The Cayan Tower in Dubai has a distinctive helical shape, twisting 90 degrees over its height. Its unique twisting form was inspired by DNA and provides structural benefits like reduced wind load. The tower was designed by Skidmore, Owings and Merrill to be an iconic landmark in Dubai. Its hexagonal floor plates rotate 1.2 degrees clockwise from the level below, simplifying the complex structure. This standardization allowed for repetitive construction. The twisting form optimizes views while the central core provides straight vertical access for mechanical systems. The design aims to take advantage of the prime waterfront site through its sculptural twisted shape.
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Report of cayan tower
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CHAPTER 1 - INTRODUCTION
1.1 INTRODUCTION
Cayan Tower, known as Infinity Tower before it was inaugurated, is a 306-metre-tall, 75-story
skyscraper in Dubai, United Arab Emirates by Cayan Real Estate Investment and Development.
The Cayan Tower is a luxury apartment building with a striking helical shape, turning 90 degrees
over the course of its height. Each floor is identical in plan, but is set 1.2 degrees clockwise from
the floor below, giving the tower a distinctive form by way of an innovative, efficient, repeatable
structure. Its shape is pure expression of the relationship between a building’s form and the
structural framework that supports it.
Figure 1.1 cayan tower view
• Official name :- cayan tower
• Other name :- infinity tower
• Country :- united arab emirates
• City :- dubai
• Construction start :- 2006
• Project opening:- june 2013
• Use:- residential
• Building height:- 307 m
• Levels:- 75-storey
• Building area:- 111,000 m2
• Architects:- skidmore,owings and merril
zaha hadid , hok & hopkins architects.
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1.2 LOCATION
Aesthetically, the twisting shape makes the building stand out from the architectural disharmony
of the Dubai waterfront, which is largely composed of indistinct towers that do not speak to their
location. Located near Dubai Internet City, Emirates Golf Club, and numerous corporate
headquarters, the tower’s twisting form provides a greater number of units with desirable views of
the Dubai Marina and Arabian Gulf, while also preserving the views for residents living in
neighboring buildings, ensuring that Cayan Tower enhances its spectacular waterfront site.
Figure 2.2 Buildings view water front
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No of storeys = 6 basements+ ground floors + mezzanine + 6 podiums + 64 residential floors
+ 2 mechanical floors + 6 floor steel structure
Total building height = 314.8 m (1,038 ft)
Area of plot = 3,160.83 sqm (34,024 sqft)
Total built-up area = 118,125.97 sqm (1,271,539 sqft)
Structural types = Super high-rise building club
Rotation degree = 900 (0.30 per metre height)
Contract value = Lump sum offer of 770,446,368 DHS
Gate level = (+3.50) DMD
Top level = (+306.365) DMD
Floor area ratio = 27.34
No of lifts = 7
No of shops/parking = 6 (11 cars)
No of studio = 17 (17 cars)
No of apartments > 1600 sqft = 91 (182 cars)
No of apartments < 1600 sqft = 404 (404 cars)
Total no of parking = 614 (cars)
Total net residential area = 64,887.21 sqm (698,463 sqft)
Total net commercial area = 1,329.89 sqm (14,315 sqft)
Total parking area = 24,328.19 sqm (261,875 sqft)
Total steel reinforcements grade 460 = 25,000 tonne
Total concrete grades(C-40, C85) = 77,000 m³ 320 kg steel/1 m³
Net area utilized per floor = 970 sqm
Total area/floors = 1,160 sqm
Concrete volume/floors = 440 m³ concrete
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1.4 COMPANIES INVOLVED
Owner/Developer Cayan Group - Real Estate Investment &
Development
ARCHITECT & STRUCTURAL ENGINEER
Design Skidmore, Owings & Merrill LLP
Architect of Record Khatib & Alam
MEP ENGINEER
Design Skidmore, Owings & Merrill LLP
Project Manager Currie & Brown
Main Contractor Arabtec
OTHER CONSULTANT
Acoustics Cerami & Associates; Shen Milsom Wilke,
Inc.
Façade Maintenance Lerch Bates
Fire Rolf Jensen & Associates
Landscape SWA Group
Lighting Fisher Marantz Stone
Property Management Rotana
Security Sato & Associates, Inc.
