Buildings with Tubed Mega Frame Structures

MASTER OF SCIENCE THESIS STOCKHOLM, SWEDEN 2016

AREZO PARTOVI JENNY SVÄRD

KTH ROYAL INSTITUTE OF TECHNOLOGY SCHOOL OF ARCHITECTURE AND THE BUILT ENVIRONMENT

Global Analysis of Tall Buildings with Tubed Mega Frame Structures

Arezo Partovi and Jenny Svärd

TRITA-BKN, Examensarbete 489, Betongbyggnad 2016 ISSN 1103-4297 ISRN KTH/BKN/EX--489--SE Master thesis in Concrete Structures

Abstract

Today, tall buildings are generally built with a central core that transfers the loads down to the ground. The central core takes up a large part of the floor space and there is less room for the actual purpose of the building, such as offices and apartments. The consequence of this is also less rental profit. At a certain height of the building, the central core will not alone manage to keep the building stable. Therefore it needs to be connected with outriggers to withstand the horizontal forces. The Tubed Mega Frame system developed by Tyréns is designed without the central core and the purpose is to transfer all the loads to the ground via the perimeter of building, making the structure more stable since the lever arm between the loads is maximized. The system has not yet been used in reality. This thesis aimed at testing the efficiency of the Tubed Mega Frame system against conventional systems for tall buildings. Two different types of the Tubed Mega Frame system were evaluated; TMF Perimeter frame and TMF Mega columns. To begin with, a pre-study was carried out with the purpose of comparing wind deflections and eigenmodes of several conventional systems and Tubed Mega Frame systems. The buildings were modeled in the finite element software ETABS. The Core, outrigger and perimeter frame system performed best compared to the other conventional systems and was therefore chosen as the conventional system to be tested in the main study. A comparison of the Core, outrigger and perimeter frame system and eight different configurations of Tubed Mega Frame systems was carried out for several different building heights as a main study, based on the tall building 432 Park Avenue, New York. The deformations due to wind and seismic loading and eigenmodes were compared. Furthermore, the models were controlled for tension at the base and P- delta convergence. Overall the TMF Perimeter frame systems had the smallest deflections as the building height was increased and could be increased the most without reaching tension at the base. As the top story height of the buildings was increased, the Tubed Mega Frame systems outperformed the conventional system. For the TMF Perimeter frame system it could be seen that belt walls were more efficient than cross walls, and for the TMF Mega columns the smaller the distance between the belt or cross wall levels was, the less deflection was achieved. The Core, outrigger and perimeter frame system could be increased to 859 m in height before collapse and the Tubed Mega Frame system that performed best – TMF: Perimeter frame single story belt walls – was increased to 1024 m in height until divergence was achieved.

Sammanfattning

Dagens skyskrapor är i allmänhet byggda med en central kärna som fördelar lasterna ner till marken. Den centrala kärnan tar upp en stor del av golvytan och utrymmet för kontor, bostäder och dylikt i byggnaden minskas. Konsekvensen av detta är också lägre hyresintäkter. Vid en viss byggnadshöjd kan den centrala kärnan inte ensam hålla byggnaden stabil. Den måste anslutas med kraftiga balkar till pelare i fasaden, så kallade utriggare, för att kunna motstå de horisontella krafterna. Tubed Mega Frame är ett nytt koncept utvecklat av Tyréns som är utformat utan den centrala kärnan och syftet med systemet är att fördela alla laster ned till marken via bärverk i periferin av byggnaden, vilket gör strukturen mer stabil eftersom den inre hävarmen mellan lasterna maximeras. Systemet har ännu inte använts i verkligheten. Detta examensarbete syftar till att testa effektiviteten av Tubed Mega Frame jämfört med konventionella system för höghus. Två olika typer av Tubed-Mega-Frame-systemet utvärderades; TMF Perimeter frame och TMF Mega Columns. Till att börja med genomfördes en förstudie i syfte att jämföra utböjningar orsakade av vindlaster och egenmoder för ett flertal konventionella system och Tubed Mega Frame system. Byggnaderna modellerades i programmet ETABS, baserat på finita elementmetoden. Systemet med kärna, utriggare och momentram i perimetern uppnådde bäst resultat jämfört med de övriga konventionella systemen och därför valdes detta system till att provas och jämföras med Tubed- Mega-Frame-systemen i huvudstudien. En jämförelse av systemet med kärna, utriggare och momentram i perimetern och åtta olika konfigurationer av Tubed-Mega-Frame-systemet utfördes sedan för flertalet olika byggnadshöjder som huvudstudie, baserat på skyskrapan 432 Park Avenue, New York. Deformationerna på grund av vind- och jordbävningslaster och egenmoder jämfördes. Dessutom kontrollerades om dragspänningar uppnåddes i upplagen för de olika modellerna och huruvida P-delta-konvergens uppnåddes. Det kan konstateras att TMF-Perimeter-frame-systemen hade lägst utböjningar när byggnadshöjden ökades, och höjden kunde ökas mest utan att dragspänningar uppkom i upplagen. När byggnadernas höjd ökades uppnådde TMF: Perimeter Frame Single Story Belt Walls bättre resultat än det konventionella systemet. För TMF-Perimeter-Frame-systemen kunde det ses att de omslutande tvärväggarna var mer effektiva än de korsande väggarna, och för TMF-Mega-Columns-systemen gällde att ju mindre det vertikala avståndet mellan de omslutande tvärväggarna alternativt korsande väggarna var, desto lägre utböjning uppnåddes. Systemet med kärna, utriggare och momentram i perimetern kunde ökas till 859 m höjd före kollaps och det Tubed-Mega-Frame-systemet som gav bäst resultat - TMF: Perimeter Frame Single Story Belt Walls – kunde ökas till 1024 m höjd innan divergens uppnåddes.

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Preface

This master thesis has been written at the division of concrete structures, department of the Civil and Architectural Engineering, at the Royal Institute of Technology (KTH). The report concludes five tough but rewarding years as students at KTH. We thank Tyréns that made it possible for us to write this work. A special thanks also to our supervisor at Tyréns, Fritz King, who provided us with great knowledge about tall buildings and for all the help and guidance. We also thank our supervisor, Adjunct Professor Mikael Hallgren, for his helpful support and feedback throughout the process. Last but not least, we thank our examiner Anders Ansell for his support and all that he has learned us about concrete during our years at KTH.

Notations

Latin capital letters

퐴 = Cross-section area of the beam

퐶푝 = External pressure coefficient 퐷 = Diameter of the building 퐸 = Young’s modulus 퐹 = Force

퐹푎 = Short period site coefficient

퐹푣 = 1-s period site coefficient 퐺 = Shear modulus

퐺퐶푝𝑖 = Internal pressure coefficient

퐺푓 = Gust-effect factor for flexible buildings 퐼 = Second moment of inertia 퐿 = Length of the beam

푆1 = Mapped MCER spectral response acceleration parameter at 1-s period

푆푎 = Design spectral response acceleration

푆퐷1 = Design spectral response acceleration parameter at 1-s period

푆퐷푆 = Design spectral response acceleration parameter at short periods

푆푀1 = MCER spectral response acceleration parameter at 1-s period adjusted for site class effects

푆푀푆 = MCER spectral response acceleration parameter at short periods adjusted for site class effects

푆푠 = Mapped MCER spectral response acceleration parameter at short periods 푆푡 = Dimensionless parameter called Strouhal number for the shape 푇 = Period of the structure 푉 = Mean wind speed at the top of the building

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Latin lower case letters

푐푝푒 = the pressure coefficient for external pressure

푐푝𝑖 = the pressure coefficient for internal pressure [푑]= Displacement vector [푓]= Force vector

푓푣 = Vortex shedding frequency [푘]= Stiffness matrix 푘 = Spring constant p = Design wind pressures for the main wind-force resisting system of flexible enclosed buildings

푞 = 푞ℎ for leeward walls, side walls and roofs, evaluated at height h

푞 = 푞푧 for windward walls evaluated at height z above the ground

푞𝑖 = 푞ℎ for windward walls, side walls, leeward walls and roofs of enclosed buildings and for negative internal pressure evaluation in partially enclosed buildings

푞푝(푧푒) = the external peak velocity pressure

푞푝(푧𝑖) = the internal peak velocity pressure 푢 = Displacement

푧푒 = the reference height for external pressure

푧𝑖 = the reference height for internal pressure

Greek letters

훾 = Shear strain 휀 = Strain 휈 = Poisson’s ratio 휎= Stress 휏 = Shear stress

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Table of Contents

Abstract ...... i Sammanfattning ...... iii Preface ...... v Notations ...... vii 1 Introduction ...... 1 1.1 Background ...... 1 1.2 Problem description ...... 1 1.3 Aim and scope ...... 3 1.4 Limitations ...... 3 2 Tall buildings ...... 5 2.1 Definition of tall building ...... 5 2.2 Structural systems in tall buildings ...... 5 2.2.1 Moment frames without braces ...... 5 2.2.2 Tubes ...... 6 2.2.3 Core systems ...... 7 2.2.4 Tubed moment frame ...... 9 2.2.5 Trussed tube ...... 11 2.2.6 Tube in a tube ...... 13 2.2.7 Outrigger system ...... 14 2.3 432 Park Avenue ...... 16 2.4 High-strength concrete ...... 18 3 Finite Element Method ...... 19 3.1 ETABS ...... 20 3.1.1 Frame elements in ETABS ...... 20 3.1.2 Shell elements in ETABS ...... 21 4 Structural mechanics and lateral loads ...... 23 4.1 P-delta effect ...... 23 4.2 Stiffness theory ...... 24 4.3 Lateral loads ...... 25 4.3.1 Wind load ...... 25 4.3.2 Seismic action ...... 28 5 Pre-study of structural systems in ETABS...... 33

5.1 Introduction ...... 33 5.2 Properties ...... 33 5.2.1 Current structural systems ...... 33 5.2.2 Tubed Mega Frame systems ...... 38 5.3 Analysis ...... 41 5.3.1 Deformations and modes ...... 41 5.3.2 Comparison of mesh sizes ...... 43 5.3.3 Dead loads ...... 44 5.4 Discussion and conclusions from the pre-study ...... 44 6 Comparison of Tubed Mega Frame systems against conventional structural system for tall buildings ...... 47 6.1 Introduction ...... 47 6.1.1 Deformations and periods ...... 47 6.1.2 Forces at the base ...... 47 6.1.3 Convergence test ...... 48 6.1.4 Model verification ...... 48 6.2 Description of models ...... 48 6.2.1 Core, outrigger and perimeter frame ...... 49 6.2.2 TMF: Perimeter frame ...... 50 6.2.3 TMF: Mega columns ...... 55 6.3 Mesh...... 59 6.4 Assumptions and limitations ...... 59 6.5 Loads ...... 59 6.5.1 Wind load ...... 60 6.5.2 Seismic action ...... 61 6.6 Results ...... 61 6.6.1 Deformations and periods ...... 61 6.6.2 Forces at the base ...... 69 6.6.3 Convergence test ...... 74 6.6.4 Model verification ...... 75 7 Discussion, conclusions and proposed further research ...... 77 7.1 Discussion and conclusions ...... 77 7.2 Proposed further research ...... 79 References ...... 81 Appendix A – Pre-study ...... 85

