Hybrid analytical and computational optimization methodology for structural shaping: Material-efficient mass timber beams

The building sector is responsible for a large portion of the global CO2e emissions. With structural materials accounting for a large part of it, the reduction of material used in buildings offers an important mitigation option to climate change. Standardized structural elements (eg. columns, beams, floors) have very low material efficiencies, as their shape does not consider the final use and load cases. New digital manufacturing technologies emerging in the field of construction and architecture, open new opportunities for the design of mass-customized structural elements, with the potential for more efficient use of materials in ubiquitous constructions. This paper offers a shaping methodology for the optimization of structural elements based on computational geometry and analytical mechanics. The paper implements the methodology for the shape optimization of mass timber beams. The methodology reveals that a large amount of structural material could be saved on standard structural timber elements. The accuracy of the solutions is benchmarked against analytical solutions and Finite Element Analysis (FEM). In order to implement the methodology for the optimization of timber beams, the analytical mechanics of shaped solid wooden beams are expanded from the existing literature and are presented in this paper. With the potential of being applied to a wider range of material systems, the methodology can significantly decrease the material consumption in a wide range of structural elements. Finally, the resulting optimized geometries demonstrate new objectives for the development of digital manufacturing techniques of mass-customized structures for the implementation in standard buildings.