Optimized dimensioning of steel-concrete composite beams

Abstract The steel-concrete composite sections are often used in civil building in Brazil and around the world. The connection of the steel profile and the concrete slab increases the performance of the composite structural element due to the use of the advantages of each material. In this article, a bar element is used with an interface element for nonlinear analysis of steel-concrete composite beams with partial interaction. The objective is to develop an algorithm that uses this analysis tool to design steel-concrete composite beams looking for project optimized in terms of material costs. Defined spans, supports, ultimate and service load, an optimization algorithm is used to define the dimensions of the rectangular cross section of the concrete slab, I-shaped steel profile, and the reinforcement bars of the concrete slab, so that the quantity of these materials are the minimum to ensure structural safety, considering the ultimate and service limit states. The design constraints are obtained from building code requirements for concrete, steel and composite structures. The objective function is defined as the cost per unit length of the composite beam, obtained from the unit cost of each material, steel, concrete and reinforcement. In the optimization process, the iterative method sequential linear programming is used, in which the nonlinear problem is approximated by a sequence of linear problems, which has its optimum point defined step by step by the Simplex method. Examples of composite beams with ultimate loads defined in the literature were used to validate the implementations. Other examples were analyzed, being evaluated at each iteration the restrictions and objective function to verify the efficiency of the algorithm.

摘要 钢-混凝土组合截面（steel-concrete composite sections）在巴西乃至全球的民用建筑中应用广泛。钢梁型材与混凝土板（concrete slab）的连接构造可充分发挥两种材料的性能优势，从而提升组合结构构件的整体性能。本文采用杆单元与界面单元（interface element）相结合的方法，对考虑部分剪力连接的钢-混凝土组合梁开展非线性分析。本研究的目标是开发一套基于该分析工具的钢-混凝土组合梁设计算法，以实现材料成本最优化的工程设计。在给定跨度、支座形式、极限荷载与正常使用荷载的前提下，该优化算法用于确定混凝土板的矩形截面尺寸、工字形钢梁（I-shaped steel profile）截面参数以及混凝土板配筋（reinforcement bars）用量，在满足极限状态与正常使用极限状态要求的前提下，使上述材料的总用量达到最小，从而保障结构安全。设计约束条件依据混凝土结构、钢结构及组合结构相关的建筑规范（building code）要求确定。目标函数定义为组合梁单位长度的总成本，该成本由钢材、混凝土及配筋的单位成本加权计算得到。优化过程采用序列线性规划（sequential linear programming）迭代方法：将非线性问题转化为一系列线性问题的近似序列，再通过单纯形法（Simplex method）逐步求解得到最优解。本文选取文献中已给出极限荷载的组合梁算例，对本算法的实现效果进行验证。此外还分析了其他算例，通过在每一次迭代中对约束条件与目标函数进行计算评估，验证了本算法的计算效率。