Introduction to Earthquake Resistant Design of Buildings 建筑抗震設計簡介 presented by Ir Dr Y. L. Wong 黄玉龍博士 Associate Professor Dept. of Civil & Structural Engineering
Content (內容) • Earthquakes（地震） What causes earthquakes and how do they happen? • Earthquake Resistant Buildings （抗震設計） How could engineers design buildings that survive in earthquakes?
Acknowledgements (致謝) • Most of the materials in this presentation were extracted from websites of “Introducing and Demonstrating Earthquake Engineering Research in Schools” (IDEERS)of Taiwan National Center for Research on Earthquake Engineering (NCREE) and University of Bristol.
PGA Zonation Map of South China南中國地震設計加速圖 HK: 0.15g for 1 in 475 years (中國地震局製作)
Earthquake(地震) • Earth‘s Structure (地球構造) • Tectonic Plates (構造板塊) • Faults (斷層) • Causes of Earthquakes (地震的成因) • Seismic Waves (地震波) • Where Earthquakes Occur? (地震發生的地點) • Size of Earthquakes (地震的大小) • How Often do Earthquakes Occur? (地震發生的頻率)
Earth‘s Structure(地球的構造) • The inner core, with a radius of 1,370 kilometers, is believed to be a solid metal body. • The outer core is a 2,000 kilometer thick layer believed to be a liquid metal layer. • The mantle is 2900 kilometers thick. • The crust is the outer layer of hard rock, ranging in thickness from 4 to 60 kilometers
Tectonic Plates (構造板塊) The surface of the earth is made up of 21 tectonic plates, some large and some small, that are constantly moving. As the plates are forced against each other, they deform, and eventually they crush and fracture. The sudden fracture of the rock sends out a shock wave that causes the earth's surface to shake. This is one way earthquakes can happen. World map showing the tectonic plates with only the larger plates labelled
Fault (斷層) • Over millions of years the earth's tectonic plates have been moving continuously and pushing against each other. These movements have forced them to deform producing mountains and valleys in the earth's surface. • Sometimes the rocky surface of the earth has just been bent and folded (Fig.1). Sometimes the movements have caused the rock to deform so much that they fracture. These fractures are called faults (Fig. 2). When the rock fractures, its sudden movement causes an earthquake as shock waves spread away from it. Fig. 1 How Rocks are bent and folded Fig. 2 How Rocks Fracture
Faults in earthquake (斷層實例) This fence crossed the San Andreas Fault. In 1906, the fault ruptured causing the Magnitude 8.3 San Francisco Earthquake. The horizontal movement of the ground caused the fence to move by about 2 metres The Shih-Kang Dam is constructed from concrete. The thrust fault broke right through it. In this picture taken on its downstream side, you can see where the right hand side of the dam rose 10 metres compared to the left hand side (Chi-Chi earthquake, Taiwan, 1999). The fault ruptured the ground surface passing right through this school in Wu Feng. It broke through a running track. (Chi-Chi earthquake, Taiwan, 1999).
Causes (地震的成因) • Earthquakes can be caused by natural events or human activities. Here are some of the different causes of earthquakes. • Tectonic Plate Movement- the most common cause • Volcanic Activity • Explosions • Collapsed Mines • Water Pressure in Reservoirs
Causes－Tectonic Plate Movement （構造板塊的移動） • The most common cause of earthquakes. • The earthquake occurs when the pressure that has built up in tectonic plates causes the rock to break suddenly. • This usually occurs at the boundaries of tectonic plates and along existing faults.
Seismic Waves (地震波) • When the rock breaks, there is a sudden release of energy. Shock waves spread out through and around the earth in all directions, starting from the focus of the earthquake. At the earth's surface the ground vibrates as the waves pass through it. The way the waves spread is a bit like the ripples spreading on a pond when a stone is dropped into it.
