MASTER OF SCIENCE THESIS

STOCKHOLM, SWEDEN 2016

KTH ROYAL INSTITUTE OF TECHNOLOGYSCHOOL OF ARCHITECTURE AND THE BUILT ENVIRONMENT

Buildings with Tubed Mega Frame StructuresAREZO PARTOVIJENNY SVÄRD

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

ISRN KTH/BKN/EX--489--SE

Master thesis in Concrete Structures

i

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.

ii

iii

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.

iv

v

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.

vi

vii

Notations

Latin capital letters

𝐴 = Cross-section area of the beam

𝐶𝑝 = External pressure coefficient

𝐷 = Diameter of the building

𝐸 = Young’s modulus

𝐹 = Force

𝐹𝑎 = Short period site coefficient

𝐹𝑣 = 1-s period site coefficient

𝐺 = Shear modulus

𝐺𝐶𝑝𝑖 = Internal pressure coefficient

𝐺𝑓 = 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

𝑆𝑎 = Design spectral response acceleration

𝑆𝐷1 = Design spectral response acceleration parameter at 1-s period

𝑆𝐷𝑆 = Design spectral response acceleration parameter at short periods

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

𝑆𝑀𝑆 = 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

𝑉 = Mean wind speed at the top of the building

viii

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 = 𝑞ℎ 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

𝑞𝑝(𝑧𝑒) = the external peak velocity pressure

𝑞𝑝(𝑧𝑖) = the internal peak velocity pressure

𝑢 = Displacement

𝑧𝑒 = the reference height for external pressure

𝑧𝑖 = the reference height for internal pressure

Greek letters

𝛾 = Shear strain

𝜀 = Strain

𝜈 = Poisson’s ratio

𝜎= Stress

𝜏 = Shear stress

ix

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

x

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

xi

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

xii

1

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

2

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.

3

(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

4

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.

5

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.

6

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

7

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.

8

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).

9

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).

10

(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.

11

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).

12

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)

13

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).

14

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)

15

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)

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)

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).

17

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)

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).

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).

19

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.

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

20

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)

21

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).

22

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).

(3-2)

(3-3)

x

y

xy

E

1 2

1

0

1

0

0

0

1

2

x

y

xy

zx

yz

G

0

0

G

zx

yz

23

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)

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.

Figure 4.2: Elementary cases for end-forces caused by end-displacements (Leander, 2014)

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.

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.

26

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:

𝑓𝑣 =𝑉×𝑆𝑡

𝐷 (4-8)

Where,

𝑓𝑣 is the vortex shedding frequency [Hz]

𝑉 is the mean wind speed at the top of the building [m/s]

27

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 = 𝑞𝐺𝑓𝐶𝑝 − 𝑞𝑖(𝐺𝐶𝑝𝑖) (𝑁/𝑚2) (4-9)

Where,

28

𝑞 = 𝑞𝑧 for windward walls evaluated at height z above the ground.

𝑞 = 𝑞ℎ for leeward walls, side walls and roofs, evaluated at height h.

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

for negative internal pressure evaluation in partially enclosed buildings.

𝐺𝑓 = gust-effect factor for flexible buildings.

𝐶𝑝 = external pressure coefficient.

𝐺𝐶𝑝𝑖 = 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 = 𝑤𝑒 − 𝑤𝑖 = 𝑞𝑝(𝑧𝑒) ∗ 𝑐𝑝𝑒 − 𝑞𝑝(𝑧𝑖) ∗ 𝑐𝑝𝑖 (𝑁/𝑚2) (4-10)

Where,

𝑞𝑝(𝑧𝑒) is the external peak velocity pressure

𝑞𝑝(𝑧𝑖) is the internal peak velocity pressure

𝑧𝑒 is the reference height for external pressure

𝑧𝑖 is the reference height for internal pressure

𝑐𝑝𝑒 is the pressure coefficient for external pressure

𝑐𝑝𝑖 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).

29

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.

𝑆𝑎 = 𝑆𝐷𝑆(0.4 + 0.6𝑇

𝑇0) 0 < 𝑇 < 𝑇0 (4-11)

𝑆𝑎 = 𝑆𝐷𝑆 𝑇0 < 𝑇 < 𝑇𝑠 (4-12)

𝑆𝑎 = 𝑆𝐷1

𝑇 𝑇𝑠 < 𝑇 < 𝑇𝐿 (4-13)

𝑆𝑎 = 𝑆𝐷1∙𝑇𝐿

𝑇2 𝑇𝐿 < 𝑇 (4-14)

Where

𝑆𝐷𝑆 = 2

3𝑆𝑀𝑆 =

2

3𝐹𝑎𝑆𝑠 (4-15)

𝑆𝐷1 = 2

3𝑆𝑀1 =

2

3𝐹𝑣𝑆1 (4-16)

𝑇 = Period of the structure [s]

𝑆𝑎 = Design spectral response acceleration

𝑆𝑠 = Mapped MCER spectral response acceleration parameter at short periods

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

𝑆𝐷𝑆 = Design spectral response acceleration parameter at short periods

𝑆𝐷1 = Design spectral response acceleration parameter at 1-s period

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

class effects 𝑆𝑀1 = 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

the Seismic Ground Motion Long-Period Transition And Risk Coefficient Maps are

shown.

30

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

31

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

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

32

33

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.

34

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 5.1: 3D view of the Core

35

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

36

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.

37

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

38

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.

39

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.

40

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

41

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 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

549.80 8.49 8.49 5.05

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

42

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 Figure 5.11: Elevation views of the first three eigenmodes

43

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

No mesh 239.30 5.21 5.21 1.76

44

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.

45

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.

46

47

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

48

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

49

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.

50

(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.

51

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.

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.

52

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.

53

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.

54

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

55

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.

56

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.

57

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.

58

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

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

59

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.

60

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)

61

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

62

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.

63

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

64

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.

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.

0

5

10

15

20

25

30

35

40

45

Core,outrigger

andperimeter

frame

TMF:perimeterframe twostory belt

walls

TMF:perimeter

framesingle

story beltwalls

TMF:perimeterframe twostory cross

walls

TMF:perimeter

framesingle

story crosswalls

TMF:Mega

columnstwo storybelt walls

TMF:Mega

columnssingle

story beltwalls

TMF:Mega

columnstwo story

cross walls

TMF:Mega

columnssingle

story crosswalls

Per

iod

[s]

Mode 1 and Mode 2

264.32 m 396.48 m 528.64 m 660.80 m 792.96 m

65

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

-20

-15

-10

-5

0

5

10

15

20

25

Core,outrigger

andperimeter

frame

TMF:perimeterframe twostory belt

walls

TMF:perimeter

framesingle

story beltwalls

TMF:perimeterframe twostory cross

walls

TMF:perimeter

framesingle

story crosswalls

TMF:Mega

columnstwo storybelt walls

TMF:Mega

columnssingle

story beltwalls

TMF:Mega

columnstwo story

cross walls

TMF:Mega

columnssingle

story crosswalls

Per

iod

[s]

Mode 3

264.32 m 396.48 m 528.64 m 660.80 m 792.96 m

66

between which models had the lowest respectively highest deflection was almost

the same with and without P-delta effects.

