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Course Modulus for PractitionersFundamentals of seismic analysis and seismic design

LecturerDr. Barbara Borzi

Day 1:09:0010:30: Fundamentals of seismology10:30 11:00: Coffee break11:00 12:30: Seismic hazard in Palestine12:30 14:30: Lunch break14:30 16:00: Single Degree of Freedom System (SDOF)

16:00

16:30: Coffee break16:30 19:00: Elastic Response Spectrum Site effects EC8Day 2:

09:00 10:30: Fundamental of ductility and Inelastic Response Spectra10:30 11:00: Coffee break11:00 12:30: Conceptual seismic design12:30 14:30: Lunch break14:30

16:00: Seismic Analysis

16:00 16:30: Coffee break16:30 19:00: Capacity Design of BuildingsDay 3:

09:00 10:30: Assignment 110:30 11:00: Coffee break

11:00

13:00: Assignment 2

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Fundamentals of Seismology

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Tectonics

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Relations between tectonic plates, earthquakes and volcanoes

Volcanoes

Seismic zones

Subduction zones

Plate motion Collision zone

Dorsal due to transform faults

(From Faccioli, 2005)

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The largest earthquakes typically occur at plate boundaries

Earthquakes almost always occur on faults, which represent the boundarybetween two rigid media that are capable of relative motion

Earthquakes that occur on land and close enough to the surface often leavevisible evidence in the form of ground dislocatione.g. the San Andreas fault.

Notes:

From Faccioli, 2005

Earthquakes are generally classified depending on their focal depth:Crustal (shallow) up to60 km

Intermediate from 60 km to 150-200 km

Deep up to 600 km

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Plate tectonics is the reference frame to understand earthquakes

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Where two plates are sliding horizontally past one another atransform-fault boundarywill form.

Sliding boundary:

Earthquakes originate in the transform fault, or inparallel strike-slip faults, when a frictional

resistance in the fault system is overcome and theplates suddenly move.

Most transform faults are found in theoceanwherethey offset spreading ridges creating a zigzagpa ern e ween e p a es. ome rans orm au s

occur onland.

E.g.:The San Andreasis one of the few transformfaults exposed on land. The San Andreas faultzone, is about 1,300 km long and in places tens of

kilometers wide. It slices through two thirds of thelength of California. Along it, the Pacific Plate hasbeen grinding horizontally past the North AmericanPlate for 10 million years, at an average rate of

about 5 cm/yr.

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Magnitude scales

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ML: Local or Richter magnitude

It was defined in 1930s by Richter in California on the basis of two mainobservations:

Peak amplitudes on seismograms from 2 events of different intensities,recorded at the same focal depth, by the same seismograph, at similardistances are different:the strongest event generates higher amplitudes.

station, it can generate a seismogram with higher amplitude than the strongerevent.

If earthquakes are recorded at various stations at various distances, therecorded peaks of amplitude as function of distances give a curve for eachearthquake. The higher curve is associated to the strongest event and thepeakamplitudes decrease with distance in a similar manner for differentearthquakes.

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In log scale the amplitude difference isdistance independent

Quantitative relative measurebetween two earthquakes in mm

Absolute measure needs a referencezero earthquake with M=0:the event that generates an amplitudepeak of 0.001 mm at 100 km,recorded by the Wood-Anderson

(WA) seismograph

The event with M=0 is the smallerevent recordable by WA instrument

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0L log A log A=

A: peak amplitude (mm) of the recorded WA trace at a given distance

A0: corresponding amplitude of the zero earthquake at the same distance

Def:


Magnitude is a measure of the earthquake intensity at the source

Magnitude is distance independent

ncrease o a un n uces e ncrease o mes n e amp u e

of motion that defines the magnitude

Application:

Amplitude record by WA in mm

Definition of epicentral distance from earthquake localization

For records from two sensors with perpendicular directions (NS, EW),

MLis obtained as an average of the two

When records from various stations are available,MLis calculated as

the average of all the values (dispersion )0 3.

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MS: Surface wave magnitude (Rayleigh wave) It was introduced in 1945 by Gutenberg It is based on the use of surface waves of period T=20 sec., which generally

carry the maximum values of seismograms recorded by long periodseismometers and are slightly influenced by crust lateral heterogeneities.

( ) ( )S H max S M log A= +

AHmax: maximum horizontal surface waves amplitude in mm (vectoriallycombined) at periods 202 sec

Modified version officially adopted by IASPEI and U.S. Geological Survey in 1962

: stance n egrees

( ) 1 66 3 3S Smax max

Alog log . log .

T T

= + = + +

Definition problems forMSless than around 5.5

MS proper for shallow earthquakes with dept < 50 km and epicentral

distances 2

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Mb: Body wave magnitude (P wave)

( )b Alog Q ,hT = +

It was introduced in 1945 by Gutenberg It is based on the use of short period (0.5-12 s) body waves

Q: empirically defined function

In the practice short period vertical seismograms of the world networkWWSSN are used; they are generally dominated by P waves with periodabout 1 s.