Appendix B - 3D pictures...... 89 Appendix C - Displacements and periods ...... 99 Appendix D – Percentage difference between including and excluding P-delta effects .. 105 Appendix E – Difference between including and excluding P-delta effects ...... 111 Appendix F – Forces at the base ...... 121 Appendix G – Dead loads and overturning moments ...... 129 Appendix H – Hand calculation of dead loads ...... 131

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1 Introduction

1.1 Background

With a vast population growth in many cities in the western world, it has in a lot of cases also led to an increase in land usage. This phenomenon is known as urban sprawl. There are several disadvantages that come with this development, for example social issues like segregation. Above all, it has a negative impact on the environment in terms of, among other things, air pollution and energy consumption (Bernhardt, 2007). An alternative solution to meet the growing population without letting it lead to drawbacks when it comes to social and environmental sustainability could be to build tall buildings. The development of tall buildings began during the 19th century. The structural system used in the beginning was based on the outer masonry walls which would carry the building’s weight. It resulted in that the walls at the base needed to be thicker for each story added in order to bear the overlying stories, which in turn required large base space. Thus, it was quite impractical and also expensive to build more than five stories. The lack of a transport system in these buildings also contributed to that the buildings were not built higher than four or five stories. With the invention of the elevator and a new structural system, the iron skeleton frame hidden behind masonry walls, so began the establishment of skyscrapers. (Haven, 2006) With tall buildings the cityscape becomes more compact which is more favorable from a social and environmental perspective (CNN, 2008). In addition, tall buildings is an effective way to provide residential and commercial space. Apart from the practical and functional advantages, tall buildings are also often constructed in hope of becoming a landmark to signify the city to the world.

1.2 Problem description

Today’s conventional way to build tall buildings is to build it with a central core, usually combined with another structural system. The central core will then act as the main load carrying structure in these buildings. One problem with this

structural system is that a relatively huge amount of each floor area must be assigned to the central core in order for the structure to withstand the vertical and horizontal loads the building is being exposed to. The problem arises when the perimeter of the building must decrease as the height increases in order for the building to maintain its stability. After a certain height, the required floor space for the core is larger than the available floor area. Consequently, this type of structural system with a central core prevents the possibility to transport people to the top. Tyréns has developed a new structural system for super tall buildings called the Tubed Mega Frame (TMF). The main purpose of this system is to transfer all loads to the perimeter of the building and thereby achieve higher stability since the lever arm between the load bearing components will be longer than in a core system. With this structural system there will be no central core. In this thesis, two different types of the Tubed Mega Frame system will be tested; TMF Perimeter frame and TMF Mega columns. Figure 1.1 illustrates the plan views of each system. The TMF Perimeter frame system consists of a tubed moment frame in the perimeter of the building and in addition to that belt walls or cross walls on certain heights. The TMF Mega columns system will contain huge vertical tubes placed at the perimeter of the building connected together by belt walls or cross walls at certain stories. These tubes will be the main load carrying elements in this structural system. With the Tubed Mega Frame system, no floor space has to be assigned for a central core and the building can therefore be made more slender. This will in turn lead to increased rentable space and function flexibility at each floor level. Less land-usage will also be needed when building this kind of tall building. There is also, unlike the conventional core, outrigger and perimeter frame system, a possibility to develop units at the stories were the belt walls or cross walls are installed. Hence, these stories do not have to be limited to use solely for placement of installations.

(a) (b) Figure 1.1: (a) Plan view of the TMF Mega columns with belt walls. (b) Plan view of the TMF Perimeter frame with cross walls. 1.3 Aim and scope

The aim of the thesis is to study the efficiency of the Tubed Mega Frame system compared to other structural systems for tall buildings. Firstly, a literature study will be carried out containing descriptions of present structural systems used in tall buildings. The literature study will also include, inter alia, how to calculate wind loads and seismic actions according to the ASCE Standard (American code) and some basic finite element method theory. Secondly, a pre-study of structural systems will be made. The finite element software ETABS will be used for modelling and analyzing these structural systems. The different models will be based on present structural systems but also on the Tubed Mega Frame concept. These models will be checked for periods and displacements due to wind load and compared to each other. Thirdly, based on the results from the pre-study, nine types of systems will be modeled in ETABS. In addition to wind load, seismic loading will also be checked for. The dimensions and configurations of the models will be inspired by the 426 m tall concrete building 432 Park Avenue in New York, USA.

1.4 Limitations

Live loads, installation loads and façade loads are neglected. The reason is that the main issue for this study is only to compare the structural systems against each other on a basic level, and provided that they are subjected to the same loads the

comparison can be made. The load cases are only controlled for in the ultimate limit state. The study is limited to structural systems of concrete, but the buildings can of course be built by another material such as steel. It would be somewhat problematic to make a valid comparison between structural systems of different materials in the sense that the members might not be equally stiff or of equal size. To reduce calculation time, the lateral loads are only applied in one direction, the x-direction. Vortex shedding effects are excluded. Material non-linearity are not accounted for in this study. The results are only applicable to the models used in this study and may thereby not be valid for the general case.

2 Tall buildings

2.1 Definition of tall building

There is no clear definition of "tall building". However, to be classified as a "tall building" it shall provide itself as a "tall building" on the basis of one or more aspects. For instance, the height of the building in terms of its environment is one aspect that can be taken into account in the determination of tall buildings. Another is its proportion. A building that is not particularly high can thus be classified as a tall building if it has enough slenderness. The final aspect that can be considered in the determination is whether the technical solutions which are typical for "tall buildings" have been used. For example, if a special transport system for vertical movement in the building is installed or the building has braces to withstand wind loads, it can be seen as a tall building. A supertall building is defined as a building over 300 m and a megatall building is defined as a building over 600 m (CTBUH, 2016).

2.2 Structural systems in tall buildings

2.2.1 Moment frames without braces

A moment frame is built by columns and beams which are connected to each other with rigid joints that thus resist moments. The vertical load is transferred via the beams to the columns and down to the foundation. Frames with moment resisting joints behave mainly in a shear mode when subjected to lateral loads. Figure 2.1 depicts the behavior of a moment resisting frame with a horizontal load at the top.

Figure 2.1: Moment resisting frame system subjected to lateral load (Merza & Zangana, 2014)

One advantage with the moment frame system is the reduction of the bending moment due to that the joints are rigid and that thanks to the joints the buckling length of the columns decreases. This leads to reduced sizes of the columns and beams, in comparison with a simply supported system. Though, this is only correct up to a certain height since the system is not economically defensible above that limit. Merza & Zangana (2014) claim that this system is effective up to circa 25 stories. If the building is higher, cost due to construction issues may increase to a large extent. If a moment frame is subjected to an asymmetric vertical load, it can suffer from side-sway. The consequence of the asymmetric vertical load on the frame is that one corner of the frame will have a larger moment. Due to that, the base restraint will be larger at this corner than the opposite corner which leads to an unfulfilled horizontal equilibrium. For the frame to be in equilibrium it sways a bit to the side, to make the moments at the corner joints equal. One has to be careful when defining loads to be aware of the effect of asymmetric loads, even if the case is simplified to symmetric loads (Merza & Zangana, 2014). Moment frames can be made of for instance concrete or steel. The steel moment frame consists of steel columns and steel beams. The concrete moment frame is built up by cast-in-place columns and beams (American Society of Civil Engineers, 2000).

2.2.2 Tubes

A tube is working as a vertical cantilever beam that is rigid at the foundation. A tube can consist of for instance a steel moment frame or concrete shear walls. Considering a concrete square tubular form, there would be four walls connected to each other similar to the form of a box. The optimal structure of a tube for achieving the highest lateral stability would consist of walls that are completely solid, i.e. without openings in form of doors and windows as in Figure 2.2. However, the lateral stability can be sufficient even though there are openings since it still

acts like box and is much better than if the four wall parts were not connected to each other.

Figure 2.2: Quadratic tubular system (Sandelin & Budajev, 2013)

If the structural elements are placed in the perimeter, the load is transferred down to the ground at the perimeter as well. This leads to a longer lever arm between the reaction forces which increases the overturning stability (Sandelin & Budajev, 2013). When lateral load is acting on a tube made of four connected walls, the box structure acts as a beam with webs and flanges. The wall that takes the load in the transverse direction is acting like the flanges by resisting the bending moment due to overturning, and the walls parallel to the load direction are acting as the webs and resist the shear forces (Merza & Zangana, 2014).

2.2.3 Core systems

The core system functions as a tube that resists both horizontal and vertical loads. The core is usually made of concrete shear walls, but can also be made of braced steel frames. The ultimate design would be to have a completely closed core, but for practical reasons the core is almost always open in some sense, since people should be able to use the space inside the core for elevators and other service areas (Sandelin & Budajev, 2013). Figure 2.3 below shows a structural system made of a reinforced concrete core with an outer steel frame.

Figure 2.3: Reinforced concrete core with steel frame (Inc., 2013)

When placing the shear walls around elevators and service risers, more consideration needs to be taken for the critical stresses at the ground level since the elevator system will require a concentration of openings there. The number and sizes of these openings throughout the height of the building also has a great impact on the torsional and flexural rigidity and needs to be considered (The Constructor, 2016). The core is usually combined with another structural system for tall buildings. For cases when it works as a structural system of its own, the floors are cantilevered off of the core and produce a column free interior. However, it is a very inefficient kind of structural system (Sandelin & Budajev, 2013). One example of a building using this type of structural system is the Turning Torso built in 2005 in Malmö, Sweden, shown in Figure 2.4. The building is 190 m high and uses a reinforced concrete core as the main load-bearing structure. It also has an external steel spine that acts as a strengthening and stiffening to the core (Lomholt, 2014).

Figure 2.4: Turning Torso, Malmö, Sweden (Malmö Stad, 2016)

2.2.4 Tubed moment frame

Moment frames can be used in a tube construction. The perimeter frame consists of a tubed moment frame at the building perimeter. One problem with the framed tube is that it suffers from shear lag. Shear lag is when the axial stresses in the columns are not evenly distributed, and instead the corner columns take much more load then the inner columns do, which is illustrated in Figure 2.5. The beams in the frame system are not fully able to distribute the load evenly to all of the columns (Sandelin & Budajev, 2013).

(a) (b)

Figure 2.5: Axial stress distribution in a tube structure. (a) Without shear lag. (b) With shear lag (Patil & Kalwane, 2015)

One example of a tall building that was using the perimeter frame system is the old World Trade Center in New York. The two towers were built in 1968-1973 and destroyed in terrorist attacks in 2011 (Silverstein Properties, 2016). The towers were 415 m and 417 m high respectively, and the lateral load bearing system was a tubed moment frame at the perimeter of the building. The columns were made of steel (Sadek, 2004). The vertical load was resisted by columns located both at the perimeter and in the core of the building, and it was distributed about evenly on these columns. The closely spaced perimeter columns were also assigned to withstand lateral forces due to wind (Gutierrez, et al., 2005). A picture of the old World Trade Center can be seen in Figure 2.6.

