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: Prof.dr.ing. Daniela Manea Consilier editorial: 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

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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

2

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

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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


� By Doina Verdes

CHAPTER I

THE SEISMICITY OF THE 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� 1.4 Measures of earthquake size

� 1.5 Record of the ground motion

� 1.6 Significant earthquakes produced in the world

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Basics of Seismic Engineering

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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 primarilySeismologists 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..

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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 chroniclesconsequences, 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.

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Fig. 1.1. Global distribution of seismicity*

*http://geology.about.com

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Fig 1.2. Europe seismic map *

*http://geology.about.com

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Structure of the Earth

6370

50002000

Crust

Mantle

Outer core

The earth consists of several discreteconcentric layers:-the inner core, is a very dense solidthought to consist mainly of iron;-outer core is a layer of similardensity, but thought to be a liquidbecause shear waves are not

2000

500

240

Outer core

(liquid)

(solid)

Inner core

because shear waves are nottransmitted through it;- next is a solid thick envelope oflesser density around;- the core that is called the mantle,- the rather thin layer at the earth’s

surface called the crust.

Fig. 1.3. Structure of the Earth

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� the mantle is considered to consist of two distinctlayers: the upper mantle together with the crustform a rigid layer called the lithosphere.

� Below that, the layer, called the asthenosphere, isthought to be partially molten rock consisting ofsolid particles incorporated within a liquidcomponent.

� Although the asthenosphere represents only asmall fraction of the total thickness of the mantle, itis because of its highly plastic character that thelithosphere does move as a single unit, however;instead it is divided into a pattern of plates ofvarious sizes, and it is the relative movementsalong the plate boundaries that cause theearthquake occurrence patterns.

Fig. 1.4 The mantle is

divided into a pattern

of plates *

*AFPS Brochure 10

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Earthquake Faults

� From the study of geology, it has become apparentthat the rock near the surface of the earth is not asrigid and motionless as it appears to be.

� There is ample evidence in many geologicalformations that the rock was subjected to extensivedeformations at a time when it was buried at somedepth.

� When such ruptures occurred, relative sliding� When such ruptures occurred, relative slidingmotions were developed between the opposite sideof the rupture surface creating what is called ageological fault. The orientation of the fault surfaceis characterized by its “strike”, the orientation fromnorth of its line of intersection with the horizontalground surface, and by its “dip”, the angle fromhorizontal of a line drawn on the fault surfaceperpendicular to this intersection line.

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Fig, 1.5. San Andreas fault, California

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Fig. 1.6. San Andreas fault, California [21]

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Fig 1.7 Types of fault slippage **BSSC California 2001

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1.3 The earthquake and the types of seismic

waves

� The important fact about any fault ruptureis that the fracture occurs when thedeformations and stresses in the rockreach the breaking strength of thematerial. Accordingly it is associated witha sudden release of strain energy whichthen is transmitted through the earth in theform of vibratory elastic waves radiatingform of vibratory elastic waves radiatingoutward in all directions from the rupturepoint. These displacement waves passingany specified location on the earthconstitute what is called an earthquake.

� The point on the fault surface where therupture first began is called theearthquake focus, and the point on theground surface directly above the focus iscalled the epicenter.

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 motionsthat are propagated deep within the earth:

� “P” waves, in which the material particles move along the path ofthe wave propagation inducing an alternation between tension andcompression deformations, and

� “S” waves, in which the material particles move in a directionperpendicular to the wave propagation path, thus inducing shearperpendicular to the wave propagation path, thus inducing sheardeformations.

� The “P” or Primary wave designation refers to the fact that thesenormal stress waves travel most rapidly through the rock andtherefore are the first to arrive at any given point.

� The “S” or Secondary wave designation refers correspondingly tothe fact that these shear stress waves travel more slowly and

therefore arrive after the “P” waves.

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surface wave

P-wave

S-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 thesurface of the earth rather than deep in the interior, twoother types of waves known as Rayleigh and Love can beidentified.

� The Rayleigh surface waves are tension-compressionwaves similar to the “P” waves except that their amplitudewaves similar to the “P” waves except that their amplitudediminishes 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 rapidlywith the distance below the surface.

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Fig. 1.10 The types of seismic waves [21]

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Reflection at

the surfaces

Seismographstation

Earthquake

focus

Core

Mantle

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

Refraction at the core

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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 isindicated quantitatively as the magnitude.

� By definition, Richter magnitude is the (base 10) logarithm of themaximum amplitude, measured in micrometers (10-6 m) of theearthquake record obtained by Wood-Anderson seismograph,corrected to a distance of 100 Km.

� This magnitude rating has been related empirically to the amount ofearthquake 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 afactor of 32 for each unit increase of magnitude. More important toengineers, however, is the empirical observation that earthquakes ofmagnitude less than 5 are not expected to cause structural damage,whereas for magnitudes greater than 5, potentially damaging groundmotions will be produced.

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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 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 earthquake-intensity observations are typically compiled in the form of isoseismal maps.

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Modified Mercalli (MM) Intensity Scale

I. No felt by people.

II. Felt only by a few persons atrest,especially on upper floors ofbuildings.

� III. Felt indoors by many people.Feels like the vibration of a lighttruck passing by. Hangingobjects swing. May not berecognized as an earthquake.

� IV. Felt indoors by most peopleand outdoors by a few. Feels likethe vibration of a heavy truck

VII. People are frightened; it is difficult to stand. Automobile drivers notice the shaking. Hanging objects quiver. Furniture breaks. Weak chimneys break. Loose bricks, stones, tiles, cornices, unbraced parapets, and architectural ornaments fall from buildings. Damage to masonry D.

…

XI. Most masonry and wood and outdoors by a few. Feels likethe vibration of a heavy truckpassing by. Hanging objectsswing noticeably

� V. Felt by most personsindoors and outdoors; sleepersawaken. Liquids disturbed, withsome spillage. Small objectsdisplaced or upset;

� VI. Felt by everyone.Many people are frightened,some run outdoors. People moveunsteadily. Dishes, glassware,and some windows break.

XI. Most masonry and wood structures collapse. Some bridges destroyed.

XII. Damage is total. Large rock masses are displaced. Waves are seen on the surface of the ground. Lines of sight and level are distorted. Objects are thrown into the air.

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

MSK 1964

EMI (PS69)

MERCALLI

I II III IV V VI VII VIII IX X XI XII

IIIIII IV V VI VII VIII IX X XI XII

MERCALLI

1956MODIFIED

JAPAN

RUSSIA

maximumaccelerationof 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

III III IV V VI VII VIII IX X XI XII

0 I II III VIV VI VII

I II III IV V VI VII VIII IX X XI XII

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1971 San Fernando earthquake1983 Coalinga earthquake

100,000x10

10,000x10

1,000x10

En

erg

y (

erg

s)

18

18

10,000,000x10

1,000,000x10

18

18

18

1964 Alaska earthquake1906 San Francisco earthquake

Daily U.S. electrical energy consumption

1976 Guatemala earthquake

1980 Italy earthquake

Atomic bomb Sei

smic

ene

rgy

of e

arth

quak

es

Largest earthquake

Nuclear bomb

Fig. 1.12 Earthquakes: Magnitude/energy

earthauake1978 Santa Barbara

10 x 10

1 x 10

4

18

100x10

18

18

Richter magnitude

5 6 87 9

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� The three components of ground motion recorded by a strong-motion 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 acceleration or sometimes by the number of acceleration peaks exceeding a specific level.

� The frequency content can be represented roughly by the number ofzero crossings per second in the accelerogram and the duration bythe length of time between the first and the last peaks exceeding agiven threshold level. It is evident, however, that all thesequantitative measures taken together provide only a very limiteddescription of the ground motion and certainly do not quantify itsdamage-producing potential adequately

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Fig, 1.13 Seismoscop – Antic China

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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 inToday, 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

� records of soil displacements produced by

seismographs, called seismograms, are used in

calculating the location and magnitude of an earthquake.

l

L

M

Fig. 1.14 The principle of seismoscop

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1.5 Record of the ground motion

� The motion of the ground at any point is three-dimensional, whichmeans that the point moves in space and not merely in a plane orin a straight line. To completely record this motion, threeseismometers must be built into each seismograph. Theseseismometers move in three perpendicular directions, twohorizontal and one vertical, and generate three correspondingseismograms.

Seismographs are designed to record small displacements caused� Seismographs are designed to record small displacements causedby distant earthquakes and are used by seismologists interested inlocating hypocenters, estimating magnitudes, and studying themechanics of earthquakes – the kind of shaking that causesdamage. To record this type of ground shaking requires a differenttype of instrument, one that measures ground acceleration insteadof ground displacement. Such instruments are calledaccelerographs, and the mass-spring system is calledaccelerometer.

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Accelerogram-Accelerograph

The record generated, known as an accelerogram, hasthe general appearance of a seismogram, but itsmathematical characteristics are quite different.Acceleorgraphs do not have a continuous recordingsystem, as seismographs do; instead, they are triggeredby an earthquake and operate form batteries (becausethe 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

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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

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Date

Location

Magnitude

Deaths Remarks

780 B.C.

China; Shaanxi Province

Widespread destruction west of Xian

373 B.C.

Greece

Helice, on the Gulf of Corinth, was destroyed. Much of the city slid into the sea.

1202 May 20

Middle East

30,000

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 1201 or 1202 with over a million deaths (which is highly improbable).

1455 Dec.5

Italy 40,000

Naples badly damaged.

1531 Jan.26

Portugal; Lisbon

30,000

1556 Jan.23

China; Shaanxi Province

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.

35

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

Italy; Naples

70,000

1667 Nov.

Azerbaijan 80,000

1668 July 25

China; Shandong Province

8.5 50,000 Widespread destruction throughout province.

1688 July 5

Turkey 15,000 Damage along Aegean coast.

1693 Jan.9

Sicily 60,000 Catania destroyed.

1703 Dec.30

Japan; Tokyo region

8.2 5,200 Tsunami.

1737 Oct.11

India; Calcutta

300,000

1755 Nov.1

Portugal; Lisbon

8.6 60,000 All Saints’ Day; many killed when churches collapsed and fire ravaged the city. and fire ravaged the city. Large tsunami killed many.

1783 Feb.5

Italy; Calabria

50,000 First earthquake to be investigated scientifically.

1868 Aug.13

Chile and Peru

8.5 25,000 Large tsunami devasted Arica (now in Chile, but then in Peru).

1891 Oct.28

Japan; Nobi Plain

7.9 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.

1897 June 12

India; Assam

8.7 1,500 Large fault scarp formed (vertical displacement 35 feet. Much building damage in Shillong.

1906 Apr.18

U.S.A.; San Francisco

8.3 700 San Andreas fault ruptured for 270 miles. Great fire burned much of the city.

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1908 Dec28

7.5 58,000 Messina destroyed.

1920 Dec.16

China; Ningxia Province

8.6 200,000 Many landslides covered villages and towns.

1923 Sept.1

Japan; Tokyo

8.3 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.

1931 Feb.3

New Zealand; Hawke Bay

7.8 225 Many buildings damaged in Napier.

1940 Nov. 10

Romania; Vrancea district

7.4 1,000 Severe damage to buildings in Bucharest.

1946 Dec.

Japan; south of

8.4 1,360 Known as the Nankai earthquake. Great tsunami. Dec.

21 south of Shikoku Island

earthquake. Great tsunami.

1948 June 28

Japan; Fukui Prefecture

7.3 5,400 Only known instance of a person being crushed in a ground fissure.

1950 Aug. 15

India; Assam (eastern)

8.7 150 Damage in region along border with Tibet Landslides and floods.

1954 Sept.9

Algeria; El Asnam

6.8 1,240 El Asnam (then Orléansville) destroyed

1957 July 8

Mexico; Guerrero

7.9 68 Tall buildings damaged in Mexico City, 180 miles away.

1968 Aug31

Iran (eastern); Khorasan

7.3 12,100 About 60,000 people homeless.

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1970 May31

Peru; Chimbote

7.8 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.

1975 Feb.4

China; Liaoning Province; Haicheng

7.3 1,300 Earthquake successfully predicted and population evacuated. Heavy damage, but many lives saved.

1976 July 28

China; Hebei Province;

7.8 243,000 Major industrial city totally destroyed. Four aftershocks on same day with magnitudes 6.5, 6.0, 7.1, and 6.0.

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28 Province; Tangshan

6.0, 7.1, and 6.0.

1977 Mar.4

Romania; Vrancea district

7.2 1,570 Many buildings collapsed in Bucharest.

1979 Apr.15

Yugoslavia southern Montenegro

7.0 156 Near the Adriatic coast. Extensive damage.

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January

1994

Northdrige USA

M 6.8 Damages to buildings and bridges

1995 Kobe Japan

6,500 deaths

26 December 2004

Sumatra 9 240,000 deaths

Major damage, The tsunami waves damaged the coast

2009 Aquila Italy

6.3 308 deaths

1500 injuried

Several buildings collapsed

12 January 2010

Haiti

7

316,000

deaths

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

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Basics of Seismic Engineering 2011 40

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

Significant tsunamis

produced in the world

Date Origin Remarks 1755 Nov.1

Lisbon, Portugal (off the coast, in the Atlantic Ocean); earthquake of magnitude 8.6 (60,000 deaths)

Several large waves washed ashore in Portugal, Spain, and Morocco. Major damage and many deaths in Lisbon from tsunamis

1868 Apr.2

Island of Hawaii (south slope of Mauna Loa); volcanic earthquake of magnitude 7.7

Local tsunami destroyed many houses and killed 46 people

1883 Aug.27

Island of Krakatoa (in the Sunda Strait, between Java and Sumatra); volcanic eruption (36,000 deaths)

Violent explosion of Krakatoa volcano. Great tsunami felt in harbors around the world. Tsunami caused much damage and loss of life on nearby islands.

1896 June 15

Japan (off the Sanriku coast); earthquake of

Numerous villages entirely destroyed by tsunami;

41

June 15 coast); earthquake of magnitude 7.5 (27,000 deaths)

destroyed by tsunami; maximum wave height 15 meters. Many lives lost by drowning.

1923 Sept.1

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

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.

Date Origin Remarks

1946

Apr.1Aleutian 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 9Greece (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.

1976Aug.17

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

Major damage and many deaths from tsunami.

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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 11Tohoku 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

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The seismic hazard in Romania is due to

contribution of two factors :

(i) the major contribution of subcrustal seismic zone

1.7 Seismic hazard in Romania

Vrancea

(ii) others contributions due to the surface seismic

zone contributions spread to country territory.

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Romanian earthquakes

Data Ora (GMT) h:m:s

Lat. N° Long.

