Technical Field The present disclosure generally relates to structural frames for high-rise buildings. In particular, a structural frame for supporting at least one slanted section of a high-rise building where the structural frame closes the perimeter of the slanted section, and a high-rise building comprising the structural frame, are provided.

Background Throughout the centuries, mankind has always been fascinated by building higher. This resulted both from the need to provide more space to the increasing urban population, as well as from the competitive urge to create a new symbol of growth and an iconic representation of the place of origin.

Tall buildings represent a new form of city planning, the so-called vertical cities, which aim to accommodate residential, office or hotel space or a combination of them. With the highest existing building reaching 828 m (Burj Khalifa) and the Jeddah Tower setting the barrier to 1008 m upon its completion in 2019, the expected question is how tall can we build, followed by what kind of structural system would be the most efficient one. Nowadays, the most popular method to construct tall buildings is to use a vertical core with elevator shafts in the center. The elevator core is typically located in the center of the building and it is the major structural member for vertical and lateral loads. Usually, the central core is combined with another system, for example outriggers, in order to provide the vertical and lateral support. Some of the most representative examples of modern tilted buildings are the Veer towers in Las Vegas, the Gate of Europe towers in Madrid and the Capital Gate in Abu Dhabi. All these buildings are built with a central core structure. Summary

One object of the present disclosure is to provide a structural frame for supporting at least one slanted section of a high-rise building where the structural frame has high stiffness and great structural performance, for example that can withstand high linear and nonlinear static and dynamic loads.

A further object of the present disclosure is to provide a structural frame for supporting at least one slanted section of a high-rise building enabling a high usable floor space.

A still further object of the present disclosure is to provide a structural frame for supporting at least one slanted section of a high-rise building that has a low weight to enable increased performance and material reduction.

A still further object of the present disclosure is to provide a structural frame for supporting at least one slanted section of a high-rise building, where a central vertical elevator shaft does not fit within the building from the base of the building to the top of the building. A still further object of the present disclosure is to provide a structural frame for supporting at least one slanted section of a high-rise building that enables a wide range of possible designs of the building.

A still further object of the present disclosure is to provide a high-rise building comprising a structural frame solving one or more of the foregoing objects. According to one aspect, there is provided a structural frame for supporting at least one slanted section of a high-rise building, the slanted section comprising a perimeter and plurality of floors, wherein the structural frame is arranged at the perimeter of the slanted section; wherein the structural frame closes the perimeter or circumference of the slanted section; and wherein at least 85% of the loads of the floors in the slanted section are transferred to the structural frame at the perimeter of the slanted section. At least 90%, such as at least 95%, such as at least 98%, such as all of the loads of the floors in the slanted section may be transferred to the structural frame at the perimeter of the slanted section. Throughout the present disclosure, the definition that the structural frame closes the perimeter or circumference of the slanted section means that the structural frame encompasses the perimeter or circumference of the slanted section. The structural frame may completely encase the perimeter. The perimeter of the slanted section may be defined as the bounds of the slanted section, for example in the horizontal plane or in a plane perpendicular to an extension direction of the slanted section. The structural frame may encompass the perimeter of the slanted section in various ways according to the present disclosure and may comprise various structural elements according to the present disclosure. The structural frame may for example comprise slanted mega columns at the perimeter and one or more belts interconnecting the slanted mega columns to encompass the perimeter; vertical mega columns, slanted support elements and one or more belts interconnecting the vertical mega columns and the slanted support elements to encompass the perimeter; slanted mega columns and support elements interconnecting the slanted mega columns to encompass the perimeter;

support elements and one or more belts interconnecting the support elements to encompass the perimeter; and/or interconnected support elements encompassing the perimeter.

By arranging the structural frame at the perimeter of the slanted section, the lever arm of the structural frame is maximized and the structural frame is made more stable in contrast to, for example, high-rise building where the main structural component is constituted by a central vertical elevator core. Since the structural frame is thereby stronger, it can also be made lighter. A structural frame according to the present disclosure may alternatively be referred to as a structural system.

Throughout the present disclosure, a floor load may be constituted by the load of the entire floor at one story, for example by a floor plate, as well as the load of components on the floor, for example furniture.

A high-rise building according to the present disclosure may be any building above 100- meters. A high-rise building according to the present disclosure may have a slenderness ratio of at least 1:5, such as at least 1:10, such as at least 1:15, such as at least 1:20. The high-rise building may be at least 100 meters, such as at least 200 meters, such as at least 300 meters (super-tall), such as at least 600 meters (mega-tall). The slanted section may have a substantially constant cross section. The slanted section may be slender, for example having a slenderness ratio of at least 1:5, such as at least 1:10, such as at least 1:15, such as at least 1:20. The slanted section is slanted with respect to a vertical direction. Thus, the slanted section is non-perpendicular to the ground. A slanted section may alternatively be referred to as an inclined section.

The slanted section may be slanted at least 5 ⁰ , such as at least 8°, such as at least io°, such as at least 15 ⁰ , such as at least 20 ⁰ , such as at least 25 ⁰ , such as at least 30 ⁰ , such as at least 35 ⁰ , such as at least 40 ⁰ , with respect to vertical. A top of the slanted section may be completely horizontally outside a base of the slanted section. The structural frame may comprise mega columns. Throughout the present disclosure, a column is a structural member that mainly carry compression loads. The mega columns may carry a substantial part or all of the vertical compression loads. The mega columns may also carry bending moments in one or both axes of the cross section. The mega columns may also carry tension loads. The use of mega columns may minimize moments, particularly at a base of the building. Throughout the present disclosure, a structural frame comprising at least one mega column may be referred to as a Tubed Mega Frame.

The mega columns may be made of concrete or a composite of steel and concrete.

Alternatively, the mega columns may be made of steel. For example, the concrete may be C90/105 and the steel may be A992Fyso.

Each mega column may be arranged with the same slant as the slanted section.

Alternatively, some or all of the mega columns may be vertical. Each mega column may be arranged to be located at a perimeter of the slanted section of a high-rise building.

The structural frame may comprise at least one closed belt closing the perimeter of the slanted section, i.e. encompassing the perimeter of the slanted section. Throughout the present disclosure, the closed belt may alternatively be referred to as a belt member or belt portion. The at least one closed belt may for example be constituted by a set of rigid beams (for example by concrete), walls or trusses. For example, if the structural frame comprises four mega columns arranged at the corners of a slanted section having a square cross sectional profile, one closed belt may be constituted by four beams (or walls or trusses), where each beam connects each pair of mega columns at the perimeter of the slanted section. Each closed belt may be substantially horizontally arranged around the perimeter of the slanted section. Each closed belt may close the perimeter alone or together with, for example, the mega columns. Each closed belt may connect the mega columns. Furthermore, each closed belt may encompass the perimeter of the slanted portion of the high-rise building.

According to one example, there is provided a structural frame of a high-rise building, at least a portion of the structural frame being slanted with respect to vertical and being configured to support a slanted portion of the high-rise building, the structural frame comprising mega columns arranged to be located at a perimeter of the slanted portion of the high-rise building; and at least one closed belt connecting the mega columns and arranged to encompass the perimeter of the slanted portion of the high-rise building, wherein the structural frame lacks a central core and at least 85% of the loads of floors in the slanted portion are transferred to the structural frame at the perimeter of the slanted section.

The structural frame may comprise elongated support elements, such as bracings, closing the perimeter of the slanted section. Each elongated support element may be made of concrete or steel. The elongated support elements may be constituted by X- bracings, for example forming an X-truss along each side of the perimeters of each slanted section. Alternatively, the elongated support elements may form a Pratt truss, a K-truss, an N-truss or a W-truss.

