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 superelements 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
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
3
4
2.4
Foundation .................................................................................................................... 10
2.5
Construction .................................................................................................................. 12
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
Conclusion ........................................................................................................................... 27
References .................................................................................................................................... 29
iii
LIST OF TABLES
Table 2-1: Burj Khalifa Floor Plan ........................................................................................3
Table 3-1: Constants Sheet ....................................................................................................13
iv
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
v
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
vi
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
1
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 windtunnel 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
2
2
2.1
DESIGN AND CONSTRUCTION OF THE BURJ KHALIFA
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
160-206
156-159
155
139-154
136-138
125-135
124
123
122
111-121
109-110
77-108
76
44-72
43
40-42
38-39
Floor Plan to Use
Mechanical
Communication and Broadcast
Mechanical
Corporate Suites
Mechanical
Corporate Suites
Observatory
Sky Lobby
Atmosphere Restaurant
Corporate Suites
Mechanical
Residential
Sky Lobby
Residential
Sky Lobby
Mechanical
Armani Hotel Suites
3
19-37
17-18
9-16
1-8
Ground
Concourse
B2-B2
Residential
Mechanical
Armani Residences
Armani Hotel
Armani Hotel
Armani Hotel
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
4
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)
5
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
6
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.
7
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)
8
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)
9
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
10
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
11
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)
12
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)
Modulus (KPa)
Density (KN/m^3)
Cost ($/m^3)
Slab Thickness (m)
13
48000
43400000
21.7
157
0.25
Steel
Allowable Stress (KPa)
Modulus (KPa)
Density (KN/m^3)
Cost ($/m^3)
207000
200000000
77
50
Weight Data
Floor Dead Load (KPa)
Floor Live Load (KPa)
Cladding Weight (KPa)
Pinnacle Weight (KN)
4.34
2.4
1.3
35584
Wind Data
Speed (m/s)
Air Density
(Kg/m3)
Reference Height (m)
Exponent Alpha
Allowable Drift
Drag Coefficient
55
1.226
274
9.5
360
2
Seismic Data
Spectral Acceleration (g)
Ductility Factor
Exponent k
Allowable Drift
3.2
0.2
3
2
50
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
14
Distance (m)
164
139-163
111-138
76-110
43-75
19-42
7-18
1
24
27
34
32
23
11
209
90
101.25
127.5
120
86.25
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
15
Figure 3-2: Dimensioned Interval 2
Figure 3-3: Dimensioned Intervals 1-6
16
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 34). 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.
17
Table 3-3: Outrigger Super-element
Stories
139-163
111-138
76-110
43-75
19-42
7-18
Member Length (m)
Member Sine
Member Area (m2)
Stiffness (k)
Member Length (m)
Member Sine
Member Area (m2)
Stiffness (k)
Member Length (m)
Member Sine
Member Area (m2)
Stiffness (k)
Member Length (m)
Member Sine
Member Area (m2)
Stiffness (k)
Member Length (m)
Member Sine
Member Area (m2)
Stiffness (k)
Member Length (m)
Member Sine
Member Area (m2)
Stiffness (k)
Outrigger P
11.91
0.6297
1.6096
4287431
8.323
0.9011
1.7009
26553198
8.323
0.9011
0.8026
12530163
8.323
0.9011
1.1126
17369468
8.323
0.9011
1.9410
30302748
8.323
0.9011
1.3094
20442161
Outrigger Q
7.23
1.0375
1.3506
32179005
7.23
1.0375
2.1216
50548697
7.23
1.0375
0.6415
15284087
7.23
1.0375
1.2176
29009604
7.23
1.0375
1.4993
35722960
Outrigger R Outrigger S Outrigger T Outrigger O
6.19
1.2108
0.7606
28803214
6.19
1.2108
2.2315
84509240
6.19
1.2108
1.7774
67312536
6.19
1.2108
1.1513
43599463
5.25
1.4275
2.1368
132595238
5.25
4.36
1.4275
1.7190
2.0960
1.0044
130064911 108845907
5.25
4.36
1.4275
1.7190
1.4168
2.9464
87919077 319296544
10.65
0.7042
0.1925
1434163
10.65
0.7042
0.5732
4270557
3-1
3-2
3-3
3-4
3-5
3-6
18
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
Spire
6
5
4
3
2
1
3.5
Stories
164
139-163
111-138
76-110
43-75
19-42
7-18
Area
15.89217
47.67651
68.67025
217.5
319.35
421.2
534.075
Inertia
0
7796
15060
29050
75932
159001
307708
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,
19
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 32).
