Group-Theoretic Symmetry Indices for Modular Building Layouts under Seismic Load Redistribution

Year : 2026 | Volume : 02 | Issue : 01 | Page : 01 07
    By

    Chethana N.S.,

  • Mohammed Almakki,

  • Mohammed El Khider,

  1. Research Student, Department of Mathematics, Central University of Karnataka, Karnataka, India
  2. Assistant Professor, School of Engineering, Architecture and Interior Design, Amity University Dubai, Dubai International Academic City, Dubai, United Arab Emirates
  3. Assistant Professor, Department of General Undergraduate Curriculum Requirements, University of Dubai, Dubai, United Arab Emirates

Abstract

Symmetry in modular buildings operates simultaneously as an architectural language, a structural regularizer, and a computational design variable. This paper develops a group-theoretic framework for evaluating and optimizing plan symmetry in modular buildings subjected to seismic load redistribution. The building layout is modeled as a finite occupancy–stiffness field defined on a rectangular lattice, where each module encodes both mass and stiffness contributions. Planar reflections and quarter-turn rotations are represented as elements of a dihedral group acting on module coordinates, enabling a rigorous algebraic description of symmetry transformations. A discrete continuous-symmetry measure is introduced to quantify the degree to which a given layout approximates invariance under these group actions. In parallel, a representation-theoretic decomposition of the mass and stiffness fields is performed, separating symmetric and antisymmetric components according to irreducible group representations. This decomposition provides insight into how deviations from symmetry influence structural behavior. Building on this, an asymmetry-driven torsional amplification index is defined to capture the coupling between lateral loads and rotational response under seismic excitation. These components are integrated into a multi-objective functional that balances structural regularity, inter-story drift control, material efficiency, and the practical advantages of modular repetition. Optimization is carried out by projecting design updates onto invariant subspaces, ensuring that symmetry constraints are preserved throughout the iterative process. To account for real-world uncertainties such as connection variability and fabrication tolerances, a fuzzy penalty term is incorporated, allowing controlled deviations from ideal symmetry. Theoretical analysis establishes bounds demonstrating that the torsional component of the seismic response is governed by the norm of the antisymmetric load–stiffness residual. A synthetic case study of a twelve-story modular frame illustrates the framework’s effectiveness: layouts with identical gross floor area exhibit significantly different seismic performance when their mass and stiffness distributions differ in symmetry content. These results highlight the critical role of symmetry in enhancing seismic resilience and guiding modular design.

Keywords: architectural symmetry, group theory, modular building, seismic design, load redistribution, continuous symmetry measure

[This article belongs to Emerging Trends in Symmetry ]

How to cite this article:
Chethana N.S., Mohammed Almakki, Mohammed El Khider. Group-Theoretic Symmetry Indices for Modular Building Layouts under Seismic Load Redistribution. Emerging Trends in Symmetry. 2026; 02(01):01-07.
How to cite this URL:
Chethana N.S., Mohammed Almakki, Mohammed El Khider. Group-Theoretic Symmetry Indices for Modular Building Layouts under Seismic Load Redistribution. Emerging Trends in Symmetry. 2026; 02(01):01-07. Available from: https://journals.stmjournals.com/etsy/article=2026/view=247377


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Regular Issue Subscription Original Research
Volume 02
Issue 01
Received 14/03/2026
Accepted 22/04/2026
Published 30/04/2026
Publication Time 47 Days
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