Understanding the cyclic response of RC walls with setback discontinuities through a finite element model and a strut-and-tie model

Slender RC walls are often used in Chile and commonly, due to architectural constraint, the length of walls increases (setback) between floors designated for parking space and upper floors. These types of elements are commonly called flag walls. In this research, the behavior of slender reinforced concrete walls with a constant axial load and a cyclic lateral displacement is numerically studied, in order to compare the results obtained with previous tests. Two different model alternatives are considered: a finite element model and a strut-and-tie model. The selected models allow understanding local response, as well as, distribution of internal forces, which is also relevant information for wall design and detailing. The studied finite element model, based on quadrilateral elements with 3 degrees of freedom per node (2 translational and 1 rotation) and a model of smeared reinforced concrete material based on a rotating angle approach, is able to correctly capture the global response, showing the capacity, degradation and failure mode obtained in the tests. On the other hand, a parametric analysis is performed for models of walls with higher aspect ratio (tall buildings) with small discontinuities, showing a larger impact in deformation capacity due to the high concentration of damage at the discontinuity. These results indicate that in 25-floor high walls (or taller) a reduction of displacement capacity of 40% for discontinuities located at the first floor could be observed. In addition, by incorporating the effect of the slabs into the model, the results indicate that a pure flexure model is an adequate and sufficient tool for analysis. Finally, a strut-and-tie model is also proposed for each direction of the lateral load, whose results are compared with the estimated load calculated with the strains measured by photogrammetry. The considered strut-and-tie model for the case of lateral load with tension in the continuous wall boundary is similar to the wall without discontinuity, which is consistent with the measured strains. For both lateral loading directions, the estimated forces of the horizontally distributed bars and boundary reinforcements are consistent with photogrammetry in the lower zone of the wall, where cracking is relevant. The strut-and-tie model also adequately interprets the effect of the discontinuous bar on the discontinuous boundary of the wall. All these results can help designing and detailing flag walls.