## 10 New Evolutions of Grid Structures: Hexgrids and Beyond  
A further development of grid tubular structures in the realization of tall buildings has been inspired by natural materials, such as the honeycomb pattern (beehive). This is the case of hexagrids, where six-node hexagonal elements are placed all over the building perimeter to resist gravity and lateral loads. Examples are the Sinosteel International Plaza in Tianjin and the Al Bahr Towers in Abu Dhabi. Hexagrids can mainly be divided into two types, according to the orientation of the hexagonal cell: horizontal hexagrids, where the hexagon is composed of four diagonal members and two horizontal beams, and vertical hexagrids, where the four diagonals are coupled with two vertical columns. The different orientation of the basic hexagonal unit obviously leads to differences in the structural performance, which need to be investigated in the preliminary design. Although the concept of hexagrids is very similar to diagrids, both exploiting an external tubular structure to withstand external actions, their structural behavior is someway different. As a matter of fact, diagrids resist gravity, shear and bending actions mainly via the axial stress of the diagonal members. Conversely, besides the axial forces in the hexagonal members, the resisting mechanism of hexagrids also involves the bending deformation of the diagonals and of the horizontal/vertical elements. Based on the seminal work from [PERSON] [62], [PERSON] et al. [63] investigate the mechanical properties of hexagrid structures and their applicability in tall buildings. A general homogenization approach is applied, where the hexagrid tube is converted into an equivalent orthotropic solid membrane (Figure 18a). The hexagonal module and the unit cell are defined (Figure 18b), and representative volume elements (RVEs) are identified based on the loading conditions. A stiffness-based approach then follows, to calculate the equivalent elastic properties of the solid tube, based on the grid's mechanical and geometrical properties. Note that in Figure 18 the horizontal hexagrid is shown, with diagonal members and horizontal beams. The same scheme has also been adopted to investigate hexagrids with vertical elements [63]. Based on the stiffness equivalence, both the equivalent elastic axial modulus \(E^{*}\) and shear modulus \(G^{*}\)are evaluated, and subsequently employed to calculate the displacements of the building's equivalent cantilever. The effect of rigid floor diaphragms is also investigated, as they are found to have a strong impact on the evaluation of \(E^{*}\) through the modification of the RVE. The application of the simplified methodology is carried out on a 90-story tall hexagrid building, by changing the module height and the inclination of the diagonal members. A comparative analysis is also performed with similar diagrid structures [63]. From the results, it is found that the optimal angle of the diagonal members is close to \(60^{\circ}\) for horizontal hexagrids, whereas it is lower for vertical hexagrids, lying in the range \(40^{\circ}\)-\(50^{\circ}\). Compared to diagrid structures, the hexagrids are usually less stiff, being more bending-dominated, and consequently less structurally efficient. However, they can provide new architectural solutions with notable aesthetic effects. The structural performance of hexagrid systems is also investigated by [PERSON] and [PERSON] [64], who focus on 60-story tall square buildings. Different patterns of horizontal and vertical hexagrids, coupled with a central core, are analyzed under gravity and load actions. It is found that the vertical hexagrids are usually stiffer than the horizontal ones under lateral actions. This is mainly due to the axial contribution of the vertical elements in the flange facades.