Generation and Evaluation of Truss Structures for the Strut-and-Tie Model

Abstract

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.