The slanted section may comprise at least five floors. The floors may be constituted by residential floors, office floors, hotels etc. For at least some of the floors, at least 85% of the loads of a floor and at least 85% of the loads on the same floor are transferred to the structural frame at the perimeter of the slanted section. According to one variant, for at least some of the floors, all of the loads of a floor and all of the loads on the same floor are transferred to the structural frame at the perimeter of the slanted section.

According to a further aspect, there is provided a slanted section comprising a structural frame according to the present disclosure. Throughout the present disclosure, the slanted section may be referred to as a slanted portion. According to a further aspect, there is provided a high-rise building comprising at least one slanted section, wherein the high-rise building comprises a structural frame according to the present disclosure for supporting the at least one slanted section. The high-rise building may comprise only one slanted section, or several slanted sections, such as two, three, four or eight slanted sections. A high-rise building comprising several interconnected slanted sections according to the present disclosure may improve the lateral stiffness of the building.

The entire high-rise building may be slanted. Alternatively, the high-rise building may be arch shaped and the at least one slanted section may form a part of the arch shape, The arch shaped building may have a height larger than its span.

The high-rise building may be constituted by, or comprise, two slanted sections arranged in a V-shape. Alternatively, the high-rise building may be constituted by four slanted sections arranged in a double zig-zag shape. Alternatively, the high-rise building may comprise two (or more) such shapes arranged on top of each other, i.e. the building may be constituted by eight slanted sections arranged in two double zig-zag shapes. Alternatively, the high-rise building may be constituted by two slanted sections arranged in an X-shape. Alternatively, the high-rise building may be constituted by four slanted sections arranged in a double X-shape (two X-shapes on top of each other).

As a further alternative, the high-rise building may be constituted by three slanted sections arranged in a tripod shape. The three slanted sections may be inclined towards an imaginary vertical center line. The three slanted sections may be joined at a trunk section and one (or more) of the three slanted sections may extend continuously through the trunk section.

The high-rise building may further comprise a substantially horizontally arranged cantilever section connected to the at least one slanted section. The high-rise building may further comprise one or more cables connecting the at least one slanted section to the cantilever section. The cables may be parallel or arranged in a fan shape (for example one or more common connection points). The building may for example comprise at least two cables. The high-rise building may comprise a base and a center of gravity of the high-rise building may be horizontally outside the base. In this case, the high-rise building may comprise only one single inclined section. Throughout the present disclosure, a base is referred to as an area of contact between the high-rise building and the ground. Thus, the high-rise building may comprise only one base or several bases.

According to one variant, the high-rise building comprises a base and a top and wherein a vertical core, such as a central vertical elevator core, cannot be accommodated within the high-rise building from the base to the top. According to one variant, the high-rise building does not comprise a central core, such as a central vertical elevator core. The high-rise building may further comprise an elevator system having a plurality of cabins, wherein the elevator system is configured to drive the cabins along a common path comprising non-vertical sections, for example horizontal and/or inclined sections.

Examples of such elevator system are described in International Patent Application No.

WO 2013159800 Ai filed on 15 December 2012, International Patent Application No. WO 2017010917 Ai filed on 10 July 2015, International Patent Application No.

WO 2017010926 Ai filed on 28 June 2016, International Patent Application No.

WO 2017010927 Ai filed on 28 June 2016, International Patent Application No.

WO 2017010928 Ai filed on 28 June 2016 and International Patent Application No.

WO 2017010929 Ai filed on 28 June 2016, all of which are incorporated by reference herein.

Elevator systems configured to transport cabins in horizontal and/or inclined sections enable removal of vertical elevator cores, which function as the main structural elements for conventional high-rise buildings. This opens up for new and radical building forms and shapes. The high-rise building may further comprise a damping arrangement. The damping arrangement may for example comprise one or more damping devices, such as visco- elastic and friction dampers, tuned mass dampers and/or liquid dampers.

As used herein, a vertical direction refers to a direction aligned with the direction of the force of gravity and a horizontal direction refers to a direction perpendicular to the vertical direction. The following itemized listing presents various embodiments of the present disclosure:

1. A structural frame of a high-rise building, at least a section of the structural frame being slanted with respect to vertical and being configured to support a slanted section of the high-rise building, the structural frame comprising:

mega columns arranged to be located at a perimeter of the slanted section of the high-rise building; and

elongated support elements connecting the mega columns and arranged to encompass the perimeter of the slanted section of the high-rise building, wherein the structural frame lacks a central core and at least 85% of the loads of floors in the slanted section are transferred to the structural frame at the perimeter of the slanted section.

2. The structural frame according to item 1, wherein the structural frame is

configured to support the slanted section slanted at least 5 ⁰ with respect to vertical.

3. The structural frame according to item 1 or 2, wherein each mega column is

arranged with the same slant as the slanted section.

4. The structural frame according to any of the preceding items, wherein the

structural frame further comprises at least one closed belt that is configured to encompass the perimeter of the slanted section.

5. The structural frame according to any of the preceding items, wherein the

elongated support elements are constituted by X-bracings.

6. The structural frame according to any of the preceding items, wherein the slanted section comprises at least five floors.

7. A high-rise building comprising the structural frame according any of the

preceding items.

8. The high-rise building according to item 7, wherein the entire high-rise building is slanted.

9. The high-rise building according to item 7, wherein the high-rise building is arch shaped and wherein the slanted section forms a part of the arch shape. 10. The high-rise building according to item 7, wherein the high-rise building is constituted by, or comprises, two slanted sections arranged in a V-shape.

11. The high-rise building according to item 7, further comprising a substantially

horizontally arranged cantilever section connected to the slanted section. 12. The high-rise building according item 11, further comprising one or more cables connecting the slanted section to the cantilever section.

13. The high-rise building according any of items 7 to 12, wherein the high-rise

building comprises a base and a top and wherein a vertical core cannot be accommodated within the high-rise building from the base to the top. 14. The high-rise building according to item 13, wherein the vertical core is a central vertical elevator core.

15. The high-rise building according to any of items 7 to 14, wherein the high-rise building does not comprise a central vertical elevator core.

16. The high-rise building according to any of items 7 to 15, further comprising an elevator system having a plurality of cabins, wherein the elevator system is configured to drive the cabins along a common path comprising non-vertical sections.

Brief Description of the Drawings

Further details, advantages and aspects of the present disclosure will become apparent from the following embodiments taken in conjunction with the drawings, wherein:

Fig. la: schematically represents a side view of a slanted high-rise building

comprising one example of a structural frame;

Fig. lb: schematically represents a perspective view of the high-rise building in Fig.

la;

Fig. 2: schematically represents a perspective view of a double zig-zag high-rise building comprising one example of a structural frame;

Fig. 3: schematically represents a perspective view of an X-shaped high-rise building comprising one example of a structural frame; Fig. 4: schematically represents a perspective view of a double X-shaped high-rise building comprising one example of a structural frame;

Fig. 5: schematically represents a perspective view of a tripod high-rise

building comprising one example of a structural frame;

Fig. 6: schematically represents a perspective view of a tripod high-rise building comprising a further example of a structural frame;

Fig. 7: schematically represents a perspective view of a tripod high-rise

building comprising a further example of a structural frame;

Fig. 8: schematically represents a perspective view of a tripod high-rise building comprising a further example of a structural frame;

Fig. 9: schematically represents a perspective view of a high-rise building

comprising a cantilever section;

Fig. 10a: schematically represents a side view of an arch shaped high-rise building comprising one example of a structural frame;

Fig. 10b: schematically represents a perspective view of the arch shaped high-rise building in Fig. 10a;

Fig. 11: schematically represents a perspective view of a V-shaped high-rise building comprising one example of a structural frame;

Fig. 12: schematically represents a perspective view of the V-shaped high-rise

building comprising a further example of a structural frame;

Fig. 13: schematically represents a perspective view of the V-shaped high-rise

building comprising a further example of a structural frame;

Fig. 14: schematically represents a perspective view of the V-shaped high-rise

building comprising a further example of a structural frame;

Fig. 15: schematically represents a perspective view of the V-shaped high-rise

building comprising a further example of a structural frame;

Fig. 16: schematically represents a perspective view of the V-shaped high-rise

building comprising a further example of a structural frame;

Fig. 17: schematically represents a perspective view of the V-shaped high-rise

building comprising a further example of a structural frame;

Fig. 18: schematically represents a perspective view of the V-shaped high-rise

building comprising a further example of a structural frame;

Fig. 19: schematically represents a perspective view of the V-shaped high-rise building comprising a further example of a structural frame;

Fig. 20: schematically represents a perspective view of the V-shaped high rise

building comprising a further example of a structural frame;

Fig. 21: schematically represents a perspective view of the V-shaped high rise

building comprising a further example of a structural frame;

Fig. 22: schematically represents a perspective view of the V-shaped high-rise

building comprising a further example of a structural frame;

Fig. 23: schematically represents a perspective view of the V-shaped high-rise

building comprising a further example of a structural frame; and

Fig. 24: schematically represents a perspective view of the V-shaped high- rise building comprising a further example of a structural frame.

