The Strut-and-Tie model (STM) is an efficient technique for the design of concrete structures, but the creation of suitable truss structures gets complicated when these structures become more complex. The topology optimization (TO) is a convenient technique that has been used in recent years for the creation of trusses of complex structures for the STM. This thesis presents a process for the creation of suitable truss structures for the STM using the results obtained with the TO, as well as, an evaluation of them to see which is the most optimal truss structure according to the total amount of tension force present on the full truss, this total amount of tension force is the selected evaluation criterion. Three deep concrete beams were analyzed using two topology optimization (SIMP and BESO approaches) for the generation of stress paths, these approaches are based on the minimization of the strain energy. The procedure starts with the computation of the principal stresses over the results of the topology optimization, then bar elements are placed over the stress paths of these diagrams creating a first (harsh) layout of the trusses. These trusses were not always found stable, but all the trusses were stabilized because, in this way, it is easy to calculate the axial force of in the truss elements, thus satisfy a basic requirement of the STM. To stabilize the truss structures two methods were explored. (i) The addition of new members outside of the stress paths (stabilizers), the essential characteristic of these new elements is that the axial force in them should be zero to not change the stress distribution found during the optimization process. A sensitivity analysis of the stabilizers was performed to track how the axial force changes in these members depending on the position of the nodes connected to them, this process was necessary because when an element outside the stress paths has axial force the stress diagrams have been changed. (ii) The creation of substructures within the stress paths, this process stabilizes the global structure without the addition of members outside the stress paths. Finally, a structural analysis was performed to obtain the axial forces in each member of the truss structure, and through an analysis of these results, the total amount of tension forces in the truss was computed. The truss with the minimum value of total tension force is assumed as the most optimal structure for each case. It is clear through the analysis that the variation of the input parameters does not cause large variations in the results of the topology optimization, but it has an impact in the stabilization process and the performance of the structures according to the evaluation criterion. Furthermore, it has been proved that suitable trusses for the STM can be created using any of the two selected optimization approaches obtaining good results, and a similar performance according to the evaluation criterion. ... Read more

The strut-and-tie method (STM) has been acknowledged as one of the most reliable tools for designing discontinuity regions in structural concrete. It is capable of producing safe designs consistently since it was developed as an extension of the lower-bound theorem of plasticity theory. However, to aptly address a physical problem of a concrete element, STM often relies heavily on engineering experience and intuition. It is because the current STM has an inability to be transparent in informing the nonlinear consequences of choosing a certain ST model design, which make the method to be troublesome in more complicated design tasks.

In this thesis, a supplementary evaluation technique that employs nonlinear finite element analysis (NLFEA) is proposed as a solution. It is advantageous to incorporate NLFEA because it can provide nonlinear behavior of a structural concrete as objective insights for making a more informed decision in determining a suitable ST model. To incorporate NLFEA to STM, the concept of 'ties-as-extended-rebars' or TER model is introduced. A TER model is a numerical model used to assess the influence of a certain ST model design toward the nonlinear behavior of a concrete element. Through a TER model, an ST model is nonlinearly evaluated as a concrete element with embedded reinforcements. Additionally, to allow the TER model to generate a representative failure, the rebars in the TER model are extended with straight anchorage length. Then, the information generated by the model, i.e. failure mode and ultimate capacity, can be utilized as additional information to find a fitting ST model.

To assess its ability, the proposed technique was implemented on six ST models generated for two complex concrete beam elements. The implementation provided the TER model versions of the ST models. At the same time, the experimental results of the ST models were also validated using NLFEA. The validation attempt generated six numerical validation (NV) results, which were then compared with the TER model results. The result of the comparison indicated that five out of six TER models were able to suggest failure mode and ultimate capacity (RTER) that are comparable with the failure mode and ultimate capacity (RNV) from the NV results. In more detail, RNV to RTER ratio of models with similar failure mode has an average of 1.04 and a coefficient of variation of 11.1%, which suggests that the proposed technique can provide representative ultimate capacity value with relatively low variability. ... Read more