Vertical Transportation Opening Solutions, Inc.; Van Deusen &
Associates
Wind Alan G. Davenport Wind Engineering Group
Table 1 list of companies involved
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1.5 ABOUT THE ARCHITECTS
The tower is designed by Skidmore, Owings and Merrill SOM architectural group—the same
group that built the Burj Khalifa in Dubai and the Trump Tower in Chicago. The Cayan Tower,
inaugurated on June 10, 2013, is yet another engineering marvel. But the unusual form of the
building presented various challenges for its designers and developers.
Figure 1.4 CTBUH
Skidmore, Owings & Merrill LLP (SOM) is an American
architectural, urban planning, and engineering firm. It was
formed in Chicago in 1936 by Louis Skidmore and Nathaniel
Owings; in 1939 they were joined by John O. Merrill. The firm
opened their first branch in New York City in 1937, and has since expanded all over the world,
with regional offices in San Francisco, Los Angeles, Washington, D.C., London, Hong Kong,
Shanghai, Mumbai and Dubai.
With a portfolio spanning thousands of projects across 50 countries, SOM is one of the largest
architectural firms in the world. Their primary expertise is in high-end commercial buildings. They
have designed several of the tallest buildings in the world, including the John Hancock Center
(1969, second tallest in the world when built), Willis Tower (1973, tallest in the world for over
twenty years), and Burj Khalifa (2010, currently the world's tallest building).
Cayan Tower (formerly
known as Infinity Tower)
in Dubai, for which
Currie & Brown
provided project
management services,
has won several
international awards, the
most recent of which is
the CTBUH (Council on
Tall Buildings and Urban
Habitat) ‘2014 Best Tall
Building Award for
Middle East and Africa
Region'.
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1.6 HISTORY
Dubai’s transformation from fishing village to global business hub has impressed the world – for
its innovation, sheer speed and dynamism. Nowhere is the progress more evident than in the
emirate’s architecture.
But now it could be the case that the city's architecture is at a crossroads, an inflection point, as
there is a gradual shift from grand to green, and from imposing to approachable. How did we get
here?
Back in the 1960s and much of the 1970s, Dubai’s charming traditional architecture with its narrow
alleys and wind tower houses still bore testimony to its Bedouin heritage. Dubai was a port town
then, and trading was a mainstay of the economy.
The typical image of Dubai in the late 1970s and even into the 1980s was of simple low-rise
buildings that were home to thousands of people from across the region and the Indian
subcontinent. When the World Trade Centre opened in 1979, it seemed impossibly far away from
the centre of the city. But Sheikh Rashid, then Ruler of Dubai, knew what he was doing when he
asked the British architect John Harris to build it there. It encouraged the city to expand. And its
stylish modernist, concrete-clad design increased its pulling power. In fact, it is the building that
you see on the back of the 100-dirham banknote even today.
Figure 1.5 view of world trade Centre old Dubai
This led to the era of glass towers as the city grew quickly through the 1980s. As George
Katodrytis, an architecture professor at the American University of Sharjah, wrote in UAE and the
Gulf: Architecture and Urbanism Now: "From the 1980s, exposed glass curtain walls were used
extensively in the design of almost every commercial and high-rise building facade in the Gulf …
Buildings looked identical. Any discourse on environmental performance and innovation did not
exist."
The WTC was the first of
the high-rises that would
begin to pop up on the
city’s arterial roads,
becoming a preferred
design statement for the
few multinational and even
large local companies
establishing offices here.
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But that era was blown away with the launch of the Burj Al Arab in 1999. The exclusive hotel was
the first symbol – and is still the most recognisable one – of Dubai’s arrival on the world stage and
its cosmopolitan vision of the future. Soon, Hazel Wong’s Emirates Towers and other
extraordinary structures followed, spurring a decade of intense construction activity that saw
landmark projects such as the Palm Jumeirah (which literally changed the map of Dubai) and
Dubai Marina come to life. Then, in 2010, came the Burj Khalifa, the tallest building in the world
and a miracle of modern engineering.
In the years that followed, the influence of architecture has broadened out to create connections
across the design sector in Dubai. Local companies in collaboration with intrepid European
designers experiment with new forms of architecture, including luxury low-rise floating
homes. The recent rise of walkable communities and eco-friendly projects has cemented Dubai’s
reputation for constantly reinventing itself.