Figure 6.19: Deflection at the top story caused by wind load. P-delta effects are excluded.

200

300

400

500

600

700

800

900

0 1 2 3 4 5 6 7 8 9

Top

sto

ry h

eigh

t [m

]

Top story deflection [m]

Deflection at the top story caused by wind load

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

67

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.

200

300

400

500

600

700

800

900

0 2 4 6 8 10 12

Top

sto

ry h

eigh

t [m

]

Top story deflection [m]

Deflection at the top story caused by seismic loading

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

68

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

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

0

5

10

15

20

25

30

35

Core,outrigger

andperimeter

frame

TMF:perimeterframe twostory belt

walls

TMF:perimeter

framesingle storybelt walls

TMF:perimeterframe twostory cross

walls

TMF:perimeter

framesingle storycross walls

TMF: Megacolumnstwo storybelt walls

TMF: Megacolumns

single storybelt walls

TMF: Megacolumnstwo story

cross walls

TMF: Megacolumns

single storycross walls

Per

iod

[s]

Mode 1 and Mode 2

264.32 m 396.48 m 528.64 m 660.80 m 792.96 m

0

1

2

3

4

5

6

7

8

9

Core,outrigger

andperimeter

frame

TMF:perimeterframe twostory belt

walls

TMF:perimeter

framesingle storybelt walls

TMF:perimeterframe twostory cross

walls

TMF:perimeter

framesingle storycross walls

TMF: Megacolumnstwo storybelt walls

TMF: Megacolumns

single storybelt walls

TMF: Megacolumnstwo story

cross walls

TMF: Megacolumns

single storycross walls

Per

iod

[s]

Mode 3

264.32 m 396.48 m 528.64 m 660.80 m 792.96 m

69

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.

70

Figure 6.23: 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 included.

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.

200

300

400

500

600

700

800

900

-300 -200 -100 0 100 200 300 400

Top

sto

ry h

eigh

t [m

]

Compression (-) /Tension (+) [MN]

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

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

71

Figure 6.24: Top story height as a function of the total force at the base when the building is subjected to dead load and seismic load in the x-direction. P-delta is included.

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.

200

300

400

500

600

700

800

900

-200 -100 0 100 200 300 400 500 600 700

Top

sto

ry h

eigh

t [m

]

Compression (-) /Tension (+) [MN]

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

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

72

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.

200

300

400

500

600

700

800

900

-250 -200 -150 -100 -50 0

Top

sto

ry h

eigh

t [m

]

Compression (-) /Tension (+) [MN]

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

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

73

Figure 6.26: Top story height as a function of the total force at the base when the building is subjected to dead load and seismic load in the x-direction. P-delta is not included.

200

300

400

500

600

700

800

900

-200 -150 -100 -50 0 50 100

Top

sto

ry h

eigh

t [m

]

Compression (-) /Tension (+) [MN]

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

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

74

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.

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

0

200

400

600

800

1000

1200

0 50 100 150 200 250

Top

sto

ry h

eigh

t [m

]

Top story deflection [m]

Deflection at the top story caused by wind load

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

Collapse Collapse

75

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 [m]

Fz [kN] %

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

76

77

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.

78

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.

79

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.

80

81

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85

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 and perimeter frame

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

86

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

Figure A.6: Deformed elevation view of the Core and diagonal braces

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

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

87

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

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

88

89

Appendix B - 3D pictures

Figure B.1: 3D pictures of the Core, outrigger and perimeter frame

56 stories, 264 m 84 stories, 396 m

112 stories, 529 m 140 stories, 661 m

90

Figure B.2: 3D pictures of the TMF: Perimeter frame two story belt walls

56 stories, 264 m 84 stories, 396 m

112 stories, 529 m 140 stories, 661 m

91

Figure B.3: 3D pictures of the TMF: Perimeter frame single story belt walls

56 stories, 264 m 84 stories, 396 m

112 stories, 529 m 140 stories, 661 m

92

Figure B.4: 3D pictures of the TMF: Perimeter frame two story cross walls

56 stories, 264 m 84 stories, 396 m

112 stories, 529 m 140 stories, 661 m

93

Figure B.5: 3D pictures of the TMF: Perimeter frame single story cross walls

56 stories, 264 m 84 stories, 396 m

112 stories, 529 m 140 stories, 661 m

94

Figure B.6: 3D pictures of the TMF: Mega columns two story belt walls

56 stories, 264 m 84 stories, 396 m

112 stories, 529 m 140 stories, 661 m

95

Figure B.7: 3D pictures of the TMF: Mega columns single story belt walls

56 stories, 264 m 84 stories, 396 m

112 stories, 529 m 140 stories, 661 m

96

Figure B.8: 3D pictures of the TMF: Mega columns two story cross walls

56 stories, 264 m 84 stories, 396 m

112 stories, 529 m 140 stories, 661 m

97

Figure B.9: 3D pictures of the TMF: Mega columns single story cross walls

56 stories, 264 m 84 stories, 396 m

112 stories, 529 m 140 stories, 661 m

98

99

Appendix C - Displacements and periods

P-delta effects included

Table C-1: Displacements and periods for the 264.32 m models with P-delta

264.32 m (P-delta effects included) Wind dislp. [m]

Seismic displ. [m]

Period Mode 1

[s]

Period Mode 2

[s]

Period Mode 3

[s]

Core, outrigger and perimeter frame 0.126 0.231 4.534 4.534 1.600

TMF: Perimeter frame two story belt walls 0.113 0.208 4.507 4.507 2.309

TMF: Perimeter frame single story belt walls 0.104 0.193 4.274 4.274 2.118

TMF: Perimeter frame two story cross walls 0.117 0.210 4.515 4.515 2.321

TMF: Perimeter frame single story cross walls 0.108 0.194 4.275 4.275 2.262

TMF: Mega columns two story belt walls 0.162 0.267 5.189 5.189 2.638

TMF: Mega columns single story belt walls 0.106 0.179 4.074 4.074 2.000

TMF: Mega columns two story cross walls 0.167 0.279 5.314 5.314 3.204

TMF: Mega columns single story cross walls 0.111 0.188 4.192 4.192 3.085

Table C-2: Displacements and periods for the 396.48 m models with P-delta

396.48 m (P-delta effects included) Wind dislp. [m]

Seismic displ. [m]

Period Mode 1

[s]

Period Mode 2

[s]

Period Mode 3

[s]

Core, outrigger and perimeter frame 0.681 1.118 9.800 9.799 2.449

TMF: Perimeter frame two story belt walls 0.511 0.851 8.797 8.797 3.458

TMF: Perimeter frame single story belt walls 0.487 0.818 8.540 8.540 3.175

TMF: Perimeter frame two story cross walls 0.532 0.867 8.859 8.859 3.498

TMF: Perimeter frame single story cross walls 0.508 0.827 8.571 8.571 3.420

TMF: Mega columns two story belt walls 0.668 0.997 9.672 9.672 4.263

TMF: Mega columns single story belt walls 0.511 0.783 8.293 8.293 3.140

TMF: Mega columns two story cross walls 0.686 1.037 9.884 9.884 5.522

TMF: Mega columns single story cross walls 0.526 0.810 8.459 8.459 5.288

100

Table C-3: Displacements and periods for the 528.64 m models with P-delta

528.64 m (P-delta effects included) Wind dislp. [m]