Seismic Waves (地震波) • Energy spreads out through the earth in three different wave types : • P-wave （P-波） • a longitudinal wave • travel through rock, liquid and the air • the fastest traveling seismic wave • S-wave （S-波） • a transverse wave • travel through rock, but not through liquid and the air • slower than a P-wave, but faster than a surface wave • Surface wave: （面波） • the slowest traveling seismic waves • Their movement is greatest at the earth's surface, and gets smaller • deeper below the surface
Where Earthquakes Occur (地震發生地點) This map shows the distribution of the world's earthquakes that happened during the 1980s. Each red dot represents an earthquake. It is clear that earthquakes happen more often in some places than others. the edges of tectonic plates
Size of Earthquake (地震的度量) • Magnitude (量級)- the amount of energy it releases into the earth's crust. • Intensity(烈度)- the amount the ground shakes.
Size of Earthquake (地震的度量) • Magnitude(量級): • It gives an idea of the strength of an earthquake. • For each unit on the scale, the energy released by an earthquake is about 30 times greater than the unit below. So, a magnitude 6 earthquake releases 30 times as much energy than a magnitude 5 earthquake, and 900 times as much energy as a magnitude 4 earthquake.
Size of Earthquake • Intensity(烈度)： • For the same earthquake, its intensity will vary from place to place. Usually, it is greatest near the epicentre, and it gets smaller further away. • Intensity is not measured on instruments. It is worked out by considering the effects on people and buildings. This is an isoseismal map for the magnitude 4.2 (ML) Warwick earthquake of September 23rd 2000, in England, showing isoseismals from intensity 2 to 5.
How Often do Earthquakes Occur (地震發生的頻率) • This table shows how often earthquakes of different magnitude occur, world-wide.
What does a Seismogram tell us (地震記錄) • Size of ground motion at the measurement station • When the different type of waves, i.e. the P-waves, the S-waves and the surface waves, arrived at the measuring station • What sort of rock they passed through on the way there • Information to calculate the magnitude of the earthquake
Earthquake Resistant Buildings （結構的抗震設計） How could engineers design buildings that survive in earthquakes? To explain how buildings: • Vibrate (振動) during earthquakes, • are strengthened(加固) to resist earthquakes, • can be isolated(隔震) from the shaking ground, • use dampers(阻尼器) to reduce vibrations from earthquakes.
Vibrating Buildings (建筑物的振動) • To understand the way buildings behave during earthquakes, you need to know: • How the ground moves. (地面運動) • How buildings vibrate naturally. (建筑物的自由振動) • How vibrations die out. (振動的耗散) • Then, you can know • How earthquakes make buildings vibrate. (建筑物在地震作用下的振動)
Ground Motion (地動) –Introduction (簡介) • During an earthquake, the motion of the ground at any location is very complicated, as the ground is shaking in all directions. This motion can be described more simply as a combination of different motions all happening at the same time. They are: • Horizontally, side to side (Animate1) • Horizontally, backwards and forwards (Animate2) • Upwards and downwards (Animate3) • Rotating backwards and forwards (Animate4) • Rotating from side to side (Animate5) • Twisting (Animate6)
Ground Motion (地動) -A Single Simple Wave (正弦波) • Amplitude: (振幅) Think of a point on the ground vibrating to and fro. If it kept moving the same distance each way, it would have a constant amplitude of vibration. If it moved 10 mm each way, its amplitude of vibration would be 10 mm. • Frequency: (頻率) If the number of times it moved to and fro every second remained the same, it would have a constant frequency of vibration. Each to and from movement is called one cycle of motion. If the patch of ground made 5 cycles every second, its frequency of vibration would be 5 Hertz.
Ground Motion (地動) • Combination of waves (波的組合) Real ground motion during an earthquake is made up of many waves of different amplitudes and frequencies. The main shaking of the ground that is felt has frequencies up to 20 Hertz. (Animate)
Single Degree of Freedom System-Static Analysis (單自由度系統-靜力分析) • System (系統) • Equation of Equilibrium (平衡方程) • Stiffness (剛度) is the resistance of an elastic body to deflection or deformation by an applied force.
SDOF System–Free Vibration (單自由度系統-自由振動) • Undamped system (無阻尼系統) • Equation of motion (運動方程) • Natural frequency (自振頻率) Note: It depends only on the system mass and the spring stiffness (i.e. any damping will not change the natural frequency of a system).