E° H Adâncimea focarului, km

Catalogul RADU C, 1994 Catalogul MARZA, 1980

I Mw1

M Mws Mw I

1903 13 Septemrie 08:02:745.7

26.6 >60 7 6.6 6.3 5.7 6.3 6.5

1904 6 Februarie 02:49:00 45.7 26.6 75 6 - 5.7 6.3 6.6 6

1908 6 Octombrie 21:39:8 45.7(45.5)

26.5 150(125)

8 7.1 6.8 6.8 7.1 8

1912 25 Mai 18:01:7 45.7 27.2 80(90) 7 6.3 6.0 6.4 6.7 7

1934 29 Martie 20:06:51 45.8 26.5 90 7 6.6 6.3 6.3 6.6 8

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 26.7 140-150*

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 45.34

26.30 109 8/9 7.5 7.2 7.2 7.4 9

1986 30 August 21:28:37 45.53

26.47 133 8 7.2 7.0 - 7.1 -

1990 30 Mai 10:40:06 45.82

26.90 91 8 7.0 6.7 - 6.9 -

1990 31Mai 00:17:49 45.83

26.89 79 7 6.4 6.1 - 6.4 -

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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 hazardwithin 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 accelerationi.e. the value of the reference peak ground accelerationon rock or firm soil ag.

� 3. The reference peak ground acceleration, chosen bythe National Authority for each seismic zone,corresponds to the reference return period chosen by thesame authority. To this reference average return periodfor Romanian territory is call

� “the design soil acceleration”

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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 ofcontrol period TC of the response spectrum for thespecific location. These values characterizesynthetically the frequencies composition of theseismic movement.

� The control period represents the border between thezone of the maximum values in the spectrum ofabsolute accelerations and the zone of maximumabsolute accelerations and the zone of maximumvalues in the spectrum of relative velocity. TC isexpressed in the seconds.

Fig. 1.21 Control periods for Romanian territory

The average interval of

return earthquake

magnitude

Values of control periods

TB, s 0,07 0,10 0,16

TC, s 0,7 1,0 1,6

IMR=100 years

For the ultimate limit

stage TD, s 3 3 2

49

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

50

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� By Doina Verdes

CHAPTER 2

THE ANALYSIS OF SEISMIC RESPONSE OF SINGLE DEGREE OF

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BASICS OF SEISMICAL ENGINEERING

2011

2

RESPONSE OF SINGLE DEGREE OF FREEDOM SYSTEM

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2.6 Response to seismic loading:

Contents

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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


2.10 Seismic response spectra of the SDOF inelastic

systems


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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

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• 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 beam-column 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.

• The behavior of the material of structural elements

could be linear-elastic (a) or nonlinear (b)

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a. b.

k, ξ

m

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

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The model for a single span frame

The model for a frame multiple spans

k, ξ

m

Fn

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The model for a multilevel framed system

F1

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:

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The methods to obtain the dynamic model are:

- the concentrated mass;

- the system with finite elements.

How can be appreciate the

degrees of freedom?

The horizontal translations of the mass

a. The case of an bridge

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The horizontal translations of the mass of bridge’s deckThe translations along the axis O-x and O-y =>

Two degrees of freedom

Important assumptions:

The building has rigid foundation slab

The movement of soil due to seismic

excitation is synchronic

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

b. The case of one level building

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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

FS(t)FA(t)

y(t)

1

ck

1

)(ty&

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y(t)

FS= Elastic force

FA= Damping force

K = Stiffness

C = damping coefficient

y(t)= displacement

a. b.

)(ty& =velocity

Non-linear Calculus System

FS(t)

FA(t)

Fs1

F

∆Fs

Tangenta la curbă

Secanta la curbă

Tangenta la curbă

FA1

FA0 ∆

∆FS

)(ty&

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y(t)

Fs0

y1yo ∆y)(ty&

1y&0y&

Level of damping in different structures

The damping varies with: the materials used, the form of thestructure, the nature of the subsoil, and the nature of thevibration.

Large-amplitudes post-elastic vibration is more heavily damped than small-amplitude vibration;

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than small-amplitude vibration;

Buildings with heavy shear walls and heavy cladding or partitions have greater damping than lightly clad skeletal structures.

Type of construction Damping ν

percentage of critical Steel frame, welded, with all walls of flexible construction Steel frame, welded, with normal floors and cladding Steel frame, bolted, with normal floors and cladding

2

5

10

Damping coefficient in different structures

ξ

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Concrete frame, with all walls of flexible construction Concrete frame, with stiff cladding and all internal walls flexible Concrete frame, with concrete or masonry shear walls Concrete and/or masonry shear wall buildings Timber shear walls construction

5

7

10

10

15


Response spectrum analysis is the dominant contemporary method for

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

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

0)()()( =++ tFtFtF eDi

Fi (t)= the inertia force

(1)

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FD (t)= the damping force

Fe (t)= the elastic force

)()( yymtF gi&&&& +=

yctFD&=)(

kytF =)(

(2)

(3)

(4)

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kytFe =)(

m= the mass of system

c= the viscous damping cœfficient

k= the stifness

(4)

The equation of equilibrium becomes:

)()()()( tymtkytyctym g&&&&& −=++

)()()()( tFtkytyctym S−=++ &&&

(5)

(6)

The frequency equation

( ) ( ) ( ) ( )tytytyty &&&&& −=++ 22 ωωξ

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( ) ( ) ( ) ( )tytytyty g&&&&& −=++ 22 ωωξ

mk /=ω

ξ = c/2mω

(7)

( ) ( ) ( )[ ]∫ −−−−++−=

t dtt

gym

mttAty

D

D

0expsin

1sinexp)( ττξωτωτ

ωϕωξω &&

The general solution of the seismic equilibrium equation is:

The first term represents the free vibration of the systemThe second term represents the forced vibrations under seismic action.

(8)

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seismic action.Neglecting the free vibrations contribution due to thequick damping of these the solution becomes:

( ) ( ) ( ) ( )[ ]∫ −−−−=t

Dg

D

dttymm

ty0

expsin1

ττξωτωτω

&& (9)


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

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( ) ( ) ( ) ( )[ ]∫ −−−−=t

Dg

D

dttymm

ty0

expsin1

ττξωτωτω

&& (9)

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

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m= the mass

mk /=ω ξ = c/2mω(10) (11)

at timeτon accelerati ground the )( =τgy&&

When the difference between the damped and the

undamped frequency is neglected, as is permissible forsmall damping ratios usually representative of realstructures (say ξ < 0.10), and when it is noted that thenegative sign has no real significance with regard toearthquake excitation, this equation can be reduced to:

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( ) ( ) ( ) ( )[ ]∫ −−−=t

g dttyty0

expsin1

ττξωτωτω

&& (12)

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North – south component of horizontal ground acceleration

El Centro 1940

The response spectrum used in seismical engineering

are:

- the velocity spectrum

2.5 The response spectrum and

the pseudospectrum

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- the velocity spectrum

- the absolute acceleration spectrum

- the displacement spectrum

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

( ) ( ) ( ) ( )[ ]

( ) ( ) ( )[ ]∫

∫−−−−

−−−=

t

t

g

dtty

dttyty0

expsin

expcos

ττξωτωτξ

ττξωτωτ

&&

&&&

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( ) ( ) ( )[ ]∫ −−−− g dtty0

expsin ττξωτωτξ &&

(13)

y(t))(-2 (t) 2ωωξ −= tyyt&&&

one obtains the total acceleration relation:

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

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( ) ( ) ( ) ( ) ( )[ ]

( ) ( ) ( )[ ]∫

∫−−−−

−−−−=

t

g

t

gt

dtty

dttyty

0

0

2

expcos2

expsin12

ττξωτωτωξ

ττξωτωτξω

&&

&&&&

(14)

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,

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- the spectral absolute acceleration,

These will be denoted herein as :

Sd(ξ ,ω),

Sv(ξ ,ω),

Sa(ξ ,ω), respectively.

As will be shown subsequently, it is usually necessary to calculate only the so-called pseudo-velocity spectral response Spv(ξ ,ω)defined by

( ) ( ) ( ) ( )[ ]max

0expsin,

−−−≡ ∫

t

gpv dttyS ττξωτωτωξ &&(15)

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

( ) ( )ωξω

ωξ ,1

, pvd SS = (16)

( ) ( ) ( ) ( )[ ]∫ −−−=t

g dttyty0

expsin1

ττξωτωτω

&&(12)

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

( ) ( ) ( )max

0cos,0

−≡ ∫

t

gv dtyS ττωτω &&

( ) ( ) ( ) t

(17)

(18)

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( ) ( ) ( )max

0sin,0

−≡ ∫

t

gpv dtyS ττωτω &&(18)

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 longperiod oscillators, i.e. very small values of ω.

For damped systems, the difference between Sv and Spv isconsiderably larger and can differ by as much as 20 percentfor ξ = 0.20. Also from Eq. (14) for ξ = 0 that

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( ) ( ) ( )max

0sin,0

−≡ ∫

t

ga dttvS ττωωω &&

( ) ( ) ( ) ( ) ( )[ ]

( ) ( ) ( )[ ]∫

∫−−−−

−−−−=

t

g

t

gt

dtty

dttyty

0

0

2

expcos2

expsin12

ττξωτωτωξ

ττξωτωτξω

&&

&&&&

(19)

• thus, from Eq. (19),

( ) ( )ωωω ,0,0 pva SS =

It can be shown that Eq. (19) is very nearly satisfied for damping values over the range 0 < ξ < 0.20;

(19)

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damping values over the range 0 < ξ < 0.20; therefore, we are able to use the approximate relation

( ) ( )ωξωωξ ,S,S pva =

with little error being introduced.

(20)

• 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

( ) ( ) ( )ωξωξωωξ ,,,max, 2

padds mSmSkSf === (21)

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

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the relations

( ) ( )ωξω

ωξ ,1

, pvd SS =

( ) ( )ωξωωξ ,, pvpa SS =

(22)

(23)

• 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 S (ξ ,ω) using Eq.

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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.

• 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

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• 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).

a) Ground acceleration(El Centro)

b) The deformation response of three SDF systems

T=0,5 s

ξ =2%

c) deformation response spectrum

a

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T=1 s

ξ =2%

T=2 s

ξ =2% bc

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

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( ) ( ) ωωξωξ log,log,log −= pvd SS

( ) ( ) ωωξωξ log,log,log += pvpa SS

(24)

(25)

Combined D-V-A

RESPONSE SPECTRUM

for El Centro 1940 ground motion

Combined D-V-A response spectrum for

El Centro ground motion

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40

From these relations, it is seen that when a plot is made with logSpv(ξ,ω) as the ordinate and logω as the abscissa, Eq. (24) is astraight 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 constantvalue of logSpa(ξ,ω). Thus, a four-way log plot allows all three typesof spectra to be illustrated on a single graph. When interpretingsuch plots, it is important to note the following limiting values:

( ) ( )[ ],lim tyS =ωξ (26)

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( ) ( )[ ]max0

,lim tyS gd =→

ωξω

( ) ( )[ ]max0

,lim tyS gpa&&=

→ωξ

ω

(26)

(27)

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

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values of damping ratio, say ξ = 0.20.

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 whichreal SDOF structures (with specific values of damping ratio andnatural period) respond to the input ground motion. The onlylimitation in their application is that the response must be linearelastic because linear response is inherent in the Duhamelintegral.

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Therefore, such response spectra cannot accurately represent theextent of damage to be expected from a given earthquakeexcitation, as damage involves inelastic (nonlinear) deformations.Nevertheless, the maximum amount of elastic deformationproduced by an earthquake is a very meaningful indication ofground motion intensity.

Moreover, such response spectra indicate the maximumdeformations for all structures having periods within the range forwhich they were evaluated; hence, the integral of a single responsespectrum over an appropriate period range can be used as aneffective measure of ground motion intensity. Housner originallyintroduced such a measure of ground motion intensity when hesuggested defining the integral of the pseudo-velocity responsespectrum over the period range 0.1 < T < 2.5 sec as the spectrumintensity:

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intensity:

( ) ( )dTTSSI pv , 5.2

1.0ξξ ∫≡

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

(28)

Usually, it is assumed that the shapes of the design spectra are thesame for both the design and maximum probable earthquakes butthan they differ in intensity as measured by peak groundacceleration. Thus, it has been common practice to first normalizethe intensity of these design spectra to the 1 g peak accelerationlevel so that Eq. (27) becomes:

( ) g1,Slim pa0

=→

ωξω

and then later to scale them down to the appropriate peak

(29)

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and then later to scale them down to the appropriate peakacceleration levels representing the design and maximumprobable earthquakes. Once the shapes of these commonnormalized spectra have been developed, taking intoconsideration local soil conditions, appropriate scaling factors areapplied representing the intensity levels of the peak free-fieldsurface ground accelerations (PGA) produced by the design andmaximum probable earthquakes.


� By Doina Verdes

CHAPTER 2

THE ANALYSIS OF SEISMIC RESPONSE OF SINGLE DEGREE OF

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RESPONSE OF SINGLE DEGREE OF FREEDOM SYSTEM

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Contents






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


2.10 Seismic response spectra of the SDOF inelastic

systems

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

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The step-by step procedure

• A severe earthquake will induce inelastic deformationin a code-designed structure. The step-by stepprocedure is suited to analysis of nonlinear responsein earthquake engineering.

• There are many different step-by-step methods, but • 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.

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The response for each step

• Thus the response for each step is an independent analysisproblem, and there is no need to combine response contributionwithin the step. Nonlinear behavior may be considered easily bythis approach merely by assuming that the structural propertiesremain constant during each step, and causing them to changein accordance with any specified form of behavior from one stepto the next; hence the nonlinear analysis actually is a sequence

6

to the next; hence the nonlinear analysis actually is a sequenceof linear analyses of a changing system.

• Any desired degree of refinement in the nonlinear behavior maybe achieved in this procedure by making the time steps’ shortenough; also it can be applied to any type of nonlinearity,including changes of mass, and damping properties as well asthe more common nonlinearities due to changes of stiffness.

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The simplest step-by-step method for analysis the SDOF system is

based on the exact solution of the equation of motion for responseof a linear structure to a loading that varies linearly during adiscrete time interval.

The loading history is divided into time intervals, usually defined bysignificant changes of shape in the actual loading history; between

this points, it is assumed that the slope of the load curveremains constant.

Step-by-step methods

7

remains constant.

The other step-by-step methods employ numerical procedures toapproximately satisfy the equation of motion during each time stepusing numerical differentiation or numerical integration.

The general numerical approach to step-by step dynamicresponse 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


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which express the final velocity and displacement in terms ofthe initial values of these quantities plus an integralexpression. The change of velocity depends on the integral ofthe acceleration history, and the change of displacement

( )∫+=h

dyyy0

01 ττ&

( )∫+=h

dyyy0

01 ττ&&& (1)

(2)

8

the acceleration history, and the change of displacementdepends on the corresponding velocity integral. In order tocarry out this type of analysis, it is necessary first to assumehow the acceleration varies during the time step; thisacceleration assumption controls the variation of the velocityas well and thus makes it possible to step forward to the nexttime step.

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In the Newmark formulation, the basic integration equation[Eqs. (1,2)] for the final velocity and displacement areexpressed as follows:

A more general step-by-step formulation was proposed byNewmark, which includes the preceding method as a specialcase, but also may be applied in several other versions.