Seismic displ. [m]

Period Mode 1

[s]

Period Mode 2

[s]

Period Mode 3

[s]

Core, outrigger and perimeter frame 2.542 3.851 18.040 18.040 3.413

TMF: Perimeter frame two story belt walls 1.694 2.617 15.156 15.156 4.651

TMF: Perimeter frame single story belt walls 1.645 2.565 14.894 14.894 4.251

TMF: Perimeter frame two story cross walls 1.775 2.687 15.326 15.325 4.700

TMF: Perimeter frame single story cross walls 1.721 2.603 14.985 14.985 4.601

TMF: Mega columns two story belt walls 2.105 2.930 16.221 16.221 6.866

TMF: Mega columns single story belt walls 1.749 2.487 14.593 14.593 4.589

TMF: Mega columns two story cross walls 2.160 3.043 16.560 16.560 11.046

TMF: Mega columns single story cross walls 1.791 2.557 14.826 14.826 10.073

Table C-4: Displacements and periods for the 660.80 m models with P-delta

660.80 m (P-delta effects included) Wind dislp. [m]

Seismic displ. [m]

Period Mode 1

[s]

Period Mode 2

[s]

Period Mode 3

[s]

Core, outrigger and perimeter frame 8.335 11.841 31.485 31.485 4.641

TMF: Perimeter frame two story belt walls 4.813 7.001 24.541 24.540 5.926

TMF: Perimeter frame single story belt walls 4.724 6.934 24.286 24.285 5.369

TMF: Perimeter frame two story cross walls 5.084 7.247 24.923 24.923 5.943

TMF: Perimeter frame single story cross walls 4.966 7.070 24.496 24.496 5.822

TMF: Mega columns two story belt walls 5.857 7.699 25.942 25.942 18.466

TMF: Mega columns single story belt walls 5.070 6.782 23.930 23.930 7.020

TMF: Mega columns two story cross walls 6.026 8.018 26.511 26.511

-13.065*

TMF: Mega columns single story cross walls 5.185 6.964 24.283 24.283

-14.638*

101

Table C-5: Displacements and periods for the 792.96 m models with P-delta

792.96 m (P-delta effects included) Wind dislp. [m]

Seismic displ. [m]

Period Mode 1

[s]

Period Mode 2

[s]

Period Mode 3

[s]

TMF: perimeter frame two story belt walls

13.260 18.331 39.454 39.452 7.346

TMF: perimeter frame single story belt walls

13.106 18.279 39.225 39.224 6.562

TMF: perimeter frame two story cross walls

14.198 19.230 40.349 40.348 7.249

TMF: perimeter frame single story cross walls

13.883 18.779 39.721 39.720 7.104

P-delta effects excluded

Table C-6: Displacements and periods for the 264.32 m models without P-delta

264.32 m (P-delta effects excluded)

Wind dislp. [m]

Seismic displ. [m]

Period Mode 1

[s]

Period Mode 2

[s]

Period Mode 3

[s]

Core, outrigger and perimeter frame 0.122 0.224 4.468 4.468 1.583

TMF: Perimeter frame two story belt walls 0.110 0.203 4.444 4.444 2.293

TMF: Perimeter frame single story belt walls 0.101 0.188 4.220 4.220 2.111

TMF: Perimeter frame two story cross walls 0.114 0.205 4.451 4.451 2.306

TMF: Perimeter frame single story cross walls 0.105 0.189 4.220 4.220 2.248

TMF: Mega columns two story belt walls 0.156 0.257 5.081 5.081 2.552

TMF: Mega columns single story belt walls 0.108 0.184 4.138 4.138 2.957

TMF: Mega columns two story cross walls 0.160 0.268 5.199 5.199 3.059

TMF: Mega columns single story cross walls 0.103 0.175 4.025 4.025 1.965

102

Table C-7: Displacements and periods for the 396.48 m models without P-delta

396.48 m (P-delta effects excluded) Wind dislp. [m]

Seismic displ. [m]

Period Mode 1

[s]

Period Mode 2

[s]

Period Mode 3

[s]

Core, outrigger and perimeter frame 0.621 1.021 9.368 9.368 2.370

TMF: Perimeter frame two story belt walls 0.476 0.794 8.496 8.496 3.409

TMF: Perimeter frame single story belt walls 0.455 0.766 8.262 8.262 3.154

TMF: Perimeter frame two story cross walls 0.495 0.808 8.551 8.551 3.457

TMF: Perimeter frame single story cross walls 0.474 0.774 8.289 8.289 3.382

TMF: Mega columns two story belt walls 0.611 0.914 9.250 9.250 3.826

TMF: Mega columns single story belt walls 0.478 0.734 8.027 8.027 2.965

TMF: Mega columns two story cross walls 0.625 0.948 9.435 9.435 4.672

TMF: Mega columns single story cross walls 0.492 0.757 8.177 8.177 4.539

Table C-8: Displacements and periods for the 528.64 m models without P-delta

528.64 m (P-delta effects excluded) Wind dislp. [m]

Seismic displ. [m]

Period Mode 1

[s]

Period Mode 2

[s]

Period Mode 3

[s]

Core, outrigger and perimeter frame 2.041 3.096 16.184 16.184 3.157

TMF: Perimeter frame two story belt walls 1.455 2.251 14.058 14.058 4.524

TMF: Perimeter frame single story belt walls 1.418 2.214 13.842 13.842 4.197

TMF: Perimeter frame two story cross walls 1.519 2.304 14.191 14.191 4.608

TMF: Perimeter frame single story cross walls 1.481 2.243 13.912 13.912 4.515

TMF: Mega columns two story belt walls 1.761 2.458 14.844 14.844 5.100

TMF: Mega columns single story belt walls 1.508 2.146 13.559 13.559 3.965

TMF: Mega columns two story cross walls 1.794 2.536 15.104 15.104 6.287

TMF: Mega columns single story cross walls 1.538 2.197 13.747 13.747 6.121

103

Table C-9: Displacements and periods for the 660.80 m models without P-delta

660.80 m (P-delta effects excluded) Wind dislp. [m]

Seismic displ. [m]

Period Mode 1

[s]

Period Mode 2

[s]

Period Mode 3

[s]

Core, outrigger and perimeter frame 5.200 7.408 24.926 24.926 4.456

TMF: Perimeter frame two story belt walls 3.568 5.201 21.164 21.163 5.640

TMF: Perimeter frame single story belt walls 3.515 5.171 20.985 20.984 5.240

TMF: Perimeter frame two story cross walls 3.737 5.339 21.405 21.405 5.759

TMF: Perimeter frame single story cross walls 3.678 5.247 21.115 21.115 5.648

TMF: Mega columns two story belt walls 4.176 5.508 21.941 21.941 6.375

TMF: Mega columns single story belt walls 3.762 5.043 20.646 20.646 4.965

TMF: Mega columns two story cross walls 4.244 5.668 22.286 22.286 7.901

TMF: Mega columns single story cross walls 3.819 5.141 20.876 20.875 7.704

Table C-10: Displacements and periods for the 792.96 m models without P-delta

792.96 m (P-delta effects excluded) Wind dislp. [m]

