On the application of the sequential simplex method in the yield-line analysis of R/C slabs

The yield-line method is extensively used in engineering practice whenever simple R/C slabs are to be analysed at ultimate. Though the kinematic method generally leads to more or less unconservative results, it is highly appreciated because in many cases it is relatively easy to workout the “true” failure mechanism by identifying its parameters through the minimization of the collapse load. Unfortunately, when the ultimate load depends on many parameters, the method is difficult to use, even for slabs with not so many parameters; in fact since the number of non-linear equations required by the method is equal to the number of the parameters, when the parameters increase the difficulty of the solution increases rapidly as well. In this paper the sequential simplex method is used in association with the yield- line method in the structural analysis of R/C slabs whose collapse mechanism requires many parameters. This algorithm is robust and efficient even with many parameters. Besides taking into account the constraints that often limit these parameters, the algorithm is easy to use with the exterior penalty function method leading to a successful solution of the problem. Considering that the yield-line method seeks the direction of each line that maximizes the ultimate moment, this paper considers a further parameter concerning the two orthogonal directions of an orthotropic reinforcement. In this way the number of unknown parameters increases, but the solution shows both the least and the most favourable direction of reinforcement.