A/T values have to be determined in the first time window of 5 s

h: focal depth

It is suitable for both shallow and deep earthquakes

Mbsaturation at values less than 6.5

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MW: Moment magnitude

023

W log M cos t =

It was introduced in 1979 by Hanks and Kanamori

It is based on the use of the seismic momentM0

M0: seismic moment

MWis the best measure of earthquake size

MW does not saturate, since M0 can increase without limits as fault and

dislocation dimensions increase It can be estimated from geological observations and paleoseismologic studies

It can be tied to plate motions and recurrence relations

. 0 0

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Seismic momentM0:

Moment of a double couple force system which generates the same straininduced by a shear dislocation on an infinitesimal element of surface.

Equivalence shear dislocation-double couple force system

u

Measure of the relevant features of an earthquake source.

It is proportional to the energy released during the earthquake.

:

u:

:

shear modulus

area of the dislocation surface

average relative displacement on the dislocation surface

0 uA=

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Magnitude scales conversions:

CORRELATION AUTHORS AREA OF REFERENCE

Empirical relations can be used to convert between magnitude scales. This isimportant in deriving magnitude recurrence statistics for a region or sourcezone, as all magnitudes should be first reported on the same scale before

characterizing their statistics

ML - MW

Correlation ML-Mw

7.0

7.5

MW= 1.17 + 0.436ML+ 0.059 ML2

Bollinger et al. (1993) estern United tatesMW= 0.997ML! 0.050 U"r"a##er et al. (1996) ali%ornia

MW=0.67+0.56ML+0.046ML2 Wa"lstr and 'rnt"al (2000) ort"ern and ort"*estern ,ro-e

MW= 0.962ML! 0.235 os"i '. and M. L. "ar#a (200/) rea aro,nd el"i

MW= 0.97ML+ 0.5/ a-aa"os et al. (1997) reee

MW= ML+ 0.57 ista, et al. (2005) estern $anada

MW= 1.2+0.2/ML+0.06ML2

Wa"lstr and 'rnt"al (2000) *eden inland and en#ar8

3.5

4.0

4.5

5.0

5.5

6.0

6.5

3.5 4 4.5 5 5.5 6 6.5 7 7.5

ML

Mw

Lineare (Tanner and Shepherd (1997))Lineare (Bollinger et al. (1993))Lineare (Uhrhammer et al. (1996))Lineare (Grnthal and Wahlstrm(2003))Lineare (Joshi G. and M. L. Sharma (2008))Lineare (Papazachos et al. (1997) )Lineare (Ristau et al. (2005) )Lineare (Wahlstrmand Grnthal (2000))

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Correlation Ms-Mw

CORRELATION SOURCE STUDIED ZONE

MW=0.67M + 2.07 (M6.2)

MW=0.99M + 0.0/ (M6.2)

ordilis 2006 World*ide

MW=0.667M + 2.34 (M6.6)

MW=M (M6.6):,nner ; "e-"erd 1997 Latin #eria and $ari

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Macroseismic intensity scales

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Main developed Scales:

RF, end 800 : Rossi and Forel, (X degrees)

Definition:Macroseismic intensity is a classification of the strength of shaking at any placeduring an earthquake, in terms of its observed effects on humans, objects,nature, and damage to buildings.

Mercalli, 1883, 1902 (RF revised) Cancani,1904 (Mercalli revised and amplified to XII degrees)

MCS, 1930: Mercalli-Cancani-Sieberg (Cancani improved)

MM, 1931, 1956: Modified Mercalli

MSK, 1964: Medvedev, Sponheuer and Krnk (MCS, previous Medvedevscale, Wood and Neumann and Richters work rearranged)

EMS98, 1998: European Macroseismic scale (MSK revised, XII degrees)

JMA, 1996: Japanese Meteorological Agency scale (9 degrees)

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I. Not felt except by a very few under especially favorable conditions.

II. Felt only by a few persons at rest, especially on upper floors of buildings.

III. Felt quite noticeably by persons indoors, especially on upper floors of buildings. Many people do notrecognize it as an earthquake. Standing motor cars may rock slightly. Vibrations similar to the passing of a

truck. Duration estimated.IV. Felt indoors by many, outdoors by few during the day. At night, some awakened. Dishes, windows, doors

disturbed; walls make cracking sound. Sensation like heavy truck striking building. Standing motor carsrocked noticeably.

V. Felt by nearly everyone; many awakened. Some dishes, windows broken. Unstable objects overturned.

MM scale

.

VI. Felt by all, many frightened. Some heavy furniture moved; a few instances of fallen plaster. Damage slight.VII. Damage negligible in buildings of good design and construction; slight to moderate in well-built ordinary

structures; considerable damage in poorly built or badly designed structures; some chimneys broken.

