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Global Analysis and Structural Performance of the Tubed Mega Frame
By
Han Zhang
June 2014
TRITA-BKN, Examensarbete 426, Betongbyggnad 2014 ISSN 1103-4297 ISRN KTH/BKN/EX--426--SE Master Thesis in Concrete Structures
i
Abstract
The Tubed Mega Frame is a new structure concept for high-rise buildings which is
developed by Tyréns. In order to study the structural performance as well as the
efficiency of this new concept, a global analysis of the Tubed Mega Frame structure is
performed using finite element analysis software ETABS. Besides, the lateral loads that
should be applied on the structure according to different codes are also studied. From
the design code study for wind loads and seismic design response spectrums, it can be
seen that the calculation philosophies are different from code to code. The wind loads
are approximately the same while the design response spectrums vary a lot from
different codes.
In the ETABS program, a 3D finite element model is built and analyzed for linear static,
geometric non-linearity (P-Delta) and linear dynamic cases. The results from the
analysis in the given scope show that the Tubed Mega Frame structural system is
potentially feasible and has relatively high lateral stiffness and global stability. For the
service limit state, the maximum story drift ratio is within the limitation of 1/400 and
the maximum story acceleration is 0.011m/sec2 which fulfill the comfort criteria.
Keywords: Tubed Mega Frame, high-rise buildings, ETABS, wind load, design response
spectrum
iii
Sammanfattning
TubedMegaFrame är ettnyttbärande system för skyskrapor somharutvecklats avTyréns. För att studera konstruktionens prestanda samt effektiviteten för det nyakonceptet har en global analys av TubedMega Frame systemet utförtsmed hjälp avFEM-programvaranETABS.Enstudieavhurolikanormertahänsyntilldehorisontellalasternaharocksåutförts.Frånstudienavvindlasterochseismiskaresponsspektraideolikadimensioneringsnormerna kanman se attberäkningsfilosofierna skiljer sig frånnorm till norm. Vindlasterna är snarlika medan responsspektra varierar en hel delmellandeolikanormerna.
En 3D-finit elementmodell är gjord och analyserad i ETABSmed hänsyn till linjärtstatiska, geometriskt olinjära (P-Delta) och linjärt dynamiska lastfall. Resultaten frånanalysernavisarattTubedMegaFramesystemetärpotentielltmöjligtochharenrelativhög styvhet i sidled samt en bra global stabilitet. För bruksgränstillstånd är denmaximala utböjningen i horisontell riktning inom begränsningen på 1/400 av envåningshöjdochdenmaximalahorisontalaccelerationenär0.011m/sec2vilketuppfyllerkomfortkriterier.
v
Preface
The thesis has been done at Tyréns, in Stockholm and the whole experience has been
very pleasant.
I want to express my huge gratitude to my supervisors, Fritz King, Mikael Hallgren and
Peter Severin and my examiner, Anders Ansell, for giving me the opportunity to work on
this exciting topic and for the great help during the whole time.
Thanks to Rita Chedid, for kindly offer suggestions and helped me with my questions.
Thanks to Tobias Dahlin, Magnus Yngvesson, Niklas Fall, Viktor Hammar, Kristian
Welchermill, David Tönseth and Sulton Azamov, for their help to the thesis.
Stockholm, June 2014
Han Zhang
vii
Notations
= tributary area.
Cp = external pressure coefficient.
D = diameter of the building.
= site coefficients determined by both site classes and mapped Risk-Targeted
Maximum Considered Earthquake (MCER) spectral response acceleration parameter (
and ) for short periods.
= site coefficients determined by both site classes and mapped Risk-Targeted
Maximum Considered Earthquake (MCER) spectral response acceleration parameter (
and ) for a period of 1 s.
GCpi = internal pressure coefficient.
Gf = gust-effect factor for flexible buildings.
= live load element factor.
Kz = velocity pressure exposure coefficient.
= reduced design live load per square meter of area supported by the member.
= unreduced design live load per square meter of area supported by the member.
= the soil factor.
= mapped Risk-Targeted Maximum Considered Earthquake (MCER) spectral response
acceleration parameter at a period of 1 s with site class B and a target risk of structural
collapse equal to 1% in 50 years.
, is the design earthquake spectral response acceleration parameter at 1 s
period.
, is the design earthquake spectral response acceleration parameter at
short period.
= the elastic response spectrum.
= mapped Risk-Targeted Maximum Considered Earthquake (MCER) spectral response
acceleration parameter at short periods with site class B and a target risk of structural
collapse equal to 1% in 50 years.
viii
St = dimensionless parameter called Strouhal number for the shape.
T = fundamental period of the structure.
= the lower limit of the period of the constant spectral acceleration branch.
= the upper limit of the period of the constant spectral acceleration branch.
= the value defining the beginning of the constant displacement response range of the
spectrum.
= the design characteristic period of ground motion, given in GB50011-2010.
V = mean wind speed at the top of the building.
cpe = pressure coefficients for external pressures.
cpi = pressure coefficients for internal pressures.
cr(z) = roughness factor.
= frequency of vortex shedding.
= terrain factor depending on the roughness length .
p = design wind pressures for the main wind-force resisting system of flexible enclosed
buildings.
q = qz for windward walls evaluated at height z above the ground.
q = qh for leeward walls, side walls and roofs, evaluated at height h.
qi = qh for windward walls, side walls, leeward walls, and roofs of enclosed buildings and
for negative internal pressure evaluation in partially enclosed buildings.
( ) = external peak velocity pressures.
( ) = internal peak velocity pressures.
= 10 min average time interval the basic wind speed.
= 3 second average time interval the basic wind speed.
= basic wind pressure.
wk = characteristic value of design wind loads.
= roughness length.
= roughness length for terrain category II.
ze = reference height for external pressures.
ix
= gradient height in ASCE 7-10 code.
zi = reference height for internal pressures.
= maximum height in calculation of terrain factor, taken as 200m.
= minimum height defined in EN 1991-1-4 2005.
= the design ground acceleration on type A ground.
= the maximum design ground acceleration parameter.
= wind vibration and dynamic response factor.
= external pressure coefficient.
= factor for wind pressures variation with height.
xi
Contents
1. Introduction ............................................................................................................................................. 1
1.1. Background ........................................................................................................................................... 1
1.2. Aim ........................................................................................................................................................... 1
1.3. Case Study ............................................................................................................................................. 1
1.4. Limitation .............................................................................................................................................. 2
2. Method ....................................................................................................................................................... 5
2.1. Literature study .................................................................................................................................. 5
2.2. Case Study ............................................................................................................................................. 5
2.2.1. Parameter study ......................................................................................................................... 5
2.2.2. Finite element model analysis .............................................................................................. 5
3. Literature review ................................................................................................................................... 9
3.1. High-rise buildings ............................................................................................................................. 9
3.1.1. The development of high-rise buildings ........................................................................... 9
3.1.2. The structural systems.......................................................................................................... 12
3.1.3. The limitation of the structural systems nowadays .................................................. 13
3.2. The Tubed Mega Frame concept ............................................................................................... 14
3.2.1. The Articulated Funiculator ................................................................................................ 14
3.2.2. The Tubed Mega Frame structural system ................................................................... 15
3.3. Wind loads ......................................................................................................................................... 16
3.3.1. Features of wind loads .......................................................................................................... 16
3.3.2. Wind velocity variation with height ................................................................................ 17
3.3.3. Vortex shedding ....................................................................................................................... 17
3.3.4. Wind load calculation methods in different codes ..................................................... 18
3.4. Seismic actions ................................................................................................................................. 30
3.4.1. Earthquakes .............................................................................................................................. 30
3.4.2. Structural responses to seismic actions ......................................................................... 32
xii
3.4.3. Design response spectrums in different codes ............................................................ 33
4. Finite element analysis ..................................................................................................................... 45
4.1. Analysis model description ......................................................................................................... 45
4.1.1. Global geometry....................................................................................................................... 45
4.1.2. Dimensions of tubes and perimeter walls ..................................................................... 47
4.1.3. Material ....................................................................................................................................... 47
4.1.4. Boundary conditions ............................................................................................................. 47
4.1.5. Element types used in ETABS program .......................................................................... 47
4.1.6. Assumptions .............................................................................................................................. 49
4.2. Applied loads ..................................................................................................................................... 49
4.2.1. Dead loads .................................................................................................................................. 49
4.2.2. Live loads.................................................................................................................................... 49
4.2.3. Wind loads ................................................................................................................................. 51
4.2.4. Earthquake ................................................................................................................................ 53
4.2.5. Load combinations ................................................................................................................. 53
4.3. Linear Static analysis ..................................................................................................................... 54
4.3.1. Model verification ................................................................................................................... 54
4.3.2. Overturning moments and base shear forces for lateral loads ............................. 54
4.3.3. Maximum deformations of the building ......................................................................... 54
4.4. Non-Linear static analysis ............................................................................................................ 54
4.4.1. P-delta.......................................................................................................................................... 54
4.5. Dynamic analysis ............................................................................................................................. 56
4.5.1. Natural frequencies and periods ....................................................................................... 56
4.5.2. Design response spectrum analysis for seismic actions .......................................... 57
4.5.3. Time-history analysis of wind loads in service limit state ...................................... 59
5. Results and discussions .................................................................................................................... 63
5.1. Linear static analysis results ....................................................................................................... 63
5.1.1. Model verification results .................................................................................................... 63
5.1.2. Overturning moments, base shear forces and story drift ratios ........................... 64
5.1.3. Deformations ............................................................................................................................ 65
5.2. P-Delta effects ................................................................................................................................... 65
5.3. Dynamic analysis results .............................................................................................................. 67
5.3.1. Natural frequencies and periods ....................................................................................... 67
xiii
5.3.2. Design response spectrum results ................................................................................... 68
5.3.3. Time-history analysis results of SLS wind loads ........................................................ 70
6. Conclusions and proposed further research ............................................................................ 73
6.1. Conclusions ........................................................................................................................................ 73
6.2. Proposed further researches ...................................................................................................... 73
References ....................................................................................................................................................... 75
Appendix .......................................................................................................................................................... 77
Appendix A: First 8 natural periods and corresponding vibration modes…….………….77
Appendix B: Wind loads calculation for main wind force-resisting system according to ASCE 7-10…………………………………………………………………..…...……………79
Appendix C: Wind loads calculation for main wind force-resisting system according to EN 1991-1-4 2005………………………………….……………………………………..89
Appendix D: Wind loads calculation for main wind force-resisting system according to GB 50009-2012…………………………………………………………………………..105
Appendix E: Gust factor variation with height……………………………...……………………...113
Appendix F: Gust factor variation with period………………………………...…….……………..117
Appendix G: Model checking – Mass of the model……………………...………...…………..…..121
1
Chapter 1
1. Introduction
1.1. Background
With the expansion and development of cities, high-rise buildings have been more and
more considered as a solution to the land shortage problem in big cities and as an
efficient way to provide residential, office and commercial space. In addition, high-rise
buildings are not only the representation of wealth of the country, but also the
representation of advanced engineering technique that engineers can achieve.
Problems arise as the height of the building increases. Tyréns has proposed a new
concept called ‘Articulated Funiculator’ to solve the vertical transportation problem in
high-rise buildings, especially in ultra-high buildings. In the meantime, a structural
system concept called Tubed Mega Frame has also been proposed by Tyréns in
correspondence to the Articulated Funiculator transportation system. The Tubed Mega
Frame structural concept is to use mega hollow columns and perimeter walls to act as
the main load bearing system and therefore remove the core from the structure to leave
more usable area for the building. However this concept is still under development and
more research is needed for this structural system. This thesis performs a preliminary
global analysis of the Tubed Mega Frame structural system and evaluates the general
performance and efficiency of the system.
1.2. Aim
The aim of this thesis is to study the global building efficiency of the Tubed Mega Frame
structural system. To be specific, this thesis will look into the different requirements and
design methods for high-rise buildings from different codes. Analysis of an 800 meter
prototype building using finite element analysis software and evaluation of the global
performance and efficiency of the Tubed Mega Frame structural system.
1.3. Case Study
The analysis will be carried out through a case study on a prototype building. The
prototype building is 800 meter high and has a similar architectural lay-out as the Ping
An Finance Center Tower in Shenzhen, China, see figure 1.1. The specific parameters of
the prototype building are described in chapter 4.
CHAPTER 1. INTRODUCTION
2
1.4. Limitation
The thesis will consider one prototype building. Therefore the analysis and study will
focus only on this prototype building.
The global structural performance study here in this thesis will focus on the evaluation
of the main load bearing structural components such as mega hollow tubes, perimeter
walls and floors etc. Detailed designs as well as secondary structural components such
as intermediate columns, inner walls, and mechanical shafts etc. are not included in the
analysis.
The analysis of the structure system with finite element analysis software will be limited
only for linear static load conditions, geometric non-linear conditions (P-Delta) and
linear dynamic load conditions. The wind loads are only considered in the along-wind
direction which means vortex shedding effects are not included in this thesis. Seismic
actions on the building will be considered using assumed parameters and site conditions.
The dimension of the structural components will be based on assumptions and input
data given by Tyréns.
CHAPTER 1. INTRODUCTION
3
Prototype Building, 800m
Ping An Finance Center Tower, 660m Figure 1.1 3D model of the prototype building compared with Ping An Finance Center
Tower.
4
5
Chapter 2
2. Method
2.1. Literature study
This thesis will start with studying the basic concepts on high-rise buildings and the
Tubed Mega Frame. After that, the literature study will focus on code studies. The
designs of high-rise buildings are mainly dominated by wind loads and seismic actions
in most cases. Therefore the literature study of design codes will focus on how the wind
loads are calculated and seismic design response spectrums are defined by different
codes. Corresponding parameters and calculation methods will be studied and a
comparison of example calculations will be carried out.
When comparing the wind loads and design response spectrums from different codes,
the assumptions and basic parameters in the formulas such as site location, basic wind
speed, maximum ground acceleration etc. were set to be the same or similar in order to
validate the results.
2.2. Case Study
2.2.1. Parameter study
The parameter study will start with collecting initial design data such as geometry
inputs of the prototype building and the assumed dimensions of structural components.
This data is given by Tyréns from previous models. The material properties are
determined by a corresponding thesis regarding this prototype building (Dahlin &
Yngvesson, 2014).
In order to verify the correct wind loads that should be applied to the model, a
verification of wind loads according to the ASCE 7-10 code and the program determined
wind loads in ETABS according to ASCE 7-10 code will be performed.
The element type used for analysis will be studied with the analysis reference manual
provided by ETABS program (Computers & Structures, Inc., 2013).
2.2.2. Finite element model analysis
The analysis model of the case study building was constructed in ETABS, version 13.1.4
(Computers and Structures, Inc, 2014). ETABS is finite element analysis software which
CHAPTER 2. METHOD
6
is specifically designed for high-rise building analysis. The initial model of the building is
given by Tyréns, then modifications to the model are carried out.
Both static analysis and dynamic analysis are performed by the ETABS program using
finite element analysis method. Finite element method (FEM) is a numerical technique
for finding approximate solutions to boundary value problems for differential equations.
It uses variational methods to minimize an error function and produces a stable solution
(Reddy, 2005).
Finite element method in structural engineering analysis is to divide the structural
components into small elements and connect them through notes. Each simple element
will be solved with individual equations and then all the elements from each subdomain
will be used to approximate a more complex equation and be solved over a larger
domain. The number of elements is determined depending on the need of accuracy and
the similarity to the actual behavior of the components. Therefore, the results from the
finite element analysis are only approximation to the actual results.
In the ETABS program, the elements that are used in the finite element analysis progress
are defined by ‘meshing’ of the structure components. With the mesh function in the
program, one can determine both the size and number and even geometrical shape of
the elements to make sure the analysis can reflect the right behavior of the structure
with reasonable accuracy. The program also provides an ‘Auto mesh’ function which
automatically determines the mesh by given input.
Static analysis The static analysis will be carried out using the finite element analysis software ETABS
considering both linear static cases and non-linear static cases. The initial design
geometry and material assumptions of the model given by Tyréns will be modified in
order to make it performs more detailed. Then, estimated loads will be applied to the
model and the linear static analysis will be performed.
For geometric non-linearity analysis, P-delta effects will be considered. The P-delta
effects will be considered as a separate load case in ETABS, and analyzed before other
load cases. Once the analysis of the P-delta effects reaches convergence, the stiffness of
the model is then used for other linear static analysis cases.
The results which are of interest in the static analysis part are self-weight of the whole
structure, base bending moment (over-turning moment), base shear forces, story drift
ratios, and the deflections of the structure. The influence of P-delta effects to the
structure will be evaluated.
Dynamic analysis The dynamic analysis will be performed on the same model. Modal analysis, assumed
seismic design response spectrum analysis and a time-history analysis of service limit
state wind loads will be carried out. From the modal analysis, the natural frequencies
and periods of the building can be obtained which lead to the evaluation of the stiffness
CHAPTER 2. METHOD
7
of the structure. The design response spectrum will be a preliminary analysis and the
response of the structure will be studied. From the time-history analysis of service limit
state wind loads, the top story acceleration will be studied to verify the comfort criteria
of the building. The more detailed analysis methods as well as the inputs in the ETABS
program for each analysis are described in chapter 4.
8
9
Chapter 3
3. Literature review
3.1. High-rise buildings
3.1.1. The development of high-rise buildings
From the first high-rise building which was built in Chicago in late 19th century to the
skyscrapers that are built nowadays, high-rise buildings are always used as an efficient
solution to increase the economic benefit with relatively low land usage. In addition to
that, the enthusiasm to build high-rise buildings comes not only from their economic
benefits, but also from the desire to build a building which can rise above the city and
become the landmark to represent the city to the world. Today, we are undoubtedly
under a rapid development period of high-rise buildings, and the reason for that remains
the same as the one that led to the first high-rise building – society demands.
In the late 19th century in Chicago, after the catastrophic fire which burnt down almost
the entire Chicago city, there was a high demand to rebuild the city and therefore
provided the chance to develop new structure systems for buildings (Hu, 2006). Due to
the high land price in the city, people started thinking about build upwards rather than
to expand the base, the initial ideas of the high-rise building then got arise.
However, there were several obstacles that must be overcome to develop high-rise
buildings. The first one was the lack of adequate construction materials and structural
systems. In old days, people were using masonry as load bearing material which has
very low strength and structural integrity. On the other hand, construct a high building
with masonry will consume large base space of the building which is not economical. In
1891, Chicago built a 16-floor high-rise building with masonry called Monadnock, and
the walls on the ground floor have a thickness of 2m. In order to build higher structures
with lighter and more efficient material, iron was considered as an alternative. With this
material, American engineer William LeBaron Jenney invented a new structural system
– iron skeleton frame (Hu, 2006). This structural system used iron as the main load
bearing material and combined with masonry as perimeter material which solved the
structural problem for buildings to be built higher.
