## 9 Twisted, Tilted, Tapered, Freeform Diagrids  
Besides the notable structural efficiency of diagrid tubes in resisting lateral forces, one of the key factors which has led to their successful exploitation is their capacity for realizing complex-shaped structures. As a matter of fact, due to the versatility and modularity of the elementary triangular unit, diagrid systems can be effectively employed to build unconventional towers, such as twisted, tilted, tapered and even freeform structures. These unconventional shapes are extensively investigated by [PERSON] in [58; 59; 60]. A number of 60-story tall, twisted diagrid towers are analyzed under lateral loads, with various twisting rates, namely 0, 1, 2 and 3 degrees per floor [58; 59]. It is found that, as the rate of twist increases, diagrid lateral stiffness decreases and the top lateral deflection increases. This is mainly due to the fact that, the reference un-twisted structure being designed with the optimal diagonal angle, increasing the twisting leads to higher deviation of the diagonal angle from its optimal value. This in turn causes the lower efficiency of the twisted tower compared to the un-twisted structure. The same analysis is conducted for 80- and 100-story tall diagrid buildings, and the same conclusions are drawn in [59]. The performance of twisted diagrids is also investigated in terms of progressive collapse resistance and seismic performance by [PERSON] and [PERSON] [61]. Based on arbitrary column removal scenarios on a set of 36-story tall, twisted diagrid buildings, it is shown that the resistance against progressive collapse is decreased as the twisting angle increases, whereas the twisting angle is beneficial for improving the failure probability under seismic events. Tilted towers are also investigated in [58; 59], under both gravity and lateral loads. For 60-story tall diagrid buildings with various tilting angles (ranging from 0\({}^{\circ}\) to 13\({}^{\circ}\)), it is found that the top lateral  
Figure 17: Research on diagrid nodes: (**a**) CFST joint, used with permission from [PERSON] et al. [54]; (**b**) steel joint, used with permission from [PERSON] et al. [55]; (**c**) concrete spatial joints, used with permission from [PERSON] et al. [57]. displacement due to wind loads is not significantly affected by the tilting angle. Conversely, lateral displacements due to the eccentricity of gravity loads in tilted towers are found to be remarkably significant, and these can become even greater than the lateral displacements due to horizontal actions for great tilting angles. This aspect obviously needs to be taken into account carefully for the realization of tilted diagrid structures. [PERSON] [59; 60] also investigates the efficiency of tapered buildings compared to traditional vertical structures. Such an effectiveness arises from the more rational employment of the structural material in tapered tall buildings, since this is more abundant in the lower part of the structure, where the gravity, shear and bending actions are more important. As pointed out by the author, attention should be paid when generating the tapered diagrid frame, as the inclination of the external facades obviously affects the inclination of the diagonal members, which is known to be a crucial parameter in diagrid behavior. The analysis is carried out on a set of 60-, 80- and 100-story tall square diagrids under wind loads, with taper angles of 0, 1, 2 and 3 degrees. From the outcomes, it is shown that, as the taper angle increases, the top lateral deflection decreases, thus enhancing the lateral stiffness of the diagrid. This result is more significant as the building aspect ratio increases [59; 60]. Finally, diagrid structures with irregular shapes along the building elevation, namely freeform diagrids, are also analyzed. In particular, in [59], freeform geometries are generated using \"sine\" curves of various amplitudes and frequencies.