basics of seismic engineering
TRANSCRIPT
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
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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
BASICS OF SEISMIC ENGINEERING
� 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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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.
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Fig. 1.18 View of an old tile fresco
placed on a house wall from
Sintra, Portugal, mentioning the
1731 earthquake.
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1626 July 30
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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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;
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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
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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.
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BASICS OF SEISMIC ENGINEERING
� By Doina Verdes
CHAPTER 2
THE ANALYSIS OF SEISMIC RESPONSE OF SINGLE DEGREE OF
Doina Verdes
BASICS OF SEISMICAL ENGINEERING
2011
2
RESPONSE OF SINGLE DEGREE OF FREEDOM SYSTEM
Doina Verdes
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2011
2.1 Modeling the buildings
2.2 The degrees of freedom
2.3 The Response Spectrum Analysis
2.4 The relative displacement response
2.5 The response spectrum and the pseudospectrum
2.6 Response to seismic loading:
Contents
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3
2.6 Response to seismic loading:
step-by-step methods
2.7 The Newmark Beta Methods
2.8. The seismic response of the SDOF nonlinear system
using the step by step numerical integration
2.9 The energy balance procedure
2.10 Seismic response spectra of the SDOF inelastic
systems
2.1 Modeling the buildings
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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
2.3 The Response Spectrum Analysis
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)
2.4 The relative displacement response
The relative displacement response of the frame to a single component
of ground acceleration yg(t) may be expressed in the time domain by means of the Duhamel integral
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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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2011
- 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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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.
BASICS OF SEISMIC ENGINEERING
� By Doina Verdes
CHAPTER 2
THE ANALYSIS OF SEISMIC RESPONSE OF SINGLE DEGREE OF
Doina Verdes
BASICS OF SEISMICAL ENGINEERING
2011
2
RESPONSE OF SINGLE DEGREE OF FREEDOM SYSTEM
Doina Verdes
BASICS OF SEISMICAL ENGINEERING
2011
Contents
2.1 Modeling the buildings
2.2 The degrees of freedom
2.3 The Response Spectrum Analysis
2.4 The relative displacement response
2.5 The response spectrum and the pseudospectrum
2.6 Response to seismic loading: step-by-step methods 2.6 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
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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.
Doina Verdes
Basics of Seismic Engineering
2011
11
The constant variation of acceleration during the incremental h time
Doina Verdes
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2011
12
The variation of acceleration during the
incremental h time interval
c. β= 1/6 e. β= 1/8
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Basics of Seismic Engineering
2011
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
Doina Verdes
Basics of Seismic Engineering
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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
Doina Verdes
Basics of Seismic Engineering
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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)
Doina Verdes
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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)
Doina Verdes
Basics of Seismic Engineering
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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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Basics of Seismic Engineering
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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)
Doina Verdes
Basics of Seismic Engineering
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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&
Doina Verdes
Basics of Seismic Engineering
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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
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2.8 The seismic response of the SDOF nonlinear system using the step by step numerical integration
We have to know:
• - the behavior of the material done by the diagram (the model can be elastic-linear or nonlinear)
• - the digitalised accelerogram
The equation of equilibrium at the time step t1
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
Doina Verdes
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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
Doina Verdes
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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
Doina Verdes
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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)
Doina Verdes
Basics of Seismic Engineering
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2.9 The energy balance procedure
• Is based on the comparison of two energies which are found on the structure during the earthquake:
• The input energy into structure by the earthquake
• The energy dissipated or stored by the structure
The equation of energy balance is useful if it can be computed in each step of integration
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
Doina Verdes
Basics of Seismic Engineering
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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.
Doina Verdes
Basics of Seismic Engineering
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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
Doina Verdes
Basics of Seismic Engineering
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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
Doina Verdes
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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
Doina Verdes
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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.
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Basics of Seismic Engineering
2011
BASICS OF SEISMIC ENGINEERING
� 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
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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)
Doina Verdes
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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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The inertia forces in equation (1) are:
aaI umFa
&&⋅=
umF ⋅=
[4]
77
bbI umFb
&&⋅=
ccI umFc
&&⋅=
[5]
[6]
Doina Verdes
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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&&
Doina Verdes
Basics of Seismic Engineering
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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.
Doina Verdes
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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]
Doina Verdes
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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
Basics of Seismic Engineering
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&
Doina Verdes
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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
Basics of Seismic Engineering
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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• 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
Doina Verdes
Basics of Seismic Engineering
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.
Doina Verdes
Basics of Seismic Engineering
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:
Doina Verdes
Basics of Seismic Engineering
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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
Doina Verdes
Basics of Seismic Engineering
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]
Doina Verdes
Basics of Seismic Engineering
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.
Doina Verdes
Basics of Seismic Engineering
2011
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=
Doina Verdes
Basics of Seismic Engineering
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.
Doina Verdes
Basics of Seismic Engineering
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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
Basics of Seismic Engineering
2011
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
Basics of Seismic Engineering
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
Doina Verdes
Basics of Seismic Engineering
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]
Doina Verdes
Basics of Seismic Engineering
2011
Exemple of a three stories frame
Response Spectrum Analysis [21]
27Doina Verdes
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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
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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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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 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
Basics of Seismic Engineering
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:
Doina Verdes
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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
Basics of Seismic Engineering
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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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Basics of Seismic Engineering
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.
Doina Verdes
Basics of Seismic Engineering
2011
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
Basics of Seismic Engineering
2011
BASICS OF SEISMIC ENGINEERING
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
Basics of Seismic Engineering
2011
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.
Doina Verdes BASICS OF SEISMIC ENGINEERING
2011
• a) the “lateral force method of analysis” for common
buildings
• b) the “modal response spectrum analysis", which is
applicable to all types of buildings.
As alternative to a linear method, a non-linear methods 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
Doina Verdes BASICS OF SEISMIC ENGINEERING
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
Doina Verdes BASICS OF SEISMIC ENGINEERING
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
Doina Verdes BASICS OF SEISMIC ENGINEERING
2011
The zonation of Romanian territory depending on soil design acceration ag for seismic events with average return period (of magnitude) IMR = 100 years
Doina Verdes BASICS OF SEISMIC ENGINEERING
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.
Doina Verdes BASICS OF SEISMIC ENGINEERING
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.
Doina Verdes BASICS OF SEISMIC ENGINEERING
2011
Linear elastic behavior
FS(t)FA(t)
y(t)
1
ck
1
)(ty&
Nonlinear elastic behaviorStiffness
Damping
Doina Verdes BASICS OF SEISMIC ENGINEERING
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.