The other obstacle was the lack of vertical transportation, which was solved by Elisha
Otis by inventing the self-break elevator in 1852 which made it possible to transport
people safely to higher floors. Besides that, the invention of telephone, which made long
distance communications possible, solved the final obstacle in front of the development
of high-rise building.
CHAPTER 3. LITERATURE REVIEW
10
Once all obstacles were solved, high-rise buildings entered into a rapid development
period and the competitions for ‘the world’s tallest’ title also initiated and continue till
today. Since the 106m tall Manhattan Life Insurance Building was built in 1894, the
height record for high-rise buildings keep being reset. In 1909, the Metropolitan Life
Insurance Company Tower in New York became the first building that over 200m high.
In 1931, the Empire State Building with the height of 381m became the tallest building
at that time and held the record for 42 years. After 1980s, the center of high-rise
buildings’ construction shifted from America to Asia. Nowadays, more tall buildings are
located in Asia and Middle East instead of North America. The newly built tall buildings
in Asia and Middle East also push the limit of height. The completed tallest building in
the world now is Burj Khalifa which is 828m high, and the tallest building under
construction is the Kingdom Tower which will be at least 1000m high when completed.
CHAPTER 3. LITERATURE REVIEW
11
Figure 3.1 World's ten tallest buildings according to height to architectural top (Council on Tall Buildings and Urban Habitat, 2013).
CHAPTER 3. LITERATURE REVIEW
12
The functions of high-rise buildings also changed from purely office usage to multiple
functions such as office, residential apartments, hotels, even entertainment facilities
integrated in one building. The concepts now for design the high-rise structures are to
design the entire living environment in vertical direction, to build the ‘vertical city’.
The future trends of high-rise buildings are not only the integration of functions, but also
to design, construct and operate buildings sustainably (Wood & Oldfield, 2008). More
and more tall buildings are using new technologies such as wind turbines, solar panels,
fuel cells and geothermal pumps to collect the surrounding low carbon dioxide emission
energy and use them to supply the buildings themselves. However, there is still a long
way to achieve fully sustainable design and operation of high-rise buildings. Because of
the massive volume that high-rise buildings have, the material for construction, air
conditioning, lighting and vertical transportation systems will all consume large
quantity of energy. Therefore, the potential of using the height of the buildings to
produce wind, solar and other sort of energy should not be neglected. The ultimate goal
is that buildings themselves balancing the energy consumption and the emissions of
carbon dioxide coming from the construction, maintenance and demolishing process
and thus lead to a zero consumption and emission result throughout the life cycle of the
buildings.
3.1.2. The structural systems
High-rise buildings are mainly subjected to vertical live and dead loads, wind loads and
seismic actions. As the height of building increases, the effects of horizontal loads will
increase as well. Therefore, for high-rise buildings, it is important to choose structural
systems which have enough horizontal stiffness.
For high-rise buildings in early 20th century, the structural systems were mainly pure
frame systems using reinforced concrete as the main construction material. This kind of
structural systems have a high capability for multi-functional usage of the floors due to
their variable arrangement of the structural plan and large space that they can provide.
However, the frame systems have a low horizontal stiffness and when subjected to wind
loads and seismic actions, the structures will have large lateral displacements, and this
limited the height of frame structures.
The development of shear wall structural systems breaks the height limit of frame
structures. With the cast-on-site reinforced concrete shear walls, the structural systems
can achieve an excellent lateral stiffness with high structural integrity which is good at
withstand both wind loads and seismic actions. Hence, buildings using shear wall
structural systems can reach much higher height than those with pure frame systems.
But the shear wall systems do not have a flexible structural plan, therefore they are
more suitable for residential and hotel buildings.
CHAPTER 3. LITERATURE REVIEW
13
Since buildings require both the variety of floor plan and enough lateral stiffness to
resist lateral loads, the frame-shear wall structural systems were developed as the
combination of frame and shear wall structural systems. The frame-shear wall structural
systems take the advantages from both systems. By adding proper amounts of shear
walls in proper positions in frame structures, the buildings can have both variable
structural plan and enough horizontal stiffness. Therefore, the frame-shear wall
structural systems can fulfill a wide range of application demands and structural height
as well.
In order to build even higher structures, the core systems were developed. The core
systems have different types. One is the inner core (the reinforced concrete shear walls
in a closure tube shape) combined with outer frames to form the so called core-frame
structural systems. The inner core can also be combined with an outer tube (a frame
tube formed with dense columns and beams) to form the tube in tube structural systems.
The core systems have great structural integrity and lateral stiffness which make them
an ideal option for ultra-high buildings.
Nowadays, as the height of buildings keeps increasing, the steel-concrete composite
structural systems which utilize the material advantages of both concrete and steel are
used favorably on ultra-high buildings. The steel structural components are light and
have high strength capacity. Therefore the structural systems usually use reinforced
concrete for the core as well as for the perimeter columns and steel for the outrigger
frames together with bracing trusses to increase the horizontal stiffness.
3.1.3. The limitation of the structural systems nowadays
Although the structural systems today already enable engineers to design and construct
ultra-high buildings such as Burj Khalifa and Kingdom Tower, there is still a limitation of
these structural systems. The core systems are indeed grantee enough for horizontal
stiffness of buildings. However, they also occupy large space on each floor. In order to
keep structures stable, ultra-high buildings usually decrease the perimeter with the
increase of height. Then the problem appears, after certain height, that buildings are
unable to lift people up to the top since the required core area for elevators will be even
larger than the floor area. For example, even though Burj Khalifa is the world’s tallest
building with the height of 828m, the actual occupied height is only 584m (Council on
Tall Buildings and Urban Habitat, 2014). Therefore, one of the limitations of the core
systems nowadays is that people cannot reach the actual top of the buildings.
CHAPTER 3. LITERATURE REVIEW
14
3.2. The Tubed Mega Frame concept
3.2.1. The Articulated Funiculator
Tyréns is now developing an evolutionary vertical transportation system for buildings
called the ‘Articulated Funiculator’, which is especially suitable for ultra-high buildings.
The Articulated Funiculator is a series of trains separated by some distance along the
vertical direction of the building, each series of trains will be responsible for the vertical
transportation of that vertical section along the building (see figure 3.2).
Figure 3.2 The Articulated Funiculator Concept Sketch (King, Severin, Salovaara, & Lundström, 2012).
The trains travel vertically between the ‘’stations’’ where the trains can load and unload
people, functioning similar to traditional subway stations. Passengers will remain
standing while the Articulated Funiculator transits from horizontal direction to vertical
direction. Traditional elevators can be used as the vertical transportation systems which
allow passengers to travel to specific floors in between the stations.
With this innovated transportation system combined with traditional elevators,
passengers can have more travel options. They can ride the Articulated Funiculator to a
station and switch to traditional elevators to go up or down, or they can take only
traditional elevators and this may require a transfer from one elevator to another.
Multiple vertical travel options can be expected to increase the volume of passenger
flow and reduce the congestion of transportation systems. In addition, less conventional
CHAPTER 3. LITERATURE REVIEW
15
elevators will be used in tall buildings and the number of elevator shafts will be reduced
as well, which may lead to more sellable area on each floor (King, Severin, Salovaara, &
Lundström, 2012).
3.2.2. The Tubed Mega Frame structural system
The Articulated Funiculator was designed to travel from one side of the building to
another. Correspond to this vertical transportation system, Tyréns proposed a structural
system called the Tubed Mega Frame that uses mega hollow tubes to house the
Articulated Funiculator trains as well as using them as the main load bearing system,
which is similar to a core. The stations will be used as horizontal structural systems
similar to outriggers. The vertical loads will be transferred to vertical tubes and carried
by them. In between the stations, there will be cross bracings and belt trusses to
increase the horizontal stiffness of the structural system.
The Tubed Mega Frame structural system removes the core from the building and
therefore leaves more sellable space for the owner. With the load bearing mega tubes
being set at the perimeter of the building, the large floor area can achieve many
functions, such as swimming pools, theaters, large conference room etc., which cannot
achieved by conventional high-rise buildings. It also offers flexible architectural
configurations and supports many architectural forms which could not have been
accomplished before.
Figure 3.3 Hollow tubes and perimeter walls in Tubed Mega Frame.
CHAPTER 3. LITERATURE REVIEW
16
3.3. Wind loads
3.3.1. Features of wind loads
Wind is the motion of air. Obstacles in the path of wind, such as buildings and other
topographic features, deflect or stop wind, converting the wind’s kinetic energy into
potential energy of pressure, thereby creating wind load (Taranath, 2011).
The wind is blowing in a quite random and turbulent way and thus the speed of wind is
usually unsteady. The sudden change of wind speed is called gustiness or turbulence
which is an important factor to be considered in dynamic design of tall buildings. There
are many factors that can influence the magnitude of wind speed such as season,
topographic features, and surface roughness and so on. These factors result a highly
varied wind speed through different time of the year and different locations. In order to
consider wind effects in the design, the mean wind velocity which is based on large
observation data is usually used. If the wind gust reaches its maximum value and
disappears in a short time less than structure’s period, then the gusty wind will cause
dynamic effects on the. On the other hand, if the wind load increases and disappears in a
much longer time than the structure’s period, then it can be considered as static effects
(Taranath, 2011). When it comes to dynamic design of the structures, instead of using
steady mean wind flow, the gust wind loads must be considered, since they usually
exceed the mean velocity and cause more effects on the structures due to their rapid
changes.
In civil engineering field, the wind effects corresponding to vertical axis (lift and yawing)
are usually negligible in the design. Therefore, except for the cases for large span roof
structures where the uplifting effects should be considered, the wind flow can be
considered as two-dimensional, as shown figure 3.4, consisting of along wind and across
wind.
Figure 3.4 Simplified 2D wind flow (Taranath, 2011).
CHAPTER 3. LITERATURE REVIEW
17
When the wind is acting on the surface of a building, two major phenomena on the
structure should be considered. One is the fluctuation on the along-wind side and the
other is vortex shedding on the across-wind side. For the along-wind side, resonance
may happen when the gust period is at or near the structure’s natural period, results
much higher damage for the structure in proportion with the load magnitude. For the
across-wind side, when wind flow passes a body with certain shape at certain speed, the
vortices will be exerted and then detach periodically from either side of the body. This
phenomenon is called vortex shedding. When the period of detachment is at or near the
natural period of the structure, resonance will occur and drive the structure to vibrate
with harmonic oscillations in the across-wind direction. Generally speaking, for tall
buildings, the crosswind effects which are perpendicular to the direction of wind are
often more critical than along-wind effects. To determine if vortex shedding is critical to
a structure, a wind tunnel test is usually required.
3.3.2. Wind velocity variation with height
The ground roughness has significant effects on wind speed, due to the reason that the
friction between wind flow and ground obstacles will cause drag on wind flow.
Therefore, wind speed varies alone with the distance above ground. Wind speed will be
lower at the surface, and the frictional drag effects will gradually decrease as the height
increases thus result a higher wind speed at higher level. At certain height, the frictional
drag effects on wind speed become negligible and the magnitude of wind speed is
depend mainly on the prevailing seasonal and local wind effects. This height where the
frictional drag effects cease to exist is called gradient height, and the corresponding
velocity is called gradient velocity. In addition, the height through which the wind speed
is affected by topography is called the atmospheric boundary layer (Taranath, 2011).
3.3.3. Vortex shedding
When a building is subjected to a smooth wind flow, the flow streamline will separate
and be displaced on both sides of the building. At low wind speeds, vortices are shed
symmetrically in pairs with one on each side and therefore can take out each other thus
no tendency for the building to vibrate in the transverse direction. However, at high
wind speeds, the vortices shed alternatively from one side to another. The transverse
impulse occurs alternatively on opposite sides of the building with a frequency that is
precisely half that of the along-wind impulse (Taranath, 2011). This effect due to the
transverse shedding gives rise to the vibration in the across-wind direction.
CHAPTER 3. LITERATURE REVIEW
18
Figure 3.5 Vortex shedding (Taranath, 2011).
The following equation can be used to determine the frequency of transverse vibration
that caused by vortex shedding (Taranath, 2011):
Eq. (3-1)
Where,
is the frequency of vortex shedding, in Hz
V is the mean wind speed at the top of the building, in m/s
St is the dimensionless parameter called Strouhal number for the shape
D is the diameter of the building, in m
If the wind speed is such that the frequency of vortex shedding becomes approximately
the same as the natural frequency of the building, resonance will occur. When the
building begins to resonate, the shedding is controlled by the natural frequency of the
building, which means further increase in wind speed by a few percent will not change
the shedding frequency. When the wind speed increases significantly above that causing
the lock-in phenomenon, the frequency of shedding is again controlled by the speed of
wind (Taranath, 2011).
3.3.4. Wind load calculation methods in different codes
Wind loads are usually the governing loads on high-rise buildings and there are many
aspects which can influence the magnitude of wind loads. Such as ground roughness,
mean wind velocity, topography conditions, natural frequency of the structures, and
geometric shape of the structures and so on. In different design codes, the calculation
methods for wind loads are different and the corresponding factors are also taken into
consideration in different ways. The following part will describe the general calculation
methods for the main wind-force resisting system of flexible enclosed high-rise
CHAPTER 3. LITERATURE REVIEW
19
buildings according to the American Code (ASCE 7-10), the Eurocode (EN 1991-1-
4:2005) and the Chinese Code (GB50009-2012).
Wind Load Calculation Formulas American Code Calculation Formula: In ASCE 7-10 code, the design wind pressures for
the main wind-force resisting system of flexible enclosed buildings shall be calculated
from the following equation:
( ) ( ) Eq. (3-2)
Where,
q = qz for windward walls evaluated at height z above the ground.
q = qh for leeward walls, side walls and roofs, evaluated at height h.
qi = qh for windward walls, side walls, leeward walls, and roofs of enclosed buildings and
for negative internal pressure evaluation in partially enclosed buildings.
Gf = gust-effect factor for flexible buildings.
Cp = external pressure coefficient.
GCpi = internal pressure coefficient.
Eurocode Calculation Formula: In Eurocode EN 1991-1-4:2005, the net pressures
acting on the surfaces should be obtained from the following equation:
( ) ( ) ( ) Eq. (3-3)
Where,
( ) and ( ) are the external and internal peak velocity pressures, respectively.
ze and zi are the reference height for external and internal pressures, respectively.
cpe and cpi are the pressure coefficients for external and internal pressures, respectively.
Chinese Code Calculation Formula: In Chinese code GB50009-2012, the wind loads for
main wind-force resisting systems should be calculated from the following equation:
( ) Eq. (3-4)
Where,
wk is the characteristic value of design wind loads.
is the wind vibration and dynamic response factor.
is the external pressure coefficient.
CHAPTER 3. LITERATURE REVIEW
20
is the factor for wind pressures variation with height.
is the basic wind pressure, in kN/m2.
Wind Load Calculation Parameters When calculating the equivalent static wind loads, the ASCE and Chinese codes use the
average wind pressures multiplied by the gustiness coefficient. The gust factor G in the
ASCE code is for the consideration of advanced structure’s dynamic response under
wind actions. The corresponding factor in Chinese Code is which is the along-wind
vibration and dynamic response factor. In the Eurocode, the calculation method uses the
average wind pressures plus the fluctuating wind pressures so that the peak velocity
pressures qp already take the fluctuation and turbulence of the wind into the
consideration.
Basic Wind Speed: Basic wind speed is the most fundamental parameter in the
calculation of wind loads on structures. The basic wind speeds (in the Chinese code is
the basic wind pressure) for different locations are provided in different codes with
wind maps, which are based on observation and measured data for a long period. The
parameters of defined basic wind speeds in different codes are listed in table 3.1.
Table 3.1 Definitions of basic wind speeds in different codes.
Code Ground
condition Reference
height Return period
Average time interval
ASCE 7-10 Exposure C 10 m 50 years 3 sec
EN 1991-1-4:2005
Open country terrain with low vegetation and
isolated obstacles with separations
of at least 20 obstacle heights
10 m 50 years 10 min
GB50009-2012 Open flat ground 10 m 50 years 10 min
Factors of Wind Pressure/Velocity Pressure Variation with Height:
All three codes considered the wind speed/pressure variation with height in different
ways using different coefficients. Due to the different calculation methods for wind loads,
the coefficients that are used in different codes affect the results from different aspects.
In ASCE 7-10, according to Chapter 27.3, the variation of wind velocity is expressed by
velocity pressure exposure coefficient Kz. Kz accounts the effects of exposure category of
the site and it can be determined from following formulas (American Society of Civil
Engineers, 2013):
( ) (
)
Eq. (3-5)
CHAPTER 3. LITERATURE REVIEW
21
( ) (
)
Eq. (3-6)
Where,
and are tabulated in following table 3.2:
Table 3.2 Terrain Exposure Constants (American Society of Civil Engineers, 2013).
In Chinese code GB50009-2012, the factor for wind pressure variation with height
is considered similarly to ASCE 7-10 code, but the calculations are depending on
different ground roughness categories as listed below:
(
)
Eq. (3-7)
(
)
Eq. (3-8)
(
)
Eq. (3-9)
(
) Eq. (3-10)
In the equations above, the minimum height for each ground roughness category A, B, C
and D is 5m, 10m, 15m and 30m respectively. The corresponding minimum value for
is 1.09, 1.00, 0.65 and 0.51 respectively. The gradient height for each ground roughness
category A, B, C and D is 300m, 350m, 450m and 550m, respectively (Ministry of
Housing and Urban-Rural Development of China, 2012).
In Eurocode EN 1991-1-4:2005, the roughness factor cr(z) accounts for the variability
of the mean wind velocity at the site of the structure due to: 1) the height above the
ground level; 2) the ground roughness of the terrain upwind of the structure in the wind
direction considered. The roughness factor can be calculated from following formulas
(European Committee for Standardization, 2008):
CHAPTER 3. LITERATURE REVIEW
22
( ) (
) Eq. (3-11)
( ) ( ) Eq. (3-12)
Where,
is the roughness length, given in table 3.3
is the terrain factor depending on the roughness length calculated using:
(
) Eq. (3-13)
Where,
=0.05 m (terrain category II, table 3.3)
is the minimum height defined in table 3.3
is to be taken as 200m
Table 3.3 Terrain categories and terrain parameters in EN 1991-1-4:2005 (European Committee for Standardization, 2008)
According to different calculation methods and formulas, the obtained factors for wind
pressure variation with height for three codes are different. The comparisons of the
coefficient’s variation with height in different exposure categories in each code are
shown in figure 3.6. The calculations were carried out for the prototype building.
