Basics of Seismic Engineering

Doina VERDEŞ

BASICS OF SEISMIC ENGINEERING

UTPRESS Cluj-Napoca, 2011

Editura U.T.PRESS Str. Observatorului nr. 34 C.P. 42, O.P. 2, 400775 Cluj-Napoca Tel.:0264-401999; Fax: 0264 - 430408 e-mail: [email protected] http://www.utcluj.ro/editura Director: Consilier editorial:

Prof.dr.ing. Daniela Manea Ing. Călin D. Câmpean

Copyright © 2011 Editura U.T.PRESS Reproducerea integrală sau parţială a textului sau ilustraţiilor din această carte este posibilă numai cu acordul prealabil scris al editurii U.T.PRESS. Multiplicarea executata la Editura U.T.PRESS. ISBN 978-973-662-641-8 Bun de tipar: 25.05.2011 Tiraj: 100 exemplare

BASICS OF SEISMIC ENGINEERING By Doina Verdes

THE CONTENTS

CHAPTER 1 THE SEISMICITY OF THE TERRITORY 1.1 Introduction 1.2 Seismicity 1.3 The earthquake and the types of seismic waves 1.4 Measures of Earthquake Size 1.5 Record of the ground motion 1.6 Significant earthquakes produced in the world

CHAPTER 2 THE ANALYSIS OF SEISMIC RESPONSE OF SINGLE DEGREE OF FREEDOM SYSTEM 2.1 Modeling the buildings 2.2 The degrees of freedom 2.3 The Response Spectrum Analysis 1

2.4 The relative displacement response 2.5 The response spectrum and the pseudospectrum 2.6 Response to seismic loading: step-by-step methods 2.7 The Beta Newmark Methods 2.8. The seismic response of the SDOF nonlinear system using the step by step numerical integration 2.9 The energy balance procedure 2.10 Seismic response spectra of the SDOF inelastic systems

CHAPTER 3 ANALYSIS OF SEISMIC RESPONSE MULTIDEGREE OF FREEDOM SYSTEMS 3.1Vibration Frequencies and Mode Shapes 3.2 Earthquake Response Analysis by Mode Superposition 3.3 Response Spectrum Analysis for Multi-degree of Freedom Systems 3.4 Step-by-Step Integration

CHAPTER 4 METHODS OF SEISMIC ANALYSIS OF STRUCTURES 4.1 Introduction 4.2 Lateral force method of analysis Romanian Code P100/1-2006 4.3 Lateral force method of analysis - EC8 4.4 Time - history representation 4.5 Non-linear static (pushover) analysis

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CHAPTER 5 EARTHQUAKE RESISTANT DESIGN 5.1 Introduction 5.2 Performance Based Engineering 5.3 Performance Requirements and Compliance Criteria 5.4 The guiding principles governing the conceptual design against seismic hazard

CHAPTER 6 INELASTIC DYNAMIC BEHAVIOR 6.1 Introduction 6.2 Global and local ductility condition 6.3 Ductility of reinforced concrete elements (local ductility) 6.4 Requirements for ductility of reinforced concrete frames 6.5 The damages of the reinforced concrete frames under seismic loads

CHAPTER 7 DESIGN CONCEPTS FOR EARTHQUAKE RESISTANT REINFORCED CONCRETE STRUCTURES 7.1 Energy dissipation capacity and ductility 7.2 Structural types 7.3 Design criteria at Ultimate Limit State (ULS) 7.4 The Global Ductility 7.5 Design criteria at Safety Limit State (SLS) 7.6 Structural types with stress concentration 7.7 The local effect of infill masonry 3

CHAPTER 8 NONSTRUCTURAL ELEMENTS 8.1 Defining nonstructural elements 8.2 Earthquake effects on buildings and nonstructural elements 8.3 Interstory displacement 8.4 The performances of nonstructural elements 8.5 Protection Strategies 8.6 Nonstructural design approaches for cladding 8.7 Prefabricated wall panels 8.8 Precast Concrete Cladding 8.9 Cladding which increase the seismic energy dissipation 8.10 Examples of damages

CHAPTER 9 THE STRUCTURAL CONTROL OF SEISMIC RESPONSE 9.1. Introduction 9.2. The control of structural response 9.3. Passive control system 9.4 The base isolation system 9.5 The energy dissipation systems 9.6 Advanced Technology Systems (9A) 9.7 Active structural Control (9B)

REFERENCES THE TEST ON SHAKE TABLE OF A HIGH BUILDING MODEL EQUIPPED WITH FRICTION DAMPERS 4


By Doina Verdes

CHAPTER I THE SEISMICITY OF THE TERRITORY

Contents

1.1 Introduction 1.2 Seismicity 1.3 The earthquake and the types of seismic waves 1.4 Measures of earthquake size 1.5 Record of the ground motion 1.6 Significant earthquakes produced in the world

Doina Verdes Basics of Seismic Engineering 2011

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1.1 Introduction The detailed study of earthquakes and earthquake mechanisms lies in the province of seismology, but in his or her studies the earthquake engineer must take a different point of view than the seismologist Seismologists have focused their attention primarily on the global or long-range effects of earthquakes and therefore are concerned with very small amplitude ground motions which induce no significant structural responses. . Doina Verdes Basics of Seismic Engineering 2011

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Engineers, on the other hand, are concerned mainly with the local effects of large earthquakes, where the ground motions are intense enough to cause structural damage


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1.2

Seismicity.

The seismicity of a region determines the extent to which earthquake loadings may control the design of any structure planned for that location. The principal indicator of the degree of seismicity is the historical record of earthquakes that have occurred in the region. Because major earthquakes often have had disastrous consequences, they have been noted in chronicles dating back to the beginning of civilization. The earthquake occurrences are not distributed uniformly on the surface of the earth; instead they tend to be Concentrated along well-defined lines which are knownto be associated with the boundaries of “plates” of the earth’s crust. Doina Verdes Basics of Seismic Engineering 2011

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Fig. 1.1. Global distribution of seismicity* *http://geology.about.com Doina Verdes Basics of Seismic Engineering 2011

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Fig 1.2. Europe seismic map *

*http://geology.about.com Doina Verdes Basics of Seismic Engineering 2011

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Structure of the Earth

6370

Outer core (liquid)

0 24

Inner core (solid)

500 0 20 00 0 50

The earth consists of several discrete concentric layers: -the inner core, is a very dense solid thought to consist mainly of iron; -outer core is a layer of similar density, but thought to be a liquid because shear waves are not transmitted through it; - next is a solid thick envelope of lesser density around; - the core that is called the mantle, - the rather thin layer at the earth’s surface called the crust.

Crust Mantle

Fig. 1.3. Structure of the Earth


9

the mantle is considered to consist of two distinct layers: the upper mantle together with the crust form a rigid layer called the lithosphere. Below that, the layer, called the asthenosphere, is thought to be partially molten rock consisting of solid particles incorporated within a liquid component. Although the asthenosphere represents only a small fraction of the total thickness of the mantle, it is because of its highly plastic character that the lithosphere does move as a single unit, however; instead it is divided into a pattern of plates of various sizes, and it is the relative movements along the plate boundaries that cause the earthquake occurrence patterns. *AFPS Brochure


Fig. 1.4 The mantle is divided into a pattern of plates *

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Earthquake Faults

From the study of geology, it has become apparent that the rock near the surface of the earth is not as rigid and motionless as it appears to be. There is ample evidence in many geological formations that the rock was subjected to extensive deformations at a time when it was buried at some depth. When such ruptures occurred, relative sliding motions were developed between the opposite side of the rupture surface creating what is called a geological fault. The orientation of the fault surface is characterized by its “strike”, the orientation from north of its line of intersection with the horizontal ground surface, and by its “dip”, the angle from horizontal of a line drawn on the fault surface perpendicular to this intersection line. Doina Verdes Basics of Seismic Engineering 2011

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Fig, 1.5. San Andreas fault, California


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Fig. 1.6. San Andreas fault, California [21] Doina Verdes Basics of Seismic Engineering 2011

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*BSSC California 2001

Fig 1.7 Types of fault slippage * Doina Verdes Basics of Seismic Engineering 2011

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1.3 The earthquake and the types of seismic waves

The important fact about any fault rupture is that the fracture occurs when the deformations and stresses in the rock reach the breaking strength of the material. Accordingly it is associated with a sudden release of strain energy which then is transmitted through the earth in the form of vibratory elastic waves radiating outward in all directions from the rupture point. These displacement waves passing any specified location on the earth constitute what is called an earthquake. The point on the fault surface where the rupture first began is called the earthquake focus, and the point on the ground surface directly above the focus is called the epicenter. Doina Verdes Basics of Seismic Engineering 2011

Fig. 1.8. The earthquake focus characteristics

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The types of seismic waves

Two types of waves may be identified in the earthquake motions that are propagated deep within the earth: “P” waves, in which the material particles move along the path of the wave propagation inducing an alternation between tension and compression deformations, and “S” waves, in which the material particles move in a direction perpendicular to the wave propagation path, thus inducing shear deformations. The “P” or Primary wave designation refers to the fact that these normal stress waves travel most rapidly through the rock and therefore are the first to arrive at any given point. The “S” or Secondary wave designation refers correspondingly to the fact that these shear stress waves travel more slowly and therefore arrive after the “P” waves.


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P-wave S-wave surface wave

1

2

3

Fig. 1.9 The time of seismic waves arrival


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The surface waves

When the vibratory wave energy is propagating near the surface of the earth rather than deep in the interior, two other types of waves known as Rayleigh and Love can be identified. The Rayleigh surface waves are tension-compression waves similar to the “P” waves except that their amplitude diminishes with distance below the surface of the ground. Similarly the Love waves are the counterpart of the “S” body waves; they are shear waves that diminish rapidly with the distance below the surface.


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Fig. 1.10 The types of seismic waves [21]


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Earthquake focus

Reflection at the surfaces

Mantle Core

Seismograph station Refraction at the core

Fig. 1. 11 The seismic waves travel into the earth


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1.4

Measures of Earthquake Size

The most important measure of size from a seismological point of view is the amount of strain energy released at the source, and this is indicated quantitatively as the magnitude. By definition, Richter magnitude is the (base 10) logarithm of the maximum amplitude, measured in micrometers (10-6 m) of the earthquake record obtained by Wood-Anderson seismograph, corrected to a distance of 100 Km. This magnitude rating has been related empirically to the amount of earthquake energy released E by the formula: log E = 11.8 + 1.5 M

in which M is the magnitude. By this formula, the energy increases by a factor of 32 for each unit increase of magnitude. More important to engineers, however, is the empirical observation that earthquakes of magnitude less than 5 are not expected to cause structural damage, whereas for magnitudes greater than 5, potentially damaging ground motions will be produced. Doina Verdes Basics of Seismic Engineering 2011

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The magnitude of an earthquake by itself is not sufficient to indicate whether structural damage can be expected. This is a measure of the size of the earthquake at its source, but the distance of the structure from the source has an equally important effect on the amplitude of its response. The severity of the ground motions observed at any point is called the earthquake intensity; it diminishes generally with the distance from the source, although anomalies due to local geological conditions are not uncommon. The oldest measures of intensity are based on observations of the effects of the ground motions on natural and man-made objects. The standard measure of intensity for many years has been the Modified Mercalli (MM) scale. This is a 12-point scale ranging from I (not felt by anyone) to XII (total destruction). Results of earthquakeintensity observations are typically compiled in the form of isoseismal maps. Doina Verdes Basics of Seismic Engineering 2011

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Modified Mercalli (MM) Intensity Scale

I. No felt by people. VII. People are frightened; it is II. Felt only by a few persons at difficult to stand. Automobile drivers rest,especially on upper floors of notice the shaking. Hanging objects buildings. quiver. Furniture breaks. Weak chimneys break. Loose bricks, III. Felt indoors by many people. stones, tiles, cornices, unbraced Feels like the vibration of a light parapets, and architectural truck passing by. Hanging ornaments fall from buildings. objects swing. May not be Damage to masonry D. recognized as an earthquake. IV. Felt indoors by most people … and outdoors by a few. Feels like XI. Most masonry and wood the vibration of a heavy truck structures collapse. Some bridges passing by. Hanging objects destroyed. swing noticeably XII. Damage is total. Large rock V. Felt by most persons masses are displaced. Waves are indoors and outdoors; sleepers seen on the surface of the ground. awaken. Liquids disturbed, with Lines of sight and level are distorted. some spillage. Small objects Objects are thrown into the air. displaced or upset; VI. Felt by everyone. Many people are frightened, some run outdoors. People move unsteadily. Dishes, glassware, and some windows break. Doina Verdes Basics of Seismic Engineering 2011

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The seismic scale grades: MSK 1964; EMI; MM; JAPAN; RUSSIA

MSK 1964

I

II

III

EMI (PS69)

I

II

III

MERCALLI MODIFIED 1956

I

II

JAPAN

0

I

RUSSIA

I

II

IV

III

IV

V

IV

V

II III

V

III IV

VI VI VI IV

V

VI

VII VII

VIII VIII

VII

VIII

V VII

IX IX IX

X X X

XI XI

IX

XII

XI

VI VIII

XII

XII VII

X

XI

XII

maximum acceleration of the soil mouvement 0.002g 0.004g 0.008g 0.015g 0.020g 0.030g 0.130g 0.200g 0.300g 0.500g 1.000g


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18

Largest earthquake

10,000,000x10

Nuclear bomb 1964 Alaska earthquake 1906 San Francisco earthquake

18

1,000,000x10

Daily U.S. electrical energy consumption

1976 Guatemala earthquake

18

Energy (ergs)

1971 San Fernando earthquake 1983 Coalinga earthquake Atomic bomb 1,000x10 18

18

100x10

Se ism ic e ne rgy

1980 Italy earthquake

10,000x10

of ea rth qu ak es

18

100,000x10

1978 Santa Barbara earthauake

18

10 x 10

18

1 x 10

4

5

6

7

8

9

Richter magnitude

Fig. 1.12 Earthquakes: Magnitude/energy


25

The three components of ground motion recorded by a strongmotion accelerograph provide a complete description of the earthquake which would act upon any structure at that site. However, the most important features of the record obtained in each component, from the standpoint of its effectiveness in producing structural response, are the amplitude, the frequency content, and the duration. The amplitude generally is characterized by the peak value of acceleration or sometimes by the number of acceleration peaks exceeding a specific level. The frequency content can be represented roughly by the number of zero crossings per second in the accelerogram and the duration by the length of time between the first and the last peaks exceeding a given threshold level. It is evident, however, that all these quantitative measures taken together provide only a very limited description of the ground motion and certainly do not quantify its damage-producing potential adequately Doina Verdes Basics of Seismic Engineering 2011

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Fig, 1.13 Seismoscop – Antic China


27

Seismographs The motion of the ground is recorded during earthquakes by instruments known as seismographs. These instruments were first developed around 1890, so we have recordings of earthquakes only since that time. Today, there are hundreds of seismographs installed in the ground throughout the world, operating as part of a worldwide seismographic network for monitoring earthquakes and studying the physics of the earth.


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Seismograms

l

records of soil displacements produced by seismographs, called seismograms, are used in calculating the location and magnitude of an earthquake.

M L

Fig. 1.14 The principle of seismoscop Doina Verdes Basics of Seismic Engineering 2011

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1.5 Record of the ground motion

The motion of the ground at any point is three-dimensional, which means that the point moves in space and not merely in a plane or in a straight line. To completely record this motion, three seismometers must be built into each seismograph. These seismometers move in three perpendicular directions, two horizontal and one vertical, and generate three corresponding seismograms. Seismographs are designed to record small displacements caused by distant earthquakes and are used by seismologists interested in locating hypocenters, estimating magnitudes, and studying the mechanics of earthquakes – the kind of shaking that causes damage. To record this type of ground shaking requires a different type of instrument, one that measures ground acceleration instead of ground displacement. Such instruments are called accelerographs, and the mass-spring system is called accelerometer. Doina Verdes Basics of Seismic Engineering 2011

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Accelerogram-Accelerograph The record generated, known as an accelerogram, has the general appearance of a seismogram, but its mathematical characteristics are quite different. Acceleorgraphs do not have a continuous recording system, as seismographs do; instead, they are triggered by an earthquake and operate form batteries (because the power often is disrupted during an earthquake).

Fig,1.15 North-south component of horizontal ground acceleration recorded at El Centro, Califonia during the Imperial Valey Irrigation district of 18 May 1940


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Fig. 1.16 The accelerogram Vrancea March 1977 Doina Verdes Basics of Seismic Engineering 2011

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1.6 Significant earthquakes and tsunamis produced in the world


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Fig. 1.17 Annual number of earthquakes recorded in the 20th century * *according with the NEC/US GS Global Hypocenter Data Base Doina Verdes Basics of Seismic Engineering 2011

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Date 780 B.C.

373

Location

Magni tude

Deaths

Widespread destruction west of Xian

China; Shaanxi Province Greece

B.C.

1202 May 20

Middle East 30,000

1455 Dec.5 1531 Jan.26 1556 Jan.23

Italy Portugal; Lisbon China; Shaanxi Province

Remarks

40,000

Helice, on the Gulf of Corinth, was destroyed. Much of the city slid into the sea. Felt over an area of 800,000 square miles, including Egypt, Syria, Asia Minor, Sicily, Armenia, and Azerbai-jan. Variously reported as occuring in 1201 or 1202 with over a million deaths (which is highly improbable). Naples badly damaged.

30,000

8.0

830,000

Greatest natural disaster in history. Occured at night in the densely populated region around Xian. Thousands of landslides on the hillsides, which consists of soft rock. Many peasants living in caves were killed. Many villages destroyed and thousands of deaths when houses collapsed.

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Fig. 1.18 View of an old tile fresco placed on a house wall from Sintra, Portugal, mentioning the 1731 earthquake.


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1626 July 30 1667 Nov. 1668 July 25 1688 July 5 1693 Jan.9 1703 Dec.3 0 1737 Oct.11 1755 Nov.1

Italy; Naples

70,000

Azerbaijan

80,000

1783 Feb.5 1868 Aug.1 3 1891 Oct.28

Italy; Calabria Chile and Peru Japan; Nobi Plain

7.9

1897 June 12

India; Assam

8.7

1906 Apr.18

U.S.A.; San Francisco

8.3

China; Shandong Province Turkey

8.5

15,000 Damage along Aegean coast. 60,000 Catania destroyed.

Sicily Japan; Tokyo region India; Calcutta Portugal; Lisbon

50,000 Widespread destruction throughout province.

8.2

5,200 Tsunami.

300,000

8.6

8.5

60,000 All Saints’ Day; many killed when churches collapsed and fire ravaged the city. Large tsunami killed many. 50,000 First earthquake to be investigated scientifically. 25,000 Large tsunami devasted Arica (now in Chile, but then in Peru). 7,300 Also known as Mino-Owari earthquake (Mino and Owari Provinces are now part of Gifu Prefec-ture). Many buildings destroyed. Large ground displacements. 1,500 Large fault scarp formed (vertical displacement 35 feet. Much building damage in Shillong. 700 San Andreas fault ruptured for 270 miles. Great fire burned much of the city.

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1908 Dec28

7.5

1920 Dec.1 6 1923 Sept.1

China; Ningxia Province Japan; Tokyo

8.6

1931 Feb.3

New Zealand; Hawke Bay Romania; Vrancea district Japan; south of Shikoku Island Japan; Fukui Prefecture India; Assam (eastern) Algeria; El Asnam Mexico; Guerrero

7.8

1940 Nov. 10 1946 Dec. 21 1948 June 28 1950 Aug. 15 1954 Sept.9 1957 July 8

1968 Aug31

Iran (eastern); Khorasan

8.3

58,000 Messina destroyed.

200,000 Many landslides covered villages and towns. 99,300 Known as Kanto earth-quake. Major damage over a large area, including Tokyo and Yokohama. Great fire in Tokyo. Large tsunami inundated coastal regions. 225 Many buildings damaged in Napier.

7.4

1,000 Severe damage to buildings in Bucharest.

8.4

1,360 Known as the Nankai earthquake. Great tsunami.

7.3

5,400 Only known instance of a person being crushed in a ground fissure. 150 Damage in region along border with Tibet Landslides and floods. 1,240 El Asnam (then Orléansville) destroyed 68 Tall buildings damaged in Mexico City, 180 miles away.

8.7

6.8 7.9

7.3

12,100

About 60,000 people homeless.

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1970 Peru; May31 Chimbote

7.8

1975 Feb.4

7.3

China; Liaoning Province; Haicheng 1976 China; July Hebei 28 Province; Tangshan 1977 Romania; Mar.4 Vrancea district 1979 Yugoslavia Apr.15 southern Montenegr o

7.8

7.2

7.0

67,000 Greatest earthquake disaster in the Western Hemisphere. About 800,000 people home-less. Huge landslide on Mt. Huascarán buried 18,000 people in Ranrahirca and Yungay. 1,300 Earthquake successfully predicted and population evacuated. Heavy damage, but many lives saved. 243,000 Major industrial city totally destroyed. Four aftershocks on same day with magnitudes 6.5, 6.0, 7.1, and 6.0. 1,570 Many buildings collapsed in Bucharest.

156 Near the Adriatic coast. Extensive damage.

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17 January

1994 1995 26

Northdrige USA Kobe Japan Sumatra

9

Decem ber

2004 2009

Aquila Italy

Damages to buildings and bridges

M 6.8

6.3

6,500 deaths 240,000 Major damage, deaths The tsunami waves damaged the coast

308 Several buildings collapsed deaths 1500 injuried

12 January 2010

Haiti

7

316,000 250,000 residences and deaths 30,000 commercial buildings were severely damaged

11 March 2011

Tohoku Japan trench

9

Began on 9 March with a M 7.2, and continued with a further three earthquakes greater than M 6.0 on the same day, the major was on 11 march with 9M -explosion hit a petrochemical plant

-Major damage in the Fukushima nuclear plant -Four trains were missed along the coast


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Date 1755 Nov.1

Significant tsunamis produced in the world

1868 Apr.2

1883 Aug.27

Origin Lisbon, Portugal (off the coast, in the Atlantic Ocean); earthquake of magnitude 8.6 (60,000 deaths) Island of Hawaii (south slope of Mauna Loa); volcanic earthquake of magnitude 7.7 Island of Krakatoa (in the Sunda Strait, between Java and Sumatra); volcanic eruption (36,000 deaths)

1896 June 15

Japan (off the Sanriku coast); earthquake of magnitude 7.5 (27,000 deaths)

1923 Sept.1

Japan (Tokyo and vicinity); earthquake of magnitude 8.3 (99,300 deaths)

Remarks Several large waves washed ashore in Portugal, Spain, and Morocco. Major damage and many deaths in Lisbon from tsunamis Local tsunami destroyed many houses and killed 46 people Violent explosion of Krakatoa volcano. Great tsunami felt in harbors around the world. Tsunami caused much damage and loss of life on nearby islands. Numerous villages entirely destroyed by tsunami; maximum wave height 15 meters. Many lives lost by drowning. Known as the Kanto earthquake (epicenter in Kanto Plain), Major damage over a large area, including Tokyo and Yokohama; great fire in Tokyo. Tsunami in Sagami Bay struck the shore 5 minutes after the earthquake; maximum wave height 10 meters. Tsunami killed 160 people.

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Date

Origin

Remarks

1946 Apr.1

Aleutian Islands (south of Unimak Island in the Aleutian trench); earthquake of magnitude 7.5 (173 deaths)

Major damage in Hilo, Hawaii (96 deaths). Minor damage in California (one death in Santa Cruz)

1956 July 9

Greece (Dodecanese Islands); earthquake of magnitude 7.8 (53 deaths)

Tsunami struck the coasts.

1960 May 22

Chile; Arauco Province (along the continental shelf, near the coast, south of Conception); earthquake of magnitude 8.5 (2,230 deats)

Major damage in Hilo (61 deaths), and Japan (120 deaths). Wave height 5 meters on Sanriku coast of Japan. Local tsunami in Chile.

1976

Philippine Islands (Moro Gulf); earthquake of magnitude 8.0 (6,500 deaths)

Major damage and many deaths from tsunami.

2004 December 26

Sumatra islands magnitude 8.0 About 47,000 more people died, from Thailand to Tanzania, when the tsunami struck without warning during the next few hours.

Major damage and 240,000 people died The worst part of it washed away whole cities in Indonesia, but every country on the shore of the Indian Ocean was also affected

2011 March 11

Tohoku earthquake was a massive earthquake with magnitude 9 Japan trench

-10m wave struck the port of Sendai, carrying ships, vehicles and other debris inland -The tsunami rolled across the Pacific at 800km/h - hitting Hawaii and the US West Coast

Aug.17


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1.7 Seismic hazard in Romania

The seismic hazard in Romania is due to contribution of two factors : (i) the major contribution of subcrustal seismic zone Vrancea (ii) others contributions due to the surface seismic zone contributions spread to country territory.


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Romanian earthquakes Data

1903

Ora (GMT) h:m:s

13 Septemrie

Lat.

°

N

08:02:7

Long.