Seismic displ. [m]

Period Mode 1

[s]

Period Mode 2

[s]

Period Mode 3

[s]

TMF: perimeter frame two story belt walls 7.535 10.453 29.825 29.825 6.756

TMF: perimeter frame single story belt walls 7.471 10.456 29.698 29.697 6.283

TMF: perimeter frame two story cross walls 7.910 10.752 30.205 30.205 6.910

TMF: perimeter frame single story cross walls 7.825 10.621 29.905 29.905 6.782

104

105

Appendix D – Percentage difference between including and

excluding P-delta effects

Wind load

Table D-1: Percentage difference between including and excluding P-delta effects considering top story deflection due to wind load for the 264.32 m models

264.32 m Displacement top story due to wind load

With P-delta

Without P-delta %

Core, outrigger and perimeter frame 0.126 0.122 2.95

TMF: perimeter frame two story belt walls 0.113 0.110 2.91

TMF: perimeter frame single story belt walls

0.104 0.101 2.57

TMF: perimeter frame two story cross walls 0.117 0.114 2.90

TMF: perimeter frame single story cross walls

0.108 0.105 2.57

TMF: Mega columns two story belt walls 0.162 0.156 4.17

TMF: Mega columns single story belt walls 0.106 0.103 2.52

TMF: Mega columns two story cross walls 0.167 0.160 4.43

TMF: Mega columns single story cross walls

0.111 0.108 2.60

Table D-2: Percentage difference between including and excluding P-delta effects considering top story deflection due to wind load for the 396.48 m models

396.48 m Displacement top story due to wind load

With P-delta

Without P-delta %

Core, outrigger and perimeter frame 0.681 0.621 9.55

TMF: perimeter frame two story belt walls 0.511 0.476 7.28

TMF: perimeter frame single story belt walls 0.487 0.455 6.92

TMF: perimeter frame two story cross walls 0.532 0.495 7.41

TMF: perimeter frame single story cross walls 0.508 0.474 6.98

TMF: Mega columns two story belt walls 0.668 0.611 9.33

TMF: Mega columns single story belt walls 0.511 0.478 6.82

TMF: Mega columns two story cross walls 0.686 0.625 9.73

TMF: Mega columns single story cross walls 0.526 0.492 7.08

106

Table D-3: Percentage difference between including and excluding P-delta effects considering top story deflection due to wind load for the 528.64 m models

528.64 m Displacement top story due to wind load

With P-delta Without P-delta %

Core, outrigger and perimeter frame 2.542 2.041 24.56

TMF: perimeter frame two story belt walls 1.694 1.455 16.43

TMF: perimeter frame single story belt walls 1.645 1.418 15.97

TMF: perimeter frame two story cross walls 1.775 1.519 16.83

TMF: perimeter frame single story cross walls 1.721 1.481 16.21

TMF: Mega columns two story belt walls 2.105 1.761 19.56

TMF: Mega columns single story belt walls 1.749 1.508 16.02

TMF: Mega columns two story cross walls 2.160 1.794 20.36

TMF: Mega columns single story cross walls 1.791 1.538 16.51

Table D-4: Percentage difference between including and excluding P-delta effects considering top story deflection due to wind load for the 660.80 m models

660.80 m Displacement top story due to wind load

With P-delta

Without P-delta %

Core, outrigger and perimeter frame 8.3354 5.200 60.31

TMF: perimeter frame two story belt walls 4.8129 3.568 34.91

TMF: perimeter frame single story belt walls 4.724 3.515 34.38

TMF: perimeter frame two story cross walls 5.084 3.737 36.04

TMF: perimeter frame single story cross walls 4.966 3.678 35.03

TMF: Mega columns two story belt walls 5.857 4.176 40.26

TMF: Mega columns single story belt walls 5.070 3.762 34.78

TMF: Mega columns two story cross walls 6.026 4.244 41.99

TMF: Mega columns single story cross walls 5.185 3.819 35.76

Table D-5: Percentage difference between including and excluding P-delta effects considering top story deflection due to wind load for the 792.96 m models

792.96 m Displacement top story due to wind load

With P-delta

Without P-delta %

TMF: perimeter frame two story belt walls 13.260 7.535 75.99

TMF: perimeter frame single story belt walls 13.106 7.471 75.43

TMF: perimeter frame two story cross walls 14.198 7.910 79.49

TMF: perimeter frame single story cross walls 13.883 7.825 77.43

107

Seismic loading

Table D-6: Percentage difference between including and excluding P-delta effects considering top story deflection due to seismic loading for the 264.32 m models

264.32 m Displacement top story due to seismic loading

With P-delta Without P-delta %

Core, outrigger and perimeter frame 0.231 0.224 2.99

TMF: perimeter frame two story belt walls 0.208 0.203 2.77

TMF: perimeter frame single story belt walls 0.193 0.188 2.50

TMF: perimeter frame two story cross walls 0.210 0.205 2.84

TMF: perimeter frame single story cross walls 0.194 0.189 2.54

TMF: Mega columns two story belt walls 0.267 0.257 4.01

TMF: Mega columns single story belt walls 0.179 0.175 2.40

TMF: Mega columns two story cross walls 0.279 0.268 4.18

TMF: Mega columns single story cross walls 0.188 0.184 2.50

Table D-7: Percentage difference between including and excluding P-delta effects considering top story deflection due to seismic loading for the 396.48 m models

396.48 m Displacement top story due to seismic loading

With P-delta Without P-delta %

Core, outrigger and perimeter frame 1.118 1.021 9.47

TMF: perimeter frame two story belt walls 0.851 0.794 7.16

TMF: perimeter frame single story belt walls 0.818 0.766 6.82

TMF: perimeter frame two story cross walls 0.867 0.808 7.29

TMF: perimeter frame single story cross walls 0.827 0.774 6.89

TMF: Mega columns two story belt walls 0.997 0.914 9.07

TMF: Mega columns single story belt walls 0.783 0.734 6.75

TMF: Mega columns two story cross walls 1.037 0.948 9.45

TMF: Mega columns single story cross walls 0.810 0.757 7.00

108

Table D-8: Percentage difference between including and excluding P-delta effects considering top story deflection due to seismic loading for the 528.64 m models

528.64 m Displacement top story due to seismic loading

With P-delta Without P-delta %

Core, outrigger and perimeter frame 3.851 3.096 24.36

TMF: perimeter frame two story belt walls 2.617 2.251 16.25

TMF: perimeter frame single story belt walls 2.565 2.214 15.82

TMF: perimeter frame two story cross walls 2.687 2.304 16.65

TMF: perimeter frame single story cross walls 2.603 2.243 16.06

TMF: Mega columns two story belt walls 2.930 2.458 19.22

TMF: Mega columns single story belt walls 2.487 2.146 15.87

TMF: Mega columns two story cross walls 3.043 2.536 20.00

TMF: Mega columns single story cross walls 2.557 2.197 16.36

Table D-9: Percentage difference between including and excluding P-delta effects considering top story deflection due to seismic loading for the 660.80 m models

