Comparative Study of Geometric and Numerical Cognitions of Structures in the Architectural Design Process
الموضوعات :
Majid Ahmadnejad Karimi
1
,
Mahdi Mahmoudi Kamelabad
2
,
Maryam Azimi
3
1 - Department of Architecture, Faculty of Architecture and Urbanism, Islamic Art University of Tabriz, Tabriz, Iran.
2 - Department of Architecture, Faculty of Architecture and Urbanism, Isfahan Art University, Isfahan, Iran.
3 - Department of Architecture, Faculty of Architecture and Urbanism, Isfahan Art University, Isfahan, Iran.
الکلمات المفتاحية: Design process, Structural knowledge, Geometric cognition, Numerical cognition, Comparative studies,
ملخص المقالة :
Structural design extends beyond merely creating forms to withstand forces; it incorporates various technical and non-technical elements within architectural design. The true value of structural knowledge emerges during the design process when these elements are thoroughly understood. Achieving this understanding necessitates the provision of diverse types of structural knowledge capable of informing design and analysis. Additionally, by exploring various structural design methodologies, two principal types of cognition — "geometric" and "numerical" — can significantly help designers navigate the complex requirements of structural design. This research aims to investigate the different forms of structured knowledge relevant to architectural design, ultimately addressing the central question of how geometric and numerical comprehension of structures contributes to the architectural design process. The research employs a descriptive-analytical method with a comparative study approach. It begins by defining and detailing the characteristics of geometric and numerical cognition within the design framework, subsequently elucidating their interrelationship in architectural design. Findings suggest that geometric and numerical cognitions of structures, articulated through distinct languages, correspond to various roles in designing mechanical and spatial aspects, as well as different levels of structural comprehension at various design stages. Geometric cognition, due to its linguistic proximity to the design step, has the capability to examine and apply structural knowledge from the initial stages of form design to its actual construction phase. On the other hand, numerical cognition primarily focuses on the detailed examination of the mechanical and load-bearing aspects of the structure in its analytical step.
Addis, B. (2003). Inventing a history for structural engineering design. In Proceedings of the First International Congress on Construction History, Madrid, 113-122. http://www.sedhc.es/biblioteca/actas/CIHC1_012_Addis B.pdf
Addis, B. (2007). Building: 3000 years of Design, Engineering and Construction. London & New York: Phaidon. 640pp. ISBN 978-0-7148-4146-5.
Adriaenssens, S., Block, P., Veenendaal, D., & Williams, C. (2014). Shell structures for architecture: Form finding and optimization. Routledge. http://bayanbox.ir/view/8385771275972717334/0415840597.pdf
Alpana, R., Dongre, S., Deshpande, A., & Ingle, R. K. (2007). Emerging architectonic forms and designed forms. Archnet-IJAR, International Journal of Architectural Research, 1(3), 55-67. https://www.researchgate.net/publication/26502830_Emerging_Architectonic_Forms_and_Designed_Forms.
Amit, S. (2007). Technology of architecture (Translated by Afshin Darki.). Tehran: Pelak. https://www.adinehbook.com/gp/product/9642862047. Persian.