Detailed description

In the following, a structural frame for supporting at least one slanted section of a high- rise building where the structural frame closes the perimeter of the slanted section, and a high-rise building comprising the structural frame will be described. The same reference numerals will be used to denote the same or similar structural features.

Fig. la schematically represents a side view of a slanted high-rise building 10 comprising one example of a structural frame 12. The building 10 comprises one single slanted section 14 and has a height of 200 m. Thus, the entire building 10 of Figs, la and lb is slanted. The slanted section 14 comprises a perimeter 16 and a plurality of floors 18. Each floor 18 may be constituted by a continuous floor plate. The dimensions of the floors 18 are 20 x 20 m. The slanted section 14 of this example (and the entire building 10) is slanted 14 ⁰ with respect to vertical (Z-direction).

Fig. lb schematically represents a perspective view of the slanted building 10 in Fig. la. The floors 18 are omitted in Fig. lb.

With collective reference to Figs, la and lb, the structural frame 12 comprises four slanted mega columns 20. One mega column 20 is arranged at each corner of the slanted section 14. The mega columns 20 may however alternatively be arranged at the exterior faces of the building 10, for example one mega column 20 centrally disposed between each pair of corners at the perimeter 16 of the building or two mega columns 20 at each exterior face of the building 10. The mega columns 20 are arranged with the same slant as the slanted section 14. The structural frame 12 further comprises a plurality of closed belts 22. Both the mega columns 20 and the closed belts 22 are arranged at the perimeter 16 of the slanted section 14. The closed belts 22 are horizontally arranged (in the X-Y plane) and close the perimeter 16 of the slanted section 14. Each closed belt 22 comprises a set of four walls and each wall connects a pair of mega columns 20. Each closed belt 22 may alternatively be constituted by a set of rigid beams or trusses. In the example of Figs, la and lb, the structural frame 12 comprises four closed belts 22. A lowermost closed belt 22 is positioned 50 m vertically distanced from a base 24 of the building 10 and an uppermost closed belt 22 is positioned adjacent to a top 26 of the building 10. The closed belts 22 are vertically distanced 50 m. Each closed belt 22 may have a height corresponding to one or two stories. The base 24 of the building 10 is fixed to a foundation or ground.

The structural frame 12 supports the single slanted section 14 of the building 10. For at least some of the floors 18, the loads of a floor 18 and the loads on the same floor 18 are transferred to the structural frame 12 at the perimeter 16 of the slanted section 14.

According to one variant, the loads of all floors 18 and the loads on all floors 18 are transferred to the structural frame 12 at the perimeter 16 of the slanted section 14.

According to a further variant, the loads of the lowermost floors 18 (for example the eleven lowermost floors 18) and the loads on the lowermost floors 18 may be transferred differently, for example not to the structural frame 12 at the perimeter 16 of the slanted section 14.

The mega columns 20 of this example each has exterior dimensions of 3.0 x 3.0 m and a thickness of 0.45 m. Thus, the mega columns 20 are here constituted by tubes. The height between two adjacent floors 18 is 4 m. Analyses of the building 10 in Figs, la and lb in ETABS ® indicate that the building 10 has relatively high stiffness in both the X- direction and the Y-direction.

The building 10 in Figs, la and lb does not comprise a central core. As can be seen in Fig. la, a vertical core does not fit within the building 10 from the base 24 to the top 26. The top 26 is entirely horizontally outside the base 24. The building 10 in Figs, la and lb may further comprise an elevator system 52 having a plurality of cabins 54. As shown in Fig. la, the elevator system 52 is configured to drive the cabins 54 along a common path 56 comprising non-vertical sections. The cabins 54 may be driven from the base 24 to the top 26 along the common path 56 comprising non-vertical sections.

Fig. 2 schematically represents a perspective view of a double zig-zag high-rise building 10 comprising one example of a structural frame 12. Mainly differences with respect to Figs, la and lb will be described. The floors 18 are omitted in Fig. 2.

The double zig-zag building 10 of Fig. 2 comprises four slanted sections 14. Two lower slanted sections 14 stand on a single base 24 of the building 10 and form a V-shape. Two upper slanted sections 14 stand on the lower slanted sections 14 and form an inverted V- shape branching together at the top 26 of the building 10. Thus, the building 10 in Fig. 2 comprises two zig-zag legs, each constituted by two slanted sections 14. As can be seen in Fig. 2, the building 10 requires a relatively small space for the base 24 on the ground.

The building 10 of Fig. 2 has a height of 200 m. The dimensions of the floors 18 in each zig-zag leg is 20 x 20 m. The inclination of each slanted section 14 is 11.5 ⁰ with respect to vertical (the inclinations change at 100 m). The height between two adjacent floors 18 is 4 m.

The structural frame 12 of Fig. 2 comprises four vertical mega columns 28. Each vertical mega column 28 extends from one corner of the base 24 of the building 10 to one corner of the top 26 of the building 10. The vertical mega columns 28 are arranged at the perimeters 16 of the slanted sections 14. The vertical mega columns 28 may be constituted by tubes having exterior dimensions of 3.0 x 3.0 m and a thickness of 0.3 m.

The structural frame 12 of Fig. 2 further comprises four slanted support elements 30 at the corners of each slanted section 14. The slanted support elements 30 are arranged at the perimeter 16 of each slanted section 14. The slanted support elements 30 have the same inclination (11.5 ⁰ in this case) as the inclination of the associated slanted section 14.

The structural frame 12 of Fig. 2 further comprises a plurality of closed belts 22. The closed belts 22 are horizontally arranged at the perimeters 16 of the slanted sections 14. The perimeter 16 of each upper slanted section 14 is closed by three closed belts 22. The perimeter 16 of each lower slanted section 14 is closed by two closed belts 22. In the example of Fig. 2, the structural frame 12 comprises five closed belts 22.

A lower intermediate closed belt 22 is positioned at 25% of the height of the building 10 (from the base 24) and closes the perimeter 16 of the two lower slanted sections 14 at the branch between these two slanted sections 14. Two middle closed belts 22 are positioned at 50% of the height of the building 10. Each middle closed belt 22 closes the perimeter 16 of one leg, i.e. over the joint between two slanted sections 14. An upper intermediate closed belt 22 is positioned at 75% of the height of the building 10 and closes the perimeter 16 of the two upper slanted sections 14 at the branch between these two slanted sections 14. An uppermost closed belt 22 is positioned adjacent to the top 26 of the building 10 and closes the perimeter 16 of the two upper slanted sections 14.

The structural frame 12 of Fig. 2 further comprises four intermediate vertical support elements 32. The vertical support elements 32 are arranged at the perimeters 16 of the slanted sections 14. Each intermediate vertical support element 32 extends from one corner of the lower intermediate closed belt 22 to one corner of the upper intermediate closed belt 22.