Doina Verdes BASICS OF SEISMIC ENGINEERING
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)
Doina Verdes BASICS OF SEISMIC ENGINEERING
2011
Determination of the fundamental vibration periods
T1
• For the determination of the fundamental vibration periods T1 of both planar models of the building, expressions based on methods of structural dynamics (e.g. by Rayleigh method) may be used for buildings with heights up to 40 m the value of T1 may be approximated by the following expression:
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)
Doina Verdes BASICS OF SEISMIC ENGINEERING
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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)
Doina Verdes BASICS OF SEISMIC ENGINEERING
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)
Doina Verdes BASICS OF SEISMIC ENGINEERING
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;
Doina Verdes BASICS OF SEISMIC ENGINEERING
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
Doina Verdes BASICS OF SEISMIC ENGINEERING
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.
Doina Verdes BASICS OF SEISMIC ENGINEERING
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
BASICS OF SEISMIC ENGINEERING 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
24Doina Verdes
BASICS OF SEISMIC ENGINEERING 2011
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.
Doina Verdes BASICS OF SEISMIC ENGINEERING
2011
The deformed shape for the 1st mode
sn
s
snFn
s1
si
zn
zi
z1
s1
siFi
F1
a. b.
Doina Verdes BASICS OF SEISMIC ENGINEERING
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
Doina Verdes BASICS OF SEISMIC ENGINEERING
2011
• When the fundamental mode shape is approximated
by horizontal displacements increasing linearly along
the height, the horizontal forces Fi are given by:
∑=
⋅
⋅⋅=
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.
Doina Verdes BASICS OF SEISMIC ENGINEERING
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)
Doina Verdes BASICS OF SEISMIC ENGINEERING
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
Doina Verdes BASICS OF SEISMIC ENGINEERING
2011
Reason for Consideration of Accidental Torsion [22]
Fk,n
Fk,n – the seismic level force at k level , in “n” th mode of vibration
Doina Verdes BASICS OF SEISMIC ENGINEERING
2011
The case of “natural” eccentricity
Mtx=Tbx e ix
Mty=Tby e iy
(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
Doina Verdes BASICS OF SEISMIC ENGINEERING
2011
The distribution of seismic force
to structural vertical elements
(4.16)
(4.17)
Doina Verdes BASICS OF SEISMIC ENGINEERING
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.
Doina Verdes BASICS OF SEISMIC ENGINEERING
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)
Doina Verdes BASICS OF SEISMIC ENGINEERING
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
BASICS OF SEISMIC ENGINEERING 2011
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)
Doina Verdes BASICS OF SEISMIC ENGINEERING
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.
Doina Verdes BASICS OF SEISMIC ENGINEERING
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.
Doina Verdes BASICS OF SEISMIC ENGINEERING
2011
The behaviour factor q• The behaviour factor q is an
approximation of the ratio of the seismic forces, that the structure would experience if its response was completely elastic with 5%viscous damping, to the minimum 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.
Doina Verdes BASICS OF SEISMIC ENGINEERING
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.
Doina Verdes BASICS OF SEISMIC ENGINEERING
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
Doina Verdes BASICS OF SEISMIC ENGINEERING
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:
Doina Verdes BASICS OF SEISMIC ENGINEERING
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.
Doina Verdes BASICS OF SEISMIC ENGINEERING
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)
Doina Verdes BASICS OF SEISMIC ENGINEERING
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)
Doina Verdes BASICS OF SEISMIC ENGINEERING
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
Doina Verdes BASICS OF SEISMIC ENGINEERING
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.
Doina Verdes BASICS OF SEISMIC ENGINEERING
2011
Seismic zones
• For the purpose of EN 1998, national territories shall be subdivided by the
• National Authorities into seismic zones, depending on the local hazard. By definition,
• the hazard within each zone is assumed to be constant.• 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.
Doina Verdes BASICS OF SEISMIC ENGINEERING
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.
Doina Verdes BASICS OF SEISMIC ENGINEERING
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.
Doina Verdes BASICS OF SEISMIC ENGINEERING
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.
Doina Verdes BASICS OF SEISMIC ENGINEERING
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;
Doina Verdes BASICS OF SEISMIC ENGINEERING
2011
• Buildings not complying with the regularity criteria shall be analysed using a spatial model.
• For buildings complying with the regularity the analysis may be performed using two planar models, one for each main horizontal direction.
• For low-rise masonry buildings, in which structural • For low-rise masonry buildings, in which structural walls are dominated by shear, each storey may be analysed independently.
Doina Verdes BASICS OF SEISMIC ENGINEERING
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.
Doina Verdes BASICS OF SEISMIC ENGINEERING
2011
Plastic mechanism
Determination of the idealized elasto - perfectly plastic force –
displacement relationship.
Doina Verdes BASICS OF SEISMIC ENGINEERING
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.
Doina Verdes BASICS OF SEISMIC ENGINEERING
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.
Doina Verdes BASICS OF SEISMIC ENGINEERING
2011
BASICS OF SEISMIC ENGINEERING
� By Doina Verdes
CHAPTER 5
EARTHQUAKE RESISTANT EARTHQUAKE RESISTANT DESIGN
Doina Verdes BASICS OF SEISMIC ENGINEERING
2011
Contents
� 5.1 Introduction
� 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
Basics of Seismic Engineering
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.
Doina Verdes BASICS OF SEISMIC ENGINEERING
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
Doina Verdes BASICS OF SEISMIC ENGINEERING
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.
Doina Verdes BASICS OF SEISMIC ENGINEERING
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.
Doina Verdes BASICS OF SEISMIC ENGINEERING
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.
Doina Verdes BASICS OF SEISMIC ENGINEERING
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.
Doina Verdes BASICS OF SEISMIC ENGINEERING
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.
Doina Verdes BASICS OF SEISMIC ENGINEERING
2011
5.2 Performance Based Engineering
Doina Verdes BASICS OF SEISMIC ENGINEERING
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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).
Doina Verdes BASICS OF SEISMIC ENGINEERING
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
Doina Verdes BASICS OF SEISMIC ENGINEERING
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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
•USE LINEAR AND NONLINEAR
-STATIC PUSHOVER AND
-DINAMYC TIME HISTORY ANALYSIS METHODS
•EXPERIMENTAL DATA AND
•INDEPENDENT REVIEW
NO
YES
ACCEPTABILITY
CHECKS OF
FINAL DESIGN
AND DETAILING
•USE LINEAR AND NONLINEAR
-STATIC PUSHOVER AND
-DINAMYC TIME HISTORY ANALYSIS
METHODS
•EXPERIMENTAL DATA AND
•INDEPENDENT REVIEW
MONITORING, MAINTENANCE AND FUNCTION
QUALITY ASSURANCE DURING CONSTRUCTION
YES
NO
Doina Verdes BASICS OF SEISMIC ENGINEERING
2011
Site suitability analysis of the selected site(Ground conditions)
The construction site and the
nature of the supporting ground
should normally be free from
risks of:
•ground rupture, •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
Doina Verdes BASICS OF SEISMIC ENGINEERING
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1989 Earthquake in Loma Prieta, California, Bridge failure.
