A Heuristic Approach to Identify the Steel Grid Direction of R/C Slabs Using the Yield-Line Method for Analysis

In the last few years, nonregular reinforced concrete (R/C) slabs have become more popular in buildings and bridges due to architectural or functional requirements. In these cases, an optimum design method to obtain the ultimate load capacity and the minimum reinforcement amount should be used. For simple R/C slabs, the yield-line method is extensively used in engineering practice. In addition to strength, the “true” failure mechanism is also obtained by identifying the parameters that define it and minimizing the collapse load. Unfortunately, when the mechanism is too complicated to be described or defined by several parameters (e.g., in slabs with complicated geometry), the method becomes more difficult because the system of nonlinear equations becomes harder to solve through traditional methods. In this case, an efficient and robust algorithm becomes necessary. In this paper, a structural analysis of R/C slabs is performed by using the yield-line method in association with a zero-th order optimization algorithm (the sequential simplex method) to avoid calculating gradients as well as any derivatives. The constraints that often limit these parameters are taken into account through the exterior penalty function method, leading to a successful solution of the problem. Considering that the direction of each yield-line is sought by minimizing the ultimate load and finding the parameters defining the collapse mechanism, another parameter concerned with the direction of an orthotropic reinforcement grid is introduced. In this way, the number of unknown parameters increases, but aside from obtaining the ultimate load and the parameters defining the collapse mechanism, the solution also finds both best and worst reinforcement orientations.

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