2.7 The Newmark Beta Methods

9

( ) 1001 yhyh1yy &&&&&& γγ +−+=

1

2

0

2

0012

1yhyhyhyy &&&&& ββ +

−++=

(3)

(4)

h=time step

h = ti+1 – ti (5)

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• It is evident in Eq. (3) that the factor γ provides a linearity varyingweighting between the influence of the initial and the finalaccelerations on the change of velocity; the factor β similarlyprovides for weighting the contributions of these initial and finalaccelerations to the change of displacement.

• From study of the performance of this formulation, it was noted

10

• 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

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h = ti+1 – ti

h

)(tys&&

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:

Conditions for step time

13

π/3pT

h

55.0pT

h(6)

h

t

1+siy&&

siy&&

ti ti+1

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Coeficient β= 1/6 (γ = 1/2)

• β = 1/6 ( γ = 1/2),

1−siy&& 1+siy&&

siy&&

∆h ∆h h h

14

h/T ≤ √3/π = 0.55i+1 i-1 i

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Linear variation of acceleration during time interval “h”

β = 1/6

(for γ = ½,)

( )1001 yy2

hyy &&&&&& ++=

(7)

(8)

15

( )10012

1

2

0

2

001 y6

hy

3

hhyyy &&&&& +++=

(9)

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( ) ( ) ( ) ( ) ( ) ( )tymtytktytctym s1111&&&&& =++ (10)

Step 1

( )yyh

yy &&&&&& ++= (11)

16

( )10012

yyh

yy &&&&&& ++=

1

2

0

2

00163

yh

yh

hyyy &&&&& +++=

(11)

(12)

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STEP 1

( )h

0

0

0

0

0

0

=

=

=

y

y

y

&&

&

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

17

( )112

yh

y &&& =

1

2

16

yh

y &&=

(13)

(14)

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symyh

kyh

cym 11

2

1162

&&&&&&&& −=++

62

1211

hk

hcm

ymy s

++

−= &&&&

(15)

(16)

The displacement and velocity increments using

eq. 13 and 14

18

62

2

62

1211

h

hk

hcm

ymy s ⋅

++

−= &&&

6

62

12

211

h

hk

hcm

ymy s ⋅

++

−= &&

(17)

(18)

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Summary of the Linear Acceleration

ProcedureFor any given time increment, the above

described explicit linear acceleration analysis

procedure consists of the following operations whichmust carried out consecutively in the order given:

Using the initial velocity and displacement values and y0, which are known either from the values at oy&

19

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.

oy&

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Linear systems can also be treated by this sameprocedure, which becomes simplified due to thephysical properties remaining constant over theirentire time-histories of response.

• As with any numerical-integration procedure theaccuracy of this step-by-step method will depend onthe length of the time increment h.

• The factors which must be considered in the selection

20

• The factors which must be considered in the selectionof this interval: the complexity of the nonlineardamping and stiffness properties, and the period T ofvibration of the structure. The time increment must beshort enough to permit the reliable representation ofall these factors, the last one being associated withthe free-vibration behavior of the system.

Doina Verdes


2011

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

21

( ) ( ) ( ) ( ) ( ) ( )tymtytktytctym s1111&&&&& =++

The equation of equilibrium at the time step t1

c(t) – the damping coefficient

k(t) – the stiffness

The coefficients c(t) and k(t) are variabletime depending

(1)

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

a. The symmetrical b. The asymmetrical

22

a. The symmetrical

elastic-plastic modelb. The asymmetrical

elastic-plastic model

c. The bilinear

elastic-plastic model

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The nonlinear system

FS(t)

FA(t)

Fs1

∆Fs

Tangent

Secant

Tangent

FA1

FA0

∆ FA

23

y(t)

Fs0

y1yo ∆ y

a. The stiffnessb. The damping

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1+siy&&

siy&&

)(tys&&

24

∆h

t ti ti+1

The digitalized accelerograme

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h = ti+1 – tiConditions for step time to

)(tys&&

We assume that the acceleration varies linearly during the time step between the initial and final values of ÿ0 and ÿ1, thus the Newmarkβ = 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

25

Conditions for step time to

π/3pT

h

55.0pT

h (2)

h

t

1+siy&&

siy&&

ti ti+1

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The incremental form of the seismic equation

During the incremental time step h the system behavior is elastically

efSDI FFFF ∆=∆+∆+∆

( ) ( ) ( ) ( )tymtFhtFtF III&&∆=−+=∆

( ) ( ) ( ) ( )tyctFhtFtF &∆=−+=∆ (5)

(4)

(3)

26

( ) ( ) ( ) ( )tyctFhtFtF DDD&∆=−+=∆

( ) ( ) ( ) ( )tyktFhtFtF SSS ∆=−+=∆

( ) ( ) ( ) ( )tymtFhtFtF sefefef&&∆=−+=∆

( ) ( ) ( ) ( )tymtyktyctym s&&&&& ∆−=∆+∆+∆

The equation can be solved using the β Newmark integration

method

(6)

(5)

(7)

(8)

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• 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

27

• Assumption: the induced energy is computed for an elastic linear system

• Sv is the pseudo-velocity spectrum

2

2

vi

mSE = (9)

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The energy balance equation

• EI = Input Energy

• EE = Elastic energy of the system

• E = Energy due to deformations

EI = EE +EH = (EES + EK )+ (EHξ + EHµ) (10)

28

• 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

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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;

29

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.

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The energetic procedure based on

the ultimate displacements

F

FE

ECAP=Ep+EH (11)

Fy - the seismicdesign force

Elastic behavior

30

Fy

∆C ∆Ue ∆u ∆

( ) ( )5,02

1−∆=∆−∆+∆= DCCCUCCCCAP FFFE ρ

∆y

(12)

design forceElastic-plastic behavior

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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) The spectral displacement

F

Fe

F =F

31

i) The spectral displacementof the nonlinear system is equal with those of a linear system;

ii) The energia of the nonlinear system is equal with the energy of the linear elastically system.

Fc=Fpl

∆c ∆u (∆e max) ∆ ∆y

Fy=Fp

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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

u

y

∆

∆=

e

y

F

F

F

Fe

F =F

32

Fc=Fpl

∆c ∆u (∆e max) ∆

d

a

d

ec

mSFF

ρρ==

Sa – Elastic acceleration spectrum.ρd – desplacement ductility factor

Fy=Fp

∆y

(13)

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The energy of the nonlinear system is equal with the

energy of the linear elastical system

eeCeuCC FFF ∆=∆−∆+∆2

1)(

2

1 F

Fe

Fc=Fpl 1212

1

−=

−= a

ec

mSFF

ρρ Fy=Fp(14)

33

The spectral response for the elastic-plastic systems one obtains by dividing elastic spectrum to the ductility factor

or by the equation

Fc=Fpl

∆c ∆u (∆e max) ∆

1212 −− dd ρρ

dρ

12 −dρ

∆y

Fy=Fp

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Newmark inelastic Spectrum (for pseudo acceleration)*

34

The Newmark-Hall spectrum may be converted into an “inelastic designresponse spectrum” by making the appropriate adjustments. To determinestrength demands, the spectrum is divided by ductility in the higher period(equal displacement) realm but is divided by (2µ - 1) in the short period(equal energy) *Source: FEMA Instructional Material

Complementing FEMA 451

Doina Verdes


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35

Elastic-plastic response spectrum for El Centro 1940 with 5% damping

coeficient and ductilities 1; 1.5; 2; 4; 8.

Doina Verdes


2011


� By Doina Verdes

CHAPTER 3

ANALYSIS OF SEISMIC

RESPONSE 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

Doina Verdes


20113

• 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.

3.1 Introduction

44

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.

Doina Verdes


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gy&&

ma

mb

mc

ya(t)

yb(t)

yc(t)

ua,1

ub,1

uc,1 uc,2 uc,3

ub,2ub,3

ua,2 ua,3

Axis of

reference

Hypothesis

55

Mode 1 Mode 2 Mode 3

Each mass has 2 DOF Due to two Horizontal Translations and rotation

Shapes of vibration due to mode 1 to 3

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)

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( )tFFFF aSDI aaa=++

( )tFFFF bSDI =++

[1]

[2]

The equations of dynamic equilibrium

66

( )tFFFF bSDI bbb=++

( )tFFFF cSDI ccc=++

[2]

[3]

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2011

The inertia forces in equation (1) are:

aaI umFa

&&⋅=

umF ⋅=

[4]

77

bbI umFb

&&⋅=

ccI umFc

&&⋅=

[5]

[6]

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2011

The inertia forces in matrix form:

=

c

b

a

c

b

a

c1

b1

a1

u

u

u

m00

0m0

00m

F

F

F

&&

&&

&&

or more generally:

[7]

88

yMFI&&⋅=

or more generally:

[8]

FI is the inertia force vector,

M is the mass matrix and

is the acceleration vector. y&&

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• 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,

99

coupling generally exists between the coordinates,

complicating the solution. This is a prime reason for

using the lumped-mass method.

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The elastic forces in equation (1) depend on the

displacement and using stiffness influence coefficients they

may be expressed:

++= cacbabaaaS ukukukF

1010

++=

++=

++=

cccbcbacaS

cbcbbbabaS

cacbabaaaS

ukukukF

ukukukF

ukukukF

c

b

a

[9]

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2011

In matrix form

=

c

b

a

cccbca

bcbbba

acabaa

Sc

Sb

Sa

u

u

u

kkk

kkk

kkk

F

F

F

[10]

or more generally:

1111

ukFS ⋅= [11]

or more generally:

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


2011

By analogy with the expression (9), (10) and (11) the

damping forces may be expressed

ycFD&⋅=

F D is the damping force vector,

c

[12]

1212

D

c is the damping matrix and

is the velocity vector.

In general it is not practicable to evaluate c

and damping is usually expressed in terms of damping

coefficients.

oy&

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( )tFFFF SDI =++

Using the Eqs. (8), (11) and (12) the equation of dynamic

equilibrium (1) may be written generally as:

[13]

1313

SDI

[14]

which is equivalent to

( )tumkuucuM g&&&&& −=++

Doina Verdes


2011

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

1414

its free vibration frequencies and mode shapes. In free

vibration there is no external force and damping is taken

as zero.

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2011

• The equation of motion (14) becomes:

0kuuM =+&&

Making the necessary steps of calcullus on obtains:

[15]

1515

0ˆˆ 2 =− uMuk ω [16]

the eigenvalue equation and is readily solved for ω

by standard computer programs

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2011

• 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

T

n

n

2

nnnnnM

tFYY2Y

φφ

φωωξ =++ &&&

16

n

T

n

nnnnnnM

YY2Yφφ

ωωξ =++ &&&

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.

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2011

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

1717

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:

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2011

The response of the n–th mode at any time demands

the solution of Eq for Yn(t).

( )tuM

LYY2Y g

n

T

n

n

n

2

nnnn&&&&&

φφωξω =++

where

[16]

1818

Yn is a generalized displacement in mode n leading to

the actual displacement and

is the row mode vector corresponding to the

column vector øn.

T

nΦ

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2011

This may be done by evaluating the Duhamel integral:

( ) ( ) ( )∫

−−t1L σξω

1919

( ) ( ) ( )∫

−−⋅=t

0

t

g

nn

T

n

n

n deu1

M

LtY n σσ

ωφφσξω

&&[17]

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2011

• 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

1n

nini tYu φ

where øin is the relative amplitude of displacement

[18]

2020

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.

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The earthquake forces

• The earthquake forces in the structure may then be expressed in terms of the effective accelerations

( ) ( )tYtY n

2

neffn ω= &&

from which the acceleration at any floor i is

[19]

2121

( ) ( )tYtu nin

2

neffin φω= &&

from which the acceleration at any floor i is

and the earthquake force at any floor “i” is

[20]

[21]( ) ( )[ ]tYmtq ninniin&&φω 2=

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2011

[ ]2

12

max3,a

2

max2,a

2

max1,amaxa uuuu ++≈

Superimposing all the modal contributions,

the earthquake forces in the total structure

may be expressed in matrix form as:

[22]

2222

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.

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R (t)

Time

Time

First mode

Nth

mode

u 1max

u 2max

Second mode

2323

Time

2max

u n max

Superimposing all the modal contributions

Doina Verdes


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3.3 Response Spectrum Analysis for Multi-

degree 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.

2424

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:

Doina Verdes


2011

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

n

vn

n

T

n

n

nmaxnnmaxn

S

M

LYu

ωφφφφ ⋅==

anT

n

nmaxn

2

nnmaxn SM

LMYMq ⋅==

ωφφωφ

[23]

[24]

2525

an

n

T

n

nmaxnnnmaxnMωφ

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

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2011

• 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

2626

an example the maximum deflection at the top of a

three-story structure (three masses) would be:

[ ]2

12

max3,a

2

max2,a

2

max1,amaxa uuuu ++≈ [25]

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Exemple of a three stories frame

Response Spectrum Analysis [21]

27Doina Verdes


2011

Solutions for System in Undamped Free Vibration

Mode Shapes for

Idealized 3-Story

Frame

28Doina Verdes


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

U=ФY

29Doina Verdes


2011

Orthogonality conditions

The orthogonality condition is an extremely important concept as itallows for the full uncoupling of the equations of motion.The damping matrix (which is not involved in eigenvaluecalculations) will be diagonalized as shown only under certainconditions. In general, C will be diagonalized if it satisfies theCaughey criterion: CM-1K = KM-1C

30Doina Verdes


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Development of uncoupled Equations of motions

31Doina Verdes


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The explicit form

32Doina Verdes


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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.

33Doina Verdes


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Rayleigh proportional Damping

34Doina Verdes


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Response Spectrum Method

35Doina Verdes


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Doina Verdes


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• 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

222 uuuu ++≈ [25]

3737

[ ]22

max3,a

2

max2,a

2

max1,amaxa uuuu ++≈ [25]

Doina Verdes


2011

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

3838

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:

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2011

• 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

3939

• 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:

( ) ( )tFutkutcuM ∆=∆+∆+∆ &&& )( [26]

Doina Verdes


2011

efSDI FFFF ∆=∆+∆+∆

( ) ( ) ( ) ( )tymtFhtFtF III&&∆=−+=∆

( ) ( ) ( ) ( )tyctFhtFtF DDD&∆=−+=∆

FS(t)

y(t)

Fs1

Fs0

y1yo ? y

?Fs

Tangenta la curba

Secanta la curba

FS(t)

y(t)

Fs1

Fs0

y1yo ? y

?Fs

Tangenta la curba

Secanta la curba

∆F

4040

( ) ( ) ( ) ( )tyktFhtFtF SSS ∆=−+=∆

( ) ( ) ( ) ( )tymtFhtFtF sefefef&&∆=−+=∆

( ) ( ) ( ) ( )tymtyktyctym s&&&&& ∆−=∆+∆+∆

∆FS

∆y y1

∆h

t

1+siy&&

siy&&

)(tys&&

ti ti+1

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2011

gy&&

1+giy&&

giy&&

(6)

• In order to avoid instability in the response calculated

by these equations the length of the time step must be

limited by the condition

NT8.1

1h ≤

4141

ti ti+1 t

where TN is the vibration period of the highest mode

(i.e., the shortest period) associated with the system

eigenproblem.

h

Doina Verdes BASICS OF SEISMICAL ENGINEERING

2011

• 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

4242

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.

