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

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.

摘要 目前主流结构设计规范均以极限状态设计理念为核心：当结构无法满足既定功能要求时，即判定其达到极限状态。在钢筋混凝土结构设计流程中，必须同时验算承载能力极限状态（Ultimate Limit State，ULS）与正常使用极限状态（Serviceability Limit State，SLS）。为此，本文提出一种钢筋混凝土平面框架的优化设计方案，以三种约束工况下的结构总造价最小化为优化目标：其一同时涵盖ULS与SLS约束；其二仅针对ULS约束；其三仅针对SLS约束。

本文遵循巴西结构设计规范的要求，在MATLAB平台中编写了梁、柱极限状态验算的专用计算程序。结构分析环节采用MASTAN2软件完成，同时考虑几何非线性因素，并采用简化物理非线性分析方法。目标函数综合考量混凝土、钢筋与模板的生产成本，优化问题通过遗传算法求解。文中给出两个平面框架数值算例。

针对不同极限状态约束对应的优化设计特性，研究结果表明：仅考虑ULS约束时，梁与柱的截面尺寸往往更大，配筋率也更高。即便如此，仅满足ULS约束的优化结构通常无法通过SLS验算，反之亦然，这说明不同极限状态对应的最优设计特性存在显著差异。此外，研究还观测到SLS约束的严苛程度低于ULS约束。