VIII.Damage slight in specially designed structures; considerable damage in ordinary substantial buildings withpartial collapse. Damage great in poorly built structures. Fall of chimneys, factory stacks, columns,monuments, walls. Heavy furniture overturned.

IX. Damage considerable in specially designed structures; well-designed frame structures thrown out of plumb.Damage great in substantial buildings, with partial collapse. Buildings shifted off foundations.

X. Some well-built wooden structures destroyed; most masonry and frame structures destroyed withfoundations. Rails bent.

XI. Few, if any (masonry) structures remain standing. Bridges destroyed. Rails bent greatly.

XII. Damage total. Lines of sight and level are distorted. Objects thrown into the air.

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robustness, i.e. minor differences in diagnostics should not make large differences in the

assessed intensity; further to this, the scale should be understood and used as acompromise solution, since no intensity scale can hope to encompass all the possibledisagreements between diagnostics that may occur in practice

such disagreements may also reflect differences in cultural conditions in the regions

EMS scale: main aspects

basis: MSK scale

simplicity of use

rejection of any intensity corrections for soil conditions or geomorphological effects,because detailed macroseismic observations should just be a tool for finding andelaborating such amplification effects

understanding of intensity values as being representative for any village, small town orpart of a larger town instead of being assigned to a point (for one house etc)

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need to include new types of buildings, especially those including earthquake-resistantdesign features, which are not covered by previous versions of the scale

need to address a perceived problem of non-linearity in the scale arrangement at the

junction of the degrees VI and VII (which, after thorough discussion for preparing theEMS-92, as well as for the EMS-98, proved to be illusory)

need to generally improve the clarity of the wording in the scale

need to decide what allowance should be made for includin hi h-rise buildin s for

EMS scale: problems to be solved

intensity evaluations whether guidelines for equating intensities to physical parameters of strong ground

motions, including their spectral representations, should be included

to design a scale that not only meets the needs of seismologists alone, but which alsomeets the needs of civil engineers and other possible users

to design a scale which should be suitable also for the evaluation of historicalearthquakes

need for a critical revision of the usage of macroseismic effects visible in the ground (rockfalls, fissures etc.) and the exposure of underground structures to shakings

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EMS scale (short form)I. Not feltNot felt.

II. Scarcely feltFelt only by very few individual people at rest in houses.

III. WeakFelt indoors by a few people. People at rest feel a swaying or light trembling.

IV. Largely Observed Felt indoors by many people, outdoors by very few. A few people are awakened.

Windows, doors and dishes rattle.V. StrongFelt indoors by most, outdoors by few. Many sleeping people awake. A few are frightened. Buildings

tremble throughout. Hanging objects swing considerably. Small objects are shifted. Doors and windowsswing open or shut.

VI. Slightly DamagingMany people are frightened and run outdoors. Some objects fall. Many houses suffer

- - .

VII. DamagingMost people are frightened and run outdoors. Furniture is shifted and objects fall from shelves inlarge numbers. Many well built ordinary buildings suffer moderate damage: small cracks in walls, fall of

plaster, parts of chimneys fall down; older buildings may show large cracks in walls and failure of fill-inwalls.

VIII. Heavily DamagingMany people find it difficult to stand. Many houses have large cracks in walls. A few wellbuilt ordinary buildings show serious failure of walls, while weak older structures may collapse.

IX. DestructiveGeneral panic. Many weak constructions collapse. Even wellc built ordinary buildings showvery heavy damage: serious failure of walls and partial structural failure.

X. Very DestructiveMany ordinary well built buildings collapse.

XI. DevastatingMost ordinary well built buildings collapse, even some with good earthquake resistant design

are destroyed.

XII. Completely DevastatingAlmost all buildings are destroyed.

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EMS scale: main distinguishing features Key aspects of the classification defined with a High level of detail, i.e.: building type, the

associated seismic vulnerability, damage degree, involved quantities

First scale with associated figures and photos to illustrate the meaning of damage degree

Introduction of differentiation of different types of buildings (masonry, reinforced concrete,wood, ) into vulnerability classes (A, B,, F). The vulnerability associated to a buildinghas to be identified accounting for degradation state, construction quality, plant andvertical regularity, level of seismic norms applied at the design stage.

n ro uc on o eren amage c ass ca on or eren ypes o s ruc ures, .e.

masonry and reinforced concrete

Introduction of quantity definition: few (up to 15-20%), many (from 15 to 55-60%), mostfrom 55 to 100%),

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It is made by converting instrumental ground motion parameters into pseudo-intensityvalues (Yamazaki et al 1998); so one has no idea whether a quoted intensity value for amodern Japanese earthquake actually corresponded to the description of effects for thatdegree of the scale being observed or not (Musson et al., 2010)

Sites where equal seismic intensities were observed did not necessarily suffer the samedegree of damage, since damage depends on the type of construction used and on thenature of the seismic ground motion

Seismic intensity is a value observed at a site where a seismic intensity meter is installed.