I believe that when people envision a city of the future, they picture a fast-paced environment
brimming with forward-thinking people against a background of skyscrapers, walkable
communities and iconic towers. But for Dubai, the future is already here. It is now up to us to
continue to innovate, breaking new boundaries and inspiring the world.
Figure 1.6 comparision between old and new dubai
While Dubai has always been associated with a penchant for luxury, the growing popularity of
ecologically sustainable and integrated built environments reflects a shift in consumers’ and the
industry’s perception of the new age of design in the city. Today, architects and interior designers
in the region are increasingly opting for recycled materials in their cutting-edge designs, with
woven vinyl flooring, reconstituted stone and consciously sourced upholstery taking centre stage.
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In Dubai we like to set world records and so it was a sign of the times when, in 2013, a two-storey
Dubai store selling eco-friendly products was ranked by the US Green Building Council as the
most sustainable building in the world.
Figure 1.7 Globle twisting icones
Today's architecture takes a wider view than that of the 1980s.
Now Emirati product designers such as Khalid Shafar, Aljoud Lootah and Latifa Saeed, as well as
regional designers like Ayah Al Bitar from Saudi Arabia and Fadi Sarieddine from Lebanon are
pushing the design frontiers by using their knowledge and experience of local design practices and
presenting them for diverse audiences. What makes Dubai even more interesting is the impact that
the wide variety of international communities has on the overall design aesthetic in the city – they
are ever-receptive to the fusion of global ideas with local practices.
With so much activity, it should come as no surprise that the UAE and Saudi Arabia boast the
largest design markets in the Mena region. By 2019, the Middle East will need more than 30,000
design graduates for the sector to thrive, according to a study released by the Dubai Design and
Fashion Council. Nearly 90 per cent of growth in the design industry is expected to stem from
architecture, interiors and fashion, with architecture and interior design considered the most in-
demand creative careers in the region today.
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CHAPTER 2 – DESIGN PHILOSOPHY
2.1 CONCEPT
Design was inspired by the human DNA composition.
The benefits of this unique form, besides the aesthetic ones, are manifold. Wind load and solar
heat gain are reduced compared to a rectilinear building of the same height, and a greater
number of tenants are afforded desirable views of the nearby marina and gulf..
Figure 2.1 human DNA Figure 2.2 concept sketches
Figure 2.3 rotation of building
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2.2 THE TWIST: SIMPLIFYING THE COMPLEX
Architecture: - Columns sloping in 3 directions
Structural: - Sloping columns & the twist
MEP Distribution: -Vertical distribution of systems
Figure 2.4 twisting of cayan tower
2.3 FORM
It has 90-degree twist sculptural form.
Building form follow its structural framework .
Hexagonal floor plates rotate around the circular base.
Each floor rotate 1.2-degree around a cylindrical
elevator and service core.
2.4 SPACE
Floor plates are identical.
The same form of system is used on every floor.
Figure 2.5 section & elevation of cayan tower
Figure 2.6 section & plan of cayan tower
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Building space include central circulation corridor
and residential units.
2.5 DESIGN COMPETITION
Paid Competition
Competition Start – February 2005
Winner Announced – May 2005
Invited Architects-
• Skidmore, Owings & Merrill LLP
• Zaha Hadid
• HOK
• Hopkins Architects
Design Brief
“A 65 story condominium building…that is
intended to be a landmark / icon in the skyline
of Dubai”
2.6 DESIGN GOALS
Create an Iconic Form
Create a Landmark Within Dubai Marina
Take Full Advantage Of the Site Prominence
Optimize Views From Within the Tower
Figure 2.8 night view of cayan tower
Figure 2.7 concept model of towers
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2.7 DESIGN PHILOSOPHY & STANDARDISATION
The tower’s design philosophy is based upon the exterior form of the building as a direct expression
of the structural framework. The engineers studied a series of options for the perimeter frame to create
the tower’s unique twisting geometry. Ultimately, it was determined that there were distinct
advantages, from the standpoint of architectural efficiency, structural performance and ease of
construction, to stacking the columns in a stepwise manner at each level, where each column slopes in
one direction, and is offset over the column below, to generate the twisting building form.
Figure 2.9 Structure Model Of Cayan Tower
“For the Cayan Tower to be realised as a viable structure, the seemingly complex building form must
ultimately be derived from a structure that is straightforward and efficient to construct. The structure
should maintain practical and repetitive architectural floor layouts.
