Assessing reinforced concrete structures with generated strut-and-tie models – Concrete E-Learning Platform

Link zur deutschen Version: Überprüfung von Stahlbetontragwerken mittels generierter Fachwerkmodelle

Strut-and-tie models enable the interpretable modelling of reinforced concrete (RC) structures with discontinuities by visualising the force flow and giving the engineer control over the load path. They are particularly useful for the design of new structures and for the validation of nonlinear finite element (NLFE) analysis results. However, when the reinforcement layout and geometry are already available, such as in the case of structural assessment, the manual derivation of strut-and-tie models remains challenging and time-intensive, and requires considerable engineering judgement similar to that in the design with strut-and-tie models. This blog post presents our newly published approach for reverse engineering strut-and-tie models given the reinforcement layout, geometry, material properties and proportional load cases [1]. The corresponding code is available open-access.

Although lean RC-specific NLFE analyses are increasingly being used in the structural assessment of existing RC structures, their results and interpretation may suffer from modelling errors or hyperparameter sensitivities. Oftentimes, practising engineers employ simple hand calculations to validate the NLFE analysis results, among which strut-and-tie models are particularly suitable for complex geometries or load patterns (discontinuity regions). An automated tool to reverse engineer strut-and-tie models could therefore support the understanding of the structural design concept and help bridge the gap between interpretability and advanced computational analysis.

Various structural optimisation methods, ranging from continuum topology optimisation and discrete layout optimisation to generative grammars (see past blog post and follow-up works [2]), have been applied to generate strut-and-tie models for structural design in new structures. For this purpose, such methods typically aim to minimise compliance (maximise stiffness), material volume (reduce environmental impact) or costs, while few consider the aspects of constructability. In structural assessment, these objectives are usually given, as the structure has already been built. Assessment is usually motivated by a change in use or loads, or by concerns regarding structural safety. Since serviceability aspects can be checked through visual inspections or measurements, they can be excluded from the optimisation process. Therefore, the primary goal in structural assessment is to maximise the load-bearing capacity while assuming sufficient stiffness. This shift in requirements changes the optimisation problem and its objectives and constraints. While the geometric design flexibility of continuum topology optimisation and generative grammars is particularly advantageous for the design of new structures, the rigid ground structure used in discrete layout optimisation allows the existing reinforcement layout to be easily incorporated.

Accordingly, our recently developed method employs the latter structural optimisation method and includes two stages. The entire process is illustrated in Figure 1. Stage 1 uses discrete layout optimisation with an adaptive layout and sequential thresholding to obtain a first topology. As this stage does not account for overlapping or closely spaced struts, Stage 2 aims to further simplify the truss topology. Stage 2 employs member reduction methods, node detection, clustering and a nonlinear nonconvex geometry optimisation to improve the topology.¹

Figure 1: Overview of the proposed two-stage method for reverse engineering strut-and-tie models.

For the implementation, general strut-and-tie modelling design guidelines are assumed, such as the provision of minimum reinforcement required for ductility. For the visualisation with plasticity-based discontinuous stress fields, the stress fields are treated as statically equivalent to the corresponding strut-and-tie models. This means that the centre lines of the concentrated stress fields coincide with the axes of the strut-and-tie model members. The struts are compressed uniaxially and the nodal zones are pseudo-hydrostatic with an effective concrete compressive strength equal to $f_{cd}$ . Hence, neither compression softening nor confinement is considered. Furthermore, a common constant maximum strut width is assumed, which limits the admissible strut force. These assumptions may result in higher predicted ultimate loads compared to models that use a more realistic material behaviour (e.g. considering compression softening or tension stiffening) or continuum-based analyses.

Figure 2 presents the classical example of the dapped-end beam taken from the literature. The dapped-end beam has a simple geometry and was originally designed for a single load case, resulting in four different solutions. Based on these reinforcement layouts, the strut-and-tie models are reverse engineered. They resemble the original strut-and-tie models and are already relatively simple after Stage 1 so that Stage 2 only provides minor improvements. Hence, for simpler problems Stage 1 is often sufficient for discovering suitable strut-and-tie models.

Figure 2: Reverse engineered strut-and-tie models (STMs) for the dapped-end beam with a) structural problem, b) reinforcement layout, ground structures and strut-and-tie models [1].

In contrast, Figure 3 depicts a more complex and more practically relevant example of a wall with two openings from the literature. The wall has been designed for multiple load cases, one of which is shown here. Both the reverse engineered strut-and-tie model and corresponding plasticity-based discontinuous stress fields visualise the force flow well. The predicted ultimate load after Stage 2 is significantly higher than the original design load (based on hand calculations). However, because the struts at the left support barely fit within the continuum geometry and because of the influence of compression softening, the actual ultimate load is likely lower and closer to the original design load of 2,000 kN.

Figure 3: Reverse engineered strut-and-tie models for a wall with two openings with a) structural problem, b) reinforcement layout and c) load case, strut-and-tie models and corresponding plasticity-based discontinuous stress fields [1].

The proposed two-stage method combines concepts from structural optimisation to bridge the gap between interpretable structural modelling and advanced computational methods for engineering practice. Nonetheless, future work should consider more realistic material modelling (including compression softening), an improved estimation of the maximum strut width and the incorporation of certain requirements (e.g. compliance or serviceability behaviour), while validation with experiments or lean RC-specific NLFE analyses is also necessary. If you have any feedback, feel free to reach out to Karin Yu.

Karin Yu

Referenzen

K. Yu, W. Kaufmann. Reverse engineering strut-and-tie models for assessing reinforced concrete structures. Structural Concrete, 2026, doi.org/10.1002/suco.70637
K. Yu, E. Chatzi, W. Kaufmann, M. A. Kraus. Guided generation of strut-and-tie models for reinforced concrete structures with parametric graph grammatical evolution. Advanced Engineering Informatics, 2026. Volume 271, 104302, doi.org/10.1016/j.aei.2025.104302