CHAPTER 3. LITERATURE REVIEW
23
Figure 3.6 Coefficient variation with height in different exposure categories in each code.
0
0.5
1
1.5
2
2.5
0 50 100 150 200 250 300 350 400 450 500 550 600 650 700 750 800 850
Ve
loci
ty p
ress
ure
co
eff
icie
nt
Height (m)
The velocity pressure exposure coefficient in ASCE 7-10
Exposure B
Exposure C
Exposure D
0
0.5
1
1.5
2
2.5
3
3.5
0 50 100 150 200 250 300 350 400 450 500 550 600 650 700 750 800 850
Win
d p
ress
ure
var
iati
on
fac
tor
Height (m)
The factor for wind pressure variation with height in GB50009-2012
Exposure A
Exposure B
Exposure C
Exposure D
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 50 100 150 200 250 300 350 400 450 500 550 600 650 700 750 800 850
The
te
rrai
n r
ou
ghn
ess
fac
tor
Height (m)
The terrain roughness factor in EN 1991-1-4:2005
Exposure 0Exposure IExposure IIExposure IIIExposure IV
CHAPTER 3. LITERATURE REVIEW
24
Figure 3.6 shows that the factors in each code increase with the height. In ASCE 7-10, the
exposure categories vary from type B to type D with the corresponding surface
roughness decrease from urban areas to flat surfaces. The velocity pressure exposure
coefficient increases with the exposure categories vary from type B to type D. The
gradient heights for each exposure category according to ASCE 7-10 are listed in table
3.2.
In the Chinese code GB50009-2012, the exposure category type A to type D varies from
sea surfaces to big cities with corresponding ground roughness increases. Therefore the
factor for wind pressure variation from exposure category type A to type D decreases
while the corresponding gradient height increases. The figure for the Chinese code
GB50009-2012 reflects the same phenomenon as ASCE 7-10 for wind speed variation
with height.
In EN 1991-1-4:2005, however, the gradient heights for each different exposure
categories are set to be fixed at 200m. The exposure category from type 0 to type IV
varies from sea areas to areas have lots of high buildings with corresponding ground
roughness increases as well. The roughness factor decreases from exposure category
type 0 to type IV.
Figure 3.7 shows the comparison of the wind velocity variation factors in all three codes
with similar ground exposure category: For ASCE 7-10, exposure category B is used; For
GB50009-2012, exposure category C is used and for EN 1991-1-4:2005, exposure
category IV is used. All exposure categories are set to be similar with urban exposure
condition.
Figure 3.7 Coefficient differences with similar exposure conditions in each code.
00.20.40.60.8
11.21.41.61.8
22.22.42.62.8
33.2
0 50 100 150 200 250 300 350 400 450 500 550 600 650 700 750 800 850
Co
eff
icie
nt
Height (m)
Coefficient differences with urban exposure condition in each code
ASCE 7-10 with Exposure B
GB50009-2012 with Exposure C
EN 1991-1-4:2005 with Exposure IV
CHAPTER 3. LITERATURE REVIEW
25
From the figure above it can be seen that the Chinese code is more conservative and has
a much higher value than Eurocode, it also has the highest gradient height among all
three codes. Within the first 100m, the differences of coefficients are not much from
each other, as the height increases, the differences increase as well.
External Pressure Coefficients:
When applying wind pressures on building surfaces, each façade of building usually
takes different wind pressures. Therefore, wind loads on buildings should be calculated
in accordance to each surface. The external pressure coefficients are used to represent
the uneven distributions of wind pressures on different surfaces. The external pressure
coefficients are usually depending on the geometric shape of the buildings and differ
from roofs and walls. Here in table 3.4, the external pressure coefficients for main wind-
force resistant walls in different codes are listed for enclosed, rectangular plan buildings.
Table 3.4 External pressure coefficients for enclosed, rectangular plan buildings.
External Pressure Coefficients For Enclosed, Rectangular Plan Buildings
Code Windward
Wall Leeward Wall Side Wall
ASCE 7-10 +0.8
L/B* Cp
-0.7 0-1 -0.5
2 -0.3 ≥4 -0.2
GB50009-2012 +0.8
D/B**
-0.7 ≤1 -0.6 1.2 -0.5 2 -0.4
≥4 -0.3
EN 1991-1-4:2005
h/d*** Cpe h/d Cpe h/d Zone****
A Zone
B Zone
C 5 +0.8 5 -0.7 5 -1.2 -0.8 -0.5 1 +0.8 1 -0.5 1 -1.2 -0.8 -0.5
≤0.25 +0.7 ≤0.25 -0.3 ≤0.25 -1.2 -0.8 -0.5
NOTE
*L is side wall width and B is windward wall width. **D is side wall width and B is windward wall width. ***h is building height and d is side wall width. ****Zone classifications are illustrated in EN 1991-1-4:2005 chapter 7.2.2 figure 7.5
From the table above, the external pressure coefficients for windward walls are similar
among different codes. Eurocode is the only one that divides side walls into different
zones based on the ratio of width and depth of buildings. The external pressure
coefficients are defined almost the same in Chinese code GB50009-2012 and ASCE 7-10,
however, GB50009-2012 is more conservative on leeward wall coefficients.
CHAPTER 3. LITERATURE REVIEW
26
Gustiness Factors:
In all three codes, the fluctuation effects of wind in along-wind direction are considered
through different factors. In ASCE 7-10, the gust factor is used to reflect the loading
effects in the along-wind direction due to wind turbulence-structure interaction. It also
accounts for along-wind effects due to dynamic amplification for flexible buildings and
structures. But it does not include allowances for across-wind loading effects or dynamic
torsional effects (American Society of Civil Engineers, 2013). Figure 3.8 and figure 3.9
shows the variation of gust factor in ASCE 7-10 with building’s fundamental period and
height, respectively.
Figure 3.8 Gust factor variations with period for 800m building.
Figure 3.9 Gust factor variations with height with fixed period of 8.68s.
0.70
0.80
0.90
1.00
1.10
1.20
1.30
0 5 10 15 20 25 30 35 40 45
Gu
st F
acto
r
Period (s)
Gust factor variation with period , with fixed height of 800m (ASCE 7-10)
Exposure B
Exposure C
Exposure D
0.80
0.90
1.00
1.10
1.20
1.30
1.40
0 50 100 150 200 250 300 350 400 450 500 550 600 650 700 750 800
Gu
st F
acto
r
Height (m)
Gust factor variation with height, with fixed period of 8.68s (ASCE 7-10)
Exposure BExposure CExposure D
CHAPTER 3. LITERATURE REVIEW
27
Figure 3.8 shows that when the height is fixed at 800m, with the building’s fundamental
period increases, the gust factor increases as well, while with higher exposure category,
the increment of gust factor decreases. From figure 3.9, it can be seen that when the
period is fixed at 8.68s, the gust factor decreases with the height of building increases,
and with higher exposure category, the gust factor is larger.
Wind Load Calculations for the Prototype Building To further compare the differences among those three codes in wind load calculations,
example calculations on the prototype building are performed. The site condition is
assumed in urban area and the corresponding exposure category in each code is chose
to fulfill the condition. Table 3.5 lists the inputs for the example wind load calculations.
Table 3.5 Input data for example wind load calculations on prototype building.
Prototype Building Inputs
Height 800m Building Width 45m Building Depth
(Parallel to wind direction ) 40m
First Natural Period 8.68s Damping Ratio 0.03
Floor Height 4.5m
Wind Parameters
Basic Wind Speed (10min average time
interval) 29.8m/s
Basic Wind Speed (3sec average time interval)
42.3m/s
Basic Wind Pressure in Chinese Code
0.55kN/m2
Exposure Category ASCE 7-10 B
GB50009-2012 C EN 1991-1-4 IV
The assumed site location is Shanghai and the corresponding 10 min average time
interval basic wind speed was chosen as the basic wind speed. The basic wind speed is
back calculated from the basic wind pressure given in GB50009-2012 Appendix E by the
following equation 3-14.
Eq. (3-14)
Where,
is the basic wind pressure given in GB50009-2012 Appendix E.
is 10 min average time interval the basic wind speed.
According to the definitions of basic wind speed in each code, the 10min average time
interval basic wind speed is used in Chinese code GB50009-2012 and Eurocode EN
CHAPTER 3. LITERATURE REVIEW
28
1991-1 while the ASCE 7-10 code uses 3sec average time interval basic wind speed.
Therefore, the basic wind speed for ASCE 7-10 is converted from the 10min average
time interval basic wind speed using the equation below (Gang, 2012).
Eq. (3-15)
In figure 3.10 presents the calculation results for wind loads on the prototype building
according to each code. Both in windward and leeward directions, only external
pressures are considered in all three codes.
0
500
1000
1500
2000
2500
0 50 100 150 200 250 300 350 400 450 500 550 600 650 700 750 800 850
Win
d p
ress
ure
(N
/m2)
Height (m)
Windward wall wind pressures (N/m2)
ASCE 7-10
GB50009-2012
En 1991-1-4 2005
-1600
-1400
-1200
-1000
-800
-600
-400
-200
0
0 50 100 150 200 250 300 350 400 450 500 550 600 650 700 750 800 850
Win
d p
ress
ure
(N
/m2)
Height (m)
Leeward wall wind pressures (N/m2)
ASCE 7-10GB50009-2012EN 1991-1-4 2005
CHAPTER 3. LITERATURE REVIEW
29
Figure 3.10 Wind pressures according to different codes.
For the windward walls, ASCE code is more conservative than other two codes. Among
all three codes, the Chinese code GB50009-2012 has the lowest value for wind loads
before gradient height. The Eurocode EN 1991-1-4 has the highest lower limit for wind
loads. After gradient height, wind loads in ASCE code are approximately 16% higher
than other codes.
For leeward walls, Eurocode EN 1991-1-4 has the largest values and the ASCE 7-10 code
has similar values with EN 1991-1-4 after gradient height. However, the Chinese code
GB50009-2012 has the lowest value for leeward wall wind pressures, and after gradient
height, the values from Eurocode are approximately 14% higher than Chinese code.
For side wall wind pressures, Eurocode divided the side walls into several zones
according to the ratio of building depth and width. For the prototype building, the side
walls in Eurocode were divided into two zones A and B, and the corresponding wind
load pressures were calculated separately. When comparing three codes, the wind
pressures on zone A according to Eurocode have the highest value while the wind
pressures on zone B according to Eurocode are similar to ASCE 7-10 and GB50009-2012.
-3000
-2500
-2000
-1500
-1000
-500
0
0 50 100 150 200 250 300 350 400 450 500 550 600 650 700 750 800 850
Win
d p
ress
ure
(N
/m2)
Height (m)
Side wall wind pressures (N/m2)
ASCE 7-10
GB50009-2012
EN 1991-1-4 2005/Zone A
EN 1991-1-4 2005/Zone B
0
500
1000
1500
2000
2500
3000
3500
4000
4500
5000
0 50 100 150 200 250 300 350 400 450 500 550 600 650 700 750 800 850
Win
d p
ress
ure
(N
/m2)
Height (m)
Total wind pressure in along-wind direction (N/m2)
ASCE 7-10
GB50009-2012
EN 1991-1-4 2005
CHAPTER 3. LITERATURE REVIEW
30
The wind pressures on zone A in Eurocode are approximately 33% larger than zone B
and other two codes.
For the total wind pressures which add up wind pressures both in windward and
leeward directions, all three codes are similar. The wind pressures that are calculated
according to the Chinese code keep increasing due to the definition of vibration and
response factor.
The wind pressures that are calculated above are characteristic values without
considering the load combination factors and partial load factors. The ASCE code has a
different safety approach in design from that in the Chinese code and the Eurocode. In
the design of structures for ultimate limit states, both the Chinese code and the
Eurocode consider the deduction of material strength while those are not considered in
the ASCE code.
3.4. Seismic actions
3.4.1. Earthquakes
Earthquake is nature disaster caused by the sudden release of energy in Earth’s crusts
and brings massive destruction if it happens near human habitations with enough
intensity. The catastrophic effects of earthquakes to the human society mainly come
from two parts: 1) the significant damage or even collapse of buildings caused by
earthquakes which lead to human lives and properties loss; 2) secondary disasters
caused by earthquakes such as flood, fire, disease etc., which can damage the
environment and human society in a greater and larger scale.
When the crusts collide or squeeze with each other due to the crust movement, it will
result in fractions and faults along the boundaries of earth’s crusts. Seismic waves are
generated and propagate through earth which can cause massive destructive effects on
the surface. The seismic waves are elastic waves and propagate in solid or fluid material.
Usually, earthquakes will create two main types of waves, body waves which travel
through the interior of the material, and surface waves travel through the surface of the
material or interfaces between materials.
The body waves are of two types which are P-waves and S-waves. P-waves are pressure
waves or primary waves which are longitudinal waves that involve compression and
expansion in the direction that the wave is traveling. P-waves are the fastest waves in
propagation and therefore always reach the surface first, causing the ground to move up
and down. The other type of body wave is the S-wave, which stands for shear waves or
secondary waves. S-waves are transverse waves that involve motions perpendicular to
the direction of propagation. S-waves are slower than P-waves so that they reach the
surface after the P-waves, causing the ground moves horizontally which is much more
CHAPTER 3. LITERATURE REVIEW
31
destructive than P-waves. Since shear cannot happen in fluids e.g. water and air, S-waves
can only travel in solids while P-waves can travel in both solids and fluids.
The surface waves have two main types as well which are Rayleigh waves and Love
waves. The surface waves are generated by the interaction of P-waves and S-waves and
travel much slower than body waves. They can be much larger in amplitude than body
waves and strongly excited by the shallow earthquakes.
The most destructive effects of earthquakes are those that shake the buildings
horizontally and produce lateral loads in structures. The shaking input will cause the
building’s foundation to oscillate back and forth in a more or less horizontal plane while
the building mass has inertia and wants to stop the oscillation. Therefore, lateral forces
are generated on the mass in order to bring it along with the foundation. When only the
horizontal seismic effects need to be considered in seismic analysis, these dynamic
actions can be simplified as a group of horizontal loads applied to the structure in
proportion to mass and height, and each floor will be simplified as a concentrated mass
and has only one degree of freedom. Those loads usually expressed in terms of a percent
of gravity weight of the building. Earthquakes will also cause vertical loads in structure
by ground shaking and the vertical forces generated by earthquakes seldom exceed the
capacity of structure’s vertical load resisting system. However, the vertical forces
induced by earthquakes are crucial for high-rise buildings and large-span structures
since they are larger than the designed live loads on the structures. The vertical forces
also increase the chance of collapse due to either increased or decreased compression
forces in the columns. Increased compression overloads columns and decreased
compression reduces the capacity of bending (Taranath, 2011).
Usually, when designing the structures for ultimate limited states; only mild uncertainty
will be faced and linear elastic conditions are idealized for section design of the
structural components. However, in earthquake engineering, the design deals with
random variables and therefore must be different from the orthodox design. The
earthquake itself has high randomness. For a specific location and return period, the
possible maximum earthquake that may happen is a random variable and both the time
and magnitude cannot be predicted. Compare with normal loads, earthquakes happen
seldom and each time with only a short duration, the magnitude of each earthquake can
varies much from each other as well. Therefore, when considering the seismic actions, if
the assumptions of the section design for structural components are still linear elastic
condition, then it will be uneconomical or even impossible to achieve. In the design for
seismic actions, large scale of uncertainties must be faced and appreciable probabilities
need be contended, particularly when dealing with building failures which may happen
in the near future (Taranath, 2011).
CHAPTER 3. LITERATURE REVIEW
32
3.4.2. Structural responses to seismic actions
When earthquakes happen, the ground suddenly starts to move while the upper
structures will not response immediately, but will lag because of the structural
components have inertial stiffness and flexibility to resist the deflections and the
induced forces. Because of the fact that the earthquake is a 3-dimensional impact, two
horizontal directions and one vertical direction, the responses of the structures are very
complex and deform in a highly complex way. Figure 3.11 illustrates a simplified
building behavior during earthquakes.
Figure 3.11 (a and b) Building behavior during earthquakes (Taranath, 2011).
The seismic actions cause a vibration problem for the structure. Earthquake effects are
not technically ‘load’ on the structure since it will not crash the structure by impact, like
a car hit, nor will it apply any external forces or pressures to the building, like wind. The
earthquakes will generate inertial forces within the structural components by force the
building mass to oscillate with the ground. However, even the increase of mass will give
CHAPTER 3. LITERATURE REVIEW
33
a better stiffness of the building, it will also cause unfavorable effects. As the stiffness of
the structure increases, the inertial forces generated by earthquakes will also increase,
resulting in larger forces within the structure. It will also increase the risk of bucking or
crushing of the columns.
The responses of high-rise buildings during earthquakes are different from low-rise
buildings. High-rise buildings are more flexible than low-rise buildings, therefore
experience lower acceleration. However when high-rise buildings are subjected to long-
period ground motions, they may experience much larger forces if the natural period is
near to the earthquake waves. Therefore, the responses of the structures during
earthquakes are not only depending on the characters of earthquakes, but also the
structure systems themselves and their foundations.
3.4.3. Design response spectrums in different codes
The responses of buildings and structures have a broad range of periods, when
summarize all the response periods together in a single graph, this graph is called
response spectrum in earthquake engineering. Nowadays, the design response spectrum
methods for seismic design are widely used in different country’s seismic design
regulations.
Figure 3.12 Graphical description of response spectrum (Taranath, 2011).
The design response spectrum method is developed based on the elastic response
spectrum and modal analysis method. The forces and displacements in the structures
that remain elastic are determined using modal superposition which combines the
response quantities for each of the structure’s modes. Through this way, the response
CHAPTER 3. LITERATURE REVIEW
34
spectrum simplifies the solutions for complex multi-degree of freedom structures in
respond to ground motions.
Although the response spectrums recorded for each earthquake are different, spectrums
which obtained from earthquakes that have similar magnitude on site and similar
features tend to have common characters. This allows the building design codes to
develop standard response spectrums that incorporate these characters and further, use
the enveloped spectrums to anticipate behaviors of building sites during design
earthquakes.
