3.1.3. Twister and Tordos

Buildings of this type are in the form of a twisted solid with the "twister" facade repeated on all floors (Figure 3a). Buildings with an orthogonal core and one or two twisted towers belong to the category of "toros" (Figure 3b). The conversion tower axis of the helical form the Revolution Tower (Figure 3c) may be derived from orientation of asymmetric floors not through the center of the circular segment stories, but the center of gravity of the floor. The body of the building belongs to the category of "sliding twister" (Figure 3c), where the floors are moved upward along the 2D or 3D curve and rotation is added to the outer structure. When the 3D curve rotation has the shape of a spiral it belongs to the category of "helical twister" (Figure 3d,e). The intersecting body of the building, in the shape of a twisted spiral, has an internal vertical zone dedicated to the lift shaft.

**Figure 3.** Twister and Tordos types of high-rise building: (**a**) Turning Torso (Malmö, mega core system), (**b**) Al Bidda Tower (Doha, wall frame system), (**c**) Revolution Tower (Panama City, core system), (**d**) Evolution Tower (Moscow, core system)) and (**e**) Mode Gakuen Spiral Towers (Nagoya, tube system), figure by authors.

### 3.1.4. Free Form

The free geometry building form is constructed using a combination of geometrically simple objects (lines, surfaces and solids), when the sequence of the architect's actions is not obvious and the form does not fit into any other category. In this category we can distinguish the subcategory "slicer". It includes buildings that have a curved facade with balconies and other extended elements. Figure 4a shows the curved outer surface obtained by the contours of winding balconies around a rectangular solid. Alternatively, the curved segments of the balconies can be repeated on the upper floors with their rotation (Figure 4b). This vertical twisting of the outer surface is formed in a cross-section that is not a straight line but a curve. The receding facade of the building in Figure 4b is decorated with flat elements. The smooth surface of the building in Figure 4c is obtained by a large number of blinds. The verticality of railings is less obvious in high-rise buildings than in low buildings (Figure 4d), where the facade is rather stepped and does not create a smoothed curve. The building is classified in the "sliced twister" category (Figure 4b) when it has repeated vertical floors with horizontal rotation.

**Figure 4.** Free form type of high-rise buildings: (**a**) Aqua Tower (Chicago, core and outrigger system), (**b**) Burj Al Arab (Dubai, composite frame system with diagonal steel trusses), (**c**) Flame Towers (Baku, frame tube system) and (**d**) Sheraton Huzhou Hot Spring Resort (Huzhou, core system), figure by authors.

High-rise shaping is largely related to the numerical modeling tools that architects have available. Simple modeling procedures enable intuitive shaping of complex geometry, however mathematical analysis is required because the consequences for the structure are considerable.

### *3.2. Innovations in Structural Systems*

### 3.2.1. Structural Systems

The relationship between structure and architectural form has reached its peak in present times. Form and structure have become inseparable and complementary [15]. The primary structural skeleton of a high-rise building can be visualized as a vertical cantilever beam with its base fixed in the ground. The structure has to carry vertical gravity loads, the lateral wind and also earthquake loads. The building must therefore have adequate shear and bending resistance and must not lose its vertical load-carrying capability.

Structural systems of tall buildings can be divided into various types due to different criteria (e.g., internal and external). The choice of system and application of constructional material is affected by many factors, in particular:


The structural system of high-rise buildings can be divided on the following types [16]: Rigid frame, shear frame (shear trussed frame, shear walled frame), flat plate, mega column (frame, truss), core, mega core, outriggered frame and tube (framed tube, truss tube).

## 3.2.2. Innovative Diagrid System

Currently the diagrid system is one of the most innovative and adaptable approaches to structuring high-rise building (Capital Gate Tower (Abu Dhabi, UAE), Swiss Re (London, UK), Hearst Tower (New York, NY, USA) and CCTV headquarters (Beijing, China)). This kind of structure has evolved from a diagonalized tube. A diagrid is a special form of spatial truss. The difference between a conventional braced-tube structure and the current diagrid structure is that the diagrid system has almost completely eliminated the use of columns [17,18]. This is possible because diagonal elements in the diagrid system can carry gravity loads as well as horizontal loads due to their triangular configuration. The constructional function is realized by transfer lateral loads through the axial action of structural components. The bending stiffness is obtained by a diagonal grid, which also gives the shear stiffness. Adoption of such forms is very beneficial for reasons of dynamic impacts. As the height of a building increases, the lateral strength becomes more important than the load-bearing system that carries gravity loads. Therefore, any modifications to the geometric form of tall buildings generally reduce the adverse effects of the wind, which is an additional reason for the greater creativity of architects.