660.80 m Displacement top story due to seismic loading

With P-delta Without P-delta %

Core, outrigger and perimeter frame 11.841 7.408 59.83

TMF: perimeter frame two story belt walls 7.001 5.201 34.60

TMF: perimeter frame single story belt walls 6.934 5.171 34.09

TMF: perimeter frame two story cross walls 7.247 5.339 35.73

TMF: perimeter frame single story cross walls 7.070 5.247 34.75

TMF: Mega columns two story belt walls 7.699 5.508 39.76

TMF: Mega columns single story belt walls 6.782 5.043 34.49

TMF: Mega columns two story cross walls 8.018 5.668 41.46

TMF: Mega columns single story cross walls 6.964 5.141 35.47

109

Table D-10: Percentage difference between including and excluding P-delta effects considering top story deflection due to seismic loading for the 792.96 m models

792.96 m Displacement top story due to seismic loading

With P-delta Without P-delta %

TMF: perimeter frame two story belt walls 18.331 10.453 75.36

TMF: perimeter frame single story belt walls 18.279 10.456 74.82

TMF: perimeter frame two story cross walls 19.230 10.752 78.84

TMF: perimeter frame single story cross walls

18.779 10.621 76.81

110

111

Appendix E – Difference between including and excluding P-

delta effects

Figure E-1: Difference between including and excluding P-delta effects considering top story deflection due to wind load for Core, outrigger and perimeter frame

0

100

200

300

400

500

600

700

0 1 2 3 4 5 6 7 8 9

Top

Sto

ry H

eigh

t [m

]

Top Story Deflection [m]

Deflection at the top story caused by wind load; Core, outrigger and perimeter frame

With P-delta Without P-delta

112

Figure E-2: Difference between including and excluding P-delta effects considering top story deflection due to wind load for TMF: Perimeter frame two story belt walls

Figure E-3: Difference between including and excluding P-delta effects considering top story deflection due to wind load for TMF: Perimeter frame sinlge story belt walls

0

100

200

300

400

500

600

700

800

900

0 2 4 6 8 10 12 14

Top

Sto

ry H

eigh

t [m

]

Top Story Deflection [m]

Deflection at the top story caused by wind load; TMF: Perimeter frame two story belt walls

With P-delta Without P-delta

0

100

200

300

400

500

600

700

800

900

0 2 4 6 8 10 12 14

Top

Sto

ry H

eigh

t [m

]

Top Story Deflection [m]

Deflection at the top story caused by wind load; TMF: Perimeter frame single story belt walls

With P-delta Without P-delta

113

Figure E-4: Difference between including and excluding P-delta effects considering top story deflection due to wind load for TMF: Perimeter frame two story cross walls

Figure E-5: Difference between including and excluding P-delta effects considering top story deflection due to wind load for TMF: Perimeter frame single story cross walls

0

100

200

300

400

500

600

700

800

900

0 2 4 6 8 10 12 14 16

Top

Sto

ry H

eigh

t [m

]

Top Story Deflection [m]

Deflection at the top story caused by wind load; TMF: Perimeter frame two story cross walls

With P-delta Without P-delta

0

100

200

300

400

500

600

700

800

900

0 2 4 6 8 10 12 14 16

Top

Sto

ry H

eigh

t [m

]

Top Story Deflection [m]

Deflection at the top story caused by wind load; TMF: Perimeter frame single story cross walls

With P-delta Without P-delta

114

Figure E-6: Difference between including and excluding P-delta effects considering top story deflection due to wind load for TMF: Mega columns two story belt walls

Figure E-7: Difference between including and excluding P-delta effects considering top story deflection due to wind load for TMF: Mega columns single story belt walls

0

100

200

300

400

500

600

700

0 1 2 3 4 5 6 7

Top

Sto

ry H

eigh

t [m

]

Top Story Deflection [m]

Deflection at the top story caused by wind load; TMF: Mega columns two story belt walls

With P-delta Without P-delta

0

100

200

300

400

500

600

700

0 1 2 3 4 5 6

Top

Sto

ry H

eigh

t [m

]

Top Story Deflection [m]

Deflection at the top story caused by wind load; TMF: Mega columns single story belt walls

With P-delta Without P-delta

115

Figure E-8: Difference between including and excluding P-delta effects considering top story deflection due to wind load for TMF: Mega columns two story cross walls

Figure E-9: Difference between including and excluding P-delta effects considering top story deflection due to wind load for TMF: Mega columns single story cross walls

0

100

200

300

400

500

600

700

0 1 2 3 4 5 6 7

Top

Sto

ry H

eigh

t [m

]

Top Story Deflection [m]

Deflection at the top story caused by wind load; TMF: Mega columns two story cross walls

With P-delta Without P-delta

0

100

200

300

400

500

600

700

0 1 2 3 4 5 6

Top

Sto

ry H

eigh

t [m

]

Top Story Deflection [m]

Deflection at the top story caused by wind load; TMF: Mega columns single story cross walls

With P-delta Without P-delta

116

Figure E-10: Difference between including and excluding P-delta effects considering top story deflection due to seismic loading for Core, outrigger and perimeter frame

0

100

200

300

400

500

600

700

0 2 4 6 8 10 12 14

Top

Sto

ry H

eigh

t [m

]

Top Story Deflection [m]

Deflection at the top story caused by seismic loading; Core, outrigger and perimeter frame

With P-delta Without P-delta

117

Figure E-11: Difference between including and excluding P-delta effects considering top story deflection due to seismic loading for TMF: Perimeter frame two story belt walls

Figure E-12: Difference between including and excluding P-delta effects considering top story deflection due to seismic loading for TMF: Perimeter frame single story belt walls

0

100

200

300

400

500

600

700

800

900

0 2 4 6 8 10 12 14 16 18 20

Top

Sto

ry H

eigh

t [m

]

Top Story Deflection [m]

Deflection at the top story caused by seismic loading; TMF: Perimeter frame two story belt walls

With P-delta Without P-delta

0

100

200

300

400

500

600

700

800

900

0 2 4 6 8 10 12 14 16 18 20

Top

Sto

ry H

eigh

t [m

]

Top Story Deflection [m]

Deflection at the top story caused by seismic loading; TMF: Perimeter frame single story belt walls

With P-delta Without P-delta

118

Figure E-13: Difference between including and excluding P-delta effects considering top story deflection due to seismic loading for TMF: Perimeter frame two story cross walls

Figure E-14: Difference between including and excluding P-delta effects considering top story deflection due to seismic loading for TMF: Perimeter frame single story cross walls

0

100

200

300

400

500

600

700

800

900

0 5 10 15 20 25

Top

Sto

ry H

eigh

t [m

]

Top Story Deflection [m]

Deflection at the top story caused by seismic loading; TMF: Perimeter frame two story cross walls

With P-delta Without P-delta

0

100

200

300

400

500

600

700

800

900

0 2 4 6 8 10 12 14 16 18 20

Top

Sto

ry H

eigh

t [m

]

Top Story Deflection [m]

Deflection at the top story caused by seismic loading; TMF: Perimeter frame single story cross walls

With P-delta Without P-delta

119

Figure E-15: Difference between including and excluding P-delta effects considering top story deflection due to seismic loading for TMF: Mega columns two story belt walls