E

°

H Adâncimea focarului, km

Catalogul RADU C, 1994

Catalogul MARZA, 1980

I

M

M

Mws

Mw

I

w1

26.6

>60

7

6.6

6.3

5.7

6.3

6.5

45.7

26.6

75

6

-

5.7

6.3

6.6

6

45.7 (45.5)

26.5

150(12

8

7.1

6.8

6.8

7.1

8

6.7

7

45.7 1904

6 Februarie

02:49:00

1908

6 Octombrie

21:39:8

5)

1912

25 Mai

18:01:7

45.7

27.2

80(90)

7

6.3

6.0

6.4

1934

29 Martie

20:06:51

45.8

26.5

90

7

6.6

6.3

6.3

1939

5 Septembrie

06:02:00

45.9

26.7

120

6

-

5.3

6.1

6.2

6

1940

22 Octombrie

06:37:00

45.8

26.4

122

7/8

6.8

6.5

6.2

6.5

7

1940

10 Noiembrie

01:39:07

45.8

26.7

9

7.7

7.4

7.4

7.7

9

1945

1 Septembrie

15:48:26

45.9

26.5

75

7/8

6.8

6,5

6.5

6.8

7.5

1945

9 Decembrie

06:08:45

45.7

26.8

80

7

6.3

6.0

6.2

6.5

7

1948

29 Mai

04:48:55

45.8

26.5

130

6/7

-

5.8

6.0

6.3

6.5

1977

4 Martie

19:22:15

45.3

26.30

109

8/9

7.5

7.2

7.2

7.4

9

45.5

26.47

133

8

7.2

7.0

-

7.1

-

45.8

26.90

91

8

7.0

6.7

-

6.9

-

45.8

26.89

79

7

6.4

6.1

-

6.4

-

140150*

6.6

8

4 1986

30 August

21:28:37 3

1990

30 Mai

10:40:06 2

1990

31Mai

00:17:49 3


The design acceleration and seismic zones of Romanian territory

1. National territory is subdivided into seismic zones, depending on the local hazard. By definition, the hazard within each zone is assumed to be constant. 2.the hazard is described in terms of a single parameter, i.e. the value of the reference peak ground acceleration on rock or firm soil ag. 3. The reference peak ground acceleration, chosen by the National Authority for each seismic zone, corresponds to the reference return period chosen by the same authority. To this reference average return period for Romanian territory is call “the design soil acceleration” Doina Verdes Basics of Seismic Engineering 2011

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Fig. 1.19 Romanian seismic network


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The design acceleration, Conforming the Romanian Code P100/1-2006, for each zone of seismic hazard corresponds to an average return period of reference equal 100 years.

Fig. 1.20 Seismic zones of Romanian territory depending on soil design acceleration ag for seismic events with average return period (of magnitude) IMR = 100 years


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The control period and the design accelerations of some Romanian cities [22]


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The control period

The local soil conditions are described by values of control period TC of the response spectrum for the specific location. These values characterize synthetically the frequencies composition of the seismic movement. The control period represents the border between the zone of the maximum values in the spectrum of absolute accelerations and the zone of maximum values in the spectrum of relative velocity. TC is expressed in the seconds. The average interval of return earthquake magnitude IMR=100 years For the ultimate limit stage

Values of control periods TB , s TC , s TD , s

0,07 0,7 3

0,10 1,0 3

0,16 1,6 2

Fig. 1.21 Control periods for Romanian territory Doina Verdes Basics of Seismic Engineering 2011

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Fig.1.22 The map of the Romanian territory with the zones on terms of TC for the horizontal components of the seismic movements due to earthquakes having the IMR=100 years.


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By Doina Verdes

CHAPTER 2 THE ANALYSIS OF SEISMIC RESPONSE OF SINGLE DEGREE OF FREEDOM SYSTEM

Doina Doina Verdes Verdes BASICS BASICS OFOF SEISMICAL SEISMICAL ENGINEERING ENGINEERING 2011 2011

2

Contents 2.1 Modeling the buildings 2.2 The degrees of freedom 2.3 The Response Spectrum Analysis 2.4 The relative displacement response 2.5 The response spectrum and the pseudospectrum 2.6 Response to seismic loading: step-by-step methods 2.7 The Newmark Beta Methods 2.8. The seismic response of the SDOF nonlinear system using the step by step numerical integration 2.9 The energy balance procedure 2.10 Seismic response spectra of the SDOF inelastic systems Doina Verdes BASICS OF SEISMICAL ENGINEERING 2011

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2.1 Modeling the buildings

Doina Verdes BASICS OF SEISMICAL ENGINEERING 2011

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Dynamic models • •

•

• •

Dynamic model of the resistance structure It has to describe the behavior to seismic action. It has to represent adequately : - the general configuration – geometry, joints, material - the distribution of inertial characteristics: mass of the levels, inertia moments of the level mass - the stiffness and damping characteristics The model of building can contain the resistance system involved into vertical and lateral loads, connected trough slabs (horizontal diaphragms) The deformability model of the structure can involve also the beamcolumn connection and /or structural walls; the model can be done also by structural elements with nonstructural elements – ex: the partition walls, or panels which can significantly increase the stiffness of the framed structure. Doina Verdes BASICS OF SEISMICAL ENGINEERING 2011

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• The behavior of the material of structural elements could be linear-elastic (a) or nonlinear (b)

a.

b. Doina Verdes BASICS OF SEISMICAL ENGINEERING 2011

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The distribution of inertial characteristics: mass of the levels, inertia moments. m k, ξ

The model for a single span frame m k, ξ

The model for a frame multiple spans Doina Verdes BASICS OF SEISMICAL ENGINEERING 2011

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Fn

F1

The model for a multilevel framed system


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2.2 The degree of freedom

The degree of freedom (DOF) is by definition: the number of pendulum which block the movement of the mass. The methods to obtain the dynamic model are: - the concentrated mass; - the system with finite elements.


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How can be appreciate the degrees of freedom?

a. The case of an bridge

The horizontal translations of the mass of bridge’s deck The translations along the axis O-x and O-y => Two degrees of freedom

Doina Verdes Doina Verdes BASICS OF SEISMICAL ENGINEERING BASICS OF SEISMICAL ENGINEERING 2011 2011

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b. The case of one level building Simplified model: Three degrees of freedom due to horizontal translations and rotation on the vertical axis of the mass (concentrated at the roof level)

Important assumptions: The building has rigid foundation slab The movement of soil due to seismic excitation is synchronic


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c. The case of one level building subjected to foundation's rotation Results in one degree of freedom


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Linear Elastic Calculus System FA(t)

FS(t)

c

k 1

1

y& (t )

y(t)

a.

b.

FS= Elastic force FA= Damping force K = Stiffness C = damping coefficient y(t)= displacement y& (t ) =velocity Doina Verdes BASICS OF SEISMICAL ENGINEERING 2011

Non-linear Calculus System Tangenta la curbă Tangenta la curbă

FA(t)

FS(t)

FA1 Fs1

∆FS Secanta la curbă

∆Fs

FA0

∆ y& (t )

Fs0 y(t) yo

∆y

y& 0

y1


y&1

y& (t )

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Level of damping in different structures The damping varies with: the materials used, the form of the structure, the nature of the subsoil, and the nature of the vibration. Large-amplitudes post-elastic vibration is more heavily damped than small-amplitude vibration; Buildings with heavy shear walls and heavy cladding or partitions have greater damping than lightly clad skeletal structures.


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Damping coefficient in different structures Type of construction

Damping ν ξ percentage of critical

Steel frame, welded, with all walls of flexible construction

2

Steel frame, welded, with normal floors and cladding

5

Steel frame, bolted, with normal floors and cladding

10

Concrete frame, with all walls of flexible construction

5

Concrete frame, with stiff cladding and all internal walls flexible

7

Concrete frame, with concrete or masonry shear walls

10

Concrete and/or masonry shear wall buildings

10

Timber shear walls construction

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2.3 The Response Spectrum Analysis

Response spectrum analysis is the dominant contemporary method for dynamic analysis of building structures under seismic loading.


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Typical SDOF system subjected to base seismically excitation unidirectional translation yg(t)


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The equilibrium of the forces based on D’Alembert low Fi (t ) + FD (t ) + Fe (t ) = 0

(1)

Fi (t)= the inertia force FD (t)= the damping force Fe (t)= the elastic force


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Fi (t ) = m( &y&g + &y&)

(2)

FD (t ) = cy&

(3)

Fe (t ) = ky

(4)

m= the mass of system c= the viscous damping cœfficient k= the stifness


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The equation of equilibrium becomes:

m&y&(t ) + cy& (t ) + ky (t ) = − m&y&g (t )

(5)

m&y&(t ) + cy& (t ) + ky (t ) = − FS (t )

(6)

The frequency equation

&y&(t ) + 2ωξy& (t ) + ω 2 y (t ) = − &y&g (t )

(7)

ω = k /m

ξ = c/2mω


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The general solution of the seismic equilibrium equation is:

y(t ) = A exp −ξωt  sin ωt +ϕ  +

1 mω

t ∫0 − m&y&g (τ )sin ω D (t −τ )exp[−ξω (t −τ )]dτ D

(8)

The first term represents the free vibration of the system The second term represents the forced vibrations under seismic action. Neglecting the free vibrations contribution due to the quick damping of these the solution becomes:

y (t ) =

1 mω D

t

∫ − m&y& (τ )sin ω (t − τ )exp[− ξω(t − τ )]dτ 0

g

D


(9)

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2.4 The relative displacement response

The relative displacement response of the frame to a single component of ground acceleration yg(t) may be expressed in the time domain by means of the Duhamel integral

y (t ) =

1 mω D

t

∫ − m&y& (τ )sin ω (t − τ )exp[− ξω(t − τ )]dτ 0

g

D


(9)

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y(t) – the mass displacement ω D – the circular damped frequency ξ - the critically damper coefficient ξ = c/ccr c= the viscous damping coefficient ccr = critically damping coefficient ξ = 0.02 … 0.1 m= the mass

&y&g (τ ) = the ground acceleration at timeτ ω = k/m

(10)

ξ = c/2mω


(11)

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When the difference between the damped and the undamped frequency is neglected, as is permissible for small damping ratios usually representative of real structures (say ξ < 0.10), and when it is noted that the negative sign has no real significance with regard to earthquake excitation, this equation can be reduced to:

y (t ) =

1

t

&y& (τ ) sin ω (t − τ ) exp[− ξω (t − τ )]dτ ∫ ω 0

g


(12)

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North – south component of horizontal ground acceleration El Centro 1940 Doina Verdes Doina Verdes BASICS OF SEISMICAL ENGINEERING BASICS OF SEISMICAL ENGINEERING 2011 2011

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2.5 The response spectrum and the pseudospectrum

The response spectrum used in seismical engineering are: - the velocity spectrum - the absolute acceleration spectrum - the displacement spectrum


• Taking the first time derivative of Eq.(12), one obtains the corresponding relative velocity time-history

t

y& (t ) = ∫ &y&g (τ ) cos ω (t − τ ) exp[− ξω (t − τ )]dτ 0

t

− ξ ∫ &y&g (τ )sin ω (t − τ ) exp[− ξω (t − τ )]dτ 0

(13)


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Further, substituting Eqs. (12) and (13) into the forced-vibration equation of motion, written in the form

&y&t (t) = -2ωξy& (t ) − ω 2 y(t) one obtains the total acceleration relation:

(

)

t

&y&t (t ) = ω 2ξ − 1 ∫ &y&g (τ )sin ω (t − τ ) exp[− ξω (t − τ )]dτ 2

0

t

− 2ωξ ∫ &y&g (τ ) cos ω (t − τ ) exp[− ξω (t − τ )]dτ 0

(14) Doina Verdes Doina Verdes BASICS OF SEISMICAL ENGINEERING BASICS OF SEISMICAL ENGINEERING 2011 2011

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The absolute maximum values of the response given by Eqs. (12), (13), and (14) are called: - the spectral relative displacement, - the spectral relative velocity, and - the spectral absolute acceleration, These will be denoted herein as : Sd(ξ ,ω), Sv(ξ ,ω), Sa(ξ ,ω), respectively.


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As will be shown subsequently, it is usually necessary to calculate only the so-called pseudo-velocity spectral response Spv(ξ ,ω) defined by t  S pv (ξ , ω ) ≡ ∫ &y&g (τ ) sin ω (t − τ ) exp[− ξω (t − τ )]dτ   0  max

(15)

Now from Eq. (12), it is seen that

y (t ) =

1

t

ω ∫0

&y&g (τ )sin ω (t − τ ) exp[− ξω (t − τ )]dτ

S d (ξ , ω ) =

1

ω

S pv (ξ , ω )


(12)

(16) 31

and from Eqs. (13) and (15) that (for ξ = 0)

t  S v (0, ω ) ≡ ∫ &y&g (τ ) cos ω (t − τ )dτ   0  max

t  S pv (0, ω ) ≡ ∫ &y&g (τ )sin ω (t − τ )dτ   0  max


(17)

(18)

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which are identical except for the trigonometric terms. It has been demonstrated by Hudson that Sv(0 ,ω) and Spv(0 ,ω) differ very little numerically, except in the case of very long period oscillators, i.e. very small values of ω. For damped systems, the difference between Sv and Spv is considerably larger and can differ by as much as 20 percent for ξ = 0.20. Also from Eq. (14) for ξ = 0 that

(

)

t

&y&t (t ) = ω 2ξ − 1 ∫ &y&g (τ )sin ω (t − τ ) exp[− ξω (t − τ )]dτ 2

0

t

− 2ωξ ∫ &y&g (τ ) cos ω (t − τ ) exp[− ξω (t − τ )]dτ 0

t  S a (0, ω ) ≡ ω ∫ v&&g (t )sin ω (t − τ )dτ   0  max


(19)

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• thus, from Eq. (19),

S a (0 , ω ) = ω S pv (0 , ω )

(19)

It can be shown that Eq. (19) is very nearly satisfied for damping values over the range 0 < ξ < 0.20; therefore, we are able to use the approximate relation

S a (ξ ,ω ) = ωS pv (ξ ,ω )

(20)

with little error being introduced. Doina Verdes BASICS OF SEISMICAL ENGINEERING 2011

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• The entire quantity on the right hand side of Eq. (20) is called the pseudo-acceleration spectral response and it is denoted herein as Spa(ξ ,ω). This quantity is particularly significant since it is a measure of the maximum spring force developed in the oscillator

f s , max = kS d (ξ , ω ) = ω 2 mS d (ξ , ω ) = mS pa (ξ , ω )

(21)

• The other response spectra can be easily obtained there from using the relations

S d (ξ , ω ) =

1

ω

S pv (ξ , ω )

S pa (ξ , ω ) = ωS pv (ξ , ω ) Doina Verdes BASICS OF SEISMICAL ENGINEERING 2011

(22)

(23)

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• As indicated above these response quantities depend not only on the ground motion time-history but also on the natural frequency and damping ratio of the oscillator. • Thus for any given earthquake accelerogram, by assuming discrete values of damping ratio and natural frequency, it is possible to calculate the corresponding discrete values of Spv(ξ ,ω) using Eq. (22) and to calculate corresponding values of Sd(ξ ,ω) and Spa(ξ ,ω) using Eqs. (22) and (23), respectively.


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• • • •

Graphs of the values for Spv(ξ ,ω), Sd(ξ ,ω), and Spa(ξ ,ω)

• plotted as functions of frequency (or functions of period T = 2π/ω) for discrete values of damping ratio are called • pseudo-velocity response spectra, • displacement response spectra, and • pseudo-acceleration response spectra, • respectively. If plotted in linear form, each type of spectra must be plotted separately similar to the set of Spv(ξ ,T) shown in Figure 2.3. for the El Centro, California, earthquake of May 18, 1940 (N S component).


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a) Ground acceleration (El Centro)

a

b) The deformation response of three SDF systems

c) deformation response spectrum

T=0,5 s

ξ =2%

T=1 s

ξ =2%

T=2 s

ξ =2%

b

c


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However, due to the simple relationships existing among the three types of spectra as given by Eqs. (22) and (23) it is possible to present them all in a single plot. This may be accomplished by taking the log (base 10) of Eqs. (24) and (25) to obtain

log S d (ξ , ω ) = log S pv (ξ , ω ) − log ω (24)

log S pa (ξ , ω ) = log S pv (ξ , ω ) + log ω

Combined D-V-A RESPONSE SPECTRUM for El Centro 1940 ground motion

(25) Doina Verdes BASICS OF SEISMICAL ENGINEERING 2011

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Combined D-V-A response spectrum for El Centro ground motion


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From these relations, it is seen that when a plot is made with log Spv(ξ,ω) as the ordinate and logω as the abscissa, Eq. (24) is a straight line with slope of +45°for a constant value of logSd(ξ,ω) and Eq. (25) is a straight line with slope of – 45° for a constant value of logSpa(ξ,ω). Thus, a four-way log plot allows all three types of spectra to be illustrated on a single graph. When interpreting such plots, it is important to note the following limiting values:

[

]

lim S d (ξ , ω ) = y g (t ) max

ω →0

[

]

lim S pa (ξ , ω ) = &y&g (t ) max

ω →0


(26)

(27)

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These limiting conditions mean that all response spectrum curves on the four-way log plot, approach asymptotically the maximum ground displacement with increasing values of oscillator period (or decreasing values of frequency) and the maximum ground acceleration with decreasing values of oscillator period (or increasing values of frequency) for typical values of damping ratio, say ξ = 0.20.


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Combined D-V-A RESPONSE SPECTRUM for El Centro 1940 with different damping coefficient values


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In fact, these response spectra show directly the extent to which real SDOF structures (with specific values of damping ratio and natural period) respond to the input ground motion. The only limitation in their application is that the response must be linear elastic because linear response is inherent in the Duhamel integral. Therefore, such response spectra cannot accurately represent the extent of damage to be expected from a given earthquake excitation, as damage involves inelastic (nonlinear) deformations. Nevertheless, the maximum amount of elastic deformation produced by an earthquake is a very meaningful indication of ground motion intensity.


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Moreover, such response spectra indicate the maximum deformations for all structures having periods within the range for which they were evaluated; hence, the integral of a single response spectrum over an appropriate period range can be used as an effective measure of ground motion intensity. Housner originally introduced such a measure of ground motion intensity when he suggested defining the integral of the pseudo-velocity response spectrum over the period range 0.1 < T < 2.5 sec as the spectrum intensity:

SI (ξ ) ≡ ∫

2.5

0.1

S pv (ξ , T )dT

(28)

As indicated, this integral can be evaluated for any desired damping ratio; however, Housner recommended using ξ = 0.20.


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Usually, it is assumed that the shapes of the design spectra are the same for both the design and maximum probable earthquakes but than they differ in intensity as measured by peak ground acceleration. Thus, it has been common practice to first normalize the intensity of these design spectra to the 1 g peak acceleration level so that Eq. (27) becomes:

lim S pa (ξ ,ω ) = 1 g

ω →0

(29)

and then later to scale them down to the appropriate peak acceleration levels representing the design and maximum probable earthquakes. Once the shapes of these common normalized spectra have been developed, taking into consideration local soil conditions, appropriate scaling factors are applied representing the intensity levels of the peak free-field surface ground accelerations (PGA) produced by the design and maximum probable earthquakes. Doina Verdes BASICS OF SEISMICAL ENGINEERING 2011

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By Doina Verdes

CHAPTER 2 THE ANALYSIS OF SEISMIC RESPONSE OF SINGLE DEGREE OF FREEDOM SYSTEM

Doina Doina Verdes Verdes BASICS BASICS OFOF SEISMICAL SEISMICAL ENGINEERING ENGINEERING 2011 2011

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Contents 2.1 Modeling the buildings 2.2 The degrees of freedom 2.3 The Response Spectrum Analysis 2.4 The relative displacement response 2.5 The response spectrum and the pseudospectrum 2.6 Response to seismic loading: step-by-step methods 2.7 The Beta Newmark Methods 2.8. The seismic response of the SDOF nonlinear system using the step by step numerical integration 2.9 The energy balance procedure 2.10 Seismic response spectra of the SDOF inelastic systems Doina Verdes Basics of Seismic Engineering 2011

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2.6 Response to seismic loading: step-by-step methods


4

The step-by step procedure • A severe earthquake will induce inelastic deformation in a code-designed structure. The step-by step procedure is suited to analysis of nonlinear response in earthquake engineering. • There are many different step-by-step methods, but in all of them the loading and the response history are divided into a sequence of time intervals or ‘steps’. The response during each step then is calculated from the initial conditions (displacement and velocity) existing at the beginning of the step and from the history of loading during the step. Doina Verdes Basics of Seismic Engineering 2011

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The response for each step • Thus the response for each step is an independent analysis problem, and there is no need to combine response contribution within the step. Nonlinear behavior may be considered easily by this approach merely by assuming that the structural properties remain constant during each step, and causing them to change in accordance with any specified form of behavior from one step to the next; hence the nonlinear analysis actually is a sequence of linear analyses of a changing system. • Any desired degree of refinement in the nonlinear behavior may be achieved in this procedure by making the time steps’ short enough; also it can be applied to any type of nonlinearity, including changes of mass, and damping properties as well as the more common nonlinearities due to changes of stiffness.


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Step-by-step methods The simplest step-by-step method for analysis the SDOF system is based on the exact solution of the equation of motion for response of a linear structure to a loading that varies linearly during a discrete time interval. The loading history is divided into time intervals, usually defined by significant changes of shape in the actual loading history; between this points, it is assumed that the slope of the load curve remains constant. The other step-by-step methods employ numerical procedures to approximately satisfy the equation of motion during each time step using numerical differentiation or numerical integration. The general numerical approach to step-by step dynamic response analysis makes use of integration to step forward from the initial to the final conditions for each time step. The essential concept is represented by the following equations: Doina Verdes Basics of Seismic Engineering 2011

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y&1 = y& 0 + ∫

h

y1 = y0 + ∫

h

0

0

y& (τ )dτ

(1)

y& (τ )dτ

(2)

which express the final velocity and displacement in terms of the initial values of these quantities plus an integral expression. The change of velocity depends on the integral of the acceleration history, and the change of displacement depends on the corresponding velocity integral. In order to carry out this type of analysis, it is necessary first to assume how the acceleration varies during the time step; this acceleration assumption controls the variation of the velocity as well and thus makes it possible to step forward to the next time step.


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2.7 The Newmark Beta Methods A more general step-by-step formulation was proposed by Newmark, which includes the preceding method as a special case, but also may be applied in several other versions. In the Newmark formulation, the basic integration equation [Eqs. (1,2)] for the final velocity and displacement are expressed as follows:

y& 1 = y& 0 + (1 − γ )h&y&0 + γh&y&1

(3)

1  2 & y1 = y 0 + h y 0 +  − β  h &y&0 + β h 2 &y&1 2 

(4)

h=time step h = ti+1 – ti

(5) Doina Verdes Basics of Seismic Engineering 2011

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• It is evident in Eq. (3) that the factor γ provides a linearity varying weighting between the influence of the initial and the final accelerations on the change of velocity; the factor β similarly provides for weighting the contributions of these initial and final accelerations to the change of displacement. • From study of the performance of this formulation, it was noted that the factor γ controlled the amount of artificial damping induced by this step-by-step procedure; there is no artificial damping if γ = 1/2, so it is recommended that this value be use for standard SDOF analyses.