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Modal Analysis Equivalent Lateral Force Procedure

Empirical period of vibration

• Smoothed response spectrum

• Compute total base shear,, as if SDOF

• Distribute T along height • Distribute T along height assuming “regular” geometry

• Compute displacements and

member forces using standard

procedures

43Doina Verdes


2011


By Doina Verdes

CHAPTER 4.

METHODS OF SEISMIC ANALYSIS OF STRUCTURESANALYSIS 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 • 4.3 Lateral force method of analysis- EC8 • 4.4 Time - history representation • 4.5 Non-linear static (pushover) analysis

Doina Verdes


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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 forThe three main techniques currently used fordynamic analysis are:Direct integration of the equation of motion by step-by-step procedures;Normal mode analysis;Response spectrum techniques.


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 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


2011

The Equivalent Lateral Force Procedure• Empirical computation of vibration

period

• Smoothed response spectrum

• Compute total base shear seismic

forceforce

• Distribute the base shear seismic

force along height assuming

“regular” geometry

• Compute displacements and member

forces using standard procedures


2011

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.

5.2 Lateral force method of analysis

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


2011

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


2011

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”.“elastic response spectrum”.

• The horizontal seismic action is described by two

orthogonal components considered as independent

and represented by the same response spectrum.


2011

Shape of horizontal elastic response spectrum

of accelerations for Vrancea sources a), b), c) and Banat d)

TC = 0.7s TC = 1.0 sa) b)

TC = 1.6sc) 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.a linear elastic response.


2011

Linear elastic behavior

FS(t)FA(t)

y(t)

1

ck

1

)(ty&

Nonlinear elastic behaviorStiffness

Damping


2011

Base shear force• The seismic base shear force Fb, for each horizontal

direction in which the building is analysed, is determined as follows:

Fb = γIIII Sd (T1) m λwhere:

• Sd (T1) ordinate of the design spectrum at period T1;

• T1 fundamental period of vibration of the building for

(4.1)

1

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 factorDoina Verdes

BASICS OF SEISMIC ENGINEERING 2011

sn

s

snFn

The deformed shape for the 1st mode:a. Computed by methods of structural dynamicsb. approximated by horizontal displacementsincreasing linearly along the height of the building

s1

si

zn

zi

z1

s1

siFi

F1

a. b.


2011

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:

1

by the following expression:

• where:

• u - lateral elastic displacement of the top of the building, in m, due to the gravity loads applied in the horizontal direction.

uT 21 = (4.2)


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:

T = C ⋅ H 3/ 4T1 = Ct ⋅ H 3/ 4

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.

(4.3)


2011

Design spectrum

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

Inelastic response spectrum

•Which can be obtained with the equation :•Which can be obtained with the equation :

• For the horizontal components of the seismic action

the design spectrum, Sd(T),

• is defined by the following expressions [EC8]:

]1[)(10

TatSN

q

Tgd

−+=

β

(4.4)


2011

( )

⋅

−

+= TT

qaTS

B

gd

1

1

0β

BTT ≤p0

T > T

Case “a”

Case “b”

(4.5)

T > TB

( ) ( )q

TaTS gd

β=

Case “b”

T the vibration periodag soil design accelerationq behavior factor

(4.6)


2011

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;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;


2011

Values of control periods for Romanian territory

T h e av e rag e in te rv a l o f

re tu rn ea rth q u ak e

m ag n itu d e

V a lu es o f co n tro l p e rio d s

T B , s 0 ,0 7 0 ,1 0 0 ,1 6

T C , s 0 ,7 1 ,0 1 ,6

IM R = 1 0 0 y ea rs

F o r th e u ltim a te lim it

Table 4.1

T C , s 0 ,7 1 ,0 1 ,6 F o r th e u ltim a te lim it

s tag e T D , s 3 3 2


2011

The behaviour factor q

• The behaviour factor q is anapproximation of the ratio of theseismic forces, that the structurewould experience if its responsewas completely elastic with 5%viscous damping, to the minimumviscous damping, to the minimumseismic forces that may be used indesign - with a conventional elasticresponse model - still ensuring asatisfactory response of thestructure.


2011

Nr.crt Sistem strctural

DCM DCH P100- 92 (1/Ψ) EC8 P100-1/2006 EC8 P100-1/2006

1.

Cadre

Clădiri cu un nivel 5,00; 6,66

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

4,00; 5,00

3,90

4,725

5,85

6,75

2.

Dual

Structuri cu cadre

preponderente

-

3,90

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

5,85

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

Structuri cu pereţi preponderenţi

Behaviour factors for horizontal seismic action Table 4.2

preponderenţi -

3,60

4,375

5,40

6,25

3.

Pereţi

Structuri cu doi pereţi în fiecare direcţie

3

3

4,00 3

3

4,00

4,00

Structuri cu mai mulţi pereţi

3 3 4,00

3 3 4,00 4,00

Structuri cu pereţi cuplaţi

4,00

3,60

4,375

5,40

6,25

4. Flexibil la torsiune(nucleu)

2 2 3 3

- 2 2 3 3

5. Pendul inversat 1,5 2 3 3 2,86 1,5 2 3 3

23Doina Verdes


Nr.crt

Sistem strctural

DCM DCH P100- 92

(1/Ψ) EC8 P100-

1/2006 EC8 P100-

1/2006

1.

Cadre necontra-vântuite

Structuri parter

4 2,5; 4 2,5;

2,94; 3,46; 5,00; 5,88

4

2,5; 4

5,50

2,50; 5,00; 5,50

Structuri etajate

4

4

5,88 4

4

6,00; 6,50.

6,00; 6,50

2.

Cadre contravântuite

centric

Contravântuiri cu diagonale întinse

4 4 4 4 4,00; 5,00 4 4 4 4

Contravântuiri cu diagonale in V

2 2 2,5 2,5 2,00; 2,50 2 2 2,5 2,5

3.

Cadre contravântuite excentric

4 4 5,00 4 4 6,00 6,00 3. Cadre contravântuite excentric

5,00 4 4 6,00 6,00

4.

Pendul inversat

2 2 1,54; 2,00 2 2 6,00 6,00

5.

Structuri cu nuclee sau pereţi de beton 2 2 3 3 - 2 2 3 3

6.

Cadre duale

Cadre necontrav. asociate cu cadre contravântuite în X şi alternante

4

4

2,00; 2,20; 4,00; 5,00

4 4 4,8 4,8

Cadre necontrav. asociate cu cadre

contravântuite excentric

-

4

-

2,00; 2,20; 4,00; 5,00

-

4

-

6,00

24Doina Verdes


Distribution of the horizontal seismic forces

• The fundamental mode shapes in the horizontal

directions of analysis of the building may be

Fb = γI Sd (T1) m λ (4.7)

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.


2011

The deformed shape for the 1st mode

sn

s

snFn

s1

si

zn

zi

z1

s1

siFi

F1

a. b.


2011

∑=

⋅

⋅⋅=

n

i

ii

iibi

sm

smFF

1

The seismic action effects shall be determined by

applying, to the two planar models, horizontal forces

Fi to all storeys.

(4.8)

=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


2011

• When the fundamental mode shape is approximated

by horizontal displacements increasing linearly along

the height, the horizontal forces Fi are given by:

∑=

⋅

⋅⋅=

n

i

ii

iibi

zm

zmFF

1

zi, zj heights of the masses;

m , m above the level

(4.9)

i j

mi, mj above the level

of application of the seismic

action (foundation or

top of a rigid basement).

F ii

The horizontal forces Fi shall be

distributed to the lateral load resisting system assuming rigid floors.


2011

Torsional effects if lateral stiffness and mass

are symmetrically distributed in plan

• If the lateral stiffness and mass are symmetricallydistributed in plan and unless the accidentaleccentricity is taken into account .

• Whenever a spatial model is used for the analysis, theaccidental torsion effects referred may be determinedas the envelope of the effects resulting from theas the envelope of the effects resulting from theapplication of static loadings, consisting of sets oftorsion moments Mai about the vertical axis of eachstorey i:

Mai = eai Fbi

e=0,05Li

(4.10)

(4.11)


2011

M torsional moment applied at storey i about its 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 massFbx – the seismic force on o-x direction Fby – the seismic force on o-y direction


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


2011

The case of “natural” eccentricity

Mtx=Tbx e ix

Mty=Tby e iy

(4.12)

(4.13)

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

(4.13)

(4.14)

(4.15)

e ix ,e iy = the “natural” eccentricity


2011

The distribution of seismic force

to structural vertical elements

(4.16)

(4.17)


2011

Ground conditions

The construction site and the nature of the supporting

ground should normally be free from risks of:

• ground rupture,

• slope stability and• slope stability and

• permanent settlements caused by liquefaction or densification in the event of an earthquake.


2011

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

1

two main directions smaller than the following valueswhere TC is given in Codes’ Tables;

b) they meet the criteria for regularity in elevation

CTT

sT

4

2

1

1

≤

≤ (4.18)(4.19)


2011

Base shear force• The seismic base shear force Fb, for each horizontal

direction in which the building is analysed, is determined as follows:

Fb = γIIII Sd (T1) m λwhere:

• Sd (T1) ordinate of the design spectrum at period T1;

• T1 fundamental period of vibration of the building for

(4.20)

1

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 factorDoina Verdes


The design spectrum• For the horizontal components of the seismic action the design

spectrum, Sd(T), is defined by the following expressions:

Where:Sd(T) ordinate of the design spectrum,

(4.21)

(4.22)spectrum,q behaviour factor,β lower bound factor for the spectrumValues of the parameters S, T B, T C, and T D are given in following tables

(4.23)

(4.24)


2011

Elastic response spectrum, Type 2Elastic response spectrum, Type 1

Values of the parameters describing

the Type 2 elastic response spectrum

Values of the parameters describing

the Type 1 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% • 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.


2011

Design spectrum for elastic analysisThe capacity of structural systems to resist seismicactions in the non-linear range generally permits theirdesign for forces smaller than those corresponding to alinear elastic response.

To avoid explicit inelastic structural analysis in design,To avoid explicit inelastic structural analysis in design,the capacity of the structure to dissipate energy, throughmainly ductile behaviour of its elements and/or othermechanisms, is taken into account by performing anelastic analysis based on a response spectrum reducedwith respect to the elastic one, henceforth called ''designspectrum'', This reduction is accomplished by introducingthe behaviour factor q.


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 viscous damping, to the minimum seismic forces that may be used in design - with aconventional elastic response model - still ensuring a satisfactory response of the structure.


2011

• 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

1998.1998.

• The value of the behaviour factor q may be different

in different horizontal directions of the structure,

although the ductility classification must be the samein all directions.


2011

qqqq the factor of structure behavior; the values are standard function of structure type and the capacity of energy dissipationExamplethe 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)

w

in structural systems

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


2011

• 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 linear-

elastic analysis may be used:


2011

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 dampingcorrection 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.


2011

TT

T

TT

B

B

)1(1)( 0 −

+=

≤

ββ

Case “a”

Case “b”

(4.26)

0)( ββ =

≤

T

TTT CB p

Case “b”

(4.27)


2011

T

TT

TTT

C

DC

0)( ββ =

≤p

Case “c”

Case “d”

(4.27)

20)(T

TTT

TT

DC

D

ββ =

f

(4.28)


2011

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 collapseon the possibility of casualties in case of collapse


2011

Importance

category Buildings

I Buildings whose integrity during earthquakes is of vital importance

for civil protection, e.g. hospitals, fire stations, power plants, etc.

II Buildings whose seismic resistance is of importance in view of the consequences

Table 4.3

importance in view of the consequences associated with a collapse, e.g. schools,

assembly halls,cultural institutions etc.

III Ordinary buildings, not belonging to the other categories

IV Buildings of minor importance for public safety, e.g. agricultural

buildings, etc.


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.• 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.


2011

• 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 corresponds to the reference return period chosen by National Authorities.


2011

5.4 Time - history representation

• The seismic motion may also be represented in terms ofground acceleration time-histories and related quantities(velocity and displacement).

• When a spatial model is required, the seismic motion shallconsist of three simultaneously acting accelerograms. Theconsist of three simultaneously acting accelerograms. Thesame accelerogram may not be used simultaneously alongboth horizontal directions.

• The description of the seismic motion may be made by usingartificial accelerograms and recorded or simulatedaccelerograms.


2011

Non-linear methods

• The mathematical model used for elastic analysis shall beextended to include the strength of structural elements and theirpost-elastic behaviour.

• As a minimum, bilinear force – deformation envelopes should beused at the element level. In reinforced concrete and masonrybuildings, the elastic stiffness of a bilinear force-deformationrelation 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.


2011

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:and of existing buildings for the following purposes:

a) to verify or revise the overstrength ratio valuesαu/α1;b) to estimate expected plastic mechanisms and thedistribution of damage;c) to assess the structural performance of existing orretrofitted buildings;


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 • For low-rise masonry buildings, in which structural walls are dominated by shear, each storey may be analysed independently.


2011

Lateral loadsThe 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 - “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.


2011

Plastic mechanism

Determination of the idealized elasto - perfectly plastic force –

displacement relationship.


2011

Capacity curveThe relation between base shear force and thecontrol displacement (the “capacity curve”) should bedetermined by pushover analysis for values of thecontrol displacement ranging between zero and thevalue corresponding to 150% of the targetdisplacement.The control displacement may be taken at the centreof mass at the roof of the building.of mass at the roof of the building.

Overstrength factorWhen the overstrength (αu/α1) should be determinedby pushover analysis, the lower value of overstrengthfactor obtained for the two lateral load distributionsshould be used.


2011

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 q q q used in the design is based.

Plastic mechanism

Target displacementTarget 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.


2011


� By Doina Verdes

CHAPTER 5

EARTHQUAKE RESISTANT EARTHQUAKE RESISTANT DESIGN


2011

Contents


� 5.2 Performance Based Engineering

� 5.3 Performance Requirements and Compliance Criteria

� 5.4 The guiding principles governing the conceptual � 5.4 The guiding principles governing the conceptual

design against seismic hazard

Doina Verdes


20113

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:criteria:

• Function;

• Cost;

• Reliability.


2011

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• 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


2011

• 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 termsof probabilities (of failure or survival).

• The required reliability is achieved if enough of the

elements of the design behave satisfactorily under theelements 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.


2011

Up to the mid-1980s it was common practice to

design normal structures or equipment to meet twocriteria:

(1) in moderate, frequent earthquakes the structureor equipment should be undamaged;or equipment should be undamaged;

(2) in strong, rare earthquakes the structure or

equipment could be damaged but should notcollapse.


2011

• The main intention of the second of these criteriawas to save human lives, while the definition of the

terms “strong”, “rare”, “moderate”, and “frequent”have varied from place to place, and have tendedto be rather imprecise because of the uncertaintiesin the state-of-the-art.in the state-of-the-art.

• Indeed, design has generally only been carried outexplicitly for criterion (2), the assumption beingmade that, in so doing, it could be deemed thatcriterion (1) would automatically be satisfied.