Analyses of the building 10 in Fig. 2 in ETABS ® indicate that the building 10 is particularly stiff in the first vibration mode (period of 8.998 s) in the Y-direction. The building 10 in Fig. 2 further has a very small deformation in the X-direction and an acceptable deflection in the Y-direction.

For at least some of the floors 18, the loads of a floor 18 and the loads on the same floor 18 are transferred to the structural frame 12 at the perimeter 16 of a slanted section 14. For the floors 18 between the upper intermediate closed belt 22 and the uppermost closed belt 22, the loads of the floors 18 may be transferred to the perimeters 16 of both legs comprised by the left slanted sections 14 and the right slanted sections 14.

The building 10 in Fig. 2 does not comprise a central core. A central vertical elevator core cannot be accommodated within the building 10 from the base 24 to the top 26. The building 10 in Fig. 2 may further comprise an elevator system (not shown) configured to drive cabins from the base 24 to the top 26 along a common path comprising non-vertical sections. Fig. 3 schematically represents a perspective view of an X-shaped high-rise building 10 comprising one example of a structural frame 12. Mainly differences with respect to Figs. 1 and 2 will be described. The floors 18 are omitted in Fig. 3.

The X-shaped building 10 of Fig. 3 comprises two slanted sections 14 joined at a waist section 34 of the building 10. Each slanted section 14 stands on a base 24 of the building 10 and form an X-shape. It may alternatively be said that the building 10 comprises four slanted sections 14, each extending to the waist section 34. In this case, the two upper slanted sections 14 form a V-shape. In the following, the X-shaped building 10 of Fig. 3 is referred to as comprising two slanted sections 14. The building 10 of Fig. 3 has a height of 200 m. The dimensions of the floors 18 in each slanted section 14 is 20 x 20 m. The inclination of each slanted section 14 is 11.5 ⁰ with respect to vertical. The height between two adjacent floors 18 is 4 m. The building 10 of Fig. 3 has a particularly high floor area to weight ratio.

The structural frame 12 of Fig. 3 comprises four vertical mega column 28. The vertical mega columns 28 are arranged at the perimeters 16 of the slanted sections 14. Each vertical mega columns 28 extends vertically from one inner corner of the base 24 of one slanted section 14 to one inner corner of the top 26 of the other slanted section 14. The vertical mega columns 28 may be constituted by tubes having exterior dimensions of 3.0 x 3.0 m and a thickness of 0.3 m. The structural frame 12 of Fig. 3 further comprises four slanted elongated support elements 30 at the corners of each slanted section 14. The slanted elongated support elements 30 are arranged at the perimeters 16 of the slanted sections 14. The slanted elongated support elements 30 have the same inclination (11.5 ⁰ in this case) as the inclination of the associated slanted section 14. The slanted support elements 30 extend along the entire length of the slanted sections 14.

The structural frame 12 of Fig. 3 further comprises a plurality of closed belts 22 arranged at the perimeters 16 of the slanted sections 14. The closed belts 22 are horizontally arranged. Each slanted section 14 is closed by four closed belts 22. In the example of Fig. 3, the structural frame 12 comprises five closed belts 22. A lower intermediate closed belt 22 is positioned at 25% of the height of the building 10 (from the bases 24) and closes the perimeter 16 of both slanted sections 14. A middle closed belt 22 is positioned at 50% of the height of the building 10, i.e. at the waist section 34. The middle closed belt 22 closes the perimeter 16 of both slanted sections 14. An upper intermediate closed belt 22 is positioned at 75% of the height of the building 10 and closes the perimeter 16 of both slanted sections 14. Two uppermost closed belts 22 are positioned adjacent to a top 26 of the building 10 and close the respective perimeter 16 of a slanted section 14 of the building 10.

The structural frame 12 of Fig. 3 further comprises eight transverse support elements 36. The transverse support elements 36 are arranged at the perimeters 16 of the slanted sections 14. Four lower transverse support elements 36 extend from one inner corner of a base 24 of the building 10 to an outer corner of the lower intermediate closed belt 22. Four upper transverse support elements 36 extend from one outer corner of the upper intermediate closed belt 22 to an inner corner of a top 26 of the building 10. Thus, each of the eight transverse support elements 36 extends transverse to the inclination of an associated slanted section 14. The perimeters 16 of each slanted section 14 are also closed by the support elements 30 and 36. The support elements 30 and 36 each has exterior dimensions of 1.0 x 1.0 m and a thickness of 0.20 m.

Analyses of the building 10 in Fig. 3 in ETABS ® indicate that the building 10 is particularly stiff in the first vibration mode (period of 8.998 s) in the Y-direction. The building 10 in Fig. 3 also has a low deflection in the X-direction.

For at least some of the floors 18, the loads of a floor 18 and the loads on the same floor 18 are transferred to the structural frame 12 at the perimeter 16 of a slanted section 14. For the floors 18 above the lower intermediate closed belt 22 at the waist section 34, the loads of the floors 18 may be transferred to the perimeters 16 of both slanted sections 14.

The building 10 in Fig. 3 does not comprise a central core. A central vertical elevator core cannot be accommodated within the building 10 from the base 24 to the top 26. The building 10 in Fig. 3 may further comprise an elevator system (not shown) configured to drive cabins from one or both bases 24 to one or both tops 26 along a common path comprising non-vertical sections. Fig. 4 schematically represents a perspective view of a double X-shaped high-rise building 10 comprising one example of a structural frame 12. Mainly differences with respect to Figs. 1 to 3 will be described. The floors 18 are omitted in Fig. 4.

The double X-shaped building 10 of Fig. 4 comprises four slanted sections 14. Two lower slanted sections 14 are joined at a lower waist section 34 and two upper slanted sections 14 are joined at an upper waist section 34. The two lower slanted sections 14 and the two upper slanted sections 14 are joined at two middle sections 38 at half the height of the building 10.

The building 10 of Fig. 4 has a height of 200 m, each X-shape has a height of 100 m. The dimensions of the floors 18 in each slanted section 14 is 20 x 20 m. The inclination of each slanted section 14 is 22 ⁰ with respect to vertical. The height between two adjacent floors 18 is 4 m. The building 10 in Fig. 4 has a particularly high floor area to weight ratio (higher than the building 10 in Fig. 3).

The structural frame 12 of Fig. 4 comprises four vertical mega column 28. The vertical mega columns 28 are arranged at the perimeters 16 of the slanted sections 14. Each vertical mega columns 28 extends vertically from one inner corner of the base 24 of one slanted section 14, through one outer corner of the lower waist section 34, through one inner corner of one of the two middle sections 38, through one outer corner of the upper waist section 34 and to one inner corner of one of the tops 26 of a slanted section 14. The vertical mega columns 28 may be constituted by tubes having exterior dimensions of 3.0 x 3.0 m and a thickness of 0.3 m.

The structural frame 12 of Fig. 4 further comprises four slanted elongated support elements 30 at the corners of each slanted section 14. The slanted support elements 30 have the same inclination (22 ⁰ in this case) as the inclination of the associated slanted section 14. The slanted support elements 30 extend along the entire length of the slanted sections 14, i.e. along half the height of the building 10. Each of the 16 slanted support elements 30 has outer dimensions of 1.0 x 1.0 m and a thickness of 0.20 m.

The structural frame 12 of Fig. 4 further comprises a plurality of closed belts 22. The closed belts 22 are arranged at the perimeters 16 of the slanted sections 14. The closed belts 22 are horizontally arranged. Each of the two upper slanted sections 14 is closed by three closed belts 22. Each of the two lower slanted sections 14 is closed by two closed belts 22. In the example of Fig. 4, the structural frame 12 comprises six closed belts 22.