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The constant variation of acceleration during the incremental h time


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The variation of acceleration during the incremental h time interval c. β= 1/6 e. β= 1/8


12

These results also may be derived by assuming that the acceleration varies linearly during the time step between the initial and final values of ÿ and ÿ1, thus the Newmark β = 1/6 method is also known as the linear acceleration method. The linear acceleration method is only conditionally stable referring the incremental value of time step: h=t –t i+1

&y&s (t )

i

Conditions for step time

h p 3/π T

&y&si +1

&y&si

h p 0.55 T ti

ti+1

(6)

t h


13

Coeficient β= 1/6 (γ = 1/2)

• β = 1/6 ( γ = 1/2),

&y&si &y&si −1

h/T ≤ √3/π = 0.55

i-1


h∆h

h∆h

i

&y&si +1

i+1

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Linear variation of acceleration during time interval “h”

β = 1/6 (for γ = ½,)

h y& 1 = y& 0 + ( &y&0 + &y&1 ) 2

h2 h2 &y&0 + &y&1 y1 = y0 + y& 0 h + 3 6


(7)

(8)

(9)

15

Step 1

m&y&1 (t ) + c(t ) y&1 (t ) + k (t ) y1 (t ) = m&y&s1 (t )

h y&1 = y& 0 + ( &y&0 + &y&1 ) 2 h2 h2 y1 = y0 + y& 0 h + &y&0 + &y&1 3 6


(10) (11)

(12)

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STEP 1 • Initial moment: ground acceleration is =0 and the response in accelerations, velocity and displacement

y& 0 = 0 &y&0 = 0 y0 = 0 h y&1 = ( &y&1 ) 2

(13)

2

h &y&1 y1 = 6

(14)


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The displacement and velocity increments using eq. 13 and 14 h h2 &y&1 = −m&y&1s m&y&1 + c &y&1 + k 2 6 &y&1 = −m&y&1s

y&1 = −m&y&1s

1 h h2 m+c +k 2 6

1 h ⋅ h h2 2 m+c +k 2 6

1 h2 y1 = −m&y&1s ⋅ h h2 6 m+c +k 2 6 Doina Verdes Basics of Seismic Engineering 2011

(15)

(16)

(17)

(18)

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Summary of the Linear Acceleration Procedure For any given time increment, the above described explicit linear acceleration analysis procedure consists of the following operations which must carried out consecutively in the order given: Using the initial velocity and displacement values y& o and y0, which are known either from the values at the end of the preceding time increment or as initial conditions of the response at time t = 0, and the specified properties of the system; (1) Determine the displacement and velocity increments using Eqs. (13 and 14); (2) Finally, evaluate the velocity and displacement at the end of the time increment. Doina Verdes Basics of Seismic Engineering 2011

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Linear systems can also be treated by this same procedure, which becomes simplified due to the physical properties remaining constant over their entire time-histories of response. • As with any numerical-integration procedure the accuracy of this step-by-step method will depend on the length of the time increment h. • The factors which must be considered in the selection of this interval: the complexity of the nonlinear damping and stiffness properties, and the period T of vibration of the structure. The time increment must be short enough to permit the reliable representation of all these factors, the last one being associated with the free-vibration behavior of the system. Doina Verdes Basics of Seismic Engineering 2011

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2.8 The seismic response of the SDOF nonlinear system using the step by step numerical integration We have to know: • - the behavior of the material done by the diagram (the model can be elastic-linear or nonlinear) • - the digitalised accelerogram The equation of equilibrium at the time step t1

m&y&1 (t ) + c(t ) y&1 (t ) + k (t ) y1 (t ) = m&y&s1 (t )

(1)

c(t) – the damping coefficient k(t) – the stiffness

The coefficients c(t) and k(t) are variable time depending Doina Verdes Basics of Seismic Engineering 2011

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The calculus model for the non-elastically behavior of the material

a. The symmetrical elastic-plastic model

b. The asymmetrical elastic-plastic model

c. The bilinear elastic-plastic model Doina Verdes Basics of Seismic Engineering 2011

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The nonlinear system

FS(t)

FA(t)

Tangent

Tangent

FA1 Fs1

∆ FA

∆Fs

Secant

FA0

Fs0 y(t) yo

∆y

y1

b. The damping

a. The stiffness


23

&y&s (t )

&y&si +1

&y&si

ti

ti+1

t ∆h

The digitalized accelerograme


24

We assume that the acceleration varies linearly during the time step between the initial and final values of ÿ0 and ÿ1, thus the Newmark β = 1/6 method is also known as the linear acceleration method. The linear acceleration method is only conditionally stable referring the incremental value of time step

&y&s (t )

h = ti+1 – ti Conditions for step time to

&y&si+1

h p 3/π T

&y&si

ti

ti+1

t h


h p 0.55 T

(2)

25

The incremental form of the seismic equation During the incremental time step h the system behavior is elastically

∆FI + ∆FD + ∆FS = ∆F ef

(3)

∆FI (t ) = FI (t + h ) − FI (t ) = m∆&y&(t )

(4)

∆FD (t ) = FD (t + h ) − FD (t ) = c∆y& (t )

(5)

∆FS (t ) = FS (t + h ) − FS (t ) = k∆y (t )

(6)

∆Fef (t ) = Fef (t + h ) − Fef (t ) = m∆&y&s (t )

(7)

m∆&y&(t ) + c∆y& (t ) + k∆y (t ) = − m∆&y&s (t )

(8)

The equation can be solved using the β Newmark integration method Doina Verdes Basics of Seismic Engineering 2011

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2.9 The energy balance procedure • Is based on the comparison of two energies which are found on the structure during the earthquake: • The input energy into structure by the earthquake • The energy dissipated or stored by the structure The equation of energy balance is useful if it can be computed in each step of integration • Assumption: the induced energy is computed for an elastic linear system mS v Ei = 2

2

(9)

• Sv is the pseudo-velocity spectrum


27

The energy balance equation EI = EE +EH = (EES + EK )+ (EHξ + EHµ) • • • • • • •

(10)

EI = Input Energy EE = Elastic energy of the system EH = Energy due to deformations EES= Energy elastic strains EK = Kinetic energy EHξ = Energy dissipated by the damping EHµ= Energy dissipated by the plastic deformation


28

All types of energy are computed in the moment of structure collapse The collapse may be produced by: The fatigue at a reduced number of cycles; By reaching the maximum deformation of the structural elements; By the overturning effect due to the large lateral displacements.


29

The energetic procedure based on the ultimate displacements ECAP=Ep+EH

(11)

F FE

Elastic behavior Elastic-plastic behavior

Fy - the seismic design force

Fy

∆∆y C ∆Ue

ECAP =

∆u

∆

1 FC ∆ C + FC (∆U − ∆ C ) = FC ∆ C (ρ D − 0,5) 2 Doina Verdes Basics of Seismic Engineering 2011

(12)

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2.10 Seismic response spectra of the inelastic systems The spectrum one obtains from elastical spectrum by ductility factors. These can be computed using two proceedings : i)

ii)

The spectral displacement of the nonlinear system is equal with those of a linear system; The energia of the nonlinear system is equal with the energy of the linear elastically system.

F Fe

Fy=F Fc=F p pl


∆∆yc

∆u (∆e max)

∆

31

i) The spectral desplacement of the nonlinear system is equal with those of a linear system The displacements in the ultimate stage are: ∆e max= ∆u F

Fy Fe Fc =

=

Fe

ρd

∆y

Fe

∆u =

mS a

ρd

Fy=F Fcp=Fpl (13)

∆∆yc

∆u (∆e max)

∆

Sa – Elastic acceleration spectrum. ρd – desplacement ductility factor Doina Verdes Basics of Seismic Engineering 2011

32

The energy of the nonlinear system is equal with the energy of the linear elastical system F

1 1 ∆ C FC + (∆ u − ∆ e ) FC = ∆ e Fe 2 2 Fc =

1 2ρ d − 1

F e=

mS a 2ρ d − 1

(14)

Fe

Fcp=Fpl Fy=F

The spectral response for the elasticplastic systems one obtains by dividing elastic spectrum to the ductility factor ρ d or by the equation

∆∆yc

∆u (∆e max)

2ρ d − 1


33

∆

Newmark inelastic Spectrum (for pseudo acceleration)*

The Newmark-Hall spectrum may be converted into an “inelastic design response spectrum” by making the appropriate adjustments. To determine strength demands, the spectrum is divided by ductility in the higher period (equal displacement) realm but is divided by (2µ - 1) in the short period *Source: FEMA Instructional Material (equal energy) Complementing FEMA 451 Doina Verdes Basics of Seismic Engineering 2011

34

Elastic-plastic response spectrum for El Centro 1940 with 5% damping coeficient and ductilities 1; 1.5; 2; 4; 8.


35


By Doina Verdes

CHAPTER 3 ANALYSIS OF SEISMIC RESPONSE MULTIDEGREE OF FREEDOM SYSTEMS

Contents

3.1Vibration Frequencies and Mode Shapes

3.2 Earthquake Response Analysis by Mode Superposition

3.3 Response Spectrum Analysis for Multi-degree of Freedom Systems

3.4 Step-by-Step Integration


3

3.1 Introduction • In the dynamic analysis of most structures it is necessary to assume that the mass is distributed in more than one discrete lump. For most buildings the mass is assumed to be concentrated at the floor levels and to be subjected to lateral displacement only. • To illustrate the corresponding multi-degree-of-freedom analysis, consider a three story-building (Figure 3.1.). Each story mass represents one degree-of-freedom each with an equation of dynamic equilibrium.


4

mc

Axis of reference

mb

ma

yc(t)

uc,1

yb(t)

ub,1

&y&g

Hypothesis - the mass is assumed to be concentrated at the floor levels - the mass is assumed to be subjected to lateral displacement only (the building base is very rigid and the ground movement is assumed to be synchronically, in the same phase)

ya(t)

ua,1

Mode 1

uc,2 uc,3

ub,3

ub,2

ua,2

Mode 2

ua,3

Mode 3

Shapes of vibration due to mode 1 to 3

Each mass has 2 DOF Due to two Horizontal Translations and rotation Doina Verdes Basics of Seismic Engineering 2011

5

The equations of dynamic equilibrium

FI a + FDa + FS a = Fa (t )

[1]

FI b + FDb + FSb = Fb (t )

[2]

FI c + FDc + FSc = Fc (t )

[3]


6

The inertia forces in equation (1) are:

FI a = ma ⋅ u&&a

[4]

FI b = mb ⋅ u&&b

[5]

FI c = mc ⋅ u&&c

[6]


7

The inertia forces in matrix form:  F1a  ma     F1b  =  0 F   0  1c  

0 mb 0

0 0  mc 

u&&a    u&&b  u&&   c

[7]

or more generally:

FI = M ⋅ &y&

[8]

FI is the inertia force vector, M is the mass matrix and &y& is the acceleration vector. Doina Verdes Basics of Seismic Engineering 2011

8

• It should be noted that the mass matrix is of diagonal form for a lumped sum-system, giving no coupling between the masses. • In more generalized shape co-ordinate systems, coupling generally exists between the coordinates, complicating the solution. This is a prime reason for using the lumped-mass method.


9

The elastic forces in equation (1) depend on the displacement and using stiffness influence coefficients they may be expressed:

 FS a = k aa u a + k ab u b + k ac u c   FSb = k ba u a + k bb u b + k bc u c F = k u + k u + k u ca a cb b cc c  Sc


[9]

10

In matrix form  FSa  k aa     FSb  =  k ba  F  k  Sc   ca

k ab k bb k cb

k ac   k bc  k cc 

u a    ub  u   c

[10]

or more generally:

FS = k ⋅ u

[11]

F S is the elastic force vector, k is the stiffness matrix and u is the displacement vector The stiffness matrix k generally exhibits coupling and will be best handled by a standard computerized matrix analysis. Doina Verdes Basics of Seismic Engineering 2011

11

By analogy with the expression (9), (10) and (11) the damping forces may be expressed

FD = c ⋅ y&

[12]

F D is the damping force vector, c is the damping matrix and y& o is the velocity vector. In general it is not practicable to evaluate c and damping is usually expressed in terms of damping coefficients. Doina Verdes Basics of Seismic Engineering 2011

12

Using the Eqs. (8), (11) and (12) the equation of dynamic equilibrium (1) may be written generally as:

FI + FD + FS = F (t )

[13]

which is equivalent to

Mu&& + cu& + ku = − mu&&g (t )


[14]

13

3.2 Vibration Frequencies and Mode Shapes • The dynamic response of a structure is dependent upon the frequency (or period T) and the displaced shape • The first step in the analysis of a MDOF system is to find its free vibration frequencies and mode shapes. In free vibration there is no external force and damping is taken as zero.


14

• The equation of motion (14) becomes:

Mu&& + ku = 0

[15]

Making the necessary steps of calcullus on obtains:

kuˆ − ω 2 Muˆ = 0

[16]

the eigenvalue equation and is readily solved for ω by standard computer programs


15

• An important simplification can be made in equations of motion because of the fact that each mode has an independent equation of exactly equivalent form to that for a single degree of freedom system. Because of orthogonality properties of mode shapes, Eq. (14) can be written T φ 2 n F (t ) & & & Yn + 2ξ nω nYn + ω n Yn = T φ n Mφ n

Yn is a generalized displacement in mode n leading to the actual displacement and ønT is the row mode vector corresponding to the column vector øn.


16

Earthquake Response Analysis by Mode Superposition • The dynamic analysis of a multi-degree-of-freedom system can be simplified to the solution of Eq. (14) for each mode, and the total response is then obtained by superposing the modal effects. • In terms of excitation by earthquake ground motion üg(t) Eq. (15) becomes:


17

Y&&n + 2ξω nY&n + ω n2Yn =

Ln u&&g (t ) T φ n Mφ n

[16]

The response of the n–th mode at any time demands the solution of Eq for Yn(t). where Yn is a generalized displacement in mode n leading to the actual displacement and T is the row mode vector corresponding to the Φn column vector øn.


18

This may be done by evaluating the Duhamel integral:

Ln 1 Yn (t ) = T ⋅ φ n Mφ n ω n

∫

t

0

u&&g (σ )e −ξω n (t −σ ) dσ


[17]

19

• This displacement of floor (or mass) i at t is then obtained by superimposing the response of all modes evaluated at this time t: N

u i = ∑ φ inYn (t )

[18]

n =1

where øin is the relative amplitude of displacement of mass i in mode n. • It should be noted that in structures with many degrees of freedom most of the vibration energy is absorbed in the lower modes, and it is normally sufficiently accurate to superimpose the effects of only the first few modes. Doina Verdes Basics of Seismic Engineering 2011

20

The earthquake forces • The earthquake forces in the structure may then be expressed in terms of the effective accelerations 2 & & Yn eff (t ) = ω n Yn (t )

[19]

from which the acceleration at any floor i is

&u&in eff (t ) = ω n2φ inYn (t )

[20]

and the earthquake force at any floor “i” is

[

]

qin (t ) = mi ω n2φinY&&n (t ) Doina Verdes Basics of Seismic Engineering 2011

[21] 21

Superimposing all the modal contributions, the earthquake forces in the total structure may be expressed in matrix form as:

[

u a max ≈ u a2,1 max + u a2,2 max + u a2,3 max

1 2

]

[22]

the entire history of displacement and force response can be defined for any multi-degree of freedom system, having first determined the modal response amplitudes.


22

R (t)

First mode Time u 1max

Second mode Time

u 2max

Nth mode

Time u n max

Superimposing all the modal contributions


23

3.3 Response Spectrum Analysis for Multidegree of Freedom Systems • As with single degree-of-freedom structures considerable simplification of the analysis is achieved if only the maximum response to each mode is considered rather than the whole response history. • If the maximum value Yn max of the Duhamel equation (17) is calculated, the distribution maximum displacement in that mode is:


24

u n max = φ nYn max

Ln S vn = φn T ⋅ φ n Mφ n ω n

[23]

and the distribution of maximum earthquake forces in that mode is: 2 n n max

q n max = Mφ nω Y

Ln = Mφ n T ⋅ S an φ n Mω n

[24]

Where Svn is the spectral velocity for mode n; San is the spectral acceleration for mode n. Eqs. (23) and (24) enable the maximum response in each mode to be determined Doina Verdes Basics of Seismic Engineering 2011

25

• As the modal maxima do not necessarily occur at the same time, not necessarily have the same sign, they cannot be combined to give the precise total maximum response. The best that can be done in a response spectrum analysis is to combine the modal responses on a probability basis. Various approximate formula for superposition are used, the most common being the Square Root of Sum of Squares (SRSS) procedure. As an example the maximum deflection at the top of a three-story structure (three masses) would be:

[



1 2

]

[25]

26

Exemple of a three stories frame Response Spectrum Analysis [21]


27

Solutions for System in Undamped Free Vibration Mode Shapes for Idealized 3-Story Frame


28

Concept of Linear Combination of Mode Shapes (Transformation of Coordinates)

U=ФY


29

Orthogonality conditions

The orthogonality condition is an extremely important concept as it allows for the full uncoupling of the equations of motion. The damping matrix (which is not involved in eigenvalue calculations) will be diagonalized as shown only under certain conditions. In general, C will be diagonalized if it satisfies the Caughey criterion: CM-1K = KM-1C Doina Verdes Basics of Seismic Engineering 2011

30

Development of uncoupled Equations of motions


31

The explicit form


32

Modal Damping Matrix • For structures without added dampers, the development of an explicit damping matrix, C, is not possible because discrete dampers are not attached to the dynamic DOF. However, some mathematical entity is required to represent natural damping. • An arbitrary damping matrix cannot be used because there would be no guarantee that the matrix would be diagonalized by the mode shapes. • The two types of damping shown herein allow for the uncoupling of the equations.


33

Rayleigh proportional Damping


34

Response Spectrum Method


35


• As the modal maxima do not necessarily occur at the same time, not necessarily have the same sign, they cannot be combined to give the precise total maximum response. The best that can be done in a response spectrum analysis is to combine the modal responses on a probability basis. Various approximate formula for superposition are used, the most common being the Square Root of Sum of Squares (SRSS) procedure. As an example the maximum deflection at the top of a three-story structure (three masses) would be:

[



1 2

]

[25]

37

3.4 Step-by-Step Integration Generally the response history is divided into very short time increments, during each of which the structure is assumed to be linearly elastic. Between each interval the properties of the structure are modified to match the current state of deformation. Therefore, the nonlinear response is obtained as a sequence of linear responses of successively differing system. In each time increment the following computation are made:


38

•

• •

• •

The stiffness of the structure for that increment is computed, based on the state of displacement existing at the beginning of the increment. Changes of displacement are computed assuming the accelerations to vary linearly during the interval. These changes of displacement are added to the displacement state of the beginning of the interval to give the displacement at the end of the interval. Stresses appropriate to the total displacement are computed. In the above procedure the equations of motion must be integrated in their original form during each time increment. For this purpose Eq. (14) may be written:

M∆u&& + c(t )∆u& + k (t )∆u = ∆F (t ) Doina Verdes Basics of Seismic Engineering 2011

[26] 39

∆FI + ∆FD + ∆FS = ∆F ef

Tangenta la curba

FS(t)

Fs1 Secanta la curba

?Fs

∆FI (t ) = FI (t + h ) − FI (t ) = m∆&y&(t )

Fs0

∆FD (t ) = FD (t + h ) − FD (t ) = c∆y& (t )

y(t) yo

?

y

y1

∆FS

∆FS (t ) = FS (t + h ) − FS (t ) = k∆y (t )

&y&s (t )

∆Fef (t ) = Fef (t + h ) − Fef (t ) = m∆&y&s (t )

∆y y1

&y&si +1

&y&si

ti

ti+1

t

m∆&y&(t ) + c∆y& (t ) + k∆y (t ) = −m∆&y&s (t )

∆h


40

• In order to avoid instability in the response calculated by these equations the length of the time step must be limited by the condition 1 h≤ TN 1.8

(6)

&y&g &y&gi +1

&y&gi

ti

ti+1

t

h

where TN is the vibration period of the highest mode (i.e., the shortest period) associated with the system eigenproblem. Doina Verdes BASICS OF SEISMICAL ENGINEERING 2011

41

• where • k(t) is the stiffness matrix for the time increment beginning at the time t, • ∆u is the change in displacement during the interval. • The determination of k for each increment is the most demanding part of the analysis, as all the individual member stiffness must be found each time or their current state of deformation. • The integration may be obtained applying the procedure ß Newmark.


42

Modal Analysis Equivalent Lateral Force Procedure Empirical period of vibration • Smoothed response spectrum • Compute total base shear,, as if SDOF • Distribute T along height assuming “regular” geometry • Compute displacements and member forces using standard procedures Doina Verdes Basics of Seismic Engineering 2011

43


By Doina Verdes

CHAPTER 4. METHODS OF SEISMIC ANALYSIS OF STRUCTURES

Doina Verdes BASICS OF SEISMIC ENGINEERING 2011

Contents • 4.1 Introduction • 4.2 Lateral force method of analysis Romanian Code P100/1-2006 • 4.3 Lateral force method of analysis- EC8 • 4.4 Time - history representation • 4.5 Non-linear static (pushover) analysis


4.1 Introduction The many methods for determining seismic forces in structures fall into two distinct categories: • Equivalent static force analysis; • Dynamic analysis. The three main techniques currently used for dynamic analysis are: Direct integration of the equation of motion by stepby-step procedures; Normal mode analysis; Response spectrum techniques. Doina Verdes BASICS OF SEISMIC ENGINEERING 2011

• a) the “lateral force method of analysis” for common buildings • b) the “modal response spectrum analysis", which is applicable to all types of buildings. As alternative to a linear method, a non-linear methods may also be used, such as: • c) non-linear static (pushover) analysis; • d) non-linear time history (dynamic) analysis


The Equivalent Lateral Force Procedure • Empirical computation of vibration period • Smoothed response spectrum • Compute total base shear seismic force • Distribute the base shear seismic force along height assuming “regular” geometry • Compute displacements and member forces using standard procedures Doina Verdes BASICS OF SEISMIC ENGINEERING 2011

5.2 Lateral force method of analysis Code P100/1-2006 procedure

• The design acceleration for each zone of seismic hazard corresponds to an average return period of reference equal 100 years. • The zonation of soil design acceleration ag of Romanian territory for seismic events with average return period of magnitude is noted: IMR = 100 years Doina Verdes BASICS OF SEISMIC ENGINEERING 2011

The zonation of Romanian territory depending on soil design acceration ag for seismic events with average return period (of magnitude) IMR = 100 years


The control period and the ag for Romanian territory (part of the table [22])

Basic representation of the seismic action • The earthquake motion at a given point of the surface is generally represented by an elastic ground acceleration response spectrum, henceforth called “elastic response spectrum”. • The horizontal seismic action is described by two orthogonal components considered as independent and represented by the same response spectrum.


Shape of horizontal elastic response spectrum of accelerations for Vrancea sources a), b), c) and Banat d)

a)

TC = 0.7s

c)

TC = 1.6s

TC = 1.0 s

b)

d)

TC = 0.7s

Design spectrum for non-linear analysis • The capacity of structural systems to resist seismic actions in the non-linear range generally permits their design for forces smaller than those corresponding to a linear elastic response.


FA(t)

FS(t)

c

k 1

1

y(t)

Linear elastic behavior

y& (t )

Stiffness

Nonlinear elastic behavior Doina Verdes BASICS OF SEISMIC ENGINEERING 2011

Damping

Base shear force • The seismic base shear force Fb, for each horizontal direction in which the building is analysed, is determined as follows: (4.1) Fb = γI Sd (T1) m λ where: • Sd (T1) ordinate of the design spectrum at period T1; • T1 fundamental period of vibration of the building for lateral motion in the direction considered; • m total mass of the building, above the foundation or above the top of a rigid basement, • λ correction factor, the value of which is equal to: • λ = 0,85 if T1 < 2 TC and the building has more than two storeys, or λ = 1,0 otherwise •

γI the importance factor


The deformed shape for the 1st mode: a. Computed by methods of structural dynamics b. approximated by horizontal displacements increasing linearly along the height of the building

Fn

sn

sn Fi

si

si zn zi

F1

s1

s1 z1

a. Doina Verdes BASICS OF SEISMIC ENGINEERING 2011

b.

The fundamental period of vibration period T1 • For the determination of the fundamental period of vibration period T1 of the building, expressions based on methods of structural dynamics (e.g. by Rayleigh method) may be used. • Alternatively, the estimation of T1 (in s) may be made by the following expression:

T1 = 2 u

(4.2)

• where: • u - lateral elastic displacement of the top of the building, in m, due to the gravity loads applied in the horizontal direction. Doina Verdes BASICS OF SEISMIC ENGINEERING 2011

Determination of the fundamental vibration periods T1 • For the determination of the fundamental vibration periods T1 of both planar models of the building, expressions based on methods of structural dynamics (e.g. by Rayleigh method) may be used for buildings with heights up to 40 m the value of T1 may be approximated by the following expression: T1 = Ct ⋅ H 3/ 4

(4.3)

Where: • T1 - fundamental period of building, in s, • C t is function of the structure type • 0,050 for all other structures • 0,075 for moment resistant space concrete frames and for eccentric braced • 0,085 for moment resistant space steel frames • H height of the building, in m. Doina Verdes BASICS OF SEISMIC ENGINEERING 2011

Design spectrum • design spectrum for the accelerations Sd(T) is an:

Inelastic response spectrum •Which can be obtained with the equation : β0

S d (t ) = a g [1 +

q

−1

TN

T]

(4.4)

• For the horizontal components of the seismic action the design spectrum, Sd(T), • is defined by the following expressions [EC8]: Doina Verdes BASICS OF SEISMIC ENGINEERING 2011

Case “a”

0 p T ≤ TB

 β0  −1   q S d (T ) = a g 1 + ⋅T  TB      

T > TB β (T ) S d (T ) = a g q

(4.5)

Case “b”

T the vibration period ag soil design acceleration q behavior factor Doina Verdes BASICS OF SEISMIC ENGINEERING 2011

(4.6)

ß(T) elastic response spectrum; T vibration period of a linear single-degree-of-freedom system; ag design ground acceleration on type A ground (ag); TB, TC limits of the constant spectral acceleration branch; TD value defining the beginning of the constant displacement response range of the spectrum; ß0 amplification factor of maximum horizontal acceleration of the soil by the structure;


Values of control periods for Romanian territory Table 4.1 T h e a v e ra g e in te rv a l o f re tu rn e a rth q u a k e m a g n itu d e IM R = 1 0 0 y e a rs F o r th e u ltim a te lim it s ta g e

V a lu e s o f c o n tro l p e rio d s T B, s T C, s TD, s

0 ,0 7 0 ,7 3


0 ,1 0 1 ,0 3

0 ,1 6 1 ,6 2

The behaviour factor q •

The behaviour factor q is an approximation of the ratio of the seismic forces, that the structure would experience if its response was completely elastic with 5% viscous damping, to the minimum seismic forces that may be used in design - with a conventional elastic response model - still ensuring a satisfactory response of the structure.


Behaviour factors for horizontal seismic action Nr.crt

DCM Sistem strctural Clădiri cu un nivel

1.

Cadre

Table 4.2

DCH

EC8

P100-1/2006

EC8

P100-1/2006

3,30

4,025

4,95

5,75

Clădiri cu mai multe niveluri şi cu o singură deschidere

4,00; 5,00

3,60

4,375

5,40

6,25

Clădiri cu mai multe niveluri şi cu mai multe deschideri

2.

Dual

Structuri cu cadre preponderente

P100- 92 (1/Ψ) 5,00; 6,66

4,00; 5,00

3,90

4,725

5,85

6,75

3,90

4,025; 4,375; 4,725;

5,85

5,75; 6,25; 6,75;

-

Structuri cu pereţi preponderenţi -

Structuri cu doi pereţi în fiecare direcţie 3.

Pereţi Structuri cu mai mulţi pereţi

3,60

4,375

5,40

3

3

3 3

3 3

4,00

3

3

4,00

6,25 4,00

4,00 4,00

4,00

Structuri cu pereţi cuplaţi Flexibil la torsiune(nucleu) 4. 5.

Pendul inversat

4,00

3,60 2 2 1,5 1,5

4,375 2 2 2 2

5,40 3 3 3 3


6,25 3 3 3 3

2,86

23

Nr.crt

Sistem strctural

4

DCM P1001/2006 2,5; 4

4

2,5; 4

4

4

4 4 4 2

4 4 4 2

2 4

EC8

DCH EC8

Structuri parter 1.

Cadre necontravântuite

2.

Cadre contravântuite centric

2,50; 5,00; 5,50

6,00; 6,50. 4 4 2,5

6,00; 6,50 4 4 2,5

2 4

2,5

2,5

2,00; 2,50 5,00

3.