Figure E-16: Difference between including and excluding P-delta effects considering top story deflection due to seismic loading for TMF: Mega columns single story belt walls

0

100

200

300

400

500

600

700

0 1 2 3 4 5 6 7 8 9

Top

Sto

ry H

eigh

t [m

]

Top Story Deflection [m]

Deflection at the top story caused by seismic loading; TMF: Mega columns two story belt walls

With P-delta Without P-delta

0

100

200

300

400

500

600

700

0 1 2 3 4 5 6 7 8

Top

Sto

ry H

eigh

t [m

]

Top Story Deflection [m]

Deflection at the top story caused by seismic loading; TMF: Mega columns single story belt walls

With P-delta Without P-delta

120

Figure E-17: Difference between including and excluding P-delta effects considering top story deflection due to seismic loading for TMF: Mega columns two story cross walls

Figure E-18: Difference between including and excluding P-delta effects considering top story deflection due to seismic loading for TMF: Mega columns single story cross walls

0

100

200

300

400

500

600

700

0 1 2 3 4 5 6 7 8 9

Top

Sto

ry H

eigh

t [m

]

Top Story Deflection [m]

Deflection at the top story caused by seismic loading; TMF: Mega columns two story cross walls

With P-delta Without P-delta

0

100

200

300

400

500

600

700

0 1 2 3 4 5 6 7 8

Top

Sto

ry H

eigh

t [m

]

Top Story Deflection [m]

Deflection at the top story caused by seismic loading; TMF: Mega columns single story cross walls

With P-delta Without P-delta

121

Appendix F – Forces at the base

Table F-1: Forces at the base due to wind load for the 264.32 m models. P-delta is included.

264.32 m (P-delta effects included) Forces at the base story [MN]

Core, outrigger and perimeter frame -140

TMF: perimeter frame two story belt walls -163

TMF: perimeter frame single story belt walls -166

TMF: perimeter frame two story cross walls -159

TMF: perimeter frame single story cross walls -159

TMF: Mega columns two story belt walls -143

TMF: Mega columns single story belt walls -141

TMF: Mega columns two story cross walls -145

TMF: Mega columns single story cross walls -142

Table F-2: Forces at the base due to wind load for the 396.48 m models. P-delta is included.

396.48 m (P-delta effects included) Forces at the base story [MN]

Core, outrigger and perimeter frame -143

TMF: perimeter frame two story belt walls -193

TMF: perimeter frame single story belt walls -197

TMF: perimeter frame two story cross walls -187

TMF: perimeter frame single story cross walls -187

TMF: Mega columns two story belt walls -153

TMF: Mega columns single story belt walls -150

TMF: Mega columns two story cross walls -156

TMF: Mega columns single story cross walls -152

122

Table F-3: Forces at the base due to wind load for the 528.64 m models. P-delta is included.

528.64 m (P-delta effects included) Forces at the base story [MN]

Core, outrigger and perimeter frame -72

TMF: perimeter frame two story belt walls -166

TMF: perimeter frame single story belt walls -172

TMF: perimeter frame two story cross walls -158

TMF: perimeter frame single story cross walls -157

TMF: Mega columns two story belt walls -95

TMF: Mega columns single story belt walls -94

TMF: Mega columns two story cross walls -97

TMF: Mega columns single story cross walls -95

Table F-4: Forces at the base due to wind load for the 660.80 m models. P-delta is included.

660.80 m (P-delta effects included) Forces at the base story [MN]

Core, outrigger and perimeter frame 174

TMF: perimeter frame two story belt walls -43

TMF: perimeter frame single story belt walls -51

TMF: perimeter frame two story cross walls -30

TMF: perimeter frame single story cross walls -31

TMF: Mega columns two story belt walls 85

TMF: Mega columns single story belt walls 74

TMF: Mega columns two story cross walls 86

TMF: Mega columns single story cross walls 76

Table F-5: Forces at the base due to wind load for the 792.96 m models. P-delta is included.

792.96 m (P-delta effects included) Forces at the base story [MN]

TMF: perimeter frame two story belt walls 294

TMF: perimeter frame single story belt walls 284

TMF: perimeter frame two story cross walls 322

TMF: perimeter frame single story cross walls 314

123

Table F-6: Forces at the base due to seismic loading for the 264.32 m models. P-delta is included.

264.32 m (P-delta effects included) Forces at the base story [MN]

Core, outrigger and perimeter frame -102

TMF: perimeter frame two story belt walls -130

TMF: perimeter frame single story belt walls -133

TMF: perimeter frame two story cross walls -128

TMF: perimeter frame single story cross walls -129

TMF: Mega columns two story belt walls -113

TMF: Mega columns single story belt walls 110

TMF: Mega columns two story cross walls 115

TMF: Mega columns single story cross walls 111

Table F-7: Forces at the base due to seismic loading for the 396.48 m models. P-delta is included.

396.48 m (P-delta effects included) Forces at the base story [MN]

Core, outrigger and perimeter frame -72

TMF: perimeter frame two story belt walls -129

TMF: perimeter frame single story belt walls -132

TMF: perimeter frame two story cross walls -127

TMF: perimeter frame single story cross walls -127

TMF: Mega columns two story belt walls -97

TMF: Mega columns single story belt walls -93

TMF: Mega columns two story cross walls -97

TMF: Mega columns single story cross walls -94

Table F-8: Forces at the base due to seismic loading for the 528.64 m models. P-delta is included.

528.64 m (P-delta effects included) Forces at the base story [MN]

Core, outrigger and perimeter frame 47

TMF: perimeter frame two story belt walls -62

TMF: perimeter frame single story belt walls -65

TMF: perimeter frame two story cross walls -60

TMF: perimeter frame single story cross walls -61

TMF: Mega columns two story belt walls -7

TMF: Mega columns single story belt walls -7

TMF: Mega columns two story cross walls -4

TMF: Mega columns single story cross walls -5

124

Table F-9: Forces at the base due to seismic loading for the 660.80 m models. P-delta is included.

660.80 m (P-delta effects included) Forces at the base story [MN]

Core, outrigger and perimeter frame 369

TMF: perimeter frame two story belt walls 119

TMF: perimeter frame single story belt walls 115

TMF: perimeter frame two story cross walls 120

TMF: perimeter frame single story cross walls 116

TMF: Mega columns two story belt walls 214

TMF: Mega columns single story belt walls 201

TMF: Mega columns two story cross walls 226

TMF: Mega columns single story cross walls 207

Table F-10: Forces at the base due to seismic loading for the 792.96 m models. P-delta is included.

792.96 m (P-delta effects included) Forces at the base story [MN]

TMF: perimeter frame two story belt walls 560

TMF: perimeter frame single story belt walls 557

TMF: perimeter frame two story cross walls 568

TMF: perimeter frame single story cross walls 554

125

Table F-11: Forces at the base due to wind load for the 264.32 m models. P-delta is excluded.

264.32 m (P-delta effects excluded) Forces at the base story [MN]

Core, outrigger and perimeter frame -142

TMF: perimeter frame two story belt walls -164

TMF: perimeter frame single story belt walls -167

TMF: perimeter frame two story cross walls -160

TMF: perimeter frame single story cross walls -160

TMF: Mega columns two story belt walls -145

TMF: Mega columns single story belt walls -143

TMF: Mega columns two story cross walls -147

TMF: Mega columns single story cross walls -142

Table F-12: Forces at the base due to wind load for the 396.48 m models. P-delta is excluded.