Figure 2.6: The old World Trade Center, New York, USA (Daily Mail, 2013)

2.2.5 Trussed tube

A trussed tube is a system with diagonals extending from side to side at the perimeter of the building, as shown in Figure 2.7. The diagonals are attached to each other at the point where they meet in the corners of the building, assuming the case of a rectangular building. A trussed tube is more efficient than a regular tubed moment frame since the diagonals have a large effect on the lateral stability of the building. As the diagonal trusses are attached to the columns in the perimeter, the shear lag effects decrease significantly. That is due to that the diagonals assist in distributing the gravitational forces that are transferred to the columns. The forces are then to a larger extent evened out on the columns. The diagonals take the load in their axial direction which results in a greater resistance against the load since the truss members are stronger axially then in bending and shear. Another advantage is that the number of columns can be reduced and the spacing between them can be increased, which improves the possibilities of window location (Merza & Zangana, 2014).

Figure 2.7: Trussed tube (Kumar & Kumar, 2016)

One example of an existing building using this type of structural system is the John Hancock Center, built 1969 in Chicago, USA, shown in Figure 2.8 below. The steel building is 344 m high and uses X-shaped braces at the perimeter of the building (Princeton University, 2011).

Figure 2.8: John Hancock Center, Chicago, USA (The man on five, 2016)

2.2.6 Tube in a tube

If a core system is combined with a perimeter moment frame, the system can be called a “tube in a tube”, since the outer tubed frame contains an inner tubed core. Figure 2.9 below illustrates a “tube in a tube” system. The combination resists lateral load much better than if only one of the systems were used alone. As the moment frame is weak in shear, the contribution of a core will assist in reducing the shear deformations, and in the same manner the frame will help reducing the bending deformation of the core. The final deflection form of this combination of systems will appear as an S-shaped deformation. The location of the maximum bending moment will move from the bottom to somewhere in the middle of the building (Sandelin & Budajev, 2013).

Figure 2.9: ”Tube in a tube” system (Kumar & Kumar, 2016)

One example of a building using this type of structural system is the Petronas Twin Towers, built 1998 in Kuala Lumpur, Malaysia, shown in Figure 2.10. The building is 452 m high and is made of a core and a perimeter frame of high-strength concrete (Charles, et al., 1997).

Figure 2.10: Petronas Twin Towers, Kuala Lumpur, Malaysia (Malaysia Truly Asia, 2016)

2.2.7 Outrigger system

Outriggers are rigid horizontal structures that link the core to the columns at the façade at one or more levels so that these structural elements work as one unit. The main advantage with this structural system is that it reduces the core’s overturning moment by inducing a tension-compression couple at the outrigger levels that act in opposition to the core’s rotation. Figure 2.11 below illustrates a core and outrigger system.

(a) (b) Figure 2.11: (a) Core and outrigger system. (b) Moment with and without outrigger bracing. (Choi, et al., 2012)

There are two types of outrigger systems; direct outrigger system and virtual outrigger system. A direct outrigger system implies a system with a core and outriggers extending to the columns along the façade of the building. The outriggers then involve the columns, forming them to a tension-compression couple that acts in opposition to the core’s rotation and hence it reduces the core’s internal overturning moment. Contrariwise, the shear forces at the outrigger levels increase and can even change direction. A virtual outrigger system implies a system with floor diaphragms and belt trusses that connects the columns together through a belt that encircle around the building. The forces then initiated by the tilting of the core makes the floor diaphragms move in altered directions at different levels. Since the belt trusses are attached to both the floors and the columns, it transfers the movements initiated by the floors to the columns. This results in a tension-compression couple in the columns that through the belt trusses push back the floor diaphragms and thus stabilizes the core (Sandelin & Budajev, 2013). One example of a building using this type of structural system is the Lotte World Tower in Seoul seen in Figure 2.12. The building is 555 m high and is built with a reinforced concrete core and outrigger belt steel truss. It is now under construction and will be completed in 2016 (Chung & Sunu, 2015) (Council on Tall Buildings and Urban Habitat, 2016).

Figure 2.12: Lotte World Tower, Seoul, South Korea (Council of Tall Buildings and Urban Habitat, 2014)

2.3 432 Park Avenue

432 Park Avenue, shown in Figure 2.14, is a super tall and super slim residential building in Manhattan, New York City. It is designed by the architect Rafael Viñoly and developed by CIM Group. The construction of the building began in 2011 and was finished at 2015. It is the third tallest building in the United States. It is also the tallest residential building in the world (The Skyscraper Center, 2016). The building is 426 m tall and is 28.5 m wide, giving it a slenderness of 1:15 (Durst, et al., 2015). The structural system is made of a core, outriggers and a perimeter frame of reinforced concrete. The core is placed in the center of the building and is 9 m long at each side and 76.2 cm thick. The core is housing the elevator shafts, the stairs and all the mechanical services (Alberts, 2014). A plan view of the building is shown in Figure 2.13.

Figure 2.13: Plan view of the 432 Park Avenue (Willis, 2015)

The columns in the perimeter frame are 112 cm wide and range in the depth from 163 cm at the bottom to 51 cm at the top of the building. The beams are also 112 cm wide, creating together with the columns the basket grid frame (Seward, 2014).

The perimeter frame and core are connected to each other by outriggers five times throughout the height of the building. The outrigger levels are two story high (Marcus, 2015). The building has 88 stories with a floor to floor height of approximately 4.72 m and with a floor thickness of approximately 254 mm. The thickness at the upper floors are however approximately 457 mm in order to add more mass to the building and damp the acceleration from wind loads. To ease the effects of wind vortex acting on the building, the basket grid modules are left empty at the outrigger levels in order to let the wind simply pass through. At the top of the building, a double tuned mass damper is installed in order to control the acceleration of the building (Seward, 2014). A simplified model of the 432 Park Avenue will be made and used in the main study for comparison with different Tubed Mega Frame models.

Figure 2.14: 432 Park Avenue, New York, USA (Cityrealty, 2016)

2.4 High-strength concrete

The use of high-strength concrete has been important when constructing tall buildings. If the columns of a tall building were to be built using normal concrete with a lower compressive strength, the dimensions of the columns would need to be very large resulting in less usable floor space. Even if high-strength concrete is more expensive than normal concrete, money can also be saved due to the fact that it is cheaper than using more reinforcement. The term “high-strength concrete” applies to concrete with a compressive strength higher than conventional concrete strengths at a certain limit. The limit strength is somewhat arbitrary and has developed over the years. In the 1970’s the limit strength for when concrete should be called high-strength concrete was 40 MPa, which was the 28-days strength. Then high-strength concrete named concrete strengths as high as 60-100 MPa, which became common to use in for instance bridges with large spans and tall buildings (Monteiro, 2002). While normal concrete has a water-cement ratio between 0.40 and 0.60, high- strength concrete needs to have a lower water-cement ratio to achieve greater strength. It can be about 0.25 but also lower than that. Other necessary admixtures may be superplasticizers, water-reducing additives, silica fume and fly ash (Nilson, et al., 2003). Along with the compressive strength a sufficiently high elastic modulus is also essential for the concrete in tall buildings. The concrete becomes stiffer when the elastic modulus is higher. The components that affects the elastic modulus is particularly the elasticity of the cement paste and the aggregates (Dahlin & Yngvesson, 2014). It is important to consider the configuration of the cement and that it works well with the additives brought into the mixture. The size and sort of aggregate in the concrete mixture has a large effect on the concrete strength and also the volume stability. Since the water-cement ratio is lower in high-strength concrete, the mixture becomes denser and could cause casting to be a problem when the concrete is in its fresh state, if not carefully proportioned. When mixing concrete, one uses different levels of fineness in the aggregate and it could be a good idea to use larger fine aggregates – the smallest parts – due to several reasons. Firstly, the mixture contains small parts in form of cement and fly ash which makes it superfluous to add super fine aggregate for the improvement of workability. Secondly, there will be higher shear stresses due to larger fine aggregates which assist in preventing that the cement paste flocculates, i.e. forms into clumps. Thirdly, the amount of water needed can be reduced when the fine aggregate is coarser. Furthermore, the size of the coarse aggregate should be smaller if a higher strength is desired (Monteiro, 2002).

3 Finite Element Method

Finite element method is a way of numerically solving field problems which are described by differential equations. There are many different areas where this method can be useful besides structural systems; heat transfer and magnetic fields among others. When using this method the structure is divided into small elements which are assigned chosen geometry and material properties. The division of a model into elements is called discretization. These elements are, as the name of the method implies, not infinitesimal but finitely small. The elements are connected to each other at nodes. The nodes are assigned boundary values and restraints. It is at these nodes the analysis yields the results, and the values are then interpolated between the nodes to get results there as well. The network of elements attached to each other is called mesh. (Cook, et al., 2002) Equation (3-1) describes the mathematical expression that the finite element method bases the calculation of the displacements at the nodes on.

[푑] = [푘]−1[푓] (3-1)

[푑]= Displacement vector [푘]= Stiffness matrix [푓]= Force vector The procedure starts with the built-up of the local stiffness matrix for each element which then are assembled to the global stiffness matrix [푘]. The force vector [푓] is determined and the system is then reduced due to boundary conditions. The displacements [푑] can then be solved, and the stresses and reaction forces can be calculated (Andersson, 2015). The results of the analysis are only approximate since the elements are finitely small. It is important to choose the right element type and size for the analysis to be able to get a result with the desired accuracy. To achieve a more accurate result and thus get as near the real solution as possible, more elements can be used. One of the advantages with the finite element method is that every structure is possible to build regardless of the complexity of the geometry. One has to be careful when performing a finite element analysis since there are different kinds of errors that can be introduced that can affect the accuracy of the results. First of all, modelling error can arise if the model is wrongly computed or too many or too incorrect simplifications are made. Another problem can be

discretization error which can occur if the elements are too large and can yield in a less accurate result since the distance between the nodes becomes greater. This can be improved by dividing the structure into more elements. Furthermore, numerical error is introduced when the computer makes calculations with finite number of decimals. These are just a few possible errors that can occur, there are others besides from these that one has to be aware of (Cook, et al., 2002). 3.1 ETABS

ETABS is software developed by Computers and Structures, Inc. that is based on the finite element method. ETABS is specially designed for buildings and is suitable for tall buildings thanks to the predefined wind loads and seismic loadings according to several different building codes; Eurocode and American code ASCE among others (Tönseth & Welchermill, 2014).

3.1.1 Frame elements in ETABS

Frame elements are used when modeling for instance columns, beams and trusses. The element is described as a combined beam and bar element with twelve degrees of freedom in three dimensions, illustrated in Figure 3.1. The frame element can be subjected to axial stress, shear stress and bending. The shape of the element is a straight line with nodes at the ends. The elements have individual local coordinate systems. The interpolation from the nodes of the element can be linear, quadratic or cubic (Computers and Structures, Inc., 2013).

