Optimal Design and Competitive Spans of Timber Floor Joists Based on Multi-Parametric MINLP Optimization

This study investigates the optimization of the design of timber floor joists, taking into account the self-manufacturing costs and the discrete sizes of the structure. This non-linear and discrete class of optimization problem was solved with the multi-parametric mixed-integer non-linear programming (MINLP). An MINLP optimization model was developed. In the model, an accurate objective function of the material and labor costs of the structure was subjected to design, strength, vibration and deflection (in)equality constraints, defined according to Eurocode regulations. The optimal design of timber floor joists was investigated for different floor systems, different materials (sawn wood and glulam), different load sharing systems, different vertical imposed loads, different spans, and different alternatives of discrete cross-sections. For the above parameters, 380 individual MINLP optimizations were performed. Based on the results obtained, a recommended optimal design for timber floor joists was developed. Engineers can select from the recommendations the optimal design system for a given imposed load and span of the structure. Economically suitable spans for timber floor joists structures were found. The current knowledge of competitive spans for timber floor joists is extended based on cost optimization and Eurocode standards.