Cadre contravântuite excentric

4

4

6,00

6,00

4.

Pendul inversat Structuri cu nuclee sau pereţi de beton

2 2 2 2

2 2 2 2

6,00 3 3

6,00 3 3

4

4

4

4

4,8

-

4

-

-

4

-

5. Cadre necontrav. asociate cu cadre contravântuite în X şi alternante 6.

4,8

Cadre duale Cadre necontrav. asociate cu cadre contravântuite excentric

P10092 (1/Ψ) 2,94; 3,46; 5,00; 5,88

5,50

Structuri etajate Contravântuiri cu diagonale întinse Contravântuiri cu diagonale in V

P1001/2006 2,5;


6,00

5,88 4,00; 5,00

1,54; 2,00 2,00; 2,20; 4,00; 5,00 2,00; 2,20; 4,00; 5,00

24

Distribution of the horizontal seismic forces Fb = γI Sd (T1) m λ

(4.7)

• The fundamental mode shapes in the horizontal directions of analysis of the building may be calculated using methods of structural dynamics or • may be approximated by horizontal displacements increasing linearly along the height of the building.


The deformed shape for the 1st mode

Fn

sn

sn Fi

si

si zn zi

F1

s1

s1 z1


b.

The seismic action effects shall be determined by applying, to the two planar models, horizontal forces Fi to all storeys.

Fi = Fb ⋅

mi ⋅ si n

∑m ⋅s i

(4.8)

i

i =1

where: Fi horizontal force acting on storey i; Fb seismic base shear according to expression (4.1 ); si, sj displacements of masses mi, mj in the fundamental mode shape; mi, mj storey masses Doina Verdes BASICS OF SEISMIC ENGINEERING 2011

• When the fundamental mode shape is approximated by horizontal displacements increasing linearly along the height, the horizontal forces Fi are given by:

Fi = Fb ⋅

mi ⋅ zi

(4.9)

n

∑m ⋅ z i

i

i =1

zi, zj heights of the masses; mi, mj above the level of application of the seismic action (foundation or top of a rigid basement).

Fi

The horizontal forces Fi shall be distributed to the lateral load resisting system assuming rigid floors. Doina Verdes BASICS OF SEISMIC ENGINEERING 2011

i

Torsional effects if lateral stiffness and mass are symmetrically distributed in plan • If the lateral stiffness and mass are symmetrically distributed in plan and unless the accidental eccentricity is taken into account . • Whenever a spatial model is used for the analysis, the accidental torsion effects referred may be determined as the envelope of the effects resulting from the application of static loadings, consisting of sets of torsion moments Mai about the vertical axis of each storey i: Mai = eai Fbi (4.10) e=0,05Li Doina Verdes BASICS OF SEISMIC ENGINEERING 2011

(4.11)

Mx torsional moment applied at storey i about its vertical axis; e 1x – the accidental eccentricity on o-x axis e 1y – the accidental eccentricity on o-y axis CM – the center of mass Fbx – the seismic force on o-x direction Fby – the seismic force on o-y direction Doina Verdes BASICS OF SEISMIC ENGINEERING 2011

Reason for Consideration of Accidental Torsion [22]

Fk,n

Fk,n – the seismic level force at k level , in “n” th mode of vibration Doina Verdes BASICS OF SEISMIC ENGINEERING 2011

The case of “natural” eccentricity

Mtx=Tbx e ix Mty=Tby e iy e ix ,e iy = the “natural” eccentricity

e 0ix ,e 0iy = the distance between the center of masse and center of rigidity at level “i” e 1ix ,e 1iy = the accidental eccentricity Doina Verdes BASICS OF SEISMIC ENGINEERING 2011

(4.12) (4.13)

(4.14) (4.15)

The distribution of seismic force to structural vertical elements (4.16)

(4.17)


Ground conditions The construction site and the nature of the supporting ground should normally be free from risks of: • ground rupture, • slope stability and • permanent settlements caused by liquefaction or densification in the event of an earthquake.


5.3 Lateral force method of analysis- EC8 • This type of analysis may be applied to buildings whose response is not significantly affected by contributions from higher modes of vibration. • These requirements are deemed to be satisfied in buildings which fulfil the two following conditions: a) they have fundamental periods of vibration T1 in the two main directions smaller than the following values where TC is given in Codes’ Tables; b) they meet the criteria for regularity in elevation

T 1≤ 2 s T1 ≤ 4TC Doina Verdes BASICS OF SEISMIC ENGINEERING 2011

(4.18) (4.19)

Base shear force • The seismic base shear force Fb, for each horizontal direction in which the building is analysed, is determined as follows: (4.20) Fb = γI Sd (T1) m λ where: • Sd (T1) ordinate of the design spectrum at period T1; • T1 fundamental period of vibration of the building for lateral motion in the direction considered; • m total mass of the building, above the foundation or above the top of a rigid basement, • λ correction factor, the value of which is equal to: • λ = 0,85 if T1 < 2 TC and the building has more than two storeys, or λ = 1,0 otherwise •

γI the importance factor


The design spectrum •

For the horizontal components of the seismic action the design spectrum, Sd(T), is defined by the following expressions: (4.21) (4.22)

Where: Sd(T) ordinate of the design spectrum, (4.23) q behaviour factor, β lower bound factor for the spectrum Values of the parameters S, T B, (4.24) T C, and T D are given in following tables


Elastic response spectrum, Type 1

Values of the parameters describing the Type 1 elastic response spectrum

Elastic response spectrum, Type 2

Values of the parameters describing the Type 2 elastic response spectrum

Classification of subsoil classes EC8

• • • • • • • • •

Where: Se (T) ordinate of the elastic response spectrum, T vibration period of a linear single degree of freedom system, ag design ground acceleration (ag = agR γI), k modification factor to account for special regional situations, TB, TC limits of the constant spectral acceleration branch, TD value defining the beginning of the constant displacement response range of the spectrum, S soil parameter, ξ damping correction factor with reference value ξ =1 for 5% viscous damping Factor λ accounts for the fact that in buildings with at least three storeys and translation degrees of freedom in each horizontal direction, the effective modal mass of the 1st (fundamental) mode is smaller – on average by 15% - than the total building mass. Doina Verdes BASICS OF SEISMIC ENGINEERING 2011

Design spectrum for elastic analysis The capacity of structural systems to resist seismic actions in the non-linear range generally permits their design for forces smaller than those corresponding to a linear elastic response. To avoid explicit inelastic structural analysis in design, the capacity of the structure to dissipate energy, through mainly ductile behaviour of its elements and/or other mechanisms, is taken into account by performing an elastic analysis based on a response spectrum reduced with respect to the elastic one, henceforth called ''design spectrum'', This reduction is accomplished by introducing the behaviour factor q. Doina Verdes BASICS OF SEISMIC ENGINEERING 2011

The behaviour factor q •

The behaviour factor q is an approximation of the ratio of the seismic forces, that the structure would experience if its response was completely elastic with 5% viscous damping, to the minimum seismic forces that may be used in design - with a conventional elastic response model - still ensuring a satisfactory response of the structure.


• The value of the behaviour factor q, which also accounts for the influence of the viscous damping being different from 5%, are given for the various materials and structural systems and according to the relevant ductility classes in the various Parts of EN 1998. • The value of the behaviour factor q may be different in different horizontal directions of the structure, although the ductility classification must be the same in all directions.


q the factor of structure behavior; the values are standard function of structure type and the capacity of energy dissipation Example the EC8 formula for reinforced concrete buildings where: q 0 basic value of the behavior factor dependent on the type of the structural system k w factor reflecting the prevailing failure mode in structural systems

(4.25)

Basic value of q 0 of behavior factor for systems regular in elevation


• The reference method for determining the seismic effects is the modal response spectrum analysis, using a linear-elastic model of the structure and the design spectrum. • Depending on the structural characteristics of the building one of the following two types of linearelastic analysis may be used:


Horizontal elastic response spectrum (1) For the horizontal components of the seismic action, the elastic response spectrum ß(T) is defined by the following expressions for damping correction factor for 5% viscous damping (2) If for special cases a viscous damping ratio different from 5% is to be used, this value will be given in the relevant Part of EN 1998.


Case “a”

T ≤ TB ( β 0 − 1) β (T ) = 1 + T TB

(4.26)

Case “b”

TB p T ≤ TC

β (T ) = β 0


(4.27)

Case “c”

TC p T ≤ TD TC β (T ) = β 0 T

(4.27)

Case “d”

T f TD TCTD β (T ) = β 0 2 T


(4.28)

Importance categories and importance factors Buildings are generally classified into 4 importance categories, which depend on the size of the building, on its value and importance for the public safety and on the possibility of casualties in case of collapse


Table 4.3 Importance category I

II

Buildings

Buildings whose integrity during earthquakes is of vital importance for civil protection, e.g. hospitals, fire stations, power plants, etc. Buildings whose seismic resistance is of importance in view of the consequences associated with a collapse, e.g. schools, assembly halls,cultural institutions etc.

III IV

Ordinary buildings, not belonging to the other categories Buildings of minor importance for public safety, e.g. agricultural buildings, etc. Doina Verdes BASICS OF SEISMIC ENGINEERING 2011

Seismic zones • For the purpose of EN 1998, national territories shall be subdivided by the • National Authorities into seismic zones, depending on the local hazard. By definition, • the hazard within each zone is assumed to be constant. • (2) For most of the applications of EN 1998, the hazard is described in terms of a single parameter, i.e. the value of the reference peak ground acceleration on rock or firm soil agR.


• Additional parameters required for specific types of structures are given in the relevant Parts of EN 1998. • The reference peak ground acceleration, chosen by the National Authorities for each seismic zone, corresponds to the reference return period chosen by National Authorities.


5.4 Time - history representation • The seismic motion may also be represented in terms of ground acceleration time-histories and related quantities (velocity and displacement). • When a spatial model is required, the seismic motion shall consist of three simultaneously acting accelerograms. The same accelerogram may not be used simultaneously along both horizontal directions. • The description of the seismic motion may be made by using artificial accelerograms and recorded or simulated accelerograms.


Non-linear methods • The mathematical model used for elastic analysis shall be extended to include the strength of structural elements and their post-elastic behaviour. • As a minimum, bilinear force – deformation envelopes should be used at the element level. In reinforced concrete and masonry buildings, the elastic stiffness of a bilinear force-deformation relation should correspond to cracked sections.

Bilinear force – deformation relation of the element

Zero post-yield stiffness may be assumed, If strength degradation is expected

In ductile elements, expected to exhibit post-yield excursions during the response, the elastic stiffness of a bilinear relation should be the secant stiffness to the yield-point. Trilinear envelopes, which take into account pre-crack and post-crack stiffnesses, are allowed.


5.5 Non-linear static (pushover) analysis Pushover analysis is a non-linear static analysis under constant gravity loads and monotonically increasing horizontal loads. It may be applied to verify the structural performance of newly designed and of existing buildings for the following purposes: a) to verify or revise the overstrength ratio values αu/α1; b) to estimate expected plastic mechanisms and the distribution of damage; c) to assess the structural performance of existing or retrofitted buildings; Doina Verdes BASICS OF SEISMIC ENGINEERING 2011

• Buildings not complying with the regularity criteria shall be analysed using a spatial model. • For buildings complying with the regularity the analysis may be performed using two planar models, one for each main horizontal direction. • For low-rise masonry buildings, in which structural walls are dominated by shear, each storey may be analysed independently.


Lateral loads The vertical distributions of lateral loads which should be applied are at least two : − “uniform” pattern, based on lateral forces that are proportional to mass regardless of elevation (uniform response acceleration) - “modal” pattern, proportional to lateral forces consistent with the lateral force distribution determined in elastic analysis Lateral loads shall be applied at the location of the masses in the model. The torsion due to accidental eccentricity shall be considered. Doina Verdes BASICS OF SEISMIC ENGINEERING 2011

Plastic mechanism

Determination of the idealized elasto - perfectly plastic force – displacement relationship.


Capacity curve

The relation between base shear force and the control displacement (the “capacity curve”) should be determined by pushover analysis for values of the control displacement ranging between zero and the value corresponding to 150% of the target displacement. The control displacement may be taken at the centre of mass at the roof of the building.

Overstrength factor

When the overstrength (αu/α1) should be determined by pushover analysis, the lower value of overstrength factor obtained for the two lateral load distributions should be used. Doina Verdes BASICS OF SEISMIC ENGINEERING 2011

Plastic mechanism The plastic mechanism shall be determined for both lateral load distributions. The plastic mechanisms should comply with the mechanisms on which the behaviour factor q used in the design is based.

Target displacement

Target displacement is defined as the seismic demand in terms of the displacement of an equivalent single-degree-of-freedom system in the seismic design situation. Doina Verdes BASICS OF SEISMIC ENGINEERING 2011


By Doina Verdes

CHAPTER 5

EARTHQUAKE RESISTANT DESIGN


Contents

5.1 Introduction 5.2 Performance Based Engineering 5.3 Performance Requirements and Compliance Criteria 5.4 The guiding principles governing the conceptual design against seismic hazard


3

5.1 Introduction • The basic principle of any design is that the product should meet the owner’s requirements, which may be reduced to the criteria: • Function; • Cost; • Reliability.


Reliability • While the terms function and cost are simple in principle, reliability concerns various technical factors relating to serviceability and safety. • As the above three criteria are interrelated, and because of the normal constraints on cost, compromises with function and reliability generally have to be made


• The term reliability is used here in its normal language qualitative sense and in its technical sense, where it is a quantitative measure of performance stated in terms of probabilities (of failure or survival). • The required reliability is achieved if enough of the elements of the design behave satisfactorily under the design earthquake. The elements that may be required to behave in agreed ways during earthquakes include structure, architectural elements, equipment, and contents.


Up to the mid-1980s it was common practice to design normal structures or equipment to meet two criteria: (1) in moderate, frequent earthquakes the structure or equipment should be undamaged; (2) in strong, rare earthquakes the structure or equipment could be damaged but should not collapse.


• The main intention of the second of these criteria was to save human lives, while the definition of the terms “strong”, “rare”, “moderate”, and “frequent” have varied from place to place, and have tended to be rather imprecise because of the uncertainties in the state-of-the-art. • Indeed, design has generally only been carried out explicitly for criterion (2), the assumption being made that, in so doing, it could be deemed that criterion (1) would automatically be satisfied.


In our days the Seismic requirements provide minimum standards for use in building design to maintain public safety in an extreme earthquake. • Seismic requirements do not necessarily limit damage, maintain function, or provide for easy repair. • Design forces are based on the assumption that a significant amount of inelastic behavior will take place in the structure during a design earthquake.


For reasons of economy and affordability, the design forces are much lower than those that would be required if the structure were to remain elastic. • In contrast, wind-resistant structures are designed to remain elastic under factored forces. • Specified code requirements are intended to provide for the necessary inelastic seismic behavior. • The buildings survival in large earthquakes depends directly on the ability of their resistance systems to dissipate hysteretic energy while undergoing (relatively) large inelastic deformations. Doina Verdes BASICS OF SEISMIC ENGINEERING 2011

5.2 Performance Based Engineering


Selection of performance design objectives The three phases of the design process of the entire building system, i.e., - conceptual overall design; - preliminary numerical design; - final design and detailing. The acceptability checks of the designs arrived at in the above three phases. Quality assurance during construction (NOT in the last point).


PERFORMANCE BASED ENGINEERING CHECK SUITABILITY OF THE SITE DISCUSS WITH CLIENT THE PERFORMANCE LEVEL AND SELECT THE MINIMUM PERFORMANCE DESIGN OBJECTIVES

SITE SUITABILITY ANALYSIS (USE MICROZONATION MAP

• USE PERFORMANCE MATRIX • SERVICEABILITY UNDER MINOR EARTHQUAKES • FUNCTIONALITY UNDER MODERATE EARTHQUAKES • STRUCTURAL STABILITY UNDER EXTREME EARTHQUAKES

CONDUCT CONCEPTUAL OVERAL DESIGN, SELECTING CONFIGRATION STRUCTURAL LAYOUT, STRUCTURAL SYSTEM, STRUCTURAL MATERIALS AND NONSTRUCTURAL COMPONENTS

NO

ACCEPTABILITY CHECKS OF CONCEPTUAL OVERAL DESIGN

USE GUIDELINES

USE PEER REVIEW


NUMERICAL PRELIMINARY DESIGN

NO

•USE LINEAR AND NONLINEAR STATIC PUSHOVER DINAMIC TIME HISTORY ANALYSIS METHODS •USE PEER REVIEW

ACCEPTABILIT Y CHECKS OF PRELIMINARY DESIGN YES FINAL DESIGN AND DETAILING

NO

DESIGN TO COMPLY SIMULTANOUSLY WITH AT LEAST TWO LIMIT STATES (Ultimate limit states, Serviceability limit states)

ACCEPTABILITY CHECKS OF FINAL DESIGN AND DETAILING

•USE LINEAR AND NONLINEAR -STATIC PUSHOVER AND -DINAMYC TIME HISTORY ANALYSIS METHODS •EXPERIMENTAL DATA AND •INDEPENDENT REVIEW •USE LINEAR AND NONLINEAR -STATIC PUSHOVER AND -DINAMYC TIME HISTORY ANALYSIS METHODS •EXPERIMENTAL DATA AND •INDEPENDENT REVIEW

YES

QUALITY ASSURANCE DURING CONSTRUCTION MONITORING, MAINTENANCE AND FUNCTION Doina Verdes BASICS OF SEISMIC ENGINEERING 2011

Site suitability analysis of the selected site (Ground conditions)

The construction site and the nature of the supporting ground should normally be free from risks of: •ground rupture, •slope stability and •permanent settlements caused by liquefaction or densification in the event of an earthquake.

The collapse of a bridge placed on the seismic fault during the earthquake Taiwan 1999


1989 Earthquake in Loma Prieta, California, Bridge failure.


Site suitability analysis of the selected site

Romanian Territory the design acceleration and Control period TC of the soil

Elastic response spectra for horizontal components of soil movement (Romanian Territory ) TC = 0.7s


5.3 Performance Requirements and Compliance Criteria i) Selection of performance design objectives SEAOC Vision 2000, 1999

ii) Conforming Eurocode 8 iii) Conforming P100/2006


Seismic performance design matrix (SEAOC Vision 2000, 1999)


Building Performance Levels and Ranges*

Source: FEMA Instructional Material Complementing FEMA 451


Total costs for different performance design objectives

Conforming SEAOC Vision 2000, 1999 Doina Verdes BASICS OF SEISMIC ENGINEERING 2011

Quality assurance during construction • Maintenance (modification and repairs) • Monitoring of occupancy (function) • Evaluation of seismic vulnerability of existing buildings • Seismic upgrading of existing hazardous buildings • Massive education and information dissemination programs


Performance requirements and compliance criteria Conforming: EUROCODE 8 and P100/2006


Fundamental requirements Structures in seismic regions shall be designed and constructed in such a way, that the following requirements are met, each with an adequate degree of reliability: No collapse requirement Damage limitation requirement


a. Requirement No collapse : The structure shall be designed and constructed to withstand the seismic action without local or global collapse, thus retaining its structural integrity and a residual load bearing capacity after the seismic events. The reference seismic action is associated with a reference probability of excedance in 50 years and a reference return period.


IZMIT Earthquake, 1999 Turkey


b. Requirement: Damage limitation The structure shall be designed and constructed to withstand a seismic action having a larger probability of occurrence than the seismic action used for the verification of the “no collapse requirement”, without the occurrence of damage and the associated limitations of use (the costs of which would be disproportionately high in comparison with the costs of the structure itself).


The Codes Target reliabilities for the “no collapse requirement” and for the “damage limitation requirement” are established by the National Authorities for different types of buildings or civil engineering works on the basis of the consequences of failure. Reliability differentiation is implemented by classifying structures into different importance categories.


Importance classes for buildings cf EC8


Compliance Criteria In order to satisfy the fundamental requirements the following limit states shall be checked : - Ultimate limit states are those associated with collapse or with other forms of structural failure which may endanger the safety of people. - Serviceability limit states are those associated with damage occurrence, corresponding to states beyond which specified service requirements are no longer met.


The structural system shall be verified as having the resistance and ductility. The resistance and ductility to be assigned to the structure are related to the extent to which its nonlinear response is to be exploited.


If the building • configuration is symmetrical or quasi-symmetrical, • a symmetrical structural layout, well distributed in-plan, is an obvious solution for the achievement of uniformity. • The use of evenly distributed structural elements increases redundancy and allows a more favourable redistribution of action effects and widespread energy dissipation across the entire structure.


Criteria for regularity in elevation All lateral load resisting systems, like cores, structural walls or frames, run without interruption from their foundations to the top of the building or, if setbacks at different heights are present, to the top of the relevant zone of the building. Both the lateral stiffness and the mass of the individual storeys remain constant or reduce gradually, without abrupt changes, from the base to the top. In framed buildings the ratio of the actual storey resistance to the resistance required by the analysis should not vary disproportionately between adjacent storeys. Within this context the special aspects of masonry infilled frames have to be treated. Doina Verdes BASICS OF SEISMIC ENGINEERING 2011

Criteria for structural regularity Building structures for the purpose of seismic design, are distinguished as regular and non-regular. This distinction has implications on the following aspects of the seismic design: − the structural model, which can be either a simplified planar or a spatial one, − the method of analysis, which can be either a simplified response spectrum analysis (lateral force procedure) or a multi-modal one, − the value of the behaviour factor q, which can be decreased depending on the type of non-regularity in elevation, i.e.: geometric non-regularity (exceeding the limits ), non-regular distribution of over strength in elevation (exceeding the limits). Doina Verdes BASICS OF SEISMIC ENGINEERING 2011

With respect to the lateral stiffness and mass distribution, the building structure is approximately symmetrical in plan with respect to two orthogonal axes. The plan configuration is compact, i.e., at each floor is delimited by a polygonal convex line. If in plan set-backs (re-entrant corners or edge recesses) exist, regularity in plan may still be considered satisfied provided that these set-backs do not affect the floor in-plan stiffness and that, for each set-back, the area between the outline of the floor and a convex polygonal line enveloping the floor does not exceed 6 % of the floor area.


The in-plane stiffness of the floors is sufficiently large in comparison with the lateral stiffness of the vertical structural elements, so that the deformation of the floor has a small effect on the distribution of the forces among the vertical structural elements. In this respect, the L, C, H, I, X plane shapes should be carefully examined, notably as concerns the stiffness of lateral branches, which should be comparable to that of the central part, in order to satisfy the rigid diaphragm condition. The application of this paragraph should be considered for the global behaviour of the building. The slenderness η=Lx/Ly of the building in plan is not higher than 4.


A simplified definition, for the classification of structural regularity in plan and for the approximate analysis of torsional effects, is possible if the two following conditions are satisfied: All lateral load resisting systems, like cores, structural walls or frames, run without interruption from the foundations to the top of the building. The deflected shapes of the individual systems under horizontal loads are not very different. This condition may be considered satisfied in case of frame systems and wall systems. In general, this condition is not satisfied in dual systems. Doina Verdes BASICS OF SEISMIC ENGINEERING 2011

The foundation elements and the foundation-soil interaction It shall be verified that both the foundation elements and the foundation-soil are able to resist the action effects resulting from the response of the superstructure without substantial permanent deformations.


Modeling Procedures for Embedded Structures* The actual soil-foundation structure system is excited by a wave field that is incoherent both vertically and horizontally and which may include waves arriving at various angles of incidence. These complexities of the ground motions cause foundation motions to deviate from free-field motions. This complex ground excitation acts on stiff, but non-rigid, foundation walls and the base slab, which in turn interact with a flexible and nonlinear soil medium having a significant potential for energy dissipation. Finally, the structural system is connected to the base slab, and possibly basement asWITH well. *INPUT GROUNDto MOTIONS FOR TALLwalls BUILDINGS SUBTERRANEAN LEVELS Authors: Jonathan P. Stewart and Salih Tileylioglu Civil & Environmental Engineering Department, UCLA Doina Verdes BASICS OF SEISMIC ENGINEERING 2011

There are two classical methods for modeling the problem soil – foundationstructure. The first is a direct approach, - a computational model of the full structure, foundation, and soil system is set up and excited by a complex and incoherent wave field. This problem is difficult to solve from a computational standpoint, and hence the direct approach is rarely used in practice.



In the second approach (referred to as the substructure approach), the complex soil-foundation-structure interaction problem is divided into three steps: Kinematic interaction, Foundation - soil flexibility and damping, Foundation flexibility and damping.


Substructure approach to solution of soil-foundation-structure interaction using rigid foundation or flexible foundation assumption


θ g = the foundation rotation u s = the foundation translation a. Rigid foundation

b. Structure with foundation flexibility - flexibility and damping)


Overturning and sliding stability • The structure as a whole shall be checked to be stable under the design seismic action. Both overturning and sliding stability shall be considered.

Influence of second order effects In the analysis the possible influence of second order effects on the values of the action effects shall be taken into account Doina Verdes BASICS OF SEISMIC ENGINEERING 2011

5.4 The guiding principles governing the conceptual design against seismic hazard


The guiding principles governing the conceptual design against seismic hazard are:

− uniformity, symmetry and redundancy - structural simplicity − bi-directional resistance and stiffness, − torsional resistance and stiffness, − diaphragmatic behaviour at storey level, − adequate foundation Doina Verdes BASICS OF SEISMIC ENGINEERING 2011

The form in plan recommended in seismic design

a.

b.

c.

d.

e.

f.