A lower intermediate closed belt 22 is positioned at 25% of the height of the building 10 and closes the perimeter 16 of both lower slanted sections 14. Two middle closed belts 22 are positioned at 50% of the height of the building 10, i.e. at the middle sections 38. The middle closed belts 22 close the perimeters 16 two pairs of slanted sections 14 (left leg and right leg). An upper intermediate closed belt 22 is positioned at 75% of the height of the building 10 and closes the perimeter 16 of both upper slanted sections 14. Two uppermost closed belts 22 are positioned adjacent to a top 26 of the building 10 and close the respective perimeter 16 of a slanted section 14 of the building 10.

Analyses of the building 10 in Fig. 4 in ETABS ® indicate that the building 10 is particularly stiff in the X-direction and acceptably stiff in the Y-direction. The building 10 in Fig. 4 is also stiff in the second vibration mode (period of 3.815 s) in the Y- direction. The building 10 in Fig. 4 also has a particularly low vibration period of 4.418 s in the third vibration mode around the Z-axis.

For at least some of the floors 18, the loads of a floor 18 and the loads on the same floor 18 are transferred to the structural frame 12 at the perimeter 16 of a slanted section 14. For the floors 18 above the upper waist section 34, the loads of the floors 18 may be transferred to the perimeters 16 of any leg of the two legs associated with each middle section 38.

The building 10 in Fig. 4 does not comprise a central core. A central vertical elevator core cannot be accommodated within the building 10 from the base 24 to the top 26. The building 10 in Fig. 4 may further comprise an elevator system (not shown) configured to drive cabins from one or both bases 24 to one or both tops 26 along a common path comprising non-vertical sections.

Each structural frame 12 of the buildings 10 in Figs. 1 to 4 may further comprise elongated support elements according to the present disclosure, for example forming an X-truss along each side of the perimeters 16 of each slanted section 14 as in Fig. 11. This type of structural frame 12 has a particularly low deflection. Alternatively, each structural frame 12 of the buildings 10 in Figs. 1 to 4 may further comprise diagrids according to the present disclosure, for example interconnecting the mega columns 20 as in Fig. 15. Alternatively, each structural frame 12 of the buildings 10 in Figs. 1 to 4 may further comprise moment frames according to the present disclosure, for example as in Figs. 7, 8, 23 and 24.

Fig. 5 schematically represents a perspective view of a tripod high-rise building 10 comprising one example of a structural frame 12. The floors 18 are omitted in Fig. 5.

The building 10 of Fig. 5 comprises three slanted sections 14. The building 10 of this example has a height of 450 m and 113 floors 18. Each slanted section 14 is slanted 7 ⁰ with respect to vertical.

Each slanted section 14 is positioned at one of three bases 24 and is inclined towards an imaginary vertical center line. As shown in Fig. 5, the three slanted sections 14 are joined at a trunk section 40 and one of the three slanted sections 14 extends

continuously through the trunk section 40. The trunk section 40 assists in cancelling out horizontal forces that are generated from the slanted sections 14 up to the trunk section 40.

The structural frame 12 in Fig. 5 comprises three slanted mega columns 20 arranged at the corners of each slanted section 14. Thus, each slanted section 14 has a triangular cross sectional profile. The mega columns 20 are arranged at the perimeters 16 of the slanted sections 14 and have the same slant as the associated slanted section 14.

The structural frame 12 further comprises a plurality of closed belts 22 associated with each slanted section 14. The closed belts 22 are arranged at the perimeters 16 of the slanted sections 14. Closed belts 22 are arranged at every eighth floor 18. Each closed belt 22 closes the perimeter 16 of an associated slanted section 14. Adjacent to the trunk section 40, the closed belts 22 close the perimeters 16 of all three slanted sections 14.

In Fig. 5, the closed belts 22 each has a height of one story and a thickness of 750 mm. The slanted mega columns 20 each has exterior dimensions of 5.0 x 3.0 m and a thickness of 0.5 m. For at least some of the floors 18, the loads of a floor 18 and the loads on the same floor 18 are transferred to the structural frame 12 at the perimeter 16 of a slanted section 14. For the floors 18 above the trunk section 40, the loads of the floors 18 are initially transferred to the structural frame 12 at the perimeter 16 of the slanted section 14 in a region above the trunk section 40 and then transferred to the structural frame 12 of any of the slanted sections 14 below the trunk section 40.

The building 10 in Fig. 5 does not comprise a central core. A vertical core, such as a central vertical elevator core, cannot be accommodated within the building 10 from a base 24 to the top 26. The building 10 in Fig. 5 may further comprise an elevator system (not shown) configured to drive cabins from one or all bases 24 to the top 26 along a common path comprising non-vertical sections.

Fig. 6 schematically represents a perspective view of a tripod high-rise building 10 comprising a further example of a structural frame 12. Mainly differences with respect to Fig. 5 will be described. The structural frame 12 of Fig. 6 comprises a plurality of elongated support elements 42 arranged at the perimeters 16 of each slanted section 14. The support elements 42 close the perimeter 16 of each slanted section 14. The support elements 42 are constituted by X-bracings. Due to the X-bracing, the dimensions of the closed belts 22 can be reduced.

In Fig. 6, the slanted mega columns 20 each has exterior dimensions of 5.0 x 3.0 m and a thickness of 0.5 m. The elongated support elements 42 each has exterior dimensions of 0.827 x 0.827 m. Analyses of the building 10 in Fig. 6 in ETABS ® indicate that the building 10 has a particularly low deflection.

Fig. 7 schematically represents a perspective view of a tripod high-rise building 10 comprising a further example of a structural frame 12. Mainly differences with respect to Figs. 5 and 6 will be described.

The structural frame 12 of Fig. 7 comprises closed belts 22 according to Fig. 5 and a plurality of support elements 42 forming a moment frame or perimeter frame. The structural frame 12 of Fig. 7 does however not comprise any slanted mega columns 20 as in Figs. 5 and 6. Each moment frame is constituted by a plurality of elongated horizontal support elements 42 and by a plurality of inclined support elements 42 rigidly connected to the horizontal support elements 42. The inclined support elements 42 are parallel with the associated slanted section 14.

In Fig. 7, the elongated horizontal support elements 42 each has exterior dimensions of 0.587 x 0.587 m. The elongated inclined support elements 42 each has exterior dimensions of 0.774 ^x 0.774 ^m - The closed belts 22 each has a thickness of 0.75 m.

Fig. 8 schematically represents a perspective view of a tripod high-rise building 10 comprising a further example of a structural frame 12. Mainly differences with respect to Fig. 5 to 7 will be described.

The building 10 of the example in Fig. 8 has a height of 270 m and 70 floors 18. Each slanted section 14 is slanted 15 ⁰ with respect to vertical.

The structural frame 12 in Fig. 8 is similar to Fig. 7 but the structural frame 12 in Fig. 8 does not comprise any closed belts 22. Also, the structural frame 12 in Fig. 8 does not comprise any slanted mega columns 20 as in Figs. 5 and 6.

In Fig. 8, the elongated horizontal support elements 42 each has exterior dimensions of 0.587 x 0.587 m. The elongated inclined support elements 42 each has exterior dimensions of 0.936 x o. 936 m

Fig. 9 schematically represents a perspective view of a high-rise building 10 comprising a slanted section 14 and a cantilever section 44. The building 10 further comprises a plurality of cables 46 connecting the slanted section 14 to the cantilever section 44. The floors 18 are omitted in Fig. 9.