2011

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.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.


2011

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 • 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.


2011

5.2 Performance Based Engineering


2011

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).


2011

CHECK SUITABILITY OF THE SITESITE SUITABILITY ANALYSIS (USE MICROZONATION MAP

DISCUSS WITH CLIENT THE

PERFORMANCE LEVEL AND SELECT

THE MINIMUM PERFORMANCE DESIGN

OBJECTIVES

CONDUCT CONCEPTUAL OVERAL

DESIGN, SELECTING CONFIGRATION

STRUCTURAL LAYOUT, STRUCTURAL

• USE PERFORMANCE MATRIX

• SERVICEABILITY UNDER MINOR EARTHQUAKES

• FUNCTIONALITY UNDER MODERATE EARTHQUAKES

• STRUCTURAL STABILITY UNDER EXTREME

EARTHQUAKES

PERFORMANCE BASED ENGINEERING

ACCEPTABILITY

CHECKS OF

CONCEPTUAL

OVERAL DESIGN

STRUCTURAL LAYOUT, STRUCTURAL

SYSTEM, STRUCTURAL MATERIALS

AND NONSTRUCTURAL

COMPONENTS

USE GUIDELINES

USE PEER REVIEW

NO


2011

NUMERICAL PRELIMINARY DESIGNDESIGN TO COMPLY SIMULTANOUSLY WITH

AT LEAST TWO LIMIT STATES

(Ultimate limit states, Serviceability limit states)

ACCEPTABILIT

Y

CHECKS OF

PRELIMINARY

DESIGN

•USE LINEAR AND NONLINEAR

STATIC PUSHOVER

DINAMIC TIME HISTORY

ANALYSIS METHODS

•USE PEER REVIEW

FINAL DESIGN AND DETAILING


-STATIC PUSHOVER AND

-DINAMYC TIME HISTORY ANALYSIS METHODS

•EXPERIMENTAL DATA AND

•INDEPENDENT REVIEW

NO

YES

ACCEPTABILITY

CHECKS OF

FINAL DESIGN

AND DETAILING


-STATIC PUSHOVER AND

-DINAMYC TIME HISTORY ANALYSIS

METHODS

•EXPERIMENTAL DATA AND

•INDEPENDENT REVIEW

MONITORING, MAINTENANCE AND FUNCTION

QUALITY ASSURANCE DURING CONSTRUCTION

YES

NO


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, •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


2011

1989 Earthquake in Loma Prieta, California, Bridge failure.


2011

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


2011

5.3 Performance Requirements and

Compliance Criteria

i) Selection of performance design objectives

SEAOC Vision 2000, 1999SEAOC Vision 2000, 1999

ii) Conforming Eurocode 8

iii) Conforming P100/2006


2011

Seismic performance design matrix (SEAOC

Vision 2000, 1999)


2011

Building Performance Levels and Ranges*

Source: FEMA Instructional Material Complementing FEMA 451


2011

Total costs for different performance design

objectives

Conforming SEAOC Vision 2000, 1999


2011

Quality assurance during construction

• Maintenance (modification and repairs)

• Monitoring of occupancy (function)

• Evaluation of seismic vulnerability of existing buildingsbuildings

• Seismic upgrading of existing hazardous buildings

• Massive education and information dissemination programs


2011

Performance requirements and compliance criteria

Conforming:Conforming:

EUROCODE 8 and P100/2006


2011

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


2011

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 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.


2011

IZMIT Earthquake, 1999 Turkey


2011

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

b. Requirement: Damage limitation

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).


2011

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 theconsequences of failure.

Reliability differentiation is implemented by classifying

structures into different importance categories.


2011

Importance classes for buildings cf EC8


2011

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 formsare 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.


2011

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 non-structure are related to the extent to which its non-linear response is to be exploited.


2011

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• 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.


2011

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, withoutstoreys 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.


2011

Criteria for structural regularity

Building structures for the purpose of seismic design, aredistinguished as regular and non-regular.

This distinction has implications on the following aspectsof the seismic design:

− the structural model, which can be either a simplifiedplanar or a spatial one,

− the method of analysis, which can be either a− the method of analysis, which can be either asimplified response spectrum analysis (lateral forceprocedure) or a multi-modal one,

− the value of the behaviour factor q, which can bedecreased depending on the type of non-regularity inelevation, i.e.: geometric non-regularity (exceeding thelimits ), non-regular distribution of over strength inelevation (exceeding the limits).


2011

With respect to the lateral stiffness and massdistribution, the building structure is approximatelysymmetrical in plan with respect to two orthogonal axes.

The plan configuration is compact, i.e., at each floor isdelimited by a polygonal convex line. If in plan set-backs(re-entrant corners or edge recesses) exist, regularity inplan may still be considered satisfied provided that theseset-backs do not affect the floor in-plan stiffness andset-backs do not affect the floor in-plan stiffness andthat, for each set-back, the area between the outline ofthe floor and a convex polygonal line enveloping the floordoes not exceed 6 % of the floor area.


2011

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. Theorder 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.


2011

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.


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 theeffects resulting from the response of the

superstructure without substantial permanent

deformations.


2011

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 wallsexcitation 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 to basement walls as well.*INPUT GROUND MOTIONS FOR TALL BUILDINGS WITH SUBTERRANEAN LEVELS

Authors: Jonathan P. Stewart and Salih Tileylioglu

Civil & Environmental Engineering Department, UCLA


2011

There are two classical methods for

modeling the problem soil – foundation-

structure.

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 waveexcited by a complex and incoherent wave

field.

This problem is difficult to solve from a

computational standpoint, and hence thedirect approach is rarely used in practice.


2011


2011

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 andKinematic interaction, Foundation - soil flexibility and

damping, Foundation flexibility and damping.


2011

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


2011

a. Rigid foundation

θ g = the foundation rotation

u s = the foundation translation

b. Structure with foundation

flexibility - flexibility and damping)

a. Rigid foundation


2011

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


2011

5.4 The guiding principles governing the conceptual design against seismic

hazard


2011

The guiding principles governing

the conceptual design against seismic

hazard are:

− uniformity, symmetry and redundancy

- structural simplicity- structural simplicity

− bi-directional resistance and stiffness,

− torsional resistance and stiffness,

− diaphragmatic behaviour at storey level,

− adequate foundation


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 intosubdividing the entire building by seismic joints into

dynamically independent units, provided that these

joints are designed against pounding of the individual

units.


2011

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 quasi-

symmetrical, a symmetrical structural layout, well

distributed in-plan, is an obvious solution for thedistributed in-plan, is an obvious solution for theachievement of uniformity.

The use of evenly distributed structural elements

increases redundancy and allows a more favourableredistribution of action effects and widespread energy

dissipation across the entire structure.


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 successfulrealizations aesthetic

• Symmetry is desirable for much the same reasons. It• 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.


2011

• The introduction of deep re-

entrant 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 Y-

shape in plan have often been

severely damaged in

a.

f.

e.

severely damaged inearthquakes.

• External lifts and stairwells

provide similar dangers, and

should be used with the

appropriate attention to analysisand design.

d.

b. c.

g.

h.


2011

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).


2011

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

according to expression.


2011

Building separation to avoid pounding


2011

Length in plan

Structures which are long in plan naturally experiencegreater variation in ground movement and soil conditionsover their length than short ones. These variations may bedue to out- of-phase effects or to differences in geologicalconditions, which are likely to be most pronounced alongconditions, which are likely to be most pronounced alongbridges where depth to bedrock may change from zero tovery large. The effects on structure will differ greatly,depending on whether the foundation structure iscontinuous, or a series of isolated footings, and whetherthe superstructure is continuous or not.


2011

• 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.


2011

Shape in elevation

Very slender structures and

those with sudden changes in

width should be avoided in

strong earthquakes areas.

Height/width ratios in excess

b.a.

L1

1h<

4L

h>

4L

1

L2

Height/width ratios in excess

of about 4 lead to increasingly

uneconomical structures and

require dynamic analysis for

proper evaluation of seismic

responses.

b.a.

h>

4L

1

L1


2011

Sudden changes in width of a structure, such assetbacks in the facades of buildings, generally imply astep in the dynamic response characteristics of thestructure at that height, and modern earthquake codeshave special requirements for them.

If such a shape is required in a structure it is bestdesigned using dynamic earthquake analysis, in orderdesigned using dynamic earthquake analysis, in orderto determine the stress concentrations at the notch andthe shear transfer through the horizontal diaphragmbelow the notch.


2011

Criteria for regularity of buildings with setbacks

(EC8)

a. b.

(setback

occurs below

0,15H)

c. d.


2011

Very slender buildings have high column forces

and foundation stability may be difficult to

achieve.

Also higher mode contributions may addsignificantly to the seismic response of thesuperstructure.

For comparison, in the design of latticed towers

for wind loadings, aspect ratios in excess of

about 6 become uneconomical.


2011

Uniform and continuous distribution of strength and stiffness

This concept is closely related to that of simplicity andsymmetry. The structure will have the

maximum chance of surviving

an earthquake if:

The load bearing members are uniformly distributed.

maximum chance of surviving


2011

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 and beams are nearly the same width;- No principal members change section suddenly;- The structure is as continuous (redundant) and monolithic as possible.

a. b.

Yes No


2011

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 stiffnessmay need to be satisfied. The criteria for the stiffness

of a structure fall into three categories, i.e. the

stiffness is required:


2011

- To create desired vibration characteristics of thestructure (to reduce seismic response, or to suitequipment or function);

- To control deformations (to protect structure, cladding,partitions, services);

- To influence failure modes- To influence failure modes

In qualification of the above recommendations it canbe said that while they are not mandatory they arewell proven, and the less they are followed the morevulnerable and expensive the structure will become.


2011

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


2011

• While it can readily be seen how theserecommendations make structures more easilyanalysed and avoid undesirable stress concentrationsand torsions.

• The restrictions to architectural freedom implied by• The restrictions to architectural freedom implied bythe above sometimes make their acceptance difficult.Perhaps the most contentious is that of uninterruptedvertical structure, especially where cantileveredfacades and columns supporting shear walls arefashionable.


2011

But sudden changes in lateral stiffness up a buildingare not wise:

first because even with the most sophisticated andexpensive computerized analysis the earthquakestresses cannot be determined adequately,

and second, in the present state of knowledge weand second, in the present state of knowledge weprobably could not detail the structure adequatelyand the sensitive spots even if we knew the forcesinvolved.


2011

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, - structure,

- cladding,

- partitions,

- and equipment

This vary widely, depending on the nature of

components and the function of the construction.


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 flexiblemay enormously stiffen an otherwise flexible

structure and hence must be allowed for in thestructural analysis


2011

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) structuresFor 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.


2011

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 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


2011

With regard to the seismic action the design andconstruction of the foundations and of the connection tothe superstructure shall ensure that the whole building isexcited in a uniform way by the seismic motion.

For structures composed of a discrete number ofstructural walls, likely to differ in width and stiffness, a

Adequate foundation

structural walls, likely to differ in width and stiffness, arigid, box-type or cellular foundation, containing afoundation slab and a cover slab should generally bechosen. For buildings with individual foundationelements (footings or piles), the use of a foundation slabor tie-beams between these elements in both maindirections is recommended.


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 isvibration characteristics of a structure whether it is

inherently stiff or flexible above the isolating layer.


2011


� By Doina Verdes

CHAPTER 6

INELASTIC DYNAMIC BEHAVIOR

2


2011

Contents


� 6.2 Global and local ductility condition

� 6.3 Ductility of reinforced concrete elements (local

ductility) ductility)

� 6.4 Requirements for ductility of reinforced concrete

frames

� 6.5 The damages of the reinforced concrete frames

under seismic loads

Doina Verdes


20113

Inelastically behavior

• Most structures for economical resistance againststrong earthquakes must behave inelastically.

• In contrast to the simple linear response model, the

4

• 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.


2011

6.1Introduction

The characteristics of inelastic dynamic behavior:

•Plasticity;

•Strain hardening and

5

•Strain hardening and strain

softening;

•Stiffness degradation;

•Ductility;

•Energy absorption. Force – deformation diagram


2011

The ductility

The ductility of a member or structure may be defined in general

terms by the ratio deformation at failure / deformation at yield:

failureat n deformatio=ρ

FS

Fe Elastoplastic system

6

yieldat n deformatio

failureat n deformatio=ρ

In various uses of this definition, “deformation” may

be measured in terms of :

deflection, ρd, , rotation, ρθ or curvature ρφ.

y

Fy

ye yu yy


2011

Mathematical models for non-linear seismic

behavior

The problems involved in establishing usable mathematical stress-strain models are obvious. It follows that many hysteresismodels have been developed, such as:

• Elastoplastic; Bilinear; Trilinear; Multilinear;

• Ramberg-Osgood; Degrading stiffness; Pinched loops;

7

Degrading stiffnessa. b. Ramberg-Osgood


2011

Hysteretic behaviour

8Doina Verdes BASICS OF SEISMIC ENGINEERING

2011


2011


2011

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 • 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.


2011

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.


2011


2011

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.

14

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.


2011

Type of construction Damping ν

percentage of critical Steel frame, welded, with all walls of flexible construction Steel frame, welded, with normal floors and cladding Steel frame, bolted, with normal floors and cladding Concrete frame, with all walls of flexible construction

2

5

10

5

15

flexible construction Concrete frame, with stiff cladding and all internal walls flexible Concrete frame, with concrete or masonry shear walls Concrete and/or masonry shear wall buildings Timber shear walls construction

5

7

10

10

15


2011

16

Source FEMA [25]


2011

6.2 Global and local ductility conditionIt 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

17

- 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


In multi-story buildings

formation of a soft story plastic mechanism shall be prevented, as such a mechanism may entail excessive local ductility

18

excessive local ductility demands in the columns of the soft story.


2011

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 theideal materials for all elements, as the choice may be dictated bylocal availability or local construction skill, cost constrains, orpolitical decisions.

19

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


2011

The stress-strain diagrams for steel

stress

20

strain


2011

Choosing the material

• To choose between steel and in situ reinforced concrete formedium-rise buildings, is arguably little as long as they are bothwell designed and detailed.

• For tall buildings steelwork is generally preferable, though eachcase must be considered on its merits.

• Timber performs well in low-rise buildings partly because of itshigh strength/weight ratio, but must be detailed with great care.

• Depending on the stage of countries developing it should have

21

• Depending on the stage of countries developing it should havespecial problems in selecting building materials, from the pointsof 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.


2011

• 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.

22

degree of stiffness.• A word of warning should be given here about the effect of non-

structural 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.


2011

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

23

• 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


2011

The effort-deformation relationship for RC elements

24

εc2 - deformation at max effort

εcu2 - ultimate deformation

fcd - Compression resistance


2011

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


2011

What is the influence on the ductility of the reinforcing

ratio from tensioned zone?

