Optimization of reinforced concrete polygonal sections under biaxial bending with axial force

Abstract Concrete is the world’s most utilized material for production of the structural elements employed in civil construction. Due to its low tensile strength and brittle nature it is reinforced with steel bars forming the reinforced concrete (RC structure). Linear elements of reinforced concrete are commonly employed in multi-story buildings, bridges, industrial sheds, among others. In this study an optimization algorithm is presented to define the amount of steel and its location within a concrete polygonal section subjected to biaxial bending with axial force, so that the amount of steel would be the minimum needed to resist the soliciting forces. Therefore, the project variables are: location, diameter and number of steel bars to be distributed within the concrete polygonal section. The sequential linear programming method is used to determine the optimized section. In this method, the non-linear problem of determining the resistance forces of the section in relation to the project variables is approximated by a sequence of linear problems, which would have its optimal point defined for each step using the Simplex method. Formulation validation is done through results of examples found in literature, and also by means of analytical solutions of simple problems, such as rectangular sections under axial force and moment in only one axis of symmetry. The results show the efficiency of the algorithm implemented in the optimized determination of the quantity and position of the bars of a given diameter in the polygonal section of reinforced concrete under biaxial bending with axial force.摘要：混凝土（Concrete）是全球民用建筑结构构件生产中应用最为广泛的材料。由于其抗拉强度低且质地脆性，通常通过配置钢筋形成钢筋混凝土（RC结构）对其进行补强。钢筋混凝土线性构件常被应用于多层建筑、桥梁、工业厂房等场景中。本研究提出了一种优化算法，用于确定承受轴力与双向弯曲作用的混凝土多边形截面内的钢筋用量及布置位置，以使钢筋用量达到抵抗外荷载所需的最小值。本次优化的设计变量为：混凝土多边形截面内需布置的钢筋的位置、直径及根数。本研究采用序列线性规划法（Sequential Linear Programming method）确定优化后的截面。该方法通过一系列线性问题近似求解与设计变量相关的截面抗力非线性问题，并在每一步骤中通过单纯形法（Simplex method）确定最优解。本研究通过文献中的算例结果以及简单问题的解析解（如单对称轴矩形截面受轴力与单轴弯矩作用的情况）对所提出的模型进行了验证。结果表明，所开发的算法可高效实现轴力与双向弯曲作用下钢筋混凝土多边形截面内给定直径钢筋的用量与布置位置的优化确定。