Buildings with Tubed Mega Frame Structures

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MASTER OF SCIENCE THESIS

STOCKHOLM, SWEDEN 2016

KTH ROYAL INSTITUTE OF TECHNOLOGY

SCHOOL OF ARCHITECTURE AND THE BUILT ENVIRONMENT

Buildings with Tubed Mega

Frame Structures

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Global Analysis of Tall Buildings

with Tubed Mega Frame Structures

By

Arezo Partovi and Jenny Svärd

TRITA-BKN, Examensarbete _{489, Betongbyggnad 2016} ISSN 1103-4297

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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.

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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.

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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.

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Notations

Latin capital letters

𝐴 = Cross-section area of the beam 𝐶_𝑝 = External pressure coefficient 𝐷 = Diameter of the building 𝐸 = Young’s modulus

𝐹 = Force

𝐹_𝑎 = Short period site coefficient 𝐹_𝑣 = 1-s period site coefficient 𝐺 = Shear modulus

𝐺𝐶_𝑝𝑖 = Internal pressure coefficient

𝐺_𝑓 = Gust-effect factor for flexible buildings 𝐼 = Second moment of inertia

𝐿 = Length of the beam

𝑆1 = Mapped MCER spectral response acceleration parameter at 1-s period

𝑆_𝑎 = Design spectral response acceleration

𝑆_𝐷1 = Design spectral response acceleration parameter at 1-s period 𝑆_𝐷𝑆 = Design spectral response acceleration parameter at short periods

𝑆𝑀1 = MCER spectral response acceleration parameter at 1-s period adjusted for

site class effects

𝑆_𝑀𝑆 = MCER spectral response acceleration parameter at short periods adjusted

for site class effects

𝑆𝑠 = Mapped MCER spectral response acceleration parameter at short periods

𝑆𝑡 = Dimensionless parameter called Strouhal number for the shape 𝑇 = Period of the structure

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Latin lower case letters

𝑐𝑝𝑒 = the pressure coefficient for external pressure

𝑐𝑝𝑖 = the pressure coefficient for internal pressure

[𝑑]= Displacement vector [𝑓]= Force vector

𝑓𝑣 = Vortex shedding frequency

[𝑘]= Stiffness matrix 𝑘 = Spring constant

p = Design wind pressures for the main wind-force resisting system of flexible enclosed buildings

𝑞 = 𝑞_ℎ for leeward walls, side walls and roofs, evaluated at height h 𝑞 = 𝑞𝑧 for windward walls evaluated at height z above the ground

𝑞𝑖 = 𝑞ℎ for windward walls, side walls, leeward walls and roofs of enclosed

buildings and for negative internal pressure evaluation in partially enclosed buildings

𝑞_𝑝(𝑧𝑒) = the external peak velocity pressure

𝑞_𝑝(𝑧_𝑖) = the internal peak velocity pressure 𝑢 = Displacement

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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

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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.

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(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

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comparison can be made. The load cases are only controlled for in the ultimate limit state.

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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

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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

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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

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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).

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

2.2.4 Tubed moment frame

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

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

2.2.5 Trussed tube

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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).

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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)

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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)

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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).

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16 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)

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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.

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18 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).

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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.

[𝑑] = [𝑘]−1_[𝑓] _(3-1)

[𝑑]= Displacement vector [𝑘]= Stiffness matrix [𝑓]= 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 [𝑘]. The force vector [𝑓] is determined and the system is then reduced due to boundary conditions. The displacements [𝑑] 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.

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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).

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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)

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

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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.

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24 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.

𝐹₁= −𝐹₂=𝐸𝐴 𝐿 (4-1) 𝐹₁ = 𝐹₂ = 6𝐸𝐼_𝐿₂ (4-2) 𝐹₃ = −𝐹₄ =12𝐸𝐼_𝐿₃ (4-3) 𝐹₁=4𝐸𝐼 𝐿 (4-4) 𝐹₁=2𝐸𝐼 𝐿 (4-4) 𝐹3 = −𝐹4 =6𝐸𝐼_𝐿2 (4-5)

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).

𝐹 = 𝑘 × 𝑢 (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.

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25 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.

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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-along-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:

𝑓_𝑣=𝑉×𝑆𝑡_𝐷 (4-8)

Where,

𝑓_𝑣 is the vortex shedding frequency [Hz]

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𝑆𝑡 is the dimensionless parameter called Strouhal number for the shape 𝐷 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:

𝑝 = 𝑞𝐺_𝑓𝐶_𝑝− 𝑞_𝑖(𝐺𝐶_𝑝𝑖) (𝑁/𝑚2₎ _(4-9)

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𝑞 = 𝑞_𝑧 for windward walls evaluated at height z above the ground. 𝑞 = 𝑞_ℎ for leeward walls, side walls and roofs, evaluated at height h.

