Application of a Simplified Skyscraper Model to the Burj Khalifa

Marc Daniel Bowman

A Project submitted to the faculty of

Brigham Young University

in partial fulfillment of the requirements for the degree of

Master of Science

Richard J. Balling

Paul Richards

Fernando S. Fonseca

Department of Civil Engineering

Brigham Young University

April 2016

Copyright © 2016 Marc Daniel Bowman

All Rights Reserved

ABSTRACT

Modified Simplified Skyscraper Model

Marc Daniel Bowman

Department of Civil Engineering, BYU

Master of Science

The Application of a Simplified Skyscraper Model for the Burj Khalifa is adapted from

the Simplified Skyscraper Model (SSM) developed by Balling and Lee (2014). The SSM is used

to prove that the SSM can be changed to analyze any skyscraper. The Burj Khalifa is the tallest

building in the world, and incorporated a buttressed core and outrigger structural system that

makes it a perfect candidate for the SSM. Because of its height, the Burj Khalifa was governed

by wind loading. Not only was the Burj Khalifa optimized in a structural sense, but measures

were taken to ensure its stability. The foundation design required testing of the concrete and the

construction used the latest advancements in construction. The SSM is a spreadsheet that can be

considered a preliminary design analysis for the Burj Khalifa. The idea is that it uses super-

elements and dominant degrees of freedom as the basis for analysis. With the use of a stiffness

matrix the lateral forces, lateral displacements, rotations, and drifts are calculated. This proves

the ease at which the SSM can be adapted for the analysis of any skyscraper that has a core,

outrigger, or belt truss.

Keywords: Burj Khalifa, buttressed core, outrigger, SSM

iii

TABLE OF CONTENTS

LIST OF TABLES ....................................................................................................................... iv

LIST OF FIGURES ...................................................................................................................... v

LIST OF EQUATIONS ............................................................................................................... vi

1 Introduction ........................................................................................................................... 1

2 Design and Construction of the Burj Khalifa ..................................................................... 3

2.1 Architecture .................................................................................................................... 3

2.2 Structural System ............................................................................................................ 4

2.2.1 Buttressed Core ........................................................................................................... 5

2.2.2 Outrigger System ........................................................................................................ 6

2.3 Structural Analysis .......................................................................................................... 7

2.3.1 Wind Engineering ....................................................................................................... 9

2.4 Foundation .................................................................................................................... 10

2.5 Construction .................................................................................................................. 12

3 Simplified model for analysis: Burj khalifa ...................................................................... 13

3.1 Constants ....................................................................................................................... 13

3.2 Super-elements .............................................................................................................. 17

3.3 Core Section .................................................................................................................. 19

3.4 Matrices ........................................................................................................................ 19

3.5 Wind and Seismic ......................................................................................................... 20

3.6 Stress ............................................................................................................................. 22

3.7 Graphs ........................................................................................................................... 22

4 Conclusion ........................................................................................................................... 27

References .................................................................................................................................... 29

iv

LIST OF TABLES

Table 2-1: Burj Khalifa Floor Plan ........................................................................................3

Table 3-1: Constants Sheet ....................................................................................................13

v

LIST OF FIGURES

Figure 1-1: Burj Khalifa.........................................................................................................2

Figure 1-2: Burj Khalifa.........................................................................................................2

Figure 2-1: Buttressed Core of a Typical Floor Plan .............................................................5

Figure 2-2: Typical Outrigger System ...................................................................................6

Figure 2-3: 3-D View of Analysis Model ..............................................................................8

Figure 2-4: Modes 1 and 2 of Analysis Model ......................................................................8

Figure 2-5: Mode 5 (Torsion) of Analysis Model .................................................................9

Figure 2-6: Wind Tunnel Model ............................................................................................9

Figure 2-7: Vortex Shedding .................................................................................................10

Figure 2-8: Raft and Pile Foundation.....................................................................................11

Figure 2-9: Concrete Test Cubes ...........................................................................................11

Figure 2-10: Pile Testing .......................................................................................................11

Figure 2-11: Auto Climbing Formwork (ACS) .....................................................................12