20
3-10
3-11
Figure 3-4: Forces and Moments
Figure 3-5: PΔ Forces and Moments
21
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.
22
Table 3-5: Core Thickness and Outrigger Volume
3
Stories
Core Thickness (m)
164
139-163
111-138
76-110
43-75
19-42
7-18
0
0.618372366
0.618372366
1.5
1.5
1.5
1.5
Outrigger P
0
57.51126616
84.93434638
40.07958727
55.55882157
96.92783866
65.38728791
Outrigger Q
0
0
58.57811532
92.01799051
27.82289291
52.80859149
65.0294701
Volume (m )
Outrigger R Outrigger S Outrigger T Outrigger O
0
0
0
0
0
0
0
0
0
0
0
0
28.26665557
0
0
0
82.93496733 67.36107733
0
0
66.0586103 66.07561979 26.29328547 12.30001413
42.78727445 44.6646792 77.13064677 36.62618684
Table 3-6: Column Areas
Stories
164
139-163
111-138
76-110
43-75
19-42
7-18
Column B
Column C
Column D
Column E
Column F
Column A
0.4264
1.4576
3.9026
5.7359
7.9517
10.9695
0.6222
2.3448
3.7417
5.3423
7.4420
0.6509
1.5186
2.4006
3.4491
0.4068
0.9518
1.4935
0.3384
0.9582
0.6150
1.4663
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
Wind Drift
Seismic Drift
Core Stress
Column Stress
Outrigger Stress
0.346552
0.308431
0.997239
0.769297
0.5914
23
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).
Wind
700
600
Height (m)
500
400
300
Wind
200
100
0
0
200
400
600
800
Lateral Force (KN)
1000
Figure 3-6: Lateral Force
24
1200
1400
700
600
Height (m)
500
400
Wind
300
200
100
0
0
0.05
0.1
0.15
0.2
0.25
Lateral Displacement (m)
0.3
0.35
Figure 3-7: Lateral Displacement
700
600
Height (m)
500
400
Wind
300
200
100
0
0
0.0002
0.0004
0.0006
Rotation (rad)
0.0008
Figure 3-8: Rotation
25
0.001
0.0012
700
600
Height (m)
500
400
Wind
300
200
100
0
0
0.0002
0.0004
0.0006
0.0008
Drift
Figure 3-9: Drift
26
0.001
0.0012
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.
27
REFERENCES
"2010 Awards - Press Release." 2010 Awards - Press Release. Ed. Nick Merrick. CTBUH, 25
Oct. 2010. Web. 23 Dec. 2015.
Abdelrazaq, Ahmad. "Design and construction planning of the Burj Khalifa, Dubai, UAE." Proc.
of ASCE Structures Congress 2010. 2010.
Ali, Mir M., and Kyoung Sun Moon. "Structural developments in tall buildings: current trends
and future prospects." Architectural Science Review 50.3 (2007): 205-223.
Baker, William F., and James J. Pawlikowski. "Higher and Higher: The Evolution of the
Buttressed Core." Civil Engineering 9 (2012): 58-65.
Baker, William F., D. Stanton Korista, and Lawrence C. Novak. "Burj Dubai: Engineering the
world's tallest building." The structural design of tall and special buildings 16.4 (2007):
361-375.
Balling, Richard J., and Jacob S. Lee. "Simplified Model for Analysis and Optimization of
Skyscrapers with Outrigger and Belt Trusses." Journal of Structural Engineering (2014).
Choi, Hi Sun, et al. "Outrigger design for high-rise buildings." (2012).
Irwin, Peter A. "Wind engineering challenges of the new generation of super-tall buildings."
Journal of Wind Engineering and Industrial Aerodynamics 97.7 (2009): 328-334.
Poulos, Harry G., and Grahame Bunce. "Foundation design for the Burj Dubai—the world’s
tallest building." Proceedings of the 6th international conference case histories in
geotechnical engineering, Arlington, Virginia, Paper. Vol. 1. 2008.
Weismantle, Peter A., Gregory L. Smith, and Mohamed Sheriff. "Burj Dubai: an architectural
technical design case study." The Structural Design of Tall and Special Buildings 16.4
(2007): 335-360.
Wood, Antony. "Best Tall Building Middle East & Africa Winner." Best Tall Buildings 2010:
CTBUH International Award Winning Projects. New York: Routledge, 2011. 144-49.
Print.
29
Zhang, Jie, et al. "Safety analysis of optimal outriggers location in high-rise building structures."
Journal of Zhejiang University Science A 8.2 (2007): 264-269.
30