SDOF System–Free Vibration (單自由度系統-自由振動) • Damped system (有阻尼系統) • Equation of motion (運動方程) • C : Damping ratio (阻尼系數), a measure of the damping of the system, expresses the damping of the system as a ratio of the critical damping level .
SDOF System–Free Vibration (單自由度系統-自由振動) • Comparison of Sample Time Behaviors (兩種系統的反應時程比較) Undamped System Damped System
SDOF System–Dynamic Response (單自由度系統-動力反應) • Earthquake Excitation (地震動激勵) • Sample Response History-Displacement (時程反應樣本-位移) • Equation of Motion (動力方程) Effective earthquake force (等效地震力)
MDOF System-Natural Vibrations (多自由度系統-自由振動) • Earthquakes can cause buildings to vibrate. There are two basic concepts on natural vibrations of a building: • Mode and Mode Shape:(模態和振型) Every building has a number of ways, or modes, in which it can vibrate naturally. In each mode, the building vibrates to and fro with a particular distorted shape called its mode shape. • Frequency of vibration:(振動頻率) The number of times it vibrates to and fro every second is the frequency of vibration for that mode.
MDOF System-Natural Vibrations (多自由度系統-自由振動) • The Fundamental Mode (基本模態) • Imagine you could push a building sideways at its top and then let go so that it swayed naturally. The number of times it swayed to and fro every second would be the fundamental frequency of vibration of the building. • If you repeated the experiment, but pushed the building a little harder or lighter, the fundamental frequency would stay the same. (Animate the fundamental mode of vibration of a 2-story typical frame building)
MDOF System-Natural Vibrations (多自由度系統-自由振動) • Higher Modes (高階模態) • The building could be made to sway at other frequencies of vibration and with other mode shapes by pushing it at lower floor levels. Animate thesecond modesand third modesof vibration of a 2-story typical frame building
MDOF System-Natural Vibrations (多自由度系統-自由振動) • The Natural Frequency of a Building (一棟建筑物的自振頻率) • The natural frequency for each mode of vibration follows this rule: f = natural frequency in Hertz. K = the stiffness of the building associated with this mode M = the mass of the building associated with this mode • Buildings tend to have lower natural frequencies when they are: • Either heavier (more mass) • Or more flexible (that is less stiff). • One of the main things that affect the stiffness of a building is its height. Taller buildings tend to be more flexible, so they tend to have lower natural frequencies compared to shorter buildings.
How Vibrations Die Out-Damping(振動的耗散-阻尼) • The vibrations die out because of damping which removes energy from the moving building. • The damping can be caused by • Friction (摩擦) as different parts of the building move against each other. • Internal friction in the materials (材料的內部摩擦) making up the structural members and other parts of the building. • Damage in the building (建筑物的破壞), for example, cracking in concrete or brickwork or permanent distortions in steel. • What can engineers do? • Engineers can design buildings to have extra damping, by adding dampers (阻尼器) to the structural frame. The dampers absorb energy from a vibrating building, so that its movement is not as violent.
Resonance in Buildings (建筑物的共振) The picture shows two buildings. Imagine the tall building has a fundamental frequency of 5.5 Hertz and the small building has a fundamental frequency of 7.5 Hertz. • If the ground moved to and fro with a frequency of 5.5 Hertz, the tall building would vibrate strongly, or resonate, while the short building hardly moved at all. (Animation) • If the ground moved to and fro with a frequency of 7.5 Hertz, the small building would resonate while the tall building hardly moved at all. (Animation) • During an earthquake, the ground shakes with a mixture of frequencies of vibration. Q: If the frequencies ranged between 5.0 and 6.0 Hertz, which of the two model buildings would you expect to vibrate most?
Strengthening Buildings for Earthquakes (結構的抗震加固) • Horizontal structural systems (floors and roofs) • Diaphragms (樓板) • Trussing(桁架) • Vertical structural systems (columns, beams, walls and bracing) • Braced frames (帶斜撐的框架) • Moment resisting frames (抗彎矩框架) • Shear walls(剪力墻)
Horizontal structural systems-Diaphragms(水平結構系統-樓板) • Horizontal diaphragms are usually floors and roofs. They are made up from a horizontal frame covered by a floor or roof deck. • When a diaphragm is stiff enough in its horizontal plane. it can share the sideways earthquake forces on a building between the vertical structural members, e.g. the columns and walls.