Baldock, C. (2007). Structural optimization in building design practice: Case-studies in topology optimization of bracing systems. PhD thesis. Cambridge University Engineering Department. https://www.ethz.ch/content/dam/ethz/special-interest/mavt/design-materials-fabrication/engineering-design-and-computing-lab/DoctoralTheses/PhD_Baldock.pdf
Beghini, L., Beghini, A., Katz, N., Baker, W. F., & Paulino, G. H. (2014). Connecting architecture and engineering through structural topology optimization. Elsevier Journal, 59, 716-726. https://doi.org/10.1016/j.engstruct.2013.10.032
Billington, D. P. (1985). The tower and the bridge: The new art of structural engineering. Princeton University Press. https://www.amazon.com/Tower-Bridge-New-Structural-Engineering/dp/069102393X
Brawne, M. (2003). Architectural thought: The design process and the expectant eye. Architectural Press. https://www.amazon.com/Architectural-Thought-design-process-expectant/dp/0750658517
Breish, F., Hamm, C., & Andresen, S. (2024). Nature's Load-Bearing Design Principles and Their Application in Engineering: A Review. Biomimetics, 9(9), 545. https://doi.org/10.3390/biomimetics9090545
Bursill-Hall, P. (2002). Why do we study geometry? Answers through the ages. DPMMS Centre for Mathematical Sciences Wilberforce Road, Cambridge, 1-31. https://books.google.com/books/about/Why_Do_We_Study_Geometry.html?id=MNauHAAACAAJ
Chai, Y., Liang, X., & Liu, Y. (2023). Construction Quality of Prefabricated Buildings Using Structural Equation Modeling. Applied Sciences, 13(17), 9629. https://doi.org/10.3390/app13179629
Consolini, L., Della Puppa, G., & Lenci, S. (2010). On the optimal design of shape-resistant structures. In Proceedings of the First International Conference on Structures and Architecture, Guimaraes: CRC Press, (pp. 1-8).
Ellis, G. W., Scordilis, G. E., & Cooke, C. M. (2003). New pedagogical approaches in engineering mechanics yield increased student understanding, confidence, and commitment. In 33rd Annual Frontiers in Education, 2003. FIE 2003. (Vol. 1, pp. T4A-15). IEEE. https://ieeexplore.ieee.org/document/1263361
Engel, H. (2009). Tragsysteme, structure systems (4th ed.). Ostfildern: Hatje Cantz. https://www.naibooksellers.nl/structure-systems-tragsysteme-heino-engel.html?___store=english&___from_store=default
Fan, W., Xu, Z., Wu, B., He, Y., & Zhang, Z. (2021). Structural multi-objective topology optimization and application based on the criteria importance through intercriteria correlation method. Engineering Optimization, 54(5), 830–846. https://doi.org/10.1080/0305215x.2021.1901087
Felicioni, L., Gaspari, J., Veselka, J., & Malík, Z. (2023). A comparative cradle-to-grave life cycle approach for addressing construction design choices: An applicative case study for a residential tower in Aalborg, Denmark. Energy and Buildings, 298, 113557. https://doi.org/10.1016/j.enbuild.2023.113557
Fivet, C., & Zastavni, D. (2014). Interactive shaping of forces. In ACADIA 2014 Conference - Design Agency, California, USA, 14, 347-356. http://papers.cumincad.org/data/works/att/acadia14_347.content.pdf
Ghannad, M. (2003). A study on the North Dome of Masjid-i-Jami Isfahan. In ISAMA-BRIDGES Conference Proceedings, University of Canada, 473-484. https://archive.bridgesmathart.org/2003/bridges2003-473.pdf
Haghir, S., Saghafi Moghaddam, S., Keramat, D., Taghizade, K., Matini, M. R., & Haghnazar, R. (2021). BIM-based decision-support tool for automating design to design-to-fabrication process of freeform lattice space structure. International Journal of Space Structures, 36(3), 164–179. https://doi.org/10.1177/09560599211033867
Herbert, G., & Donchin, M. (2013). The collaborators: Interactions in the architectural design process. Ashgate Publishing Company. https://www.amazon.com/Collaborators-Interactions-Architectural-Process-Architecture-ebook/dp/B01DCDFFO2
Ilkovic, J. (2014). To think in architecture, to feel in structure: Teaching structural design in the Faculty of Architecture. Global Journal of Engineering Education, 16(2), 59-65. http://www.wiete.com.au/journals/GJEE/Publish/vol16no2/01-Ilkovicova-L.pdf
