# Optimization of unbonded post-tensioned concrete ribberd floors

## Palavras-chave:

ribbed slabs, unbonded tendons, structural optimization, genetic algorithm, grid analogy, load-balancing method## Resumo

Floors represent a great portion of the total cost of multistory reinforced concrete structures.

The ribbed slabs, benefited by the reduction of concrete in the tension region, become a good alternative

when it is necessary to overcome large spans. Solutions more efficient with respect to structural behavior

and economy can be obtained combining the ribbed slabs with post-tensioning unbonded tendons. This

way, it is important to find the optimum section and vertical tendons profile which improve its capabili-

ties. The traditional design process can be aided by the use of optimization techniques. Hence, several

works with cost optimization of isolated ribbed slabs of reinforced and prestressed concrete have indica-

ted new design trends of formwork. In this research, it is performed the optimization of a typical one-way

multiple spans ribbed floor. Formulations to minimize the cost of the slab are studied, considering the

cost of material, formwork and labor. The design variables are the dimensions of formwork, the vertical

profile of unbonded post-tensioned tendons and the number of tendons, considering all variables as dis-

crete ones. The analysis is performed by grid analogy considering the entire floor, considering the beams

as non-deformable elements. A Finite Element Model is used to stress analyses. The load balancing

method is used to simulate the effect of prestressed unbonded tendons. Constraints on Serviceability and

Ultimate Limit States are verified. A Genetic Algorithm of an open-source program, that has presented

robustness for structural optimization, is used to solve the discrete optimization problem. In order to

investigate the effects of optimization process against the traditional modeling, literature examples have

been chosen trying to represent the widest range of cases faced in practice.