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

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 Tubed Mega Frame är ett nytt bärande system för skyskrapor som har utvecklats av Tyréns. För att studera konstruktionens prestanda samt effektiviteten för det nya konceptet har en global analys av Tubed Mega Frame systemet utförts med hjälp av FEM-programvaran ETABS. En studie av hur olika normer ta hänsyn till de horisontella lasterna har också utförts. Från studien av vindlaster och seismiska responsspektra i de olika dimensioneringsnormerna kan man se att beräkningsfilosofierna skiljer sig från norm till norm. Vindlasterna är snarlika medan responsspektra varierar en hel del mellan de olika normerna.

En 3D-finit elementmodell är gjord och analyserad i ETABS med hänsyn till linjärt statiska, geometriskt olinjära (P-Delta) och linjärt dynamiska lastfall. Resultaten från analyserna visar att Tubed Mega Frame systemet är potentiellt möjligt och har en relativ hög styvhet i sidled samt en bra global stabilitet. För bruksgränstillstånd är den maximala utböjningen i horisontell riktning inom begränsningen på 1/400 av en våningshöjd och den maximala horisontalaccelerationen är 0.011m/sec 2 vilket uppfyller komfortkriterier.



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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 Maximum Considered Earthquake (MCER) spectral response acceleration parameter ( and ) for a period of 1 s. GCpi = internal pressure coefficient. Gf = gust-effect factor for flexible buildings. = live load element factor. Kz = velocity pressure exposure coefficient. = reduced design live load per square meter of area supported by the member. = unreduced design live load per square meter of area supported by the member. = the soil factor. = mapped Risk-Targeted Maximum Considered Earthquake (MCER) spectral response acceleration parameter at a period of 1 s with site class B and a target risk of structural collapse equal to 1% in 50 years. , is the design earthquake spectral response acceleration parameter at 1 s period. , is the design earthquake spectral response acceleration parameter at short period. = the elastic response spectrum. = mapped Risk-Targeted Maximum Considered Earthquake (MCER) spectral response acceleration parameter at short periods with site class B and a target risk of structural collapse equal to 1% in 50 years.

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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

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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. viii

= 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

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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 xi

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 xii

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.

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CHAPTER 1. INTRODUCTION

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.

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CHAPTER 1. INTRODUCTION

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

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CHAPTER 2. METHOD 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 6

CHAPTER 2. METHOD 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. 9

CHAPTER 3. LITERATURE REVIEW 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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CHAPTER 3. LITERATURE REVIEW

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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CHAPTER 3. LITERATURE REVIEW 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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CHAPTER 3. LITERATURE REVIEW 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.

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CHAPTER 3. LITERATURE REVIEW

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 14

CHAPTER 3. LITERATURE REVIEW 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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CHAPTER 3. LITERATURE REVIEW

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).

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CHAPTER 3. LITERATURE REVIEW 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.

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CHAPTER 3. LITERATURE REVIEW

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

18

CHAPTER 3. LITERATURE REVIEW buildings according to the American Code (ASCE 7-10), the Eurocode (EN 1991-14:2005) 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: ( Where, wk is the characteristic value of design wind loads. is the wind vibration and dynamic response factor. is the external pressure coefficient.

19

)

Eq. (3-4)

CHAPTER 3. LITERATURE REVIEW 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 ASCE 7-10

EN 1991-14:2005

GB50009-2012

Ground condition Exposure C Open country terrain with low vegetation and isolated obstacles with separations of at least 20 obstacle heights Open flat ground

Reference height 10 m

50 years

Average time interval 3 sec

10 m

50 years

10 min

10 m

50 years

10 min

Return period

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): (

)

( ) 20

Eq. (3-5)

CHAPTER 3. LITERATURE REVIEW

(

)

( )

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): 21

CHAPTER 3. LITERATURE REVIEW ( ) ( )

( ) (

)

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.