The design spectrums that are used in different codes for different countries are based
on similar approaches. The spectrums are generated based on the studies for local
seismic geologies and earthquake activities to determine the maximum ground motion
acceleration and site responses for the design earthquakes. There are several factors
need to be taken into consideration to adjust the parameters for seismic responses.
Those factors are different from codes to codes and presented in different ways. In the
following sections, the comparisons of horizontal response spectrums in accordance to
the American code ASCE 7-10, the Chinese code GB50011-2010 and the Eurocode 8, EN
1998-1:2004, will be studied.
Defined Design Response Spectrums in Different Codes The design response spectrums are usually described with 3 parameters, which are the
design earthquake spectral response acceleration parameters, periods and reduction
factor for defining the long-period response spectrum curves.
1) American code ASCE 7-10:
In the American code ASCE 7-10, the design response spectrums are defined as follow:
(
) Eq. (3-16)
Eq. (3-17)
Eq. (3-18)
Eq. (3-19)
Where,
T = the fundamental period of the structure, s.
, is the design earthquake spectral response acceleration parameter at
short period.
, is the design earthquake spectral response acceleration parameter at 1 s
period.
CHAPTER 3. LITERATURE REVIEW
35
= mapped Risk-Targeted Maximum Considered Earthquake (MCER) spectral response
acceleration parameter at short periods with site class B and a target risk of structural
collapse equal to 1% in 50 years.
= mapped Risk-Targeted Maximum Considered Earthquake (MCER) spectral response
acceleration parameter at a period of 1 s with site class B and a target risk of structural
collapse equal to 1% in 50 years.
Both and can be obtained from the Seismic Ground Motion Long-Period Transition
and Risk Coefficient Maps given in ASCE 7-10.
and are site coefficients determined by both site classes and mapped Risk-Targeted
Maximum Considered Earthquake (MCER) spectral response acceleration parameter (
and ) for short periods and a period of 1 s, respectively. Table 3.6 and 3.7 show and
that are defined in ASCE 7-10.
Table 3.6 Site Coefficient, Fa in ASCE 7-10 (American Society of Civil Engineers, 2013).
Table 3.7 Site Coefficient, Fv in ASCE 7-10 (American Society of Civil Engineers, 2013).
CHAPTER 3. LITERATURE REVIEW
36
The horizontal part starts at period
, and end at period
. is the
long-period transition period which can be obtained from ASCE Seismic Ground Motion
Long-Period Transition and Risk Coefficient Maps. ranges from 4s to 16s depending
on the geographical locations of sites.
2) Chinese Code GB50011-2010:
In the Chinese code GB50011-2010, the design response spectrums are defined using
design ground acceleration α. The design ground acceleration α is determined by basic
design ground motion acceleration, design seismic groups, site classes and damping
ratios. The design response spectrums are consisting of 4 parts as well, which are
increasing part, horizontal part, decreasing curve and decreasing line. The characteristic
period can be obtained from the code incorporate with site classes and design seismic
groups. The effects of damping ratio are taken into consideration by coefficients ,
and . In GB50011-2010, the damping ratio should be taken as 0.05 except there are
specific requirements. Therefore, the design response spectrums in GB50011-2010 are
defined as follow with the damping ratio of 0.05:
Eq. (3-20)
Eq. (3-21)
(
) Eq. (3-22)
[ ( )] Eq. (3-23)
Where,
T = the fundamental period of the building.
= the design characteristic period of ground motion, given in GB50011-2010.
= the maximum design ground acceleration parameter.
Table 3.8 and 3.9 shows the maximum design ground acceleration parameters and the
design characteristic periods of ground motion given in GB50011-2010:
Table 3.8 The maximum values for design ground acceleration parameter ( ) (Ministry of Housing and Urban-Rural Development of China, 2010).
Seismic Precautionary Intensity
Level 6 Level 7 Level 8 Level 9 Frequent
Earthquake* 0.04g 0.08g(0.12g)*** 0.16g(0.24g) 0.32g
Rare Earthquake**
0.28g 0.50g(0.72g) 0.90g(1.20g) 1.40g
Note: * Frequent Earthquake is defined as seismic intensity with 63% risk of exceed in
50 years.
CHAPTER 3. LITERATURE REVIEW
37
** Rare Earthquake is defined as seismic intensity with 2%-3% risk of exceed in 50
years.
*** The values in brackets are used for locations with design basic acceleration of
ground motion with 0.15g and 0.30g.
Table 3.9 Design characteristic period of ground motion (Tg) (Ministry of Housing and Urban-Rural Development of China, 2010).
Design Group
Site Class I0 I1 II III IV
Group 1 0.20 0.25 0.35 0.45 0.65 Group 2 0.25 0.30 0.40 0.55 0.75 Group 3 0.30 0.35 0.45 0.65 0.90
3) Eurocode EN 1998-1:2004:
The design response spectrums in EN 1998-1:2004 are defined as follow with 5%
damping:
(
) Eq. (3-24)
Eq. (3-25)
(
) Eq. (3-26)
(
) Eq. (3-27)
Where,
= the elastic response spectrum.
T = the vibration period of a linear single-degree-of-freedom system.
= the design ground acceleration on type A ground.
= the lower limit of the period of the constant spectral acceleration branch.
= the upper limit of the period of the constant spectral acceleration branch.
= the value defining the beginning of the constant displacement response range of the
spectrum.
= the soil factor.
In EN 1998-1:2004, when deep geology is not accounted for, the recommended
spectrums have two types: Type 1 and Type 2. If the earthquakes that contribute most to
the seismic hazard defined for the site for the purpose of probabilistic hazard
assessment have a surface-wave magnitude not greater than 5.5, then Type 2 spectrum
CHAPTER 3. LITERATURE REVIEW
38
is recommended to use (European Committee for Standardization, 2004). Here the
surface-wave magnitude is considered to be greater than 5.5, thus Type 1 spectrum is
used for comparisons. Table 3.10 shows the values of the parameters describing the
recommended Type 1 elastic response spectrums.
Table 3.10 Values of the parameters describing the recommended Type 1 elastic response spectrums (European Committee for Standardization, 2004).
Ground Type S TB (s) TC (s) TD (s) A 1.0 0.15 0.4 2.0 B 1.2 0.15 0.5 2.0 C 1.15 0.20 0.6 2.0 D 1.35 0.20 0.8 2.0 E 1.4 0.15 0.5 2.0
The comparisons of parameters in design response spectrums 1) The constant spectral acceleration parameters:
In the American code ASCE 7-10, the shapes of the design response spectrums are
adjusted by two site coefficients and . The constant part of spectral response
acceleration parameter in the design spectrum
takes the site conditions
into account through factors , and which vary with the spectral response
acceleration parameter .
While in the Chinese code GB50011-2010, the constant part of design ground
acceleration parameter in the design spectrum is depending only on the design
seismic intensity level and the site conditions are not taken into consideration for .
The site class effects are considered in the two decrease parts through the characteristic
period .
In the Eurocode EN 1998-1:2004, the constant part in the response spectrum
also takes site effects into consideration through the soil factor . The value
of constant part in the response spectrum varies with design ground acceleration as
well as the site location.
2) The periods in design response spectrums:
In the American code ASCE 7-10, the lower limit of the period of the constant spectral
part is
, and the upper limit of the period of the constant spectral part is
. Both of the periods depending on the site coefficients as well as the spectral
response acceleration parameters and .
In the Chinese code GB50011-2010, the lower limit of the period of the constant spectral
part is set to be a fixed value of 0.1s, and the upper limit of the period of the constant
CHAPTER 3. LITERATURE REVIEW
39
spectral part is which should be determined by the seismic design groups and site
classes.
In the Eurocode EN 1998-1:2004, both the lower and upper limit of the periods of the
constant spectral part and are determined with site classes.
In all three codes, the periods that define the constant spectral parts in the design
response spectrums are taken site effects into account. In the American code, the
periods also account for the effects from the mapped spectral response acceleration
parameters while neither the Chinese code nor the Eurocode takes that into
consideration.
3) The factors influence the decreasing parts of the response spectrums:
In the American code ASCE 7-10, the decreasing parts are defined in two curves, the
design response spectrum decreases faster in the second curve part which is for the long
period range. It reflects that for long period buildings, the design criteria tend to be
lower.
In the Chinese code GB50011-2010, the decreasing parts are defined in one curve part
and one linear part. For the curve part, the reduction exponent is 0.9 which is lower than
the American code and the Eurocode. The linear part defined in a range from 5 to 6s
and this corresponds to the first curve part in the American code. If extend the period
range of the linear part to in the American code, then the long period decreasing in
the Chinese code is more conservative than that in the American code.
In the Eurocode EN 1998-1:2004, the design response spectrum is similar to the
American code in the first decreasing curve part with a period limit of 2s. After 2s, the
second decreasing curve part in the Eurocode decreases faster than that in the American
code.
The comparisons of response spectrums in different codes for an example In order to present the differences of response spectrums in three different codes, a
quantify analysis is performed based on assumed conditions stated as follow:
1) Design spectral response acceleration parameter:
In the Chinese code GB 50011-2010, the design ground acceleration parameters
are given in two types of seismic, as listed in Table 3.8. Since the design spectral
response acceleration parameters in the ASCE 7-10 code are defined as the target
risk of collapse is 1% in 50 years, which is similar to the ‘Rare Earthquake’ in the
Chinese code. Thus, the ground acceleration parameters are chosen as 0.5g from
Table 3.8 for the comparisons between the ASCE 7-10 and the GB 50011-2010,
representing and , respectively. From the Seismic Ground Motion Long-
Period Transition and Risk Coefficient Maps given in the ASCE 7-10, when is
0.5g, the corresponding ranges from 0.2g-0.25g, on conservative side, is set
CHAPTER 3. LITERATURE REVIEW
40
to be 0.25g. The long-period transition is set to be 4s for the ASCE 7-10 code
(Yu Zhan, 2008).
In the Eurocode 8, the design earthquake is defined uniformly with exceed
probability of 10% in 50 years, which is similar to ‘Precautionary Earthquake’ in
the Chinese code which also has an exceed probability of 10% in 50 years. The
ground acceleration parameters are then set to be 0.10g, representing and
in the Eurocode 8 and the Chinese code, respectively.
2) For other calculation parameters required in the Chinese code, the design seismic
resistance level is set to be level VII with the basic ground motion acceleration as
0.1g. The design seismic group is set to be group 1.
3) The ground condition is chose as Site B in accordance to the ASCE 7-10. The
corresponding ground conditions in the Chinese code and the Eurocode 8 are
selected to match the Site B class in the ASCE 7-10.
The site classification is depending on the soil profiles of the site. The soil
categories are defined differently in three codes. In order to be able to use similar
site conditions for comparisons, the soils that defined in each code are compared
according to their shear wave velocities and the result are listed in Table 3.11.
Table 3.11 Shear wave velocities of different site classes from different codes.
Code Site Class
A B C D E
ASCE 7-10 >1500 m/s 760-1500
m/s 370-760
m/s 180-370
m/s <180 m/s
EN1998-1:2004
>800 m/s 360-800
m/s 180-360
m/s <180 m/s Elsewise
GB 50011-2010
>800 m/s (I0)
500-800 m/s (I1)
250-500 m/s (II)
150-250 m/s (III)
<150 m/s (IV)
From the table above, site class A in the Eurocode and site class I0 in the Chinese
code are equivalent to site class B in the ASCE 7-10 code, and site class D in the
Eurocode and site class IV in the Chinese code are equivalent to site class E in the
ASCE code. Therefore, the comparisons of design response spectrums will be
carried out for both site conditions, which are site conditions equivalent to site
class B in the ASCE code and site conditions equivalent to site class E in the ASCE
code.
4) Damping ratio of the building is assumed to be 0.05 for all the cases.
The comparisons of design response spectrums
CHAPTER 3. LITERATURE REVIEW
41
According to the conditions and inputs of the calculation example given above, the
comparisons of design response spectrums of ASCE 7-10, GB50011-2010 and EN
1998:1-2004 are listed below. Figure 3.13 and 3.14 show the design response spectrums
calculated according to ASCE 7-10 and GB50011-2010 for the earthquakes with 2-3%
target risk of exceed in 50 years and for site conditions equivalent to site class B and E in
the ASCE 7-10 code, respectively.
*Note: The site condition is set to be equivalent to site class B in the ASCE code, e.g. site class I0 in the Chinese code is used. Figure 3.13 Design response spectrums according to ASCE 7-10 and GB50011-2010, site class B in ASCE 7-10.
*Note: The site condition is set to be equivalent to site class E in the ASCE code, e.g. site class IV in the Chinese code is used. Figure 3.14 Design response spectrum according to ASCE 7-10 and GB50011-2010, site class E in ASCE 7-10.
0
0.1
0.2
0.3
0.4
0.5
0.6
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5
Spe
ctra
l Re
spo
nse
Acc
ele
rati
on
, g
Period, s
Design Response Spectrums* ASCE 7-10
GB50011-2010
0
0.1
0.2
0.3
0.4
0.5
0.6
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5
Spe
ctra
l Re
spo
nse
Acc
ele
rati
on
, g
Period, s
Design Response Spectrums*
ASCE 7-10GB50011-2010
CHAPTER 3. LITERATURE REVIEW
42
From the two figures above, it can be seen that for earthquakes with 2% target risk of
exceed in 50 years and site condition equivalent to site class B in the ASCE code, the
design response spectrum of the Chinese code have a higher maximum response
acceleration (horizontal part of the spectrum) but a shorter period. However, for weak
site condition which was set to be equivalent to site class E in the ASCE 7-10 code, as
shown in figure 3.14, the design response spectrum of the ASCE 7-10 code has both
higher maximum response acceleration (horizontal part of the spectrum) and longer
period. For short period parts in the response spectrums, the ASCE 7-10 code also has
higher response acceleration than GB50011-2010. For the long-period transition parts,
however, the Chinese code becomes more conservative than the ASCE code.
Figure 3.15 and 3.16 show the design response spectrums calculated according to
GB50011-2010 and EN 1998:1-2004 for earthquakes with 10% target risk of exceed in
50 years and for site conditions equivalent to site class B and E in the ASCE 7-10 code,
respectively.
*Note: The site condition is set to be equivalent to site class B in the ASCE code, e.g. site class I0 in the Chinese code and site class A in the Eurocode are used. Figure 3.15 Design response spectrums of GB50011-2010 and Eurocode 8, site class B in ASCE 7-10.
0
0.05
0.1
0.15
0.2
0.25
0.3
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6
Spe
ctra
l Re
spo
nse
Acc
ele
rati
on
, g
Period, s
Design Response Spectrums*
GB50011-2010Eurocode 8
CHAPTER 3. LITERATURE REVIEW
43
*Note: The site condition is set to be equivalent to site class E in the ASCE code, e.g. site class IV in the Chinese code and site class D in the Eurocode are used. Figure 3.16 Design response spectrums of GB50011-2010 and Eurocode 8, site class E in ASCE 7-10.
From figure 3.15 and 3.16, for earthquakes with 10% target risk of exceed in 50 years
and site conditions equivalent to both site class B and E in the ASCE code, the design
response spectrums show that the Eurocode 8 has a much larger spectral response
acceleration than that in the Chinese code.
From the comparisons of elastic design response spectrums among all three codes, it can
be seen that in the Chinese code GB50011-2010, the site condition only affects the
period, but not the maximum spectral response acceleration. While in both ASCE 7-10
and Eurocode 8, the different site conditions will result in different spectral response
acceleration. The spectral response acceleration in the Chinese code GB50011-2010 is
lower than that in ASCE 7-10 and Eurocode 8 in short period. However, with the
increase of period, the deduction in the Chinese code is slower which result in higher or
similar values for acceleration compared with ASCE 7-10 and Eurocode 8.
The elastic design response spectrums defined in Eurocode 8 end at 4s and it is
suggested in the Eurocode 8 that for structures with vibration periods longer than 4.0s,
the design response spectrums should be defined in combination with displacement
response spectrums. The similar limitation also appears in the Chinese code, which
suggests that for buildings with periods longer than 6s, a special study for the design
ground acceleration parameters is required. Since more and more buildings nowadays
have periods longer than 6s, the design criteria for the long-period structures under
earthquake effects need to be further studied.
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6
Spe
ctra
l Re
spo
nse
Acc
ele
rati
on
, g
Period, s
Design Response Spectrums*
GB50011-2010Eurocode 8
44
45
Chapter 4
4. Finite element analysis
4.1. Analysis model description
4.1.1. Global geometry
For a better understanding of the structural performance of the Tubed Mega Frame
structural system, an analysis using the finite element method is carried out in the
ETABS program.
The analysis model in ETABS is a 3-D finite element model of the building that was
described in the case study. The model has 157 occupied stories with a corresponding
structural height of 723m (total height 800m when including the pike), see figure 4.1.
The model is divided into 3 sections according to the variation of the geometry of the
structural plan. Section 1 ranges from base to story 39, with the geometry of each floor
plan varying linearly from 58m×58m to 42m×42m. Section 2 ranges from story 39 to
story 137 with the geometry of each floor plan remaining constant of 42m×42m. Section
3 ranges from story 137 to story 156 with the geometry of each floor plan varying
linearly from 42m×42m to 25m×25m.
The standard floor height is 4.5m. However, at certain perimeter wall floors, the floor
heights are different from the standard floor height in order to fulfill the requirements
for the floor functions as well as the structural performance. To be specific, the base
story is 5m high, story 17, 18, 57, 58, 97 and 98 have a floor height of 6m and story 35,
75 and 115 have a floor height of 2.3m.
CHAPTER 4. FINITE ELEMENT ANALYSIS METHOD
46
Figure 4.1 The global geometry of the model.
CHAPTER 4. FINITE ELEMENT ANALYSIS METHOD
47
4.1.2. Dimensions of tubes and perimeter walls
The building has eight mega hollow tubes at the perimeter as the main structural
components. The perimeter dimensions of the each tube vary from 8m×4m to 6m×4m in
section 1, remain constant as 6m×4m in section 2 and vary from 6m×4m to 2m×2m. The
thicknesses of the tubes vary from 1750mm at the bottom to 200mm at the top.
The thicknesses of perimeter walls vary from 1750mm at the bottom section to 200mm
at the top.
The floor slabs are uniformly 100mm thick.
4.1.3. Material
Both the vertical tubes and perimeter walls are using reinforced concrete as material.
The concrete is C100 with compression strength of 100MPa, elastic modulus 50GPa and
poisson’s ratio of 0.2.
The floor slabs are using concrete C30/37, with compression strength of 30MPa, elastic
modulus 27GPa and poisson’s ratio of 0.2.
The concrete has a weight density of 2400kg/m3.