Figure 3.1: Frame element (Princeton, 2016)

3.1.2 Shell elements in ETABS

A shell element is similar to a plate but with curved surfaces. The thickness of the shell is small in comparison to the length and width of the shell (Cook, et al., 2002). The shell element uses a combination of plate-bending and membrane behavior. It can be three-noded or four-noded. Floors, walls and decks are examples of structures that are modeled with shell elements. The stresses of a shell element are evaluated using four integration points (Gauss points). Similar to the frame elements, the shell elements also have individual local coordinate systems. Figure 3.2 below shows a quadrilateral shell element.

Figure 3.2: Four-node shell element (Computers and Structures, Inc., 2013)

One can decide to use Kirchhoff or Mindlin elements as shell elements. The Kirchhoff elements are thin-plate elements where the shear stresses are ignored. The other choice is Mindlin which are thick-plate elements that take account for the shear stresses (Computers and Structures, Inc., 2013). According to Figure 3.3, the straight normal to the mid-surface remains straight in both cases. In the Kirchhoff element the normal remains normal to the mid-surface but in the Mindlin element the normal has an angle to the mid-surface which cause shear stresses (Pacoste, 2015).

Figure 3.3: Basic assumptions for Mindlin and Kirchhoff theory, respectively (Pacoste, 2015)

The stresses in Kirchhoff elements can be evaluated according to Equation (3-2). In a Mindlin element there will in addition also be shear stresses calculated as in Equation (3-3).

1  0  x     x        E   1 0   y    y  2  1    (3-2)    1   0 0    xy  2  xy      

 zx G 0   zx           yz  0 G  yz (3-3)

4 Structural mechanics and lateral loads

4.1 P-delta effect

P-delta effect is a nonlinear effect for when the geometry of a structure changes due to loading. These second order effects occur when a member is exposed to both axial load and lateral load. The axial force can be either a compressive force or a tensile force, causing the member to either be more flexible respectively be more stiffened concerning bending or shear in the transverse direction (Computers and Structures, Inc., 2013). As lateral forces cause side-way deflection, the axial forces will act eccentrically. The foundation of e.g. a tall building will then be affected by an additional moment which in turn increases the deflection. These effects becomes very important when designing tall buildings since the deflections will be larger the higher the building is. There are two different kinds of P-delta effects considered in ETABS; the P-δ effect accounts for local deflections between the ends of a structural member while the P-Δ effect handles the deflection in member ends (CSI Knowledge Base, 2013). Figure 4.1 shows the P-delta effect for a column subjected to axial and transverse loads.

Figure 4.1: P-delta effect for the bending moment of a column subjected to axial and transverse loading (CSI Knowledge Base, 2013)

4.2 Stiffness theory

The stiffness of a beam can be determined by the elementary cases for end-forces caused by end-displacements. A number of them are shown below in Figure 4.2.

퐸퐴 퐹 = −퐹 = (4-1) 1 2 퐿

6퐸퐼 퐹 = 퐹 = (4-2) 1 2 퐿2

12퐸퐼 퐹 = −퐹 = (4-3) 3 4 퐿3

4퐸퐼 퐹 = (4-4) 1 퐿

2퐸퐼 퐹 = (4-4) 1 퐿 6퐸퐼 퐹 = −퐹 = (4-5) 3 4 퐿2 Figure 4.2: Elementary cases for end-forces caused by end-displacements (Leander, 2014)

Based on the formulas above, it appears that the beam length is the parameter that gives the greatest effect on the beam stiffness since the beam length’s exponent is greater than one, except for the first elementary case. The shorter the beam is, the greater the beam’s stiffness becomes. From the equation below, it is understood that the stiffer a beam is, the less the beam’s deflection becomes due to external load (Leander, 2014).

퐹 = 푘 × 푢 (4-6) In the elementary cases above, u is applied as one unit length, and therefore F equals k in the end-forces formulas in the figure above.

4.3 Lateral loads

4.3.1 Wind load

Wind arises from pressure differences in the atmosphere. The air moves from areas with high pressure towards areas with low pressure. The greater the difference there is in air pressure, the stronger the wind becomes (SMHI, 2016). Wind load is a vital part when designing a tall building since the effect of it will become significantly greater with an increase in height of the building. The wind rarely blows with the same speed all the time. Instead it changes in an intermittently, irregular way in both its intensity and direction. This sudden variation in wind intensity is called gustiness and is important to consider in dynamic design of tall buildings (SMHI, 2015). The wind speed is affected by season, terrain and surface roughness and so on, which in turn results in a wide-ranging wind speed through changing time of the year and locations. To be able to consider the effects of wind in the design, a mean speed velocity is used. The mean speed velocity is in turn based on a mass of observations. Whether the wind gust is seen as a dynamic or static effect depends on how quickly the wind gust reaches its maximum value and disappears relatively to the structures period. If it reaches its maximum value and disappears in a time shorter than the structures period it will cause a dynamic effect. Contrariwise, if the wind gust switches between maximum value and disappearing in a time much longer than the structures period, it is considered as a static effect. When it comes to dynamic design of the structures, it is important to consider the gust wind load above the steady mean wind flow. This is because the gusty wind usually exceeds the mean velocity and has a greater impact on the structures due to their rapid changes. In design within the civil engineering field, the wind flow can be considered as two- dimensional since the wind effects along the vertical axis often can be neglected. The wind flow can thus be seen as operating at the along wind direction and across wind direction as shown in Figure 4.3.

Figure 4.3: Simplified wind flow (Zhang, 2014)

Two major phenomena occurs when the wind is acting on the surface of a building and that needs to be considered. The first one is the fluctuation on the along-wind side and the second one is vortex shedding on the across-wind side. Resonance may occur on the along-wind side when the gust period is the same as or close to the structure’s natural period, resulting in much higher damage on the structure in proportion to the magnitude of the wind load (Zhang, 2014). As mentioned, there are also wind effects acting on the structure at the across-wind direction. These effects are especially common for tall and slender buildings. The cause for these effects comes from that wind at high speed stops spreading to both sides of the body simultaneously and instead it spreads first to one side of the body and then to the other, creating eddies and vertices as forces in the winds transverse direction. The phenomenon for when wind creates oscillations in both the along- wind and across-wind direction is called vortex shedding (Sandelin & Budajev, 2013). If the frequency of the vortex shedding is the same as or close to the structures natural frequency, it will cause resonance. The frequency due to vortex shedding can be determined by using the following formula:

푉×푆푡 푓 = (4-8) 푣 퐷 Where,

푓푣 is the vortex shedding frequency [Hz] 푉 is the mean wind speed at the top of the building [m/s]

푆푡 is the dimensionless parameter called Strouhal number for the shape 퐷 is the diameter of the building [m]

For tall buildings, the across-wind effects are usually more critical than the along- wind effects. To determine if the vortex-shedding effects are at a critical level for a certain structure, a wind tunnel test is usually required (Zhang, 2014). Below is a figure showing the vortex shedding phenomenon.

Figure 4.4: Vortex Shedding (Sandelin & Budajev, 2013)

Wind speed variation with distance above the ground

The roughness of the ground has a great impact on the wind speed. The smaller distance to the ground the more obstacles there is, causing friction and drag on the wind flow, thus the wind speed becomes lower closer to the surface. The frictional drag will however decrease as the height increases, leading to a higher wind speed at increasing distance from ground level. At a certain distance above ground, the wind speed will predominantly depend on the current local and seasonal wind effects at the same time as the frictional drag effects are considered to be negligible. The height where the frictional drag effects are considered to be negligible on the wind speed is called gradient height. The corresponding velocity at that height is called gradient velocity (Zhang, 2014).

Wind load provisions according to ASCE

According to the ASCE 7-10 code, the design wind pressure for the main wind- force resisting system of flexible enclosed buildings shall be calculated with the following formula:

2 푝 = 푞퐺푓퐶푝 − 푞𝑖(퐺퐶푝𝑖) (푁/푚 ) (4-9)

Where,

푞 = 푞푧 for windward walls evaluated at height z above the ground.

푞 = 푞ℎ for leeward walls, side walls and roofs, evaluated at height h.

푞𝑖 = 푞ℎ for windward walls, side walls, leeward walls and roofs of enclosed buildings and for negative internal pressure evaluation in partially enclosed buildings.

퐺푓 = gust-effect factor for flexible buildings.

퐶푝 = external pressure coefficient.

퐺퐶푝𝑖 = internal pressure coefficient.

Wind load provisions according to Eurocode

According to the Eurocode En 1991-1-4:2005, the net pressure acting on the surfaces is obtained from Equation (4-10).

2 푤 = 푤푒 − 푤𝑖 = 푞푝(푧푒) ∗ 푐푝푒 − 푞푝(푧𝑖) ∗ 푐푝𝑖 (푁/푚 ) (4-10)

Where,

푞푝(푧푒) is the external peak velocity pressure

푞푝(푧𝑖) is the internal peak velocity pressure

푧푒 is the reference height for external pressure

푧𝑖 is the reference height for internal pressure

푐푝푒 is the pressure coefficient for external pressure

푐푝𝑖 is the pressure coefficient for internal pressure

4.3.2 Seismic action

The crust of the Earth is divided into several plates which are floating on magma in the mantle part of the Earth. When these plates are interacting with each other in form of collision, sliding or subduction, stresses arise. As the stresses are released, earthquakes are initiated. The effect of an earthquake can be measured through different entities such as acceleration, velocity, displacement, duration and magnitude (Lorant, 2012). As an earthquake takes place, the ground moves back and forth causing the bottom of a building to move with it. The top of the building will however not react at the same time. Instead there will be a short delay of the movement of the top due to inertial stiffness of the building (Zhang, 2014).

When an earthquake is taking place inertial forces are induced in buildings. The magnitude of these inertial forces are given by the mass of the building times the acceleration. This implies that with increasing mass the inertial forces increase as well. Therefore by building lightweight constructions at least one factor for the risk of damage can be reduced (Lorant, 2012). When designing a building considering seismic action in the American code ASCE 7-10, design response spectrum for acceleration is used, shown in Figure 4.5. It consists of four different parts described by the four different functions below.

푇 푆푎 = 푆퐷푆(0.4 + 0.6 ) 0 < 푇 < 푇0 (4-11) 푇0

푆푎 = 푆퐷푆 푇0 < 푇 < 푇푠 (4-12)

푆 푆 = 퐷1 푇 < 푇 < 푇 (4-13) 푎 푇 푠 퐿

푆 푆 = 퐷1∙푇퐿 푇 < 푇 (4-14) 푎 푇2 퐿 Where

2 2 푆 = 푆 = 퐹 푆 (4-15) 퐷푆 3 푀푆 3 푎 푠

2 2 푆 = 푆 = 퐹 푆 (4-16) 퐷1 3 푀1 3 푣 1 푇 = Period of the structure [s] 푆푎 = Design spectral response acceleration 푆푠 = Mapped MCER spectral response acceleration parameter at short periods 푆1 = Mapped MCER spectral response acceleration parameter at 1-s period 푆퐷푆 = Design spectral response acceleration parameter at short periods 푆퐷1 = Design spectral response acceleration parameter at 1-s period 푆푀푆 = MCER spectral response acceleration parameter at short periods adjusted for site class effects 푆푀1 = MCER spectral response acceleration parameter at 1-s period adjusted for site class effects 퐹푎 = Short period site coefficient 퐹푣 = 1-s period site coefficient There are different site classes according to the American code ASCE 7-10 - A, B, C, D, E and F – which are determined depending on the properties of the soil on the building site. Values for Fa and Fv are found in Table 4-1 respectively Table 4-2. The parameters Ss and S1 can be taken from chapter 22 in ASCE 7-10 where the Seismic Ground Motion Long-Period Transition And Risk Coefficient Maps are shown.