Doina Verdes BASICS OF SEISMIC ENGINEERING
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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
Doina Verdes BASICS OF SEISMIC ENGINEERING
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
Doina Verdes BASICS OF SEISMIC ENGINEERING
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Seismic performance design matrix (SEAOC
Vision 2000, 1999)
Doina Verdes BASICS OF SEISMIC ENGINEERING
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Building Performance Levels and Ranges*
Source: FEMA Instructional Material Complementing FEMA 451
Doina Verdes BASICS OF SEISMIC ENGINEERING
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Total costs for different performance design
objectives
Conforming SEAOC Vision 2000, 1999
Doina Verdes BASICS OF SEISMIC ENGINEERING
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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
Doina Verdes BASICS OF SEISMIC ENGINEERING
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Performance requirements and compliance criteria
Conforming:Conforming:
EUROCODE 8 and P100/2006
Doina Verdes BASICS OF SEISMIC ENGINEERING
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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
Doina Verdes BASICS OF SEISMIC ENGINEERING
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.
Doina Verdes BASICS OF SEISMIC ENGINEERING
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IZMIT Earthquake, 1999 Turkey
Doina Verdes BASICS OF SEISMIC ENGINEERING
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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).
Doina Verdes BASICS OF SEISMIC ENGINEERING
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.
Doina Verdes BASICS OF SEISMIC ENGINEERING
2011
Importance classes for buildings cf EC8
Doina Verdes BASICS OF SEISMIC ENGINEERING
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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.
Doina Verdes BASICS OF SEISMIC ENGINEERING
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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.
Doina Verdes BASICS OF SEISMIC ENGINEERING
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.
Doina Verdes BASICS OF SEISMIC ENGINEERING
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.
Doina Verdes BASICS OF SEISMIC ENGINEERING
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).
Doina Verdes BASICS OF SEISMIC ENGINEERING
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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.
Doina Verdes BASICS OF SEISMIC ENGINEERING
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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.
Doina Verdes BASICS OF SEISMIC ENGINEERING
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.
Doina Verdes BASICS OF SEISMIC ENGINEERING
2011
The foundation elements and the foundation-soil
interaction
It shall be verified that both the foundation elements
and the foundation-soil are able to resist the action
effects resulting from the response of theeffects resulting from the response of the
superstructure without substantial permanent
deformations.
Doina Verdes BASICS OF SEISMIC ENGINEERING
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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
Doina Verdes BASICS OF SEISMIC ENGINEERING
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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.
Doina Verdes BASICS OF SEISMIC ENGINEERING
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Doina Verdes BASICS OF SEISMIC ENGINEERING
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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.
Doina Verdes BASICS OF SEISMIC ENGINEERING
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Substructure approach to solution of soil-foundation-structure interaction using rigid foundation or flexible foundation assumption
Doina Verdes BASICS OF SEISMIC ENGINEERING
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a. Rigid foundation
θ g = the foundation rotation
u s = the foundation translation
b. Structure with foundation
flexibility - flexibility and damping)
a. Rigid foundation
Doina Verdes BASICS OF SEISMIC ENGINEERING
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Overturning and sliding stability
• The structure as a whole shall
be checked to be stable under
the design seismic action. Both
overturning and sliding stability
shall be considered.
Influence of second order effects
In the analysis the possible influence of second order effects on the values of the action effects shall be taken into account
Doina Verdes BASICS OF SEISMIC ENGINEERING
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5.4 The guiding principles governing the conceptual design against seismic
hazard
Doina Verdes BASICS OF SEISMIC ENGINEERING
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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
Doina Verdes BASICS OF SEISMIC ENGINEERING
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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.
Doina Verdes BASICS OF SEISMIC ENGINEERING
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.
Doina Verdes BASICS OF SEISMIC ENGINEERING
2011
Symmetry
• In seismic area it has to be searched building shapes
as simplest and symmetric as possible, in plan as
much as in elevation. Many of the 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.
Doina Verdes BASICS OF SEISMIC ENGINEERING
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.
Doina Verdes BASICS OF SEISMIC ENGINEERING
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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).
Doina Verdes BASICS OF SEISMIC ENGINEERING
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.
Doina Verdes BASICS OF SEISMIC ENGINEERING
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Building separation to avoid pounding
Doina Verdes BASICS OF SEISMIC ENGINEERING
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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.
Doina Verdes BASICS OF SEISMIC ENGINEERING
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• 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.
Doina Verdes BASICS OF SEISMIC ENGINEERING
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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
Doina Verdes BASICS OF SEISMIC ENGINEERING
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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.
Doina Verdes BASICS OF SEISMIC ENGINEERING
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Criteria for regularity of buildings with setbacks
(EC8)
a. b.
(setback
occurs below
0,15H)
c. d.
Doina Verdes BASICS OF SEISMIC ENGINEERING
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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.
Doina Verdes BASICS OF SEISMIC ENGINEERING
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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
Doina Verdes BASICS OF SEISMIC ENGINEERING
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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
Doina Verdes BASICS OF SEISMIC ENGINEERING
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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:
Doina Verdes BASICS OF SEISMIC ENGINEERING
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.
Doina Verdes BASICS OF SEISMIC ENGINEERING
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1971 San Fernando Valley Earthquake“Soft story” failure of the Hospital building [21]
Doina Verdes BASICS OF SEISMIC ENGINEERING
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• 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.
Doina Verdes BASICS OF SEISMIC ENGINEERING
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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.
Doina Verdes BASICS OF SEISMIC ENGINEERING
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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.
Doina Verdes BASICS OF SEISMIC ENGINEERING
2011
• A word of warning should be given here about the
effect of non-structural elements on the structural
response of buildings.
• The non-structure, mainly in the form of partitions,
may enormously stiffen an otherwise flexiblemay enormously stiffen an otherwise flexible
structure and hence must be allowed for in thestructural analysis
Doina Verdes BASICS OF SEISMIC ENGINEERING
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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.
Doina Verdes BASICS OF SEISMIC ENGINEERING
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
Doina Verdes BASICS OF SEISMIC ENGINEERING
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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.
Doina Verdes BASICS OF SEISMIC ENGINEERING
2011
However, if we turn to new techniques and
technologies, notably the use of base isolation, is
often possible to greatly modify the horizontal
vibration characteristics of a structure whether it isvibration characteristics of a structure whether it is
inherently stiff or flexible above the isolating layer.
Doina Verdes BASICS OF SEISMIC ENGINEERING
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BASICS OF SEISMIC ENGINEERING
� By Doina Verdes
CHAPTER 6
INELASTIC DYNAMIC BEHAVIOR
2
Doina Verdes BASICS OF SEISMIC ENGINEERING
2011
Contents
� 6.1 Introduction
� 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
Basics of Seismic Engineering
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.