4.1.4. Boundary conditions
The ‘Base’ as shown in figure 4.1 is defined as the top of the foundation plate. Because
the site location of this case study is not specified and the soil conditions are not
modeled or considered in this thesis, the boundary conditions of the model are set to be
hinges at the bottom of each tube to simulate the situation that the building rotates
together with the foundation plate.
4.1.5. Element types used in ETABS program
The tube walls and the perimeter walls in the ETABS model are using four-node
quadrilateral ‘’thick-shell’’ elements as defined in the ETABS program. The shell
elements that are used can have both membrane and plate-bending behaviors, which
means the shell elements have both in-plane and out-of-plane stiffness components as
well as plate rotational stiffness and a translational stiffness components in the direction
normal to the plane of the elements. The thick-shell formulation includes the effects of
transverse shearing deformations (Computers & Structures, Inc., 2013).
CHAPTER 4. FINITE ELEMENT ANALYSIS METHOD
48
Figure 4.2 Four-node quadrilateral shell element used in ETABS program (Computers & Structures, Inc., 2013).
The floor slabs in the model are using four-node quadrilateral ‘‘thin-shell’’ elements
which have the same behaviors as ‘’thick-shell’’ elements, but do not include the effects
of transverse shearing deformations.
The meshes of the wall elements are chosen to be 3 by 3 auto mesh in the ETABS
program. The meshes of the floor are meshed at the wall edges and according to the grid
lines with a maximum element size of 3000mm. Figure 4.3 shows the meshes of
structural elements.
Mesh of tube walls and perimeter walls
Mesh of floor
Figure 4.3 The meshes of tube walls, perimeter walls and floors in the ETABS program.
CHAPTER 4. FINITE ELEMENT ANALYSIS METHOD
49
4.1.6. Assumptions
Several assumptions are applied to the model in order to simplify the model as well as
reduce the calculation time. The model for the case study includes only the main load
bearing components, which means the model consists only of mega tubes, perimeter
walls and floors. Intermediate columns, and other secondary structural components and
non-structural components are not included in the model.
The concrete floor slabs typically have very high in-plane stiffness. Therefore they are
simplified as rigid diaphragms in the model. All constrained joints of each rigid
diaphragm move together and the diaphragms are rigid against membrane deformations,
yet not affect out-of-plane (plate) deformations. This simplification can results a
significant reduction in the size of the eigenvalue problem to be solved in the lateral
(horizontal) dynamic analysis of buildings (Computers & Structures, Inc., 2013).
According to the recommendation given in commentary chapter C27 in the ASCE 7-10
code, it is suggested that the method for wind loads calculation given in the code may be
inadequate for buildings with a height exceeding the limit or with low frequencies or
with unusual and irregular geometries. Usually, wind tunnel tests for those kinds of
buildings are recommended. However, the case study building in this thesis is only used
for feasibility study and at schematic design level. Therefore the wind loads calculations
for this case study building still follow the method provided in the ASCE 7-10 code.
4.2. Applied loads
The loads that are applied on the model so as for the model verification are determined
according to the ASCE 7-10 code with risk category III.
4.2.1. Dead loads
The dead loads applied on the model are determined by the ETABS program itself based
on the material properties.
The model also includes façade loads and installation loads. The façade loads are taken
as 3kN/m and the installation loads are taken as 0.8kN/m2. Those loads are considered
as ‘super dead’ loads in the ETABS program since the program separates them with
structural dead loads (columns, beams etc.).
4.2.2. Live loads
The live loads are determined according to chapter 4 in ASCE 7-10 code. Due to the
reason that the occupancy type of the case study building is not designed in this thesis,
CHAPTER 4. FINITE ELEMENT ANALYSIS METHOD
50
the value of live loads before reduction is set to be 2.4 kN/m2 (the larger value between
office occupancy and residential occupancy).
According to ASCE 7-10 chapter 4.7, the live loads on members which have a value of
is 37.16m2 or more are permitted to be designed for a reduction in accordance
with the following formula:
(
√ ) Eq. (4-1)
Where,
reduced design live load per m2 of area supported by the member
unreduced design live load per m2 of area supported by the member
live load element factor, see table 4.1 below
tributary area in m2
shall not be less than 0.50 for members supporting one floor and shall not be less
than 0.40 for members supporting two or more floors.
Table 4.1 Live Load Element Factor KLL (American Society of Civil Engineers, 2013).
Element Interior columns
4
Exterior columns without cantilever slabs 4 Edge columns with cantilever slabs
3
Corner columns with cantilever slabs
2
Edge beams without cantilever slabs
2
Interior beams
2
All other members not identified, including: Edge beams with cantilever slabs Cantilever beams One-way slabs Two-way slabs Members without provisions for continuous shear transfer normal to their span
1
In this case, the reduction of live loads are performed by ETABS program’s live load
reduction function according to the ASCE 7-10 code using attribute area method.
CHAPTER 4. FINITE ELEMENT ANALYSIS METHOD
51
4.2.3. Wind loads
Ultimate limit state wind loads There is a program-defined auto wind load pattern in the ETABS program according to
ASCE 7-10 code. However, in order to understand how the auto wind loads are applied
in the program as well as to understand the differences between the program-
determined loads and the loads that are calculated in accordance to the ASCE code, a
comparison of the wind loads for the case study building is performed.
The inputs for the wind loads calculation are listed in the table 4.2 below. The basic wind
speed is chosen from a site condition similar to southern China and the corresponding
basic wind speed is converted from Chinese code GB50001-2012 as illustrated in
chapter 3.3.4. The building width, depth as well as floor height for each floor is using the
same value as the model in ETABS.
Table 4.2 Input for wind load calculation according to ASCE 7-10 code.
Building Inputs
Total Height 800m Calculated Height 723m (Structure height)
Building Width Varies from 58m to 25m Building Depth
(Parallel to wind direction ) Varies from 58m to 25m
First Natural Period 8.35s (From ETABS
program) Damping Ratio 0.03
Floor Height Standard: 4.5m
Rest see chapter 4.1.1
Wind Speed Parameters
Basic Wind Speed (3sec average time interval)
42.3m/s (Used for ASCE code)
Basic Wind Pressure in Chinese Code
0.55kN/m2
Wind pressure calculation parameters
Exposure Category B Nominal height of
atmosphere boundary layer, zg
365.76m
Gust factor, Gf 0.88 Wind directionality factor,
Kd 1 (0.85 for load combination)
Topographic factor, Kzt 1 Enclosure classification Enclosed building
External pressure coefficients
Windward 0.8 Leeward -0.5 Side wall -0.7
Using the inputs listed in table 4.2, a hand calculation for wind loads is performed in
accordance to chapter 26 and 27 in the ASCE 7-10 code. The auto wind load forces which
CHAPTER 4. FINITE ELEMENT ANALYSIS METHOD
52
are applied in the ETABS program are extracted from the program. Figure 4.4 shows the
comparison of the two wind load forces.
Figure 4.4 Comparison between ETABS auto wind loads and hand-calculated wind loads.
The figure above shows that the result from hand calculation is little conservative than
the auto wind loads used in the ETABS program, but the load profiles along the whole
structure appear to be close. Notice that the peak and sag values in the figure are due to
the floor height differences, for those 6m or 2.3m high floors, the attribute areas for
wind loads for those floors are either larger or smaller than those for standard floors,
result in peak or sag values of wind loads in those floors. However, the overall difference
between the auto wind loads in the ETABS program and the hand calculated wind loads
is only 5.3%. Therefore, in this case study, the auto wind loads according to ASCE 7-10
code that are defined in the ETABS program are used to represent the wind actions on
the building.
Service limit state wind load In order to verify the top story acceleration of the building under service limit state, a
ten years reoccurrence wind speed is used for the service limit state wind loads
calculation. According to Chinese code GB50001-2012, the ten years reoccurrence basic
wind pressure for the same site location is 0.4kN/m2, as converted to ASCE wind speed
is 35.9m/s. The rest of parameters are the same as defined in the ultimate limit state
wind loads.
0
100
200
300
400
500
600
700
0 50 100 150 200 250 300 350 400 450 500 550 600 650 700 750 800
Win
d f
orc
e (
kN)
Height (m)
Comparison between ETABS Auto wind load and Hand-calcuated wind load
ETABS Auto wind load
Hand Calculated
CHAPTER 4. FINITE ELEMENT ANALYSIS METHOD
53
4.2.4. Earthquake
An earthquake load case is also considered in the ETABS analysis. The earthquake load
case is defined using ETABS program’s auto lateral load function in accordance to ASCE
7-10 code. The inputs that are used for analysis are showed in figure 4.5.
Figure 4.5 Earthquake load case inputs for the ETABS program.
4.2.5. Load combinations
The load combinations are defined according to ASCE 7-10 chapter 2.3. Table 4.3 lists
the load combinations considered for this case study.
Table 4.3 The load combinations.
Load combination 1. 1.4D 2. 1.2D+1.6L 3. 1.2D+(L or 0.5W) 4. 1.2D+1.0W+L 5. 1.2D+1.0E+L 6. 0.9D+1.0W 7. 0.9D+1.0E
Note: D = dead load, L = live load, W= wind load (ULS), E= earthquake load
For service limit state (SLS) analysis, the following load combination is used:
CHAPTER 4. FINITE ELEMENT ANALYSIS METHOD
54
D+0.5L+WSLS
Where, WSLS is the wind loads with 10-year return period basic wind speed instead of
50-year return period wind speed.
4.3. Linear Static analysis
4.3.1. Model verification
When completing the analysis model in the ETABS program, it is necessary to perform
model checks before the model is used for more complex and detailed analysis. The
model should be first studied and verified with linear static load cases to make sure the
model behaves properly as expected. In this case, the model checks are done by
compare the reactions obtained from the ETABS program and those from hand
calculations for several linear static load cases.
4.3.2. Overturning moments and base shear forces for lateral loads
In order to examine the influence of seismic actions and wind loads on structure design,
the overturning moments and base shear forces in the building are studied for the worst
case scenario of those lateral loads. The wind loads and earthquake inputs are the same
as stated in chapter 4.2. The risk category for earthquake is determined in accordance to
ASCE 7-10 as category III and the corresponding seismic design category is B.
4.3.3. Maximum deformations of the building
The maximum deformations of the building are examined for both ultimate limit state
and service limit state. For ultimate limit state, all load combinations are examined to
find out the largest deformation of the building on top story. For service limit state, only
the load combination for service limit state is examined with SLS wind loads in the
combination.
4.4. Non-Linear static analysis
4.4.1. P-delta
The P-delta effects are nonlinear geometric effects of large tensile or compressive
stresses upon transverse bending and shear behaviors (Computers & Structures, Inc.,
2013). When a building is subjected to both lateral and axial loads, an additional
moment by axial loads acting on the transverse displacement which caused by the
lateral loads will be generated. Therefore the P-delta effects are also called second order
effects of gravity. The additional moment from the transverse displacement varies non-
CHAPTER 4. FINITE ELEMENT ANALYSIS METHOD
55
linearly with the height of the building but depends on the deflected shape, and it has
effects on structure’s lateral stiffness and stability. Figure 4.6 illustrates the basic
concepts behind the P-delta effects.
Figure 4.6 Moment diagrams for cantilever beam example for P-delta effects (Computers & Structures, Inc., 2013).
For high and slender structures, the P-delta effects can be very significant and thus need
to be considered during the analysis and design process. The axial forces in the tall
buildings are compression force and the most concern occurs in the columns due to
gravity loads, including dead loads and live loads. The P-delta effects therefore make the
structure more flexible against lateral loads and reduce the stability of the structure.
In this case, in order to study the global stability of the structural system, only the P-
delta effects due to overall sway of the structure are considered. Using the
recommended analysis methods of initial P-delta load case for building structures in the
ETABS Analysis Reference (Computers & Structures, Inc., 2013), the P-delta load case is
defined by using factored dead loads and live loads. Here, the P-delta load case is
accounted for, conservatively, the load combination of 1.2 times the dead loads
(including façade and installation loads) and 1 times the live loads. As the load
CHAPTER 4. FINITE ELEMENT ANALYSIS METHOD
56
combinations for this model are described in chapter 4.2.5, this P-delta load case will
accurately account the effects for load combinations 3, 4 and 5, and conservatively
account the effects for load combinations 6 and 7. For load combinations 1 and 2, since
no lateral load cases are combined in those load combinations, the P-delta effects are
then not important for those load combinations.
After the P-delta load case is defined, all the linear static load cases and load
combinations listed previously are modified with the initial condition considering the P-
delta effects in the ETABS program and analyzed again. The results are compared with
those not considering the P-delta effects, to evaluate the influence of P-delta effects to
the building.
4.5. Dynamic analysis
4.5.1. Natural frequencies and periods
The natural frequencies and vibration modes can be determined by the ETABS modal
analysis function. The natural frequencies and modes are useful for a better
understanding of the behavior of the building and for evaluating the stiffness and
efficiency of the structure. Furthermore, the modal analysis results can be the basis for
other dynamic analysis such as response spectrum analysis and time-history analysis.
The modal analysis for the case study building is done by creating modal load case in the
ETABS program, figure 4.7 shows the inputs for the analysis. The modal case type is set
to be ‘Eigen’ which determines the undamped free-vibration modes and frequencies for
the system (Computers & Structures, Inc., 2013). The results from eigen modal analysis
are natural modes which provide a good in-sight into the behavior of the structure. Both
with and without initial P-delta conditions are considered separately for the modal cases.
CHAPTER 4. FINITE ELEMENT ANALYSIS METHOD
57
Figure 4.7 Modal case inputs in the ETABS program.
4.5.2. Design response spectrum analysis for seismic actions
The response spectrum is a concept that the responses of the building within a large
range of periods can be summarized in one graph. The design response spectrum for
seismic actions requires a given ground motion acceleration as well as the damping of
the system.
The design response spectrum for the prototype building is defined according to ASCE 7-
10 in the ETABS program, with the parameters determined in chapter 3.4.3 for site class
B. Figure 4.8 lists the parameters that are entered in the ETABS program.
CHAPTER 4. FINITE ELEMENT ANALYSIS METHOD
58
Figure 4.8 Parameters defined in the ETABS program.
Figure 4.9 shows the design response spectrum according to the parameters that are
listed in chapter 3.4.3.
Figure 4.9 Applied design response spectrum for the ETABS model.
The total responses of the structure are calculated using modal combinations in the
ETABS program, which means for a given direction of acceleration, in this case X-
direction, the maximum displacements, forces and stresses are computed throughout
the structure for each of the vibration modes. The modal values for a given response
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5
Spe
ctra
l Re
spo
nse
Acc
ele
rati
on
, g
Period, s
Design Response Spectrum, site class B
ASCE 7-10
CHAPTER 4. FINITE ELEMENT ANALYSIS METHOD
59
quantity are combined to produce a single, positive result for the given direction. From
the defined design response spectrum above, the largest ground acceleration happens
when the period is smaller than 1s. Therefore only consider the first ten vibration
modes for modal combinations may not be sufficient to yield the maximum responses of
the structure. Thus another modal case that will calculate the first 100 modes is
specially defined for the design response spectrum analysis to see how the number of
modes for modal combinations influences the response results.
4.5.3. Time-history analysis of wind loads in service limit state
High-rise buildings will vibrate under wind loads, if the acceleration of the vibration
exceeds the comfortable limit of human perception, the vibration will cause
uncomfortable feelings or even panic the residents inside the buildings. As the building
height keep increasing, the demands for a better and more comfortable working and
living condition in the building are also increasing. Therefore, the comfort level of
tenants in the building is a crucial criterion for wind load vibrations in service limit state.
A time-history analysis of wind loads under service limit state is performed to evaluate
the building’s maximum acceleration for the simulated wind loads. The basic wind speed
for the time-history simulating is taken from 10-year return period wind, as stated in
chapter 4.2.3. The simulation is done with the help of NatHaz (Nature Hazards) Online
Wind Simulator (Kwon & Kareem, 2006) developed by the University of Notre Dame in
Unite States (Chedid, 2013). Figure 4.10 shows the inputs to the simulator for story 157
as an example for illustration.
CHAPTER 4. FINITE ELEMENT ANALYSIS METHOD
60
Figure 4.10 NatHaz Online Wind Simulator input window.
The simulator however will only generate wind speed profile for a specified location. For
this case, the simulated locations are chosen as every ten stories, from story 157 to story
7, e.g. story 157, story 147, story 137, story 127 and so on. These stories are the
locations that the wind forces are applied. The attribute areas for each wind force are
taken into account for 5 stories above and 5 stories below the simulated location. The
corresponding wind loads are calculated with the simulated wind speeds according to
ASCE 7-10 code and are used as inputs for the ETABS program time-history function.
Notice that the wind speeds that are simulated from the NOWS do not consider the
correlation between windward and leeward directions, thus this effect is taken into
account when calculating the wind loads in hand-calculation. Figure 4.11 shows an
example of the simulated time-history wind speed profile for story 157.
CHAPTER 4. FINITE ELEMENT ANALYSIS METHOD
61
Figure 4.11 Simulated time-history wind speed profile.
The load, ( ), for time-history analysis in the ETABS program is defined as a finite sum
of spatial load vectors, , multiplied by the time functions, ( ), as:
( ) ∑ ( ) Eq. (4-2)
The program uses Load Patterns to represent the spatial load vectors. The time
functions can be arbitrary functions of time or periodic functions. In this case, the
simulated wind speed profiles are calculated and converted to the wind force time-
history profiles for each simulated floor. Then the variations of converted wind forces
against time are used to define the time functions, as ( ) in Eq. (4-2), in the ETABS
program for each applied floor. Figure 4.12 shows an example of the time function
defined in the ETABS program for story 157, represented by wind forces. The spatial
load vectors , in this case, are represented by concentrate loads in X-direction applied
on the center of every simulated story, e.g. every 10th story from top to bottom, with the
magnitude of 1 kN. Then in the time-history analysis load case, all the time functions and
corresponding loads are added together to get the overall responses of the structure.
Figure 4.13 shows the time-history analysis load cases defined in the ETABS program.
CHAPTER 4. FINITE ELEMENT ANALYSIS METHOD
62
Figure 4.12 Time-history function defined for story 157 in the ETABS program.
Figure 4.13 Defined load cases for wind loads time-history analysis in the ETABS program.
63
Chapter 5
5. Results and discussions
5.1. Linear static analysis results
5.1.1. Model verification results
The vertical control is done by hand calculating the mass of the model, see Appendix G,
and then compare with the reaction forces obtained from the ETABS program for dead
loads. Table 5.1 shows the comparison of the results.
