global analysis and structural performance of the tubed...

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

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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

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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.

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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

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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


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.


acceleration parameter at short periods with site class B and a target risk of structural


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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.

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= 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.

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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

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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

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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

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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

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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

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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.

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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

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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.

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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

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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.


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Figure 3.1 World's ten tallest buildings according to height to architectural top (Council on Tall Buildings and Urban Habitat, 2013).


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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.


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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.


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


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.


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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).


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.


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


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.


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)


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):


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.


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


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


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.


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


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


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


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


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


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).


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


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


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.


35


acceleration parameter at short periods with site class B and a target risk of structural



acceleration parameter at a period of 1 s with site class B and a target risk of structural


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


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).


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.


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


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


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


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


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


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


GB50011-2010Eurocode 8


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


GB50011-2010Eurocode 8

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.


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).


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.


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,


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.


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


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


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:


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-


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


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.


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.


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


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.


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.


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.


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.


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%


Shear force in X-direction MN

53.2 MN 56.36 MN 5.6%


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%


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.


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.


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.


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.


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.


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).

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.

REFERENCES

76

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.

ZouYun. (2006). Studies on the Performanced-Based Seismic Deisgn of Shanghai World

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


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


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


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


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


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


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


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


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


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


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


V 29.8:= Basic wind speed, m/s


n11P



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


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


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


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


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


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


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


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×³if

:=

KEY "e>=d"=

96


ebd

1=

cpeA 1.2-:= cpeB 0.8-:= cpeD 0.8:= cpeE 0.7-:= (Table 7.1)

97


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


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


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


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


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


1.2 106´ 1.6 106´ 2 106´0

200

400

600

800


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




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)


n11P


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


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


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


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


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


ö÷÷÷÷÷÷÷÷÷÷÷÷÷÷÷÷÷÷÷÷÷÷÷÷÷÷÷÷ø

:=

μz μza Ground 1=if

μzb Ground 2=if

μzc Ground 3=if

μzd Ground 4=if

:=

106


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


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


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


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


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







n11P





α14

expo 2=if

16.5

expo 3=if

19

expo 4=if


b 0.45 expo 2=if

0.65 expo 3=if

0.80 expo 4=if


c 0.3 expo 2=if

0.2 expo 3=if

0.15 expo 4=if


113


zmin 9.14 expo 2=if

4.57 expo 3=if

2.13 expo 4=if


l 97.54 expo 2=if

152.4 expo 3=if

198.12 expo 4=if


ε13

expo 2=if

15

expo 3=if

18

expo 4=if


Flexible or Dynamically Sensitive Structures.

Eguivalent height: zh zmin 0.6 h× zmin£if

0.6 h× 0.6 h× zmin>if

...=:=



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



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)


Rh1β

Rnh× Rhh

× RBh× 0.53 0.47 RLh

×+æè

öø

× ...=:= (26.9-12)

115


gR 2 ln 3600 n1×( )×0.577

2 ln 3600 n1×( )×+ 3.638=:= (26.9-11)


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






P 1 50..:= Building natural period, s, from ETABS program

nP1P

...=:= Building natural frequency:




α14

expo 2=if

16.5

expo 3=if

19

expo 4=if


b 0.45 expo 2=if

0.65 expo 3=if

0.80 expo 4=if


c 0.3 expo 2=if

0.2 expo 3=if

0.15 expo 4=if


117


zmin 9.14 expo 2=if

4.57 expo 3=if

2.13 expo 4=if


l 97.54 expo 2=if

152.4 expo 3=if

198.12 expo 4=if


ε13

expo 2=if

15

expo 3=if

18

expo 4=if


Flexible or Dynamically Sensitive Structures.

Eguivalent height: z zmin 0.6 h× zmin£if

0.6 h× 0.6 h× zmin>if

480=:=



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



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)


RP1β

RnP× RhP

× RBP× 0.53 0.47 RLP

×+æè

öø

× ...=:= (26.9-12)

119


gRP2 ln 3600 nP×( )×

0.577

2 ln 3600 nP×( )×+ ...=:= (26.9-11)


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


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


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


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

global analysis and structural performance of the tubed...

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