Figure 3-1: Forces and Moments ...........................................................................................21

Figure 3-2: PΔ Forces and Moments .....................................................................................21

Figure 3-3: Lateral Force .......................................................................................................24

Figure 3-4: Lateral Displacement ..........................................................................................25

Figure 3-5: Rotation ...............................................................................................................25

Figure 3-6: Drift .....................................................................................................................26

vi

LIST OF EQUATIONS

Equation 3-1………………………………………………………….. .................................18

Equation 3-2………………………………………………… ...............................................18

Equation 3-3……………………………………. ..................................................................18

Equation 3-4…………………. ..............................................................................................18

Equation 3-5…………………………. ..................................................................................18

Equation 3-6………………………………………. ..............................................................18

Equation 3-7……………………………………………….. .................................................19

Equation 3-8……………………………… ...........................................................................19

Equation 3-9………………………….. .................................................................................19

Equation 3-10…………………………… .............................................................................21

Equation 3-11……………………… .....................................................................................21

Equation 3-12………………………… .................................................................................22

Equation 3-13……………………………………….. ...........................................................22

Equation 3-14………………………………………. ............................................................22

Equation 3-15………………………… .................................................................................22

1

1 INTRODUCTION

The structural system that incorporates mega-columns, a solid core, and outrigger trusses

has become more popular with many modern skyscrapers. This particular type of system allows

for an unobstructed view to the outside of the skyscraper. A Simplified Skyscraper Model (SSM)

for analysis and optimization of skyscrapers with outriggers and belt trusses was developed by

Balling and Lee (2014). The SSM creates a preliminary design using dominant degrees of

freedom and super-elements in a spreadsheet. This specific method shows a skyscraper’s linear

and nonlinear response to gravity, wind, and seismic loading for a 100-story skyscraper. This

report describes the application of the SSM to analyze and optimize the Burj Khalifa, the tallest

building in the world. The Burj Khalifa’s structural system uses only a reinforced concrete core

and outrigger trusses. The SSM spreadsheet was applied to only analyze and optimize the

skyscraper using only the core and outrigger systems and not the belt trusses. This Project shows

the flexibility of the SSM for other skyscrapers, and will be used to teach structural engineering

students about the design of skyscrapers using the SSM.

The Burj Khalifa is the world’s tallest structure and was completed in 2010. The Burj

Khalifa has a height of 829.8 m, and a total gross floor area of 309,473 m2 with over 160 stories.

The main architects for the Burj Khalifa were Skidmore, and Owings & Merrill. They

incorporated a unique design that set it apart from all the other skyscrapers of the world. The

Burj Khalifa has a “Y” shaped structure with a hexagonal buttressed core. This allows for

maximum amount of perimeter for windows (Wood, 2011). It is almost completely constructed

2

of reinforced concrete, except for the spire which is constructed of steel. It is also built on a large

reinforced concrete mat which is then supported by reinforced concrete piles. Over 40 wind-

tunnel tests were conducted on the structure to ensure its stability. Figures 1-1 and 1-2 display

the completed skyscraper. The Burj Khalifa is not just a tall building, but a modern feat of

engineering.

Figure 1-1: Burj Khalifa (Merrick, 2010)

Figure 1-2: Burj Khalifa (Merrick, 20

3

2 DESIGN AND CONSTRUCTION OF THE BURJ KHALIFA

2.1 Architecture

The design of the Burj Khalifa was born from a “desert flower” with a tri-axial shape. This

particular shape offers many benefits other than just structural considerations. The Y-shape

allows for the outward views to be maximized, it is perfect for the new buttressed core concept,

and it helps reduce the effect of wind loading, especially wind vortices (Wood, 2011). Because

of the buildings considerable height, it will provide space for residential, commercial, and

business. Table 2-1 shows a breakdown of all the floors in the Burj Khalifa.