JMA scale

Seismic intensity is usually measured on the ground surface, so in general, the shaking

on upper stories of buildings may be amplified greatly

A large earthquake generates long-period seismic waves. Even at locations far from theepicenter, where the seismic intensity is rather small, the long-period waves mayoccasionally cause unusual types of damage, such as the sloshing of oil in a tank ortroubles with elevators

The scale is prepared based mainly on the examples collected from recent destructiveearthquakes. It is subject to revision when new examples are collected or the present

descriptions become inconsistent with actual situations, due to the improvement of

earthquake resistant buildings, etc.

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JMA scale

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JMA scale

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Intensity Scales conversions:

Conversions should be used with care, and checks made if at all possible. Conversion in this manner should only be used where absolutely necessary.

(From Musson et al., 2010)

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Intensity is often used in seismic hazard, since it relates directly to damageand yields hazard values, which are relevant to planners and insurers

Site classification by intensity is associated to quality and typology ofconstructions and depends on housing concentration. Therefore, a strongearthquake that strikes a desert site can be classified with a low intensitydegree, while a moderate earthquake which strikes a site with vulnerable

Notes:

buildings and causes victims is classified with a relative high intensity

degree

A magnitude scale expresses the seismic energy released by anearthquake, while an intensity scale denotes how strongly an earthquakeaffects a specific place.

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M-I relations:

0

0

aI c

aI blog h c

= +

= + +

General forms of empirical relations:

h: earthquake depth

0

21

3I= +

Empirical relationship derived by Gutemberg and Richter (1956), basedexclusively on data from Californian earthquakes:

M: Modified Mercalli-1931

I0: maximum earthquake intensity

, , ,

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M-I relations:

From Karnik, 1965

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Ground motion prediction equations(GMPEs)

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Global (based on worldwide data) or regional (developed for selected region)

Models used in engineering seismology applications to estimate the distributionof future ground-motions, to quantify the severity of an earthquake at a site withthe aim of structures design or risk assessment

Definition:

Main properties:

parameters of ground motion

Use of one measure of earthquake intensity at source: magnitude

Use of one measure accounting of effects of waves propagation from sourceto site: distance

Significant variability associated with the estimates of these equations Partly reflects the simplicity of the models

Partly reflects the inherent variability of earthquake ground-motions

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Global (based on worldwide data) or regional (developed for selected region)

Models used in engineering seismology applications to estimate the distributionof future ground-motions, to quantify the severity of an earthquake at a site withthe aim of structures design or risk assessment

Definition.:

Main properties:

parameters of ground motion

Use of one measure of earthquake intensity at source: magnitude

Use of one measure accounting of effects of waves propagation from sourceto site: distance

Significant variability associated with the estimates of these equations Partly reflects the simplicity of the models

Partly reflects the inherent variability of earthquake ground-motions

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Functional form:

The basic form is motivated by waves propagating from a point source

cRe

Y

DISTANCE DEPENDENCE:

Point source ina whole space Functional form

4 5log Y a R a log R= +

2 2R h D= +

Y: measure of the ground motion

D: measure of the source-site distance

h: pseudo-depth to be determined from the regression, correction term for distance

ai: regression coefficient which can be function of the period

with

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More com licated forms are develo ed e. .:

MAGNITUDE DEPENDENCE:

( ) ( )2

1 2 1 3 2 4 5r rlog Y a a M M a M M a R a log R= + + + +

Magnitude scaling is accounted for with a first or second order polinomial

M: earthquake magnitude

Mr1, r2: reference magnitudes to center the equation and to attemp prevention of

decreasing motion for largeM

( ) ( )( )2

26 7 6 7R D a exp a M , R D a exp a M ,= + = + + K

To accomodate saturation at close distances

Describe the INCREASE of amplitude with magnitude at a given distance

Describe the CHANGE of amplitude with distance for a given magnitude(usually, but not necessarily, a DECREASE of amplitude with increasingdistance).

NOTES:

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Site

Stile of faulting

Non linear site response

Directivity

Footwall, hanging wall

FURTHER DEPENDENCES:

Additional terms to capture further effects

as n response

( ) ( )21 2 1 3 2 4 5r r

site fault nl dir hng ba sin

log Y a a M M a M M a R a log R

f f f f f f

= + + + + +

+ + + + + +

Measure of data dispersion

logY= + K: runcertainty of the predictive relation. It is a random variable assumed with normal

distribution with null average value. The standard deviation is used to quantify the errorassociated to the average value estimated by the correlation. Intra-event standarddeviation and inter-event aleatory uncertainty can be accounted for.