The slanted section 14 and hence the entire building 10 in Fig. 9 has a height of 257 m. The slanted section 14 is slanted 7 ⁰ with respect to vertical. The slanted section 14 comprises 66 floors 18. Each floor 18 has a height of 3.9 m except the top floor 18 which has a height of 5.25 m. Seven floors 18 in the slanted section 14 aligned with the cantilever section 44 extend from the slanted section 14 into the cantilever section 44. The cantilever section 44 is placed between story 35 and 42, i.e. the lower side of the cantilever section 44 is positioned at a height of approximately 137 m. The cantilever section 44 has a length (i.e. in the horizontal direction) of 73.4 m. The structural frame 12 for the slanted section 14 in Fig. 9 comprises a plurality of slanted mega columns 20. More specifically, the structural frame 12 comprises eight slanted mega columns 20 parallel with the slanted section 14, i.e. 7 ⁰ with respect to vertical. The mega columns 20 are arranged at the perimeter 16 of the slanted section 14. Four slanted mega columns 20 are arranged at the corners of the slanted section 14. Four slanted mega columns 20 are arranged centrally disposed at the sides of the slanted section 14. Each slanted mega column 20 extends from the base 24 of the building 10 to the top 26 of the building 10. The mega columns 20 may be of steel or reinforced concrete columns. The outer dimensions of each mega column 20 in this example is 2 x 2 m (for both steel and reinforced concrete). Steel mega column 20 may have a thickness of 0.1 m. Mega columns 20 of reinforced concrete may be solid and may be reinforced with A6isGr6o bars that cover a total of 1.1% of the respective cross sectional area.

The structural frame 12 for the slanted section 14 in Fig. 9 further comprises a plurality of elongated support elements 42. The support elements 42 close the perimeter 16 of the slanted section 14. In Fig. 9, the elongated support elements 42 are constituted by X- bracings. The support elements 42 for the slanted section 14 may be made of steel.

The structural frame 12 in Fig. 9 also supports the cantilever section 44. The structural frame 12 for the cantilever section 44 comprises a plurality of elongated support elements 42 arranged as a Pratt truss. As can be seen in Fig. 9, also the support elements 42 for the cantilever section 44 is arranged at the perimeter 16 of the cantilever section 44.

The cables 46 may for example have a diameter of 250 mm, 350 mm or 450 mm. The cables 46 may be prestressed, for example with forces of 10 MN, 15 MN or 20 MN. The building 10 in Fig. 9 comprises six cables 46 arranged in a fan shape. Three cables 46 are connected to a single point on one side of the slanted section 14 and the three cables 46 are connected to two different points on one side of the cantilever section 44 and three cables 46 are connected to a single point on the opposite side of the slanted section 14 and the three cables 46 are connected to two different points on the opposite side of the cantilever section 44. Simulations in ETABS ® of the building 10 in Fig. 9 have positively indicated that the building 10 has a range of periods of 4.8 to 6.4 s. The building 10 in Fig. 9 is thus a stiff structure.

For at least some of the floors 18, the loads of a floor 18 and the loads on the same floor 18 are transferred to the structural frame 12 at the perimeter 16 of the slanted section 14. The building 10 in Fig. 9 does not comprise a central core. A central vertical elevator core cannot be accommodated within the building 10 from the base 24 to the top 26. The building 10 in Fig. 9 may further comprise an elevator system (not shown) configured to drive cabins from the base 24 to the top 26 along a common path comprising non-vertical sections. The elevator system may drive cabins horizontally into the cantilever section 44.

Fig. 10a schematically represents a side view of an arch shaped high-rise building 10 comprising one example of a structural frame 12 and Fig. 10b schematically represents a perspective view of the high-rise building 10 in Fig. 10a. With collective reference to Figs. 10a and 10b, the arch shaped building 10 has a span (distance between the bases 24) of 300 m and a height of 400 m. Thus, the span/rise ratio is 0.75. The width of the building 10 is 30 m and the slenderness ratio is approximately 1:10. There are 80 floors 18 and the height of each story is 5 m.

The structural frame 12 of Figs. 10a and 10b comprises four mega columns 20. Each mega column 20 forms an arch shape conforming to the general arch shape of the building 10. At the base sections 48, the arch shaped building 10 comprises substantially straight slanted sections 14.

At the top 26 (i.e. the crown) of the building 10, the height (Z-direction) of the structural frame 12 is 10 m, the width (Y-direction) of the structural frame 12 is 30 m, the height of each mega column 20 is 2 m, the width of each mega column 20 is 2 m and the thickness of each mega column 20 is 0.4 m.

At each base 24 of the building 10, the structural frame 12 is quadratic with a width of 30 m and each mega column 20 is quadratic with a width of 6 m and a thickness of 0.4 m. The center of gravity of the building 10 is horizontally between the bases 24. As can be gathered from Figs. 10 and 11, a vertical core, such as a central vertical elevator core, cannot be accommodated within the arch shaped building 10 from a base 24 to the top 26. The building 10 may comprise an elevator system having a plurality of cabins, wherein the elevator system is configured to drive the cabins along a common path comprising non-vertical sections. The structural frame 12 further comprises a plurality of elongated support elements 42. The support elements 42 are arranged at the perimeter 16 of the structural frame 12. Each support element 42 connects two mega columns 20. In Figs. 10a and 10b, the support elements 42 are constituted by steel braces arranged in cross formation forming an X-bracing. The support elements 42 may be made of steel such as steel S355. The outer dimensions of each support element 42 may be 0.5 x 0.25 m and the thickness may be 0.025 m. The support elements 42 may be pin connected to each mega column 20 and may be fixedly connected to each other at their intersection points.

The structural frame 12 of Figs. 10a and 10b performs structurally like a bridge. The X- bracing provides a low buckling, low bending moments in the mega columns 20 and a maximum deflection at the top story (story 80) of approximately 1 m.

For each of the two slanted sections 14 in Figs. 10a and 10b, the structural frame 12 comprises four mega columns 20 and elongated support elements 42 interconnecting the mega columns 20. Thereby, the mega columns 20 and the elongated support elements 42 of the structural frame 12 close the perimeter 16 of each slanted section 14. At each base 24 of the two legs, each mega column 20 is slanted io° with respect to vertical. Thus, the building 10 does not comprise any perfectly vertical sections.

As an alternative to the X-bracing in Figs. 10a and 10b, the support elements 42 may be arranged in an F-bracing. The F-bracing utilizes the principles of steel moment frames. As a further alternative, the structural frame 12 in Figs. 10a and 10b may alternatively comprise B-bracing, for example closed belts 22 (not shown) arranged at every 25 m (every fifth floor 18) in the base sections 48 (up to 100 m) of the building 10 and closed belts 22 arranged at every 50 m (every tenth floor 18) in the sections above the base sections 48. The closed belts 22 may be constituted by steel trusses having a height of 5 m (corresponding to the height of one story). The closed belts 22 may close the perimeters 16 of each slanted section 14. As a further alternative to the X-bracing in Figs. 10a and 10b, the structural frame 12 of the buildings 10 may comprise diagrids according to the present disclosure, for example interconnecting the mega columns 20 as in Fig. 15. As a further alternative to the X- bracing in Figs. 10a and 10b, the structural frame 12 of the buildings 10 may comprise moment frames according to the present disclosure, for example as in Figs. 7, 8, 23 and 24.

Fig. 11 schematically represents a perspective view of a V-shaped high-rise building 10 comprising one example of a structural frame 12. The floors 18 are omitted in Fig. 11.

The building 10 of this example is 300 m tall. The building 10 comprises two slanted sections 14 and a base section 48. Each slanted sections 14 comprises a perimeter 16 and a plurality of floors 18. In this example, there are 94 floors 18 in each slanted section 14. The floors 18 of the slanted sections 14 are of equilateral triangular shape and the floors 18 of the base section 48 are square. The widths of the slanted sections 14 are each 30 m. The dimensions of the floors 18 of the base section 48 are 19.5 x 19.5 m. Each slanted section 14 is slanted io° with respect to vertical. The building 10 of Fig. 11 has a weight of about 135 000 tons.