G1 G2

L

P P

26

h h

b b

AS1 AS2

AS1 > AS2

Both beams have

the same

Concrete class


2011

The influence of the reinforcing ratio from tensioned zone

M M

M

My1

My2

Mu1; Mu2

2

1

1

1

Φ

Φ

Φ

Φ

Φ=

Φ

Φ=

Φ

Φ=

ρ

ρ

ρ

u

y

u

u

y

27

Φu1 Φu2 Φy2 Φy1

Φ

21

21

2

ΦΦ

Φ

ΦΦ

Φ=

ρρ

ρ

p

f yy

y

The increasing of the reinforcement ratio

of the transversal tensioned reinforcement,

do not lead to increasing of ductility.

ρФ = CURVATURE DUCTILITY

COEFICIENT


2011

The influence of the reinforcing ratio of transversal reinforcement

b b

h h A S 1

A S 1

A S 3 A S 2

M

Mu1

My1

Mu2

Craking of

concrete

covering layer

G1 G2

28

Φ

Φu2 Φu1 Φy1

Φy2

1221

2

22

1

11

ΦΦ

Φ

Φ

⇒Φ=Φ

Φ

Φ=

Φ

Φ=

ρρ

ρ

ρ

fyy

y

u

y

u

Increasing of the reinforcement ratio

of the transversal reinforcement one

Obtains the increasing of the ductility

AS2<AS3


2011

Φ

M

Mu1

My1

Mu2

Craking of concrete

covering layer

b b

h h AS1 AS1

AS3 AS2

The influence of transversal reinforcement ratio

B1

B2

Φ

Φu2 Φu1 Φy1

Φy2

1221

2

22

1

11

ΦΦ

Φ

Φ

⇒Φ=Φ

Φ

Φ=

Φ

Φ=

ρρ

ρ

ρ

fyy

y

u

y

u

5/23/2011 29

d/2 d/2 B2

d d d

B1

Etrieri indesiti

Fisurarea si

expulzarea betonului

din zona comprimata


2011

Collapse of the Parking building during Northridge earthquake,

1994,(some of columns emphasize DUCTILITY)


2011

6.4 Requirements for ductility of

reinforced concrete frames


2011

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

Detailing for local ductility

32

condition should be satisfied

∑∑ ≥ BC MM 3,1


2011

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

33

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 beamsframing into the joint.


2011

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.

34

considered as critical regions.

In primary beams supporting discontinued (cut-

off) vertical elements, the regions up to a distance

of 2hw on each side of the supported vertical

element should be considered as critical.


2011

The conformation of the critical zones

of RC frames

Column

Beam

35

Column Column

Beam

Critical regions


2011

Beams - Detaling for local ductility


2011

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.

37

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


2011

Column

Beam

38

The diameter of the tiers dbw ≥ 6 mm

Medium ductility class (M)High ductility class (H)

P100-2006


2011

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

39

symmetrical cross-sections symmetrical

reinforcement should be provided (ρ = ρ’).


2011

Confinement of concrete core

40

•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.


2011

• 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:

41

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.


2011

The detailles of column cross section reinforcement


2011

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

43

• 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.


2011

The beam – column joint stresses

Exterior column Interior column


2011

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

prismsa.

b.

45

a.b.

The concrete resistance can be calculate :

N≤mRCbh'


2011

The joint design

Corner

46

Corner

d) Roof

Interior

e) Roof

Exterior

f) Roof

Corner


2011

The joint reinforcement design


2011

The reinforcement of the joints


2011

The critical regions are at a

distance from the joint [4]


2011

The reinforcement bars anchorage [4]


2011

The reinforcement bars anchorage [4]


2011

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


2011

The damaged columns


2011

The damaged columns


2011

55

The effect of short columnThe “ductile columns”


2011

The damage of beam-

column joints and the effects

on the buildings


2011

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 Historically, building codes use inelastic response

procedure.

Inelastic response occurs through structural damage

(yielding).


2011


� By Doina Verdes

CHAPTER 7

DESIGN CONCEPTS FOR

EARTHQUAKE RESISTANT EARTHQUAKE RESISTANT REINFORCED CONCRETE

STRUCTURES


2011

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� 7.4 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

Doina Verdes


20113

The design of earthquake resistant concrete

buildings shall provide an adequate energy

dissipation capacity to the structure without

7.1 Energy dissipation capacity and ductility

dissipation capacity to the structure without

substantial reduction of its overall resistance

against horizontal and vertical loading.


2011

Behaviour factors for horizontal seismic action

The behaviour factor q, is introduced to account the

energy dissipation capacity.


2011

7.2 Structural types and behaviour factorsaccordingly P100 and EC8

Concrete buildings may be classified to one of the followingstructural types according to their behaviour under horizontalseismic actions:

a) frame system;

b) dual system (frame- or wall- equivalent);b) dual system (frame- or wall- equivalent);

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 structuralsystem in one horizontal direction and to another in the other.


2011

Frame system

Dual system(frame- or wall-

equivalent)Braced frame

7

moment frame

frames

diafragmes


2011

Ductile wall system

(coupled or uncoupled)

Inverted pendulum system


2011

BearingBearingBearingBearing WallWallWallWall SystemSystemSystemSystem — A structural system withbearing walls providing support, for all or major portionsof the vertical loads. Shear walls or braced framesprovide seismic force resistance.

Structural types

conforming the code SEI-ASCE 7-02

provide seismic force resistance.

BuBuBuBuiiiildingldingldinglding FrameFrameFrameFrame SystemSystemSystemSystem — A structural system with anessentially complete space frame providing support forvertical loads. Seismic force resistance is provided byshear walls or braced frames.


2011

MomentMomentMomentMoment----ResistingResistingResistingResisting FrameFrameFrameFrame SystemSystemSystemSystem — A structural systemwith an essentially complete space frame providingsupport for gravity loads. Moment-resisting frames provideresistance to lateral load primarily by flexural action ofmembers.members.


2011

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 totalat 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.


2011

Bulding Performance Levels and Range [21]


2011

7.3 Design criteria at Ultimate Limit

State (ULS)State (ULS)


2011

The Ultimate Limit State (ULS)

The requirements :

a.Strength

b.Ductility

c. Limitation of interstorey drifts

e. Seismic joints

d. Foundation resistance

14

d. Foundation resistance

a. Strenght

Ed < Rd

Second order effect has to be known


2011

b. Ductility

ρ =δ u /δ y

ρDefinition of ductility

Deformation control


2011

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 increase of the concrete class

- the confinement of concrete from the compressed

zone

- the disposal of ties and transversal reinforcement


2011

� 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 failure of tensioned zones

� The nonstructural mechanism for energy dissipation

The infill walls – masonry panels.


2011

� Design concepts

Low dissipative structural behaviour

Dissipative structural behavior

a. b.


2011

� Dissipative Structural Behavior

Elastically response

Inelastically response

19

q= behaviour factor

Inelastically response

Design code response


2011

The behaviour factor “q” depends on :

Ductility

Redundancy

Overstrenght

Inelastic deformations are constrained to appear in

20

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.


2011

Nr.crt Sistem strctural

DCM DCH P100- 92 (1/Ψ) EC8 P100-1/2006 EC8 P100-1/2006

1.

Cadre

Clădiri cu un nivel 5,00; 6,66

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

4,00; 5,00

3,90

4,725

5,85

6,75

2.

Dual

Structuri cu cadre

preponderente

-

3,90

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

5,85

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

Structuri cu pereţi preponderenţi

Behaviour factors for horizontal seismic action

preponderenţi -

3,60

4,375

5,40

6,25

3.

Pereţi

Structuri cu doi pereţi în fiecare direcţie

3

3

4,00 3

3

4,00

4,00

Structuri cu mai mulţi pereţi

3 3 4,00

3 3 4,00 4,00

Structuri cu pereţi cuplaţi

4,00

3,60

4,375

5,40

6,25

4. Flexibil la torsiune(nucleu)

2 2 3 3

- 2 2 3 3

5. Pendul inversat 1,5 2 3 3 2,86 1,5 2 3 3


2011

Nr.crt

Sistem strctural

DCM DCH P100- 92

(1/Ψ) EC8 P100-

1/2006 EC8 P100-

1/2006

1.

Cadre necontra-vântuite

Structuri parter

4 2,5; 4 2,5;

2,94; 3,46; 5,00; 5,88

4

2,5; 4

5,50

2,50; 5,00; 5,50

Structuri etajate

4

4

5,88 4

4

6,00; 6,50.

6,00; 6,50

2.

Cadre contravântuite

centric

Contravântuiri cu diagonale întinse

4 4 4 4 4,00; 5,00 4 4 4 4

Contravântuiri cu diagonale in V

2 2 2,5 2,5 2,00; 2,50 2 2 2,5 2,5

3.

Cadre contravântuite excentric

4 4 5,00 4 4 6,00 6,00 3. Cadre contravântuite excentric

5,00 4 4 6,00 6,00

4.

Pendul inversat

2 2 1,54; 2,00 2 2 6,00 6,00

5.

Structuri cu nuclee sau pereţi de beton 2 2 3 3 - 2 2 3 3

6.

Cadre duale

Cadre necontrav. asociate cu cadre contravântuite în X şi alternante

4

4

2,00; 2,20; 4,00; 5,00

4 4 4,8 4,8

Cadre necontrav. asociate cu cadre

contravântuite excentric

-

4

-

2,00; 2,20; 4,00; 5,00

-

4

-

6,00


2011

c. Limitation of interstory drifts

F

23

The interstory drift δ


2011

Drift requirements

The structure must have

sufficient stiffness.The

story drift ∆X is the

parameter which can give parameter which can give

the appropriateness of the

general stiffness of the

structure

Story drift computation


2011

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 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 (11)


2011

P-∆ effect

P-∆ effect must be taken into

account. Current analysis are "first-order methods." This means thatduring analysis equilibrium isstated on the undeformedstructure. In a flexible structure thisstructure. In a flexible structure thisleads to error, because there is anadditional lateral deflectionintroduced by the overturningeffect caused by the gravity loadsdisplacing along with the structurewhich is not taken into account by

the first-order analysis procedure.


2011

P-∆ effect

For inelastic systems:Reduced stiffness andincreased displacements

Including P - ∆


2011

•Therefore, the additional overturning effect correspondsto the gravity load, P multiplied by the lateral relativedeflection.

•This is the reason for the name P-∆. This is an analysis

problem caused by the way equilibrium is stated. Theway to deal with it is to find the magnitude of the error by

using a stability coefficient θ.

• If the stability coefficient obtained from Equation atany story and direction is equal or greater than 0.10

all forces and displacements obtained from analysismust be adjusted for this effect.

dsxx

x

ChV

∆P=ϑ


2011

Where:Px is the vertical design load at and abowe level. When computing P no individual load factor need exceed 1.0;

dsxx

x

ChV

∆P=ϑ

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


2011

Structure

Seismic Use Group

I II III

Structures for stories or less with interior walls, partitions, ceilings and exterior wall system that have been

0.025 hsx 0.020 hsx 0.015 hsx

Allowable Story Drift for Reinforced Concrete Structures conf UBC

system that have been designed to accommodate story drifts All other structures 0.020 hsx 0.015 hsx 0.010 hsx


2011

Conforming P100 2006

10,0≤=hV

dP

tot

rtotθ

Where:θ interstorey drift sensitivity coefficient,Ptot total gravity load at and above the storey considered in the seismic design situation,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.


2011

Separation of buildings with different dynamic

characteristics

-allow independent vibrations

-limit the effect of collisions


2011

Prevention of of loss of life due to total

fialure of nonstructural elements

Limitation of interstorey drift at ULS (P100/2006)

33

Displacement analysis

d s = c q d e

Check of interstory drift at ULSd ULS

s = c q d re < d ULSra =0.025h


2011

Analysis methods

Equivalent lateral force analysis

Modal response spectrum analysis

Linear response history analysis

Nonlinear response history analysisNonlinear response history analysis


2011

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 - 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.


2011

- 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


2011

Avoid undesirable mechanism


2011

38

Undesirable mechanism – level story damage [ ]


2011

Behaviour under

seismic excitation

inelastic response

of a RC frame [21]


2011

Behaviour under

seismic excitation

inelastic response

of a RC frame [ 21 ]


2011

Ordinary Concrete Moment frame [ 21]


2011

Intermediate Concrete Moment frame [ 21]


2011

Special Concrete Moment frame [21]


2011

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

d lateral displacement at SLS

44

d s lateral displacement at SLS

d e lateral displacement of the story level under

seismic loads

ν reduction factor (0,4-0,5)


2011

7.6 Structural types with stress

concentration


2011

Stress concentration at the first level

a. b. c.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


2011

Stress concentration

The soft story collapse mechanism


2011

Collapses of buildings with stress concentrations


2011

Infill

The infill masonry placed above a free first story can

develop the collapse mechanism (due to the stress

concentration)

Very stiff

Infill

masonry


2011

8.6 The local effects of infill masonry


2011

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;

Local effects due to masonry or concrete infills

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


2011

• 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 onlyadjacent 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.


2011

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 ofinfill, 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.


2011

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

Masonry panel in interaction with the structure

opposite corners

Tkj

Tjk

Masonry panel


2011

The effect of compressed diagonal

Actions on beam

and column

a. b.


2011

Short column effect


2011

Short column effect

Masonry panel


2011

Short beam effect

Masonry panel

Column

Short beam

Short beam

Beam

Masonry panel

a.

Masonry panel

Short beam

b.Beam


2011

• 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 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.


2011

Conclusions referring to system concept

�Optimal performance one obtains by:

�Providing competent load path

�Providing redundancy

�Avoid configuration irregularities

�Proper consideration of nonstructural elements

60

�Proper consideration of nonstructural elements

�Avoid excessive mass

�Detailing of structural and nonstructural

elements for energy dissipation

�Limiting deformations demands


2011


� By Doina Verdes

CHAPTER 8

NONSTRUCTURAL ELEMENTS


2011

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 � 8.6 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


20113

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 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


2011

Structural and Nonstructural Elements

of a Building

Source: FEMA_Instructional Material Complementing FEMA 451, Design Examples


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 elementsdescribe 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.


2011

18.0%

62.0%

20.0%

70.0%

17.0%

48.0%

44.0%

20%

40%

60%

80%

100%

Contents

Nonstructural

Structural

18.0%

62.0%

20.0%

70.0%

17.0%

48.0%

44.0%

20%

40%

60%

80%

100%

Contents

Nonstructural

Structural

Investments in building constructions

18.0% 13.0% 8.0%0%

20%

Office Hotel Hospital

18.0% 13.0% 8.0%0%

20%

Office Hotel 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


• are typically the visible elements of the building; structuraland building systems elements are generally hidden;

• architectural elements are often designed to supportoccasional or light loading, such as a partition wall towhich a cabinet or shelves are mounted, a ceiling to whicha light fixture is supported, or an exterior cladding panel;

Architectural nonstructural elements

• are not permanent and can be moved or removed fromthe building without affecting the structural safety of thebuilding. behind architectural finishes;

• are usually designed by an architect. However, sometimesarchitectural elements are designed by a specialtyengineer (specializes in designing exterior claddingpanels).


2011

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:

Architectural 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


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;


2011

• 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;• Communications equipment and distribution cabling;

• Some buildings, such as hospitals or other special

occupancy facilities, may include other, more specialized

systems.