Kent, P., & Noss, R. (2002). The mathematical components of engineering expertise: The relationship between doing and understanding mathematics. In Proceedings of the I.E.E. Second Annual Symposium on Engineering Education, London, 2, 39-1. https://www.researchgate.net/publication/3964782_The_mathematical_components_of_engineering_expertise_the_relationship_between_doing_and_understanding_mathematics
Khadka, B. (2015). Structural analysis and design of commercial buildings for earthquake resistance. Thesis for Bachelor's Education. Tongji University. https://www.researchgate.net/publication/303818187_Structural_Analysis_and_Design_of_Commercial_Building_for_Earthquake_Resistance
Kingman, J. J., Tsavdaridis, K. D., & Toropov, V. V. (2014). Applications of topology optimization in structural engineering. In Civil Engineering for Sustainability and Resilience International Conference 2014. Amman, Jordan. https://www.researchgate.net/publication/266851087_Applications_of_Topolgy_Optimisation_in_Structural_Engineering_High-rise_Buildings_Steel_Components
Kurrer, K. E. (2008). The history of the theory of structures: From arch analysis to computational mechanics. Wiley. https://books.google.com/books/about/The_History_of_the_Theory_of_Structures.html?id=BcbxRXYUFc0C
Lai, Y., Li, Y., Liu, Y., Chen, P., Zhao, L., Li, J., & Xie, Y. M. (2024). Application of bi-directional evolutionary structural optimization to the design of an innovative pedestrian bridge. AI in Civil Engineering, 3(1). https://doi.org/10.1007/s43503-024-00027-5
Larsen, O. P., & Tyas, A. (2003). Conceptual structural design: Bridging the gap between architects and engineers. Thomas Telford. https://www.amazon.com/Conceptual-Structural-Design-Architects-Engineers/dp/0727761102
Lawson, B. (2008). How designers think? (Translated by: H. Nadimi). Tehran: Shahid Beheshti University. https://rayabook.net/?option=com_hikashop&ctrl=product&task=show&cid=3429. Persian.
Lee, J., Maria, E., & Moreyra, G. (2009). Eladio Dieste and Félix Candela: A comparative analysis. In Proceedings of the International Association for Shell and Spatial Structures (IASS) Symposium 2009. Valencia. https://www.researchgate.net/publication/50838886_Eladio_Dieste_and_Felix_Candela_a_comparative_analysis
Leopold, C. (2006). Geometry concepts in architectural design. In 12th International Conference on Geometry and Graphics. Salvador, Brazil, 35, 1-9. https://www.researchgate.net/publication/237544451_GEOMETRY_CONCEPTS_IN_ARCHITECTURAL_DESIGN
Lewis, W. (2005). Understanding novel structures through form-finding. Proceedings of ICE - Civil Engineering, 158(4), 178-185. https://www.icevirtuallibrary.com/doi/abs/10.1680/jciei.2007.13968
Li, Y., Ding, J., Zhang, Z., Zhou, X., Makvandi, M., Yuan, P. F., & Xie, Y. M. (2023). Practical application of multi-material topology optimization to performance-based architectural design of an iconic building. Composite Structures, 325, 117603. https://doi.org/10.1016/j.compstruct.2023.117603
Liapi, K. A. (2002). Geometry in architectural engineering education revisited. Journal of Architectural Engineering, 8(3), 80-88. https://ascelibrary.org/doi/10.1061/(ASCE)1076-0431(2002)8%3A3(80)
Lin, S., & Huang, Z. (2016). Comparative design structures: Concepts and methodologies. Springer-Verlag Heidelberg. https://www.amazon.com/Comparative-Design-Structures-Concepts-Methodologies/dp/3662508672
Luyten, L. (2012). Structurally informed architectural design. PhD Thesis. Department of Architecture, Chalmers University of Technology. Gothenburg, Sweden. https://core.ac.uk/download/pdf/70596763.pdf
Macdonald, A. J. (2019). Structure and architecture (3rd ed.). Routledge Press. https://www.routledge.com/Structure-and-Architecture/Macdonald/p/book/9781138629240
Mainstone, R. J. (2001). Developments in structural form. Architectural Press. https://www.amazon.com/Developments-Structural-Form-Rowland-Mainstone/dp/0750654511
Medaković, J., Nedučin, D., Ecet, D., Atanacković Jeličić, J., & Krklješ, M. (2024). The Interplay between Spatial Layout and Visitor Paths in Modern Museum Architecture. Buildings, 14(7), 2147. https://doi.org/10.3390/buildings14072147
Millais, M. (2005). Building structures: From concepts to design. Taylor & Francis Press. https://www.amazon.com/Building-Structures-Concepts-Malcolm-Millais/dp/0415336236
Mahmoudi Kamel Abad, M. (2012). Implicit knowledge of structures in the design process. PhD dissertation, Shahid Beheshti University, Tehran. Persian.
