## 1 Introduction  
The evolution of tall buildings has undergone remarkable developments in the last century. The first buildings reaching a few tens of stories were first built in the United States in the late 19 th century, mostly in the cities of New York and Chicago. At the beginning of the 20 th century, a race for the realization of the tallest skyscrapers took place, which led to the completion of the 102-story tall Empire State Building in 1931 (Figure 1a). Although at that time the height of those buildings was worthy of note, their realization was not achieved by means of significant technological innovations. They usually employed the same steel frames which were adopted for shorter buildings, leading to excessive material usage and rather over-designed solutions [1]. Bracings were employed to withstand lateral loads arising from wind pressures and earthquake actions. It was already recognized that lateral actions usually govern the design solutions in tall buildings. In fact, as the building becomes taller, the lateral drifts turn out to be more critical, and there is greater demand for suitable structural systems to carry lateral forces. This leads to a dramatic increase of material consumption with the increase in the number of stories, which is usually referred to as the \"premium for height\" [1,2]. Due to aesthetic and constructability considerations, the bracings were usually embedded within the interior core of the building. Although their shear resistance, based on the axial deformation of the diagonals, was beneficial in resisting the lateral actions, compared to the mechanism of the conventional moment resisting frames, their placement within the interior of the building prevented their effective employment in withstanding the overturning moment. Therefore, new solutions exploiting bracings on the external perimeter of the building were developed. One of the first examples was the 100-story tall John Hancock Center built in Chicago in 1970 (Figure 1b). The John Hancock is an example of braced tube, where the mega-diagonals spanning over several stories are effective in resisting the shear and bending moment deriving from lateral actions. The braced tube was a variation of the typical framed tube, where closely spaced perimeter columns were in charge of providing the necessary lateral stiffness. The adoption of mega-diagonals on the external surface offered higher lateral stiffness, while reducing some detrimental phenomena of the framed tube, such as the shear-lag effect. With this new solution, a greater number of stories and an overall enhanced structural performance could be achieved, leading also to important advantages from a material consumption perspective. Based on the structural behavior of the braced tube, where vertical columns and external bracings were designed to carry gravity and lateral loads respectively, it was realized that the external mega-diagonals were able to resist vertical and horizontal loads simultaneously, without the need for conventional vertical columns. This led to the realization of the diagrid (\"diagonal\" + \"grid\") structural system. The idea of removing vertical columns and considering only inclined diagonals was not new. As a matter of fact, the first diagrid structure was realized before the construction of the [PERSON] braced tube, in the 1920s, by the Russian architect [PERSON], for the realization of a broadcasting tower in Moscow [3]. The external pattern, made up of a triangular tessellation, allowed the reduction of the wind load while reaching a stable stiff configuration. The first application of a diagrid system in building design occurred in the 1960s, with the completion of the 13-story tall IBM Building (Pittsburgh, USA). The steel diagrid exoskeleton was integrated with the glazing system, and assisted in the overall stability of the building [3]. However, it was not until the early 21 st century that diagrid systems started to be thoroughly applied in the design and construction of tall buildings.