Table 2-1: Burj Khalifa Floor Plan (Weismantle et al., 2007)

Floors Floor Plan to Use

160-206 Mechanical

156-159 Communication and Broadcast

155 Mechanical

139-154 Corporate Suites

136-138 Mechanical

125-135 Corporate Suites

124 Observatory

123 Sky Lobby

122 Atmosphere Restaurant

111-121 Corporate Suites

109-110 Mechanical

77-108 Residential

76 Sky Lobby

44-72 Residential

43 Sky Lobby

40-42 Mechanical

38-39 Armani Hotel Suites

4

19-37 Residential

17-18 Mechanical

9-16 Armani Residences

1-8 Armani Hotel

Ground Armani Hotel

Concourse Armani Hotel

B2-B2 Parking, Mechanical

There are also many important design considerations that affected the design of the Burj

Khalifa. The organization and order of the construction of such a large building creates a

challenge. The designers were concerned about the materials, in particular the exterior wall

systems. A prefabricated curtain wall system was designed to interlock with the other 4 adjoining

panels and also allow for deflections due to temperature change, wind, seismicity, and any other

movements of the building. The aesthetics of the curtain wall system was chosen to emphasis the

vertical height of the building. The overall architecture of the Burj Khalifa is designed to

accentuate the height and beauty of the building.

2.2 Structural System

The Y-shaped design of the Burj Khalifa was not only chosen for its natural aesthetics, but

also for its structural benefits. This design was perfect because it was able to incorporate the

buttressed core concept and outrigger system. It also helps reduce wind forces and promotes

constructability. As the building increases in height, intervals step back in a spiral pattern. This

helps the load transfer through the columns and allows construction to continue without

challenges related to load transfer. These step backs also help to “confuse” the wind to prevent

dangerous wind vortices. The two main structural systems that will be explored are the

buttressed core and outrigger systems. The Burj Khalifa engages these two systems to counter

act the gravity and wind loads (Baker & Pawlikowski, 2012). The core and outrigger systems can

5

be compared to sailing ship. The core would be related to the mast of the ship, the columns to the

stays, and the outriggers would be the spreaders. They all work together to help the sails resist

the wind and make the masts stable (Ali et al., 2007).

2.2.1 Buttressed Core

The buttressed core is a modern feat of engineering that has allowed skyscrapers to soar

even higher. It has allowed the Burj Khalifa to exceed the Taipei 101 skyscraper by more than

60%. The central core provides torsional resistance throughout its entire height, and the

buttressed wings help resist shear forces and also increase the moment of inertia of the building.

This technique continues to expand with new ideas that will continue to amaze the world.

The buttressed core of the Burj Khalifa begins with a center hexagonal reinforced concrete

core. Three wings are buttressed out to complete the system. Figure 2-1 depicts a typical floor

plan with its buttressed core.

Figure 2-1: Buttressed Core of a Typical Floor Plan (Weismantle et al., 2007)

6

2.2.2 Outrigger System

The buttressed core would be nothing without the outrigger system for support. Because

of the height of the Burj Khalifa, extreme uplift forces on the core and moments on the

foundations are created. Without the outrigger systems, these forces would prove too much for

the skyscraper. The main purpose of the outriggers is to join the columns with the lateral force

resisting system. This in turn permits all vertical concrete columns to support both lateral loads

and gravity (Choi et al., 2012). This combination of buttressed core and outrigger system results

in a building that is extremely stiff both laterally and torsionally. The outriggers and the spire are

the only parts of the Burj Khalifa that are constructed entirely of steel. Figure 2-2 shows an

example of what an outrigger looks like.

Figure 2-2: Typical Outrigger System (Balling & Lee, 2014)

The Burj Khalifa has five sets of outriggers throughout the structure that are situated on the

mechanical floors. The location of these outriggers is very important in skyscrapers to reduce

horizontal deflection (Zhang et al., 2007). Many would think that the optimal location for the

outriggers would be at the level that produces the least horizontal deflection but this is not the

case. The effects that the outriggers at different levels incur must also be considered. Outrigger

7

systems are very efficient at increasing a structures stiffness by causing an internal force

redistribution (Zhang et al., 2007). This causes a change in the structures rigidity at certain

points, which is of concern when determining the proper location for the outriggers. The analysis

for the outriggers is very important to the safety of the structure. This is of concern especially

for seismic loading.