2011

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 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.


2011

8.2 Earthquake effects on buildings and nonstructural elements

Building response [ 25 ]


2011

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


The accelerograms recorded to different levels of Sylmar

County Hospital during Northridge earthquake, 1994

The accelerographs

positions in plan and

elevation [4] of the elevation [4] of the

Sylmar County Hospital


2011

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


2011

Interaction of Building and Nonstructural Elements

The motion of nonstructural elements within

a building are influenced by the response of theportion of the building to which they are attached.


2011

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 beof 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.


2011

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 • These elements are referred to as

flexible elements since they will flex

or move differently than the floor to

which they are attached.


2011

• 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.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


2011

Examples of damages to nonstructural

elements

Suspended ceiling damage

Exit canopy damage


Chimney damage

Parapet damage


Sliding and overturning

Nonstructural elements can

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


2011

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 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.


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 .


2011

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 .

Short column effect

Masonry panel

26


2011

Short beam effect

Masonry panel

Column

Short beam

Short beam

Beam

Masonry panel

a.

Masonry panel

Short beam

b.Beam

27


2011

A.Operational performance describes nonstructural

elements that will continue to perform during and after

an earthquake.

B.Immediate Occupancy describes a post-

earthquake state in which nonstructural elements

8.4 The performances of nonstructural elements

earthquake 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.


2011

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•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.


2011

Building Performance and Levels Ranges [ ]

30


2011

8.5 Protection Strategies

Improved Structural Performance

Improved Nonstructural Performance

• Better Engineered Conventional Anchors• Better Engineered Conventional Anchors

• Newer Technologies


2011

Equipment with restraints

Anchor Bolts or Expansion Bolts Resistant straps, Braces,Anchor Bolts or Expansion Bolts Resistant straps, Braces,

Tendons or Plumber’s Tapes

Spring Mounts or Isolators


2011

b.

There are several issues that need tobe considered to mitigate the hazard ofdamage to the raised floor. Diagonalbraces should be installed betweenthe floor slab and the top of thepedestals. Alternately, the pedestalbase plates can be rigidly anchored to

Raised floor

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

d. c.a.

base plates can be rigidly anchored tothe structural floor to allow thepedestal to act as a cantilever to resistlateral forces.


2011

Partitions

a.a. Partition free to slide at top but

restrained laterally

b. Partition doweled at base

b.


2011

Improved Nonstructural PerformanceNewer Technologies

Semi-active device (Rana and Soong, 1998)


2011

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

8.6 Nonstructural design approaches for cladding

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 flooror structural framing above.


2011

Common types of cladding are :

a. Infill masonry

b. Glazing (glass panels)

c. Prefabricated wall panelsc. Prefabricated wall panels

• Concrete

• GFRC (Glass Fiber Reinforced Concrete)

• Steel or Aluminum


2011

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 • Steel Moment Frames with Cladding (window wall or panels)

• Steel Braced Frames with Cladding (window wall or panels)


2011

Concrete Frames

with Infill Masonry Shear Walls


2011

Concrete Frames with Cladding

(window wall or panels)


2011

Steel Moment Frames


2011

Steel Braced Frames


2011

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 • 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.


2011

The assembly panels and R C framed structure: (a) Fully integrated, interacting with the

surrounding elements and (b) fully separated

ß


2011

• 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. 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.


2011

a

b

a. Panel interactingb. Panel separated


2011

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, andmotion 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.


2011

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


2011

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

PossibilitiesPossibilities

• fixed joint

a. Panel fixed at bottom part

b. Panel fixed at upper part

c. Restrains of movements

c.


2011

Connections of precast claddings to the structure

permitting the separation

Beam

PanelPanel

PanelBeam


2011

Laboratory tests on panels equipped

with connections to “separate” the

panel from the structure [15]


2011

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 calculations. panelcalculations.

r0 the horizontal gap

r0v the vertical gap

panel


2011

• 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.


2011

FISIE DE CAUCIUCr

rv.

vt.

DIN ALUMINIUPROFIL

The gap panel - structural element coverings


2011

The seismic design of fully separated precast

cladding

The equivalent static Seismic force conforming

the Code P100/2006 [ ]

cns

CNS

zCNSgCNS

CNS mq

kaF

βγ=


2011

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

dynamic amplification coefficientCNSβ dynamic amplification coefficient

Kz

γ CNS importance factor of the elementq CNS behaviour factor of the element

CNSβ

H

zKZ 21+=


2011

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


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:

dr SLS = ν q dr≤ dr a

Safety limit state (SLS)

dr Fdr 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= 0,008h for separated elements

dr a= 0,025h

q the behavior factor


2011

8.9 Cladding which increase the seismic energy dissipation


2011

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 • 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.


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 moment-resisting steel frames.

• The panel is divided by slits into a group of vertical ductile beam elements connected by horizontal ductile

• 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.

• Reinforced concrete energy dissipaters


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. 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


2011

• 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;

Pure shear mechanismFull bay type


2011

- 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


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.


2011

Exemple of separated claddings implementation

High rise building in

Tokyo, Japan


2011

Concrete cladding

Models tested in the laboratory of Civil Buildings and Foundation

Chair, Civil Engineering Faculty of Cluj-Napoca [16]

Panel A Panel B


2011

Details of panel connection to the structure [ ]


2011

Panel type A cracks pattern


2011

The joint concrete subjected to shear force


2011

The diagrams of panel deformations


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.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.


2011

The claddings fallen

down

8.10. Examples of damages of building claddings


2011

Broken glass panels


2011

Damaged :

•infill masonry,

•frame joint

•glass panels


2011

Damage of partition walls


2011

Damaged :

•infill

masonry(parapets),

•frame columns,

•glass panels.•glass panels.


2011


� By Doina Verdes

CHAPTER 9

Doina Verdes


2011

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

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� 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

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• 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

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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 loopPassive control of the response

• The passive control of the seismic response allows a

structural control with an open loop or non feedback.

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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

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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.

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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

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(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.

9

THE CONTROL OF THE STRUCTURAL RESPONSE

♦ Base isolation

DYNAMIC

CHARACTERISTICS

OF THE BUILDING

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

INCREASING OF THE

ENERGY DISSIPATION

CAPACITY

THE SYSTEMS TO

CONTROL STRUCTURAL

RESPONSE

CONTROL OF THE

STRUCTURAL RESPONSE

10

The energy balance equation

EI = Energy input

E = Elastic energy of the system

The energy – based approach is way to solve the

structural control. The energy balance equation is:

EI = EE +EH = (EES + EK )+ (EHξ + EHµ)

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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

11

• Conventional seismic design is based on preparing thestructures to dissipate energy in specially detailed ductileplastic hinge regions at the end of beam members aswell as at base of the columns.

• Inelastic deformations of the structural componentsshould desirably lead to a ductile beam sideswaymechanism. Such beam and column members also

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mechanism. Such beam and column members alsoserve 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)

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(PLASTIC HINGES)

BUILDING RESPONSE

GROUND

ACCELERATION

13

• Following a strong earthquake damage to these criticalregions, plastic hinge regions is to be expected, incondition of structural collapse prevention - to ensurethe preservation of life – safety maintained.

• There are a number of situations where such structuralbehavior may be either unattainable or undesirable.During an earthquake, a fixed – base shear frame

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behavior may be either unattainable or undesirable.During an earthquake, a fixed – base shear framestructure filters the generally broad – band groundexcitation into narrow – band responses at variouselevations.

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 USE OF PASSIVE ENERGY ACTIVE CONTROL

SYSTEM CONTROL DISSIPATION CONTROL SYSTEM

(DECREASE) OF Ei SYSTEM Ei = EE + ED

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HYBRID HYBRID

ISOLATORS AND PASSIVE ENERGY DISSIPATION RESPONSE CONTROL

DEVICES STRUCTURES

DYNAMIC SMART STRUCTURAL

INTELLIGENT STRUCTURAL ACTIVE

BUILDING SYSTEM HINGES

(STRUCTURAL

ROBOTICS)

15

9.3 Passive Control systems

Passive Control Systems

- Base Isolation Systems

- Mass Effect Systems

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Passive Control Systems - Mass Effect Systems

- Energy Dissipation Systems

16

The base isolation system

• In the base isolation system, increasing the naturalperiod through isolators reduces the accelerationresponse of the structure.

• The seismic isolation devices are usually installedbetween the foundation and the structure or between tworelevant parts of the structure itself, as in the case of the

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relevant parts of the structure itself, as in the case of thesuspension buildings.

• The practical solving of base isolation can be done bymeans of sliding or rolling mechanisms (ball bearing,slide plate bearing, sliding layer) as well as flexibleelements (multi-rubber bearing, double column, flexiblepiles).

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

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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.

18

The energy dissipation systems

• The energy dissipation systems consist of specialdevices that act as hysteretic and/or viscous damper,absorbing the seismic input energy and protecting theprimary framed structure from damage.

• The hysteretic dampers include devices based on

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• The hysteretic dampers include devices based onyielding of metal and friction, while viscous dampersinclude both devices operating by deformation ofviscoelastic solid and fluid materials (viscoelasticdampers) and the ones operating by forcing fluidmaterials to pass through orifices (viscous dampers).

19

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)

9.4 The base isolation system

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(e.g., Immediate Occupancy Performance Level)

• Reducing damaging deformations in structural and

nonstructural components

• Reducing acceleration response to minimize

contents related damage

20

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

The base isolation system with rubber bearings

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structure; the design of the system is to change the

fundamental periods of the buildings from the site ground

period.

21

∆ ab∆

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a. b.

The deformed shape of structure: a. With base

isolation, b. Without isolation

22

The energy that is transmitted to the structure is largely

dissipated by efficient energy dissipation mechanisms

within the isolation system.

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Effect of Seismic Isolation:

Increase Period of Vibration of Structure

to Reduce Base Shear [21]

23

Softer soils tend to produce ground motion at higher periods whichin 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

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Effect of Soil Conditions onIsolated Structure Response

- Structure on Stiff Soil

- Structure with Low

Fundamental Period

(Low-Rise Building)

24

Configuration of a building structure with

Base Isolation system [21]

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25

T=2π/ωω2=k/m

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26

The soil conditions in Romania

The behavior of the ruber bearing to sher force

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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)

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(Low damping natural rubber with lead core)

Sliding Bearings- Flat Sliding Bearing

- Spherical Sliding Bearing

28

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

Buildings in the US having base isolation systems

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- 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)

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

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- Steel-framed superstructure


- 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)

30

The dynamic model of the building equipped with rubber bearings

msus

kb = the base stiffness,

cb = the base damping

ks = the structure stiffness,

cs = the structure damping

ms= the structure mass

mb= the base massT=2π/ω

ω2=k/m

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2011

m b ub

ug

ks , cs

kb , cb

31

a. The equation for fixed base

b. The equation for isolated base

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32

Case (a)

Case (b)

Making the notations:

one obtains:

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Solving the equations one obtains the seismic response:

-the acceleration

-the velocity

-the desplacement

33

Reazem din cauciuc cu tole de oţel

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Details of elastomeric bearings

34

The Seismic Isolation With Penduls [9]

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Exemple of Pasiv Isolation System with Penduls

and Friction Absorbers

35

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36

Seismic response, time history, of a four levels

building under El Centro accelerogram

with and without seismic isolation system with

pendulum.

With seismic isolation system

a g

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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

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• 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.

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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

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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

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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

Frames with concentric diagonal bracings (dissipative

zones in tension diagonals only)

Steel frames with dissipatives zones conforming EC 8

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Frames with concentric V bracings (dissipative

zones in tension and compression diagonals)

Frames with eccentric bracings (dissipative

zones in bending or shear links)

42

Typical dissipative chevron bracing systems

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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

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2011

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

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;

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Pure shear mechanismFull bay type

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

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Partially bay type

Bracing type and Pillar type

46

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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

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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

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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

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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 beendesigned with supplemental energy dissipation devicesEDD to absorb some of the vibration energy caused byearthquakes. By adding EDD to the structural system,the structural dynamic properties are modified, theseismic response is controlled, and the energydissipation demand on the structural members is

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dissipation demand on the structural members isreduced.

• Supplemental EDDs have become a popular strategy fordesigning 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 usedeffectively in a number of tall buildings in Japan. Itconsists of a precast panel designed to fit betweenadjacent pairs of columns and beams of moment-resisting steel frames. The panel is divided by slits intoa group of vertical ductile beam elements connectedby horizontal ductile beams at the top and at the

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a group of vertical ductile beam elements connectedby horizontal ductile beams at the top and at thebottom, thus suppressing shear failure modes andcreating a stiff energy-dissipating device. It isconnected to the beams of the steel frame andeffectively stiffness the building against wind load whileproviding high energy dissipation in largerearthquakes.

52

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53

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Panel with vertical discontinue slits

Panel with vertical continue slits

54

The panel behavior after the cracking along the

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The panel behavior after the cracking along the

vertical slits

The stiffness of the teeth form vertical edge

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

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gives large deformations due mainly the post-elastic

behavior.

56

Energy dissipaters in diagonal bracing

• Diagonal bracings incorporating energy dissipatersprovide a structurally comparable alternative to the Mutoslitted wall panel in that they control the horizontaldeflections of the frame and also the locations of thedamage, thus protecting both the main structure and thenon-structural elements. A practical example is a six-storey government office building constructed in

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storey government office building constructed inWanganui, New Zealand, in 1980 This building obtainsits lateral load resistance from diagonally braced precastconcrete cladding panels thus minimizing the amount ofinternal structure to suit architectural planning.

• The rehabilitation of Quebec Police Headquarters,Montreal [1] was achieved by incorporating frictiondampers in the existing and new bracing.

57

Pictures of Buildings in seismic areas

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58

Tokyo , Japan

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59

Tokyo , Japan

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60

Transamerica building, San Francisco, California

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61

Transamerica building, San Francisco, California

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62

Imperial palace, Japan

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63


� By Doina Verdes

CHAPTER 9


2

Contents





� 9.5 The energy dissipation systems� 9.5 The energy dissipation systems



3

9.6 Advanced Technology Systems

4Doina Verdes


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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)(e.g.,Immediate Occupancy Performance Level)

Reducing damaging deformations in structural and

nonstructural components.

Reducing acceleration response to minimize

contents related damage

5

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Distinction Between Natural

and Added Damping

Natural (Inherent) Damping

6Doina Verdes


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Added Damping

7Doina Verdes


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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 energygiven amount of input energy, the hysteretic energy

dissipation demand can be reduced if a supplemental

(or added) damping system is utilized.

8Doina Verdes


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Energy Balance:

HDADIKSI EEEEEE ++++= )(

Added DampingInherent Damping

Hysteretic Energy

Reduction in Seismic Damage

Damage Index:

( ) ( )

ulty

H

ult

max

uF

tE

u

utDI ρ+=

Source: Park and Ang (1985)

DI

1.0

Damage

State

0.0Collapse

9

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Damage index “DI”

A damage index “DI”, can be used to characterize the time-dependent damage to a structure. For the definition given, the time-dependence is in accordance with the time-dependence of the hysteretic energy dissipation.