• Uniformity is characterised by an even distribution of the structural elements which, if fulfilled in-plan, allows short and direct transmission of the inertia forces created in the distributed masses of the building. If necessary, uniformity may be realised by subdividing the entire building by seismic joints into dynamically independent units, provided that these joints are designed against pounding of the individual units.


Uniformity in the development of the structure along the height of the building is also important, since it tends to eliminate the occurrence of sensitive zones where concentrations of stress or large ductility demands might prematurely cause collapse. If the building configuration is symmetrical or quasisymmetrical, a symmetrical structural layout, well distributed in-plan, is an obvious solution for the achievement of uniformity. The use of evenly distributed structural elements increases redundancy and allows a more favourable redistribution of action effects and widespread energy dissipation across the entire structure. Doina Verdes BASICS OF SEISMIC ENGINEERING 2011

Symmetry • In seismic area it has to be searched building shapes as simplest and symmetric as possible, in plan as much as in elevation. Many of the successful realizations aesthetic • Symmetry is desirable for much the same reasons. It is worth pointing out that symmetry is important in both directions in plan and in elevation as well. Lack of symmetry produces torsion effects which are sometimes difficult to asses and can be very destructive.


• The introduction of deep reentrant angles into the facades of buildings introduces complexities into the analysis which makes them potentially less reliable than simple forms. Buildings of H-, L-, T-, and Yshape in plan have often been severely damaged in earthquakes. • External lifts and stairwells provide similar dangers, and should be used with the appropriate attention to analysis and design. Doina Verdes BASICS OF SEISMIC ENGINEERING 2011

a. e.

f.

b.

c.

g.

d.

h.

Seismic joint condition Buildings shall be protected from earthquake-induced pounding with adjacent structures or between structurally independent units of the same building. If the floor elevations of the building or independent unit under design are the same as those of the adjacent building or unit, the above referred distance may be reduced by a factor of 0,7 (EC8).


This is deemed to be satisfied if the distance from the boundary line to the potential points of impact is not less than the maximum horizontal displacement of the adjacent parts according to expression.

∆= ∆ 1+ ∆ 2+20 mm


Building separation to avoid pounding


Length in plan Structures which are long in plan naturally experience greater variation in ground movement and soil conditions over their length than short ones. These variations may be due to out- of-phase effects or to differences in geological conditions, which are likely to be most pronounced along bridges where depth to bedrock may change from zero to very large. The effects on structure will differ greatly, depending on whether the foundation structure is continuous, or a series of isolated footings, and whether the superstructure is continuous or not.


• Continuous foundations may reduce the horizontal response of the superstructure at the expense of push-pull forces in the foundation itself. Such effects should be allowed for in design, either by designing for the stressed induced in the structure or by permitting the differential movements to occur by incorporating movement gaps.


Shape in elevation

h>4L1

L1

L2

a.

b.

Height/width ratios in excess of about 4 lead to increasingly uneconomical structures and require dynamic analysis for proper evaluation of seismic responses. Doina Verdes BASICS OF SEISMIC ENGINEERING 2011

h>4L1

those with sudden changes in width should be avoided in strong earthquakes areas.

h<4L1

Very slender structures and

L1 a.

b.

Sudden changes in width of a structure, such as setbacks in the facades of buildings, generally imply a step in the dynamic response characteristics of the structure at that height, and modern earthquake codes have special requirements for them. If such a shape is required in a structure it is best designed using dynamic earthquake analysis, in order to determine the stress concentrations at the notch and the shear transfer through the horizontal diaphragm below the notch.


Criteria for regularity of buildings with setbacks (EC8)

a.

c.

b.

d.

(setback occurs below 0,15H)


Very slender buildings have high column forces and foundation stability may be difficult to achieve. Also higher mode contributions may add significantly to the seismic response of the superstructure. For comparison, in the design of latticed towers for wind loadings, aspect ratios in excess of about 6 become uneconomical.


Uniform and continuous distribution of strength and stiffness This concept is closely related to that of simplicity and symmetry. The structure will have the maximum chance of surviving an earthquake if: The load bearing members are uniformly distributed.


All columns and walls are continuous and without offsets from roof to foundation; All beams are free of offsets; Columns and beams are coaxial - Reinforced concrete columns and beams are nearly the same width; - No principal members change section suddenly; - The structure is as continuous (redundant) and monolithic as possible. a.

Yes Doina Verdes BASICS OF SEISMIC ENGINEERING 2011

b.

No

Appropriate stiffness In designing constructions to have reliable seismic behavior the design of structures to have appropriate stiffness is an important task which is often made difficult because so many criteria, often conflicting, may need to be satisfied. The criteria for the stiffness of a structure fall into three categories, i.e. the stiffness is required:


- To create desired vibration characteristics of the structure (to reduce seismic response, or to suit equipment or function); - To control deformations (to protect structure, cladding, partitions, services); - To influence failure modes In qualification of the above recommendations it can be said that while they are not mandatory they are well proven, and the less they are followed the more vulnerable and expensive the structure will become.


1971 San Fernando Valley Earthquake “Soft story” failure of the Hospital building [21]


• While it can readily be seen how these recommendations make structures more easily analysed and avoid undesirable stress concentrations and torsions. • The restrictions to architectural freedom implied by the above sometimes make their acceptance difficult. Perhaps the most contentious is that of uninterrupted vertical structure, especially where cantilevered facades and columns supporting shear walls are fashionable.


But sudden changes in lateral stiffness up a building are not wise: first because even with the most sophisticated and expensive computerized analysis the earthquake stresses cannot be determined adequately, and second, in the present state of knowledge we probably could not detail the structure adequately and the sensitive spots even if we knew the forces involved.


Stiffness to control deformation Deformation control is important in enhancing safety and reducing damage and thus improving the reliability of construction in earthquakes. The stiffness levels required to control damaging interaction between: - structure, - cladding, - partitions, - and equipment This vary widely, depending on the nature of components and the function of the construction. Doina Verdes BASICS OF SEISMIC ENGINEERING 2011

• A word of warning should be given here about the effect of non-structural elements on the structural response of buildings. • The non-structure, mainly in the form of partitions, may enormously stiffen an otherwise flexible structure and hence must be allowed for in the structural analysis


Stiffness to suit required vibration characteristics It would be desirable in general to avoid resonance of the structure with the dominant period of the site as indicated by the peak in the response spectrum. For example, short-period (stiff, low-rise) structures are good for long-period sites, i.e. those sites where the local soil is soft and deep enough to filter out much of the high-frequency ground motion, as in Mexico City.


Similarly taller, more flexible structures will suit rock sites. Unfortunately, in terms of conventional construction, often it will not be possible to arrange the structure to benefit in this respect. In industrial installations it may be necessary to have very stiff structures for functional reasons or to suit the equipment mounted thereon, and this will of course overrideany preference for seismic performance.

The Nyigata earthquake, Japan


Adequate foundation With regard to the seismic action the design and construction of the foundations and of the connection to the superstructure shall ensure that the whole building is excited in a uniform way by the seismic motion. For structures composed of a discrete number of structural walls, likely to differ in width and stiffness, a rigid, box-type or cellular foundation, containing a foundation slab and a cover slab should generally be chosen. For buildings with individual foundation elements (footings or piles), the use of a foundation slab or tie-beams between these elements in both main directions is recommended. Doina Verdes BASICS OF SEISMIC ENGINEERING 2011

However, if we turn to new techniques and technologies, notably the use of base isolation, is often possible to greatly modify the horizontal vibration characteristics of a structure whether it is inherently stiff or flexible above the isolating layer.



By Doina Verdes

CHAPTER 6 INELASTIC DYNAMIC BEHAVIOR


2

Contents

6.1 Introduction 6.2 Global and local ductility condition 6.3 Ductility of reinforced concrete elements (local ductility) 6.4 Requirements for ductility of reinforced concrete frames 6.5 The damages of the reinforced concrete frames under seismic loads


3

Inelastically behavior • Most structures for economical resistance against strong earthquakes must behave inelastically. • In contrast to the simple linear response model, the pattern of inelastic stress-strain behavior is not constant, varying with the member size and shape, the materials used, and the nature of the loading.


4

6.1Introduction The characteristics of inelastic dynamic behavior: •Plasticity; •Strain hardening and strain softening; •Stiffness degradation; •Ductility; •Energy absorption.

Force – deformation diagram


5

The ductility The ductility of a member or structure may be defined in general terms by the ratio deformation at failure / deformation at yield: FS

Fe

deformation at failure ρ= deformation at yield

Elastoplastic system

Fy

yy

ye

yu

y

In various uses of this definition, “deformation” may be measured in terms of : deflection, ρd, , rotation, ρθ or curvature ρφ. Doina Verdes BASICS OF SEISMIC ENGINEERING 2011

6

Mathematical models for non-linear seismic behavior The problems involved in establishing usable mathematical stressstrain models are obvious. It follows that many hysteresis models have been developed, such as: • Elastoplastic; Bilinear; Trilinear; Multilinear; • Ramberg-Osgood; Degrading stiffness; Pinched loops;

a.

Degrading stiffness

b.

Ramberg-Osgood


7

Hysteretic behaviour


8


9


10

Ductility and Energy Dissipation Capacity

• The structure should be able to sustain several

cycles of inelastic deformation without significant loss of strength. • Some loss of stiffness is inevitable, but excessive stiffness loss can lead to collapse. • The more energy dissipated per cycle without excessive deformation, the better the behavior of the structure.


11

The art of seismic-resistant design is in the details • With good detailing, structures can be designed for force levels significantly lower than would be required for elastic response.


12


13

Level of damping in different structures

Damping varies with: the materials used, the form of the structure, the nature of the subsoil, and the nature of the vibration. Large-amplitudes post-elastic vibration is more heavily damped than small-amplitude vibration; Buildings with heavy shear walls and heavy cladding and partitions have greater damping than lightly clad skeletal structures. Doina Verdes BASICS OF SEISMIC ENGINEERING 2011

14

Type of construction

Damping ν percentage of critical

Steel frame, welded, with all walls of flexible construction

2

Steel frame, welded, with normal floors and cladding

5

Steel frame, bolted, with normal floors and cladding

10

Concrete frame, with all walls of flexible construction

5

Concrete frame, with stiff cladding and all internal walls flexible

7

Concrete frame, with concrete or masonry shear walls

10

Concrete and/or masonry shear wall buildings

10

Timber shear walls construction

15


15

Source FEMA [25] Doina Verdes BASICS OF SEISMIC ENGINEERING 2011

16

6.2 Global and local ductility condition It shall be verified that both the structural elements and the structure as a whole possess adequate ductility; Ductility depends on: - the structural system - specific material requirements, - capacity design provisions in order to obtain the hierarchy of resistance of the various structural components - these ensure the intended configuration of plastic hinges avoiding brittle failure modes. The requirements are deemed to be satisfied if: a) plastic mechanisms obtained by pushover analysis are satisfactory; b) global, interstory and local ductility and deformation demands from pushover analyses (with different lateral load patterns) do not exceed the corresponding capacities; c) brittle elements remain in the elastic region. Doina Verdes BASICS OF SEISMIC ENGINEERING 2011

17

In multi-story buildings formation of a soft story plastic mechanism shall be prevented, as such a mechanism may entail excessive local ductility demands in the columns of the soft story.


18

Construction materials Reliability of construction in earthquakes is greatly affected by the materials used for the constituent elements of structure, architecture, and equipment. It is seldom possible to use the ideal materials for all elements, as the choice may be dictated by local availability or local construction skill, cost constrains, or political decisions. Particulary in terms of earthquake resistance the best materials have the following properties: High ductility; High strength/weight ratio; Homogeneity; Orthotropy; Ease in making full strength connections Doina Verdes BASICS OF SEISMIC ENGINEERING 2011

19

The stress-strain diagrams for steel stress

strain


20

Choosing the material • To choose between steel and in situ reinforced concrete for medium-rise buildings, is arguably little as long as they are both well designed and detailed. • For tall buildings steelwork is generally preferable, though each case must be considered on its merits. • Timber performs well in low-rise buildings partly because of its high strength/weight ratio, but must be detailed with great care. • Depending on the stage of countries developing it should have special problems in selecting building materials, from the points of view of cost, availability, and technology. • The choice of construction material is important in relation to the desirable stiffness. • if a flexible structure is required then some materials, such as masonry, are not suitable.


21

• On the other hand, steelwork is used essentially to obtain flexible structures, although if greater stiffness is desired diagonal bracing or reinforced concrete shear panels may sometimes be incorporated into steel frames. • Concrete, of course, can readily be used to achieve almost any degree of stiffness. • A word of warning should be given here about the effect of nonstructural materials on the structural response of buildings. • The non-structure, mainly in the form of partitions, may enormously stiffen an otherwise flexible structure and hence must be allowed for in the structural analysis.


22

2.3 Ductility of Reinforced concrete elements (local ductility) The factors which influence the local ductility of reinforced concrete elements: • • • • -

The influence of the reinforcing ratio from tensioned zone The influence of the reinforcing ratio from compressed zone The influence of the reinforcing ratio of transversal reinforcement The influence of the effort type Bending moment Axial force Shear force Combination of efforts: M+N, M+N+T


23

The effort-deformation relationship for RC elements

εc2 - deformation at max effort εcu2 - ultimate deformation fcd - Compression resistance Doina Verdes BASICS OF SEISMIC ENGINEERING 2011

24

Diagram of admissible deformations on the limit state

A – limit deformation at limit tension of the reinforcement B – limit deformation at the concrete compression C – limit deformation of concrete compression

εc2 - deformation at max effort, εcu2 - ultimate deformation Doina Verdes BASICS OF SEISMIC ENGINEERING 2011

What is the influence on the ductility of the reinforcing ratio from tensioned zone? P

P

L

G1

G2

h

h

AS1

AS2

b

Both beams have the same Concrete class

b AS1 > AS2


26

The influence of the reinforcing ratio from tensioned zone M

Φu ρΦ = Φy Φ u1 ρ Φ1 = Φ y1

M

M Mu1; Mu2 My1 My2

Φu2 ρΦ = Φ y2 Φ Φ y2 Φ y1

Φu1 Φu2

Φ y1 f Φ y 2

ρ Φ1 p ρ Φ 2 The increasing of the reinforcement ratio of the transversal tensioned reinforcement, do not lead to increasing of ductility. Doina Verdes BASICS OF SEISMIC ENGINEERING 2011

ρФ = CURVATURE DUCTILITY COEFICIENT

27

The influence of the reinforcing ratio of transversal reinforcement

G1

G2

A S2

A S3 Craking of concrete covering layer

M

h A S1

Mu1

h

My1

A S1

Mu2

b

b Φ Φy1 Φy2

AS2
Increasing of the reinforcement ratio of the transversal reinforcement one Obtains the increasing of the ductility Doina Verdes BASICS OF SEISMIC ENGINEERING 2011

ρ Φ1 =

Φ u1 Φ y1

ρΦ2 =

Φu2 Φ y2

Φu1

Φu2

Φ y1 = Φ y 2 ⇒ ρ Φ 2 f ρ Φ1 28

The influence of transversal reinforcement ratio AS2

AS3

h AS1

h AS1

M

Craking of concrete covering layer

B1

B2

Mu1 My1

b

b

Mu2

Φ

Fisurarea si expulzarea betonului din zona comprimata

B1

d

d

d/2

d

d/2

B2

Etrieri indesiti 5/23/2011

Φy1 Φy2

ρ Φ1 =

Φ u1 Φ y1

ρΦ2 =

Φu2 Φ y2

Φu1

Φu2

Φ y1 = Φ y 2 ⇒ ρ Φ 2 f ρ Φ1


29

Collapse of the Parking building during Northridge earthquake, 1994,(some of columns emphasize DUCTILITY)


30

6.4 Requirements for ductility of reinforced concrete frames


31

Detailing for local ductility

The specifications from EC8 recommend to satisfy the requirement at all beam-column joints of frame buildings, including frame-equivalent ones in the meaning, with two or more stories, the following condition should be satisfied

∑M

C

≥ 1,3∑ M B


32

ΣMc sum of moments at the center of the joint corresponding to development of the design values of the resisting moments of the columns framing into the joint. The minimum value of column resisting moments within the range of column axial forces produced by the seismic design situation should be used. ΣMB sum of moments at the center of the joint corresponding to development of the design values of the resisting moments of the beams framing into the joint. Doina Verdes BASICS OF SEISMIC ENGINEERING 2011

33

The regions of a primary beam up to a distance lcr =hw (where hw denotes the depth of the beam) from an end cross-section where the beam frames into a beam column joint, as well as from both sides of any other cross-section liable to yield in the seismic design situation, shall be considered as critical regions. In primary beams supporting discontinued (cutoff) vertical elements, the regions up to a distance of 2hw on each side of the supported vertical element should be considered as critical. Doina Verdes BASICS OF SEISMIC ENGINEERING 2011

34

The conformation of the critical zones of RC frames Beam

Column

Column

Beam

Critical regions


35

Beams - Detaling for local ductility


36

Critical regions of beams • Within the critical regions of primary beams, hoops satisfying the following • conditions shall be provided: • a) The diameter dbw of the tiers is not less than 6 mm. • b) The spacing “s” of tiers does not exceed (EC8): s = min{hw/4; 24dbw; 225mm; 8dbL} where dbL is the minimum longitudinal bar diameter • The first hoop is placed not more than 50 mm from the beam end section Doina Verdes BASICS OF SEISMIC ENGINEERING 2011

37

Column

Beam

P100-2006

The diameter of the tiers dbw ≥ 6 mm High ductility class (H)

Medium ductility class (M)


38

Detailing of columns for local ductility

The total longitudinal reinforcement ratio ρl shall not be less than 0,01 and not more than 0,04. In symmetrical cross-sections symmetrical reinforcement should be provided (ρ = ρ’).


39

Confinement of concrete core

•At least one intermediate bar shall be provided between corner bars along each column side, for reasons of integrity of beam-column joints. The minimum cross-sectional hc dimension of columns shall not be less than 250 mm. Doina Verdes BASICS OF SEISMIC ENGINEERING 2011

40

• The regions up to a distance lcr from both end sections of a primary column shall be considered as critical regions. The length of the critical region lcr , in the absence of more precise information, may be computed as follows: • lcr = max{1,5hc ; lcl / 6; 600mm} Where: • hc largest cross-sectional dimension of the column, • lcl clear length of the column. • The distance between consecutive longitudinal bars restrained by hoops or cross-ties does not exceed 150 mm. Doina Verdes BASICS OF SEISMIC ENGINEERING 2011

41

The detailles of column cross section reinforcement


42

Detailing of beam-column joint for local ductility The confining of joint concrete by periphery reinforcement and introducing of hoops double or simple. • The reinforcement like mesh or supplementary bars avoiding the stress concentration and obtaining of uniform distributions of stresses • The anchorage of longitudinal reinforcement from beam and columns outside of the joint.


43

The beam – column joint stresses Exterior column

Interior column


44

The transmission of shear force to the joint • i. by a concrete prism between the compressed corners of the joint • ii. through the connecting mechanism due to the horizontal hoops and compressed concrete prisms a.

b.

The concrete resistance can be calculate : N≤mRCbh' Doina Verdes BASICS OF SEISMIC ENGINEERING 2011

45

The joint design

Corner

d) Roof Interior

e) Roof Exterior

f) Roof Corner


46

The joint reinforcement design


47

The reinforcement of the joints


48

The critical regions are at a distance from the joint [4]


49

The reinforcement bars anchorage [4]


50

The reinforcement bars anchorage [4]


51

6.5.The damages of the reinforced concrete frames under seismic loads


52

The damaged columns


53

The damaged columns


54

The “ductile columns”

The effect of short column


55

The damage of beamcolumn joints and the effects on the buildings


56

How to Deal with Huge Earthquake Force? Isolate structure from ground (base isolation) Increase damping (passive energy dissipation) Allow controlled inelastic response Historically, building codes use inelastic response procedure. Inelastic response occurs through structural damage (yielding).


57


By Doina Verdes

CHAPTER 7 DESIGN CONCEPTS FOR EARTHQUAKE RESISTANT REINFORCED CONCRETE STRUCTURES


Contents

7.1 Energy dissipation capacity and ductility 7.2 Structural types 7.3 Design criteria at Ultimate Limit State (ULS) 7.4 The Global Ductility 7.5 Design criteria at Safety Limit State (SLS) 7.6 Structural types with stress concentration 7.7 The local effect of infill masonry


3

7.1 Energy dissipation capacity and ductility The design of earthquake resistant concrete buildings shall provide an adequate energy dissipation capacity to the structure without substantial reduction of its overall resistance against horizontal and vertical loading.


4

Behaviour factors for horizontal seismic action The behaviour factor q, is introduced to account the energy dissipation capacity.


5

7.2 Structural types and behaviour factors accordingly P100 and EC8 Concrete buildings may be classified to one of the following structural types according to their behaviour under horizontal seismic actions: a) frame system; b) dual system (frame- or wallequivalent); c) ductile wall system (coupled or uncoupled); d) system of large lightly reinforced walls; e) inverted pendulum system; f) torsionally flexible system. Except for those classified as torsionally flexible systems, concrete buildings may be classified to one type of structural system in one horizontal direction and to another in the other. Doina Verdes BASICS OF SEISMIC ENGINEERING 2011

6

Frame system

Dual system (frame- or wallequivalent)

Braced frame

frames moment frame

diafragmes


7

Ductile wall system (coupled or uncoupled)

Inverted pendulum system


8

Structural types conforming the code SEI-ASCE 7-02 Bearing Wall System — A structural system with bearing walls providing support, for all or major portions of the vertical loads. Shear walls or braced frames provide seismic force resistance. Bui Building Frame System — A structural system with an essentially complete space frame providing support for vertical loads. Seismic force resistance is provided by shear walls or braced frames. Doina Verdes BASICS OF SEISMIC ENGINEERING 2011

9

MomentMoment-Resisting Frame System — A structural system with an essentially complete space frame providing support for gravity loads. Moment-resisting frames provide resistance to lateral load primarily by flexural action of members.


10

Dual System — A structure system with an essentially complete space frame providing support to vertical loads. Seismic force-resistance is provided by moment-resisting frames, and shear walls or braced frames. For a dual system, the moment frame must be capable of resisting at least 25% of the design seismic forces. The total seismic force resistance is to be provided by the combination of the moment frame and the shear walls or braced frames in proportion to their rigidities.


11

Bulding Performance Levels and Range [21]


12

7.3 Design criteria at Ultimate Limit State (ULS)


13

The Ultimate Limit State (ULS) The requirements : a.Strength b.Ductility c. Limitation of interstorey drifts e. Seismic joints d. Foundation resistance a. Strenght Ed < Rd Second order effect has to be known Doina Verdes BASICS OF SEISMIC ENGINEERING 2011

14

b. Ductility Definition of ductility ρ ρ =δ u /δ y

Deformation control


15

Local ductility

The local ductility can be increased by: - the increase of the compressed reinforcement - the decrease of the tensioned reinforcement - the increase of the concrete class - the confinement of concrete from the compressed zone - the disposal of ties and transversal reinforcement


16

The prevention of brittle failure It must prevent: - the failure due to shear forces - the loss of the reinforcement anchorage and the destroying of the adherence in the continuity zones - the failure of tensioned zones The nonstructural mechanism for energy dissipation The infill walls – masonry panels.


17

Design concepts Low dissipative structural behaviour Dissipative structural behavior

a.

b. Doina Verdes BASICS OF SEISMIC ENGINEERING 2011

18

Dissipative Structural Behavior

Elastically response Inelastically response

Design code response

q= behaviour factor Doina Verdes BASICS OF SEISMIC ENGINEERING 2011

19

The behaviour factor “q” depends on : Ductility Redundancy Overstrenght Inelastic deformations are constrained to appear in certain areas called dissipative zones. Rules are specified in the codes, to obtain ductile elements: ductility class H and class M (EC8 and P100/2006) A structure has both ductile and brittle elements ; brittle elements should be prevented to reach the elastic limit. Doina Verdes BASICS OF SEISMIC ENGINEERING 2011

20

Behaviour factors for horizontal seismic action Nr.crt

DCM Sistem strctural Clădiri cu un nivel

1.

Cadre

DCH

EC8

P100-1/2006

EC8

P100-1/2006

3,30

4,025

4,95

5,75

Clădiri cu mai multe niveluri şi cu o singură deschidere

4,00; 5,00

3,60

4,375

5,40

6,25

Clădiri cu mai multe niveluri şi cu mai multe deschideri

2.

Dual

Structuri cu cadre preponderente

P100- 92 (1/Ψ) 5,00; 6,66

4,00; 5,00

3,90

4,725

5,85

6,75

3,90

4,025; 4,375; 4,725;

5,85

5,75; 6,25; 6,75;

-

Structuri cu pereţi preponderenţi -

Structuri cu doi pereţi în fiecare direcţie 3.

Pereţi Structuri cu mai mulţi pereţi

3,60

4,375

5,40

3

3

3 3

3 3

4,00

3

3

4,00

6,25 4,00

4,00 4,00

4,00

Structuri cu pereţi cuplaţi Flexibil la torsiune(nucleu) 4. 5.

Pendul inversat

4,00

3,60 2 2 1,5 1,5

4,375 2 2 2 2

5,40 3 3 3 3


6,25 3 3 3 3

2,86

21

Nr.crt

Sistem strctural

4

DCM P1001/2006 2,5; 4

4

2,5; 4

4

4

4 4 4 2

4 4 4 2

2 4

EC8

DCH EC8

Structuri parter 1.

Cadre necontravântuite

2.

Cadre contravântuite centric

2,50; 5,00; 5,50

6,00; 6,50. 4 4 2,5

6,00; 6,50 4 4 2,5

2 4

2,5

2,5

2,00; 2,50 5,00

3.

Cadre contravântuite excentric

4

4

6,00

6,00

4.

