Automatic generation of strut-and-tie models in R.C. elements using load paths

The Strut-and-Tie (S&T) method is an effective and widely used tool for the design of disturbed regions (D-regions) in reinforced concrete structures. The manual search of S&T models is inefficient, time-consuming and requires a considerable amount of expertise, especially in the case of complex D-regions. This work presents the theoretical framework, the mathematical formulation and the algorithms of a novel procedure for the automatic generation of S&T models in two-dimensional (2D) reinforced concrete elements. The proposed procedure represents a first attempt to combine a ground structure approach with the load path theory. In particular, the search for optimal S&T models is translated into a non-linear mathematical programming problem in which both topology and geometry of an initial ground structure, generated through a curvature analysis of load paths, are simultaneously optimized. The consistency of the solution with the elastic stress field and the practicality of the final reinforcement layout are accounted in the mathematical formulation of the optimization problem. A possible solution strategy based on an implicit programming approach is also presented. Results of several case studies demonstrate that the proposed procedure is qualified for the automatic generation of suitable S&T models in D-regions.