22

CHAPTER 3. LITERATURE REVIEW

Velocity pressure coefficient

2.5

The velocity pressure exposure coefficient in ASCE 7-10

2 1.5 1

Exposure B Exposure C Exposure D

0.5 0 0

50 100 150 200 250 300 350 400 450 500 550 600 650 700 750 800 850 Height (m)

The factor for wind pressure variation with height in GB50009-2012

Wind pressure variation factor

3.5 3 2.5 2 1.5

Exposure A Exposure B Exposure C Exposure D

1 0.5 0 0

50 100 150 200 250 300 350 400 450 500 550 600 650 700 750 800 850 Height (m)

The terrain roughness factor in EN 1991-1-4:2005 The terrain roughness factor

2 1.8 1.6 1.4 1.2 1 0.8

Exposure 0 Exposure I Exposure II Exposure III Exposure IV

0.6 0.4 0.2 0 0

50 100 150 200 250 300 350 400 450 500 550 600 650 700 750 800 850 Height (m)

Figure 3.6 Coefficient variation with height in different exposure categories in each code.

23

CHAPTER 3. LITERATURE REVIEW 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.

Coefficient

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.

Coefficient differences with urban exposure condition in each code

3.2 3 2.8 2.6 2.4 2.2 2 1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0 0

50 100 150 200 250 300 350 400 450 500 550 600 650 700 750 800 850 Height (m) ASCE 7-10 with Exposure B GB50009-2012 with Exposure C EN 1991-1-4:2005 with Exposure IV

Figure 3.7 Coefficient differences with similar exposure conditions in each code.

24

CHAPTER 3. LITERATURE REVIEW 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 windforce 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 Windward Code Leeward Wall Side Wall Wall L/B* Cp 0-1 -0.5 ASCE 7-10 +0.8 -0.7 2 -0.3 ≥4 -0.2 D/B** ≤1 -0.6 GB50009-2012 +0.8 1.2 -0.5 -0.7 2 -0.4 ≥4 -0.3 Zone**** Zone h/d*** Cpe h/d Cpe h/d A B 5 +0.8 5 -0.7 5 -1.2 -0.8 EN 1991-1-4:2005 1 +0.8 1 -0.5 1 -1.2 -0.8 ≤0.25 +0.7 ≤0.25 -0.3 ≤0.25 -1.2 -0.8 *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. NOTE ****Zone classifications are illustrated in EN 1991-1-4:2005 chapter 7.2.2 figure 7.5

Zone C -0.5 -0.5 -0.5

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. 25

CHAPTER 3. LITERATURE REVIEW 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. Gust factor variation with period , with fixed height of 800m (ASCE 7-10) 1.30

Gust Factor

1.20 1.10 1.00

Exposure B Exposure C Exposure D

0.90 0.80

0.70 0

5

10

15

20 25 Period (s)

30

35

40

45

Figure 3.8 Gust factor variations with period for 800m building.

Gust factor variation with height, with fixed period of 8.68s (ASCE 7-10) 1.40

Gust Factor

1.30 1.20 Exposure B Exposure C Exposure D

1.10 1.00 0.90 0.80 0

50

100 150 200 250 300 350 400 450 500 550 600 650 700 750 800 Height (m)

Figure 3.9 Gust factor variations with height with fixed period of 8.68s.

26

CHAPTER 3. LITERATURE REVIEW 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.

Height Building Width Building Depth Prototype Building Inputs (Parallel to wind direction ) First Natural Period Damping Ratio Floor Height Basic Wind Speed (10min average time interval) Wind Parameters Basic Wind Speed (3sec average time interval) Basic Wind Pressure in Chinese Code ASCE 7-10 Exposure Category GB50009-2012 EN 1991-1-4

800m 45m 40m 8.68s 0.03 4.5m 29.8m/s 42.3m/s 0.55kN/m2 B C 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 27

CHAPTER 3. LITERATURE REVIEW 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.