396.48 m (P-delta effects excluded) Forces at the base story [MN]

Core, outrigger and perimeter frame -155

TMF: perimeter frame two story belt walls -201

TMF: perimeter frame single story belt walls -204

TMF: perimeter frame two story cross walls -195

TMF: perimeter frame single story cross walls -194

TMF: Mega columns two story belt walls -164

TMF: Mega columns single story belt walls -158

TMF: Mega columns two story cross walls -168

TMF: Mega columns single story cross walls -160

Table F-13: Forces at the base due to wind load for the 528.64 m models. P-delta is excluded.

528.64 m (P-delta effects excluded) Forces at the base story [MN]

Core, outrigger and perimeter frame -122

TMF: perimeter frame two story belt walls -199

TMF: perimeter frame single story belt walls -203

TMF: perimeter frame two story cross walls -190

TMF: perimeter frame single story cross walls -189

TMF: Mega columns two story belt walls -139

TMF: Mega columns single story belt walls -129

TMF: Mega columns two story cross walls -144

TMF: Mega columns single story cross walls -132

126

Table F-14: Forces at the base due to wind load for the 660.80 m models. P-delta is excluded.

660.80 m (P-delta effects excluded) Forces at the base story [MN]

Core, outrigger and perimeter frame -41

TMF: perimeter frame two story belt walls -155

TMF: perimeter frame single story belt walls -159

TMF: perimeter frame two story cross walls -144

TMF: perimeter frame single story cross walls -142

TMF: Mega columns two story belt walls -66

TMF: Mega columns single story belt walls -53

TMF: Mega columns two story cross walls -72

TMF: Mega columns single story cross walls -56

Table F-15: Forces at the base due to wind load for the 792.96 m models. P-delta is excluded.

792.96 m (P-delta effects excluded) Forces at the base story [MN]

TMF: perimeter frame two story belt walls -66

TMF: perimeter frame single story belt walls -71

TMF: perimeter frame two story cross walls -54

TMF: perimeter frame single story cross walls -48

127

Table F-16: Forces at the base due to seismic loading for the 264.32 m models. P-delta is excluded.

264.32 m (P-delta effects excluded) Forces at the base story [MN]

Core, outrigger and perimeter frame -104

TMF: perimeter frame two story belt walls -133

TMF: perimeter frame single story belt walls -135

TMF: perimeter frame two story cross walls -130

TMF: perimeter frame single story cross walls -131

TMF: Mega columns two story belt walls -116

TMF: Mega columns single story belt walls -113

TMF: Mega columns two story cross walls -118

TMF: Mega columns single story cross walls -112

Table F-17: Forces at the base due to seismic loading for the 396.48 m models. P-delta is excluded.

396.48 m (P-delta effects excluded) Forces at the base story [MN]

Core, outrigger and perimeter frame -90

TMF: perimeter frame two story belt walls -141

TMF: perimeter frame single story belt walls -143

TMF: perimeter frame two story cross walls -139

TMF: perimeter frame single story cross walls -138

TMF: Mega columns two story belt walls -112

TMF: Mega columns single story belt walls -105

TMF: Mega columns two story cross walls -113

TMF: Mega columns single story cross walls -106

Table F-18: Forces at the base due to seismic loading for the 528.64 m models. P-delta is excluded.

528.64 m (P-delta effects excluded) Forces at the base story [MN]

Core, outrigger and perimeter frame -32

TMF: perimeter frame two story belt walls -110

TMF: perimeter frame single story belt walls -112

TMF: perimeter frame two story cross walls -108

TMF: perimeter frame single story cross walls -107

TMF: Mega columns two story belt walls -66

TMF: Mega columns single story belt walls -56

TMF: Mega columns two story cross walls -67

TMF: Mega columns single story cross walls -57

128

Table F-19: Forces at the base due to seismic loading for the 660.80 m models. P-delta is excluded.

660.8 m (P-delta effects excluded) Forces at the base story [MN]

Core, outrigger and perimeter frame 70

TMF: perimeter frame two story belt walls -39

TMF: perimeter frame single story belt walls -40

TMF: perimeter frame two story cross walls -39

TMF: perimeter frame single story cross walls -37

TMF: Mega columns two story belt walls 22

TMF: Mega columns single story belt walls 35

TMF: Mega columns two story cross walls 22

TMF: Mega columns single story cross walls 35

Table F-20: Forces at the base due to seismic loading for the 792.96 m models. P-delta is excluded.

792.96 m (P-delta effects excluded) Forces at the base story [MN]

TMF: perimeter frame two story belt walls 72

TMF: perimeter frame single story belt walls 71

TMF: perimeter frame two story cross walls 70

TMF: perimeter frame single story cross walls 71

129

Appendix G – Dead loads and overturning moments

Table G-1: Dead loads and overturning moments for the 264.32 m models. P-delta is included.

264.32 m (P-delta effects included) Fz [kN] Myw [kNm] Mys [kNm]

Core, outrigger and perimeter frame 818827.3 -1860785 -3067518

TMF: perimeter frame two story belt walls 843080.4 -1862853 -3171708

TMF: perimeter frame single story belt walls 851185.4 -1857186 -3173393

TMF: perimeter frame two story cross walls 826107.8 -1862910 -3101161

TMF: perimeter frame single story cross walls 825825.8 -1857230 -3073832

TMF: Mega columns two story belt walls 770384.8 -1883344 -2913927

TMF: Mega columns single story belt walls 775722.6 -1853746 -2880971

TMF: Mega columns two story cross walls 779754.6 -1886651 -2958306

TMF: Mega columns single story cross walls 779473.5 -1856393 -2899511

Table G-2: Dead loads and overturning moments for the 396.48 m models. P-delta is included.

396.48 m (P-delta effects included) Fz [kN] Myw [kNm] Mys [kNm]

Core, outrigger and perimeter frame 1226556 -4946994 -7279290

TMF: perimeter frame two story belt walls 1262936 -4885549 -7397376

TMF: perimeter frame single story belt walls 1275093 -4864051 -7408718

TMF: perimeter frame two story cross walls 1237477 -4888786 -7243476

TMF: perimeter frame single story cross walls 1237054 -4866059 -7183335

TMF: Mega columns two story belt walls 1154051 -4975392 -6853846

TMF: Mega columns single story belt walls 1162058 -4854147 -6730795

TMF: Mega columns two story cross walls 1168106 -4992792 -6967420

TMF: Mega columns single story cross walls 1167684 -4866854 -6781617

Table G-3: Dead loads and overturning moments for the 528.64 m models. P-delta is included.