For each slanted section 14, the structural frame 12 of Fig. 11 comprises three slanted mega columns 20 arranged at the perimeter 16 and elongated support elements 42 arranged at the perimeter 16 and interconnecting the mega columns 20. Thereby, the mega columns 20 and the elongated support elements 42 of the structural frame 12 close the perimeter 16 of each slanted section 14. Each mega column 20 is also slanted io° with respect to vertical.

Each support element 42 may have a circular cross section. The mega columns 20 may be constituted by composite columns with several (for example four) encased steel profiles. The mega column 20 may have substantially constant cross section along the height of the building 10.

The mega columns 20 may be made of concrete, steel and/or composite material. Also the elongated support elements 42 may be made of concrete, steel and/or composite material. The two outer mega columns 20 (one associated with each slanted section 14) of the building 10 extend from a base 24 of the building 10 to the top 26 of the building 10. The four inner mega columns 20 (two associated with each slanted section 14) of the building extend from the top of the base section 48 of the building 10 to the top 26 of the building 10. The structural frame 12 comprises four mega columns 20, 28 associated with the base section 48: the two outer mega columns 20 and two vertical mega columns 28. Each vertical mega column 28 associated with the base section 48 branch (at the 22 ^nd floor 18 in Fig. 11) to two inner mega columns 20, one associated with each slanted section 14. The two outer mega columns 20 may be constituted by tubed concrete columns with a substantially constant cross sectional profile. In the example of Fig. 11, the two outer mega columns 20 have external dimensions of 4.50 x 6.70 m and a thickness of 1.20 m.

The four inner mega columns 20 extending from the top of the base section 48 and the two vertical mega columns 28 extending from the base 24 may be constituted by tubed concrete columns with a substantially constant rectangular cross sectional profile. In the example of Fig. 11, the four inner mega columns 20 extending from the top of the base section 48 have external dimensions of 4 x 6 m and a thickness of 1.20 from story 22 to 51 and external dimensions of 2 x 2 m and a thickness of 0.5 m from story 52 to 94. The two vertical mega columns 28 extending from the base 24 have external dimensions of 3 x 5 m and a thickness of 1 m from story 1 to 6 and external dimensions of 3 x 5 m and a thickness of 0.80 m from story 7 to 21.

In Fig. 11, the elongated support elements 42 are constituted by X-bracings. The elongated support elements 42 form an X-truss along each side of the perimeters 16 of the slanted sections 14. In the outside trusses, i.e. the two trusses adjacent to the outside mega column 20 of each slanted section 14, the elongated support elements 42 are made of steel having external dimensions of 2 x 1.5 m and a thickness of 0.20 m. In the inside trusses, i.e. the truss between the two inner mega columns 20 of each slanted section 14 extending from the top of the base section 48, the elongated support elements 42 are made of steel having external dimensions of 1.5 x 1.5 and a thickness of 0.2 m.

For each slanted section 14 in Fig. 11, the mega columns 20 and the elongated support elements 42 form a structural frame 12 that is arranged at the perimeter 16 of the slanted section 14, that closes the perimeter 16 of the slanted section 14 and that carries at least 85% of the loads of the floors 18 in the slanted section 14. The structural frame 12 of Fig. 11 has a particularly low horizontal deflection, for example live load deflection and wind load deflection. Analyses in ETABS ® of the building in Fig. 11 have shown that the maximum

displacement for the top floor 18 is 272 mm in the X-direction and 284 mm in the Y direction. The maximum acceleration reaches 2251 mm/s ² in the X-direction. The maximum story drifts are constrained in the points where the support elements 42 are connected. The maximum story drift is 0.0019 in the Y-direction and 0.0013 in the X- direction. The structural frame 12 of Fig. 11 also has a buckling factor over 15 under dead loads and under dead, live and wind loads.

The structural frame 12 having an X-truss according to Fig. 11 is flexible and does not limit window space significantly. The structural frame 12 has a particularly low deflection under static loads. A central vertical elevator core cannot be accommodated within the building 10 from the base 24 to the top 26. The building 10 in Fig. 11 may further comprise an elevator system (not shown) configured to drive cabins from the base 24 to one or both tops 26 along a common path comprising non-vertical sections.

Fig. 12 schematically represents a perspective view of the V-shaped high-rise building 10 comprising a further example of a structural frame 12. Mainly differences with respect to Fig. 11 will be described.

For each slanted section 14, the structural frame 12 of Fig. 12 comprises three mega columns 20 and elongated support elements 42 interconnecting the mega columns 20. In Fig. 12, the elongated support elements 42 are constituted by bracings forming a K- truss along each side of the perimeters 16 of the slanted sections 14.

For each slanted section 14 in Fig. 12, the mega columns 20 and the elongated support elements 42 form a structural frame 12 that is arranged at the perimeter 16 of the slanted section 14, that closes the perimeter 16 of the slanted section 14 and that carries at least 85% of the loads of the floors 18 in the slanted section 14. Fig. 13 schematically represents a perspective view of the V-shaped high-rise building 10 comprising a further example of a structural frame 12. Mainly differences with respect to Figs. 11 and 12 will be described.

For each slanted section 14, the structural frame 12 of Fig. 13 comprises three mega columns 20 and elongated support elements 42 interconnecting the mega columns 20. In Fig. 13, the elongated support elements 42 are constituted by bracings forming an N- truss along each side of the perimeters 16 of the slanted sections 14.

For each slanted section 14 in Fig. 13, the mega columns 20 and the elongated support elements 42 form a structural frame 12 that is arranged at the perimeter 16 of the slanted section 14, that closes the perimeter 16 of the slanted section 14 and that carries at least 85% of the loads of the floors 18 in the slanted section 14.

Fig. 14 schematically represents a perspective view of the V-shaped high-rise building 10 comprising a further example of a structural frame 12. Mainly differences with respect to Figs. 11 to 13 will be described. For each slanted section 14, the structural frame 12 of Fig. 14 comprises three mega columns 20 and elongated support elements 42 interconnecting the mega columns 20. In Fig. 14, the elongated support elements 42 are constituted by bracings forming a W- truss along each side of the perimeters 16 of the slanted sections 14. In the W-truss, each support element 42 is angled 45 ⁰ with respect to an associated mega column 20. For each slanted section 14 in Fig. 14, the mega columns 20 and the elongated support elements 42 form a structural frame 12 that is arranged at the perimeter 16 of the slanted section 14, that closes the perimeter 16 of the slanted section 14 and that carries at least 85% of the loads of the floors 18 in the slanted section 14.

Fig. 15 schematically represents a perspective view of the V-shaped high-rise building 10 comprising a further example of a structural frame 12. Mainly differences with respect to Figs. 12 to 15 will be described.

For each slanted section 14, the structural frame 12 of Fig. 15 comprises three mega columns 20 and diagrids 50 interconnecting the mega columns 20. The diagrids 50 form net structures at the perimeter 16 and over the entire outer surfaces of each slanted section 14. Thus, the perimeter 16 of each slanted section 14 is closed by the mega columns 20 and the diagrids 50. The diagrids 50, which may be referred to as a diagonalized grid structure, constitute a triangulated member system that creates resistance to gravity and lateral loads on the building 10. The mega columns 20 and the diagrids 50 form a tube at the perimeter 16 of each slanted section 14. The building 10 of Fig. 15 has a weight of about 110 000 tons.

The diagrids 50 are constituted by a plurality of elongated support elements 42. The elongated support elements 42 are arranged at two different angles relative to the extension direction of an associated slanted section 14. Each elongated support element 42 of the diagrids 50 is either tensed or compressed.

In the example of Fig. 15, the two outer mega columns 20 comprise a composite section with four encased "jumbo" steel profiles. The four inner mega columns 20 are

rectangular, hollowed steel tubes filled with high strength concrete. The support elements 42 are constituted by braces chosen according to the demanded capacity and consist of circular concrete sections.