Windward wall wind pressures (N/m2)

Wind pressure (N/m2)

2500

2000 1500 1000 ASCE 7-10 GB50009-2012 En 1991-1-4 2005

500 0 0

50 100 150 200 250 300 350 400 450 500 550 600 650 700 750 800 850 Height (m)

Leeward wall wind pressures (N/m2) 0

Height (m) 50 100 150 200 250 300 350 400 450 500 550 600 650 700 750 800 850

0 ASCE 7-10 GB50009-2012 EN 1991-1-4 2005

Wind pressure (N/m2)

-200 -400 -600 -800 -1000 -1200 -1400 -1600

28

CHAPTER 3. LITERATURE REVIEW

Side wall wind pressures (N/m2) 0

Height (m) 50 100 150 200 250 300 350 400 450 500 550 600 650 700 750 800 850

Wind pressure (N/m2)

0 ASCE 7-10 GB50009-2012 EN 1991-1-4 2005/Zone A EN 1991-1-4 2005/Zone B

-500 -1000

-1500 -2000 -2500 -3000

Wind pressure (N/m2)

Total wind pressure in along-wind direction (N/m2) 5000 4500 4000 3500 3000 2500 2000 1500 1000 500 0

ASCE 7-10 GB50009-2012 EN 1991-1-4 2005 0

50

100 150 200 250 300 350 400 450 500 550 600 650 700 750 800 850 Height (m)

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. 29

CHAPTER 3. LITERATURE REVIEW 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

30

CHAPTER 3. LITERATURE REVIEW 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).

31

CHAPTER 3. LITERATURE REVIEW

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 32

CHAPTER 3. LITERATURE REVIEW 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 longperiod 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 33

CHAPTER 3. LITERATURE REVIEW 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. 34

CHAPTER 3. LITERATURE REVIEW = mapped Risk-Targeted Maximum Considered Earthquake (MCER) spectral response acceleration parameter at short periods with site class B and a target risk of structural collapse equal to 1% in 50 years. = mapped Risk-Targeted Maximum Considered Earthquake (MCER) spectral response acceleration parameter at a period of 1 s with site class B and a target risk of structural collapse equal to 1% in 50 years. Both and can be obtained from the Seismic Ground Motion Long-Period Transition and Risk Coefficient Maps given in ASCE 7-10. and are site coefficients determined by both site classes and mapped Risk-Targeted Maximum Considered Earthquake (MCER) spectral response acceleration parameter ( and ) for short periods and a period of 1 s, respectively. Table 3.6 and 3.7 show and that are defined in ASCE 7-10. Table 3.6 Site Coefficient, Fa in ASCE 7-10 (American Society of Civil Engineers, 2013).

Table 3.7 Site Coefficient, Fv in ASCE 7-10 (American Society of Civil Engineers, 2013).

35

CHAPTER 3. LITERATURE REVIEW 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).

Level 6

Seismic Precautionary Intensity Level 7 Level 8

)

Level 9

Frequent 0.04g 0.08g(0.12g)*** 0.16g(0.24g) 0.32g Earthquake* Rare 0.28g 0.50g(0.72g) 0.90g(1.20g) 1.40g Earthquake** Note: * Frequent Earthquake is defined as seismic intensity with 63% risk of exceed in 50 years. 36

CHAPTER 3. LITERATURE REVIEW ** 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 Group 1 Group 2 Group 3

I0 0.20 0.25 0.30

Site Class II 0.35 0.40 0.45

I1 0.25 0.30 0.35

III 0.45 0.55 0.65

IV 0.65 0.75 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 37

CHAPTER 3. LITERATURE REVIEW 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 A B C D E

S 1.0 1.2 1.15 1.35 1.4

TB (s) 0.15 0.15 0.20 0.20 0.15

TC (s) 0.4 0.5 0.6 0.8 0.5

TD (s) 2.0 2.0 2.0 2.0 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 into account through factors acceleration parameter .

, and

takes the site conditions

which vary with the spectral response

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 38

CHAPTER 3. LITERATURE REVIEW spectral part is classes.

which should be determined by the seismic design groups and site

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 LongPeriod 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

39

CHAPTER 3. LITERATURE REVIEW to be 0.25g. The long-period transition (Yu Zhan, 2008).

is set to be 4s for the ASCE 7-10 code

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 ASCE 7-10 EN19981:2004 GB 500112010

A >1500 m/s >800 m/s >800 m/s (I0)

B 760-1500 m/s 360-800 m/s 500-800 m/s (I1)

Site Class C 370-760 m/s 180-360 m/s 250-500 m/s (II)

D 180-370 m/s

E