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When adequate data are lacking:

Based on regression analysis of data simulation (making use of motions from

When adequate data are available:

Based on empirical approach

Derived by regression analysis of a large suite of recorded earthquake motions

Derivation:

Based on hybrid methods, capturing complex source effects from observed dataand modifying for regional differences

Basic procedure:

Dependent variable Yis calculated from available data

Starting from the adopted functional form a statistical multivariate regression (linear or

not linear) is computed as function of the independent variablesMandD

Various iterations are performed to determine the assumed coefficients (i.e. h) for which

the residual is minimum

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Measure of the ground motion:Macroseismic intensity

Peak Ground Acceleration PGA, Velocity PGV or Displacement PGD

Ordinates of acceleration Sa, velocity Svor displacement Sdresponse spectra at

a fixed period

Data origin:

World-wide

Seismotectonic environment:Shallow earthquakes in active tectonic regions

Stable continental regions

Subduction zones

American

European

Japanese

Regional

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Prediction variables:

Preferred moment magnitudeMw

Different distancemeasured are used (), although the closest distance to the

rupture surface is probably the distance most commonly used

D1: HypocentralD2: Epicentral

D3: from the most energetic zone

D4: from the source

D5: from the source projection to thesurface

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Used site classifications:

Rock/Soil

Rock: less than 5 m soil over rock (granite, limestone, etc)

Soil: everything else

Continuous variable VS30

NEHRP Site classes

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EC8 Site classes

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Main criteria of reliability:

Homogeneity of recording instruments and processing method

Influence of features of recording sites (interactions, burial depth with respect

to the ground level, as recordings at the base of buildings; in factamplification of acceleration peaks can be highlighted due to uppermost

layers of a few meters)

an are eore ca y assume n epen en var a es, w e ere s a

degree of correlation due to the fact that earthquakes with high Mare rarewith respect to those with lowMand the probability to record them at smallD

is lower

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Campbell KW & Bozorgnia Y (2008)

Boore DM & Atkinson GM (2008)

Chiou BS-J & Youngs RR (2008)

Abrahamson NA & Silva W (2008)

Some of most widely applied GMPEs:

for spectral accelerations

Next Generation of Attenuation(NGA) Relations Project

for spectral displacement (more suitable for displacement-based design

methodology)

Akkar S & Bommer JJ (2007)

Cauzzi & Faccioli (2008)

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Youngs et al. (1997)

Atkinson and Boore (2003-2008)

Zhao et al (2006)

Kanno et al. (2006)

Lin and Lee (2008)

Youn s et al. 1997

for subduction zones (both interface and inslab events)

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NGA GMPEs: comparison of median value of spectral acceleration at T=1.s

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Spectral acceleration scaling with distance

(From Campbell and Bozorgnia, 2008)

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Spectral acceleration scaling with earthquake magnitude


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Spectral acceleration scaling with site conditions

Rrup=10 km


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Spectral acceleration scaling with sediments depth

(M=7, Rrup=10 km)


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Seismic hazard in Palestina


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Earthquake hazard assessmentfor building codes (2007)


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Earthquake hazard assessment for building codes (2007)

Participants:

The Geophysical Institute of Israel, Seismology Division

Geological Survey of Israel

Haifa Technion

Israel Atomic Energy Commission

Palestinian National Authority:

An Najah National University, Nablus

UNESCO (United Nations Educational, Scientific and Cultural Organization)

Jordan:Natural Resources Authority of the Hashemite Kingdom of Jordan

Royal Scientific SocietyUSA USGS

Lawrence Livermore National Laboratory


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Earthquake hazard assessment for building codes (2007)

Main product:

Newly developed regional probabilistic seismic hazard map of peak ground

acceleration(PGA) levels that have a probability of 10% of being exceeded atleast once within a period of 50 years

development and implementation of modern building codes and regulations inJordan,Israeland thePalestinian National Authority


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it allows to take into account the uncertainties in location and magnitude ofearthquakes, their process of time occurrence and ground motion attenuation

it assumes exponential distribution of magnitude it assumes that earthquakes have no memory (Poissonoccurrence model)

Adopted method: Cornell-McGuire method (1968)

Steps of analysis:

Step 1: definition of

earthquake sourcescharacterized by uniformseismic potential

(fromReiter, 1993)

Step 2: definition of

earthquake probabilitydistribution (GR) foreach source

Step 4:definition of seismic

hazard integrating effects ofall earthquakes of differentsizes, occurring at differentlocations in differentsources at differentprobabilities of occurrence

Step 3: determinationof earthquake effectsthrough attenuationrelationships (with )


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( )

==

>=01

max

min

),|()()(r

M

M

rm

N

i

i

i

iidrdmrmzZPrfmfzE

whereE(z) = expected number of exceedances of ground motion level z during a

specified time period t

Adopted method: Cornell-McGuire method (1968)

i = mean rate of occurrence of earthquakes between lower/upper bounds

magnitude being considered for the ith source

fmi(m) = probability density distribution of magnitude within the ith source

fri(m) = probability density distribution of epicentral distance between various

locations within source ith

and the site where hazard is estimated

P(Z > z |m,r)= probability that a given earthquake of magnitude m and epicentral

distance r will exceed ground motion level z


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PROBABILISTIC SEISMIC HAZARD ANALYSIS