Figure 4.5: Design Response Spectrum (American Society of Civil Engineers, 2013)

Table 4-1: Site coefficient, Fa (American Society of Civil Engineers, 2013)

Table 4-2: Site coefficient, Fv (American Society of Civil Engineers, 2013)

5 Pre-study of structural systems in ETABS

5.1 Introduction

To gain knowledge about the behavior of structural systems used in tall buildings, a pre-study is performed. Ten models of different structural systems for tall buildings are modeled in ETABS and compared to each other. There will be six models built with structural systems that are used in buildings built today. Furthermore there will also be four models based on the Tubed Mega Frame system. The lateral displacements on the top story due to design wind load in the ultimate limit state according to the Eurocode and also the periods of the first three modes are evaluated; movement in the two diagonal directions and torsional movement. 5.2 Properties

The buildings are quadratic with the dimensions 51x51 m2 and are 271.5 m high. There are 60 stories and the height of each story is 4.5 m, except for the base story which is 6 m high. In all the different structural systems the floor is modelled by a 250 mm thick concrete slab with the concrete strength class C30/37. The concrete walls are 400 mm thick, and concrete strength class of the walls is C40/50, the concrete strength class of the concrete columns is C45/55 and the steel strength is S355 in all structural steel members.

5.2.1 Current structural systems

Core

This system consists of a quadratic core built by concrete walls. At the perimeter there are VKR400×400×16 steel columns. The core is the only thing resisting the wind loads since the steel columns are pinned and their only purpose is to support the dead load from the floors. A 3D picture of the model can be seen in Figure 5.1.

Figure 5.1: 3D view of the Core

Perimeter frame

In this system the perimeter frame is the system resisting the wind load. The core is removed and replaced by pinned VKR400×400×16 steel columns to resist the dead load. At the perimeter of the building there is a moment frame consisting of continuous concrete columns with the size 1200×800 mm2 except at the corners where there are 1000×1000 mm2 concrete columns. The concrete beams connecting to the columns are 400×1200 mm2. All the concrete members are solid. A 3D picture of the model can be seen in Figure 5.2.

Figure 5.2: 3D view of the Perimeter frame

Core and perimeter frame

This system is often called a tube in a tube and consists of both a concrete core and a concrete perimeter frame with the same properties as described in the two previous models. This means that both these parts assist in resisting the wind load. A 3D picture of the model can be seen in Figure 5.3.

Figure 5.3: 3D view of the Core and perimeter frame

Core and outriggers

In this model the concrete core is placed similar to the Concrete core model, but it is now also connected via outrigger walls to concrete outrigger columns with the dimensions 800×2000 mm. The outrigger walls are 9 m high walls with the upper side located at story 20, 40 and 60. A 3D picture of the model can be seen in Figure 5.4.

Figure 5.4: 3D view of the Core and outriggers

Core, outriggers and perimeter frame

This system is a combination of three systems and consists of a concrete core, a concrete perimeter frame and concrete outriggers with the same properties as in the Core model, the Perimeter frame model and the Core and outriggers model, respectively. A 3D picture of the model can be seen in Figure 5.5.

Figure 5.5: 3D view of the Core, outriggers and perimeter frame Core and diagonal braces

The system has a concrete core as in the Core model, but also has pinned concrete diagonal braces at the perimeter that start from the bottom and changes direction at story 20 and 40, i. e. extends 20 stories in height, and ends at the top story. The braces have the dimensions 1200×800 mm2. A 3D picture of the model can be seen in Figure 5.6.

Figure 5.6: 3D view of the Core and diagonal braces

5.2.2 Tubed Mega Frame systems

In the Tubed Mega Frame systems the core is removed and there are instead pinned VKR400×400×16 steel columns placed where the core walls would have been placed. TMF: Perimeter frame with belt walls on three levels

The system consists of a perimeter frame with the same properties as in the Perimeter Frame model. In addition to that there are belt walls encircling the building on three levels; 20, 40 and 60 m. The upper side of the walls starts at the mentioned story. A 3D picture of the model can be seen in Figure 5.7.

Figure 5.7: 3D view of the TMF: Perimeter frame with belt walls on three levels

TMF: Perimeter frame with cross walls on three levels

This system is basically the same as the previous model with one exception and that is a change in the location of the walls. The walls are now crossing from one perimeter side to the opposite of the building, but still on the same story heights as before, namely 20, 40 and 60 stories. A 3D picture of the model can be seen in Figure 5.8.

Figure 5.8: 3D view of the TMF: Perimeter frame with cross walls on three levels

TMF: Mega columns with belt walls on three levels

Eight large hollow concrete columns are placed at the perimeter of the building. The columns are made by concrete walls. At three heights - story 20, 40 and 60 – there are belt walls connecting the hollow concrete columns to each other. The belt walls are 9 m high, i.e. two stories. A 3D picture of the model can be seen in Figure 5.9.

Figure 5.9: 3D view of the TMF: Mega columns with belt walls on three levels

TMF: Mega columns with cross walls on three levels

This model is the based on the previous model with three belt wall levels but instead of belt walls it uses cross walls from one mega column to another one on the opposite side. A 3D picture of the model can be seen in Figure 5.10.

Figure 5.10: 3D view of the TMF: Mega columns with cross walls on three levels

5.3 Analysis

The models will be run both with and without P-delta effects to see if and how much the difference is for the different cases. A study of the element size contribution to the results will be made on the Core, outrigger and perimeter frame model. This is the model with the largest amount of walls, which is why it is chosen for this test. The meshing of the walls will be varied and compared to each other for being able to see how small elements that are needed for the accuracy to be sufficient. In the pre-study, there is no other load than dead load and wind load acting on the structure. Furthermore, cracking of concrete is not considered.

5.3.1 Deformations and modes

As can be seen in

Table 5-1 below where the P-delta effects are excluded, the largest horizontal displacement at the top story was achieved in the TMF: Mega columns with cross walls on three levels and was 1291.90 mm. The lowest displacement was achieved in the Core, outrigger and perimeter frame model and was 159.30 mm. If comparing only the conventional structural systems, i. e. excluding the Tubed Mega Frame models, it was the Perimeter frame model that had the largest displacement which was 611.60 mm. The deformed elevation views of the models can be found in Appendix A.

Table 5-1: Results without P-delta effects. Mode 1 and 2 are the periods in the diagonal directions and Mode 3 is the torsional movement.

System Displacement Mode Mode Mode top story 1 [s] 2 [s] 3 [s] [mm] Core 502.20 7.07 7.07 1.57 Perimeter frame 611.60 8.67 8.67 5.17 Core and perimeter frame 247.50 5.77 5.77 1.86 Core and outriggers 244.40 5.26 5.26 1.70 Core, outriggers and perimeter frame 159.30 4.73 4.73 1.90 Core and diagonal braces 400.50 6.53 6.31 1.49

TMF: Perimeter frame with belt walls on three 526.5 8.34 8.34 5.12 levels TMF: Perimeter frame with cross walls on three 549.80 8.49 8.49 5.05 levels TMF: Mega columns with belt walls on three levels 1265.6 12.56 12.56 8.43 TMF: Mega columns with cross walls on three levels 1291.90 12.79 12.79 8.88

When including the P-delta effects the displacements and periods were larger than when P-delta was excluded as the values indicates in Table 5-2 below.

Table 5-2: Results with P-delta effects. Mode 1 and 2 are the periods in the diagonal directions and Mode 3 is the torsional movement.

System Displacement Mode Mode Mode top story 1 [s] 2 [s] 3 [s] [mm] Core 543.80 7.35 7.35 1.58 Perimeter frame 682.50 9.17 9.17 5.31 Core and perimeter frame 260.20 5.91 5.91 1.88 Core and outriggers 255.00 5.38 5.38 1.71 Core, outriggers and perimeter frame 164.70 4.81 4.81 1.92 Core and diagonal braces 427.70 6.74 6.52 1.50

TMF: Perimeter frame with belt walls on three 586.20 8.82 8.82 5.29 levels TMF: Perimeter frame with cross walls on three 614.40 9.00 9.00 5.21 levels TMF: Mega columns with belt walls on three levels 1775.40 15.05 15.05 10.65 TMF: Mega columns with cross walls on three levels 1836.30 15.42 15.42 11.84

Figure 5.11 shows an example of the three first eigenmodes for the Core model.

Mode 1 Mode 2 Mode 3 Figure 5.11: Elevation views of the first three eigenmodes

Table 5-3 shows the displacements and the percentage difference between the analyses with the P-delta effect excluded respectively included. In the comparison it can be seen that P-delta effects had the greatest effect on the TMF: Mega columns with cross walls on three levels and the difference was as high as 42 %.

Table 5-3: Percentage difference between when P-delta effects are excluded and included

System Displacement top story [mm] Without P- With P- % delta delta Core 502.20 543.80 8.28 Perimeter frame 611.60 682.50 11.59 Core and perimeter frame 247.50 260.20 5.13 Core and outriggers 244.40 255.00 4.34 Core, outriggers and perimeter frame 159.30 164.70 3.39 Core and diagonal braces 400.50 427.70 6.79

TMF: Perimeter frame with belt walls on three 526.5 586.20 levels 11.34 TMF: Perimeter frame with cross walls on three 549.80 614.40 levels 11.75 TMF: Mega columns with belt walls on three levels 1265.6 1775.40 40.28 TMF: Mega columns with cross walls on three levels 1291.90 1836.30 42.14

5.3.2 Comparison of mesh sizes

Table 5-4 shows the difference in the results depending on which element size that was used for the analysis. “No mesh” means that the structure is not divided into an element mesh. The difference is rather small between the different element sizes, and it can be seen that when using smaller elements the displacements and periods are marginally increased. Table 5-4: Comparison of different mesh sizes on the Core and outrigger model without P- delta

Element size [m] Displacement Mode 1 [s] Mode 2 [s] Mode 3 [s] top story [mm] Core 1×4, Outrigger 1×2 244.40 5.26 5.26 1.70 2×2 247.40 5.30 5.30 1.71 1×1 247.70 5.30 5.30 1.71 0.5×0.5 247.90 5.30 5.30 1.71 No mesh 239.30 5.21 5.21 1.76

5.3.3 Dead loads

Table 5-5 shows the total dead loads of the different systems.