The diagonal grid module has a trapezoid shape and its height is several floors. Depending on the number of stories, the modules are divided into small (2–4 stories), medium (6–8 stories) and large (over 8 stories). Modules and diagonal angles play a key role in the structural, architectural and aesthetic concept of the design of the building. Due to the form, they may be flat, crystalline or multi-curved. The steel construction expresses regular diagonals in the facade of the building, is easier and quicker to assemble and is highly compatible with the concept of a sustainable building. In the design of the diagrid construction, an important factor is to choose the right diagonal angle. If the diagonal angle deviates from the optimum value, the required amount of steel is substantially increased. Since the optimum angle of placement of the columns for maximum bending stiffness is 90 degrees, and diagonals achieve maximum shear stiffness at an angle of 350, the optimum angle for diagrid construction elements is therefore taken between the values of these angles. The arrangement of diagonal elements with larger angles in the corners of the building increases its bending stiffness. High-rise buildings with a high ratio (height/width) behave like bent beams. Therefore, when a building's height rises, the optimum diagonal angle also increases. Buildings in this construction system are designed on a circle, ellipse, or other curved geometric form. The diagrid system is perfectly matched in the modification of the classical geometrical form. In this system, the following forms are known: Hyperboloidal, cylindrical, twisted, tilted and free [15].

### *3.3. Advanced Vibration Damping Systems*

The development of the advanced damping system has been characterized on the basis of Japan, which has the most active seismic zone in the world and which paradoxically occupies third place in terms of the number of skyscrapers.

An essential aspect of designing tall buildings is their dynamic reaction to earthquakes and counteracting wind vortices. Moreover, high buildings are sensitive to wind-induced vibrations, and the impact of such vibrations becomes dominant for buildings higher than 200 m. Under the action of the wind, a building not only deflects statically from its vertical position in the direction of wind pressure, but can also fall into the vibrations, which are transverse to the wind direction. These vibrations become dangerous, and even resonant when taking place with the frequency of air vortexing from the sides of the building. A simple measure of the quality of a skyscraper, i.e., its resistance to oscillatory swaying and resonance with the wind, and also its dynamic stiffness under bending is the fundamental (minimum) natural frequency of the building. Possible oscillations form a spectrum of waves with different vibration frequencies—higher or shorter. However, more diverse waves occur when the building bends. The longest wave with the smallest frequency, called the fundamental frequency, represents the shaking of the entire building. Such oscillations are most easily created at the lowest wind speed—hence their fundamental importance for the comfort of use and safety of the structure (risk of resonance with the wind). A better building has a higher fundamental frequency of vibrations, is stiffer, vibrates faster and introducing it into dangerous resonance vibrations requires a wind with a higher speed, which occurs less often and is less likely.

While the strength of building materials, such as steel, has doubled in the last few decades, its stiffness has not increased significantly. This has led to an elastic-based approach to design in which lateral deflections and accelerations are the dominant structural constraints for tall buildings. Vibrations can be partially damped by the structure itself. Increasing the stability of the structure causes an increase in the natural frequency. According to the numerical simulation of a construction's response to wind, if the natural frequency is greater, the maximum acceleration decreases in proportion to half of the natural frequency.

The light steel structure used in high-rise buildings has little natural damping or natural dissipation of energy and is sensitive to dangerous accelerations in conditions close to resonance. The dynamic reinforcement of load conditions can be reduced by redistributing stiffness in order to avoid resonance, or by the implementation of a damping system in the building (Figure 5). The need for motion control has led to the development of various methods and devices for dissipating energy. Damping devices can be passive, which do not require an additional energy supply, or active (AMD), which suppress the reaction with input energy, usually through the use of actuators [19,20]. Although there are many effective applications for active dampers, the increased complexity, maintenance and cost and lower reliability of passive dampers means that they are more often used. In addition to passive and active systems, there are mixed hybrid systems.

**Figure 5.** Vibration damping systems (figure by authors).

### 3.3.1. Passive Damping—Material Based Dissipation System

The material based dissipation dampers are an integral part of primary structural systems, and they are positioned in optimal locations (e.g., in bracing systems). There are different types of devices that belong to this category, and among all, the most important are: Hysteretic dampers and viscous dampers.

Hysteretic damping uses steel vibration absorbers SD (steel damper) and SJD (steel joint damper), as well as viscoelastic dampers (VED), lead dampers (LD) and friction dampers (FD), which are used to reinforce material interactions at the FD connections. Steel vibration absorbers dissipate energy through the cyclic inelastic deformation of materials. These damping systems are often designed in the form of a triangular plate, or are X-shaped. Due to this shape, plastic deformations appear in a much larger area, which leads to a more efficient dissipation of energy. This system was used in the Ohjiseishi Building (Tokyo, Japan), Art Hotels Sapporo (Sapporo, Japan) and Kobe Fashion Plaza (Kobe, Japan).

In friction dampers, energy dissipation occurs as a result of friction between two solids moving in relation to each other. There are two types of friction dampers used in steel framed buildings: Rigid frame friction dampers and braced frame friction dampers. For example, friction dampers were used in the Sonic City Office Tower (Ohmiya, Japan) and Asahi Beer Tower (Tokyo, Japan).

Viscous dampers (VD) and oleo-dynamic dampers (OD) use viscous materials in which the resistance force acting on the body moving in the material is proportional to the speed of the body [21]. In this case, high viscosity chemicals such as silicone oil are used. The thermal effect is also significant. VDs are particularly effective in the high frequency range and low vibration levels against moderate earthquakes and strong winds. This type of damper, consisting of steel plates, is installed as a part of a diagonal brace, where it can dissipate vibrational energy by the shearing action of the VE material.

Viscoelastic dampers were used in the TV-Shizuoka Media City buildings (Tokyo, Japan) and in the Torishima Riverside Hill Tower (Osaka, Japan) to counteract the vibrations caused by extremely large earthquakes.
