## 4 Optimization of Diagrid Performance Based on the Geometrical Features  
Besides the great stiffness of the diagonalized facades and their capacity for realizing complex-shaped systems, one of the main successful aspects of diagrids is the possibility they  
Figure 7: External steel diagrid tube coupled with a central concrete core. Distribution of: (**a**) shear forces; (**b**) bending moments; (**c**) torque moments, according to the matrix-based method (MBM) and General Algorithm (GA). Used with permission from [PERSON] et al. [18]. offer of reaching high structural performance standards, thanks to the optimization of the geometrical features. In the last decade, various researchers have thoroughly investigated the structural behavior of diagrids upon changing the external diagonal pattern, in order to reach the optimal solutions. [PERSON] et al. [10] show for the first time that there exists a diagonal angle capable of satisfying the stiffness requirements with the minimum amount of employed material. The optimal angle results from the need to limit both shear and bending deformation, and it is found to increase as the aspect ratio of the building increases. As already remarked in Section 2, for 60-story tall diagrids with an aspect ratio of about 7, the optimal angle is in the range 65\({}^{\circ}\)-75\({}^{\circ}\), while it decreases to about 10\({}^{\circ}\) for aspect ratios close to 5 [10]. Approximately the same results are found in [12] for a set of 40- to 100-story tall diagrids. Under lateral actions, shear forces and bending moments have different trends along the building's elevation. For example, if we consider a uniform horizontal load, the shear force is zero at the top of the building and increases linearly towards the base, while the bending moment increases quadratically. This means that the need to resist shear and bending actions is different in different parts of the structure. Shear force prevails in the upper portion, while bending moment drives the design of the lower part. Based on this consideration, [PERSON] investigates diagrid buildings with different patterns of diagonal angles [12]. Figure 8a shows a varying-angle diagrid with steeper angles at the base, Figure 8b a uniform-angle diagrid, and Figure 8c a varying-angle diagrid with steeper angles at the top. Steeper diagonals are more suitable for carrying bending moment, while shallower diagonals are more appropriate for carrying shear force. Therefore, the solution in Figure 8a should enhance the structural performance of the diagrid. Conversely, the solution with steeper diagonals at the top behaves against structural logic, and is only considered for the sake of completeness, as it is not supposed to provide any beneficial effect. Based on the results, it is found that, for shorter buildings with aspect ratios lower than 7, the uniform-angle configuration provides the most efficient design in terms of material consumption. Shorter buildings behave like shear beams, and while the steeper diagonals at the base enhance the bending stiffness, the negative effect of the reduced shear rigidity causes the varying-angle diagrids to lose efficiency. Contrariwise, for taller buildings with aspect ratios greater than 7, the bending behavior prevails. The reduced shear rigidity at the base due to the steeper diagonals is balanced by the significant increase in bending stiffness. Therefore, in this case, the varying-angle configuration is found to provide the most efficient solution [12]. The same results are found in another paper by [PERSON] [30], where the author also takes into account the \"speed\" of variation of the diagonal angles along the height of the building, with smooth or more radical changes.