2.3 Structural Analysis

The Burj Khalifa was analyzed for gravity, wind, and seismic loads. A program called

ETABS version 8.4 (Baker et al., 2007) was used to perform the analysis. This program offers a

three-dimensional model of the skyscraper. The model comprises of reinforced concrete walls,

link beams, slabs, raft, piles, and the spire. Figure 2-3 depicts a completed model of the Burj

Khalifa. The analysis results showed that under wind loading the structures deflections were well

below the criteria. Figures 2-3 and 2-4 show 3 different dynamic modes of analysis that were

done using ETABS. Under seismic loads, only the spire and podium buildings at the base were

the governing loads. For the inputs for the seismic loading, a site-specific seismic report was

developed that included a seismic hazard analysis. This report also showed that liquefaction was

not to be considered.

8

Figure 2-3: 3-D View of Analysis Model (Baker et al., 2007)

Figure 2-4: Modes 1 and 2 of Analysis Model (Baker et al., 2007)

9

Figure 2-5: Mode 5 (Torsion) of Analysis Model (Baker et al., 2007)

2.3.1 Wind Engineering

One of the biggest factors when designing a large building comes from the effects of the

wind at such high altitudes. This is especially the case for the Burj Khalifa because it is the

tallest skyscraper in the world. Wind tunnel testing was performed at RWDI in Ontario. Figure

2-6 shows one of the wind tunnel models used.

Figure 2-6: Wind Tunnel Model (Weismantle et al., 2007)

10

These wind tunnel tests were performed throughout the design process, and helped alter

the design accordingly. All these tests helped develop the shape that the Burj Khalifa now has. It

was optimized so much that from a wind loading point of view, there was no need for a damping

system (Irwin, 2009). One of the main concerns dealt with vortex shedding. The plan was to

create disorganized vortex shedding so that it would minimize the effects on the structure as seen

in Figure 2-7. The model also helped obtain measurements of localized pressures around the

structure, pedestrian wind environment studies, and wind climate studies. These are also

important design concerns, especially because of the balconies surrounding the building.

Figure 2-7: Vortex Shedding (Baker et al., 2007)

2.4 Foundation

The foundation for the Burj Khalifa consists of a raft supported by piles. The reinforced

concrete raft is 3.7 m thick, which is supported by 194 piles that are 1.5 m in diameter and 43 m

deep (Abdelrazaq et al., 2010). The raft and pile foundation is shown in Figure 2-8. Because of

the geology in the Arabian Gulf area, many tests had to be performed to ensure that the

11

foundation design would suffice. Geotechnical models were created to assess the response of the

foundation (Poulos & Bunce, 2008).

Figure 2-8: Raft and Pile Foundation (Abdelrazaq et al., 2010)

Self-consolidating concrete was used for both the raft and piles. Standard cube tests were

carried out, and was field tested prior to the pour. The test cubes were 3.7 m on each side as

shown in Figure 2-9 (Baker et al., 2007). The piles were tested and supported over 6000 tons

(Figure 2-10) (Baker et al., 2007).

Figure 2-9: Concrete Test Cubes

Figure 2-10: Pile Testing

The groundwater in the areas surrounding the Burj Khalifa have high concentrations of

chloride and sulfide. This is a major concern when dealing with foundations and piles. The piles

12

where designed to be durable with a 60 MPa mix. Measures were taken to prevent corrosion to

ensure the durability of the foundation and piles.

2.5 Construction

The Burj Khalifa employs the latest advancements in construction. It was expected to be

completed following a tight schedule and a 3-day cycle. In order to accomplish this many

technologies were used:

Auto climbing formwork (ACS)

Rebar pre-fabrication

High performance concrete

Advanced concrete pumping technology

The ACS in Figure 2-11 (Baker et al., 2007) had to follow a certain sequence in order to be

efficient. The center core wall construction is followed by center core slab construction, wing

wall construction is followed by wing slab construction, and nose columns are followed by slab

construction.