Mohammadi, A. A., Nejad Ebrahimi, A., & Shahbazi, Y. (2019). Geometric design of a masonry lattice space dome titled KARBANDI in Persian architecture. International Journal of Space Structures, 34(1–2), 22–39. https://www.researchgate.net/publication/332876186_Geometric_design_of_a_masonry_lattice_space_dome_titled_KARBANDI_in_Persian_architecture
Mora, R., Bedard, C., & Rivard, H. (2004). A framework for computer-aided conceptual design of building structures. In Proceedings of the 10th International Conference on Computing in Civil and Building Engineering (ICCCBE-X). Bauhaus-University Weimar. https://www.researchgate.net/publication/244955895_A_Framework_for_Computer-Aided_Conceptual_Design_of_Building_Structures
Morales, M. M., Branco, R., Tankova, T., & Rebelo, C. (2023). Additive Manufacturing of a Steel Splice Joint for Tubular Elements in a Modular Wind Tower. Ce/Papers, 6(3–4), 763–768. https://doi.org/10.1002/cepa.2729
Mueller, C. (2014). Computational exploration of the structural design space. PhD Thesis. Massachusetts Institute of Technology, USA. https://www.researchgate.net/publication/279810934_Computational_exploration_of_the_structural_design_space
Mueller, C., & Ochsendorf, J. (2013). From analysis to design: A new computational strategy for structural creativity. In Proceedings of the 2nd International Workshop on Design in Civil and Engineering. 46-56.
Nadimi, H. (2012). Engineering sciences education or engineering design: A reflection on engineering education in Iran. Iranian Journal of Engineering Education, 14(56), 1-16. https://ijee.ias.ac.ir/article_3007.html. Persian.
Omranipour, A. (2005). Art and Islamic architecture of Iran: A memorial for Professor Dr. Latif Abolghasemi. Urban Development and Renovation Organization, Tehran. https://www.adinehbook.com/gp/product/9640655384. Persian.
Pedreschi, R. (2014). Eminent structural engineer: Eladio Dieste—Engineer, master builder, and architect. Structural Engineering International, 24(2), 301-304. https://www.tandfonline.com/doi/abs/10.2749/101686614X13830790993320
Pedron, C. (2006). An innovative tool for teaching structural analysis and design. PhD thesis. Institute of Structural Engineering, Swiss Federal Institute of Technology, Trento, Italy. https://www.amazon.com/Innovative-Teaching-Structural-Analysis-Design/dp/3728130966
Pottmann, H. (2013). Architectural geometry and fabrication-aware design. Nexus Network Journal, 15(2), 195-208. https://www.amazon.com/Architectural-Geometry-Helmut-Pottmann/dp/193449304X
Pottmann, H., Asperl, A., Hofer, M., & Kilian, A. (2007). Architectural geometry. Bentley Institute Press.