Doina Verdes BASICS OF SEISMIC ENGINEERING
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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
Doina Verdes BASICS OF SEISMIC ENGINEERING
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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
Doina Verdes BASICS OF SEISMIC ENGINEERING
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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
Doina Verdes BASICS OF SEISMIC ENGINEERING
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Hysteretic behaviour
8Doina Verdes BASICS OF SEISMIC ENGINEERING
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9Doina Verdes BASICS OF SEISMIC ENGINEERING
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10Doina Verdes BASICS OF SEISMIC ENGINEERING
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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.
11Doina Verdes BASICS OF SEISMIC ENGINEERING
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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.
12Doina Verdes BASICS OF SEISMIC ENGINEERING
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13Doina Verdes BASICS OF SEISMIC ENGINEERING
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.
Doina Verdes BASICS OF SEISMIC ENGINEERING
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
Doina Verdes BASICS OF SEISMIC ENGINEERING
2011
16
Source FEMA [25]
Doina Verdes BASICS OF SEISMIC ENGINEERING
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
BASICS OF SEISMIC ENGINEERING 2011
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.
Doina Verdes BASICS OF SEISMIC ENGINEERING
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
Doina Verdes BASICS OF SEISMIC ENGINEERING
2011
The stress-strain diagrams for steel
stress
20
strain
Doina Verdes BASICS OF SEISMIC ENGINEERING
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.
Doina Verdes BASICS OF SEISMIC ENGINEERING
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.
Doina Verdes BASICS OF SEISMIC ENGINEERING
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
Doina Verdes BASICS OF SEISMIC ENGINEERING
2011
The effort-deformation relationship for RC elements
24
εc2 - deformation at max effort
εcu2 - ultimate deformation
fcd - Compression resistance
Doina Verdes BASICS OF SEISMIC ENGINEERING
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
Doina Verdes BASICS OF SEISMIC ENGINEERING
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
Doina Verdes BASICS OF SEISMIC ENGINEERING
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
Doina Verdes BASICS OF SEISMIC ENGINEERING
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
Doina Verdes BASICS OF SEISMIC ENGINEERING
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
Doina Verdes BASICS OF SEISMIC ENGINEERING
2011
Collapse of the Parking building during Northridge earthquake,
1994,(some of columns emphasize DUCTILITY)
30Doina Verdes BASICS OF SEISMIC ENGINEERING
2011
6.4 Requirements for ductility of
reinforced concrete frames
31Doina Verdes BASICS OF SEISMIC ENGINEERING
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
Doina Verdes BASICS OF SEISMIC ENGINEERING
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.
Doina Verdes BASICS OF SEISMIC ENGINEERING
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.
Doina Verdes BASICS OF SEISMIC ENGINEERING
2011
The conformation of the critical zones
of RC frames
Column
Beam
35
Column Column
Beam
Critical regions
Doina Verdes BASICS OF SEISMIC ENGINEERING
2011
Beams - Detaling for local ductility
36Doina Verdes BASICS OF SEISMIC ENGINEERING
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
Doina Verdes BASICS OF SEISMIC ENGINEERING
2011
Column
Beam
38
The diameter of the tiers dbw ≥ 6 mm
Medium ductility class (M)High ductility class (H)
P100-2006
Doina Verdes BASICS OF SEISMIC ENGINEERING
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’).
Doina Verdes BASICS OF SEISMIC ENGINEERING
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.
Doina Verdes BASICS OF SEISMIC ENGINEERING
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.
Doina Verdes BASICS OF SEISMIC ENGINEERING
2011
The detailles of column cross section reinforcement
42Doina Verdes BASICS OF SEISMIC ENGINEERING
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.
Doina Verdes BASICS OF SEISMIC ENGINEERING
2011
The beam – column joint stresses
Exterior column Interior column
44Doina Verdes BASICS OF SEISMIC ENGINEERING
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'
Doina Verdes BASICS OF SEISMIC ENGINEERING
2011
The joint design
Corner
46
Corner
d) Roof
Interior
e) Roof
Exterior
f) Roof
Corner
Doina Verdes BASICS OF SEISMIC ENGINEERING
2011
The joint reinforcement design
47Doina Verdes BASICS OF SEISMIC ENGINEERING
2011
The reinforcement of the joints
48Doina Verdes BASICS OF SEISMIC ENGINEERING
2011
The critical regions are at a
distance from the joint [4]
49Doina Verdes BASICS OF SEISMIC ENGINEERING
2011
The reinforcement bars anchorage [4]
50Doina Verdes BASICS OF SEISMIC ENGINEERING
2011
The reinforcement bars anchorage [4]
51Doina Verdes BASICS OF SEISMIC ENGINEERING
2011
6.5.The damages of the reinforced concrete frames under seismic loads
52Doina Verdes BASICS OF SEISMIC ENGINEERING
2011
The damaged columns
53Doina Verdes BASICS OF SEISMIC ENGINEERING
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The damaged columns
54Doina Verdes BASICS OF SEISMIC ENGINEERING
2011
55
The effect of short columnThe “ductile columns”
Doina Verdes BASICS OF SEISMIC ENGINEERING
2011
The damage of beam-
column joints and the effects
on the buildings
56Doina Verdes BASICS OF SEISMIC ENGINEERING
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).
57Doina Verdes BASICS OF SEISMIC ENGINEERING
2011
BASICS OF SEISMIC ENGINEERING
� By Doina Verdes
CHAPTER 7
DESIGN CONCEPTS FOR
EARTHQUAKE RESISTANT EARTHQUAKE RESISTANT REINFORCED CONCRETE
STRUCTURES
Doina Verdes BASICS OF SEISMIC ENGINEERING
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
Basics of Seismic Engineering
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.
4Doina Verdes BASICS OF SEISMIC ENGINEERING
2011
Behaviour factors for horizontal seismic action
The behaviour factor q, is introduced to account the
energy dissipation capacity.
5Doina Verdes BASICS OF SEISMIC ENGINEERING
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.
6Doina Verdes BASICS OF SEISMIC ENGINEERING
2011
Frame system
Dual system(frame- or wall-
equivalent)Braced frame
7
moment frame
frames
diafragmes
Doina Verdes BASICS OF SEISMIC ENGINEERING
2011
Ductile wall system
(coupled or uncoupled)
Inverted pendulum system
8Doina Verdes BASICS OF SEISMIC ENGINEERING
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.
9Doina Verdes BASICS OF SEISMIC ENGINEERING
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.
10Doina Verdes BASICS OF SEISMIC ENGINEERING
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.
11Doina Verdes BASICS OF SEISMIC ENGINEERING
2011
Bulding Performance Levels and Range [21]
12Doina Verdes BASICS OF SEISMIC ENGINEERING
2011
7.3 Design criteria at Ultimate Limit
State (ULS)State (ULS)
13Doina Verdes BASICS OF SEISMIC ENGINEERING
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
Doina Verdes BASICS OF SEISMIC ENGINEERING
2011
b. Ductility
ρ =δ u /δ y
ρDefinition of ductility
Deformation control
15Doina Verdes BASICS OF SEISMIC ENGINEERING
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
16Doina Verdes BASICS OF SEISMIC ENGINEERING
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.