Figure 2-11: Auto Climbing Formwork (ACS)

13

3 SIMPLIFIED MODEL FOR ANALYSIS: BURJ KHALIFA

The SSM is an easy way to analyze skyscrapers for gravity, wind, and seismic loading. It is

used as a preliminary design, and will be much faster than creating a finite element model. The

SSM changes a few constraints to match the effects in the area surrounding the Burj Khalifa. The

Burj Khalifa uses a core, mega-column, and outrigger configuration which makes it ideal to use

the SSM. The SSM was applied to neglect the analysis of belt trusses because the Burj Khalifa

doesn’t incorporate these in its design.

3.1 Constants

The constants (Table 3-1) for the SSM remained the same from the SSM except for the

cost variables. Cost variables have changed with time as expected. These constants were chosen

from a few factors, including design codes, design restrictions, and a few others. All the

constants and a few design pictures are included on the first page of the spreadsheet.

Table 3-1: Constants Sheet

Concrete

Allowable Stress (KPa) 48000

Modulus (KPa) 43400000

Density (KN/m^3) 21.7

Cost ($/m^3) 157

Slab Thickness (m) 0.25

14

Steel

Allowable Stress (KPa) 207000

Modulus (KPa) 200000000

Density (KN/m^3) 77

Cost ($/m^3) 50

Weight Data

Floor Dead Load (KPa) 4.34

Floor Live Load (KPa) 2.4

Cladding Weight (KPa) 1.3

Pinnacle Weight (KN) 35584

Wind Data

Speed (m/s) 55

Air Density (Kg/m3) 1.226

Reference Height (m) 274

Exponent Alpha 9.5

Allowable Drift 360

Drag Coefficient 2

Seismic Data

Spectral Acceleration (g) 0.2

Ductility Factor 3

Exponent k 2

Allowable Drift 50

3.2 Geometry

Any type of structural analysis will include the geometry of the structure. The geometry

will often define how easy it is to analyze the structure. For the SSM, the analysis was divided into

6 intervals. They were determined by the location of the outriggers, which are on the mechanical

floors and can be seen in Table 2-1. Table 3-2 shows the numbered levels for each interval and

how tall each interval is.

Table 3-2: Interval Information

Stories # of Stories Distance (m)

15

164 1 209

139-163 24 90

111-138 27 101.25

76-110 34 127.5

43-75 32 120

19-42 23 86.25

7-18 11 41.25

A plan view of the 2nd interval in the Burj Khalifa can be seen in Figure 3-1. The

locations of the columns for each interval was derived from this plan view. In Figure 3-2 the

dimensions of interval 2 are show and it is from these dimensions that the others were derived.

Figure 3-3 will show the dimensions used for each interval. The dimension lines will show

locations of the columns and outriggers, and the total dimension will show the total length of the

core.

Figure 3-1: Plan View with Columns, Outriggers, and Core

16

Figure 3-2: Dimensioned Interval 2

Figure 3-3: Dimensioned Intervals 1-6

17

3.3 Super-elements

The super-elements section is where the properties for core, mega-columns, and outriggers

are calculated and defined. The sheet starts by defining core and outrigger properties such as

volumes, thicknesses, and tributary areas. The calculated outrigger lengths, areas, and inertia’s

can be seen in Table 3-3. All outriggers have a depth of 3.75 meters. Another page calculates

core inertia’s at each interval. Axial forces for the core and 6 columns (based on symmetry) are

calculated (Equation 3-1, 3-2, 3-3) and can then be used to solve for column areas (Equation 3-

4). This is done assuming that the axial strains in the columns is the same as the axial strain in

the core under gravitational loads (Equation 3-5).The most important part of this sheet calculates

the super-elements for the core, columns, and outriggers (Equation 3-6, 3-7, 3-8). There is also a

section that is used for the optimization of the structure. It looks at wind drift, seismic drift, core

stress, column stress, and outrigger stress. The spreadsheet uses the solver add-in to optimize the

spreadsheet.

