Sinan dönemi camilerinin kubbe ve alt destek sistemlerinin dijital stereotomi yaklaşımıyla yeniden ele alınması
Revisiting the dome and lower support systems of the Sinan period mosques with digital stereotomy approach
Yazar: NECMETTİN SANCAK
Danışman: DOÇ. DR. SEMA ALAÇAM
İstanbul Teknik Üniversitesi / Lisansüstü Eğitim Enstitüsü / Bilişim Ana Bilim Dalı / Mimari Tasarımda Bilişim Bilim Dalı
Derece: Yüksek Lisans, 2021
Konu: Mimarlık = Architecture

Özet:
Geçmişten günümüze Sinan Dönemi Camileri, şehirlerin siluetlerine kattığı değerle, anıtsal nitelik taşıyan biçimiyle, strüktürel, akustik, deprem dayanımı vb. açılardan geliştirilen tasarım çözümleriyle günümüz yapım tekniklerine ve mimarisine ışık tutmaktadır. Sinan tarafından geliştirilen kubbe sistemlerinin tarihsel süreç içerisinde günümüze kadar sağlam bir şekilde gelebilmesinin nedenleri, strüktürel çalışmalar, malzeme araştırmaları, biçim araştırmaları gibi pek çok çalışmanın konusu olmuştur. Bu kubbelerin ortak özelliklerinden birisi de Horasan tuğlaları ve harcı ile yığma yapım tekniğiyle inşa edilmiş olmalarıdır. Çalışma kapsamında yığma kubbeler, üç boyutlu katı cisimlerin fiziksel olarak şekil değiştirmeleri sonucu oluşan parçaların anlamlı bir bütün oluşturması olarak nitelendirilen stereotomi yaklaşımı ile ele alınmaktadır. Çalışmanın amacı, Sinan Dönemi Camilerinde kullanılan farklı kubbelerin biçimsel (geometrisi ve geometriyi oluşturan ilişkilerle birlikte) ve strüktürel açıdan incelenmesi, incelenen kubbelerin dijital ortamda üretken hesaplamalı modelde kullanılmak üzere temsil parametrelerinin araştırılmasıdır. 
Çalışma kapsamında kubbelerin taşıyıcı sistem bileşenleri, kubbe çapı, strüktürel açıdan davranışı, kubbeyi oluşturan alt birimlerin ölçüleri çözümlenerek biçimsel varyasyon, standart olmayan birimlerle yeniden üretilebilirliği ve kubbe geometrisi dışında çift eğrilikli yüzeylere uygulanabilirliği gibi potansiyeller araştırılmıştır. Çözümlenen kubbe örneklerinden elde edilen veriler ışığında serbest biçimli yüzeylere uygulanabilecek hesaplamalı bir model geliştirilmiştir. Çalışmada strüktür sistemi, ölçek, biçimsel çeşitlilik ve kullanılan malzeme etkenleri göz önünde bulundurularak 25 Sinan Dönemi Camisi örnek olarak seçilmiştir. Seçilen yapıların taşıyıcı sistem ve kubbelerinin dijital ortamda üç boyutlu modelleri oluşturulmuş, üç boyutlu kubbe modelleri üzerinde dijital stereotomi yaklaşımı ile farklı bölümlemelere (tiling) sahip yığma kubbe model alternatifleri araştırılmıştır. 
Çalışmada yapılan literatür taramaları kapsamında, Sinan'ın hayatı, üslubu, özgünlüğü ve etkilendiği mimari yapılara değinilmiş, cami mimarisinin tarihsel süreç içerisinde nasıl geliştiği ve evrildiği incelenmiş, alt ölçekte Sinan'ın Osmanlı Cami Mimarisini nasıl şekillendirdiği ve özelleştirdiği saptanmıştır. Sinan Dönemi Camilerinin incelemelerinden yola çıkılarak, camilerin yapı elemanları grafik kodlama tekniği kullanılarak detaylı bir şekilde anlatılmıştır. İncelemeler sonucu Sinan'ın camilerdeki baldaken sistemi; kasnak, kasnak dayanağı, payanda, ağırlık kulesi, yarım kubbe, çeyrek kubbe, eksedra, geçiş elemanları (pandantif, tromp, Türk üçgeni) gibi geliştirdiği taşıyıcı sistem birimleri ile destekleyerek Klasik Osmanlı Cami Mimarisini olgunluğa eriştirdiği gözlemlenmiştir.