Table 5.1 Model mass verification results for dead loads.
Hand
Calculation From ETABS
Program Difference
Total weight of the model
(MN) 3524 3549 0.7% OK
The overturning moments and base shear forces control are done with the linear static
wind loadsapplied on the model. Hand calculations for overturning moment and base
shear force are performed to compare with those obtained from the ETABS program for
the same load case. Table 5.2 shows the comparison of the results.
Table 5.2 Overturning moments and base shear forces verification for wind loads.
Hand
Calculation From ETABS
Program Difference
Overturning Moment (MN*m)
25445 25331 0.45% OK
Base shear force (MN)
69.44 69.12 0.46% OK
From the tables above, it can be seen that the differences are very small so that the
model behaves properly as expected.
CHAPTER 5. RESULTS AND DISCUSSIONS
64
5.1.2. Overturning moments, base shear forces and story drift ratios
Figure 5.1 shows the comparisons of overturning moments and base shear forces in the
building under lateral loads. From the figure, it shows that the building is taken more
lateral forces under earthquake actions than wind loads. Figure 5.2 shows the story drift
ratios of the building under service limit state. The story drift ratios are defined as the
differences of horizontal displacements between two consecutive stories divided by the
floor heights, as .
Figure 5.1 Overturning moments and base shear forces for lateral load cases.
Figure 5.2 Story drift ratios for service limit state wind loads.
CHAPTER 5. RESULTS AND DISCUSSIONS
65
According to the ASCE 7-10 code, the maximum story drift ratio is recommended to be
limited between 1/400 and 1/600 for service limit state verifications. Figure 5.2 shows
that the maximum story drift ratio of the prototype building exceeds the limit of 1/500
but doesn’t exceed the lower limit, which is 1/400.
5.1.3. Deformations
The maximum deformations of top occupied story (story 156) for different load cases
are listed in table 5.3.
Table 5.3 Maximum deformations of story 156 for different load cases and combinations.
Load Pattern Maximum
deformation (mm) Load case/combination Direction
Earthquake 1649.1 Earthquake, Y-direction Y Wind without P-delta 1316 Wind, Y-direction Y
Wind with P-delta 1420.3 Wind, Y-direction Y Load combination, with
Earthquake 1648.9 0.9D+E Y
Load combination, with Wind
1315.8 0.9D+W Y
The overall maximum deformation is obtained from earthquake load case in Y-direction.
The results from load combinations are very close to those from only lateral load cases.
Therefore it can be seen that the lateral forces, especially the earthquakes are governing
the design of this building, which also corresponds that the lateral forces are the most
critical loads for high-rise buildings
5.2. P-Delta effects
In order to identify the influence of P-delta effects to the structure, specific load cases
and parameters for an arbitrary location are studied and the results are listed in table
5.4.
Table 5.4 Comparisons of load cases for P-delta effects.
Load case
Location Parameter Without P-
delta With P-
delta Difference
%
Wind Story 40 Bottom
Moment in Y-direction MN*m
14704.7 MN*m
16045.75 MN*m
8.36%
Wind Story 40 Bottom
Shear force in X-direction MN
53.2 MN 56.36 MN 5.6%
Wind Story 40 Bottom
Maximum deformation in X-direction, mm
95.1 mm 100.9 mm 5.7%
Modal - Fundamental period, s 8.354 s 8.708 s 3.5%
CHAPTER 5. RESULTS AND DISCUSSIONS
66
Figure 5.3, 5.4, 5.5 show the overturning moments, base shear forces and deformations
of all stories for wind load cases both with and without P-delta effects.
Figure 5.3 Overturning moments for wind loads considering P-delta effects.
Figure 5.4 Base shear forces for wind loads considering P-delta effects.
CHAPTER 5. RESULTS AND DISCUSSIONS
67
Figure 5.5 Deformations for wind loads considering P-delta effects.
When considering P-delta effects in the analysis, the results are about 5-8% larger than
those without P-delta effects. As the height of the building increases, the effects of P-
delta are more severe. As it can be seen from this case, the P-delta effects give about
2000 MN*m rise in bending moment and around 3 MN rise in shear force, which can
make a lot of differences in design of the components. It also can be seen that if the P-
delta effects are not considered in the design of high-rise buildings, then the structure
systems can be almost 10% overstressed when subjected to lateral loads and thus may
lead to serious damage to the structural components.
5.3. Dynamic analysis results
5.3.1. Natural frequencies and periods
Table 5.5 shows the first ten natural frequencies, periods and vibration modes for the
prototype building, both with and without P-delta effects. Appendix A shows the first 8
vibration modes in figures.
CHAPTER 5. RESULTS AND DISCUSSIONS
68
Table 5.5 Modal analysis results.
Mode number
Vibration mode
Without P-delta effects With P-delta effects
Period (s) Frequency
(Hz) Period (s)
Frequency (Hz)
1 X-axis Bending 8.354 0.12 8.708 0.115 2 Y-axis Bending 8.348 0.12 8.701 0.115 3 Torsion 2.818 0.355 3.039 0.329
4 2nd X-axis Bending
2.619 0.382 2.655 0.377
5 2nd Y-axis Bending
2.61 0.383 2.646 0.378
6 3rd X-axis Bending
1.459 0.685 1.475 0.678
7 3rd Y-axis Bending
1.456 0.687 1.471 0.68
8 2nd Torsion 1.384 0.723 1.42 0.704
From the table it can be seen that the first natural frequency is 8.354s, due to the
geometric symmetry of building, the first and second natural frequencies are close.
Compare to other high-rise buildings in the world, the Shanghai Center has a
fundamental frequency of 9.05s while the total height is only 632m (Ding, Chao, Zhao, &
Wu, 2010); the Ping An Finance Center has a fundamental frequency of 8.65s (Yang, Fu,
& Huang, 2011) while the total height is 660m (structural height 588m). Even though
the analysis model in this case study is rough and contains many simplifications, the
results can still provide a preliminary idea that the Tubed Mega Frame structural system
has a relatively high stiffness.
When P-delta effects are considered, it can be also seen that the fundamental period of
the structure increases from 8.354s to 8.708s, which is approximately 3.5% larger. This
means that the stiffness of the structure is reduced by the P-delta effects.
5.3.2. Design response spectrum results
Figure 5.6 and figure 5.7 show the comparisons of base shear forces and overturning
moments from the design response spectrum load case for both situations: considering
only 10 vibration modes and 100 vibration modes for the modal combinations.
CHAPTER 5. RESULTS AND DISCUSSIONS
69
10 modes
100 modes
Figure 5.6 Base shear forces for design response spectrum load case.
10 modes
100 modes
Figure 5.7 Overturning moments for design response spectrum load case.
From the figures above it can be seen that with more modes included in the modal
combinations, the base shear force from the design response spectrum analysis is
increased from around 80MN to around 100MN, while the overturning moment is not
changed much.
Figure 5.8 shows the story drift ratios for the design response spectrum load case.
CHAPTER 5. RESULTS AND DISCUSSIONS
70
Figure 5.8 Story drift ratios for the design response spectrum load case.
From the story drift ratios figure, it can be seen that the building does not have any
particular weak stories at lower height. When above story 120, the story drift ratios
have a large increment which means the story stiffness decreases at those stories.
5.3.3. Time-history analysis results of SLS wind loads
Figure 5.9 show the base forces in the building according to the time-history load case in
the ETABS program.
Figure 5.9 Base forces according to the time-history load case in the ETABS program.
CHAPTER 5. RESULTS AND DISCUSSIONS
71
The story accelerations for service limit state wind loads are showed in figure 5.10.
Figure 5.10 Story accelerations.
The maximum story acceleration of the top story is only 0.011m/sec2, much smaller
than the allowed acceleration for comfort verification which is 0.15m/sec2 according to
Chinese Code for Tall Concrete Buildings JGJ3-2010 (Ministry of Housing and Urban-
Rural Development of China, 2010).
72
73
Chapter 6
6. Conclusions and proposed further research
6.1. Conclusions
The purpose of the thesis is to evaluate the global structural performance of the Tubed
Mega Frame structural system. The analysis of a high-rise building structural system is
complex. Especially in this case, since there are no buildings that been built with the
Tubed Mega Frame structural system. However, from the simplified prototype building
model, the analysis can provide a general idea of how the structural system behaves in
the global point of view and shows that the Tubed Mega Frame structural system is a
potential feasible and efficient structural system for high-rise buildings.
The thesis starts with the literature study of the high-rise building concepts and existing
structural systems, and then the lateral loads that are defined in different codes which
are usually critical to high-rise buildings were studied. Wind loads and design response
spectrums were calculated according to each code and compared. From the comparisons,
it can be seen that each code has its own character and each of them has its different
parameters that are used in the calculations as well as different safety philosophies for
the design.
The results from the ETABS analysis of the prototype building show that the structural
system has a relatively high stiffness comparing to similar existing high-rise buildings
and it also has a good structural stability. The P-delta effects have a significant influence
on the structure so that they cannot be neglected in the design process. By removing the
core and using the mega hollow tubes in the perimeter as the main load bearing
components, the structural system can sustain the lateral loads that are applied to the
building. These results ensure the structural form has the potential to be used in future
as the new high-rise building structural system. However, the analysis carried out in this
thesis is preliminary and is based on the limitations and assumptions stated in the
previous chapters.
6.2. Proposed further researches
Further research on this topic could be a study of the effects of material non-linearity on
the results of analysis. The main structural components in the Tubed Mega Frame are
made of concrete, thus the creep and shrinkage of the concrete can have significant
effects on the analysis results. Another suggestion could be a further study of structural
CHAPTER 6. CONCLUSIONS AND PROPOSED FURTHER RESEARCH
74
behaviors for more detailed seismic actions, since the seismic actions are usually the
most critical actions for the high-rise buildings.
REFERENCES
75
References
American Society of Civil Engineers. (2013). ASCE/SEI 7-10 Minimum Design Loads for
Buildings and Other Structures . American Society of Civil Engineers.
Chedid, R. (2013). Dynamic Response of Low Frequency Buildings to Along Wind Gust
Buffeting. Sweden: KTH Royal Institute of Technology.
Computers & Structures, Inc. (2013). CSI Analysis Reference Manual. California: CSI.
Computers and Structures, Inc. (2014). ETABS 2013 Version 13.1.4 Release Notes. CSI.
Council on Tall Buildings and Urban Habitat. (2013, September). CTBUH Height Criteria.
Retrieved June 3, 2014, from Hight to Architectural Top:
http://www.ctbuh.org/HighRiseInfo/TallestDatabase/Criteria/tabid/446/langu
age/en-US/Default.aspx
Council on Tall Buildings and Urban Habitat. (2014). CTBUH-The Skyscraper Center.
Retrieved May 2014, from Burj Khalifa:
http://skyscrapercenter.com/dubai/burj-khalifa/3/
Dahlin, T., & Yngvesson, M. (2014). Construction Methodology of Tubed Mega Frame
Structures in High-rise Buildings. Stockholm: KTH.
Ding, J., Chao, S., Zhao, X., & Wu, H. (2010). Critical issues of structural analysis for the
Shanghai Center project. Journal of Building Structures, 122-131.
European Committee for Standardization. (2004). Eurocode 8: Design of structures for
earthquake resistance-Part 1: General rules, seismic actions and rules for buildings.
European Committee for Standardization.
European Committee for Standardization. (2008). Eurocode 1: Actions on Structures -
Part 1-4: General actions - Wind actions. European Committee for Standardization.
Fall, N., & Hammar, V. (2014). Perimeter Wall Design in Tubed Mega Frame Buildings.
Stockholm: KTH.
Fan, X., Ma, C., & Su, B. (2013). Introduction and Comparison of Wind Load Codes for
Advanced Structure between Chinese, American and British. Advanced Materials
Research , 85-88.
GangLiu. (2012). Wind Load Analysis and Comparison Between Chinese Code and
American Standard. Steel Construction, 47-52.
Hu, Y. (2006). Origin, Development and Prospect of Super Tall Building. Building
Construction, 71-73.
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King, F., Severin, P., Salovaara, S., & Lundström, M. (2012). Articulated Funiculator and
the Tubed Mega Frame. Council on Tall Buildings and Urban Habitat: Shanghai (p.
563). Shanghai: CTBUH.
Kwon, D., & Kareem, A. (2006). NatHaz on-line wind simulator (NOWS) : simulation of
Gaussian multivariate wind fields. Univ. of Notre Dame.
Ministry of Housing and Urban-Rural Development of China. (2010). Code for Seismic
Design of Buildings. Beijing: China Architecture&Building Press.
Ministry of Housing and Urban-Rural Development of China. (2010). Technical
speicification for concrete structures of tall building. Beijing: China
Architecture&Building Press.
Ministry of Housing and Urban-Rural Development of China. (2012). Load code for the
design of building structures. Beijing: China Architecture&Building Press.
Reddy, J. (2005). An Introduction to the Finite Element Method.
Taranath, B. S. (2011). Structural Analysis and Design of Tall Buildings Steel and
Composite Construction. CRC Press.
Wood, A., & Oldfield, P. (2008). Global Trends of the High-rise Building Design. Council
on Tall Buildings and Urban Habitat (pp. 14-16). Council on Tall Buildings and
Urban Habitat.
Yang, X., Fu, X., & Huang, Y. (2011). Dynamic Elasto-Plastic Analysis of the Shenzhen
Ping'an Financial Center Tower. Journal of Building Structures, 40-49.
Yu ZhanShuzhong, Shen Jianwen, Liu ZhengShi. (2008). Discussing the Seismic Response
Spectrum of China from the Comparison of Seismic Codes of China, America and
Europe. Technology for Earthquake Disaster Prevention, 136-144.
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Financial Center Tower. Shanghai: Tongji University.
APPENDIX
77
Appendix
Appendix A: First 8 natural periods and corresponding vibration modes.
Mode 1, X-axis Bending, 8.354s
Mode 2, Y-axis Bending, 8.348s
Mode 3, First Torsion, 2.818s
Mode 4, 2nd X-axis Bending, 2.619s
APPENDIX
78
Mode 5, 2nd Y-axis Bending, 2.61s
Mode 6, 3rd X-axis Bending, 1.459s
Mode 7, 3rd Y-axis Bending, 1.456s
Mode 8, 2nd Torsion, 1.384s
Appendix BASCE wind load calculation
Appendix BWind loads calculation for main wind force-resisting system
according to ASCE 7-10:
General information
This wind loads calculation is carried out according to ASCE/SEI 7-10, Chapter 27
All units in this calculation are SI.
Inputs
h 800:= Building height, m, for gust factor calculation
z 800:= Building height, m, for wind loadscalculation
B 42:= Building width, m
L 42:= Building width parallel to the wind direction, m
hf 4.5:= Floor Height, m
V 1.42 29.8× 42.316=:= Basic wind speed, m/s
**Convert 10min time interval wind speedto 3sec time interval wind speed.
P 8.35:= Building natural period, s, from ETABS program
n11P
0.12=:= Building natural frequency:
β 0.03:= Damping ratio, percent of critical
expo 2:= Exposure category: (2=B, 3=C, 4=D)
zg 365.76 expo 2=if
274.32 expo 3=if
213.36 expo 4=if
365.76=:= Nominal height of the atmospheric boundart layer, m
α3 7.0 expo 2=if
9.5 expo 3=if
11.5 expo 4=if
7=:= 3-sec gust-speed power law exponent from Table 26.9-1
79
Appendix BASCE wind load calculation
Gust Effect Factor calculation, according to ASCE 7-10 chapter 26.9:
Constants listed in Table 26.9-1:
α14
expo 2=if
16.5
expo 3=if
19
expo 4=if
0.25=:= mean hourly wind-speed power law exponent in Eq. 26.9-16
b 0.45 expo 2=if
0.65 expo 3=if
0.80 expo 4=if
0.45=:= mean hourly wind speed factor in Eq. 26-16
c 0.3 expo 2=if
0.2 expo 3=if
0.15 expo 4=if
0.3=:=turbulence intensity factor in Eq. 26.9-7
zmin 9.14 expo 2=if
4.57 expo 3=if
2.13 expo 4=if
9.14=:= minimum height
l 97.54 expo 2=if
152.4 expo 3=if
198.12 expo 4=if
97.54=:= integral length scale factor
ε13
expo 2=if
15
expo 3=if
18
expo 4=if
0.333=:= integral length scale power law exponent in Eq. 26.9-9
80
Appendix BASCE wind load calculation
For Flexible or Dynamically Sensitive Structures.
