Continuous sizing optimization of cold-formed steel portal frames with semi-rigid joints using generalized reduced gradient algorithm

Abstract The primary aim of this paper is to develop a sizing design optimization framework to address the optimization difficulties associated with semi-rigid Cold-Formed Steel (CFS) portal frames. The paper adopted the mathematical model to embed the influence of semi-rigidity for joints and column bases into the fully automated user-friendly program that was written by the authors to establish a relation between the finite element model, design formulations and optimization model. The paper employed Generalized Reduced Gradient (GRG) algorithm to optimize the cross-sectional areas for CFS Back-to-Back lipped channel sections. These sections used for primary load-carrying elements; in which sections' dimensions treated as continuous variables. The design constraints are set to satisfy design criteria proposed by British Standards and practical constraints from the industry. A systematic approach was followed in the parametric study to investigate the influence of several design parameters on the optimal solutions and performance of proposed buildings. The main parameters considered were the semi-rigidity effect of the apex and eave connections and column bases flexibility. The optimal results reached demonstrate the feasibility and efficiency of applying the proposed framework in solving the sizing optimization problem. GRG algorithm proved its reliability and validity with respect to its ability to achieve the optimal configurations of optimized sections. It showed that the frames modelled their joints as semi-rigid joints have smaller cross-sectional areas compared with the same frames having fully rigid joints. It found that the frames having semi-rigid column bases are lighter compared with their counterparts that modelled their bases as nominally pinned. The written program was effectively able to analyze, design and search the optimal solutions with a promising computational time.