Strut-and-Tie modelling (STM) is a well-known approach to design D-regions in reinforced concrete structures. Because the STM method is based on lower-bound analysis, finding a suitable truss-analogy model is the most important aspect to guarantee good structural and economic performance of a resulting design. Continuum topology optimization (TO) methods have been studied for two decades to solve this problem. However, while these studies provide inspiration to designers, they lack the capability to automatically generate valid truss-analogy models as needed in the STM method. In order to prevent manual interpretation and automatically generate suitable STM models for various D-regions, a method is proposed for the generation of optimization-based STM (OPT-STM) models. The proposed method includes three phases: the TO phase, the topology extraction phase and the shape optimization phase. Next, in order to evaluate the effectiveness of the generated OPT-STM models, an evaluation using Nonlinear Finite Element Analysis (NLFEA) is performed to analyze the performance of STM models. For two D-region problems, two OPT-STM models and 11 manually constructed STM models from literature are evaluated, and their performance is compared and discussed, demonstrating the validity and effectiveness of the proposed automated generation method.

Strut-and-Tie modelling (STM) has proven to be a powerful method to design D-regions of reinforced concrete structures. STM uses truss analogy models to represent the stress field within the D-regions of concrete elements. Schematizing a suitable truss model is one of the most important aspects in the STM. Over the past decades, the use of Topology Optimization (TO) methods has been explored to inspire efficient truss models for the STM. However, it is at present still unclear whether these TO-based truss models benefit the STM. In order to investigate this question, this paper presents a case study based on a deep beam with an opening. Firstly, a TO-based STM model is generated which satisfies requirements of the axial force equilibrium and stress constraints of the STM method. Secondly, different STM designs are analysed by Nonlinear Finite Element Analysis (NFLEA), based both on classical STM models and TO-based models. The resulting steel usage, ultimate capacity and failure mode are used as measures to evaluate the designs. Finally, based on the generated STM model, two practical steel designs considering construction complexity are proposed and evaluated by NLFEA. The effectiveness of the TO-based STM model for this deep beam case has been demonstrated based on the evaluation results.

Defining a suitable truss model is one of the most important steps of applying the strut-and-tie modeling (STM) method to design D-regions in reinforced concrete (RC) structures. The truss model is a discrete representation of the stress field developed within a region of a concrete element. Topology optimization (TO) methods have been investigated by researchers for about two decades to generate suitable models for the STM method. Several truss models and numerous continuum TO results that could serve as an inspiration for suitable truss models have been proposed. However, limited attention has been paid to the evaluation of various TO results in the perspective of the STM method. As a result, it is at present unclear to what extent TO results offer a benefit for STM modeling, and which method should be preferred. In order to address this gap, an automatic and objective evaluation procedure is proposed in this paper. First, a TO result extraction method is proposed to systematically convert optimized topologies to truss-like structures. Next, based on the extracted structures, three evaluation measures are formulated to evaluate TO results. These measures indicate whether an analyzable truss model could be extracted, to which extent tensile stress regions are covered by tensile ties and how economical the design will be. The effectiveness of the proposed evaluation procedure is validated using known STM solutions. Subsequently, the evaluation procedure is applied to 23 TO results from the literature, covering three different design problems. Most TO results show a good performance in covering tensile regions and would result in economical designs, and some undesired topologies are also identified by the evaluation method. Nevertheless, the use of continuum TO is most hampered by difficulties in identifying a suitable truss from the TO results.

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.