Horizontal structural systems-Trussing (水平結構系統-桁架) • Horizontal trussing is usually used in roofs where there is not enough deck to allow the roof to act as a stiff horizontal diaphragm. • The trussing transfers the sideways earthquake forces on a building to its vertical structural members e.g. the columns and walls.
Vertical structural systems-Braced Frames (豎直結構系統-帶斜撐的框架) • Single Diagonals (單斜撐) If a single diagonal, or brace, is used, it must be able to resist tension (stretching) and compression (squashing) caused by sideways forces in both directions on a frame. Single diagonals in a 3-storey frame
Vertical structural systems-Braced Frames (豎直結構系統-帶斜撐的框架) If two diagonals are used, in the form of cross-bracing, they only need to resist tension. This is because one brace is in tension for the sideways force in one direction on the frame, while the other brace is in tension when the force is reversed. Steel cables can be used for cross-bracing, as they can be stretched, but not squashed. • Cross Bracing (交叉斜撐) Cross-bracing in a 3-storey frame
K Bracing Inverted V Bracing Vertical structural systems-Braced Frames (豎直結構系統-帶斜撐的框架) • Miscellaneous Methods (混合方法) Knee Bracing V Bracing
Vertical structural systems-Moment Resisting Frames(豎直結構系統-抗彎矩的框架) • In moment resisting frames, the joints, or connections, between columns and beams are designed to be rigid. This causes the columns and beams to bend during earthquakes. So these structural members are designed to be strong in bending. • Moment resisting frames simply means frames that resist forces by bending.
Vertical structural systems-Shear Walls (豎直結構系統-剪力墻) • Shear walls are vertical walls that are used to stiffen the structural frames of buildings. They help frames resist sideways earthquake forces. • It is better to use walls with no openings in them. So, usually the walls around lift shafts and stairwells are used. Also, walls on the sides of buildings that have no windows can be used.
Isolating Buildings –Introduction(隔震結構-簡介) • Normally, a building is supported directly on its foundations. When base isolation is used, special structural bearings are inserted between the bottom of the building and its foundation. These bearings are not very stiff in the horizontal direction, so they reduce the fundamental frequency of vibration of a building. The frequency becomes so low that the building does not vibrate as strongly during an earthquake. • During an earthquake, a fixed-base building can sway from side to side. When a base isolation system is used, the sideways movement occurs mainly in the bearings, and the building hardly distorts at all. Click the figure
Isolating Buildings – Bearings(隔震結構-支撐) • Rubber Bearings (橡膠支撐) Layers of rubber + thin steel plates between them + a thick steel plate on the top and bottom Click the figure • Friction pendulum Bearings (摩擦擺錘支撐) two horizontal steel plates that can slide over each other because of their shape + an additional articulated slider. Click the figure
Adding Dampers –Introduction(阻尼器-簡介) • Dampers can be installed in the structural frame of a building to absorb some of the energy going into the building from the shaking ground during an earthquake. The dampers reduce the energy available for shaking the building. This means that the building deforms less, so the chance of damage is reduced. • There are many types of dampers that can be installed in buildings. Here are some of them: • Metallic Dampers (金屬阻尼器) • Friction Dampers (摩擦阻尼器) • Viscous Fluid Dampers (粘滯阻尼器)
Adding Dampers-Metallic Dampers (阻尼器-金屬阻尼器) • There are different types of metallic damper. One type, the X-shaped Plate Damper, is used where two braces meet. As the building vibrates, the braces stretch and compress, pulling and pushing the damper sideways and making it deform. They are designed to deform so much when the building vibrates during an earthquake that they cannot return to their original shape. This permanent deformation is called inelastic deformation, and it uses some of the earthquake energy which goes into building.
Adding Dampers-Friction Dampers (阻尼器-摩擦阻尼器) • Friction dampers are designed to have moving parts that will slide over each other during a strong earthquake. When the parts slide over each other, they create friction which uses some of the energy from the earthquake that goes into the building. Click the figure