Pendul inversat Structuri cu nuclee sau pereţi de beton

2 2 2 2

2 2 2 2

6,00 3 3

6,00 3 3

4

4

4

4

4,8

-

4

-

-

4

-

5. Cadre necontrav. asociate cu cadre contravântuite în X şi alternante 6.

4,8

Cadre duale Cadre necontrav. asociate cu cadre contravântuite excentric

P10092 (1/Ψ) 2,94; 3,46; 5,00; 5,88

5,50

Structuri etajate Contravântuiri cu diagonale întinse Contravântuiri cu diagonale in V

P1001/2006 2,5;


6,00

5,88 4,00; 5,00

1,54; 2,00 2,00; 2,20; 4,00; 5,00 2,00; 2,20; 4,00; 5,00

22

c. Limitation of interstory drifts F

The interstory drift δ


23

Drift requirements The structure must have sufficient stiffness.The story drift ∆X is the parameter which can give the appropriateness of the general stiffness of the structure Story drift computation


24

Story drift • The structure being designed must have sufficient stiffness as stated before. The traditional procedure to judge the appropriateness of the general stiffness of the structure has been story drift, ∆x , defined as the different of the lateral deflections at the top and bottom of the story x under consideration, δx and δx-1 , respectively. The lateral deflection δx at the center of mass of level x must be computed from: ∆x= δx - δx-1 Doina Verdes BASICS OF SEISMIC ENGINEERING 2011

(11) 25

P-∆ effect P-∆ effect must be taken into account. Current analysis are "firstorder methods." This means that during analysis equilibrium is stated on the undeformed structure. In a flexible structure this leads to error, because there is an additional lateral deflection introduced by the overturning effect caused by the gravity loads displacing along with the structure which is not taken into account by the first-order analysis procedure. Doina Verdes BASICS OF SEISMIC ENGINEERING 2011

26

P-∆ effect For inelastic systems: Reduced stiffness and increased displacements Including P - ∆


27

•Therefore, the additional overturning effect corresponds to the gravity load, P multiplied by the lateral relative deflection. •This is the reason for the name P-∆. This is an analysis problem caused by the way equilibrium is stated. The way to deal with it is to find the magnitude of the error by using a stability coefficient θ.

ϑ=

Px ∆ Vx h sx C d

• If the stability coefficient obtained from Equation at any story and direction is equal or greater than 0.10 all forces and displacements obtained from analysis must be adjusted for this effect. Doina Verdes BASICS OF SEISMIC ENGINEERING 2011

28

Px ∆ ϑ= Vx h sx C d Where: Px is the vertical design load at and abowe level. When computing Px no individual load factor need exceed 1.0; ∆ is the design story drift occurring simultaneously with Vx ; Vx is the seismic story shear force acting at story x; hsx is the story height of story x. hsx=hx – hx-1 ; Cd is the lateral deffection amplification factor given in Code for each of seismic lateral-force resisting systems; If Θ < 0.1, ignore P-delta effects Doina Verdes BASICS OF SEISMIC ENGINEERING 2011

29

Allowable Story Drift for Reinforced Concrete Structures conf UBC Seismic Use Group I II III

Structure Structures for stories or less with interior walls, partitions, ceilings and exterior wall system that have been designed to accommodate story drifts All other structures

0.025 hsx

0.020 hsx

0.015 hsx

0.020 hsx

0.015 hsx

0.010 hsx


30

Conforming P100 2006 Ptot d r θ= ≤ 0,10 Vtot h Where: θ interstorey drift sensitivity coefficient, Ptot total gravity load at and above the storey considered in the seismic design situation, dr design interstorey drift, Vtot total seismic storey shear, h interstorey height. If 0,1 < θ < 0,2, the second-order effects may approximately be taken into account by multiplying the relevant seismic action effects by a factor equal to 1/(1 - θ). The value of the coefficient θ shall not exceed 0,3. Doina Verdes BASICS OF SEISMIC ENGINEERING 2011

31

Separation of buildings with different dynamic characteristics -allow independent vibrations -limit the effect of collisions


32

Limitation of interstorey drift at ULS (P100/2006)

Prevention of of loss of life due to total fialure of nonstructural elements

Displacement analysis ds=cqde Check of interstory drift at ULS d ULSs = c q d re < d ULSra =0.025h


33

Analysis methods

Equivalent lateral force analysis Modal response spectrum analysis Linear response history analysis Nonlinear response history analysis


34

7.4 The Global Ductility (The Capacity of Energy Consumption) a) The structural mechanism of seismic energy consumption – the plastification mechanism - the potential plastic hinges are uniform distributed on the structure - the plastic zones of the framed structure are at the end of the beams and have small values in the columns, or do not exist at all.


35

- the plastic zones of the shear walls are in the coupling beams or, if these do not exist, in the base of the walls; - the lateral displacements due to the ductility requirements are sufficiently reduced to avoid the danger of stability loss, or do not increase substantially the second order effect


36

Avoid undesirable mechanism


37

Undesirable mechanism – level story damage [ ]


38

Behaviour under seismic excitation inelastic response of a RC frame [21]


39

Behaviour under seismic excitation inelastic response of a RC frame [ 21 ]


40

Ordinary Concrete Moment frame [ 21]


41

Intermediate Concrete Moment frame [ 21]


42

Special Concrete Moment frame [21]


43

7.5 Design criteria at Safety Limit State SLS

Maintain function of a building by limiting degradation of nonstructural elements and building facilities Displacement analisys at SLS (P100/2006) : d s= ν q d e ds lateral displacement at SLS de lateral displacement of the story level under seismic loads ν reduction factor (0,4-0,5)


44

7.6 Structural types with stress concentration


45

Stress concentration at the first level

a.

b.

c.

The most serious condition of vertical irregularity is the soft or week level in which one story usually the first with taller, fewer columns is significantly weaker or more flexible than the stories above


46

Stress concentration The soft story collapse mechanism


47

Collapses of buildings with stress concentrations


48

The infill masonry placed above a free first story can develop the collapse mechanism (due to the stress concentration)

Infill masonry Very stiff


49

8.6 The local effects of infill masonry


Local effects due to masonry or concrete infills If the height of the infills is smaller than the clear length of the adjacent columns, the following measures should be taken: a) The entire length of the columns is considered as critical region and should be reinforced with the amount and pattern of stirrups required for critical regions; b) The consequences of the decrease of the shear span ratio of those columns should be appropriately covered; c) The transverse reinforcement to resist this shear force should be placed along the length of the column and extend along a length hc Doina Verdes BASICS OF SEISMIC ENGINEERING 2011

51

• d) If the length of the column not in contact with the infills is less than 1,5hc, then the shear force should be resisted by diagonal reinforcement. Where the infills extend to the entire clear length of the adjacent columns, and there are masonry walls only on one side of the column (this is e.g. the case for all corner columns), the entire length of the column should be considered as critical region and be reinforced with the amount and pattern of stirrups required for critical regions. Doina Verdes BASICS OF SEISMIC ENGINEERING 2011

52

The length lc of columns over which the diagonal strut force of the infill is applied, should be verified in shear for the smaller of the following two shear forces: i) the horizontal component of the strut force of the infill, taken equal to the horizontal shear strength of the panel, as estimated on the basis of the shear strength of bed joints; or ii) the shear force computed assuming that the overstrength flexural capacity of the column, develops at the two ends of the contact length, lc.


53

Masonry panel in interaction with the structure The effect of compressed diagonal: - the masonry cracking at the end of compressed diagonal; - the separation of it from the structural elements at the opposite corners Tkj

Masonry panel

Tjk


54

The effect of compressed diagonal

Actions on beam and column

b.


55

Short column effect


56

Short column effect

Masonry panel


57

Short beam effect Short beam

Column Beam

Masonry panel

Short beam

a. Beam

b. Masonry panel


58

• The contact length should be taken equal to the full vertical width of the diagonal strut of the infill. Unless a more accurate estimation of this width is made, taking into account the elastic properties and the geometry of the infill and the column, the strut width may be taken as a fixed fraction of the length of the panel diagonal.


59

Conclusions referring to system concept Optimal performance one obtains by: Providing competent load path Providing redundancy Avoid configuration irregularities Proper consideration of nonstructural elements Avoid excessive mass Detailing of structural and nonstructural elements for energy dissipation Limiting deformations demands


60


By Doina Verdes

CHAPTER 8 NONSTRUCTURAL ELEMENTS


Contents

8.1 Defining nonstructural elements 8.2 Earthquake effects on buildings and nonstructural elements 8.3 Interstory displacement 8.4 The performances of nonstructural elements 8.5 Protection Strategies 8.6 Nonstructural design approaches for cladding 8.7 Prefabricated wall panels 8.8 Precast concrete cladding 8.9 Cladding which increase the seismic energy dissipation 8.10 Examples of damages Doina Verdes Basics of Seismic Engineering 2011

3

8.1 Defining nonstructural elements The general types of nonstructural elements • Architectural elements, which are typically built-in nonstructural components that form part of the building • Building utility systems, are typically built-in nonstructural components that form part of the building which include • Mechanical • Electrical • Telecommunications

• Furniture and building contents are nonstructural components belonging to tenants or occupants Doina Verdes BASICS OF SEISMIC ENGINEERING 2011

Structural and Nonstructural Elements of a Building

Source: FEMA_Instructional Material Complementing FEMA 451, Design Examples Doina Verdes BASICS OF SEISMIC ENGINEERING 2011

Nonstructural elements serve specific purposes • Nonstructural elements are placed in a building to serve specific purposes. • Their presence within the building can affect the seismic behavior of the building. It is important to describe how the behavior of nonstructural elements differentiates nonstructural elements from structural elements. • Many types of nonstructural elements can resemble or behave as structural elements. Ideally, nonstructural elements are clearly distinguishable from structural elements. Doina Verdes BASICS OF SEISMIC ENGINEERING 2011

Investments in building constructions 100%

20.0%

17.0% 44.0%

80% 60%

62.0%

70.0%

40% 20%

48.0% 18.0%

13.0%

0% Office

Hotel

Contents Nonstructural Structural

8.0%

Hospital

• Nonstructural elements make up most of the building • Earthquake damage to nonstructural elements also makes up the largest percentage of the total cost of damage repair for most earthquakes. Doina Verdes BASICS OF SEISMIC ENGINEERING 2011

Architectural nonstructural elements • are typically the visible elements of the building; structural and building systems elements are generally hidden; • architectural elements are often designed to support occasional or light loading, such as a partition wall to which a cabinet or shelves are mounted, a ceiling to which a light fixture is supported, or an exterior cladding panel; • are not permanent and can be moved or removed from the building without affecting the structural safety of the building. behind architectural finishes; • are usually designed by an architect. However, sometimes architectural elements are designed by a specialty engineer (specializes in designing exterior cladding panels). Doina Verdes BASICS OF SEISMIC ENGINEERING 2011

Architectural elements Architectural nonstructural elements are interior and exterior elements of the building. Architectural elements can serve many purposes, from aesthetic ornamentation to partitions that are provided for sound or fire separations. The examples of architectural nonstructural elements, which can include exterior elements are: •Parapets and chimneys •Exterior ornamentation •Curtain walls, cladding, and glazing And interior elements such as: •Non-load bearing partitions •Ceilings and access floors Doina Verdes BASICS OF SEISMIC ENGINEERING 2011

Building Utility Systems Nonstructural Elements The typical categories are: • Heating, ventilation, and air conditioning (HVAC) system, including equipment and distribution; • Plumbing system, including pumps and piping for fire suppression, potable water, sanitary system; • Gas piping;


• Storage tanks for water or fuel, or other liquids; • Electrical equipment and distribution conduits and cabling, including generators and lighting; • Communications equipment and distribution cabling; • Some buildings, such as hospitals or other special occupancy facilities, may include other, more specialized systems.


Characteristics of Building Utility Systems Elements • large, heavy equipment, such as generators, boilers, and pumps. Because of their size and weight, these elements require specific attention in the structural design of the building to support their weight. Building utility systems are usually attached to the building structural elements. • can be designed by a mechanical or electrical engineer, particularly for large building projects. For smaller projects, the mechanical or electrical contractor may select the elements of the systems. Doina Verdes BASICS OF SEISMIC ENGINEERING 2011

8.2 Earthquake effects on buildings and nonstructural elements

Building response [ 25 ]


Earthquake Response of the building

The floor accelerations due to an earthquake [21]

The vibrational characteristics of the building cause the earthquake ground motion to be amplified within the building. For multi-story buildings, there is a difference in the horizontal movement or acceleration of the floors over the height. Doina Verdes BASICS OF SEISMIC ENGINEERING 2011

The accelerograms recorded to different levels of Sylmar County Hospital during Northridge earthquake, 1994

The accelerographs positions in plan and elevation [4] of the Sylmar County Hospital


The accelerograms recorded to different levels of Sylmar County Hospital during Northridge earthquake,1994; presenting the amplification of building response acceleration on the height of the building


Interaction of Building and Nonstructural Elements

The motion of nonstructural elements within a building are influenced by the response of the portion of the building to which they are attached.


Nonstructural element are very rigid and well anchored The stiffness of each nonstructural element also affects its response to an earthquake. For items that are very rigid and well anchored to the floor of a building, the horizontal response of the element will be Approximately equal to the response of the floor to which it is attached.

Very rigid elements therefore, go along with the movement of the floor. Building codes generally consider an element to be very rigid if the period of vibration of the element is less than 0.06 second.


Response of Flexible Nonstructural Elements • Many nonstructural elements are not rigid or are not rigidly attached to the structure. • These elements are referred to as flexible elements since they will flex or move differently than the floor to which they are attached.


• The flexibility of the element and/or its attachment to the structure causes the earthquake motion felt by the element to be amplified so that the response of the element is greater than that of the floor to which it is attached. • Similar to building response, the response of flexible nonstructural elements depends on the period of vibration of the element. The period of vibration depends on the stiffness of the element and its attachment and the weight of the element


Examples of damages to nonstructural elements

Exit canopy damage Suspended ceiling damage

Source: FEMA_Instructional Material Complementing FEMA 451, Design Examples

Chimney damage

Parapet damage

Source: FEMA_Instructional Material Complementing FEMA 451, Design Examples

Sliding and overturning

SLIDING

Nonstructural elements can be characterized as either acceleration sensitive or displacement sensitive. Those elements that are acceleration sensitive are affected by the horizontal acceleration.

The overturning of the equipment


8.3 Interstory displacement • Nonstructural elements can also be damaged by the displacement of the building during an earthquake. • This is referred to as being displacement sensitive. Most often it is the interstory displacement that can cause damage since nonstructural elements are connected to two adjacent floors of a building. • Nonstructural elements are often placed so that they are attached or restrained by the structural frame of the building. • The nonstructural cladding or sheathing elements in a building are stiffer than the building frame. Doina Verdes BASICS OF SEISMIC ENGINEERING 2011

The interstory displacement “d” may cause the frame to deform enough to make the cladding or sheathing crack, but not enough to damage the frame – the case of partitions, claddings made of soft materials .


The interstory displacement “d” may cause the frame to deform enough to make damage the frame elements – the case of partitions, claddings made of strength materials .

Masonry panel

Short column effect Doina Verdes BASICS OF SEISMIC ENGINEERING 2011

26

Short beam effect Short beam

Column Beam

Masonry panel

Short beam

a. Beam

b. Masonry panel


27

8.4 The performances of nonstructural elements A.Operational performance describes nonstructural elements that will continue to perform during and after an earthquake. B.Immediate Occupancy describes a postearthquake state in which nonstructural elements generally remain available and operable provided power is available. C.Life Safety performance describes the condition where nonstructural elements may be damaged due to an earthquake, but the damage is not life-threatening.


D.Hazard Reduced performance describes the condition where nonstructural elements that could pose a hazard to areas of public assembly can be damaged but will not be life-threatening, but other nonstructural elements could fail. •Not Considered performance describes the condition where none of the nonstructural elements within a building have been specifically evaluated for seismic hazards. If not considered, some nonstructural elements may pose a hazard and some may not be hazardous.


Building Performance and Levels Ranges [ ]


30

8.5 Protection Strategies Improved Structural Performance Improved Nonstructural Performance • Better Engineered Conventional Anchors • Newer Technologies


Equipment with restraints

Anchor Bolts or Expansion Bolts

Resistant straps, Braces, Tendons or Plumber’s Tapes

Spring Mounts or Isolators


Raised floor There are several issues that need to be considered to mitigate the hazard of damage to the raised floor. Diagonal braces should be installed between the floor slab and the top of the pedestals. Alternately, the pedestal base plates can be rigidly anchored to the structural floor to allow the pedestal to act as a cantilever to resist lateral forces.

b.

a.

d.

c.

Various schemes for cabinets Solutions: a. Diagonal braces and bolt pedestal b. Place angles around cables opening c. Bold pedestal bases to concrete slab d. Bases to concrete slab


Partitions

a. a. Partition free to slide at top but restrained laterally b. Partition doweled at base b.


Improved Nonstructural Performance Newer Technologies

Semi-active device (Rana and Soong, 1998) Doina Verdes BASICS OF SEISMIC ENGINEERING 2011

8.6 Nonstructural design approaches for cladding Building can have several types of nonstructural cladding attached to the exterior of the building. The purpose for the cladding is to provide thermal and acqustic protection and protection from wind and rain. Cladding is distinguished from structural wall in that cladding does not support the weight of the floor or structural framing above.


Common types of cladding are : a. Infill masonry b. Glazing (glass panels) c. Prefabricated wall panels • Concrete • GFRC (Glass Fiber Reinforced Concrete) • Steel or Aluminum


8.7 Prefabricated wall panels Types of structures which include nonstructural panels • Concrete Frames with Infill Masonry Shear Walls • Concrete Frames with Cladding (window wall or panels) • Steel Moment Frames with Cladding (window wall or panels) • Steel Braced Frames with Cladding (window wall or panels)


Concrete Frames with Infill Masonry Shear Walls


Concrete Frames with Cladding (window wall or panels)


Steel Moment Frames


Steel Braced Frames


8.8 Precast Concrete Cladding • Precast concrete cladding varies in its relationship to the building structure, from being fully integrated to being fully separated from frame action. • Ideally the cladding should be either fully integrated or fully separated, with no intermediate conditions. • Fully integrated structural precast concrete cladding should be treated like any other precast structural element; in the certain conditions the panels should be involved to dissipate the seismic energy.


The assembly panels and R C framed structure: (a) Fully integrated, interacting with the surrounding elements and (b) fully separated

ß


• For very flexible buildings in strong earthquakes the story drift may be so large as to make full separation difficult to achieve, and some interactions of frame and cladding through bending of the connections may have to be accepted. Ductile behavior of the cladding and of its connections to the structure is most important in such cases to ensure that the cladding does not fall from the building during an earthquake or its damage does not produce injuries to building occupants. Doina Verdes BASICS OF SEISMIC ENGINEERING 2011

a

b

a. Panel interacting b. Panel separated


Stiff (shear wall) buildings In stiff (shear wall) buildings the storey drift will generally be small enough to significantly reduce the problem of detailing of connections which give full separation. On the other hand, protection of the cladding from seismic motion is less necessary in stiff buildings, and connections permitting movement through bending may be satisfactory as long as the interaction between cladding and frame can be allowed for in the frame analysis.


The cladding which is not considered as part of the structure • In flexible beam and column buildings it is desirable to effectively separate the cladding from the frame action, both to protect the cladding from seismic deformations and also to ensure that the structure behaves as assumed in the analysis.

Details to separate the claddings from seismic deformations of structure


The panels separated from the structure Models tested in the laboratory of Civil Buildings and Foundation Chair, Civil Engineering Faculty of Cluj-Napoca [15]

Movement Possibilities • fixed joint

a. Panel fixed at bottom part b. Panel fixed at upper part c. Restrains of movements

c.


Connections of precast claddings to the structure permitting the separation Beam

Panel

Beam


Panel

Laboratory tests on panels equipped with connections to “separate” the panel from the structure [15]


Gaps • Gaps between adjacent precast units are often specified to be 20 mm to allow for seismic movements and construction tolerances, but gaps dimension may be determined from drift panel calculations. r0 the horizontal gap r0v the vertical gap


• The requirements for gaps material-filled joints have to accomplish the insulation: thermal, phonic, against fire, and waterproofing. • Such connections and must be designed to carry the gravity and wind loads of the cladding back into the structure as well as to allow the free movement of the frame to take place. These should be made of corrosion-resistant materials.


The gap panel - structural element coverings FISIE DE CAUCIUC

PROFIL DIN ALUMINIU

r vt.

r v.


The seismic design of fully separated precast cladding The equivalent static Seismic force conforming the Code P100/2006 [ ]

FCNS =

γ CNS a g β CNS k z qCNS


mcns

where: FCNS horizontal seismic force, acting at the centre of mass of the non-structural element in the most unfavourable direction, mCNS mass of the element,

β CNS Kz γ CNS q CNS

dynamic amplification coefficient KZ = 1 + 2

z H

importance factor of the element behaviour factor of the element


FCNS ≤ 4 gCNS ag mCNS FCNS ≥ 0,75 gCNS ag mCNS Dynamic amplification coefficient βCNS is function of period of vibration of the nonstructural element • rigid

components (perioad TCNS ≤0, 06 s): βCNS = 1,0

•flexibile components (period TCNS > 0,06 s): β CNS = 2,5 Doina Verdes BASICS OF SEISMIC ENGINEERING 2011

Relative displacement of the structure dr has to be checked to prevent the damage of the infill panels The recommendations of Code P100/2006 are: Safety limit state (SLS) dr

dr SLS = ν q dr≤ dr a F

dr a= 0,005h for fragil elements attached to structure dr a= 0,008h for separated elements Ultimate limit state (ULS)

d r ULS = c q d r ≤ d r, a dr a= 0,025h q the behavior factor Doina Verdes BASICS OF SEISMIC ENGINEERING 2011

8.9 Cladding which increase the seismic energy dissipation


Panel integrated with the structure • The case of integrated panels gives the effect of interaction panel – structure; • if it is designed properly may add stiffness to the system and also change the dynamic characteristics of the structure. • The behavior of the panel is that of an elasto-plastic system, and can contribute at the total stiffness of the frame, increasing it (Fig.1). • When the partition panels are properly designed they can be used to passively dissipate significant amounts of energy through inelastic hysteretic deformation driven by interstory drift. Doina Verdes BASICS OF SEISMIC ENGINEERING 2011

Mutto slitted wall • Developed by Muto in the 1960s, it has been used effectively in a number of tall buildings in Japan. It consists of a precast panel designed to fit between adjacent pairs of columns and beams of momentresisting steel frames. • The panel is divided by slits into a group of vertical ductile beam elements connected by horizontal ductile beams at the top and at the bottom, thus suppressing shear failure modes and creating a stiff energydissipating device. It is connected to the beams of the steel frame and effectively stiffness the building against wind load while providing high energy dissipation in larger earthquakes. • Reinforced concrete energy dissipaters Doina Verdes BASICS OF SEISMIC ENGINEERING 2011

Shear panels • Shear panels are another type of metal based device used to control the dynamic response of framed buildings, whose dissipative action is activated by interstorey displacements. • Firstly, they can be used as basic seismic resistance system under earthquake loading, due to their considerable lateral stiffness and strength. • In addition, due to the large energy dissipation capacity related to the considerable size where plastic deformations take place, they are very effective for the seismic protection of structures under strong loading conditions, serving as dissipative elements


• Steel plate shear walls can be applied in the steel frame buildings with the following arrangements: • -as large panels rigidly and continuously connected along columns and beams of frame mesh, serving also as cladding panels;

Full bay type

Pure shear mechanism


- or

as smaller elements installed in the frameworks of a building at nearly middle height of the storey and connected to rigid support members to transfer shear forces to the main frames

Partially bay type

Bracing type Pillar type Doina Verdes BASICS OF SEISMIC ENGINEERING 2011

Implementation of steel panel in the building from Japan

The hysteretic behaviour of LYS steel panels is very good, providing that suitable stiffeners are arranged, in order to prevent shear buckling, and a rigid panel-to-frame connecting system is adopted, so to avoid any slipping phenomenon in the recovery characteristic of the system. The majority of practical applications of low-yield shear panels are located in Japan. Doina Verdes BASICS OF SEISMIC ENGINEERING 2011

Exemple of separated claddings implementation

High rise building in Tokyo, Japan


Concrete cladding Models tested in the laboratory of Civil Buildings and Foundation Chair, Civil Engineering Faculty of Cluj-Napoca [16]

Panel B

Panel A


Details of panel connection to the structure [ ]


Panel type A cracks pattern


The joint concrete subjected to shear force


The diagrams of panel deformations Doina Verdes BASICS OF SEISMIC ENGINEERING 2011

Conclusions of the experimental program • The passive energy absorbing system consists of special panels which can be placed in the frame’s span. The panel is composed of narrow vertical elements which have keyed vertical joints. • The experimental tests were performed to statically alternant forces; the results demonstrated that the system has hight ductility and can dissipate the seismic energy.


8.10. Examples of damages of building claddings

The claddings fallen down


Broken glass panels


Damaged : •infill masonry, •frame joint •glass panels


Damage of partition walls


Damaged : •infill masonry(parapets), •frame columns, •glass panels.



By Doina Verdes

CHAPTER 9 THE CONTROL OF STRUCTURAL SEISMIC RESPONSE


2

Contents

9.1. Introduction 9.2. The types of structural control systems 9.3. Passive control system 9.4 The base isolation system 9.5 The energy dissipation systems 9.6 Advanced technology systems (9A) 9.7 Active structural control (9B)


3

9.1 Introduction • Buildings are complex systems in which the resistance structure represents the main mechanical systems. • The structure interacts with the existing subsystems and responds with the performances imposed by the destination and function.