zeq zmin 0.6 h× zmin£if
0.6 h× 0.6 h× zmin>if
480=:= Eguivalent height, m
gQ 3.4:= peak factor for background responce in E.q 26.9-6 and 26.9-10
gv 3.4:= peak factor for wind responce in E.q 26.9-6 and 26.9-10
Lz lzeq10
æçè
ö÷ø
ε
× 354.484=:= (26.9-9)
Q1
1 0.63B h+
Lz
æçè
ö÷ø
0.63×+
0.692=:=(26.9-8)
Iz c10zeq
æçè
ö÷ø
1
6× 0.157=:= (26.9-7)
According to Section 26.9.5 Eq. 26.9-16:
Vz bzeq10
æçè
ö÷ø
α
× V× 50.122=:= mean hourly wind speed at height z
ηh 4.6 n1×h
Vz×:= ηB 4.6 n1×
BVz×:= ηL 15.4 n1×
LVz×:=
Rh 1 ηh 0£if
1ηh
1
2 ηh2
×1 e
2- ηh×-
æè
öø×- ηh 0>if
0.107=:= (26.9-15a&b)
RB 1 ηB 0£if
1ηB
1
2 ηB2
×1 e
2- ηB×-
æè
öø×- ηB 0>if
0.752=:= (26.9-15a&b)
RL 1 ηL 0£if
1ηL
1
2 ηL2
×1 e
2- ηL×-
æè
öø×- ηL 0>if
0.447=:=
(26.9-15a&b)
81
Appendix BASCE wind load calculation
N1 n1LzVz× 0.847=:= (26.9-14)
Rn7.47 N1×
1 10.3 N1×+( )5
3
0.143=:= (26.9-13)
Resonant response factor:
R1β
Rn× Rh× RB× 0.53 0.47 RL×+( )× 0.533=:= (26.9-12)
gR 2 ln 3600 n1×( )×0.577
2 ln 3600 n1×( )×+ 3.649=:= (26.9-11)
Gust factor for Flexible or Dynamically Sensitive Structures:
Gf 0.9251 1.7 Iz× gQ
2 Q2× gR
2 R2×+×+
1 1.7 gv× Iz×+
æççè
ö÷÷ø
× 0.88=:= (26.9-10)
82
Appendix BASCE wind load calculation
Determine wind load parameters
Table 26.6-1. Only used for loadcombinationWind directionality factor: Kd 0.85:=
Topographic fac tor: Kzt 1.0:= Figure 26.8-1
Enclosure classification: Enclosed Building Section 26.10
Internal pressure coefficient: GCpip 0.18:= Positive Table 26.11-1
GCpin 0.18-:= Negative
Determine velocity pressure exposure coefficient, K i
N floorz
hf2
-
hf
æçççè
ö÷÷÷ø
177=:= i 0 N..:= Number of floor centers
zi
hf2
i hf×+æçè
ö÷ø
...=:= Elevation of each floor center
Ki 2.014.6zg
æçè
ö÷ø
2
α3×
éêêêë
ùúúúû
zi 4.6<if
2.01zi
zg
æççè
ö÷÷ø
2
α3
×
éêêêêë
ùúúúúû
4.6 zi£ zg£if
2.01zgzg
æçè
ö÷ø
2
α3
×
éêêêë
ùúúúû
zi zg>if
:=
83
Appendix BASCE wind load calculation
0.5 1 1.5 2 2.50
200
400
600
800
Velocity Pressure Exposure Coefficients
Velocity pressure exposure coefficients
Hei
ght,
m
zi
Ki
Determine velocity pressure
From Eq 27.3-1
qi 0.613 Ki× Kzt× V2× ...=:= qcomi
0.613 Ki× Kzt× Kd× V2× ...=:=
500 1 103´ 1.5 103´ 2 103´ 2.5 103´0
200
400
600
800Velocity Pressure (N/m^2)
Velocity Pressure, N/m^2
Hei
ght,m
zi
qi
84
Appendix BASCE wind load calculation
Determine external pressure coefficient
X direction:
Wall Pressure Coefficients, Cp
Windward wall: Cpww 0.8:=
Leeward wall: Cplw 0.5- 0LB
£ 1£if
"Need Interpolation" 1LB
< 4<if
0.2-LB
4³if
0.5-=:=
Side wall: Cpsw 0.7-:=
Due to symmetry, Y direction have sam e values for Cp as X direction
85
Appendix BASCE wind load calculation
Calculated wind pressure, p, on each buildng surface
X direction, Walls
Windward:
pwwi qi Gf× Cpww× qi GCpin( )×- ...=:=
500 1 103´ 1.5 103´ 2 103´0
200
400
600
800
Wind Pressure--X, Windward, N/m2
Hei
ght,
m
zi
pwwi
Leeward:
plwi qi Gf× Cplw× qi GCpip( )×-:=
1.4- 103´ 1- 103´ 600- 200-0
200
400
600
800Wind Pressure--X, Leeward (N/m2)
Wind Pressure--X, Leeward, N/m2
Hei
ght,
m
zi
plwi
86
Appendix BASCE wind load calculation
Sidewall:
pswi qi Gf× Cpsw× qi GCpip( )×- ...=:=
2- 103´ 1.5- 103´ 1- 103´ 500-0
200
400
600
800Wind Pressure--X, Side wall (N/m2)
Wind Pressure--X, Side wall, N/m2
Hei
ght,
m
zi
pswi
87
Appendix BASCE wind load calculation
When considering torsion in load cases, according to Figure 27.4-8
Torsional Case 1: Three quarters of the design wind pressure acting on the projectedarea perpendicular to each principal axis of the structure in conjunction with a torsionalmoment, consider separately for each principal axis
Torsional Moment:
ex 0.15B:= ey 0.15L:=
Mi 0.75 pwwi plwi+( )× B× ex× ...=:=
2 104´ 6 104´ 1 105´0
200
400
600
800
Torsional Moment, N*m
Hei
ght,
m
zi
Mi
Torsional Case 2: Wind loading considered to act simultaneously at 75% of the specified value
Torsional Moment:
Mi 0.563 pwwi plwi+( )× B× ex× 0.563 pwwi plwi+( )× L× ey×+ ...=:=
0 1 105´ 2 105´0
200
400
600
800
Torsional Moment, N*m
Hei
ght,
m
zi
Mi
88
Appendix CEurocode wind load calculation
Appendix CWind loads calculation for main wind force-resisting system
according to EN 1991-1-4 2005:
General information
This wind loads calculation is carried out according to EN 1991-1, Part 1-4
Definition of ''Foundamental basic wind velocity'': The 10 minute mean wind velocity with anannual risk of being exceeded of 0.02, irrespective of wind direction, at height of 10m above flatopen country terrain and accounting for altitude effect (if required)
Inputs
Building height, m, for wind loadscalculationh 800:=
b 42:= Building width, m
d 42:= Building width parallel to the wind direction, m
hf 4.5:= Floor Height, m
V 29.8:= Basic wind speed, m/s
P 8.35:= Building natural period, s, from ETABS program
n11P
0.12=:= Building natural frequency:
β 0.03:= Damping ratio, percent of critical
TC 4:= Terrain category: (0, I, II, III, IV)
N floorh
hf2
-
hf
æçççè
ö÷÷÷ø
177=:= i 0 N..:= Number of floors:
p 0.02:= Annual exceedence probability,p
89
Appendix CEurocode wind load calculation
Basic values
Direction factor, c.dir cdir 1.0:=
NOTE: may be given in National Annex, here the recom mended value 1.0 is used.
Season factor, cseason cseason 1.0:=
NOTE: may be given in National Annex, here the recom mended value 1.0 is used.
Basic wind velocity, vb
vb cdir cseason× V× 29.8=:= (Eq 4.1)
The probability for annual exceedence, cprob
K 0.2:= n 0.5:=
cprob1 K ln ln 1 p-( )-( )×-
1 K ln ln 0.98( )-( )×-æçè
ö÷ø
n1=:= (Eq 4.2)
Mean wind--variation with height
Roughness length z0 and minimum height zmin
z0 0.003 TC 0=if
0.01 TC 1=if
0.05 TC 2=if
0.3 TC 3=if
1.0 TC 4=if
1=:= zmin 1 TC 0=if
1 TC 1=if
2 TC 2=if
5 TC 3=if
10 TC 4=if
10=:=
(Table 4.1)
zmax 200:=
z0.II 0.05:= Terrain categoty II
Terrain factor kr
kr 0.19z0
z0.II
æçè
ö÷ø
0.07
× 0.234=:= (Eq 4.5)
90
Appendix CEurocode wind load calculation
Terrain roughness factor, crz
zi
hf2
i hf×+æçè
ö÷ø
...=:=
crzikr ln
zminz0
æçè
ö÷ø
×æçè
ö÷ø
zi zmin£if
kr lnzi
z0
æççè
ö÷÷ø
×æççè
ö÷÷ø
zmin zi< zmax<if
kr lnzmax
z0
æçè
ö÷ø
×æçè
ö÷ø
zi zmax³if
:= (Eq 4.4)
zi
2.256.75
11.25
15.75
20.25
24.75
...
= crzi
0.540.54
0.567
0.646
0.705
0.752
...
=
Orography factor, co co 1.0:=
The mean wind velocity, vm, at height z
vmicrzi
co× vb× ...=:= (Eq 4.3)
10 20 30 400
200
400
600
800Mean wind speed variation with height
Mean wind speed, m/s
Hei
ght,
m
zi
vmi
91
Appendix CEurocode wind load calculation
Wind turbulence
The turbulence factor, k l kl 1.0:= (Recomended value)
The turbulence intensity, Iv
Ivi
kl
co lnzminz0
æçè
ö÷ø
×
zi zmin£if
kl
co lnzi
z0
æççè
ö÷÷ø
×
zmin zi< zmax<if
kl
co lnzmax
z0
æçè
ö÷ø
×
zi zmax³if
:= (Eq 4.7)
Peak velocity pressure
Air density, ρ ρ 1.25:= (Recommended value,kg/m 3)
Peak velocity pressure, qp
qpi1 7 Ivi
×+æè
öø
12× ρ× vmi
æè
öø
2× ...=:= (Eq 4.8)
500 1 103´ 1.5 103´ 2 103´0
200
400
600
800
Peak velocity pressure, N/m2
Hei
ght,
m
zi
qpi
92
Appendix CEurocode wind load calculation
qb 0.5 ρ× vb2
× 555.025=:= (Eq 4.10)
cei
qpi
qb...=:= (Eq 4.9)
1 2 3 40
200
400
600
800
Exposure Factor Ce
Hei
ght,
m
zi
cei
Structural factor, cscd
Reference height, zs zs 0.6 h× 480=:= Figure 6.1
Wind trubulence
Reference length scale, Lt Lt 300:=
Reference height, zt zt 200:=
Factor, α α 0.67 0.05 ln z0( )×+ 0.67=:=
The turbulence length scale, Lz
LziLt
zminzt
æçè
ö÷ø
α
× zi zmin£if
Ltzi
zt
æççè
ö÷÷ø
α
× zmin zi< zt<if
Ltztzt
æçè
ö÷ø
α
× zi zt³if
...=:= (Eq B.1)
93
Appendix CEurocode wind load calculation
The non-dimensional frequency, fL
fLi
n1 Lzi×
vmi
...=:=
The wind distribution over frequency is expressed by the non-dimensional powerspectral density function SL
SLi
6.8 fLi×
1 10.2 fLi×+æ
èöø
5
3
...=:= (Eq B.2)
0.1 10.12
0.14
0.16
0.18
0.2
SLi
fLi
Structural factor (Parameters in Eq 6.1)
Background factor, B2
B1
1 0.9b h+
max Lz( )æçè
ö÷ø
0.63×+
0.606=:= (Eq B.3)
B( )2 0.367=
The aerodynamic admittance, Rh and Rb
ηh4.6 h×
max Lz( )max fL( )× 11.912=:=
ηb4.6 b×
max Lz( )max fL( )× 0.625=:=
94
Appendix CEurocode wind load calculation
Rh1ηh
1
2 ηh2
×1 e
2- ηh×-
æè
öø×- 0.08=:= (Eq B.7)
Rb1ηb
1
2 ηb2
×1 e
2- ηb×-
æè
öø×- 0.687=:= (Eq B.8)
The resonance response factor, R2
Rπ2
2 β×min SL( )× Rh× Rb× 1.058=:= (Eq B.6)
R2 1.118=
The up-crossing frequency, v
v n1R2
B2 R2+
× 0.104=:= (Eq B.5)
The peak factor, kp (Eq B.4)
The averaging time for the mean wind velocity, s T 600:=
kp 2 ln v T×( )×0.6
2 ln v T×( )×+æ
çè
ö÷ø
2 ln v T×( )×0.6
2 ln v T×( )×+ 3³if
3 2 ln v T×( )×0.6
2 ln v T×( )×+ 3<if
3.084=:=
Structural factor, cscd
The size factor, cs
cs1 7 min Iv( )× B2
×+
1 7 min Iv( )×+0.776=:= (Eq 6.2)
The dynamic factor, cd
cd1 2 kp× min Iv( )× B2 R2
+×+
1 7 min Iv( )× B2×+
1.343=:= (Eq 6.3)
The structural factor
cs cd× 1.042=
95
Appendix CEurocode wind load calculation
Pressure coefficients for buildings
Vertical walls of rectangular plan bui ldings
According to figure 7.4, the following case will be used.
Choose hstrip= floor height
hstrip 4.5:=
External pressure coefficients for vertical walls of rectangular plan buildings
hd
19.048= (Figure 7.5)
eb b b 2 h×£if
2 h× otherwise
42=:=
KEY "e<d" eb d<if
"e>=d" 5 d× eb> d³if
"e>=5d" eb 5 d׳if
:=
KEY "e>=d"=
96
Appendix CEurocode wind load calculation
ebd
1=
cpeA 1.2-:= cpeB 0.8-:= cpeD 0.8:= cpeE 0.7-:= (Table 7.1)
97
Appendix CEurocode wind load calculation
Wind Pressure on surfaces
Windward
wewiqp9
cpeD× zi b£if
qpicpeD×æ
èöø
b zi< h b-£if
qp177cpeD× h b- zi< 800£if
...=:= (Eq 5.1)
800 1 103´ 1.2 103´ 1.4 103´ 1.6 103´0
200
400
600
800
Windward wind pressure, N/m2
Hei
ght,
m
zi
wewi
Leeward
weliqp9
cpeE× zi b£if
qpicpeE×æ
èöø
b zi< h b-£if
qp177cpeE× h b- zi< 800£if
...=:= (Eq 5.1)
1.4- 103´ 1.2- 103´ 1- 103´ 800-0
200
400
600
800
Leeward wind pressure, N/m2
Hei
ght,
m
zi
weli
98
Appendix CEurocode wind load calculation
Sidewalls
wesAiqp9
cpeA× zi b£if
qpicpeA×æ
èöø
b zi< h b-£if
qp177cpeA× h b- zi< 800£if
...=:= (Eq 5.1)
2.4- 103´ 2- 103´ 1.6- 103´0
200
400
600
800
Sidewall (Zone A) wind pressure, N/m2
Hei
ght,
m
zi
wesAi
wesBiqp9
cpeB× zi b£if
qpicpeB×æ
èöø
b zi< h b-£if
qp177cpeB× h b- zi< 800£if
...=:= (Eq 5.1)
1.6- 103´ 1.4- 103´ 1.2- 103´ 1- 103´ 800-0
200
400
600
800
Sidewall (Zone B) wind pressure, N/m2
Hei
ght,
m
zi
wesBi
99
Appendix CEurocode wind load calculation
Wind Forces
Windward
Fwics cd× wew9
× b× hstrip×æè
öø
zi b£if
cs cd× wewi× hstrip× b×æ
èöø
b zi< h b-£if
cs cd× wew177× b× hstrip×æ
èöø
h b- zi<if
...=:= (Eq 5.5)
1.5 105´ 2 105´ 2.5 105´ 3 105´ 3.5 105´0
200
400
600
800
Windward wind force, N
Hei
ght,
m
zi
Fwi
Leeward
Flics cd× wel9
× b× hstrip×æè
öø
zi b£if
cs cd× weli× hstrip× b×æ
èöø
b zi< h b-£if
cs cd× wel177× b× hstrip×æ
èöø
h b- zi<if
...=:= (Eq 5.5)
100
Appendix CEurocode wind load calculation
3- 105´ 2.5- 105´ 2- 105´ 1.5- 105´0
200
400
600
800
Leeward wind force, N
Hei
ght,
m
zi
Fli
Sidewalls
FsAics cd× wesA9
×e5× hstrip×æç
èö÷ø
zi b£if
cs cd× wesAi× hstrip×
e5×æç
èö÷ø
b zi< h b-£if
cs cd× wesA177× hstrip×
e5×æç
èö÷ø
h b- zi<if
...=:= (Eq 5.5)
7- 103´ 6- 103´ 5- 103´ 4- 103´ 3- 103´0
200
400
600
800
Sidewall (Zone A) wind force, N
Hei
ght,
m
zi
FsAi
FsBics cd× wesB9
× de5
-æçè
ö÷ø
× hstrip×éêë
ùúû
zi b£if
cs cd× wesBi× hstrip× d
e5
-æçè
ö÷ø
×éêë
ùúû
b zi< h b-£if
cs cd× wesB177× hstrip× d
e5
-æçè
ö÷ø
×éêë
ùúû
h b- zi<if
...=:= (Eq 5.5)
101
Appendix CEurocode wind load calculation
3.5- 105´ 2.5- 105´ 1.5- 105´0
200
400
600
800
Sidewall (Zone B) wind force, N
Hei
ght,
m
zi
FsBi
Asymmetric and counteracting pressures and forces
The torsional moment on windward wall
MTi
12
wew9× hstrip× b×
b3×æç
èö÷ø
zi b£if
12
wewi× hstrip× b×
b3×æç
èö÷ø
b zi< h b-£if
12
wew177× b× hstrip×
b3×æç
èö÷ø
h b- zi<if
...=:=
102
Appendix CEurocode wind load calculation
1.2 106´ 1.6 106´ 2 106´0
200
400
600
800
Torsional Moment, N*m
Hei
ght,
m
zi
MTi
103
Appendix DChina code wind load calculation
Appendix D:Wind loads calculation for main wind force-resisting system
according to GB50009-2012
General information
This wind loads calculation is carried out according to GB50009-2012.
All units in this calculation are SI.
Inputs
z 800:= Building height, m, for wind loadscalculation
B 42:= Building width, m
L 42:= Building width parallel to the wind direction, m
hf 4.5:= Floor Height, m
v0 29.8:= Basic wind speed, m/s
w012
0.00125× e 0.0001- 100×× v0
2× 0.55=:= Basic wind pressure (kN/m2): (Eq. E.2.4-1)
P 8.35:= Building natural period, s, from ETABS program
n11P
0.12=:= Building natural frequency:
ζ 0.03:= Damping ratio, percent of critical
Ground 3:= Ground roughness category: (1=A, 2=B, 3=C, 4=D)
N floorz
hf2
-
hf
æçççè
ö÷÷÷ø
177=:= Number of floors: i 0 N..:=
z2i
hf2
i hf×+æçè
ö÷ø
...=:= Height of each floor center above ground
105
Appendix DChina code wind load calculation
Determine factor for wind pressure variation with height, μz
According to GB50003-2012, Chapter 8.2.1
Method 1: Use table determined values, from table 8.2.1:
z1
5
10
15
20
30
40
50
60
70
80
90
100
150
200
250
300
350
400
450
500
550
800
æççççççççççççççççççççççççççççè
ö÷÷÷÷÷÷÷÷÷÷÷÷÷÷÷÷÷÷÷÷÷÷÷÷÷÷÷÷ø
:= μza
1.09
1.28
1.42
1.52
1.67
1.79
1.89
1.97
2.05
2.12
2.18
2.23
2.46
2.64
2.78
2.91
2.91
2.91
2.91
2.91
2.91
2.91
æççççççççççççççççççççççççççççè
ö÷÷÷÷÷÷÷÷÷÷÷÷÷÷÷÷÷÷÷÷÷÷÷÷÷÷÷÷ø
:= μzb
1.00
1.00
1.13
1.23
1.39
1.52
1.62
1.71
1.79
1.87
1.93
2.00
2.25
2.46
2.63
2.77
2.91
2.91
2.91
2.91
2.91
2.91
æççççççççççççççççççççççççççççè
ö÷÷÷÷÷÷÷÷÷÷÷÷÷÷÷÷÷÷÷÷÷÷÷÷÷÷÷÷ø
:= μzc
0.65
0.65
0.65
0.74
0.88
1.00
1.10
1.20
1.28
1.36
1.43
1.50
1.79
2.03
2.24
2.43
2.60
2.76
2.91
2.91
2.91
2.91
æççççççççççççççççççççççççççççè
ö÷÷÷÷÷÷÷÷÷÷÷÷÷÷÷÷÷÷÷÷÷÷÷÷÷÷÷÷ø
:= μzd
0.51
0.51
0.51
0.51
0.51
0.60
0.69
0.77
0.84
0.91
0.98
1.04
1.33
1.58
1.81
2.02
2.22
2.40
2.58
2.74
2.91
2.91
æççççççççççççççççççççççççççççè
ö÷÷÷÷÷÷÷÷÷÷÷÷÷÷÷÷÷÷÷÷÷÷÷÷÷÷÷÷ø
:=
μz μza Ground 1=if
μzb Ground 2=if
μzc Ground 3=if
μzd Ground 4=if
:=
106
Appendix DChina code wind load calculation
0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5 2.75 30
100200300400500600700800
Factor for wind pressure variation with height
Hei
ght,
mz1
μz
Method 2: Use formula determined values, from comment chapter 8.2.1 of GB50009-2012:
α 1.284 Ground 1=if
1.000 Ground 2=if
0.544 Ground 3=if
0.262 Ground 4=if
:= β 0.24 Ground 1=if
0.30 Ground 2=if
0.44 Ground 3=if
0.60 Ground 4=if
:= γ 5 Ground 1=if
10 Ground 2=if
15 Ground 3=if
30 Ground 4=if
15=:=
η 1.09 Ground 1=if
1.00 Ground 2=if
0.65 Ground 3=if
0.51 Ground 4=if
:= λ 300 Ground 1=if
350 Ground 2=if
450 Ground 3=if
550 Ground 4=if
450=:=
μi η z2iγ<if
αz2i
10
æçè
ö÷ø
β
×
éêêë
ùúúû
γ z2i£ λ£if
αλ10
æçè
ö÷ø
β×
éêë
ùúû
z2iλ>if
:=
μi
0.650.65
0.65
0.664
0.742
...