Figure 2.10 Rotation Plan Of Cayan Tower
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The system, as described above, offers significant construction simplification by permitting a high
level of repetition in the formwork, which directly impacts the construction cycle time,” adds
Qudsiyeh. Also, this system leads to residential floor layouts, which are repetitive at each level
despite the twisting nature of the building form. Six typical floor layouts were used, with each
residential unit designed to allow terraces to exist in one of two or three locations
Mechanical systems, which are normally housed in risers that pass vertically through the building, do
not have such a free-ranging straight vertical path in Cayan Tower. “Althoughthe floor below has the
same area and layout, the building’s twist dictates that the demising walls are shifted about 1.30, about
the tower’s plan centre, from level to level,” he states. For the Cayan Tower, major mechanical risers
are located in the circular central core, which allows a straight vertical path through the tower.
Figure 2.11 structure plan
The balance of the building’s mechanical, electrical and plumbing systems is located within a deep
demising wall between the central circulation corridor and the residential units. The zone is specifically
located and designed to create a minimally obtrusive vertical path for the building
services to access all residential units as they rotate about the central core as the building ascends. As
the typical units and their entrance doors rotate, they shift to new positions within the corridor demising
wall. Similarly, the exterior wall was designed with an emphasis on standardised parts sized and fit
together to enclose bays that are not identical. For example, the opening on each bay is slightly larger
or smaller than the one next to it. To use exterior wall units of the same size, the joints were designed
Rectangular R/C
Perimeter Tube
Frame Columns
R/C Spandrel
Beams at Perimeter
Tube Frame
Square R/C
Interior
Columns (6)
R/C Walls
at Circular
Central Core Slab Penetrations
at Circulation
Corridor
230 mm Thick
R/C Flat Plate
Shaped Corner
Columns (4)
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To allow a slightly varied relationship between pieces. The spandrel caps, which ring the building, are
deeper on one end of each bay than they are at the other end of the same bay, accommodating panel
adjustments for each bay’s geometric conditions.
Qudsiyeh elaborates, “Because of the building’s singular formal gesture, the design team wanted to
reduce or minimise elements that distracted from or contradicted the smoothness of the twist. Two
such elements were the balconies and the stepped columns. Each unit was required to have a balcony,
and with standard unit layouts, the balconies initially stacked one on top of another, thereby creating
vertical slots of deeper reveals in the façade. Byorganising each standard unit to have the flexibility to
position its terraces in one of two or three locations, the designers gave themselves the freedom to shift
the terraces more randomly along the façade and eliminate the vertical stacking.”
Careful consideration was given to the standardisation of the Cayan Tower in order to limit the number
of unique conditions that would require customisation, such that construction could proceed as quickly
and be as straightforward as possible. “When compared to a similar building taken as a straight
extrusion with height (no twist), it is estimated that the twisting form of the Cayan Tower reduced the
structure’s across-wind excitation by around 25% or more,” he says.
Figure 2.12 structural concept
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2.8 SITE PLAN & FUNCTIONS
• It is located near the north inlet to the Dubai Marina and this positioning, halfway between
the new city and the water, became the design’s driving force.
• At its base, the project addresses the marina’s River walk, a twelve meter wide ribbon of
pedestrian walkways, outdoor cafes, seating and green space that provides a continuous
communal amenity for the Marina. Residents living lower in the tower benefit most from
views back into the marina.
• As the building asce ds, the more desirable views become those of the Gulf. By incorporating
incremental plan rotations at each level to generate the building’s distinctive twist the designers
were able to capitalize on the changing prevailing views as the building ascends.
• Contemporary internationally styled interiors, Marble and wood finishes, and premium fixtures
and
fittings.
• Comprehensive automation system to control lights, Air-conditioning and other functions from
a central handset.
Figure 2.13 Site Plan
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2.9 BUILDING FUNCTIONS
• Cayan Tower has six podium floors in which there are tower lobby, car parks, retails and public
cafes.
• There are two mechanical floor in Cayan Tower and they are located on 28th and 72nd floors.
Both mechanical floor are in two story−height.
Figure 2.14 Apartment Configurations And Section
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PENT HOUSE
Figure 2.19 Plan Of Pent House
2.10 FACADE DESIGN
• The winding shape of Cayan Tower reveals a structure that helps protect its interior from the
sun.