The calibration factor ρ accounts for the type of structural 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

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100

120

140

160

180

200A

bs

orb

ed

En

erg

y, in

ch

-kip

s

DAMPING

KINETIC +

STRAIN

10% DampingE

ne

rgy (

kip

-in

ch)

Energy response histories for a SDOF

elasto-plastic system subjected to seismic loading

10% damping

0

20

40

60

80

100

0 4 8 12 16 20 24 28 32 36 40 44 48

Time, Seconds

Ab

so

rbe

d E

ne

rgy

, in

ch

-kip

s

HYSTERETIC

Damping reduces the hysteretic energy dissipation demand

En

erg

y (

kip

11Doina Verdes


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80

100

120

140

160

180

200

Ab

so

rbe

d E

ne

rgy

, In

ch

-Kip

s

DAMPING

KINETIC +

STRAIN

En

erg

y (

kip

-in

ch)

20% Damping

Energy response histories for a SDOF

elasto-plastic system subjected to seismic loading

0

20

40

60

0 4 8 12 16 20 24 28 32 36 40 44 48

Time, Seconds

Ab

so

rbe

d E

ne

rgy

, In

ch

-Kip

s

HYSTERETIC

En

erg

y (

kip

An increase in added damping reduces the hysteretic energydissipation demand by about 57%. Damping reduces thehysteretic energy dissipation demand

12Doina Verdes


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Velocity-Dependent Systems• Viscous fluid or viscoelastic solid dampers

• May or may not add stiffness to structure

Displacement-Dependent Systems

Classification of Passive Energy Dissipation Systems

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)

13Doina Verdes


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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).

14Doina Verdes


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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 rate-

independent. More accurately, the force output of independent. More accurately, the force output of

displacement-dependent dampers generally depends on

both the displacement and the sign of the velocity.

15Doina Verdes


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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 • Displacement-Dependent Damping Systems: Steel Plate Dampers, Unbonded Brace Dampers, and Friction Dampers

• Modeling Considerations for Structures with Passive Damping Systems

16

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Cross-Section of Viscous Fluid Damper

Source: Taylor Devices, Inc.

17Doina Verdes


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Possible Damper Placement Within Structure

18Doina Verdes


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San Francisco State Office

Building

San Francisco, CA

Fluid Damper within Diagonal Brace*

Huntington Tower

Boston, MA

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19

*Source: FEMA Instructional Material


Harmonic behaviour of fluid damper

Source: FEMA Instructional Material


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

21

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Disadvantages of Fluid Dampers

Somewhat higher cost

Not force limited (particularly when exponent = 1.0)

Necessity for nonlinear analysis in most practical 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

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Vicoelastic dampers*

A -A

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23



High reliability

May be able to use linear analysis

Somewhat lower cost

Advantages of Viscoelastic Dampers

Somewhat lower cost

24

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Strong Temperature Dependence

Lower Force and Displacement Capacity

Not Force Limited

Necessity for nonlinear analysis in most

Disadvantages of Viscoelastic Dampers

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

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Steel Plate Dampers*

(Added Damping and Stiffness System - ADAS)

Doina Verdes


201126



Wells Fargo Bank,

San Francisco, CA

- Seismic Retrofit of Two-

Story Nonductile Concrete

Frame; Constructed in 1967

Implementation of ADAS System*

Frame; Constructed in 1967

- 7 Dampers Within Chevron

Bracing Installed in 1992

- Yield Force Per Damper:

150 kips

Doina Verdes


2011 27



Hysteretic Behavior of ADAS Device

ADAS Device(Tsai et al. 1993)

Experimental Response (Static)(Source: Tsai et al. 1993)

28

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Force-Limited

Easy to construct

Relatively Inexpensive

Advantages of ADAS System

and Unbonded Brace Damper


Adds both “Damping” and Stiffness

29Doina Verdes


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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

30Doina Verdes


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Friction Dampers: Slotted-Bolted Damper*

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31



Sumitomo Friction Damper(Sumitomo Metal Industries, Japan)

32Doina Verdes


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Cross-Bracing Friction Damper*

Interior of Webster

Library at Concordia

University, Montreal,

Canada

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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 tosubject 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.

34Doina Verdes


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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- RC Frames with Flat Slabs

- 143 Cross-Bracing Friction

Dampers Installed in 1987

- 60 Dampers Exposed for

Aesthetics

Doina Verdes


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35

Source: FEMA Instructional Material


Hysteretic Behavior of Slotted-Bolted

Friction Damper

36Doina Verdes


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Ideal hysteretic behavior

of cross-bracing friction damper

37Doina Verdes


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Force-Limited

Easy to construct

Advantages of Friction Dampers


38Doina Verdes


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Disadvantages of Friction Dampers

May be Difficult to Maintain over Time

Highly Nonlinear Behavior

Adds Large Initial Stiffness to SystemAdds Large Initial Stiffness to System

Undesirable Residual Deformations Possible

39Doina Verdes


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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)

40Doina Verdes


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� By Doina Verdes

CHAPTER 9

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2

Contents





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� 9.5 The energy dissipation systems



3

9.7 Active structural control systems

4


2011

5


2011

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


2011

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:

mVytv

tymVytkytyctym g

/)(

)()()()(

=

−=+++ &&&&& (1)

(2)

To see the effect of applying an active control force to

the linear structure, equation (1) in this case becomes

)()()()( tymVytkytyctym g&&&&& −=+++

The object of a response-control structure is to reduce

these factors by controlling or adjusting m, c, k, V.

(3)

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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 withfunction 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.

8


2011

• 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 mitigationground 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;

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2011

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• 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


2011

Active structural control research

1989 US Panel on Structural Control Research (US-NSF)1990 Japan Panel on Structural Response Control (Japan-SCJ)1991 Five-Year Research Initiative on Structural Control (US-NSF)1993 European Association for Control of Structures1994 International Association for Structural Control1994 First World Conference on Structural Control (Pasadena, California, USA)1996 First European Conference on Structural Control (Barcelona, Spain)1998 China Panel for Structural Control1998 China Panel for Structural Control1998 Korean Panel for Structural Control1998 Second World Conference on Structural Control (Kyoto, Japan)2000 Second European Conference on Structural Control (Paris, France)2002 Third World Conference on Structural Control (Como, Italy)2004 Third European Conference on Structural Control (Vienna, Austria)2006 Fourth World Conference on Structural Control (San Diego, California,USA)

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The performance-based design by the use of

energy concepts and the energy balance equationCONTROL OF STRUCTURAL RESPONSE THROUGH THE USE OF

INNOVATIVE CONTROL OR PROTECTIVE SYSTEMS

USE OF SEISMIC ISOLATION USE OF PASSIVE ENERGY ACTIVE CONTROL

SYSTEM CONTROL DISSIPATION CONTROL SYSTEM

(DECREASE) OF Ei SYSTEM Ei = EE + ED

HYBRID HYBRID

ISOLATORS AND PASSIVE ENERGY DISSIPATION RESPONSE CONTROL

DEVICES STRUCTURES

DYNAMIC SMART STRUCTURAL

INTELLIGENT STRUCTURAL ACTIVE

BUILDING SYSTEM HINGES

(STRUCTURAL

ROBOTICS)

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2011

• Hybrid systems are a combination of active and passivesystems, supplying energy to enhance the dampingeffect of the passive system.

• The active systems provide various countermeasuresby using the external disturbance signals generated bysensors installed either inside or outside the building.

• Active systems require energy to directly resist theexternal disturbances, semi-active systems requireenergy to indirectly resist external disturbances byenergy to indirectly resist external disturbances bychanging the dynamic characteristics of the buildingstructure, and passive systems do not require anyenergy input. Active systems use both feed forwardcontrol, in which sensors outside the building detectdisturbance before it reaches the building, or feedbackcontrol, in which sensors in the building detect thebuilding's response [ ].

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2011

STRUCTURE

WITH PED

EXCITATION RESPONSE

Structure with Hybrid Control

SENSORS COMPUTER

CONTROLER

SENSORS

CONTROL

ACTUATORS

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2011

Hybrid Mass Damper Systems (HMD)

The hybrid mass damper (HMD) is the most common control deviceemployed in full-scale civil engineering applications. An HMD is acombination of a passive tuned mass damper (TMD) and an activecontrol actuator. The ability of this device to reduce structural responsesrelies mainly on the natural motion of the TMD. The forces from thecontrol actuator are employed to increase efficiency of the HMD and toincrease its robustness to changes in the dynamic characteristics of thestructure

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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 iceactuators 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).

16


2011

Sendagaya INTES building with hybrid mass dampers

(Higashino and Aizawa, 1993)

17


2011

Top view of hybrid mass damper configuration

(Higashino and Aizawa, 1993)

18


2011

Response time histories (Higashino and Aizawa, 1993)

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2011

Structural Control, closed-loop (feedback)

In 1972, prof. James T.P. Yao, in his paper entitled“Concept of Structural Control” (Yao, 1972), marks thebeginning of this new field in Structural Analysis. Theauthor states that it seems the limit in structure size hasauthor states that it seems the limit in structure size hasbeen reached. In order to extend these limits withoutloss of safety, he proposes the concept of StructuralControl, especially closed-loop (feedback) controlsystems.

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2011

BASICS OF ACTIVE CONTROL CONFIGURATION

SEISMIC ACTION

STRUCTURE Structural Response

Control Forces

Actuators Sensors Sensors

Electrical power

Actuators

Control forces calculation

Structure with Active Control

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The Dynamic Intelligent Building

Dynamic intelligent building is an important concept of activesystem, which tries to unify the perspective of lifeline systemsbelonging to an urban community. The information network isthe infrastructure of very crowded metropolis, which shouldinclude buildings with dynamic behavior. The data from thesurroundings or from long distance sent trough cables, radioand via satellite should be processed by the general and localand via satellite should be processed by the general and localcomputers and this way the structures will be better preparedto respond to strong earthquakes.The control mechanism is infact an active bracing system or an active mass damperincorporated into the structure.

Optimal active control is a time domain strategy, which allowsminimizing the energy induced in structure. The equation ofmotion for an n degree of freedom controlled system underseismic action is:

22


2011

)()()()()( tutftzKtzCtMz +=++ &

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 actionsf(t) = n-dimensional vector of external actions; f(t) is proportional to the seismic ground acceleration:

)()()()()( 11 tutftzKtzCtMz +=++ &

where: h1 = n-dimensional vector showing the points of applicationand the values of inertiaThe object of a response-control structure is to reduce thesefactors by controlling or adjusting m, c, k, f, or p.

)()( 1 thtf gχ&&=

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2011

The available structural response-control methods

According to these basic principles of dynamics, theavailable structural response-control methods can beclassified 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• Methods based on the control and adjustment of c, suchas variable damping mechanisms and building-to-building connection mechanisms.

• Methods based on control and adjustment of k, such asvariable-stiffness and flexible-base mechanisms.

• Methods based on the control and adjustment of p, suchas using reaction walls, jet or injection devices.

24


2011

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


2011

Principle of the DUOX system

(Nishimura et al., 1993)

26


2011

BUILDING

AMD Atachet mass damper

TMD Tuned mass damper

27


2011

The simplified principle: active & passive control

The Kyobashi Seiwa Building in Tokyo

28


2011

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 aprimary 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.

29


2011

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 whencritical 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


2011

• 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 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


2011

SAVS system configuration (Kurata et al., 1999)

32


2011

Variations of such an HMD configuration include multi-

stage 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.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


2011

Yokohama Landmark Tower and HMD

(Yamazaki et al., 1992)

34


2011

Yokohama Landmark Tower and Shinjuku Park Tower

35


2011

Kajima Shizuoka Building and semi-active

hydraulic dampers (Kurata et al., 1999)

36


2011

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 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.

37


2011

38

Schematic of a controllable fluid damper


2011

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

39


2011

The scheme of active control of seismic response

Desplacements

Traductor

CONTROLSERVO-VALVE

Actuator

Active Tendon

System

COMPUTER PC

..gy

DIFERENTIALANALOG

CONDITIONING

40


2011

High rise building in Japan

41


2011

1


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

2

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 Performance-

based 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

3

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

23.05.2011

1

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.

23.05.2011

2

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

3. Structural Model and Testing • 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 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.

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.

23.05.2011

3

4. Additional Requirements • 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.

Instrumentation and Data Processing

Horizontal acceleration table will be measured in the direction of

shaking using accelerometers mounted on the roof of the

structure and on the shake

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.

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

23.05.2011

4

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.

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.

SEISMIC DESIGN COMPETITION 2011

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.

10th -12th of February 2011 SAN-DIEGO

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TECHNICAL UNIVERSITY OF CLUJ-NAPOCA, ROMANIA

THE CITY UNIVERSITY

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The Team


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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


�Structural simplicity, uniformity,

symmetry and redundancy;

Project design criteria


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�Bi-directional resistance and

stiffness;

�Diaphragmatic behaviour at

storey level;

�Adequate foundation.


Our project – Valahia Tower


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Floor Plan view

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Cross section of the tower


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Details of the cross section


Moment Frame Connection Detail


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� The friction

dampers based on

metallic plates



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Why Friction Dampers?

Force-Limited

Easy to construct


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Cutting of the wood plates


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Chopping the columns accidentally


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Manufacturing and mounting the dampers


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Two models were build

- first one -> to see how dampers work in the structure


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Images of the first model: construction and testing



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The final model


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


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Max acc =2.02m/s^2

= 6.62ft/s^2

Max displacement =5.57cm

= 2.19in

Max velocity =3.36m/s

=11.02ft/s

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

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

Max acc =2.02m/s^2

= 4.36ft/s^2

Max displacement =3.74cm

= 1.47in Max velocity =3.36m/s

= 7.87ft/s


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


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The model before the test on shake table at

Seismic Design Contest


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The accelerograms

Artificial accelerogram UCDavis

Accelerogram Northridge, 1994

Accelerogram El Centro, 18 Mai 1940

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9. Conclusions after the test

The model was subjected to three accelerograms- behavior of model was very good at all threeaccelerograms ;- the model bars were not damaged ;- the friction dampers have worked very wellallowing the deformation of the structural elementsand dissipating energy.

The collapse of the model arrived after the testwith sinus wave having the frequency equalfundamental frequency of the model.



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10. The award ceremony

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The 8th Seismic Design Competition, 2011

winner teams


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The top three teams:

Oregon State University

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 prize plaque Egor Popov Award for Structural Innovation

for the model “Valahia tower” made by the team from

Technical University of Cluj-Napoca, Romania



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The annoncement of Karthik Ramanathan vice president of SLC, of the award Egor Popov



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Romanian delegation together with Nima Tafazolli, co president of SLC



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Romanian delegation together with colleagues from American universities



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Romanian delegation together with colleagues from University of Technologi , Malaysia


11. Models Presented by the

Participants Universities


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Oregon State University



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University of Illinois Urbana Champaign

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UC Davis



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California State University, Los Angeles



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Purdue University

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Roger Williams University



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Roger Williams University



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Brigham Young University



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UC Irvine

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University of Massachusetts Amherst



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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!

Documents

Basics of Seismic Engineering