17Doina Verdes BASICS OF SEISMIC ENGINEERING
2011
� Design concepts
Low dissipative structural behaviour
Dissipative structural behavior
a. b.
18Doina Verdes BASICS OF SEISMIC ENGINEERING
2011
� Dissipative Structural Behavior
Elastically response
Inelastically response
19
q= behaviour factor
Inelastically response
Design code response
Doina Verdes BASICS OF SEISMIC ENGINEERING
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.
Doina Verdes BASICS OF SEISMIC ENGINEERING
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
21Doina Verdes BASICS OF SEISMIC ENGINEERING
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
22Doina Verdes BASICS OF SEISMIC ENGINEERING
2011
c. Limitation of interstory drifts
F
23
The interstory drift δ
Doina Verdes BASICS OF SEISMIC ENGINEERING
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
24Doina Verdes BASICS OF SEISMIC ENGINEERING
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)
25Doina Verdes BASICS OF SEISMIC ENGINEERING
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.
26Doina Verdes BASICS OF SEISMIC ENGINEERING
2011
P-∆ effect
For inelastic systems:Reduced stiffness andincreased displacements
Including P - ∆
27Doina Verdes BASICS OF SEISMIC ENGINEERING
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
28Doina Verdes BASICS OF SEISMIC ENGINEERING
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
29Doina Verdes BASICS OF SEISMIC ENGINEERING
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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
30Doina Verdes BASICS OF SEISMIC ENGINEERING
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.
31Doina Verdes BASICS OF SEISMIC ENGINEERING
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Separation of buildings with different dynamic
characteristics
-allow independent vibrations
-limit the effect of collisions
32Doina Verdes BASICS OF SEISMIC ENGINEERING
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
Doina Verdes BASICS OF SEISMIC ENGINEERING
2011
Analysis methods
Equivalent lateral force analysis
Modal response spectrum analysis
Linear response history analysis
Nonlinear response history analysisNonlinear response history analysis
34Doina Verdes BASICS OF SEISMIC ENGINEERING
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.
35Doina Verdes BASICS OF SEISMIC ENGINEERING
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
36Doina Verdes BASICS OF SEISMIC ENGINEERING
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Avoid undesirable mechanism
37Doina Verdes BASICS OF SEISMIC ENGINEERING
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38
Undesirable mechanism – level story damage [ ]
Doina Verdes BASICS OF SEISMIC ENGINEERING
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Behaviour under
seismic excitation
inelastic response
of a RC frame [21]
39Doina Verdes BASICS OF SEISMIC ENGINEERING
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Behaviour under
seismic excitation
inelastic response
of a RC frame [ 21 ]
40Doina Verdes BASICS OF SEISMIC ENGINEERING
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Ordinary Concrete Moment frame [ 21]
41Doina Verdes BASICS OF SEISMIC ENGINEERING
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Intermediate Concrete Moment frame [ 21]
42Doina Verdes BASICS OF SEISMIC ENGINEERING
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Special Concrete Moment frame [21]
43Doina Verdes BASICS OF SEISMIC ENGINEERING
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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)
Doina Verdes BASICS OF SEISMIC ENGINEERING
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7.6 Structural types with stress
concentration
45Doina Verdes BASICS OF SEISMIC ENGINEERING
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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
46Doina Verdes BASICS OF SEISMIC ENGINEERING
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Stress concentration
The soft story collapse mechanism
47Doina Verdes BASICS OF SEISMIC ENGINEERING
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Collapses of buildings with stress concentrations
48Doina Verdes BASICS OF SEISMIC ENGINEERING
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Infill
The infill masonry placed above a free first story can
develop the collapse mechanism (due to the stress
concentration)
Very stiff
Infill
masonry
49Doina Verdes BASICS OF SEISMIC ENGINEERING
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8.6 The local effects of infill masonry
Doina Verdes BASICS OF SEISMIC ENGINEERING
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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
51Doina Verdes BASICS OF SEISMIC ENGINEERING
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• 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.
52Doina Verdes BASICS OF SEISMIC ENGINEERING
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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.
53Doina Verdes BASICS OF SEISMIC ENGINEERING
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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
54Doina Verdes BASICS OF SEISMIC ENGINEERING
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The effect of compressed diagonal
Actions on beam
and column
a. b.
55Doina Verdes BASICS OF SEISMIC ENGINEERING
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Short column effect
56Doina Verdes BASICS OF SEISMIC ENGINEERING
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Short column effect
Masonry panel
57Doina Verdes BASICS OF SEISMIC ENGINEERING
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Short beam effect
Masonry panel
Column
Short beam
Short beam
Beam
Masonry panel
a.
Masonry panel
Short beam
b.Beam
58Doina Verdes BASICS OF SEISMIC ENGINEERING
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• 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.
59Doina Verdes BASICS OF SEISMIC ENGINEERING
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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
Doina Verdes BASICS OF SEISMIC ENGINEERING
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BASICS OF SEISMIC ENGINEERING
� By Doina Verdes
CHAPTER 8
NONSTRUCTURAL ELEMENTS
Doina Verdes BASICS OF SEISMIC ENGINEERING
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
Basics of Seismic Engineering
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
Doina Verdes BASICS OF SEISMIC ENGINEERING
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Structural and Nonstructural Elements
of a Building
Source: FEMA_Instructional Material Complementing FEMA 451, Design Examples
Doina Verdes BASICS OF SEISMIC ENGINEERING
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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.
Doina Verdes BASICS OF SEISMIC ENGINEERING
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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
BASICS OF SEISMIC ENGINEERING 2011
• 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).
Doina Verdes BASICS OF SEISMIC ENGINEERING
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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
Doina Verdes BASICS OF SEISMIC ENGINEERING
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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;
Doina Verdes BASICS OF SEISMIC ENGINEERING
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.
Doina Verdes BASICS OF SEISMIC ENGINEERING
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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.
Doina Verdes BASICS OF SEISMIC ENGINEERING
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8.2 Earthquake effects on buildings and nonstructural elements
Building response [ 25 ]
Doina Verdes BASICS OF SEISMIC ENGINEERING
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Earthquake Response of the
building
The floor accelerations due to an earthquake [21]
The vibrational characteristics of the building
cause the earthquake ground motion to be
amplified within the building. For multi-story
buildings, there is a difference in the horizontal
movement or acceleration of the floors over the
height.Doina Verdes
BASICS OF SEISMIC ENGINEERING 2011
The accelerograms recorded to different levels of Sylmar
County Hospital during Northridge earthquake, 1994
The accelerographs
positions in plan and
elevation [4] of the elevation [4] of the
Sylmar County Hospital
Doina Verdes BASICS OF SEISMIC ENGINEERING
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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
Doina Verdes BASICS OF SEISMIC ENGINEERING
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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.