Figure 2.20 Façade Of Tower Figure 2.21 Section Of Window
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• Yet, in order to protect the building from the intense desert heat and to provide additional
shade, reinforced concrete structure on the exterior is fully clad in metal (titanium) panels and
screens.
Figure 2.22 Window Spacing In Façade Figure 2.23 Screens On Windows
• Balconies of the residents are covered with sun blinds which are again made out of titanium
panels in order to control the sunlight.
Figure 2.24 Titanium Panels On Exterior
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CHAPTER 3 – STRUCTURE
3.1 STRUCTURAL SYSTEM
• The design philosophy for the Tower is based upon the exterior form of the building as a direct
expression of the structural framework.
• The lateral load resisting system for the Tower consists of a combination of a reinforced
concrete moment-resisting perimeter tube frame and a circular central core wall, connected at
each level by the two−way spanning reinforced concrete flat plate slabs acting as diaphragms.
Perimeter columns are also connected to each other with spandrel beams.
• Floor to floor height of each identical structural floor is 3.7 meters.
Figure 3.1 Structure Plan
Interior Twisting
Gravity Columns (6)
Reinforced Concrete
Flat Plate
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Figure 3.2 Structure Detail In View
Circular & Vertical Reinforced
Concrete Shear Walls at Central
Core
Reinforced Concrete ‘Stepped’
Perimeter Moment Frame
Pile Supported Mat Foundation
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A series of options are studied for the perimeter frame in order to create the unique twisting geometry
of the Tower. For its distinct advantages, from the standpoint of ‘architectural efficiency, structural
performance and ease of construction’, stacking the columns in a step−wise manner at each level,
where each column slopes in one direction, and is offset over the column below is applied as the
perimeter columns system
Figure 3.3 Columns In Step Wise Manner
As the perimeter columns ascend from story to story, they lean in or out, in a direction perpendicular
to the slab edge. At every level, the columns make a small step to the side, shifting in position along
the spandrel beams so that as the building twists, each column maintains a consistent posit on at each
floor relative to the tower envelope. The corner columns and the six (6) interior columns follow a
different rule, twisting as they ascend.
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•
•
•
•
•
•
Figure 3.4 Column Detail Plan
The structural system offers significant construction simplification by permitting a high levell of
repetition in the formwork, which directly impacts the construction cycle time. Also, this system leads
to residential floor layouts which are repetitive at each level despite the twisting nature of the building
form.
Column Position
Below Beam
Column Position
Overhead
Column Position
Above Beam
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3.2 WIND ENGINEERING
• Due to the Tower’s significant height and unique shape, detailed wind tunnel testing was
performed in order to understand the wind forces acting on the building.
• A series of 1:400 scale model tests were performed in order to determine the design wind loads
for the structure as well as peak pressures for the design of the cladding.
• Pedestrian wind studies were also performed to ensure a comfortable wind environment for
those spaces designated for outdoor use, and for adja ent public thoroughfare, respecting air,
and sun rights of the surrounding.
Figure 3.7 Twisting View Of Tower Table 2- Wind Control By Design
• For the twisting Cayan Tower, the variation in the building silhouette over its height creates a
constantly changing frontal wind sail dimension as the building ascends, acting to disorganize
the wind forces which are generated.
• This disorganization of the wind forces, and therefore a reduced correlation of the Tower’s
wind response over its height, results in reduced lateral motion and thus reduced effective wind
forces acting upon t e building. Moreover, corners are also design ted as notched to contribute
buildings performan e against the wind forces.
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• When compared to a similar buil ing taken as a straight extrusioi n with height (no twist), iit is
estimated that the twisting fo m of the Cayan Tower reduced the structure’s across-wind
excitation by some 25% or more.
Figure 3.8 Structural System Concept , Wind Deflection Daigram & Perimeter Punched Wall Axial Force Daigrams
Slab Building
Figure 3.9 Wind Load Actions On Blocks
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CHAPTER 4 – MEP SYSTEMS
• In Cayan Tower, major mechanical risers are located in the circular central core, which
allows a straight vertical path through the Tower.
• The balance of the building’s mechanical, electrical and plumbing systems is located
within a deep demising wall between the central circulation corridor and the residential
units.
• This zone is specifically located and designed to c eate a minimally obtrusiive verticall
path for the building servi es to acc ss all residential units as they rotate about the central
core as the building ascends.