Table 5-5: Total dead loads of the different models

System Fz [kN] Core 973928 Perimeter frame 1012805 Core and perimeter frame 1264612 Core and outriggers 1078211 Core, perimeter frame and outriggers 1298548 Core and diagonal braces 1002122

TMF: Perimeter frame with belt walls on three levels 1065820 TMF: Perimeter frame with cross walls on three levels 1064108 TMF: Mega columns with belt walls on three levels 987544 TMF: Mega columns with cross walls on three levels 999206

5.4 Discussion and conclusions from the pre-study

As Table 5-4 indicates, the size of the elements did not have any major influence on the result and thus does not need to be further concerned in this pre-study or the main study. From Table 5-3 it can be stated that the P-delta effect is important to consider in the analysis since the displacements become significantly higher when the P-delta effect is included. From the tables above, considering the conventional systems, one can clearly see that the more main load bearing systems that are combined into one structural system, the more stable the system becomes. The dead load differs some between the models, as can be seen in Table 5-5, which indicates the difference in amount of concrete between them. Although the Core, outrigger and perimeter frame model clearly outperforms the other models concerning the wind displacement and modes, it is important to keep in mind that this model also is the heaviest model. Thus it is the model with the highest amount of concrete, which increases the stability of the model. It is however not a completely fair comparison between the different structural systems since they do not only differ in the structural system design but also in amount of concrete which affects the stabilization of the structure. The amount of concrete will be considered in the main study so that the comparison will be a pure structural comparison. In this test, the models with outrigger levels or equivalent have these horizontal members only on three levels and are placed at the same stories for all of them. This may however not be the optimal stories to place the outriggers or equivalent.

For a fair comparison the location of them should be tailored to what is optimal for each individual model. The results for wind displacement may not be correct since the wind load is designed according to Eurocode and the Eurocode is not appropriate to use for buildings higher than 200 m and the buildings in these models are 271.5 m high. However, this should not affect how the models relate to each other in terms of wind displacement. As can be seen in the elevation view in Figure A.1 and Figure A.2 in Appendix A, the Core model and the Perimeter frame model bends in different ways. The core model bends like a cantilever beam while the Perimeter frame bends back at the top due to sliding in shear. When the two systems are combined the sideway deformation is S-shaped as a result of both bending of the core and shear of the perimeter frame.

6 Comparison of Tubed Mega Frame systems against conventional structural system for tall buildings

6.1 Introduction

The main study will contain an evaluation of nine different types of models of tall buildings made in the finite element software ETABS. Each type will also be built in several different heights. As the pre-study in Chapter 5 implied, the Core, outrigger and perimeter frame model had the lowest deformations due to wind load compared to the other conventional systems, and is therefore the structural system that will be compared against Tubed Mega Frame systems in this study. The buildings will be based on the quadratic 432 Park Avenue building in New York, USA, described in Section 2.3, which has a system consisting of a core, outriggers and a perimeter frame. One of the model types will be a simplified version of the 432 Park Avenue building according to its original structural system, while the other eight model types will be based on Tubed Mega Frame systems.

6.1.1 Deformations and periods

The models will be compared against each other to see how well they can resist the lateral loads, in this case wind load and seismic load. A comparison of the deformation in the ultimate limit state at the top story due to design wind load and design seismic action, individually, will be made. The periods of the three first eigenmodes will also be noted, which are movement in the two diagonal directions and torsional movement. All of the nine structural systems will be built with four different heights; 264 m, 396 m, 529 m and 661 m, since they are increased with two outrigger levels or equivalent, i. e. 28 stories. The deformations and periods of the systems that has not reached tension according to Section 6.1.2 below will also be registered.

6.1.2 Forces at the base

Tension at the base will be checked for, when the building is subjected to load combinations of dead load and wind load added together, and also dead load and seismic load. For every model, the reaction forces of the columns on the side of the

perimeter that the wind and seismic loads hit will be added together, i. e. one out of four sides since the buildings will be quadratic. The models that have not reached tension at the base when the building is 661 m high will be increased with outrigger levels or equivalent – 28 stories or 132 m – iteratively until tension is attained at the base.

6.1.3 Convergence test

The Tubed Mega Frame model that performed best considering reaching tension with a top story height as high as possible will be increased in height until the P- delta diverges and the structure collapses. For comparison, the Core, outrigger and perimeter frame model will also be increased in height until divergence is obtained. The models will be increased in height in such a way that the outrigger level or equivalent for the Tubed Mega Frame model always will be located at the top story. Whether a model has converged or not can be checked for in the analysis log in ETABS. Even if the program states convergence it has to be further controlled for numerical calculation failure, for instance if the lateral deformation is larger than the building height.

6.1.4 Model verification

To be able to verify the results, model verifications will be made. The values of the dead loads and overturning moments due to wind and seismic loading according to the results in ETABS of the various models will be compared. If the values are close enough to each other, it shows that the loads and structural elements probably are applied equivalent on all models. A hand calculation will be carried out on one of the model types, namely the TMF: Perimeter frame two story cross walls. The weight of the dead loads for all the different heights will be calculated and compared to the dead loads generated in ETABS.

6.2 Description of models

There will be one model with the original structural system inspired by the 432 Park Avenue and two types of the Tubed Mega Frame system with four subtypes respectively, thus a total of nine types of building models, and each type will be built with a number of different heights. All of the models will have the same cross- sectional area of concrete for obtaining validity in the comparison, i. e. the amount of concrete from the core in the model with the original system will be added to the load bearing systems in the other models that do not have a core. The space in the center will be left empty for all of the models for obtaining the same dead weight

of the floors. The reason for the empty space is that the original structural system has a core in the center which leaves an empty space inside it. The story height is 4.72 m in all models. The floors are 250 mm thick and have the concrete strength class C30/37, with the compressive strength 30 MPa and the modulus of elasticity 27 GPa. The models will be run both including and excluding P-delta effects. The buildings will be subjected to design wind load and design seismic load in the ultimate limit state according to the American code ASCE/SEI 7-10 (American Society of Civil Engineers, 2013). A more complete collection of 3D pictures of the models described for all heights can be found in Appendix B.

6.2.1 Core, outrigger and perimeter frame

The Core, outrigger and perimeter frame model will be based on the 432 Park Avenue building described in Section 2.3. The structural system will be composed of a concrete perimeter frame, a concrete central core and concrete outriggers. The core will have the dimensions 9.5 x 9.5 m with a wall thickness of 750 mm and concrete strength class of C100 with a compressive strength of 100 MPa. The modulus of elasticity in C100 will be 50 GPa. The columns in the perimeter frame will be 1120 mm wide and 1630 mm deep and have a concrete strength class of C100. The corner columns will however differ in the dimensions. It will instead be formed as a square with each side being 1350 mm wide. The beams in the perimeter frame will be 1120 mm in width and depth and have the same concrete strength as the columns. The beams and columns will be continuous and the columns will be rigidly restrained to the ground. The outrigger walls will go from the core and connect to the perimeter frame. It will be made of the same concrete strength as the core wall. The outriggers will be two story high and placed at every 14th floor. Thus there will be twelve floors between each outrigger level. A plan view and a 3D picture of the Core, outrigger and perimeter frame can be found in Figure 6.1.

(a) (b) Figure 6.1: Core, outrigger and perimeter frame system. (a) Plan view. (b) 3D picture.

6.2.2 TMF: Perimeter frame

The Tubed Mega Frame with a perimeter frame will be made of a moment frame of concrete. There will be seven columns per each side of the building. The columns in the moment frame will have a width of 1421 mm and 2068 mm in depth. The corner columns will however have the dimensions 1713x1713 mm. The beams will have the dimensions 1120x1120 mm. The beams and columns will be continuous and the columns will be rigidly connected to the ground. The beams and columns will both have the concrete strength class C100 with a compressive strength of 100 MPa, and the modulus of elasticity will be 50 GPa. At certain levels there will be belt or cross walls installed for increased stability of the building. There will be two different distances between the walls for testing how the column length affects the stiffness. The walls will be 750 mm thick and have the concrete strength class of C100 and 50 GPa as the modulus of elasticity. The different wall designs will be described further below. The core will be replaced with VKR 400x400x16 steel columns to support the dead load of the floors. The steel columns will be pinned. There will however not be steel columns at the same stories as the belt or cross walls and the floor below since their only purpose is to transfer the dead load of the floors down to a steel truss or cross wall level. Otherwise the VKR steel columns would contribute to the lateral stability, which is unwanted in these models. The yield strength of the steel columns is 355 MPa and the modulus of elasticity is 199.9 GPa.

Plan views of the TMF Perimeter frame systems with belt walls and cross walls can be seen in Figure 6.2.

(a) (b) Figure 6.2: (a) Plan view of the TMF: perimeter frame system with belt walls. (b) Plan view of the TMF: perimeter frame system with cross walls.

TMF: Perimeter frame two story belt walls

In this model, the walls will encircle the building at regularly spaced levels. The walls in this model will be two story high and placed at every 14th floor. There will also be an interior steel truss installed at the same stories as the belt walls are placed, connecting to the belt walls. The steel truss will be made of W14x500 steel columns with pinned end conditions. This is to transfer all the loads to the belt walls at the perimeter without increasing the weight of the building significantly. The steel truss will have a yield strength of 355 MPa and a modulus of elasticity of 199.9 GPa. The steel truss will also be two story high. A 3D picture of the TMF: Perimeter frame two story belt walls can be found in Figure 6.3.

Figure 6.3: 3D picture of the TMF: Perimeter frame two story belt walls

TMF: Perimeter frame single story belt walls

In this model, the walls will again encircle the building and there will be an interior steel truss connecting to it at the same floor, but in this model the belt wall and steel truss will only be one story high. Thus the belt wall levels will be installed at every 7th floor. The steel truss, shown in Figure 6.5 will have the same dimensions and material properties as in the TMF: Perimeter frame two story belt walls model. A 3D picture of the TMF: Perimeter frame single story belt walls can be found in Figure 6.4.

Figure 6.4: 3D picture of the TMF: Perimeter frame single story belt walls

Figure 6.5: 3D view of the one story high steel truss.

TMF: Perimeter frame two story cross walls

In this model, the walls will be installed as interior cross walls, connecting from one side of the building to the opposite side. The crossing walls will be placed at every 14th floor and will be two floors high. A 3D picture of the TMF: Perimeter frame two story cross walls can be found in Figure 6.6.

Figure 6.6: 3D picture of the TMF: Perimeter frame two story cross walls

TMF: Perimeter frame single story cross walls

The walls will here be installed in the same way as in TMF: Perimeter frame two story cross walls, but the walls will here only be one story high. Therefore the walls will instead be placed at every 7th floor. A 3D picture of the TMF: Perimeter frame single story cross walls can be found in Figure 6.7.

