PSI - Issue 78

Alfonso Ferdinando Coniglio et al. / Procedia Structural Integrity 78 (2026) 1389–1395

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1. Introduction As highlighted in Jellen et al. (2013) and Coniglio et al. (2024), modular constructions are widely adopted in scenarios where the construction life cycle must be characterized by several core features, such as cost reduction, as well as the simplification of the design process and the possibility of structural component reuse. Literature largely encompasses studies in which the structural performance of a single component or the one related to building global behavior are considered. For example, inter-module connections are largely studied by Choi et al. (2015), Deng et al. (2017), Qiu et al. (2018), Dhanapal et al. (2020), Chen et al. (2017), Palmiotta et al. (2023, 2024), who studied connections behavior under lateral and vertical loads, carrying out numerical analyses and experimental tests. From a global perspective, in the study of Zhou et al. (2024) modular buildings behavior is optimized in an integrated design process, while Gunawardena et al. (2016), Srisangeerthanan et al. (2017), Lacey et al. (2021), Fathieh et al. (2016) and Palmiotta et al. (2023), analyse modular building from a seismic performance perspective. Modular buildings can be constructed with different levels of preassembly. Entire modules may be built off-site, as well as their sub-parts (i.e. beams, columns, bracings), as described in Gibb et al. (2003) and in Building and Construction Authority (2016). If sub-parts prefabrication is considered, many important characteristics should be highlighted: the assembly of the component in situ is more flexible, so more possibilities from an architectural point of view are guaranteed; the construction time in situ is longer because this technique needs more workmanship. From an emergency perspective, it is reasonable to focus on having a stock in which modular sub-parts are prefabricated regardless of the building yet to be realized. In fact, in emergency situations (i.e. construction after the earthquake), avoiding the production of sub part is crucial for the reduction of construction time. Consequently, modules sub-parts should be designed to guarantee certain performance in as many as possible scenarios, each of those defined by combinations of potential building geometries, use destinations and construction sites. Because literature presently lacks optimization methodologies that aim at this goal, the present work proposes a design methodology, based on a mathematical optimization process, that permits us to design the optimal structural properties of modules sub-parts. Following this methodology, it is possible to assemble bracing systems of predefined modular building typologies, that guarantee certain structural performance in as many site as possible of Italian territory. Initially, the methodology is presented. Then, some case studies regarding different types of modular buildings are analyzed, showing comparisons between the structural performance of the modular building typologies assembled using optimized sub-parts and those assembled with non-optimized ones. 2. Methodology The methodology proposed in this work is grounded in the formulation of a mathematical optimization problem, as first introduced in Dantzig (1947). Such problems involve the minimization or maximization of an objective function ( ): → , where x = (x 1 , x 2 , … , x n ) is the vector of independent variables. The goal is to determine the optimal values of that minimize or maximize ( ) . An optimization problem can be classified as either constrained or unconstrained, in the first case the independent variables must lie within a feasible interval defined by boundary conditions, in the unconstrained case, the variables can assume arbitrary values. The design of modules sub-parts can be cast as a mathematical optimization problem, as outlined below. 2.1. Definition of scenario vectors: functional configurations and loads conditions Modules sub-parts must be designed to work in different scenarios, i.e. in buildings with different functional configurations, as well as different load conditions. For this reason, as first, all the potential combination of geometrical configurations and load conditions must be defined. As for the functional configuration, Figure 1 represents a typological modular building of plant dimensions × and height = ℎ × , where ℎ and are respectively the inter-story height and the number of stories. , and are assumed as multiple of a base modular unit, having dimension 1 × 2 × ℎ . Moreover, is the number of bracing systems that absorb the seismic action in the direction considered. Now, for defining a number of building typologies that may be potentially realized with the module sub-parts, is fundamental to collect the geometrical parameters in the vectors =( 1 , 2 ,…, ), =( 1 , 2 ,…, ), =( 1 , 2 ,…, ) . Finally, for simplicity, only one value for each parameter 1 , 2 , ℎ, is assumed for the optimization problem, so these last parameters are represented as scalars. As for the seismic action, this is represented referring to MIT (2018), through which it is possible to define normalized pseudo-acceleration and displacement response spectra. Those spectra consist of a spectral shape multiplicated with the maximum value of ground acceleration on rigid soil. The pseudo-acceleration and displacement response spectra ordinates are thus function of the period T of a single degree of freedom (SDOF) oscillator schematizing the structure of modular buildings, the soil coefficient , the period , , that delimit respectively the constant acceleration, velocity and displacement fields of the spectra, the reduction factor for equivalents viscous damping coefficients different from