University of Kashan Journal of Iranian Architecture Studies 2252-0635 13 26 2025 03 15 Systemic Analysis of the Equilibrium Process in the Structural Components of Historical Buildings (Case Study: Graphical Analysis of a Quadrilateral Vault) Systemic Analysis of the Equilibrium Process in the Structural Components of Historical Buildings (Case Study: Graphical Analysis of a Quadrilateral Vault) 205 224 114868 10.22052/jias.2025.255200.1313 FA Nima Keynejad Ph.D. Candidate, School of Architecture, College of Fine Arts, University of Tehran. Mohammad Hassan Talebian Professor, School of Architecture, College of Fine Arts, University of Tehran 0000-0002-9568-1819 Saeid Khaghani Assistant Professor, School of Architecture, College of Fine Arts, University of Tehran. Journal Article 2024 07 20 The behavior of historical buildings is not easily predictable, and one way to better understand this behavior is to consider it as a complex system. Complex systems theory examines phenomena layer by layer and focuses on the relationships between information. Each layer of the system exhibits a specific behavioral pattern, and the behavior of the whole system becomes predictable through the synergy between these layers. From the perspective of this theory, behavior in a historical building encompassed a more comprehensive concept and included the structure. On the other hand, the history of structural analysis in historical buildings highlighted the importance of geometry in maintaining the building's equilibrium. At the same time, machine tools that are common today use other principles in their analyses and do not provide reliable results due to their simplistic assumptions. As a result of introducing a conceptual framework for understanding a historical building based on the theory of complex systems in this article, it is argued that the analysis of behavior in a historical building depends both on the examination of the processes occurring in different layers of the building, and on the application of empirical knowledge. As a result of examining historical equilibrium analysis in historical buildings, it is concluded that combining the limit method with graphical statics enables the determination of a building's structural elements' complexity through an information-driven process, based on the path of the thrust force. This descriptive-analytical article presented its proposal practically by implementing this method on a Quadrilateral vault as a component of a historical building. The behavior of historical buildings is not easily predictable, and one way to better understand this behavior is to consider it as a complex system. Complex systems theory examines phenomena layer by layer and focuses on the relationships between information. Each layer of the system exhibits a specific behavioral pattern, and the behavior of the whole system becomes predictable through the synergy between these layers. From the perspective of this theory, behavior in a historical building encompassed a more comprehensive concept and included the structure. On the other hand, the history of structural analysis in historical buildings highlighted the importance of geometry in maintaining the building's equilibrium. At the same time, machine tools that are common today use other principles in their analyses and do not provide reliable results due to their simplistic assumptions. As a result of introducing a conceptual framework for understanding a historical building based on the theory of complex systems in this article, it is argued that the analysis of behavior in a historical building depends both on the examination of the processes occurring in different layers of the building, and on the application of empirical knowledge. As a result of examining historical equilibrium analysis in historical buildings, it is concluded that combining the limit method with graphical statics enables the determination of a building's structural elements' complexity through an information-driven process, based on the path of the thrust force. This descriptive-analytical article presented its proposal practically by implementing this method on a Quadrilateral vault as a component of a historical building. https://jias.kashanu.ac.ir/article_114868_df2b93222d981e275d3407d919bd34ae.pdf