the joint type for the frames will be made not only with respect to the weight and primary costs of the building but also to the mounting & erection issues and secondary costs.