Reid, S. G. (2010). Structural design procedures to support the development of innovative architectural structures. In Proceedings of the First International Conference on Structures and Architecture, ICSA 2010 (pp. 1-8). University of Minho, Portugal: CRC Press. https://www.amazon.com/Structures-Architecture-International-Conference-Guimaraes-ebook/dp/B00UVBRGTG
Rezazadeh, M., & Etessam, I. (2020). Geometrical model of relations among patterns in Iranian architecture. Creative City Design, 3(1), 30-44. http://crcd.sinaweb.net/article_676984.html
Romeo, F. (2010). The P.L. Nervi structural route: From intuition to computation through geometry. In Proceedings of the First International Conference on Structures and Architecture, University of Minho, Portugal, 45, 1-8. https://iris.uniroma1.it/handle/11573/206097
Saint, A. (2007). Architect and engineer: A study in sibling rivalry. Yale University Press. https://www.amazon.com/Architect-Engineer-Study-Sibling-Rivalry/dp/0300124430
Sandaker, B. N. (2010). An ontology of structured space. Structures and Architecture. CRC Press. https://doi. org/10.1201/b10428.
Sandaker, B. N. (2008). On span and space: Exploring structures in architecture. London & New York: Routledge. https://www.routledge.com/On-Span-and-Space-Exploring-Structures-in-Architecture/Sandaker/p/book/9780415357920
Schlaich, M. (2006). Challenges in Education: Conceptual and Structural Design. IABSE Reports, 92, 22-29. https://www.researchgate.net/publication/233702173_Challenges_in_Education_-_Conceptual_and_Structural_Design
Schodek, D. L. and Bechthold, M. (2013). Structures (7th ed). Prentice Hall. https://www.amazon.com/Structures-7th-Daniel-Schodek/dp/0132559137#detailBullets_feature_div.
Simitch, A., & Warke, V. (2014). The language of architecture: 26 principles every architect should know. Rockport Publishers. https://www.amazon.com/Language-Architecture-Principles-Architect-Should/dp/1592538584
Tam, M. M., & Mueller, C. T. (2015). Stress line generation for structurally performative architectural design. In Proceedings of the 35th Annual Conference of the Association for Computer Aided Design in Architecture (ACADIA), Cincinnati, 95-109. https://www.researchgate.net/publication/310645017_Stress_Line_Generation_for_Structurally_Performative_Architectural_Design
Torres-Peña, R. C., Peña-González, D., & Ariza-Echeverri, E. A. (2025). Exploring geometric reasoning development in early civil engineering education through structured problem-solving. Mathematical Thinking and Learning, 1–18. https://doi.org/10.1080/10986065.2025.2453773
Turrin, M., Buelow, P., & Stouffs, R. (2011). Design explorations of performance-driven geometry in architectural design using parametric modeling and genetic algorithms. Advanced Engineering Informatics, 25 (4), 656-675. https://doi.org/10.1016/j.aei.2011.07.009
Ugail, H. (2011). Partial differential equations for geometric design. Springer-Verlag. https://link.springer.com/book/10.1007/978-0-85729-784-6
Unwin, S. (2014). Analysing architecture. Routledge. https://www.amazon.com/Unwin-Student-Pack-Analysing-Architecture/dp/041571916X
Van Niekerk, R. (2010). The State of Geometry Education in South Africa. In Proceedings of the 16th Annual AMESA National Congress, South Africa, 1, 34-50. https://files.eric.ed.gov/fulltext/EJ835495.pdf
Velásquez Posada, A. M. (2013). Geometry as a tool for visual organization and proportion in designing aesthetic and attractive products. In DS 76: Proceedings of E&PDE 2013, the 15th International Conference on Engineering and Product Design Education, Dublin, Ireland, 288-293. https://asiachapter.designsociety.org/publication/34727/Geometry+as+a+tool+for+visual+organization+and+proportion+in+designing+aesthetic+and+attractive+products
Voyatzaki, M., & Spiridonidis, C. (Eds.). (2009). Architectural Design & Aconstruction Education: Experimentation Towards Integration. EAAE. https://architecture.web.auth.gr/wp-content/uploads/2014/02/voyatzaki-bio-short.pdf
Yu, R., Khan, A., Gu, N., & Lee, G. (2022). A Systematic Review of Architectural Design Collaboration in Immersive Virtual Environments. Designs, 6(5), 93. https://doi.org/10.3390/designs6050093
