Optimization-based three-dimensional strut-and-tie model generation for reinforced concrete

Strut-and-tie modelling (STM) is an effective and widely used method to design disturbed regions (D-regions) of reinforced concrete structures. Among the various steps of STM, finding a suitable truss-analogy model is the most challenging part. Even for experienced engineers it is difficult to find representative models for complex D-regions, and this task is even harder for three-dimensional (3D) D-regions. To date, only a few 3D STM models have been proposed by researchers for several complex D-regions, which leaves practitioners with little guidance. In order to solve this problem, a method is proposed to automatically generate 3D optimization-based STM (3D-OPT-STM) models. The generation method comprises a compliance-based topology optimization process that generates optimized structural forms by maximizing stiffness, a topology extraction method, and a shape optimization method. In this study, three 3D-OPT-STM models are generated for typical 3D D-regions, and their performances are compared to manually created STM models. The generated 3D-OPT-STM models result in more economical designs. Moreover, geometrical and loading parameter studies demonstrate the applicability and robustness of the proposed method.