Optimal configuration of RC frames considering ultimate and serviceability limit state constraints

Marcela Alejandra Juliani,Wellison José de Santana Gomes

doi:10.1590/s1983-41952021000200004

Marcela Alejandra Juliani, Wellison José de Santana Gomes

Open Access

https://doi.org/10.1590/s1983-41952021000200004

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Abstract

Abstract Most current structural design codes are based on the concept of limit states, that is, when a structure fails to meet one of its purposes, it is said that it has reached its limit state. In the design of reinforced concrete structures, the Ultimate Limit State (ULS) and the Serviceability Limit State (SLS) must be checked. Therefore, this paper presents an optimization scheme for reinforced concrete plane frames, in which the objective is to minimize the cost of structures for three cases of constraints: the first is related to ULS and SLS; the second refers only to the ULS; and the third is related only to the SLS. Computational routines for checking limit states of beams and columns are implemented in MATLAB, following the requirements of the Brazilian code. Structural analyses are performed by using the MASTAN2 software, taking into account geometric nonlinearities and a simplified physical nonlinearity method. The objective function considers the cost of concrete, reinforcement and formwork, and the optimization problems are solved by genetic algorithms. Two numerical examples of frames are presented. Regarding the optimal characteristics related to each type of limit state, it is noted that the beams and columns tend to have larger and more reinforced cross sections in the case of the ULS. Even so, optimal structures related to the ULS often do not satisfy SLS and vice versa, which indicates that the optimal characteristics related to each limit state may be different. In addition, it is observed that the SLS is less restrictive than ULS.

Highlights

Due to the development of new technologies and the increase of market competitiveness, the search for more efficient and lower-cost designs has increased
Following a research which was started by Juliani and Gomes [33], [34], the present paper proposes to analyze the optimal configuration of reinforced concrete plane frames, through the minimization of its costs, considering three cases of constraints: the first is related to Ultimate Limit State (ULS) and Serviceability Limit State (SLS); the second refers only to the ULS; and the third is related only to the SLS
The design variables to be determined in the optimization process are adopted as discrete and illustrated in Figure 1, where: b and h are the cross section width and height, respectively, and the height is parallel to the plane of the frame; ns is the number of longitudinal reinforcement bars, whose diameter is represented by φs ; nsw is the number of transverse reinforcement bars, whose diameter is represented by φsw

Summary

Introduction

Due to the development of new technologies and the increase of market competitiveness, the search for more efficient and lower-cost designs has increased. At the same time, reinforced concrete has become a dominant structural material in engineering construction in many countries [1]. In this scenario, the importance of studies related to the design concept of reinforced concrete structures is valid. To ensure the safety of a structure, the engineer must choose a design option which meets the requirements related to its purpose. Due to the large number of variables usually involved in the design of reinforced concrete structures, there are several different configurations that can meet the required conditions, with different costs and performances. The choice of a configuration is not simple, which makes it difficult to obtain an optimal design using traditional methods. Optimization techniques have been widely employed with this purpose [2]–[4]

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Discussion

Conclusion