Doina Verdes BASICS OF SEISMIC ENGINEERING
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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.
Doina Verdes BASICS OF SEISMIC ENGINEERING
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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.
Doina Verdes BASICS OF SEISMIC ENGINEERING
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• 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
Doina Verdes BASICS OF SEISMIC ENGINEERING
2011
Examples of damages to nonstructural
elements
Suspended ceiling damage
Exit canopy damage
Source: FEMA_Instructional Material Complementing FEMA 451, Design Examples
Chimney damage
Parapet damage
Source: FEMA_Instructional Material Complementing FEMA 451, Design Examples
Sliding and overturning
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
Doina Verdes BASICS OF SEISMIC ENGINEERING
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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.
Doina Verdes BASICS OF SEISMIC ENGINEERING
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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 .
Doina Verdes BASICS OF SEISMIC ENGINEERING
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
Doina Verdes BASICS OF SEISMIC ENGINEERING
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Short beam effect
Masonry panel
Column
Short beam
Short beam
Beam
Masonry panel
a.
Masonry panel
Short beam
b.Beam
27
Doina Verdes BASICS OF SEISMIC ENGINEERING
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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.
Doina Verdes BASICS OF SEISMIC ENGINEERING
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.
Doina Verdes BASICS OF SEISMIC ENGINEERING
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Building Performance and Levels Ranges [ ]
30
Doina Verdes BASICS OF SEISMIC ENGINEERING
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8.5 Protection Strategies
Improved Structural Performance
Improved Nonstructural Performance
• Better Engineered Conventional Anchors• Better Engineered Conventional Anchors
• Newer Technologies
Doina Verdes BASICS OF SEISMIC ENGINEERING
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
Doina Verdes BASICS OF SEISMIC ENGINEERING
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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.
Doina Verdes BASICS OF SEISMIC ENGINEERING
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Partitions
a.a. Partition free to slide at top but
restrained laterally
b. Partition doweled at base
b.
Doina Verdes BASICS OF SEISMIC ENGINEERING
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Improved Nonstructural PerformanceNewer Technologies
Semi-active device (Rana and Soong, 1998)
Doina Verdes BASICS OF SEISMIC ENGINEERING
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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.
Doina Verdes BASICS OF SEISMIC ENGINEERING
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
Doina Verdes BASICS OF SEISMIC ENGINEERING
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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)
Doina Verdes BASICS OF SEISMIC ENGINEERING
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Concrete Frames
with Infill Masonry Shear Walls
Doina Verdes BASICS OF SEISMIC ENGINEERING
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Concrete Frames with Cladding
(window wall or panels)
Doina Verdes BASICS OF SEISMIC ENGINEERING
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Steel Moment Frames
Doina Verdes BASICS OF SEISMIC ENGINEERING
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Steel Braced Frames
Doina Verdes BASICS OF SEISMIC ENGINEERING
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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.
Doina Verdes BASICS OF SEISMIC ENGINEERING
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The assembly panels and R C framed structure: (a) Fully integrated, interacting with the
surrounding elements and (b) fully separated
ß
Doina Verdes BASICS OF SEISMIC ENGINEERING
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• 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.
Doina Verdes BASICS OF SEISMIC ENGINEERING
2011
a
b
a. Panel interactingb. Panel separated
Doina Verdes BASICS OF SEISMIC ENGINEERING
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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.
Doina Verdes BASICS OF SEISMIC ENGINEERING
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
Doina Verdes BASICS OF SEISMIC ENGINEERING
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.
Doina Verdes BASICS OF SEISMIC ENGINEERING
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Connections of precast claddings to the structure
permitting the separation
Beam
PanelPanel
PanelBeam
Doina Verdes BASICS OF SEISMIC ENGINEERING
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Laboratory tests on panels equipped
with connections to “separate” the
panel from the structure [15]
Doina Verdes BASICS OF SEISMIC ENGINEERING
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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
Doina Verdes BASICS OF SEISMIC ENGINEERING
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• 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.
Doina Verdes BASICS OF SEISMIC ENGINEERING
2011
FISIE DE CAUCIUCr
rv.
vt.
DIN ALUMINIUPROFIL
The gap panel - structural element coverings
Doina Verdes BASICS OF SEISMIC ENGINEERING
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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=
Doina Verdes BASICS OF SEISMIC ENGINEERING
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+=
Doina Verdes BASICS OF SEISMIC ENGINEERING
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FCNS ≤ 4 gCNS ag mCNS
FCNS ≥ 0,75 gCNS ag mCNS
Dynamic amplification coefficient βCNS is function of
period of vibration of the nonstructural element
• rigid components (perioad TCNS ≤0, 06 s):
βCNS = 1,0
•flexibile components (period TCNS > 0,06 s):
β CNS = 2,5
Doina Verdes BASICS OF SEISMIC ENGINEERING
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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
Doina Verdes BASICS OF SEISMIC ENGINEERING
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8.9 Cladding which increase the seismic energy dissipation
Doina Verdes BASICS OF SEISMIC ENGINEERING
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.
Doina Verdes BASICS OF SEISMIC ENGINEERING
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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
Doina Verdes BASICS OF SEISMIC ENGINEERING
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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
Doina Verdes BASICS OF SEISMIC ENGINEERING
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• 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
Doina Verdes BASICS OF SEISMIC ENGINEERING
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- or as smaller elements installed in the
frameworks of a building at nearly middle height of
the storey and connected to rigid support members
to transfer shear forces to the main frames
Partially bay type
Bracing type
Pillar type
Doina Verdes BASICS OF SEISMIC ENGINEERING
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Implementation of steel panel in the building from Japan
The hysteretic behaviour of LYS steel panels is very good, providing
that suitable stiffeners are arranged, in order to prevent shear
buckling, and a rigid panel-to-frame connecting system is adopted,
so to avoid any slipping phenomenon in the recovery characteristic
of the system. The majority of practical applications of low-yield
shear panels are located in Japan.
Doina Verdes BASICS OF SEISMIC ENGINEERING
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Exemple of separated claddings implementation
High rise building in
Tokyo, Japan
Doina Verdes BASICS OF SEISMIC ENGINEERING
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Concrete cladding
Models tested in the laboratory of Civil Buildings and Foundation
Chair, Civil Engineering Faculty of Cluj-Napoca [16]
Panel A Panel B
Doina Verdes BASICS OF SEISMIC ENGINEERING
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Details of panel connection to the structure [ ]
Doina Verdes BASICS OF SEISMIC ENGINEERING
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Panel type A cracks pattern
Doina Verdes BASICS OF SEISMIC ENGINEERING
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The joint concrete subjected to shear force
Doina Verdes BASICS OF SEISMIC ENGINEERING
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The diagrams of panel deformations
Doina Verdes BASICS OF SEISMIC ENGINEERING
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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.