=
107
Appendix DChina code wind load calculation
0 1 2 30
100200300400500600700800
Factor for wind pressure variation with heightH
eigh
t,m
z2i
μi
Determine shape factor of wind loads, μs
According to GB50003-2012, Table 8.3.1
Walls
Windward μs1 0.80:=
Leeward μs2 0.5-:=
Side Wall μs3 0.7-:=
Determine along-wind vibration and dynamic response factor, βz
peak factor g 2.5:=
turbulance coefficient at 10m height, I10
I10 0.12 Ground 1=if
0.14 Ground 2=if
0.23 Ground 3=if
0.39 Ground 4=if
0.23=:=
Resonance factor, R:
ground roughness correction coefficient, kw
kw 1.28 Ground 1=if
1.0 Ground 2=if
0.54 Ground 3=if
0.26 Ground 4=if
0.54=:=
108
Appendix DChina code wind load calculation
x130 n1×
kw w0×6.596=:= (Eq. 8.4.4-2)
Rπ
6 ζ×
x12
1 x12
+æè
öø
4
3
× 2.194=:= (Eq. 8.4.4-1)
Background factor, Bz:
horizontal coefficient ρx
ρx10 B 50 e
B-
50×+ 50-×
B0.878=:= (Eq. 8.4.6-2)
veritical coefficient ρz
ρz10 z 60 e
z-
60×+ 60-×
z0.34=:= (Eq. 8.4.6-1)
coefficient k,a1
k 0.944 Ground 1=if
0.670 Ground 2=if
0.295 Ground 3=if
0.112 Ground 4=if
0.295=:= (Table 8.4.5-1)
a1 0.155 Ground 1=if
0.187 Ground 2=if
0.261 Ground 3=if
0.346 Ground 4=if
0.261=:= (Table 8.4.5-1)
vibration coefficient for the first virbration mode (Table G.0.3)
ϕzi
6 z2iæè
öø
2× z2
× 4 z2iæè
öø
3× z×- z2i
æè
öø
4+
3 z4×
...=:= (Commentary chapter 8.4.7)
109
Appendix DChina code wind load calculation
background factor, Bz
Bzik z
a1× ρx× ρz×
ϕzi
max μz( )× ...=:= (Eq. 8.4.5)
Along-wind vibration and dynamic response factor, βz
βzi1 2 g× I10× Bzi
× 1 R2+×+ ...=:= (Eq. 8.4.3)
Determine the characteristic value wind pressure, wk (kN/m2)
Walls
Windward
wk1iβzi
μi× μs1× w0× ...=:= (Eq. 8.1.1-1)
0.2 0.38 0.56 0.74 0.92 1.1 1.28 1.46 1.64 1.82 20
100200300400500600700800
Characteristic value of windward wind pressure, kN/m2
Hei
ght,
m
z2
wk1
Leeward walls
wk2iβzi
μi× μs2× w0× ...=:= (Eq. 8.1.1-1)
1.2- 1.08- 0.96- 0.84- 0.72- 0.6- 0.48- 0.36- 0.24- 0.12- 00
100200300400500600700800
Characteristic value of leeward wind pressure, kN/m2
Hei
ght,
m
z2
wk2
110
Appendix DChina code wind load calculation
Side walls
wk3iβzi
μi× μs3× w0× ...=:= (Eq. 8.1.1-1)
1.8- 1.64- 1.48- 1.32- 1.16- 1- 0.84- 0.68- 0.52- 0.36- 0.2-0
100
200
300
400
500
600
700
800
Characteristic value of side wall wind pressure, kN/m2
Hei
ght,
m
z2
wk3
111
Appendix EGust factor variation with height
Appendix E:Gust Factor Variation with Height
All calculation is carried out according to ASCE/SEI 7-10, all units are in SI (m,s,Hz)
General information
h 0 800..:= Building height, m, for gust factor calculation
B 42:= Building width, m
L 42:= Building width parallel to the wind direction, m
hf 4.5:= Floor Height, m
V 1.42 29.8× 42.316=:= Basic wind speed, m/s
**Convert 10min time interval wind speedto 3sec time interval wind speed.
P 8.68:= Building natural period, s, from ETABS program
n11P
0.115=:= Building natural frequency:
β 0.03:= Damping ratio, percent of critical
expo 2:= Exposure category: (2=B, 3=C, 4=D)
Constants listed in Table 26.9-1:
α14
expo 2=if
16.5
expo 3=if
19
expo 4=if
0.25=:= mean hourly wind-speed power law exponent in Eq. 26.9-16
b 0.45 expo 2=if
0.65 expo 3=if
0.80 expo 4=if
0.45=:= mean hourly wind speed factor in Eq. 26-16
c 0.3 expo 2=if
0.2 expo 3=if
0.15 expo 4=if
0.3=:=turbulence intensity factor in Eq. 26.9-7
113
Appendix EGust factor variation with height
zmin 9.14 expo 2=if
4.57 expo 3=if
2.13 expo 4=if
9.14=:= minimum height
l 97.54 expo 2=if
152.4 expo 3=if
198.12 expo 4=if
97.54=:= integral length scale factor
ε13
expo 2=if
15
expo 3=if
18
expo 4=if
0.333=:= integral length scale power law exponent in Eq. 26.9-9
Flexible or Dynamically Sensitive Structures.
Eguivalent height: zh zmin 0.6 h× zmin£if
0.6 h× 0.6 h× zmin>if
...=:=
gQ 3.4:= peak factor for background responce in E.q 26.9-6 and 26.9-10
gv 3.4:= peak factor for wind responce in E.q 26.9-6 and 26.9-10
Lzhl
zh
10
æçè
ö÷ø
ε
× ...=:= (26.9-9)
Qh1
1 0.63B h+Lzh
æçè
ö÷ø
0.63×+
...=:=(26.9-8)
(26.9-7)Izh
c10zh
æçè
ö÷ø
1
6× ...=:=
114
Appendix EGust factor variation with height
According to Section 26.9.5 Eq. 26.9-16:
Vzhb
zh
10
æçè
ö÷ø
α
× V× ...=:= mean hourly wind speed at height z
ηhh4.6 n1×
hVzh
×:= ηBh4.6 n1×
BVzh
×:= ηLh15.4 n1×
LVzh
×:=
Rhh1 ηhh
0£if
1ηhh
1
2 ηhhæè
öø
2×
1 e2- ηhh×
-æçè
ö÷ø×- ηhh0>if
...=:= (26.9-15a&b)
RBh1 ηBh
0£if
1ηBh
1
2 ηBhæè
öø
2×
1 e2- ηBh×
-æçè
ö÷ø×- ηBh0>if
...=:= (26.9-15a&b)
RLh1 ηLh
0£if
1ηLh
1
2 ηLhæè
öø
2×
1 e2- ηLh×
-æçè
ö÷ø×- ηLh0>if
...=:=
(26.9-15a&b)
N1hn1
Lzh
Vzh
× ...=:=(26.9-14)
Rnh
7.47 N1h×
1 10.3 N1h×+æ
èöø
5
3
...=:= (26.9-13)
Resonant response factor:
Rh1β
Rnh× Rhh
× RBh× 0.53 0.47 RLh
×+æè
öø
× ...=:= (26.9-12)
115
Appendix EGust factor variation with height
gR 2 ln 3600 n1×( )×0.577
2 ln 3600 n1×( )×+ 3.638=:= (26.9-11)
Gust factor for Flexible or Dynamically Sensitive Structures:
Gfh0.925
1 1.7 Izh× gQ
2 Qh( ) 2× gR
2 Rh( ) 2×+×+
1 1.7 gv× Izh×+
éêêêë
ùúúúû
× ...=:= (26.9-10)
0 200 400 600 8000.80.9
1
1.1
1.21.3
1.4Gust Factor Variation With Height
Height, m
Gus
tfac
tor
Gfh
h
116
Appendix FGust factor variation with period
Appendix F:Gust Factor Variation with Period
All calculation is carried out according to ASCE/SEI 7-10, all units are in SI (m,s,Hz)
General information
h 800:= Building height, m, for gust factor calculation
B 42:= Building width, m
L 42:= Building width parallel to the wind direction, m
hf 4.5:= Floor Height, m
V 1.42 29.8× 42.316=:= Basic wind speed, m/s
**Convert 10min time interval wind speedto 3sec time interval wind speed.
P 1 50..:= Building natural period, s, from ETABS program
nP1P
...=:= Building natural frequency:
β 0.03:= Damping ratio, percent of critical
expo 2:= Exposure category: (2=B, 3=C, 4=D)
Constants listed in Table 26.9-1:
α14
expo 2=if
16.5
expo 3=if
19
expo 4=if
0.25=:= mean hourly wind-speed power law exponent in Eq. 26.9-16
b 0.45 expo 2=if
0.65 expo 3=if
0.80 expo 4=if
0.45=:= mean hourly wind speed factor in Eq. 26-16
c 0.3 expo 2=if
0.2 expo 3=if
0.15 expo 4=if
0.3=:=turbulence intensity factor in Eq. 26.9-7
117
Appendix FGust factor variation with period
zmin 9.14 expo 2=if
4.57 expo 3=if
2.13 expo 4=if
9.14=:= minimum height
l 97.54 expo 2=if
152.4 expo 3=if
198.12 expo 4=if
97.54=:= integral length scale factor
ε13
expo 2=if
15
expo 3=if
18
expo 4=if
0.333=:= integral length scale power law exponent in Eq. 26.9-9
Flexible or Dynamically Sensitive Structures.
Eguivalent height: z zmin 0.6 h× zmin£if
0.6 h× 0.6 h× zmin>if
480=:=
gQ 3.4:= peak factor for background responce in E.q 26.9-6 and 26.9-10
gv 3.4:= peak factor for wind responce in E.q 26.9-6 and 26.9-10
Lz lz10
æçè
ö÷ø
ε× 354.484=:= (26.9-9)
Q1
1 0.63B h+
Lz
æçè
ö÷ø
0.63×+
0.692=:=(26.9-8)
(26.9-7)Iz c
10z
æçè
ö÷ø
1
6× 0.157=:=
118
Appendix FGust factor variation with period
According to Section 26.9.5 Eq. 26.9-16:
Vz bz10
æçè
ö÷ø
α× V× 50.122=:= mean hourly wind speed at height z
ηhP4.6 nP×
hVz×:= ηBP
4.6 nP×BVz×:= ηLP
15.4 nP×L
Vz×:=
RhP1 ηhP
0£if
1ηhP
1
2 ηhPæè
öø
2×
1 e2- ηhP×
-æçè
ö÷ø×- ηhP0>if
...=:= (26.9-15a&b)
RBP1 ηBP
0£if
1ηBP
1
2 ηBPæè
öø
2×
1 e2- ηBP×
-æçè
ö÷ø×- ηBP0>if
...=:= (26.9-15a&b)
RLP1 ηLP
0£if
1ηLP
1
2 ηLPæè
öø
2×
1 e2- ηLP×
-æçè
ö÷ø×- ηLP0>if
...=:=
(26.9-15a&b)
(26.9-14)N1P
nP
LzVz× ...=:=
RnP
7.47 N1P×
1 10.3 N1P×+æ
èöø
5
3
...=:= (26.9-13)
Resonant response factor:
RP1β
RnP× RhP
× RBP× 0.53 0.47 RLP
×+æè
öø
× ...=:= (26.9-12)
119
Appendix FGust factor variation with period
gRP2 ln 3600 nP×( )×
0.577
2 ln 3600 nP×( )×+ ...=:= (26.9-11)
Gust factor for Flexible or Dynamically Sensitive Structures:
GfP0.925
1 1.7 Iz× gQ2 Q2× gRP
æè
öø
2 RP( ) 2×+×+
1 1.7 gv× Iz×+
éêêë
ùúúû
× ...=:= (26.9-10)
0 5 10 15 20 25 30 35 40 45 500.75
0.805
0.86
0.915
0.97
1.025
1.08
1.135
1.19
1.245
1.3Gust Factor Variation With Period
Period,s
Gus
tFac
tor
GfP
P
Gf
0
01
2
3
4
5
6
7
8
00.791
0.795
0.803
0.814
0.828
0.842
0.858
...
=
120
Appendix GModel Checking-Mass of the model
Appendix GModel Checking - Mass of the model
l1 50m
l2 26m
t3 200mm
l3 90m h3 3m
w3 4m
t4 300mml4 85.5m
h4 4m
w4 6m
t5 500mml5 92.3m
h5 4m
w5 6mConcrete C100
t6 750mmρc100 2400
kg
m3
l6 93mh6 4m
w6 6m
fc.c100 100MPat7 1000mm
l7 87.8mh7 4m
Ec100 50GPaw7 6m
νc100 0.2
t8 1250mml8 93m
h8 4mGc100
Ec100
2 1 νc100 20.833 GPa
w8 6m
t9 1500mm
l9 92.3m h9 4m
w9 6.69m
t10 1750mm
l10 89m h10 4m
w10 7.69m
121
Appendix GModel Checking-Mass of the model
Volume of Columns
Lcol
l3
l4
l5
l6
l7
l8
l9
l10
90
85.5
92.3
93
87.8
93
92.3
89
m hcol
h3
h4
h5
h6
h7
h8
h9
h10
3
4
4
4
4
4
4
4
m wcol
w3
w4
w5
w6
w7
w8
w9
w10
4
6
6
6
6
6
6.69
7.69
m tcol
t3
t4
t5
t6
t7
t8
t9
t10
0.2
0.3
0.5
0.75
1
1.25
1.5
1.75
Acol 8 2 hcol wcol tcol
22.4
48
80
120
160
200
256.56
327.32
m2
Area for all 8 columns at each section
Volume for alla 8 columns at each sectionVcol Acol Lcol
2.016 103
4.104 103
7.384 103
1.116 104
1.405 104
1.86 104
2.368 104
2.913 104
m3
Total volume for allcolumnsVcol.tot Lcol Acol 1.101 10
5 m
3
mcol Vcol.tot ρc100 2.643 108
kg Total mass of all columns
Wcol mcol g 2.592 GN Total weight off columns
122
Appendix GModel Checking-Mass of the model
Perimeter Walls
Vw.3 4 39.18 m2
4 36.63 m2
8 14.47 m2
8 22.65 m2
t3 120.04 m3
Vw.4 12 31.82 m2
12 54 m2
t4 308.952 m3
Vw.5 16 31.82 m2
16 54 m2
4 27.6 m2
4 16.26 m2
t5 774.28 m3
Vw.6 8 42.43 m2
8 72 m2
4 31.82 m2
4 54 m2
t6 944.04 m3
Vw.7 16 31.82 m2
16 54 m2
4 27.6 m2
4 16.26 m2
t7 1.549 103
m3
Vw.8 12 54 m2
12 31.82 m2
8 72 m2
8 42.43 m2
t8 2.432 103
m3
Vw.9 24 54 m2
20 31.82 m2
4 41.43 m2
4 27.6 m2
4 16.26 m2
t9 3.41 103
m3
Vw.10 12 54 m2
8 72 m2
12 54.94 m2
8 73.26 m2
t10 4.321 103
m3
Top roof: Vroof 181.7m2
100 mm 18.17 m3
Total volume of perimeter walls including top roof:
Vw Vw.3 Vw.4 Vw.5 Vw.6 Vw.7 Vw.8 Vw.9 Vw.10 Vroof 1.388 104
mw Vw ρc100 3.331 107
kg
Ww mw g 0.327 GN
123
Appendix GModel Checking-Mass of the model
Floors
Toppart:
Afloor.top504m
21530m
2
21.017 10
3 m
2 Average
Afloor.mid 1449m2
Middlepart:
Afloor.bot1658m
22621m
2
22.139 10
3 m
2 Average Bottom
part:
Afloors 20 Afloor.top 98 Afloor.mid 40 Afloor.bot 2.479 105
m2
tfloor 100mm
Vfloors Afloors tfloor 2.479 104
m3
mfloors Vfloors ρc100 5.95 107
kg
Wfloors mfloors g 0.584 GN
Facade
qfacade 3kN
m
Total lengt of the perimeters where the facade loadappliedlfacadebeam 13284.7m
Wfacade qfacade lfacadebeam 39.854 MN
Total Calculated Weight
Wcalc Wcol Ww Wfloors Wfacade 3.542 103
MN
Total Weight from Model
Obtained from reaction forces.
Wmodel 3.549GN
σdead.d
Wmodel
Acol7
10.843 MPa fcd.c100 100MPa OK! <
124