Optimized Design of Reinforced Concrete Cross-Sections and Beams by Material Efficiency

Abstract

Reinforced concrete is the most popular construction material in the world and the production of one of its ingredients, Portland Cement, is responsible for 8% of global carbon emissions. The global focus on reducing carbon emissions is driving the development of novel materials and design methods to minimize the embodied carbon of reinforced concrete structures, such as optimization. A novel two-stage optimization approach was developed in this research which is based on maximizing the ratio of element resistance to embodied carbon, called the material efficiency. Unlike conventional optimization, the two-stage approach can search the solution space without the strength constraints being satisfied before converging to a final solution which satisfies the strength constraints. The freedom to temporarily violate the strength constraints increases the number of viable starting points for the optimization and allows the two-stage approach to advance where the conventional approach stops since it must satisfy the strength constraints at every iteration. The two-stage and conventional optimization approaches were implemented for the design of cross-sections in pure flexure and the design of beams considering flexure and shear, and the performance of both approaches was compared. It was found that the two-stage approach generally identified cross-sections with comparable embodied carbon to the conventional approach and converged in a comparable amount of time. The exceptions to that trend were design situations where the required strength and dimensional limits of the solution space severely limited the number of viable starting points for the conventional approach. In these cases, the two-stage approach identified solutions with lower embodied carbon although it required more time to converge. For the design of beams, the two-stage approach identified designs with similar or lower embodied carbon to the conventional approach although again taking more time to converge, constituting a trade-off between solution quality and speed. It was found that cross-sections could be effectively optimized with 25 randomly selected input designs and beams could be effectively optimized with 10 randomly selected input designs, both of which take less than 1 second with the conventional or two-stage optimization approach.