Doina Verdes BASICS OF SEISMIC ENGINEERING
2011
The claddings fallen
down
8.10. Examples of damages of building claddings
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Broken glass panels
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Damaged :
•infill masonry,
•frame joint
•glass panels
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Damage of partition walls
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Damaged :
•infill
masonry(parapets),
•frame columns,
•glass panels.•glass panels.
Doina Verdes BASICS OF SEISMIC ENGINEERING
2011
BASICS OF SEISMIC ENGINEERING
� By Doina Verdes
CHAPTER 9
Doina Verdes
BASICS OF SEISMIC ENGINEERING
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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� 9.4 The base isolation system
� 9.5 The energy dissipation systems
� 9.6 Advanced technology systems (9A)
� 9.7 Active structural control (9B)
3
9.1 Introduction
• Buildings are complex systems in which the
resistance structure represents the main mechanical
systems.
• The structure interacts with the existing subsystems
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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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- Weight = 29,300 kips
- 98 High damping elastomeric bearings
- 2 sec fundamental lateral period
- 0.1 sec vertical period
- +/- 16 inches displacement capacity
- Damping ratio = 10 to 20%
(dependent on shear strain
Source: NEHRP Recommended Provisions:Instructional Materials (FEMA 451B)
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
- Weight = 120,000 kips
- Granite exterior & marble, plaster,
and hardwood interior
- Damaged in 1989 Loma Prieta EQ
- Seismic retrofit in 1994
- 256 Sliding bearings (FPS)
- Displacement capacity = +/-14 in.
Source: NEHRP Recommended Provisions:Instructional Materials (FEMA 451B)
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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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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BASICS OF SEISMIC ENGINEERING
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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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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
BASICS OF SEISMIC ENGINEERING
� By Doina Verdes
CHAPTER 9
THE CONTROL OF STRUCTURAL SEISMIC RESPONSE
2
Contents
� 9.1. Introduction
� 9.2. The types of structural control systems
� 9.3. Passive control system
� 9.4 The base isolation system
� 9.5 The energy dissipation systems� 9.5 The energy dissipation systems
� 9.6 Advanced technology systems (9A)
� 9.7 Active structural control (9B)
3
9.6 Advanced Technology Systems
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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
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Added Damping
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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.
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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
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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
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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)
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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).
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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.
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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.
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Possible Damper Placement Within Structure
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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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BASICS OF SEISMIC ENGINEERING
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19
*Source: FEMA Instructional Material
Complementing FEMA 451
Harmonic behaviour of fluid damper
Source: FEMA Instructional Material
Complementing FEMA 45120
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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BASICS OF SEISMIC ENGINEERING
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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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BASICS OF SEISMIC ENGINEERING
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Vicoelastic dampers*
A -A
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BASICS OF SEISMIC ENGINEERING
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23
*Source: FEMA Instructional Material
Complementing FEMA 451
High reliability
May be able to use linear analysis
Somewhat lower cost
Advantages of Viscoelastic Dampers
Somewhat lower cost
24
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BASICS OF SEISMIC ENGINEERING
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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
BASICS OF SEISMIC ENGINEERING
201126
*Source: FEMA Instructional Material
Complementing FEMA 451
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
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BASICS OF SEISMIC ENGINEERING
2011 27
*Source: FEMA Instructional Material
Complementing FEMA 451
Hysteretic Behavior of ADAS Device
ADAS Device(Tsai et al. 1993)
Experimental Response (Static)(Source: Tsai et al. 1993)
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BASICS OF SEISMIC ENGINEERING
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Force-Limited
Easy to construct
Relatively Inexpensive
Advantages of ADAS System
and Unbonded Brace Damper
Relatively Inexpensive
Adds both “Damping” and Stiffness
29Doina Verdes
BASICS OF SEISMIC ENGINEERING
2011
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
BASICS OF SEISMIC ENGINEERING
2011
Friction Dampers: Slotted-Bolted Damper*
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BASICS OF SEISMIC ENGINEERING
2011
31
*Source: FEMA Instructional Material
Complementing FEMA 451
Sumitomo Friction Damper(Sumitomo Metal Industries, Japan)
32Doina Verdes
BASICS OF SEISMIC ENGINEERING
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Cross-Bracing Friction Damper*
Interior of Webster
Library at Concordia
University, Montreal,
Canada
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BASICS OF SEISMIC ENGINEERING
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33
*Source: FEMA Instructional Material
Complementing FEMA 451
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
BASICS OF SEISMIC ENGINEERING
2011
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
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BASICS OF SEISMIC ENGINEERING
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35
Source: FEMA Instructional Material
Complementing FEMA 451
Hysteretic Behavior of Slotted-Bolted
Friction Damper
36Doina Verdes
BASICS OF SEISMIC ENGINEERING
2011
Ideal hysteretic behavior
of cross-bracing friction damper
37Doina Verdes
BASICS OF SEISMIC ENGINEERING
2011
Force-Limited
Easy to construct
Advantages of Friction Dampers
Relatively Inexpensive
38Doina Verdes
BASICS OF SEISMIC ENGINEERING
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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
BASICS OF SEISMIC ENGINEERING
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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
BASICS OF SEISMIC ENGINEERING
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BASICS OF SEISMIC ENGINEERING
� By Doina Verdes
CHAPTER 9
Doina Verdes
BASICS OF SEISMIC ENGINEERING
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
Doina Verdes
BASICS OF SEISMIC ENGINEERING
2011
� 9.4 The base isolation system
� 9.5 The energy dissipation systems
� 9.6 Advanced technology systems (9A)
� 9.7 Active structural control (9B)
3
9.7 Active structural control systems
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Doina Verdes BASICS OF SEISMIC ENGINEERING
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Doina Verdes BASICS OF SEISMIC ENGINEERING
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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.
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Doina Verdes BASICS OF SEISMIC ENGINEERING
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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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Doina Verdes BASICS OF SEISMIC ENGINEERING
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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.
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Doina Verdes BASICS OF SEISMIC ENGINEERING
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• 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;
9
Doina Verdes BASICS OF SEISMIC ENGINEERING
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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.
