Sustainable design of reinforced concrete frames with non-prismatic beams

In this paper, sustainable design of reinforced concrete frames with non-prismatic beams is studied and relationship between optimal cost and optimal carbon dioxide emission in design of this type of frames is investigated. The objective functions are minimizing the CO₂ emissions and construction cost, and the design variables are defined as the geometry of the cross sections and reinforcing bars of the beams and columns, as well as the tapered length ratio for the non-prismatic beams. The performance of five metaheuristic algorithms consisting of the particle swarm optimization, colliding bodies optimization, enhanced colliding bodies optimization, vibrating particles system and enhanced vibrating particles system is compared for solution of Example 1. The most competent algorithm is identified, and the remaining examples are optimized using the identified algorithm to minimize the cost and CO₂ emissions. Numerical examples include reinforced concrete frames with prismatic beams, and frames with non-prismatic beams are optimally designed under equivalent static analysis to evaluate the objectives. Study of the results shows that compared to prismatic beams, in addition to achieving acceptable height in the floor of the structure, the use of non-prismatic beams in RC frames reduces the optimal economic costs and optimal CO₂ emissions.