Classical Cornell-McGuire approach (1968)

Adopted method : SEISMOTECTONIC SETTING

EARTHQUAKE CATALOGUE AND PROCESSING

Seismogenic zones

Declustering

Completeness periods

Gutenberg-Richter recurrence relationships

Ground motion prediction equations

PGA HAZARD MAP


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Creation of a unified earthquake catalogue for the period 1900-2004:Used sources:

1) Historical earthquakeinformation from different Arabic, Islamic, Jewish and Christianhistorians who assembled descriptions of earthquakes mentioned in ancient literature

2) Lists ofhistorical earthquakesfrom revised earthquake catalogs of the region andadded after cross checking the quality and the authenticity of the data sourcespublished.

3) Instrumental data available from the beginning of the 20" century owing to theoperation of seismic stations in Egypt (HLW), Lebanon (KSR), Israel (JER, EIL) and

several tens of stations in Europe.Earthquake information for the period 1900-1982 from:

International Seismological Summary (ISS), England International Seismological Center (ISC), England National Earthquake Information Service (NEIS), USA

Compilation of Arieh et al. (1985).4) Instrumental earthquakedata from :

National seismic networks of Jordan and Israel (Since 1982 ) Israel Seismic Network-ISN (since 1980) Jordanian Seismic Network- JSN (since 1983)


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Regional seismicity:


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Homogenization of magnitude scalesMLvalues as determined by the ISN assigned to most of the events:

MLof the earthquakes recorded by JSN:

( )

( )

0 7 1 54 0 001

0 6 2 0 0015

L

L

M . . log t . R

M . log t . R

= + +

= + +

( )0 7 1 54 0 001LM . . log t . R= + +

(Modified since 1987)t: durationR: epicentral distance

ML

(Israel) correlation with seismic momentM0

Correlation between the inferredMLfromM0estimations, theML(ISN) andML(JSN),

used to unify the local magnitude:

( ) ( ) ( )00 97 0 2 16 9 0 36LM . . log M . .=

1 01 0 66LM . . M= + Jordan Israel

The correlations are valid for the magnitude range 1.0 to 5.0.For earthquakes which occurred prior to 1956 or for which local seismograms were not

available,MLequal to the given magnitude value (usuallyMS) forM~>4.8 is assumed.

1 11 0 61LM . . M= +


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Identification of seismogenic zones

Studies of seismic zonation developed in the past

Earthquake catalogue

Compiled and integrated all relevant, existing geological and geophysical information for the

region Improved seismic monitoring by the Jordanian and Israeli seismic networks, with the

resolution of mapping and kinematical analysis of fault systems and the supporting studiesin archaeo-seismology, palaeo-seismology and geodesy.

Basis data:

Catalogue of young faults in Israel and active faults

Mapped fault systems along the seismically active boundaries of the Israel-Sinai sub-plate,specifically in the Gulf of Eilat, the Gulf of Suez and in the Roum-Yamune fault system

A: Measurable seismicity clearly associated with active faults

B: Measurable seismicity associated with mapped geological structures, which have not beendefined as active in post Pliocene times

C: Measurable seismicity with no apparent association with known geological structures

D: Active faults and sporadic seismicity with no coherent relation between them

E: Active faults with no recorded seismicity associated with them

Seismic zones classification:


Id ifi i f i i

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Identification of seismogenic zones

Studies of seismic zonation developed in the past

Earthquake catalogue

Compiled and integrated all relevant, existing geological and geophysical information for the

region Improved seismic monitoring by the Jordanian and Israeli seismic networks, with the

resolution of mapping and kinematical analysis of fault systems and the supporting studiesin archaeo-seismology, palaeo-seismology and geodesy.

Basis data:

Catalogue of young faults in Israel and active faults

Mapped fault systems along the seismically active boundaries of the Israel-Sinai sub-plate,specifically in the Gulf of Eilat, the Gulf of Suez and in the Roum-Yamune fault system

A: Measurable seismicity clearly associated with active faults

B: Measurable seismicity associated with mapped geological structures, which have not beendefined as active in post Pliocene times

C: Measurable seismicity with no apparent association with known geological structures

D: Active faults and sporadic seismicity with no coherent relation between them

E: Active faults with no recorded seismicity associated with them

Seismic zones classification:


Completeness:

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Based on the availability of earthquake data and following previous studiesinformation available for the Dead Sea Rift system is complete for the followingperiods and magnitudes:

Completeness:

Estimation of mean annual rates of exceedance: MN . events M M

completeness period

> =

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Area of the Dead Sea transform system. b=0.96

