Parametric Optimization of a Cross-Beam Glulam Floor System Using Response Surface Methodology

Cross-beam glued-laminated timber (glulam) floor systems offer material efficiency but pose a complex design challenge due to three-dimensional (3D) load interactions, and systematic optimization guidelines are lacking. This study implements a parametric optimization framework using a three-factor Design of Experiments (DOE) approach (beam spacing ratio, height-to-span ratio, width-to-height ratio). A total of 27 full-factorial finite element models (FEMs) were simulated in Dlubal RFEM. A second-order response surface methodology (RSM) model was developed to predict the load utilization factor (Y) in accordance with Eurocode 5. The predictive model demonstrated high statistical accuracy (R2 > 0.98). A multi-criteria optimization using the Pareto frontier identified a balanced solution (x1 = 0.250, x2 = 0.042, x3 = 0.5) that achieved 97.4% load utilization (Y = 0.974). This optimal configuration reduces the required timber volume by approximately 10% compared with other efficient designs and by over 60% compared with inefficient (Y ≈ 0.5) but safe designs within the experimental space. The resulting regression model provides a validated engineering tool for designing materially efficient glulam floor systems, allowing designers to balance structural safety with material economy.