Figure 4.1 Horizontal Distribution From Unit to Core Risers
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CHAPTER 5 – BUILDING MOVEMENT & MONITORING PROGRAM
5.1 LONG TERM CREEP ANALYSIS INCLUDING CONSTRUCTION & LOADING
SEQUENCING.
• Construction start: - 2006
• Project opening: - June 2013
• The idea was flagged in 2006, with Cayan wanting an iconic design that the world would talk
about. And the world indeed is … But the journey was not smooth; the project comprised seven
years of construction and received the certificate of completion in May 2013.
Figure 5.1 Process Of Construction Along Days
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5.2 MACHINES AND MANPOWER CREATE A MARVEL
To construct this magnificent structure, two tower cranes with a total height equivalent to the full
height of the tower were utilised. One of the tower cranes was positioned inside the tower, while the
other was positioned outside the tower. The latter was dismantled upon the whole skeleton of the
tower to allow the installation of the façade glazing and cladding panels, while the other was utilised
until completion of all work. A hydraulically manoeuvred sliding form was utilised for the
construction of the cylindrical core. At the peak, a workforce of about 3,000 personnel was engaged
in construction, including labourers, foremen, logistical staff, engineers, consultants and experts from
all four corners of the globe. Cayan Tower is an architectural vision, which is not only poised to
become the tall standing icon of Dubai but will also serve as inspiration for engineers across the
globe.
Figure 5.2 Core Construction
Table 3- Construction Process Along Years Figure 5.3 Top Detail Of Tower
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5.3 CONSTRUCTING THE TWIST
Figure 5.4 Joint Details Of Structure Members
The tower’s twisting shape is designed for enhanced indoor comfort. Its twist generates self-shading
for the tower, ensuring that many of the interior spaces are protected from solar exposure. The
building’s exterior terraces and the façade’s metal cladding panels, high-performance glass, and deep
sills around the recessed glass line further protect the building from direct solar radiation, while
providing diffuse daylight to interior spaces. This enhanced design for solar control reduces the
building’s demand for cooling, provides a thermally comfortable environment, and minimizes the risk
of glare, while optimizing occupant views of the surrounding marina environment and gulf.
Lenton Products
Formwork & Rebar
SOM 3D Rebar Model
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CHAPTER 6 – CHALLENGES FACED
• The main challenge… To ensure clarity despite the glazing sunrays while still responding to
the specific climatic conditions of the Emirates, the glass is set back from the face of the
building, allowing the recessed terraces, spandrels and columns to act as passive solar
protection.
• Faced by the team was the collapse that happened on February 7, 2007, which delayed the
project for two years.
• The site was completely excavated, all piles were driven and the full shoring system was
developed. “Due to the collapse of the shoring system, the whole site was totally flooded; the
primary objective was to separate the flooded site from the bordering marina with a buffer zone
in an excess of 10-m width,” Qudsiyeh explains.
• To achieve this, a 12-m wide and 30-m long ‘coffer dam’ was constructed to block the breached
portion of the shoring system (this is in combination with stabilisation work of existing
structure). The second objective was to discharge the water back into the marina and
simultaneously stabilise the remaining yet much weaker and vulnerable shoring system, which
was followed by an elaborate rectification works to reinstate the original site conditions that
prevailed prior to the collapse.
• Upon successful completion of these measures, normal construction work resumed. “There are
different theories explaining the reason(s) for the collapse. All of these indicate that the shoring
system failed to counter resist the applied earth and hydrostatic pressures that arrived at their
maximum values when the excavation reached the cut-off levels of the pile heads at 24 m below
the ground surface,” expresses Qudsiyeh.
Figure 6.1 Window Fixing In Twist Foam
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CHAPTER 7 – CONCLUSION
The Dubai’s cayan skyscraper is a pure expression of the idea that a building’s form should directly
follow its structural framework. The magnificient surface qualities of the cayan tower is secondary to
its powerful geometric presence, a mighty twisting prism. The purity of the building’s sculptural
profile is all the more striking when you consider that it has hundreds of balconies-all tucked stealthily
into the recesses created by pulling the curtain wall from the outside screens. The Dubai’s cayan tower
is another example of the hidden design work that is required in a project that started by twisting the
rational, and concluded by rationalizing the twist.
Figure 7.1 Human Eye View From Ground Level