Figure 6.7: 3D picture of the TMF: Perimeter frame single story cross walls

6.2.3 TMF: Mega columns

The lateral load bearing system of the mega columns systems consists of eight concrete mega hollow columns standing in the periphery of the building. There are two mega columns per side and each one is placed at the center of one respective half of the side. The mega columns are squared with the outer dimensions 3.7×3.7 m and the wall thickness 0.93 m and built up of concrete walls. The concrete will have the strength class C100 with a compressive strength of 100 MPa, and the modulus of elasticity will be 50 GPa. There are four different versions of the TMF Mega columns which are described below. The difference between the models is the arrangement of belt or cross walls, but the mega columns remains the same. These belt or cross walls made of concrete will be located at regularly spaced stories and have the same material properties as the mega columns, and will be 0.75 m thick. As for the TMF Perimeter frame models, there will be two different distances between the walls for testing how the column length affects the stiffness. In the same place as the core was standing there will be VKR 400×400×16 steel columns instead to support the dead load of the floors. The yield strength of the columns is 355 MPa and the modulus of elasticity is 199.9 GPa. These columns will land on either the steel truss that are connected to the belt walls, or on the cross walls depending on which model it is. The same stories that contain the belt walls or the cross walls and the one story below will not have any VKR steel columns. Plan views of the TMF: Mega columns system with belt walls and cross walls can be seen in Figure 6.8.

(a) (b) Figure 6.8: (a) Plan view of the TMF: mega columns system with belt walls. (b) Plan view of the TMF: mega columns system with cross walls.

TMF: Mega columns two story belt walls

The belt walls are connected to the corners of the mega columns and extend around the building. In addition to the belt walls, this system also has steel trusses at the same levels, with the purpose of transferring all of the loads to the outer limits of the building. The steel truss is built up of W14×500 steel columns with pinned end conditions. The steel strength is 355 MPa and the modulus of elasticity is 199.9 GPa. In this model the height of the belt walls are two stories high, or 9.44 m high. The belt walls are placed at every 14th floor. Thus there are twelve stories, 56.6 m, between the belt wall levels. A 3D picture of the TMF: Mega columns two story belt walls can be found in Figure 6.9.

Figure 6.9: 3D picture of the TMF: Mega columns two story belt walls

TMF: Mega columns single story belt walls

The height of the belt walls in this model is one story, or 4.72 m. The belt walls are placed at every 7th floor. Thus there are six stories, 28.3 m, between the belt wall levels. A 3D picture of the TMF: Mega columns single story belt walls can be found in Figure 6.10.

Figure 6.10: 3D picture of the TMF: Mega columns single story belt walls

TMF: Mega columns two story cross walls

The cross walls connect the mega columns on the opposite sides to each other. There are four cross walls per plan view that extend from one side, along the line where one side of the core would stand in the Core, outrigger and perimeter frame model, and to the other side. In this model the height of the cross walls are two stories, or 9.44 m. The cross walls are placed at every 14th floor. Thus there are twelve stories, 56.6 m, between the cross wall levels. A 3D picture of the TMF: Mega columns two story cross walls can be found in Figure 6.11.

Figure 6.11: 3D picture of the TMF: Mega columns two story cross walls

TMF: Mega columns single story cross walls

The height of the cross walls in this model is one story high, or 4.72 m high. The cross wall are placed at every 7th floor. Thus there are six stories, 28.3 m, between the cross wall levels. A 3D picture of the TMF: Mega columns single story cross walls can be found in Figure 6.12.

Figure 6.12: 3D picture of the TMF: Mega columns single story cross walls

6.3 Mesh

The floors slabs in all of the models are chosen to be automatically meshed with maximum element size of 1 m. The element type will be four-node quadrilateral thin-shell elements. The walls are meshed by using an auto rectangular mesh option with the maximum element size of 1.25 m. The wall mesh also uses thin-shell elements.

6.4 Assumptions and limitations

The amount of concrete per cross section area will remain the same along the height, except for the different arrangement of belt walls or cross walls in the models which is described in Section 6.2, even though the dimensions of the columns in the 432 Park Avenue varies with the height. The only loads considered are wind and seismic loads. The floors are modeled as rigid diaphragms. Cracking of concrete is not considered.

6.5 Loads

The wind and seismic loads are defined according to the American code ASCE 7- 10 (American Society of Civil Engineers, 2013) and based on input values from a previous study of the Tubed Mega Frame system.

6.5.1 Wind load

The input values for wind load are shown in Figure 6.13.

Figure 6.13: Input values for wind load (Zhang, 2014)

6.5.2 Seismic action

The input values for seismic loading can be seen in Figure 6.14.

Figure 6.14: Input values for seismic loading (Zhang, 2014)

6.6 Results

6.6.1 Deformations and periods

Including P-delta effects

The displacements at the top story are shown in Figure 6.15 and Figure 6.16 for all the different types of models with the heights: 264 m, 396 m, 529 m, 661 m and for the TMF Perimeter frame models also 793 m. The P-delta effects are included. The displacements and periods of the three first eigenmodes for all the different types of models can be found in tables in Appendix C. As can be seen in Figure 6.15 the TMF: Perimeter frame single story belt walls model had the lowest deformation due to wind load at all heights. At 264 m and 396 m the TMF: Mega columns two story cross walls had the highest top story displacement, while the Core, outrigger and perimeter frame model had the largest deformation from 529 m and 661 m. As the top story height increased, the

deformation of the Core, outrigger and perimeter frame model increased faster compared to the other models, while the others behaved rather similar to each other. However, for the TMF: Mega columns two story cross walls and the TMF: Mega columns single story cross walls at 661 m, the P-delta does not converge which implies that the values might be incorrect. The TMF Perimeter frame models deformed relatively equally to each other through all of the different heights. The models with belt walls performed slightly better than the models with cross walls as the buildings became higher. The TMF Mega columns with single story belt or cross walls approximately had the same deflections and it was slightly better than the TMF Mega columns with two story belt or cross walls.

Figure 6.15: Deflection at the top story caused by wind load. P-delta effects are included. Note that the values for the TMF Mega columns models with cross walls at 661 m may be incorrect due to P-delta divergence.

Figure 6.16 shows the deformation at the top story due to seismic loading. The lowest deformation was obtained in the TMF: Mega columns single story belt walls at all heights. The TMF: Mega columns two story cross walls had the highest deformation at 264 m, and at 396 m and higher the Core, outrigger and perimeter frame model had the highest deformation. The models that acted similarly to each other due to wind load still acted about the same.

Figure 6.16: Deflection at the top story caused by seismic loading. P-delta effects are included. Note that the values for the TMF Mega columns models with cross at 661 m walls may be incorrect due to P-delta divergence.

The lowest period of the first eigenmodes was obtained in the TMF: Mega columns single story belt walls, while the highest was obtained in the TMF: Mega columns

two story cross walls at 264 m and 396 m and in the Core, outrigger and perimeter frame model for 529 m and 661 m. The second mode was the same as the first since the buildings had a quadratic footprint. The periods of the first and second modes are shown in Figure 6.17.

Mode 1 and Mode 2 45

Period [s] Period 10

0 Core, TMF: TMF: TMF: TMF: TMF: TMF: TMF: TMF: outrigger perimeter perimeter perimeter perimeter Mega Mega Mega Mega and frame two frame frame two frame columns columns columns columns perimeter story belt single story cross single two story single two story single frame walls story belt walls story cross belt walls story belt cross walls story cross walls walls walls walls

264.32 m 396.48 m 528.64 m 660.80 m 792.96 m

Figure 6.17: Periods of the first and second mode. P-delta effects are included. Note that the values for the TMF Mega columns models with cross walls at 661 m may be incorrect due to P-delta divergence.

The third mode, torsional movement, was highest in the TMF: Mega columns two story cross walls at all heights except for 661 m where the TMF: Mega columns two story belt walls had the highest period. The lowest period regarding the third mode was obtained in the Core, outrigger and perimeter frame model at all heights. The periods of the third mode are shown in Figure 6.18.

Mode 3 25

Period[s] 0 Core, TMF: TMF: TMF: TMF: TMF: TMF: TMF: TMF: -5 outrigger perimeter perimeter perimeter perimeter Mega Mega Mega Mega and frame two frame frame two frame columns columns columns columns -10 perimeter story belt single story cross single two story single two story single frame walls story belt walls story cross belt walls story belt cross walls story cross -15 walls walls walls walls

-20

264.32 m 396.48 m 528.64 m 660.80 m 792.96 m

Figure 6.18: Periods of the third mode. P-delta effects are included. Note that the values for the TMF Mega columns models with cross walls at 661 m may be incorrect due to P- delta divergence.

For the TMF Perimeter frame models at 793 m, the TMF: Perimeter frame single story belt walls had the lowest displacements and periods while the TMF: Perimeter frame two story cross walls had the highest, except for the third mode where the TMF: Perimeter frame two story belt walls had the highest displacements and modes.

Excluding P-delta effects

Figure 6.19 and Figure 6.20 shows the displacements caused by wind load and seismic loading respectively when the P-delta effects are excluded. The deformations and periods – as can be seen in Appendix C – were lower when running the models without P-delta effects than with P-delta effects. The difference became greater the higher the models were. The relation of the wind deformations between the different models are the same as for the models including P-delta effects, i. e. the model that had the highest deformation when including P-delta also had the highest deformation excluding P- delta and vice versa. Considering the seismic loading, the relation of the deformations are almost the same except for at 793 m where the TMF: Perimeter frame two story belt walls had the lowest displacement. Overall the relation

between which models had the lowest respectively highest deflection was almost the same with and without P-delta effects.

Deflection at the top story caused by wind load 900

800

700

600

500 Top story height [m] story Topheight

400

300

200 0 1 2 3 4 5 6 7 8 9 Top story deflection [m]

Deflection at the top story caused by seismic loading 900

800

700

600

500 Top story height [m] story Topheight

400

300

200 0 2 4 6 8 10 12 Top story deflection [m]

Core, outrigger and perimeter frame TMF: perimeter frame two story belt walls TMF: perimeter frame single story belt walls TMF: perimeter frame two story cross walls TMF: perimeter frame single story cross walls TMF: Mega columns two story belt walls TMF: Mega columns single story belt walls TMF: Mega columns two story cross walls TMF: Mega columns single story cross walls Figure 6.20: Deflection at the top story caused by seismic loading. P-delta effects are excluded. Considering the periods of the first and the second mode, the same models had the highest respectively lowest periods both when including and excluding P-delta effects. For the third mode, the Core, outrigger and perimeter frame model had the lowest periods at all heights, as when P-delta was included, and the TMF: Mega columns two story cross walls had the highest periods at all heights, even at 661 m this time compared to when P-delta was included. The periods of the first and second mode are shown in Figure 6.21 and the periods of the third mode are shown in Figure 6.22.

Mode 1 and Mode 2

35 30 25 20

15 Period[s] 10 5 0 Core, TMF: TMF: TMF: TMF: TMF: MegaTMF: MegaTMF: MegaTMF: Mega outrigger perimeter perimeter perimeter perimeter columns columns columns columns and frame two frame frame two frame two story single story two story single story perimeter story belt single story story cross single story belt walls belt walls cross walls cross walls frame walls belt walls walls cross walls

264.32 m 396.48 m 528.64 m 660.80 m 792.96 m

Figure 6.21: Periods of the first and second mode. P-delta effects are excluded.

Mode 3 9 8 7 6 5 4

3 Period[s] 2 1 0 Core, TMF: TMF: TMF: TMF: TMF: Mega TMF: Mega TMF: Mega TMF: Mega outrigger perimeter perimeter perimeter perimeter columns columns columns columns and frame two frame frame two frame two story single story two story single story perimeter story belt single story story cross single story belt walls belt walls cross walls cross walls frame walls belt walls walls cross walls

264.32 m 396.48 m 528.64 m 660.80 m 792.96 m

Figure 6.22: Periods of the third mode. P-delta effects are excluded.