18

Table 3-3: Outrigger Super-element

3-1

3-2

3-3

3-4

3-5

3-6

Stories Outrigger P Outrigger Q Outrigger R Outrigger S Outrigger T Outrigger O

139-163 Member Length (m) 11.91

Member Sine 0.6297

Member Area (m2) 1.6096

Stiffness (k) 4287431

111-138 Member Length (m) 8.323 7.23

Member Sine 0.9011 1.0375

Member Area (m2) 1.7009 1.3506

Stiffness (k) 26553198 32179005

76-110 Member Length (m) 8.323 7.23 6.19

Member Sine 0.9011 1.0375 1.2108

Member Area (m2) 0.8026 2.1216 0.7606

Stiffness (k) 12530163 50548697 28803214

43-75 Member Length (m) 8.323 7.23 6.19 5.25

Member Sine 0.9011 1.0375 1.2108 1.4275

Member Area (m2) 1.1126 0.6415 2.2315 2.1368

Stiffness (k) 17369468 15284087 84509240 132595238

19-42 Member Length (m) 8.323 7.23 6.19 5.25 4.36 10.65

Member Sine 0.9011 1.0375 1.2108 1.4275 1.7190 0.7042

Member Area (m2) 1.9410 1.2176 1.7774 2.0960 1.0044 0.1925

Stiffness (k) 30302748 29009604 67312536 130064911 108845907 1434163

7-18 Member Length (m) 8.323 7.23 6.19 5.25 4.36 10.65

Member Sine 0.9011 1.0375 1.2108 1.4275 1.7190 0.7042

Member Area (m2) 1.3094 1.4993 1.1513 1.4168 2.9464 0.5732

Stiffness (k) 20442161 35722960 43599463 87919077 319296544 4270557

19

3-7

3-8

3.4 Core Section

This is an important section that does a preliminary calculation. This section calculates the

moment of inertia for the core (Equation 3-9). This is done using the assumption that the core

section can be subdivided into rectangles of equal thicknesses. Even though the Burj Khalifa has

a buttressed core, this same equation can still be used.

3-9

The thickness of the core can be optimized which in turn will optimize the inertia of the

core. Table 3-4 displays the optimized core area and inertia for each interval.

Table 3-4: Optimized Area and Inertia

Interval Stories Area Inertia

Spire 164 15.89217 0

6 139-163 47.67651 7796

5 111-138 68.67025 15060

4 76-110 217.5 29050

3 43-75 319.35 75932

2 19-42 421.2 159001

1 7-18 534.075 307708

3.5 Matrices

A stiffness matrix is created to compute wind and seismic displacements. This is done by

taking the dominant degrees of freedom (DOF) that consist of horizontal displacement, rotation,

20

and vertical displacement of columns at the top of each interval. Using wind and seismic forces

taken from the Wind and Seismic sheet, simple matrix multiplication is carried out to compute

the corresponding displacements. This sheet also allows for the optional non-linear calculations.

The non-linear calculation uses iteration to help compute the displacements.

3.6 Wind and Seismic

These two sections are very important to the SSM. The first part of each of these sections

list the floors analyzed and parameters such as story height, perimeter, floor area, concrete

volume, and steel volume. The next stage is to calculate lateral forces caused by wind and

seismic forces (Equation 3-10, 3-11). From these lateral forces, using statics, forces and

moments are calculated for the tops and bottoms of each floor (Figure 3-1). Next, using the

displacements computed on the Matrices sheet, displacements, rotations, and drifts are calculated

for each floor correlating to the lateral forces from wind and seismic loading. PΔ forces and

moments for the non-linear analysis on the Matrices sheet are calculated using statics (Figure 3-

2).

21

3-10

3-11

Figure 3-4: Forces and Moments

Figure 3-5: PΔ Forces and Moments

22

3.7 Stress

This section is important for the gravity load analysis. Maximum stress was evaluated in

each of the super-elements (Equation 3-12, 3-13, 3-14, 3-15). These are all taken at the bottom of

the intervals where the greatest gravitational force would be felt. In Equation 3-13 and 3-14, the

12.5 is replaced by the distance from the neutral axis to that location, and in Equation 3-15, the

25 is replaced by the length of the corresponding outrigger.