Area along fault systems that are branching-off the Dead Sea Rift b=0.96

Cyprus zone b=1.07

Gulf of Suez zones b=0.98

Background seismicity b=0.96

bvalues:Seismicity of seismogenic zones


Seismicity of seismogenic zones

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Maximum magnitudesMmax:


Area of the Dead Sea transform system Mmax= 7.5

Exception for the Yamouneh fault Mmax= 7.75

Based on previous assessments

Average activity rates (N. events of M>2.0 per kilometer): 0.26(excluding the Arnona, Aragonese, Arava and the Yamunehseismogenic zones, which require further investigations)



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Faults that are branches of the Dead Sea Rift Mmax= 5.5,Mmax= 6

Based mainly on the limited seismic history and partially on the length of the mapped fault

Average activity rates (N. events of M>2.0 per kilometer): 0.05



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Faults that are branches of the Dead Sea Rift Mmax= 5.5,Mmax= 6

Carmel fault Mmax= 6.5 Background seismicity

Based on seismicity record



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Adopted seismic parameters for each zone:

y g

= 2.303b

= N. of events/year (MMmin)


Horizontal Peak Ground Acceleration Attenuation Relationship (GMPEs)

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Horizontal Peak Ground Acceleration Attenuation Relationship (GMPEs)

Adopted GMPE: Boore et al. (1997)Considered GMPEs

Following the comparison with recorded data, Boore et al. (1997) attenuation function forstrike slip faults and for Vs=620 m/s ("Generic Rock") is adopted implemented into theProbabilistic Earthquake Hazard Analysis


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Seismic hazard map:

Horizontal Peak Ground Accelerations(PGA) with a probability of 10% of being

exceeded at least once within anexposure time of 50 years.

conditions.

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Dynamics of SDOF System

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Dissipative system:

To account for the dissipation of energy, the idea is to add to the system a viscous damper

c

z

Lagrange equations:

1...nkQQq

L

q

L

dt

dKdk

kk

=+=

&

conservative world non conservative world dissipative force

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Non dissipative SDOF system

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k

m

F(t)

v

Equation of motion:

22 kv2

1V;vm

2

1T == &

)t(Fkvvm =+&&

Inertial force

Elastic force

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Definitions

Hzvibrationoffrequencynatural2

f

rad/secpulsfrequency/angularm

k

11

1

=

=

secv rat onoper onaturaf1

1=

Free vibrations:

0vv0kvvm 21 =+=+ &&&&

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The solution could be in the form:

)tsin(B)tcos(A)t(v 11 +=

With A and B defined through the initial conditions:

1B(0)v;A)0(v == &

t)(sink

Ft)(sinm

Fvvt)Fsin(kvvm 2121 ==+=+ &&&&

The solution could be in the form:

)t(v)tsin(B)tcos(A)t(v p11 ++=

solution of associatedhomogeneous eq./freevibrations

response due to appliedharmonic force

A i

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)tsin(V)t(v

)tcos(V)t(v

)tsin(V)t(v

2p

p

p

+=

+=

+=

&&

&

Assumption:

Does the assumption satisfy the equation of motion?

)tsin(k

F

)tsin(V)tsin(V2

1

2

1

2

=+++

If =0

2

1

2

222

1

212

121

2 ;1

1

k

F

k

F V)tsin(

k

F)tsin(V)tsin(V

=

=

==+

If =

2221

212

121

2

1

1

k

F

k

F V)tsin(

k

F)tsin(V)tsin(V

=

==

H

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resonance1if

phaseofoppositioninresponse)(i.e.1if

phaseinresponse)0(i.e.1if

=

=>

=

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k

mF(t)

vc

Equation of motion:

222 vc2

1D;kv

2

1V;vm

2

1T && ===

)t(Fkvvcvm =++ &&&

Inertial force

Elastic force

Dissipative force

Definition

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Definition

tcoefficiendampingkm2

c=

Free vibrations:

0vv2v0kvvcvm 2 =++=++ &&&&&&

Associated characteristic equation

02 2112 =++

1211 =

Solutions:

coniugatedandcomplexsolutions1if

coincidentandrealsolutions1if

thembetweendifferentandrealsolutions1if

I h k i i l d l i h h h 1!

