On the automatic generation of strut and tie patterns under multiple load cases with application to the aseismic design of concrete structures

Strut-and-tie modelling (STM) is a well-known technique for the design of the discontinuity regions in reinforced concrete structures, that is mainly based on the research of suitable load paths to transfer external forces to constraints. A simple energetic approach resorting to the minimum compliance optimization is herein implemented to derive truss-like models for the preliminary design of discontinuity regions under multiple load conditions. Peculiar attention is paid to the effect of the horizontal forces, as the ones induced by the seismic action, which act upon corbels and beam-column connections along with gravity loads. Numerical investigations in the bidimensional framework point out the remarkable crossing of stress-fluxes that must be handled in the bulk of the joints and calls for ad hoc shear reinforcement in the critical zone at the top of the columns. The methodology is also applied within the three-dimensional framework, addressing the design of box-shaped structures under multiple load cases. The achieved results show the arising of helix-shaped strut-and-tie layouts that are well-suited to cope with torsional actions. In the case of holes in the sides of the specimen, such a reinforcement must be detailed in order to handle peak stresses in the corner regions.