3-12

3-13

3-14

3-15

3.8 Optimization

Excel has a couple solving methods that are used to optimize the SSM. The first is called

the evolutionary method. It is used for non-smooth nonlinear problems, which basically means a

more complicated problem. The second is called GRG nonlinear. This is used for a smoother

nonlinear problem. Using these methods you can optimize the SSM to obtain the lowest total cost

based off of steel and concrete costs. The process will optimize the core thickness, the outrigger

volume, and the column area. Figure 3-5 shows the optimized thickness for the core and the

volumes for the outriggers, and Figure 3-6 shows the optimized area for the columns.

23

Table 3-5: Core Thickness and Outrigger Volume

Table 3-6: Column Areas

All these values are optimized based on some constraints to the system. In order to be

considered “optimized,” all these constraint values need to be under 1. There are 5 constraints that

are used in the SSM. The five constraints are as follows: wind drift, seismic drift, core stress,

column stress, and outrigger stress. Table 3-7 displays all the constraint values below.

Table 3-7: Design Constraints

Outrigger P Outrigger Q Outrigger R Outrigger S Outrigger T Outrigger O

164 0 0 0 0 0 0 0

139-163 0.618372366 57.51126616 0 0 0 0 0

111-138 0.618372366 84.93434638 58.57811532 0 0 0 0

76-110 1.5 40.07958727 92.01799051 28.26665557 0 0 0

43-75 1.5 55.55882157 27.82289291 82.93496733 67.36107733 0 0

19-42 1.5 96.92783866 52.80859149 66.0586103 66.07561979 26.29328547 12.30001413

7-18 1.5 65.38728791 65.0294701 42.78727445 44.6646792 77.13064677 36.62618684

Stories Core Thickness (m) Volume (m3)

Stories Column B Column C Column D Column E Column F Column A

164

139-163 0.4264

111-138 1.4576 0.6222

76-110 3.9026 2.3448 0.6509

43-75 5.7359 3.7417 1.5186 0.4068

19-42 7.9517 5.3423 2.4006 0.9518 0.3384 0.6150

7-18 10.9695 7.4420 3.4491 1.4935 0.9582 1.4663

Wind Drift 0.346552

Seismic Drift 0.308431

Core Stress 0.997239

Column Stress 0.769297

Outrigger Stress 0.5914

24

3.9 Graphs

This sheet displays the results of the analysis in simple easy to read graphs. There are four

graphs that display lateral force, lateral displacement, rotation, and drift for each floor that was

analyzed. Previously was discussed that wind loading governed most of the design for the Burj

Khalifa, so these graphs only display the effects and results of wind loading (Figure 3-3, 3-4, 3-5,

3-6).

Figure 3-6: Lateral Force

0

100

200

300

400

500

600

700

0 200 400 600 800 1000 1200 1400

Heig

ht

(m)

Lateral Force (KN)

Wind

Wind

25

Figure 3-7: Lateral Displacement

Figure 3-8: Rotation

0

100

200

300

400

500

600

700

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

Heig

ht

(m)

Lateral Displacement (m)

Wind

0

100

200

300

400

500

600

700

0 0.0002 0.0004 0.0006 0.0008 0.001 0.0012

Heig

ht

(m)

Rotation (rad)

Wind

26

Figure 3-9: Drift

0

100

200

300

400

500

600

700

0 0.0002 0.0004 0.0006 0.0008 0.001 0.0012

Heig

ht

(m)

Drift

Wind

27

4 CONCLUSION

The SSM is a simple means for analyzing wind, seismic, and gravity loading for the Burj

Khalifa. The SSM was successfully altered to analyze the Burj Khalifa. The SSM also effectively

optimized the design constraints of core, column, and outrigger stress. The SSM is a simplified

analysis tool and should be treated as such. Although the results are reasonable, they should only

be taken as an estimation, and should never take place as a full analysis using software such as

ETABS. But, because the results are reasonable they can be used for preliminary design of

skyscrapers. Seeing that the SSM was successfully applied for the Burj Khalifa, it can be done

with almost any building with a core, outrigger system, or belt trusses. It was proved that the

SSM can be adapted easily and quickly for any skyscraper, and it will provide reliable results

that can be used in preliminary design.

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