4

• The seismic loads are chaotic and to keep the building performances during the earthquakes is a requirement which have driven in last years to new innovative technical solutions. • These confer the possibility of a structural control which in some approaches can be continually and automatically. The structural control can be : • With open loop (non feedback) • With closed loop (with feedback)


5

Structural control with open loop Passive control of the response • The passive control of the seismic response allows a structural control with an open loop or non feedback. • The building is equipped with a seismic isolation system and / or with devices for energy dissipation.


6

Structural control with closed loop (feed back) It is supposing to have in building an active seismic isolation system The active seismic isolation approaches can be the cybernetic systems with active structural control sometimes optimal, which includes at least one closed loop (feedback); The seismic performances of the structure are nonstop kept during the severe earthquakes.


7

How can be controlled the seismic response? Over the last 25 years, considerable attention has been paid to research and development of structural control devices, with particular emphasis on seismic response of buildings and bridges. Serious efforts have been undertaken to develop the structural control concept into a workable technology; today there are many such devices installed in a wide variety of structures.


8

9.2 The types of structural control systems Structural control systems can be grouped into three broad areas: (a) base isolation, (b) passive energy dissipation, and (c) active, hybrid, and semi-active control. The base isolation can now be considered a more mature technology with application as compared with the other two. Doina Verdes BASICS OF SEISMIC ENGINEERING 2011

9

THE CONTROL OF THE STRUCTURAL RESPONSE

DYNAMIC CHARACTERISTICS OF THE BUILDING

CONTROL OF THE STRUCTURAL RESPONSE

THE SYSTEMS TO CONTROL STRUCTURAL RESPONSE

♦ Base isolation ♦ Passive energy dissipation ♦ Active, hybrid, and semi-active control

INCREASING OF THE ENERGY DISSIPATION CAPACITY


10

The energy balance equation The energy – based approach is way to solve the structural control. The energy balance equation is: EI = EE +EH = (EES + EK )+ (EHξ + EHµ) EI = Energy input EE= Elastic energy of the system EH= Energy due to deformations EES= Energy elastic strains EK= Kinetic energy EHξ = Energy dissipated by the damping EHµ= Energy dissipated by the plastic deformation Doina Verdes BASICS OF SEISMIC ENGINEERING 2011

11

• Conventional seismic design is based on preparing the structures to dissipate energy in specially detailed ductile plastic hinge regions at the end of beam members as well as at base of the columns. • Inelastic deformations of the structural components should desirably lead to a ductile beam sidesway mechanism. Such beam and column members also serve as the principal gravity load–bearing elements.


12

THE USE OF TRADITIONAL OR CONVENTIONAL APPROACHES

ELASTICAL BEHAVIOR Ei = EE

PLASTIC BEHAVIOUR Ei = EE+ EH

THE YELDING OF MATERIAL IN CRITICAL ZONES (PLASTIC HINGES)

BUILDING

RESPONSE

GROUND ACCELERATION


13

• Following a strong earthquake damage to these critical regions, plastic hinge regions is to be expected, in condition of structural collapse prevention - to ensure the preservation of life – safety maintained. • There are a number of situations where such structural behavior may be either unattainable or undesirable. During an earthquake, a fixed – base shear frame structure filters the generally broad – band ground excitation into narrow – band responses at various elevations.


14

The performance-based design by the use of energy concepts and the energy balance equation [23] CONTROL OF STRUCTURAL RESPONSE THROUGH THE USE OF INNOVATIVE CONTROL OR PROTECTIVE SYSTEMS

USE OF SEISMIC ISOLATION SYSTEM CONTROL (DECREASE) OF Ei

USE OF PASSIVE ENERGY DISSIPATION CONTROL SYSTEM Ei = EE + ED

HYBRID

ISOLATORS

AND

ACTIVE CONTROL SYSTEM

HYBRID

PASSIVE ENERGY DISSIPATION DEVICES

DYNAMIC INTELLIGENT BUILDING


RESPONSE CONTROL STRUCTURES

SMART STRUCTURAL SYSTEM

STRUCTURAL ACTIVE HINGES (STRUCTURAL ROBOTICS)

15

9.3 Passive Control systems

- Base Isolation Systems Passive Control Systems

- Mass Effect Systems - Energy Dissipation Systems


16

The base isolation system • In the base isolation system, increasing the natural period through isolators reduces the acceleration response of the structure. • The seismic isolation devices are usually installed between the foundation and the structure or between two relevant parts of the structure itself, as in the case of the suspension buildings. • The practical solving of base isolation can be done by means of sliding or rolling mechanisms (ball bearing, slide plate bearing, sliding layer) as well as flexible elements (multi-rubber bearing, double column, flexible piles). Doina Verdes BASICS OF SEISMIC ENGINEERING 2011

17

The mass effect systems • The mass effect systems are based on supplementary masses connected to the structure by means of springs and dampers in order to reduce the dynamic response of the structure. These devices are tuned to the particular structural frequency so that when that frequency is excited, the devices will resonate out of phase with structural motion, dissipating energy by inertia forces applied on the structure by such masses. The structural response control technology by mass effect mechanism can be principally applied by tuned mass dampers as mass-spring systems and pendulum systems and by tuned liquid dampers systems based on sloshing of liquid. Doina Verdes BASICS OF SEISMIC ENGINEERING 2011

18

The energy dissipation systems • The energy dissipation systems consist of special devices that act as hysteretic and/or viscous damper, absorbing the seismic input energy and protecting the primary framed structure from damage. • The hysteretic dampers include devices based on yielding of metal and friction, while viscous dampers include both devices operating by deformation of viscoelastic solid and fluid materials (viscoelastic dampers) and the ones operating by forcing fluid materials to pass through orifices (viscous dampers).


19

9.4 The base isolation system Objectives of Seismic Isolation Systems • Enhance performance of structures at all hazard levels by: Minimizing interruption of use of facility (e.g., Immediate Occupancy Performance Level) • Reducing damaging deformations in structural and nonstructural components • Reducing acceleration response to minimize contents related damage


20

The base isolation system with rubber bearings The structures with base isolation systems have the isolation system placed under the main mass of the structure; the design of the system is to change the fundamental periods of the buildings from the site ground period.


21

∆a

∆b

a.

b.

The deformed shape of structure: a. With base isolation, b. Without isolation Doina Verdes BASICS OF SEISMIC ENGINEERING 2011

22

The energy that is transmitted to the structure is largely dissipated by efficient energy dissipation mechanisms within the isolation system.

Effect of Seismic Isolation: Increase Period of Vibration of Structure to Reduce Base Shear [21] Doina Verdes BASICS OF SEISMIC ENGINEERING 2011

23

Softer soils tend to produce ground motion at higher periods which in turn amplifies the response of structures having high periods. Thus, seismic isolation systems, which have a high fundamental period, are not well-suited to soft soil conditions.

MOST EFFECTIVE - Structure on Stiff Soil - Structure with Low Fundamental Period (Low-Rise Building)

Effect of Soil Conditions on Isolated Structure Response Doina Verdes BASICS OF SEISMIC ENGINEERING 2011

24

Configuration of a building structure with Base Isolation system [21]


25

T=2π/ω ω2=k/m

The soil conditions in Romania Doina Verdes BASICS OF SEISMIC ENGINEERING 2011

26

The behavior of the ruber bearing to sher force


27

Types of Seismic Isolation Bearings

Elastomeric Bearings - Low-Damping Natural or Synthetic Rubber Bearing - High-Damping Natural Rubber Bearing - Lead-Rubber Bearing (Low damping natural rubber with lead core) Sliding Bearings - Flat Sliding Bearing - Spherical Sliding Bearing


28

Buildings in the US having base isolation systems Foothill Community Law and Justice Center, Rancho Cucamonga, CA - Application to new building in 1985 - 12 miles from San Andreas fault - Four stories + basement + penthouse - Steel braced frame - Weight = 29,300 kips - 98 High damping elastomeric bearings - 2 sec fundamental lateral period - 0.1 sec vertical period - +/- 16 inches displacement capacity - Damping ratio = 10 to 20% (dependent on shear strain Source: NEHRP Recommended Provisions: Instructional Materials (FEMA 451B) Doina Verdes BASICS OF SEISMIC ENGINEERING 2011

29

Example of Seismic Isolation Retrofit U.S. Court of Appeals, San Francisco, CA - Original construction started in 1905 - Significant historical and architectural value - Four stories + basement - Steel-framed superstructure - Weight = 120,000 kips - Granite exterior & marble, plaster, and hardwood interior - Damaged in 1989 Loma Prieta EQ - Seismic retrofit in 1994 - 256 Sliding bearings (FPS) - Displacement capacity = +/-14 in. Source: NEHRP Recommended Provisions: Instructional Materials (FEMA 451B) Doina Verdes BASICS OF SEISMIC ENGINEERING 2011

30

The dynamic model of the building equipped with rubber bearings ms= the structure mass mb= the base mass ks = the structure stiffness, cs = the structure damping

T=2π/ω ω2=k/m

kb = the base stiffness, cb = the base damping ms

us

ks , cs m b kb , cb

ub ug


31

a. The equation for fixed base

b. The equation for isolated base


32

Making the notations: one obtains: Case (a) Case (b) Solving the equations one obtains the seismic response: -the acceleration -the velocity -the desplacement


33

Reazem din cauciuc cu tole de oţel

Details of elastomeric bearings


34

The Seismic Isolation With Penduls [9]

Exemple of Pasiv Isolation System with Penduls and Friction Absorbers Doina Verdes BASICS OF SEISMIC ENGINEERING 2011

35


36

Seismic response, time history, of a four levels building under El Centro accelerogram with and without seismic isolation system with pendulum. ag With seismic isolation system

t


37

9.5 The energy dissipation systems • diagonal bracing; • panel systems, are typical energy dissipation systems currently used in steel framed structure. • Both systems are based on metallic-yielding approach and are activated by the relative interstorey drift occurring during the loading process of the structure.


38

Diagonal Bracing Systems • A common way for seismic protecting of both new and existing framed structures is traditionally based on the use of concentric steel members arranged into a frame mesh, according to single bracing, cross bracing, chevron bracing and any other concentric bracing scheme.


39

Some drawback Even if such systems posses high lateral stiffness and strength for wind loads and moderate intensity earthquakes, some drawback have to be taken into account, concerning the unfavorable hysteretic behaviour under severe earthquake, due to buckling of the relevant members, which generally causes a poor dissipation behaviour of the whole system.


40

The placing in the conventional bracing system additional special devices • In case of seismic retrofitting, in addition to the strengthening of the existing frame, it is necessary to improve the global seismic performance of the structure, also in terms of dissipative capacities. • Therefore, it is necessary to avoid the mentioned drawback by preventing the buckling and the premature rupture of braces. • This requirement can be achieved by placing in the conventional bracing system additional special devices that dissipate the input energy seismic. It can be made by damping devices placed into the bracings, which has to be easily accessible and replaceable.


41

Steel frames with dissipatives zones conforming EC 8

Frames with concentric diagonal bracings (dissipative zones in tension diagonals only)

Frames with concentric V bracings (dissipative zones in tension and compression diagonals)

Frames with eccentric bracings (dissipative zones in bending or shear links) Doina Verdes BASICS OF SEISMIC ENGINEERING 2011

42

Typical dissipative chevron bracing systems


43

Panel Systems • Shear panels are another type of metal based device used to control the dynamic response of framed buildings, whose dissipative action is activated by interstorey displacements. • Firstly, they can be used as basic seismic resistance system under earthquake loading, due to their considerable lateral stiffness and strength. • In addition, due to the large energy dissipation capacity related to the considerable size where plastic deformations take place, they are very effective for the seismic protection of structures under strong loading conditions, serving as dissipative elements Doina Verdes BASICS OF SEISMIC ENGINEERING 2011

44

• Steel plate shear walls can be applied in the steel frame buildings with the following arrangements: • -as large panels rigidly and continuously connected along columns and beams of frame mesh, serving also as cladding panels;

Full bay type

Pure shear mechanism


45

- or

as smaller elements installed in the frameworks of a building at nearly middle height of the storey and connected to rigid support members to transfer shear forces to the main frames

Partially bay type

Bracing type and Pillar type Doina Verdes BASICS OF SEISMIC ENGINEERING 2011

46

The hysteretic behaviour of LYS steel panels is very good, providing that suitable stiffeners are arranged, in order to prevent shear buckling, and a rigid panel-to-frame connecting system is adopted, so to avoid any slipping phenomenon in the recovery characteristic of the system. The majority of practical applications of low-yield shear panels are located in Japan


47

The Use Of Passive Energy Dissipation Systems

There are a lot of passive energy dissipation developed after ‘60s; following energy dissipaters (dampers) are used with base isolated structures: 1. Lead plugs, in lead-rubber bearings 2. Steel torsion-beam 3. Lead extrusion devices 4. Flexural beam dampers 5. Curved steel bars or plates


48


49

Supplemental energy dissipation devices

• During an earthquake event, a structure is subjected to a large amount of energy input. The typical approach designs the structural members so they can absorb earthquake input energy through inelastic cyclic deformation. Repairing the damages caused by these inelastic deformations will require significant costs.


50

• In recent years, many buildings or structures have been designed with supplemental energy dissipation devices EDD to absorb some of the vibration energy caused by earthquakes. By adding EDD to the structural system, the structural dynamic properties are modified, the seismic response is controlled, and the energy dissipation demand on the structural members is reduced. • Supplemental EDDs have become a popular strategy for designing new buildings or retrofitting existing buildings.


51

Reinforced concrete energy dissipaters A notable first entry to this field is the Mutto slitted wall. Developed by Muto in the 1960s, it has been used effectively in a number of tall buildings in Japan. It consists of a precast panel designed to fit between adjacent pairs of columns and beams of momentresisting steel frames. The panel is divided by slits into a group of vertical ductile beam elements connected by horizontal ductile beams at the top and at the bottom, thus suppressing shear failure modes and creating a stiff energy-dissipating device. It is connected to the beams of the steel frame and effectively stiffness the building against wind load while providing high energy dissipation in larger earthquakes.


52


53

Panel with vertical discontinue slits

Panel with vertical continue slits


54

The panel behavior after the cracking along the vertical slits

The stiffness of the teeth form vertical edge Doina Verdes BASICS OF SEISMIC ENGINEERING 2011

55

• The stiffness of the panel must be calibrated in respect of required interstory drift of the frame; the seismic response of the structures accordingly the design codes gives large deformations due mainly the post-elastic behavior.


56

Energy dissipaters in diagonal bracing • Diagonal bracings incorporating energy dissipaters provide a structurally comparable alternative to the Muto slitted wall panel in that they control the horizontal deflections of the frame and also the locations of the damage, thus protecting both the main structure and the non-structural elements. A practical example is a sixstorey government office building constructed in Wanganui, New Zealand, in 1980 This building obtains its lateral load resistance from diagonally braced precast concrete cladding panels thus minimizing the amount of internal structure to suit architectural planning. • The rehabilitation of Quebec Police Headquarters, Montreal [1] was achieved by incorporating friction dampers in the existing and new bracing. Doina Verdes BASICS OF SEISMIC ENGINEERING 2011

57

Pictures of Buildings in seismic areas


58

Tokyo , Japan


59

Tokyo , Japan


60

Transamerica building, San Francisco, California


61

Transamerica building, San Francisco, California


62

Imperial palace, Japan


63


By Doina Verdes


2

Contents


3

9.6 Advanced Technology Systems


4

Objectives of Energy Dissipation and Seismic Isolation Systems Enhance performance of structures at all hazard levels by: Minimizing interruption of use of facility (e.g.,Immediate Occupancy Performance Level) Reducing damaging deformations in structural and nonstructural components. Reducing acceleration response to minimize contents related damage Doina Verdes BASICS OF SEISMIC ENGINEERING 2011

5

Distinction Between Natural and Added Damping Natural (Inherent) Damping


6

Added Damping


7

Alternate source of energy dissipation

Seismic damage can be reduced by providing an alternate source of energy dissipation. The energy balance must be satisfied at each instant in time. For a given amount of input energy, the hysteretic energy dissipation demand can be reduced if a supplemental (or added) damping system is utilized.


8

Reduction in Seismic Damage Hysteretic Energy

Energy Balance:

EI = ES + E K + ( EDI + E DA ) + EH Added Damping

Inherent Damping

DI

Damage Index:

umax EH (t ) DI (t ) = +ρ uult Fy uult Source: Park and Ang (1985)

1.0

0.0


Collapse Damage

State 9

Damage index “DI” A damage index “DI”, can be used to characterize the timedependent damage to a structure. For the definition given, the time-dependence is in accordance with the timedependence of the hysteretic energy dissipation. The calibration factor ρ accounts for the type of structural system and is calibrated such that a damage index of unity corresponds to incipient collapse. Damage index values less than about 0.2 indicate little or no damage. This index is one of the first duration-dependent damage indices to be proposed.


10

Energy response histories for a SDOF elasto-plastic system subjected to seismic loading 10% damping 200

10% Damping

180 Absorbed Energy, inch-kips Energy (kip-inch) (kip

160 KINETIC + STRAIN

140

DAMPING

120 100 80 60 40

HYSTERETIC

20 0 0

4

8

12

16

20

24

28

32

36

40

44

48

Time, Seconds

Damping reduces the hysteretic energy dissipation demand Doina Verdes BASICS OF SEISMIC ENGINEERING 2011

11

Energy response histories for a SDOF elasto-plastic system subjected to seismic loading 200

Absorbed(kip Energy, Inch-Kips Energy (kip-inch)

180

20% Damping

160 140

KINETIC + STRAIN

120 100

DAMPING 80 60 40 20

HYSTERETIC

0 0

4

8

12

16

20

24

28

32

36

40

44

48

Time, Seconds

An increase in added damping reduces the hysteretic energy dissipation demand by about 57%. Damping reduces the hysteretic energy dissipation demand Doina Verdes BASICS OF SEISMIC ENGINEERING 2011

12

Classification of Passive Energy Dissipation Systems Velocity-Dependent Systems • Viscous fluid or viscoelastic solid dampers • May or may not add stiffness to structure

Displacement-Dependent Systems • Metallic yielding or friction dampers • Always adds stiffness to structure

Other • Re-centering devices (shape-memory alloys, etc.) • Vibration absorbers (tuned mass dampers) Doina Verdes BASICS OF SEISMIC ENGINEERING 2011

13

Velocity-dependent systems consist of dampers whose force output is dependent on the rate of change of displacement having the name rate-dependent. Viscous fluid dampers, the most commonly utilized energy dissipation system, are generally exclusively velocity-dependent and thus add no additional stiffness to a structure (assuming no flexibility in the damper framing system).


14

Viscoelastic solid dampers exhibit both velocity and displacement-dependence. Displacement-dependent systems consist of dampers whose force output is dependent on the displacement and NOT the rate of change of the displacement, often call, systems rateindependent. More accurately, the force output of displacement-dependent dampers generally depends on both the displacement and the sign of the velocity.


15

Types of Damping Systems • • • • •

Velocity-Dependent Damping Systems : Fluid Dampers and Viscoelastic Dampers Models for Velocity-Dependent Dampers Effects of Linkage Flexibility Displacement-Dependent Damping Systems: Steel Plate Dampers, Unbonded Brace Dampers, and Friction Dampers Modeling Considerations for Structures with Passive Damping Systems


16

Cross-Section of Viscous Fluid Damper

Source: Taylor Devices, Inc. Doina Verdes BASICS OF SEISMIC ENGINEERING 2011

17

Possible Damper Placement Within Structure


18

Fluid Damper within Diagonal Brace*

San Francisco State Office Building San Francisco, CA

Huntington Tower Boston, MA

*Source: FEMA Instructional Material Complementing FEMA 451


19

Harmonic behaviour of fluid damper


20

Advantages of Fluid Dampers High reliability High force and displacement capacity Force Limited when velocity exponent < 1.0 Available through several manufacturers No added stiffness at lower frequencies Damping force (possibly) out of phase with structure elastic forces Moderate temperature dependency May be able to use linear analysis Doina Verdes BASICS OF SEISMIC ENGINEERING 2011

21

Disadvantages of Fluid Dampers Somewhat higher cost Not force limited (particularly when exponent = 1.0) Necessity for nonlinear analysis in most practical cases (as it has been shown that it is generally not possible to add enough damping to eliminate all inelastic response)


22

Vicoelastic dampers*

A -A



23

Advantages of Viscoelastic Dampers High reliability May be able to use linear analysis Somewhat lower cost


24

Disadvantages of Viscoelastic Dampers Strong Temperature Dependence Lower Force and Displacement Capacity Not Force Limited Necessity for nonlinear analysis in most practical cases (as it has been shown that it is generally not possible to add enough damping to eliminate all inelastic response)


25

Steel Plate Dampers* (Added Damping and Stiffness System - ADAS)



26

Implementation of ADAS System*

Wells Fargo Bank, San Francisco, CA - Seismic Retrofit of TwoStory Nonductile Concrete Frame; Constructed in 1967 - 7 Dampers Within Chevron Bracing Installed in 1992 - Yield Force Per Damper: 150 kips



27

Hysteretic Behavior of ADAS Device

ADAS Device

Experimental Response (Static)

(Tsai et al. 1993)

(Source: Tsai et al. 1993) Doina Verdes BASICS OF SEISMIC ENGINEERING 2011

28

Advantages of ADAS System and Unbonded Brace Damper Force-Limited Easy to construct Relatively Inexpensive Adds both “Damping” and Stiffness


29

Disadvantages of ADAS System and Unbonded Brace Damper

Must be Replaced after Major Earthquake Highly Nonlinear Behavior Adds Stiffness to System Undesirable Residual Deformations Possible


30

Friction Dampers: Slotted-Bolted Damper*



31

Sumitomo Friction Damper (Sumitomo Metal Industries, Japan)


32

Cross-Bracing Friction Damper*

Interior of Webster Library at Concordia University, Montreal, Canada *Source: FEMA Instructional Material Complementing FEMA 451


33

The cross-bracing friction damper consists of cross-bracing that connects in the center to a rectangular damper. The damper is bolted to the cross-bracing. Under lateral load, the structural frame distorts such that two of the braces are subject to tension and the other two to compression. This force system causes the rectangular damper to deform into a parallelogram, dissipating energy at the bolted joints through sliding friction.


34

Implementation of cross-bracing friction damper

McConnel Library at Concordia University, Montreal, Canada - Two Interconnected Buildings of 6 and 10 Stories - RC Frames with Flat Slabs - 143 Cross-Bracing Friction Dampers Installed in 1987 - 60 Dampers Exposed for Aesthetics



35

Hysteretic Behavior of Slotted-Bolted Friction Damper


36

Ideal hysteretic behavior of cross-bracing friction damper


37

Advantages of Friction Dampers Force-Limited Easy to construct Relatively Inexpensive


38

Disadvantages of Friction Dampers May be Difficult to Maintain over Time Highly Nonlinear Behavior Adds Large Initial Stiffness to System Undesirable Residual Deformations Possible


39

Modeling Considerations for Structures with Passive Energy Dissipation Devices Damping is almost always nonclassical (Damping matrix is not proportional to stiffness and/or mass) For seismic applications, system response is usually partially inelastic For seismic applications, viscous damper behavior is typically nonlinear (velocity exponents in the range of 0.5 to 0.8)


40


By Doina Verdes



2

Contents



3

9.7 Active structural control systems


4


5

Basic Principles of active control

The basic principles are illustrated using a simple single-degree-of-freedom (SDOF) structural model. Consider the lateral motion of the SDOF model consisting of a mass m, supported by springs with the total linear elastic stiffness k, and a damper with damping coefficient c.


6

The SDOF system is subjected to an earthquake load. The excited model responds with a lateral displacement y(t) relative to the ground which satisfies the equation of motion: m&y&(t ) + cy& (t ) + ky (t ) + Vy = − m&y&g (t )

(1)

v(t ) = Vy / m

(2)

To see the effect of applying an active control force to the linear structure, equation (1) in this case becomes m&y&(t ) + cy& (t ) + ky (t ) + Vy = − m&y&g (t )

(3)

The object of a response-control structure is to reduce these factors by controlling or adjusting m, c, k, V. Doina Verdes BASICS OF SEISMIC ENGINEERING 2011

7

The effect of feedback control The effect of feedback control is to modify the structural properties so that it can respond more favorably to the ground motion. The form of Vx is governed by the control law chosen for a given application, which can change as a function of the excitation. The advantages associated with active control systems in comparison with passive systems,several can be cited; e.g. one may emphasize human comfort over other aspects of structural motion during noncritical times, whereas increased structural safety may be the objective during severe dynamic loading. Doina Verdes BASICS OF SEISMIC ENGINEERING 2011

8

• among them are (a) enhanced effectiveness in the response control where the degree of effectiveness is, by and large, only limited by the capacity of the control systems; (b) relative insensitivity to site conditions and ground motion; (c) applicability to multi-hazard mitigation situations, where an active system can be used, for example, for motion control against both strong wind and earthquakes; and (d) selectivity of control objectives;


9

Active, hybrid, and semi-active structural control systems • are a natural evolution of passive control technologies; • are force delivery devices integrated with real-time processing evaluators/controllers and sensors within the structure; • they act simultaneously with the hazardous excitation to provide enhanced structural behavior for improved service and safety; • it is reached the stage where active systems have been installed in full-scale structures for seismic hazard mitigation.