Sinan ve Mimarisi bölümünde, ele alınan stereotomik üretim yöntemi detaylı olarak incelenmiş, Sinan Dönemi Camilerindeki kubbe ve alt destek sistemleri bu yöntemle oluşturulmaya çalışılmıştır. Son yıllarda ele alınan yığma yapıların dijital stereotomiyle ele alındığı çalışmalar incelenmiş, tonozların, kubbelerin ve çift eğrilikli yüzeylerin dijital steretomiyle oluşumunu inceleyen çalışmalar analiz edilmiştir.
Deneysel çalışmalar kapsamında, oluşturulan kubbe ve alt destek sistemleri hesaplamalı tasarım araçları yardımıyla hem dijital ortamda hem de üç boyutlu yazıcı ile üretilen ölçekli fiziksel modellerinde strüktürel davranış testleri yapılmıştır. Dijital olarak oluşturulmuş modelin strüktürel davranış testi ile fiziksel model üzerinde uygulanacak strüktürel davranış deneyleri; geometrinin bütünü ile bütünü oluşturan tuğlaların boyutu üzerinden karşılaştırılmalı şekilde incelenmiştir. Karşılaştırma ve araştırma sonucunda elde edilen bilginin çalışma kapsamında geliştirilen hesaplamalı modeli beslemesi ve kubbe harici serbest biçimli yüzeylere uygulanabilecek bir model önerilmiştir.
Bu çalışma; İTÜ Bilimsel Araştırma Projeleri Birimince desteklenmiştir. Proje numarası: MYL-2020-42710.

Abstract:
From the past to the present, the Sinan Period Mosques continue to  provide insights for today's construction techniques and architecture with design solutions developed from different points of views and the value they add to the silhouettes of the cities, with their monumental form, structural, acoustic, earthquake resistance, etc. The reasons why the dome systems developed by Sinan have remained structurally strong to the present day throughout the historical process have been the subject of many studies such as structural studies, material researches, and form studies. One of the common features of these domes is that they were built with Khorasan bricks and mortar using the masonry technique. In the scope of the study, masonry domes are investigated with the stereotomy approach, which is characterized as the formation of a meaningful whole by the parts formed as a result of the physical deformation of three-dimensional solid objects. The aim of the study is to examine the different domes used in the Sinan Period Mosques in terms of form (with their geometry and the relationships that make up the geometry) and structure, and to investigate the representation parameters of the examined domes to be used in the generative computational model in the digital environment.
In the scope of the study, the structural system components of the domes, the diameter of the dome, the behavior of the structural aspects, the dimensions of the sub-units that make up the dome were analyzed, and the potentials such as morphological variation, reproducibility with non-standard units and applicability to double curved surfaces other than dome geometry were investigated. Considering the structural system, scale, stylistic diversity and material used, 25 Sinan Period Mosques were chosen as an example in the study. Three-dimensional models of the structural systems and domes of the selected structures were created in the digital environment, and masonry dome model alternatives with different subdivisions were investigated with the digital stereotomy approach on three-dimensional dome models.
As a part of literature review, Sinan's life,  style, and original contributions were mentioned, the architectural structures he was influenced by were presented as well as the development and evolution of the mosque architecture through the historical process. In which ways Sinan has contributed to shape and customize the Ottoman Mosque Architecture in the lower scale was discussed. Based on the detailed examinations of the Sinan Period Mosques, the structural elements of the mosques are explained in detail with use of a graphical coding technique. Classical Ottoman Mosque Architecture has achieved it golden ages with Sinan's contributions on development of baldachin system, supporting dome with structural elements such as pulley, pulley support, buttress, weight tower, semi-dome, quarter dome, exedra, transition elements (pendant, squinch, Turkish triangle).
The scope of this thesis covers collection of mosque data, transfer of collected data to the digital environment, generation of physicaş prototypes of the computational geometric model, analysis and comparison of the structural behavior of the physical model and the digital model,generation of different geometric variations depending on the insights obtained during prototyping, and the feedback received from the variations. At the beginning,  25 Sinan Mosques, which are diverse in form, spatial and structural aspects, location, period, reason of construction, etc. were selected and redrawn to translate into digital environment. Among the data transferred to the digital environment, the structural systems of the mosques (pillars, columns, walls, arches…) and the dome sub-support systems (vault, pendentive, squinch, Turkish triangle…) were examined in detail and these systems were modeled with the polygon modeling method. Polygonal models were generated and the domes were remodeled depending on parameters such as the number of bricks, brick size, brick type and dome diameter by using the Digital Stereotomy approach in relation to the masonry dome construction technique. Models were divided into sub-parts and these models were physically produced at 1:200 scale by using a 3D printer. The deformation rates in the geometry of the domes were investigated using the structural analysis program in digital environment, which is the Millipede add-on of the Rhino-Grasshopper modeling tool, and in the physical environment,  a pressure bar to test structural performance of the physical models. Experiments on digital and physical models were evaluated with the structural analysis method, and the contribution of the dome support systems in the Sinan Period Mosques to the structural performance were investigated. The outcomes and results obtained from the structural analysis fed the computational model, and the process  as well iteratively.As a result of the analyzes and experiments, a generative system has been developed.  This generative system model provides a potential to be adapted into non-standard units of a novel stereotomic structure with freeform surfaces, based on the parameters(brick size, brick type, brick angle, etc.), relations (topology) and algorithms obtained from analysis of the masonry dome construction technique. 