In the example of Fig. 15, the two outside mega columns 20 have external dimensions of 3 x 3 m and are solid. The four inner mega columns 20 extending from the top of the base section 48 (from story 25) have external dimensions of 1.5 x 1.5 m and a thickness of 0.10 m. All support elements 42 are solid. From story 1 to 20, the support elements 42 have external dimensions of 2 m. From story 21 to 56, the support elements 42 have external dimensions of 1.50 m. From story 57 to 80, the support elements 42 have external dimensions of 1.20 m. From story 81 to 94 (i.e. to the top 26 of the building 10), the support elements 42 have external dimensions of 0.80 m.

For each slanted section 14 in Fig. 15, the mega columns 20 and the elongated support elements 42 form a structural frame 12 that is arranged at the perimeter 16 of the slanted section 14, that closes the perimeter 16 of the slanted section 14 and that carries at least 85% of the loads of the floors 18 in the slanted section 14.

A structural frame 12 comprising diagrids 50 has lower vibration periods. Analyses in ETABS ® of the building in Fig. 15 have shown that the maximum displacement for the top floor 18 is 273 mm in the X-direction and 279 mm in the Y-direction. The calculated maximum acceleration reached 2600 mm/s ² in the Y-direction. The maximum story drift is below the limit for risk category III (0.015). Drifts for stories 36, 46 and 56 were closed to o. This is due to the elongated support elements 42 connected to the vertical mega columns 28 of the base section 48. The structural frame 12 of Fig. 15 also has a buckling factor over 15 under dead loads and under dead, live and wind loads.

Fig. 16 schematically represents a perspective view of the V-shaped high-rise building 10 comprising a further example of a structural frame 12. Mainly differences with respect to Figs. 11 to 15 will be described. The structural frame 12 of Fig. 16 differs from Fig. 15 in that the diagrids 50 are constituted by a plurality of elongated support elements 42 that are arranged parallel with the extension direction of an associated slanted section 14 and by a plurality of elongated support elements 42 that are arranged at an angle, such as 45 ⁰ , relative to the extension direction of the associated slanted section 14.

Fig. 17 schematically represents a perspective view of the V-shaped high-rise building 10 comprising a further example of a structural frame 12. Mainly differences with respect to Figs. 11 to 16 will be described. The structural frame 12 of Fig. 17 differs from Fig. 16 in that the diagrid 50 also comprises slanted elongated support elements 42 replacing the mega columns 20. To fulfill the load requirements, the dimensions of all support elements 42 are increased in comparison with Fig. 16.

Fig. 18 schematically represents a perspective view of the V-shaped high-rise building 10 comprising a further example of a structural frame 12. Mainly differences with respect to Figs. 11 to 17 will be described. For each slanted section 14, the structural frame 12 of Fig. 18 comprises three slanted mega columns 20 and closed belts 22 interconnecting the mega columns 20. The mega columns 20 and the closed belts 22 are arranged at the perimeters 16 of the slanted sections 14. The perimeter 16 of each slanted section 14 is closed by the mega columns 20 and the closed belts 22. Each closed belt 22 may be constituted by a rigid beam (for example by concrete), a wall or a truss. As can be seen in Fig. 18, the closed belts 22 are horizontally arranged. The closed belts 22 may be vertically spaced 20 m to 40 m, such as approximately 30 m, from each other. Each closed belt 22 may have a thickness of 1500 mm. In Fig. 18, the perimeter 16 of every seventh floor 18 of the slanted sections 14 is occupied by closed belts 22 and the perimeter 16 of every sixth floor 18 of the base section 48 is occupied by closed belts 22. Each closed belt 22 may occupy the entire perimeter 16 associated with a story. The floors 18 of the stories associated with closed belts 22 may be used as mechanical floors, for example for accommodating stations for an elevator system. In the example of Fig. 18, all mega columns 20 are constituted by tubed rectangular concrete columns. The mega columns 20 are divided into three groups along the height of the building 10. The mega columns 20 have external dimensions of 6.80 x 4.60 and a thickness of 1.30 m from story 1 to 32. The mega columns 20 have external dimensions of 5.50 x 3.50 m and a thickness of 1.00 m from story 33 to 58. The mega columns 20 have external dimensions of 5.00 x 3.00 and a thickness of 0.80 m from story 59 to 94 (i.e. at the top 26 of the building 10). Analyses in ETABS ® of the building 10 in Fig. 18 have shown that the maximum story displacement was 262 mm in both the X-direction and the Y- direction. The maximum acceleration reaches 1769 mm/s ² in the X-direction. The drifts were lower on the floors 18 with closed belts 22. The maximum story drift does not exceed the value of 0.0014, which is below the limit for risk category III (ASCE 2010). The structural frame 12 of Fig. 18 also has a buckling factor over 15 under dead loads and under dead, live and wind loads.

Fig. 19 schematically represents a perspective view of the V-shaped high-rise building 10 comprising a further example of a structural frame 12. The structural frame 12 of Fig. 19 differs from Fig. 18 in that the structural frame 12 in Fig. 19 comprises two outer mega columns 20 and one inner mega column 20 associated with each slanted section 14. For each slanted section 14, the two outer mega columns 20 extend from the base 24 to the top 26 of the building 10. The structural frame 12 further comprises one vertical mega column 28 arranged in the base section 48. For each slanted section 14, the inner mega column 20 extends from the top of the vertical mega column 28 in the base section 48 to the top 26 of the building 10.

Fig. 20 schematically represents a perspective view of the V-shaped high-rise building 10 comprising a further example of a structural frame 12. Mainly differences with respect to Fig. 18 will be described. For each slanted section 14, the structural frame 12 in Fig. 20 comprises six slanted mega columns 20. The floors 18 of the building 10 in Fig. 20 have hexagonal cross sectional profiles.

Fig. 21 schematically represents a perspective view of the V-shaped high-rise building 10 comprising a further example of a structural frame 12. Mainly differences with respect to Fig. 18 will be described. For each slanted section 14, the structural frame 12 in Fig. 21 additionally comprises three slanted mega columns 20, one arranged between each pair of mega columns 20 in the corners.

Fig. 22 schematically represents a perspective view of the V-shaped high-rise building 10 comprising a further example of a structural frame 12. Mainly differences with respect to Fig. 18 will be described. For each slanted section 14, the structural frame 12 in Fig. 22 additionally comprises six slanted mega columns 20 arranged between the mega columns 20 in the corners. Two slanted mega columns 20 are arranged between each pair of mega columns 20 in the corners.

Fig. 23 schematically represents a perspective view of the V-shaped high-rise building 10 comprising a further example of a structural frame 12. Mainly differences with respect to Fig. 17 will be described. For each slanted section 14, the structural frame 12 of Fig. 23 comprises a moment frame constituted by slanted elongated support elements 42 and horizontal elongated support elements 42 rigidly connected to the horizontal support elements 42. The inclined support elements 42 are parallel with the associated slanted section 14. The structural frame 12 of Fig. 23 comprises two slanted elongated support elements 42 between each pair of slanted elongated support elements 42 in the corners of the slanted sections 14. The structural frame 12 of Fig. 23 does not comprise any mega columns 20.

Fig. 24 schematically represents a perspective view of the V-shaped high-rise building 10 comprising a further example of a structural frame 12. Mainly differences with respect to Fig. 23 will be described. The structural frame 12 of Fig. 24 comprises three slanted elongated support elements 42 between each pair of slanted elongated support elements 42 in the corners of the slanted sections 14. The structural frame 12 of Fig. 23 does not comprise any mega columns 20.

While the present disclosure has been described with reference to exemplary

embodiments, it will be appreciated that the present invention is not limited to what has been described above. For example, it will be appreciated that the dimensions of the parts may be varied as needed. Accordingly, it is intended that the present invention may be limited only by the scope of the claims appended hereto.