10

Active structural control research 1989 1990 1991 1993 1994 1994 1996 1998 1998 1998 2000 2002 2004 2006

US Panel on Structural Control Research (US-NSF) Japan Panel on Structural Response Control (Japan-SCJ) Five-Year Research Initiative on Structural Control (US-NSF) European Association for Control of Structures International Association for Structural Control First World Conference on Structural Control (Pasadena, California, USA) First European Conference on Structural Control (Barcelona, Spain) China Panel for Structural Control Korean Panel for Structural Control Second World Conference on Structural Control (Kyoto, Japan) Second European Conference on Structural Control (Paris, France) Third World Conference on Structural Control (Como, Italy) Third European Conference on Structural Control (Vienna, Austria) Fourth World Conference on Structural Control (San Diego, California,USA)


11

The performance-based design by the use of energy concepts the energy balance equation CONTROL OFand STRUCTURAL RESPONSE THROUGH THE USE OF INNOVATIVE CONTROL OR PROTECTIVE SYSTEMS

USE OF SEISMIC ISOLATION SYSTEM CONTROL (DECREASE) OF Ei

HYBRID

ISOLATORS

AND

USE OF PASSIVE ENERGY DISSIPATION CONTROL SYSTEM Ei = EE + ED

ACTIVE CONTROL SYSTEM

HYBRID

PASSIVE ENERGY DISSIPATION DEVICES

DYNAMIC INTELLIGENT BUILDING

RESPONSE CONTROL STRUCTURES

SMART STRUCTURAL SYSTEM


STRUCTURAL ACTIVE HINGES (STRUCTURAL ROBOTICS)

12

• Hybrid systems are a combination of active and passive systems, supplying energy to enhance the damping effect of the passive system. • The active systems provide various countermeasures by using the external disturbance signals generated by sensors installed either inside or outside the building. • Active systems require energy to directly resist the external disturbances, semi-active systems require energy to indirectly resist external disturbances by changing the dynamic characteristics of the building structure, and passive systems do not require any energy input. Active systems use both feed forward control, in which sensors outside the building detect disturbance before it reaches the building, or feedback control, in which sensors in the building detect the building's response [ ]. Doina Verdes BASICS OF SEISMIC ENGINEERING 2011

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Structure with Hybrid Control

EXCITATION

STRUCTURE WITH PED

RESPONSE

CONTROL ACTUATORS

SENSORS

COMPUTER CONTROLER


SENSORS

14

Hybrid Mass Damper Systems (HMD)

The hybrid mass damper (HMD) is the most common control device employed in full-scale civil engineering applications. An HMD is a combination of a passive tuned mass damper (TMD) and an active control actuator. The ability of this device to reduce structural responses relies mainly on the natural motion of the TMD. The forces from the control actuator are employed to increase efficiency of the HMD and to increase its robustness to changes in the dynamic characteristics of the structure Doina Verdes BASICS OF SEISMIC ENGINEERING 2011

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Implementation of Hybrid Mass Damper Systems Is installed in the Sendagaya INTES building in Tokyo in 1991. The HMD was installed at top to 11th floor and consists of two masses to control transverse and torsional motions of the structure, while hydraulic actuators provide the active control capabilities. The ice thermal storage tanks are used as mass blocks so that no extra mass was introduced. The masses are supported by multistage rubber bearings intended for reducing the control energy consumed in the HMD and for insuring smooth mass movements (Higashino and Aizawa, 1993; Soong et al., 1994). Doina Verdes BASICS OF SEISMIC ENGINEERING 2011

16

Sendagaya INTES building with hybrid mass dampers (Higashino and Aizawa, 1993)


17

Top view of hybrid mass damper configuration (Higashino and Aizawa, 1993)


18

Response time histories (Higashino and Aizawa, 1993)


19

Structural Control, closed-loop (feedback) In 1972, prof. James T.P. Yao, in his paper entitled “Concept of Structural Control” (Yao, 1972), marks the beginning of this new field in Structural Analysis. The author states that it seems the limit in structure size has been reached. In order to extend these limits without loss of safety, he proposes the concept of Structural Control, especially closed-loop (feedback) control systems.


20

BASICS OF ACTIVE CONTROL CONFIGURATION SEISMIC ACTION

STRUCTURE

Structural Response

Control Forces Electrical power Sensors

Actuators

Sensors

Control forces calculation

Structure with Active Control


21

The Dynamic Intelligent Building Dynamic intelligent building is an important concept of active system, which tries to unify the perspective of lifeline systems belonging to an urban community. The information network is the infrastructure of very crowded metropolis, which should include buildings with dynamic behavior. The data from the surroundings or from long distance sent trough cables, radio and via satellite should be processed by the general and local computers and this way the structures will be better prepared to respond to strong earthquakes.The control mechanism is in fact an active bracing system or an active mass damper incorporated into the structure. Optimal active control is a time domain strategy, which allows minimizing the energy induced in structure. The equation of motion for an n degree of freedom controlled system under seismic action is: Doina Verdes BASICS OF SEISMIC ENGINEERING 2011

22

where: M1 = n x n mass matrix of the structure; C1 = n x n damping matrix; K1 = n x n stiffness matrix; z(t) = n-dimensional vector of generalized displacements; u(t) = n-dimensional vector of control actions f(t) = n-dimensional vector of external actions; f(t) is proportional to the seismic ground acceleration:

Mz (t ) + C1 z& (t ) + K1 z (t ) = f (t ) + u (t ) f (t ) = h1 χ&&g (t ) where: h1 = n-dimensional vector showing the points of application and the values of inertia The object of a response-control structure is to reduce these factors by controlling or adjusting m, c, k, f, or p. Doina Verdes BASICS OF SEISMIC ENGINEERING 2011

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The available structural response-control methods

• •

• •

According to these basic principles of dynamics, the available structural response-control methods can be classified as follows: Methods based on the control and adjustment of m, such as rigid- or liquid- mass dampers. Methods based on the control and adjustment of c, such as variable damping mechanisms and building-tobuilding connection mechanisms. Methods based on control and adjustment of k, such as variable-stiffness and flexible-base mechanisms. Methods based on the control and adjustment of p, such as using reaction walls, jet or injection devices. Doina Verdes BASICS OF SEISMIC ENGINEERING 2011

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Active Mass Damper Systems Design constraints, such as severe space limitations, can preclude the use of an HMD system. Such is the case in the active mass damper or active


25

Principle of the DUOX system (Nishimura et al., 1993)

BUILDING

AMD Atachet mass damper TMD Tuned mass damper


26

The simplified principle: active & passive control


27

The Kyobashi Seiwa Building in Tokyo


28

The system designed and installed in the Kyobashi Seiwa Building in Tokyo • This building, the first full-scale implementation of active control technology, is an 11-story building with a total floor area of 423 m2. • The control system consists of two AMDs where the primary AMD is used for transverse motion and has a weight of 4 tons, while the secondary AMD has a weight of 1 ton and is employed to reduce torsional motion. The role of the active system is to reduce building vibration under strong winds and moderate earthquake excitations and consequently to increase the comfort of occupants in the building. Doina Verdes BASICS OF SEISMIC ENGINEERING 2011

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Semi-active Damper Systems • Control strategies based on semi-active devices combine the best features of both passive and active control systems. • semi-active control devices offer the adaptability of active control devices without requiring the associated large power sources; in fact, many can operate on battery power, which is critical during seismic events when • The semi-active control devices offer the adaptability of active • control devices without requiring the associated large power sources the main power source to the structure may fail.


30

• a variable-stiffness device, a full-scale variable-orifice damper in a semi-active variable-stiffness system (SAVS) was implemented to investigate semi-active control at the Kobori Research Complex (Kobori et al., 1993; Kamagata and Kobori, 1994). • The semi-active hydraulic dampers are installed inside the walls on both sides of the building to enable it to be used as a disaster relief base in post-earthquake situations (Kobori, 1998; Kurata et al., 1999). Each damper contains a flow control valve, a check valve, and an accumulator, and can develop a maximum damping force of 1000 kN.


31

SAVS system configuration (Kurata et al., 1999)


32

Variations of such an HMD configuration include multistage pendulum HMDs, which have been installed in, for example, the Yokohama Landmark Tower in Yokohama (Yamazaki et al., 1992), the tallest building in Japan, and in the TC Tower in Kaohsiung, Taiwan. Additionally, the DUOX HMD system which, as shown schematically in Figure 1.8, consists of a TMD actively controlled by an auxiliary mass, has been installed in, for example, the Ando Nishikicho Building in Tokyo (Nishimura et al., 1993).


33

Yokohama Landmark Tower and HMD (Yamazaki et al., 1992)


34

Yokohama Landmark Tower and Shinjuku Park Tower


35

Kajima Shizuoka Building and semi-active hydraulic dampers (Kurata et al., 1999)


36

Controllable dampers Two fluids that are viable contenders for development of controllable dampers are: (a) electrorheological (ER) fluids and (b) magnetorheological (MR) fluids. The essential characteristic of these fluids is their ability to change reversibly from a free-flowing, linear viscous fluid to a semi-solid with a controllable yield strength in milliseconds when exposed to an electric (for ER fluids) or a magnetic (for MR fluids) field. In the absence of an applied field, these fluids flow freely and can be modeled as Newtonian. Doina Verdes BASICS OF SEISMIC ENGINEERING 2011

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Schematic of a controllable fluid damper


38

Full-scale 20-ton MR fluid damper (Dyke et al., 1998)


39

The scheme of active control of seismic response

Desplacements Traductor

Active Tendon System

CONDITIONING

Actuator

SERVO-VALVE CONTROL

.. yg

ANALOG DIFERENTIAL

COMPUTER PC


40

High rise building in Japan


41

BASICS OF SEISMIC ENGINEERING By Doina Verdes

REFERENCES 1. Bozornia Y., Bertero,V., Earthquake Engineering from Engineering Seismology to Performance – Based Engineering, CRC Press, Boca Raton, London, New York, Washington, D.C., ISBN 0-8493-1439-9, 2007 2. Bors, I. , Dinamica structurilor, UTPRESS, 2010 3. Chopra, Anil K. , Dynamics of structures, Theory and applications to Earthquake engineering, 2007, Pearson Education, Inc., ISBN 0-13-156174-X 4. Clough Ray W., Penzien J. - Dynamic of Structures, John Wiley & Sons, 1993 5. Crainic, l., Proiectarea nodurilor cadrelor de beton în codurile de proiectare actuale, Rev AICPS, 2008 6. Dungale S. Taranath, Wind and Earthquake resistant buildings Structural analisis and design, ISBN 0-8247-5934-b, 2004 7. Ifrim M., Dinamica structurilor si inginerie seismica, Bucuresti Editura didactica si pedagogica, 1985 8. Kelly J.,- Resistant Earthquake Design with Rubber, second edition, Springer 1997 9. Manea Daniela, Reducerea efectelor dinamice asupra constructiilor prin sisteme de protectie aplicate la nivelul fundatiilor, PhD Thesis, 1997 10. Negoita Al. si colectiv , Inginerie seismica, EDP 1985 11. Pop I., Verdeş D, Manea D., - 1998, Pasiv System of Seismic Isolation with Penduls and Friction Absorbers, Proceedings of 11TH 1

European Earthquake Engineering Conference, Septembre 9 − 12, Paris, France, ISBN 90 5410 982 3; 12. Rosenblueth – Earthquake Engineering, John Wiley & Sons, 1980 13. Skiner R. I., Robinson W.H., G. H. Mc VERRY – An introduction to Seismic Isolation, John Wiley & Sons, 1993 14. Soong T. T., Nonstructural Performance and Performancebased Earthquake Engineering, Iassy Romania, 2004 15. Verdes, D., Pop I, Berindean O., 2002 “Passive Dissipation System for Framed Structures”, Analele Universitatii Ovidius Constanta, ISSN,12223-721 16. Verdeş D. - Magnification Factors for Local Seismic Response of Nonstructural Panel - Simpozionul international Construcţii 2000, oct.1993, Cluj-Napoca, vol.4, pag. 1369-1373; 17. Verdeş, D., - Seismic Response of Nonstructural Panels Flexible Connected with Structural Elements - Simpozionul international Construcţii 2000, oct.1993, Cluj-Napoca, vol.4, pag. 1373 – 1377 18. Verdeş, D., – Study of the panels in seismic resisting buildings, PhD Thesis, TUCluj-Napoca, Romania 1993 19. Verdeş, D., Pop, I., 2000, Panouri neportante - Risc şi siguranţă la acţiuni seismice, Analele Universităţii Ovidius Constanţa, 325-328, ISSN,12223-721 20. Verdeş, D., Pop, I., 2003, Panels and RC framed Structure, Proceedings of the International Conference Constructions 2003 Cluj-Napoca, 281-289, ISBN, 973-9350-89-9 21. Y. S.Chu, T.T. Soong, and A.M. Reinhorn, Active, Hybrid, and Semi-active Structural Control – A Design and Implementation Handbook 2005 John Wiley & Sons, Ltd 22. *** Earquake protection with seismic isolation, Dynamic Isolation Systems, 775-359-333 DVD rev (3.0) 23. *** EUROCODE 8 24. *** FEMA – NEHRP: Recommended Provisions for New Buildings and Other Structures: Training and Instruction Materials, FEMA 415 B 2

25. *** P100/2006 Romanian seismic design code 26. *** Seismic Design Methodologies for the Next Generation of Codes Balkema/Rotterdam/Bookfield/1997 27. ***Earthquake Hazard Mitigation for Nonstructural Elements, FEMA P – 74 CD/ September 2005 28. ***FEMA Instructional Material Complementing FEMA 451

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The Test on Shake Table of a High Building Model Equipped with Friction Dampers The Valahia Tower Project Is awarded with Egor Popov award for Structural Innovation to Seismic Design Contest 10th -12th of February 2011 SAN-DIEGO CA, USA Organised by: EERI Student Leadership Council (SLC) held in conjunction with the 63rd EERI Annual Meeting on February 10th and 11th 2011 at the Hyatt Regency La Jolla, Aventine in San Diego, California, USA

1. Competition Objectives •

The objectives of the Eighth Annual Undergraduate Seismic

Design Competition sponsored by EERI are: • To promote the study of earthquake engineering amongst undergraduate students. • To provide civil engineering undergraduate students an opportunity to work on a hands-on project by designing and constructing a cost-effective frame structure to resist earthquake excitations. • To build the awareness of the versatile activities at EERI among the civil engineering students and Faculty as well as the general public and to encourage nation-wide participation in these activities. • To increase the attentiveness of the value and benefit of the Student Leadership Council (SLC) representatives and officers among the universities for the recruitment and development of SLC, a key liaison between students and EERI.

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3. Structural Model and Testing

2. Structural Design Objectives • •

The students team has been hired to submit a design for a multi-story commercial office building. •

To verify the seismic load resistance system, a scaled model have been constructed from balsa wood. It was subjected to severe ground motion excitations. The time histories and response spectrums were availables online in the competition website. • The seismic performance of the structure was evaluated according to the rules described in the following sections

• • • • • • • • • • • • • • •

Structural Frame Members Structures shall be made of balsa wood and the maximum member cross section dimensions are: Rectangular column: 1/4 in x 1/4 in (6.4 mm x 6.4 mm) Circular column: 1/4 in (6.4 mm) diameter Beam: 1/8 in x 1/4 in (3.2 mm x 6.4 mm) Diagonal: 1/8 in x 1/4 in (3.2 mm x 6.4 mm) Shear Walls Shear walls constructed out of balsa wood must comply with the following requirements: Maximum thickness: 1/8 in (3.2mm) Minimum length: 1 in (25.4mm) Columns can be attached to the ends of a shear wall. Floors Floor isolation in the horizontal and vertical planes is allowed in the middle third of the building. Every floor must be labeled. There is no requirement on where the floors are labeled; however, the floor at the base of the structure will be labeled ground, and the floor above the lobby will be labeled 2nd. Every floor must have a system of interior beams running perpendicular to each other with a minimum of 2 beams in each direction.

• • • • • • • • • • • • •

• • • • • • •

•

•

Structure Dimensions The structure must comply with the following dimensions. For penalties refer to Section 6.2. Max floor plan dimension: 15 in x15 in (38.1 cm x 38.1 cm) Min individual floor dimension: 6 in x 6 in (15.2 cm x 15.2 cm) Max number of floor levels: 29 levels Min number of floor levels: 15 levels Floor height: 2 in (5.08 cm) Lobby level height (1st level): 4 in (10.2 cm) Min building height: 32 in (81.28 cm) Max building height: 60 in (153.4 cm) Max rentable total floor area: 4650 in2 (3 m2) Structural height shall be measured from the top of the base floor to the top of the uppermost beam member of the top level. The base floor is defined as the top of the base plate. Total floor area includes the core of the structure. Weight of Scale Model The total weight of the scale model, including the base and roof plate and any damping devices, should not exceed 4.85 lbs (2.2 kg).

Structural Loading Dead loads and inertial masses will be added through steel threaded bars tightened with washers and nuts. These will be firmly attached to the frame in the direction perpendicular to shaking. Floor mass: 2.6 lbs (1.18 kg) Roof mass: 3.5 lbs (1.59 kg) Mass spacing: Increments of 1/10th the height (H/10) Threaded bar length: 36 in (914 mm) Threaded bar diameter: 1/2 in (12.7 mm) The dead load will be placed at nine floor levels in increments of (H/10), corresponding to (1/10) x H to (9/10) x H. In cases where a floor does not exist at an exact increment of (H/10), the weight will be attached to the nearest higher floor. Weights will be secured to the structure using nuts and washers; they cannot be secured to the beam alone. It is strongly recommended that each team purchase a sample weight to try out and ensure proper attachment. The roof dead weight will consist of a steel plate with dimensions of 6 in x 6 in x 1/2 in (15.24 cm x 15.24 cm x 1.27 cm), and an accelerometer, which weigh 3.5 lbs (1.59 kg) in total. See Figure 2-3 for roof configuration. The direction of shaking will be decided by the judges. Therefore, it will be prudent to design structures that are symmetric in both directions.

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4. Additional Requirements

Instrumentation and Data Processing

• Oral Presentation • Each team is required to give a five-minute oral presentation to a panel of judges. Judges will have three minutes to ask questions following the presentation. The presentations will be open to the public. • Poster • The teams are required to display a poster providing an overview of the project. The dimensions of the poster are restricted to a height of 42 inch (1.1 m) and a width of 36 inch (0.91 m). • The university name and EERI logo should appear at the top of the poster and a font size of 40 is recommended. The font size shall not be less than 18. • Scoring will be based on the scoring sheet provided in the Appendix.

5. Scoring Method • This section describes the method used to score the performance of the structures in the seismic competition. Scoring is based on three primary components: 1. Annual income, 2. Initial building cost, and 3. Annual seismic cost. • The final measure of structural performance is the annual revenue, calculated as the annual income minus annual building construction cost minus annual seismic cost.

Horizontal acceleration table will be measured in the direction of shaking using accelerometers mounted on the roof of the structure and on the shake

6. Scoring Multipliers The following section describes the calculation of the overall final score for each team. The final score will be based on the annual revenue and will be a function of: - Annual Income - Oral Presentation - Poster - Architecture - Penalties - Structural Performance - Performance Predictions

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7. The Awards Three prizes and three special awards Special awards Charles Richter Award for the Spirit of the Competition

• The most well known earthquake magnitude scale is the Richter scale which was developed in 1935 by Charles Richter, of the California Institute of Technology. In honor of his contribution to earthquake engineering, the team which best exemplifies the spirit of the competition will be awarded the Charles Richter Award for the Spirit of Competition. The winner for this award will be determined by the judges.

Egor Popov Award for Structural Innovation

Egor Popov had been a Professor at the University of California, Berkeley for almost 55 years before he passed away in 2001. Popov conducted research that led to many advances in seismic design of steel frame connections and systems, including eccentric bracing. Popov was born in Russia, and escaped to Manchuria in 1917 during the Russian Revolution. After spending his youth in China, he immigrated to the U.S. and studied at UC Berkeley, Cal Tech, MIT and Stanford. In honor of his contribution to structural and earthquake engineering, the team which makes the best use of technology and/or structural design to resist seismic loading will be awarded the Egor Popov Award for Structural Innovation. The winner for this award will be determined by the judges.

SEISMIC DESIGN COMPETITION 2011

Fazlur Khan Award for Architectural Design • As a Structural Engineer Fazlur Khan played a central role behind the “Second Chicago School” of Architecture in the 1960’s and is regarded as the “Father of tubular design for high-rise buildings”. His most famous buildings designs are the John Hancock Center and Willis Tower (formerly Sears Towers). He was born in Bangladesh in 1929. He obtained his bachelor’s degree from the Engineering Faculty at the University of Dhaka. In 1952 he immigrated to the U.S. where he pursued graduate studies at the University of Illinois at Urbana-Champaign, he earned two Master’s degrees (one in Structural Engineering and one in Theoretical and Applied Mechanics) and a PhD in Structural Engineering. In honor of his contribution to Structural Engineering and Architecture Design of high-rise buildings, the team whose building provides a remarkable expression of architecture design and inherently integrates a sound structural design will be awarded the Fazlur Khan Award for Architectural Design. The winner for this award will be determined by the judges.

8. The project of Valahia Tower model • The project was built by a team of fourth year undergraduate students from Faculty of Constructions, Technical University of Cluj-Napoca.

TECHNICAL UNIVERSITY OF CLUJ-NAPOCA, ROMANIA THE CITY UNIVERSITY

10th -12th of February 2011 SAN-DIEGO CA, USA

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The Team

Project design criteria

The undergraduate students in Civil Engineering Artur AUNER Adrian BORSA Ioana HATEGAN Alexandru Ioan MANEA Daniela SELAGEA Ovidiu SERBAN The supervising Professors Doina VERDES Msc PhD Pavel ALEXA Msc PhD 10th -12th of February 2011 SAN-DIEGO CA, USA

Structural simplicity, uniformity, symmetry and redundancy; Bi-directional resistance and stiffness; Diaphragmatic behaviour at storey level; Adequate foundation.

17




Our project – Valahia Tower

Floor Plan view


18

19

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Cross section of the tower


Details of the cross section


Moment Frame Connection Detail

21



22


Why Friction Dampers? The friction dampers based on metallic plates

Force-Limited Easy to construct Relatively Inexpensive 10th -12th of February 2011 SAN-DIEGO CA, USA

23


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Cutting of the wood plates


25




Chopping the columns accidentally

Manufacturing and mounting the dampers


27


26

28

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Two models were build - first one -> to see how dampers work in the structure

The final model

Images of the first model: construction and testing 10th -12th of February 2011 SAN-DIEGO CA, USA


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Results for 5% damping for integration to artificial accelerogram GM3 (UCDavis)

Predictions for the structure were made using numerical analysis as follows: •

Computation of the seismic response of the structure using SAP2000 for 5% damping

•

Computation of the seismic response of the structure using SAP2000 for 15% damping Max displacement =5.57cm = 2.19in 10th -12th of February 2011 SAN-DIEGO CA, USA

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Max velocity =3.36m/s =11.02ft/s 10th -12th of February 2011 SAN-DIEGO CA, USA

Max acc =2.02m/s^2 = 6.62ft/s^2 32

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Results with 15% damping for intergration to artificial accelerogram GM3 (UCDavis)

Performances of the structure according to the rules of the competition • Annual Income : 735,000 $/year • Annual Initial Building Cost : 322,000 $/year • Annual Seismic Cost : 50,900 $/year

Max displacement =3.74cm = 1.47in

Max velocity =3.36m/s = 7.87ft/s

Max acc =2.02m/s^2 = 4.36ft/s^2


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The accelerograms

Accelerogram El Centro, 18 Mai 1940

Accelerogram Northridge, 1994

The model before the test on shake table at Seismic Design Contest

Artificial accelerogram UCDavis 35

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9. Conclusions after the test The model was subjected to three accelerograms - behavior of model was very good at all three accelerograms ; - the model bars were not damaged ; - the friction dampers have worked very well allowing the deformation of the structural elements and dissipating energy. The collapse of the model arrived after the test with sinus wave having the frequency equal fundamental frequency of the model. 10th -12th of February 2011 SAN-DIEGO CA, USA


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10. The award ceremony


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The 8th Seismic Design Competition, 2011 winner teams

The prize plaque Egor Popov Award for Structural Innovation for the model “Valahia tower” made by the team from Technical University of Cluj-Napoca, Romania

The top three teams: Oregon State University California Polytechnic State University, San Luis Obispo California Polytechnic State University, San Luis Obispo Charles Richter Award for the Spirit of the Competition: UC Davis Honorable Mention Nominees: Penn State University, Universiti Teknologi Malaysia Egor Popov Award for Structural Innovation: Technical University Cluj-Napoca, Romania Honorable Mention Nominee: UC Davis Fazlur Khan Award for Architectural Design: San Jose State University Honorable Mention Nominees: Brigham Young University, California Polytechnic University, Pomona


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The annoncement of Karthik Ramanathan vice president of SLC, of the award Egor Popov 10th -12th of February 2011 SAN-DIEGO CA, USA

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Romanian delegation together with colleagues from American universities Romanian delegation together with Nima Tafazolli, co president of SLC



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11. Models Presented by the Participants Universities

Romanian delegation together with colleagues from University of Technologi , Malaysia 10th -12th of February 2011 SAN-DIEGO CA, USA

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Oregon State University


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California Polytechnic State University, San Luis Obispo University of Illinois Urbana Champaign 10th -12th of February 2011 SAN-DIEGO CA, USA

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UC Davis



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Purdue University

California State University, Los Angeles 10th -12th of February 2011 SAN-DIEGO CA, USA

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Roger Williams University Roger Williams University


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Brigham Young University


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UC Irvine


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University of Massachusetts Amherst 10th -12th of February 2011 SAN-DIEGO CA, USA

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12. The tour in San Diego city


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Many thanks to the generous sponsors of the TUCN team !

Many thanks to the generous sponsors of the 2011 SDC!


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Basics of Seismic Engineering

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