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

𝐺_𝑓 = gust-effect factor for flexible buildings. 𝐶_𝑝= external pressure coefficient.

𝐺𝐶_𝑝𝑖= 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).

𝑤 = 𝑤_𝑒− 𝑤_𝑖 = 𝑞_𝑝(𝑧𝑒) ∗ 𝑐𝑝𝑒− 𝑞𝑝(𝑧𝑖) ∗ 𝑐𝑝𝑖 (𝑁/𝑚2) (4-10)

Where,

𝑞_𝑝(𝑧_𝑒) is the external peak velocity pressure 𝑞_𝑝(𝑧_𝑖) is the internal peak velocity pressure 𝑧𝑒 is the reference height for external pressure

𝑧𝑖 is the reference height for internal pressure

𝑐_𝑝𝑒 is the pressure coefficient for external pressure 𝑐_𝑝𝑖 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).

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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.

𝑆_𝑎= 𝑆_𝐷𝑆(0.4 + 0.6𝑇 𝑇0) 0 < 𝑇 < 𝑇0 (4-11) 𝑆_𝑎= 𝑆_𝐷𝑆 𝑇₀ < 𝑇 < 𝑇_𝑠 (4-12) 𝑆_𝑎= 𝑆𝐷1 𝑇 𝑇𝑠< 𝑇 < 𝑇𝐿 (4-13) 𝑆_𝑎= 𝑆𝐷1∙𝑇𝐿 𝑇2 𝑇𝐿 < 𝑇 (4-14) Where 𝑆𝐷𝑆= 2₃𝑆𝑀𝑆=2₃𝐹𝑎𝑆𝑠 (4-15) 𝑆_𝐷1= 2₃𝑆_𝑀1=2₃𝐹_𝑣𝑆₁ (4-16)

𝑇 = Period of the structure [s]

𝑆𝑎= Design spectral response acceleration

𝑆_𝑠= Mapped MCER spectral response acceleration parameter at short periods

𝑆₁= Mapped MCER spectral response acceleration parameter at 1-s period

𝑆_𝐷𝑆= Design spectral response acceleration parameter at short periods 𝑆_𝐷1= Design spectral response acceleration parameter at 1-s period

𝑆_𝑀𝑆= MCER spectral response acceleration parameter at short periods adjusted for site

class effects

𝑆_𝑀1= MCER spectral response acceleration parameter at 1-s period adjusted for site class

effects

𝐹𝑎 = Short period site coefficient

𝐹𝑣 = 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

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

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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

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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.

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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.

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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

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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.

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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

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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

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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.

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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 top story [mm] Mode 1 [s] Mode 2 [s] Mode 3 [s] 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

levels

526.5 8.34 8.34 5.12 TMF: Perimeter frame with cross walls on three

levels

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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 top story [mm] Mode 1 [s] Mode 2 [s] Mode 3 [s] 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 levels

586.20 8.82 8.82 5.29 TMF: Perimeter frame with cross walls on three

levels

614.40 9.00 9.00 5.21 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

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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-delta With P-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 levels

526.5 586.20

11.34 TMF: Perimeter frame with cross walls on three

levels

549.80 614.40

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 top story [mm]

Mode 1 [s] Mode 2 [s] Mode 3 [s] 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

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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.

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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.

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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

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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

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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.

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(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.

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

(a) (b)

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.

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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}

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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}

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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.

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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)

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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}

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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}

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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.

Buildings with Tubed Mega Frame Structures

MASTER OF SCIENCE THESIS

STOCKHOLM, SWEDEN 2016

KTH ROYAL INSTITUTE OF TECHNOLOGY

SCHOOL OF ARCHITECTURE AND THE BUILT ENVIRONMENT

Buildings with Tubed Mega

Frame Structures

Global Analysis of Tall Buildings

with Tubed Mega Frame Structures

By

Arezo Partovi and Jenny Svärd

Abstract

Sammanfattning

Preface

Notations

Table of Contents

1 Introduction

2 Tall buildings

3 Finite Element Method

4 Structural mechanics and lateral loads

5 Pre-study of structural systems in ETABS

6 Comparison of Tubed Mega Frame systems against

conventional structural system for tall buildings