In Section 2, relevant studies on the use of stereotomic approach in relation to digital design and fabrication technologies were presented in a systematic way. The focus of the reviewed studies can be listed as follows: formation of vaults, formation of domes, structural and geometric basis of double curved surfaces.
One of the crucial parts of the study can be considered as the division of the dome into equal sub-parts. While the dome was being divided into equal sub-parts, more than one representation method (mesh geometry partitioning, meridional and parallel partitioning, partitioning by rotation of identical brick units to the center, etc.) were determined, and the most appropriate representation for the study was compared in terms of their compatibility with the traditional masonry dome construction technique has been selected. 
In the model divided into equal sub-parts, the bricks were represented as units with equal area instead of equivalent units. Khorasan mortar, which is located between each brick in the domes generated with the masonry construction technique, is at least one brick deep and adds flexibility to the production, is represented in the physical model in a way that creates vertical and horizontal interlocking. The joints in the digital model were designed to provide a joint without using any adhesive in the assembly of the physical model produced by 3D printers. The scale of the physical model was determined as 1:200, the brick sizes were determined to correspond to the thickness of 10 bricks of 5*25 cm size actually used, and these numerical values were linked to the parametric model for experimental study analysis. The sub-parts were labeled for the assembly of the bricks generated for the physical model.
In the scope of experimental studies, structural behavior tests were carried out both in the digital environment and in the scaled physical models to be produced with a 3D printer, conducted with the computational design tools. In the context of structural behavior tests of the digital model and structural behavior tests to be applied on the physical model,  overall geometry as a whole and the size of the bricks that make up the whole were examined comparatively. 
As a result, in the study, dome and structural systems from the Sinan Period Mosques were transferred to digital media, and structural analysis studies were carried out on the domes by parameterizing the transferred digital model. Questions such as how to divide the domes into identical sub-parts, how to convert them to a model depending on the desired parameters, which joint details will be to produce the physical model, and how the labeling will be for the preparation of the assembly have been answered in the design process of the dome and the supporting systems. Depending on the results of the structural analysis on the models made in both digital and physical environments, the behavior of the dome under certain loads was simulated in digital environment to gain a better understanding about the relationship between the determined parameters and the structural behavior. As a result of all the determinations made, it was seen that both the structural and formal arrangement in Sinan's domes ensured the homogeneous transfer of the loads on the dome to the ground.
Results of structural behavior analysis made in digital and physical environments provided insights on the appropriateness in  the use of semi-dome and a form with double curved instead of  piles, walls, buttresses as supporting components of the dome in Edirne Selimiye Mosque. This finding led to the idea of form generation in which a double curved surface is structurally supported by another double curved surface that can be used as a form generation tactic in contemporary studies. In other words, it has been determined that the construction information obtained from the findings and analysis results can be used on any double curved surface, and it has been seen that the generated productive system can be used on double curved surfaces. Moreover, it has been observed that in Sinan's mosques, he optimizes the structural performance of the dome and sub-support systems by supporting the dome with semi-domes.
The findings and outcomes of this stıdy are expected to contribute to architectural education in terms of precedent analysis and research methods that might shed light on novel designs.  In this study the use of computational design tools, which have become widespread recently but still remained unexplored exhaustively, is expected to be a resource for students, instructors and researchers who will work on the research of experimental form-finding tools. In the early design phase of the developed digital model, the masonry dome system includes different building typologies other than mosques, and forms such as pressure-operated dome, vault, double curved surface, which are necessary for material, geometry, subdivision of geometry, part-whole relationship and digital production tools. It is considered that developed digital models might perform as a generative design tool that can support design decisions related to the workflows. Although this study manifest a potential to support analysis of the pressure-based dome and structural systems with digital stereotomy approach, it also provides an opportunity to support designers  testing various   structural performance scenarios in the early design phase of double curved surface geometry such as generation of double curved surface with monocoque shell system, or truss systems, etc.
This work was supported by Research Fund of Istanbul Technical University. Project Number: MYL-2020-42710.