528.64 m (P-delta effects included) Fz [kN] Myw [kNm] Mys [kNm]

Core, outrigger and perimeter frame 1634285 -10614979 -14511182

TMF: perimeter frame two story belt walls 1682791 -10113036 -14158422

TMF: perimeter frame single story belt walls 1699001 -10055957 -14179090

TMF: perimeter frame two story cross walls 1648846 -10135887 -13893736

TMF: perimeter frame single story cross walls 1648282 -10069383 -13765577

TMF: Mega columns two story belt walls 1537718 -10393706 -13243818

TMF: Mega columns single story belt walls 1548393 -10039165 -12892862

TMF: Mega columns two story cross walls 1556457 -10459281 -13499508

TMF: Mega columns single story cross walls 1555895 -10082865 -13012622

130

Table G-4: Dead loads and overturning moments for the 660.80 m models. P-delta is included.

660.80 m(P-delta effects included) Fz [kN] Myw [kNm] Mys [kNm]

Core, outrigger and perimeter frame 2042013 -21856072 -28511891

TMF: perimeter frame two story belt walls 2102646 -19078954 -25295997

TMF: perimeter frame single story belt walls 2122909 -18952153 -25326055

TMF: perimeter frame two story cross walls 2060215 -19195260 -24932853

TMF: perimeter frame single story cross walls 2059510 -19018982 -24650301

TMF: Mega columns two story belt walls 1921384 -19873370 -23988519

TMF: Mega columns single story belt walls 2122909 -18952153 -25326055

TMF: Mega columns two story cross walls 1944809 -20100461 -24579166

TMF: Mega columns single story cross walls 2059510 -19018982 -24650301

Table G-5: Dead loads and overturning moments for the 792.96 m models. P-delta is included.

792.96 m (P-delta effects included) Fz [kN] Myw [kNm] Mys [kNm]

TMF: perimeter frame two story belt walls 2522501 -36358419 -46526308

TMF: perimeter frame single story belt walls 2546816 -36100585 -46585761

TMF: perimeter frame two story cross walls 2471583 -36932786 -46338619

TMF: perimeter frame single story cross walls 2470738 -36424346 -45610311

131

Appendix H – Hand calculation of dead loads

TMF: Perimeter frame two story cross walls

s 7827kg

m3

Geometry

The height of one story

The width of the building

The width of the core

Number of stories

The height of the building

Number of stories with cross walls

Gravitational acceleration

Material properties

The density for concrete with strength class C100

The density for concrete with strength class C30/37

The density for steel

hstory 4.72m

Lside 28.5m

Lcore 9.5m

nstories

56

84

112

140

168

hc hstory nstories

264.32

396.48

528.64

660.8

792.96

m

ncross.walls

8

12

16

20

24

g 9.807m

s2

C100 2402.451kg

m3

C3037 1902.6kg

m3

132

Mass of cross walls

The total length of the cross walls for each cross walls story

The thickness of the cross walls

The total area of the cross walls for each cross walls story

The total volume of cross walls for the whole building

The total mass of cross walls for the whole building

The total force of cross walls for the whole building

tw 0.75m

Lw.tot 4 Lside tw 111m

Aw.tot Lw.tot tw 83.25m2

Vw.tot Aw.tot hstory ncross.walls

3.144 103

4.715 103

6.287 103

7.859 103

9.431 103

m3

mw.tot Vw.tot C100

7.552 106

1.133 107

1.51 107

1.888 107

2.266 107

kg

Ww.tot mw.tot g

7.406 104

1.111 105

1.481 105

1.852 105

2.222 105

kN

133

Mass of perimeter frame

Rectangular columns

The width of the rectangular columns

The depth of the rectangular columns

The volume of one rectangular column

The total mass of the rectangular columns for the whole building

The total force of the rectangular columns for the whole building

wc.rect 1.421m

dc.rect 2.068m

Vc.rect wc.rect dc.rect hc

776.738

1.165 103

1.553 103

1.942 103

2.33 103

m3

mc.rect.tot 20 C100 Vc.rect

3.732 107

5.598 107

7.464 107

9.33 107

1.12 108

kg

Wc.rect.tot mc.rect.tot g

3.66 105

5.49 105

7.32 105

9.15 105

1.098 106

kN

134

Corner columns

The width of the square columns

The depth of the square columns

The volume of one square column

The total mass of the square columns for the whole building

The total force of the square columns for the whole building

Beams

The width of the beams

The depth of the beams

The total length of the beams for one story

The total volume of the beams for one story

wc.square 1.713m

dc.square wc.square 1.713m

Vc.square wc.square dc.square hc

775.612

1.163 103

1.551 103

1.939 103

2.327 103

m3

mc.square.tot 4 C100 Vc.square

7.453 106

1.118 107

1.491 107

1.863 107

2.236 107

kg

Wc.square.tot mc.square.tot g

7.309 104

1.096 105

1.462 105

1.827 105

2.193 105

kN

wb 1.120m

hb 1.120m

Lb.tot 4 Lside wc.square 5 dc.rect 65.788m

Vb wb hb Lb.tot 82.524m3

135

mb.tot C100Vb nstories

1.11 107

1.665 107

2.221 107

2.776 107

3.331 107

kg

Wb mb.tot g

1.089 105

1.633 105

2.178 105

2.722 105

3.266 105

kN

The total mass of the beams for the whole building

The total force of the beams for the whole building

Mass of floor slabs

The thickness of the floors

The area of the floors for each story

The total area of the floors for the whole building

tf 0.25m

Af Lside2

Lcore2

722m2

Af.tot nstories Af

4

6

8

10

12

Aw.tot

4.01 104

6.015 104

8.02 104

1.002 105

1.203 105

m2

136

Vf.tot Af.tot tf

1.002 104

1.504 104

2.005 104

2.506 104

3.007 104

m3

mf C3037Vf.tot

1.907 107

2.861 107

3.815 107

4.768 107

5.722 107

kg

Wf mf g

1.87 105

2.806 105

3.741 105

4.676 105

5.611 105

kN

The total volume of the floors for the whole building

The total mass of the floors for the whole building

The total force of the floors for the whole building

137

Mass of VKR

The depth of the VKR columns

The width of the VKR columns

The thickness of the VKR columns

The area of one VKR column

The volume of one VKR column

The total volume of the VKR columns for the whole building

The total mass of the VKR columns for the whole building

The total force of the VKR columns for the whole building

dVKR 0.4m

wVKR dVKR 0.4m

tVKR 0.016m

AVKR 4 tVKR2

4 dVKR 2tVKR tVKR 0.025m2

VVKR AVKR hstory 0.116m3

VVKR.tot 8 nstories

12

18

24

30

36

VVKR

40.832

61.247

81.663

102.079

122.495

m3

mVKR s VVKR.tot

3.196 105

4.794 105

6.392 105

7.99 105

9.588 105

kg

WVKR mVKR g

3.134 103

4.701 103

6.268 103

7.835 103

9.402 103

kN

138

Total dead load

The total mass of the whole building

The total force of the whole building

The total force of the whole building given by ETABS

The ratio between the dead loads given by hand calculation and ETABS

mtot mw.tot mc.rect.tot mc.square.tot mb.tot mf mVKR

8.282 107

1.242 108

1.656 108

2.071 108

2.485 108

kg

Fdead mtot g

8.1221064544 105

1.2183159682 106

1.6244212909 106

2.0305266136 106

2.4366319363 106

kN

Fdead.ETABS

826107.7727

1237477

1648846

2060215

2471583

kN

Fdead.ETABS

Fdead

1.017

1.016

1.015

1.015

1.014