## 7 Non-Linear Analyses and Seismic Performance of Diagrid Structures  
Most of the studies that have been reported in Sections 2-6 deal with the investigation of the structural behavior of diagrid systems under static loads and within the linear elastic regime. Figure 16: Shear-lag coefficient in diagrids depending on the diagonal angle and building aspect ratio: (**a**) effect of aspect ratio under optimal angle; (**b**) effect of diagonal angle under fixed aspect ratio. Used with permission from [PERSON] and [PERSON] [40]. Although linear static analyses can provide extremely important information for the preliminary design stages, the non-linear response of diagrid tubes is of paramount importance for the evaluation of their performance. In the same way, analyses under dynamic loading conditions can reveal significant information, especially regarding the seismic assessment as well as the resistance against progressive collapse. One of the first works dealing with the seismic performance of diagrid tubes was carried out by [PERSON] and [PERSON] in 2012 [41]. In the study, the authors analyze a set of 36-story tall square buildings, with diagonal angles ranging from 50.2\({}^{\circ}\) to 79.5\({}^{\circ}\). Non-linear static analyses, i.e., push-over analyses, are carried out by applying lateral loads proportional to multi-mode story-wise distribution patterns. The non-linearity in the behavior of the structural members is also considered, according to FEMA-356's suggestions [42]. The outcomes show a rather brittle response from the diagrid structure when compared to the traditional framed tube, which shows more ductile behavior. Increasing the diagonal angle leads to lower ultimate shear forces carried by the diagrid before the final collapse. Non-linear dynamic analyses are also performed, where the equations of the motion of the structure subjected to seven different earthquakes are numerically solved. The outcomes reveal that greater diagonal angles are usually found to induce greater lateral displacements. It is also found that both the strength and ductility of the diagrid are increased when the diagonal members are replaced by buckling-restrained braces [41]. In a following paper, [PERSON] and [PERSON] [43] make use of non-linear static and dynamic analyses to investigate the existing capacity of axisymmetric rotor-type diagrid buildings against progressive collapse. Based on arbitrary column removal scenarios, the robustness of 33-story tall diagrids, with cylindrical, concave, convex and gourd shapes, is evaluated. The outcomes show satisfactory resisting capability against progressive collapse when one or two diagonal members are removed from the first level, regardless of the geometrical shape. However, concave-type buildings exhibit lower collapse resistance when two pairs of bracings are removed from the first story. In the study, a thorough investigation of the collapse strength and formation of plastic hinges is also carried out, depending on the diagonal inclination and location of member removal [43]. The ultimate capacity of diagrids in the damaged state, when certain diagonals are removed from the nominal structure, is also investigated by means of FE non-linear analyses, by [PERSON] et al. [44]. The results show that the ultimate resistance of diagrids upon damage is quite satisfactory, although it depends on the specific location of the bracing removal. In the same study, push-over analyses are carried out on a set of 40-story tall buildings, and their performance is evaluated in terms of strength, stiffness, ductility and sustainability aspects. Although not common, experimental tests on prototype models can also be carried out to investigate the dynamic properties of diagrid tubes. For example, [PERSON] et al. [45] perform shaking table tests on a Plexiglas model of the Guangzhou West Tower, and compare the resulting dynamic features (mode shapes, vibrational frequencies, acceleration magnification coefficients, etc.) to FE time-history calculations.