The percentage difference of the displacements when including respectively excluding the P-delta effects are presented in Appendix D. The difference for all

the model types is also shown in graphs in Appendix E. The model that was affected the most by difference in P-delta effects was the Core, outrigger and perimeter frame model. 6.6.2 Forces at the base

Figure 6.23 below shows the total force of the side of the building that withstand the wind force for all models, and where each point on the graph represents the height of the top story for the certain model. The P-delta effects are included in the graphs below. The forces at the base can also be found in tables in Appendix F. As can be seen in Figure 6.23, the TMF: perimeter frame single story belt walls model was the system that could be increased the most in height before it reached tension at the base story. The other models that were raised in height after 661 m were: TMF: perimeter frame two story belt walls, TMF: perimeter frame single story cross walls, TMF: perimeter frame two story cross walls. All the four TMF: perimeter frame models do however go over to tension at around 675 m with slightly small differences between them. The model that performed the worst under the action of dead and wind load combination was the Core, outrigger and perimeter frame model.

Base forces due to dead load and wind load in x-direction 900

800

700

600

500 Top story height [m] story Topheight

400

300

200 -300 -200 -100 0 100 200 300 400 Compression (-) /Tension (+) [MN]

Figure 6.24 below shows the total force of the side of the building that withstand the seismic force for all models, and where each point on the graph represents the height of the top story for the certain model. The P-delta effects are included in the graphs below. As can be seen in Figure 6.24, all the TMF: perimeter frame models went over to tension at the base story at almost the same height, 590 m. All the TMF: Mega columns models also went over to tension at the base story at almost the same height, but at a significantly lower height than the TMF: perimeter frame models. They went over to tension at around 520 m instead. The model that performed the worst under the action of dead and seismic load combination is the Core, outrigger and perimeter frame model.

Base forces due to dead load and seismic loading in x-direction 900

800

700

600

500 Top story height [m] story Topheight

400

300

200 -200 -100 0 100 200 300 400 500 600 700 Compression (-) /Tension (+) [MN]

Figure 6.25 below shows the total force of the side of the building that withstand the wind force for all models, and where each point on the graph represents the height of the top story for the certain model. The P-delta effects are not included in the graphs below. As can be shown in Figure 6.25, P-delta had a big influence for however the systems went over to tension under the action of wind load and for which height in that case. None of the models went over to tension when the P-delta effects were not included. The model that performed the worst under the action of dead and wind load combination, where the P-delta effects were not included, was the Core, outrigger and perimeter frame model.

Base forces due to dead load and wind load in x-direction 900

800

700

600

500 Top story height [m] story Topheight

400

300

200 -250 -200 -150 -100 -50 0 Compression (-) /Tension (+) [MN] Core, outrigger and perimeter frame TMF: perimeter frame two story belt walls TMF: perimeter frame single story belt walls TMF: perimeter frame two story cross walls TMF: perimeter frame single story cross walls TMF: Mega columns two story belt walls TMF: Mega columns single story belt walls TMF: Mega columns two story cross walls TMF: Mega columns single story cross walls Figure 6.25: Top story height as a function of the total force at the base when the building is subjected to dead load and wind load in the x-direction. P-delta is not included.

Figure 6.26 below shows the total force of the side of the building that withstand the seismic force for all models, and where each point on the graph represents the height of the top story for the certain model. The P-delta effects are not included in the graphs below. As can be shown in Figure 6.26, P-delta had a big influence for when the different models went over to tension. When compared with Figure 6.24 it can be seen that all models could be increased with almost 100 m for the top story height before the building went over to tension, in comparison with when the P-delta effects are included. The model that however performed the worst under the action of dead and seismic load combination, where the P-delta effects were not included, was the Core, outrigger and perimeter frame system.

Base forces due to dead load and seismic loading in x-direction 900

800

700

600

500 Top story height [m] story Topheight

400

300

200 -200 -150 -100 -50 0 50 100 Compression (-) /Tension (+) [MN]

6.6.3 Convergence test

According to Figure 6.23, the TMF: Perimeter frame single story belt walls could be increased the most in height before reaching tension at the base. The TMF: perimeter frame model could later be increased to 1024 m before it diverged, in comparison with the Core, outrigger and perimeter frame model that could only be increased to 859 m before it diverged, as can be seen in Figure 6.27.

Deflection at the top story caused by wind load 1200

1000

800

600

400 Topstory height [m]

200

0 0 50 100 150 200 250 Top story deflection [m]

Core, outrigger and perimeter frame TMF: perimeter frame single story belt walls Collapse Collapse

Figure 6.27: Convergence test, height of the top story for when the buildings collapse.

6.6.4 Model verification

The dead loads and overturning moments due to wind and seismic loading can be found in Appendix G. The values show that the dead loads and overturning moments are almost the same for the different model types of the same height. Table 6-1 shows a comparison of the weight of the dead loads of the TMF: Perimeter frame two story cross walls model for all heights, obtained in ETABS versus from a hand calculation. The values of the dead loads correspond fairly well. The hand calculation can be found in Appendix H.

Table 6-1: Verification of dead loads for the TMF: Perimeter frame two story cross walls model

Height Fz [kN] % [m] ETABS Hand calculation 264.32 826108 812211 1.7 396.48 1237477 1218316 1.6 528.64 1648846 1624421 1.5 660.80 2060215 2030527 1.5 792.96 2471583 2436632 1.4

7 Discussion, conclusions and proposed further research

7.1 Discussion and conclusions

The results showed that the Tubed Mega Frame systems performed significantly better than the Core, outrigger and perimeter frame system as the buildings got higher. The reason could be that the lateral load bearing system is placed in the periphery of the building rather than in the center as in a core system. The model that performed best when subjected to wind load was the TMF: Perimeter frame single story belt walls. When subjected to seismic loading, the TMF: Mega Column single story belt walls had the lowest deformations. From the result above, it can be stated that the difference in result when P-delta is included and excluded becomes bigger the higher the building is. The reason is probably that the higher the building is the larger deflection it has and the dead load is increased as well, which affects the P-delta iterations. It should be taken into consideration that the hollow concrete columns in the TMF Mega columns models do not have the optimal design. They may have performed better if they were designed in a rectangular shape instead of quadratic shape since the second moment of inertia will be bigger for a rectangular section than for a quadratic section, if placed in the desired direction due to the loading. The optimal location for the mega columns should also have been studied. Optimal design check in general should have been done regarding dimensions for the TMF Mega columns models and TMF Perimeter frame models for a more fair and accurate comparison regarding structural efficiency. As mentioned before, the Core, outrigger and perimeter frame system is a replication of the 432 Park Avenue. It is however a simplified model. In the existing 432 Park Avenue building, the sizes of the columns changes throughout the height. Thus stating from the comparison above that the TMF structural systems outperform the structural system that 432 Park Avenue use would not be correct. To be able to state that, the changes in column sizes should have been taken into consideration in the Core, outrigger and perimeter frame model instead of simplifying it. The columns in the perimeter frames in the models have been placed for obtaining the highest resistance against lateral loads, but it is noteworthy that in reality they may have to be rotated for the purpose of larger window areas, which would lead to less resistance.

Since the only loads considered are dead load, wind load and seismic loading, a large portion of loads are missing, for instance façade load. It is important to add all the possible loads when designing the buildings in reality. Material nonlinearity such as cracking of concrete is neglected in this study, which may have a great impact on the results by enlarging the deformations and worsen the stability of the buildings. The result for the TMF Mega columns showed that the distance between the belt or cross walls had a large impact on the deformations and periods. It could be explained by help of the stiffness theory, which implies that the column length has a major influence on the column stiffness. The Tubed Mega Frame models are built with the same footprint area – and the same amount of concrete per cross section area – as the Core, outrigger and perimeter frame system. This makes the comparison a pure structural comparison, but if the focus would have been to make a fair comparison regarding the floor area efficiency of the models, the Tubed Mega Frame models should probably have been reduced since the core is removed. The point of the Tubed Mega Frame is among other things to be able to make the building more slender, and if efficiency should be compared that must be taken into consideration. In this report, a convergence test has been done for one of the models, i.e. the model has been increased in height as high as possible before it diverged due to P-delta or numerical calculation failure. It is however important to examine whether all of the models converge due to P-delta even if they were not increased in height, which also have been done in this study. Even though the structural systems perform well considering displacement at the top story and forces at the base relatively to the other models, there is still a possibility that the structures diverge, making them impossible to construct from a stabilization point of view. At 661 m the TMF Mega columns models with cross walls did not converge, which means that the displacements and periods shown for these models may be incorrect. The periods of the third mode are showing negative values which implies that the divergence probably has affected the results. The decision to do a convergence test on the TMF: Perimeter frame single story belt walls was taken since it outperformed the other models based in the Forces at the base test. However, if the possibility of anchoring the structure to the ground is given there is a possibility that another model can be increased more in height than the TMF Perimeter frame single story belt walls system before it diverges. In this test however, it is assumed that anchoring will not be used and therefore increasing the height of the models and doing a convergence test has not been performed on all models. Since this study is limited to an ultimate limit state study, the accelerations due to eigenmodes of the building become less important than the deformations of the building. However, when studying the serviceability limit state the values for modes becomes more important since they control the feeling of motion for humans.

When these values are too high, people get uncomfortable. It is therefore possible to state from the result above that TMF Mega columns single story belt walls is preferred in view of serviceability limit state since it has the lowest periods for mode 1 and mode 2. Although considering mode 3, the Core, outrigger and perimeter frame caused the lowest period, meaning that in the torsional movement this system is the most stable. The reason is probably that this system had more mass closer to the center than Tubed Mega Frame models. Furthermore, the core in the model was closed while the outer structures in the other models were open to a larger extent which can affect the torsional stiffness.

7.2 Proposed further research

Further research within this subject could be to perform a serviceability limit state study on Tubed Mega Frame buildings. Material nonlinearity could be an important issue to investigate when designing concrete structures due to creep and shrinkage. Another suggestion is optimization design of the Tubed Mega frame systems.

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Appendix A – Pre-study

Figure A.1: Deformed elevation view of the Core Figure A.2: Deformed elevation view of the Perimeter frame

Figure A.3: Deformed elevation view of the Core Figure A.4: Deformed elevation view of and perimeter frame the Core and outriggers

Figure A.5: Deformed elevation view of the Figure A.6: Deformed elevation view of Core, outriggers and perimeter frame the Core and diagonal braces

Figure A.7: Deformed elevation view of the Figure A.8: Deformed elevation view of the TMF: Perimeter frame with belt walls on three TMF: Perimeter frame with cross walls on levels three levels

Figure A.9: Deformed elevation view of the Figure A.10: Deformed elevation view of TMF: Mega columns with belt walls on three the TMF: Mega columns with cross levels walls on three levels

Appendix B - 3D pictures

56 stories, 264 m 84 stories, 396 m