Optimality criteria-based minimum-weight design method for modular building systems subjected to generalised stiffness constraints: A comparative study

Recently, modular building construction has gained massive momentum as it continues to help many cities around the globe to tackle the ongoing housing crisis and the pressing demand for healthcare facilities during the pandemic. As a relatively new structural solution, there is a need to study modular buildings' optimal design. In this regard, previous studies focused only on employing optimisation techniques at the member level to enhance the structural capacity of steel beams in modular building systems (MBS). This paper explores the applicability and effectiveness of an optimality criteria (OC)-based minimum-weight design method in reducing self-weight of MBS while maintaining their overall lateral stiffness measured by natural frequency. This is achieved by pursuing an innovative optimisation investigation involving a three-storey, standalone MBS with hinged inter-module joints, together with a comparative moment-resisting frame (MRF) benchmark structure with two different beam-column connection rigidities. Continuous-valued sizing optimisation of two structural systems under a single frequency constraint is achieved through a novel, numerically stable, iterative OC algorithm. The latter is developed from frequency-related OC formulated rigorously through the Lagrange multiplier approach. The discrete minimum-weight design is supported by a mapping strategy designed to round the continuous optimum to the most economical standard steel sections. Pertinent numerical results show that the proposed method can achieve significant steel savings for the adopted MBS without compromising its modal stiffnesses. Further, it is found that the MRF structure with semi-rigid connections can meet the same target frequencies with slightly smaller steel tonnages. It is envisioned that this study will pave the way towards achieving more resilient and cost-effective modular units and tall modular buildings that further support the building industry in meeting its goals of construction efficiency and sustainability.