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Doina Verdes BASICS OF SEISMIC ENGINEERING
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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)
11
Doina Verdes BASICS OF SEISMIC ENGINEERING
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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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Doina Verdes BASICS OF SEISMIC ENGINEERING
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• 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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Doina Verdes BASICS OF SEISMIC ENGINEERING
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STRUCTURE
WITH PED
EXCITATION RESPONSE
Structure with Hybrid Control
SENSORS COMPUTER
CONTROLER
SENSORS
CONTROL
ACTUATORS
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Doina Verdes BASICS OF SEISMIC ENGINEERING
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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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Doina Verdes BASICS OF SEISMIC ENGINEERING
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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
Doina Verdes BASICS OF SEISMIC ENGINEERING
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Sendagaya INTES building with hybrid mass dampers
(Higashino and Aizawa, 1993)
17
Doina Verdes BASICS OF SEISMIC ENGINEERING
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Top view of hybrid mass damper configuration
(Higashino and Aizawa, 1993)
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Response time histories (Higashino and Aizawa, 1993)
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Doina Verdes BASICS OF SEISMIC ENGINEERING
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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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Doina Verdes BASICS OF SEISMIC ENGINEERING
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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
21
Doina Verdes BASICS OF SEISMIC ENGINEERING
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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:
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Doina Verdes BASICS OF SEISMIC ENGINEERING
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)()()()()( 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&&=
23
Doina Verdes BASICS OF SEISMIC ENGINEERING
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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.
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Doina Verdes BASICS OF SEISMIC ENGINEERING
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Active Mass Damper Systems
Design constraints, such as severe space limitations,
can preclude the use of an HMD system. Such is the
case in the active mass damper or active
25
Doina Verdes BASICS OF SEISMIC ENGINEERING
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Principle of the DUOX system
(Nishimura et al., 1993)
26
Doina Verdes BASICS OF SEISMIC ENGINEERING
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BUILDING
AMD Atachet mass damper
TMD Tuned mass damper
27
Doina Verdes BASICS OF SEISMIC ENGINEERING
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The simplified principle: active & passive control
The Kyobashi Seiwa Building in Tokyo
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Doina Verdes BASICS OF SEISMIC ENGINEERING
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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
Doina Verdes BASICS OF SEISMIC ENGINEERING
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Semi-active Damper Systems
• Control strategies based on semi-active devices combine the
best features of both passive and active control systems.
• semi-active control devices offer the adaptability of active
control devices without requiring the associated large power
sources; in fact, many can operate on battery power, which is
critical during seismic events 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
Doina Verdes BASICS OF SEISMIC ENGINEERING
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• 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
Doina Verdes BASICS OF SEISMIC ENGINEERING
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SAVS system configuration (Kurata et al., 1999)
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Doina Verdes BASICS OF SEISMIC ENGINEERING
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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).
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Doina Verdes BASICS OF SEISMIC ENGINEERING
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Yokohama Landmark Tower and HMD
(Yamazaki et al., 1992)
34
Doina Verdes BASICS OF SEISMIC ENGINEERING
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Yokohama Landmark Tower and Shinjuku Park Tower
35
Doina Verdes BASICS OF SEISMIC ENGINEERING
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Kajima Shizuoka Building and semi-active
hydraulic dampers (Kurata et al., 1999)
36
Doina Verdes BASICS OF SEISMIC ENGINEERING
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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
Doina Verdes BASICS OF SEISMIC ENGINEERING
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38
Schematic of a controllable fluid damper
Doina Verdes BASICS OF SEISMIC ENGINEERING
2011
Full-scale 20-ton MR fluid damper (Dyke et al., 1998)
39
Doina Verdes BASICS OF SEISMIC ENGINEERING
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The scheme of active control of seismic response
Desplacements
Traductor
CONTROLSERVO-VALVE
Actuator
Active Tendon
System
COMPUTER PC
..gy
DIFERENTIALANALOG
CONDITIONING
40
Doina Verdes BASICS OF SEISMIC ENGINEERING
2011
High rise building in Japan
41
Doina Verdes BASICS OF SEISMIC ENGINEERING
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1
BASICS OF SEISMIC ENGINEERING
By Doina Verdes
REFERENCES
1. Bozornia Y., Bertero,V., Earthquake Engineering from
Engineering Seismology to Performance – Based Engineering,
CRC Press, Boca Raton, London, New York, Washington, D.C.,
ISBN 0-8493-1439-9, 2007
2. Bors, I. , Dinamica structurilor, UTPRESS, 2010
3. Chopra, Anil K. , Dynamics of structures, Theory and
applications to Earthquake engineering, 2007, Pearson
Education, Inc., ISBN 0-13-156174-X
4. Clough Ray W., Penzien J. - Dynamic of Structures, John Wiley &
Sons, 1993
5. Crainic, l., Proiectarea nodurilor cadrelor de beton în codurile
de proiectare actuale, Rev AICPS, 2008
6. Dungale S. Taranath, Wind and Earthquake resistant buildings
Structural analisis and design, ISBN 0-8247-5934-b, 2004
7. Ifrim M., Dinamica structurilor si inginerie seismica, Bucuresti
Editura didactica si pedagogica, 1985
8. Kelly J.,- Resistant Earthquake Design with Rubber, second
edition, Springer 1997
9. Manea Daniela, Reducerea efectelor dinamice asupra
constructiilor prin sisteme de protectie aplicate la nivelul
fundatiilor, PhD Thesis, 1997
10. Negoita Al. si colectiv , Inginerie seismica, EDP 1985
11. Pop I., Verdeş D, Manea D., - 1998, Pasiv System of Seismic
Isolation with Penduls and Friction Absorbers, Proceedings of 11TH
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.
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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
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7. The Awards
Three prizes and three special awards
Special awards
Charles Richter Award for the Spirit of the Competition
• The most well known earthquake magnitude scale is the Richter scale which was developed in 1935 by Charles Richter, of the California Institute of Technology. In honor of his contribution to earthquake engineering, the team which best exemplifies the spirit of the competition will be awarded the Charles Richter Award for the Spirit of Competition. The winner for this award will be determined by the judges.
Egor Popov Award for Structural Innovation
Egor Popov had been a Professor at the University of California, Berkeley for almost 55 years before he passed away in 2001. Popov conducted research that led to many advances in seismic design of steel frame connections and systems, including eccentric bracing. Popov was born in Russia, and escaped to Manchuria in 1917 during the Russian Revolution. After spending his youth in China, he immigrated to the U.S. and studied at UC Berkeley, Cal Tech, MIT and Stanford. In honor of his contribution to structural and earthquake engineering, the team which makes the best use of technology and/or structural design to resist seismic loading will be awarded the Egor Popov Award for Structural Innovation. The winner for this award will be determined by the judges.
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.
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TECHNICAL UNIVERSITY OF CLUJ-NAPOCA, ROMANIA
THE CITY UNIVERSITY
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SEISMIC DESIGN COMPETITION 2011
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
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�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.
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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
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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
Relatively Inexpensive
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SEISMIC DESIGN COMPETITION 2011
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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
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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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SEISMIC DESIGN COMPETITION 2011
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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
SEISMIC DESIGN COMPETITION 2011
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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SEISMIC DESIGN COMPETITION 2011
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
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
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11. Models Presented by the
Participants Universities
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Oregon State University
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California Polytechnic State University, San Luis Obispo
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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!