Abstract
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.
Highlights
As seções mistas de aço e concreto estão cada vez mais sendo utilizadas na construção civil, tanto no cenário mundial quanto no Brasil
A bar element is used with an interface element for nonlinear analysis of steel-concrete composite beams with partial interaction
Considering composite beam simulated by a bar element for the section above of the slip interface and another bar element for the section below that interface, the interface element has the function of connecting these bar elements and simulating the deformable connection at the slip interface
Summary
With the increasing use of computers together with computational mechanics to solve structural analysis problems, optimization processes have become an important tool for engineering. There exists an unlimited number (continuous variables) or large (discrete variables) of solutions to the problem In view of this context, the objective of this work is to create an algorithm that uses tools for composite beam structural analysis searching for an optimized design in terms of quantity and cost of materials. The technique used was MINLP (Mixed Integer Nonlinear Programming) that solves problems of nonlinear optimization with discrete and continuous variables For this analysis, the authors verified the ultimate and service limit state and the objective function considers execution and material cost. Silva et al [20] presented the optimization of steel-concrete composite beams modeled and discretized in bar finite elements using the linear programming method associated with the Simplex method. The design constraints were defined from the maximum stresses in the materials obtained considering physical linear analysis
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