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In earthquake engineering we always deal with systems that have

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Shape of the solution:

2/d

The amplitude of free vibration decreases exponentially and the distance between the peaks isconstant and equal to 2/d

The influence of free vibration after a short interval of time is attenuated in dissipativesystem, also if the dissipation is small (

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Vibrations due to an harmonic applied force:

t)cos(k

F

ss2st)(cosF(t)if

t)sin(k

Fvv2vt)(sinF(t)if

2

1

2

11

21

211

=++=

=++=

&&&

&&&

If we consider z=s+iv, the equation to study become:

ti21

211 e

k

Fzz2z =++ &&&

Where:(i) the real part of z is the response of the system to cosen excitation(ii) the imaginary part of z is the response of the system to sin excitation

Assumption:

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ti2p

tip

tip

e)(H~F)t(z

e)(H~

Fi)t(z

e)(H~

F)t(z

=

=

=

&&

&

Assumption:

Does the assumption satisfy the equation of motion?

factorionamplificattheis)N(;4)1(

1

k

1)(N)(H

~

functiontransfertheasdefinedis)(H~

;i21

1

k

1

i2k

1)(H

~

ek

F

e)(H

~

Fe)(H

~

Fi2e)(H

~

F

2222

21

221

21

ti2

1

ti2

1

ti

1

ti2

+

==

+

=+

=

=++

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N

1 increases

resonance

For damped system, also at resonance (applied frequency correspondent to natural vibrationfrequency) the amplification does not go to infinite

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)t(v)t(s)t(v)t(r)t(v 21p +=

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)t(v)t(s)t(v)t(r)t(v

0)t(v)t(s)t(v)t(r

:2Assumption

)t(v)t(s)t(v)t(r)t(v)t(s)t(v)t(r)t(v

)()()()()(

21p

21

2121p

p

&&

&&&

&&

&&&&&

+=

=+

+++=+

tvtstvtrtvtstvtrtv 2121p &&&&&&&& +++=

Substituting in the equation of motion:

( ) ( ) )t(m

Fvsvrvv2vsvv2vr 212

212121

21111 =+++++++ &&&&&&&&&&

= 0 because solution of homogeneous equation associated

=+ )t(F

vsvr &&&&

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=+

=+

0vsvr

)t(m

vsvr

21

21

&&

Solving the system:

)t(F)tsin(em

1)t(r d

t1

= &

F(t))tcos(em

1)t(s

d

t

d

1

= &

We want that r and s satisfy the initial condition:

0)0(v;0)0(v pp == &

+= d

t

dtp d)(F)sin(em1)tcos(ev11

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[ ]

=

t

d

)t(

p

d

t

0 d

d

t

0 d

d)(F)t(sinem

1v

d)(F)cos(em

1)tsin(e

)()(m)(

1

11

This integral is known as Duhamel integral or convolution integral.By solving numerically the convolution integral, the response of the system to a genericexcitation can be found.

Case of SDOF system subjected to seismic exitation

(t)

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k

m

vc

(t)

uvv2vumkvvcvm 211 &&&&&&&&&& =++=++

Equation of motion:

The peak of relative displacement, relative velocity and absolute acceleration of and SOFsystem with period of vibration T

1, is the displacement, velocity and acceleration spectral

ordinate of (t) in T=T1

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Elastic response spectrum

The simplest model used in the seismic assessment of structures is the single

degree of freedom (SDOF) oscillator

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Equation of motion

ky cy mx =& &&

( )F mx := &&

m: Oscillator massx: Mass absolute displacement

u: Ground absolute displacement

ForcesSDOF oscillator

y:x-u e a ve sp acemen

k: Recalling constant of the elastic suspension

c: Viscous constant of the damping mx cy ky mu+ + = && & &&

22 n ny y y u+ + = && & &&

n k m =

2 n cr

c c

m c = =

Introducing:

Natural vibration of the system

Damping coefficient with respectto the critic one


Oscillator motion:

For damping less than the critic one ( )1

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( ) ( ) ( ) ( )

( ) ( ) ( )0

0 0 10

nnt tt n

d d d

d d

y yy t e y cos t s en t _ u e s en t d

+ = +

&

&&

21d n = With: Damping vibration of the oscillator

RELATIVE DISPLACEMENT

( ) ( )0 0 0 0y , y= =& ( ) ( ) ( ) ( )

0

nt t

d

d

y t u e s en t d

=

&&

Duhamel integral

For structures design the maximum response value is of interest,

thus, for a given accelerogram, curves of the maximum responsesof the oscillator varying and

ncan be developed:

RESPONSE SPECTRA


Response spectra are developed as function of the oscillator natural period Tn

,

for a given

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Maximum response can be calculated in terms of relative displacement, velocityor absolute acceleration:

RELATIVE VELOCITY

ABSOLUTE ACCELERATION

( ) ( ) ( ) ( ) ( )0

nt t

d n

y t u e cos t d y t

=

& &&

( ) ( ) ( )2 2n nx t y t y t= && &

RELATIVE DISPLACEMENTRESPONSE SPECTRUM

RELATIVE VELOCITYRESPONSE SPECTRUM

ABSOLUTE ACCELERATIONRESPONSE SPECTRUM

( ) ( )n tD T , max y t = ( ) ( )n tV T , max y t = & ( ) ( )n tA T , max y t = &&


Gemona 15-09-1976

Construction of the acceleration response spectrum:

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ration(g)

Acceleration spectrum 5%

Time (s)

Time (s)Time (s)Time (s)

Spectralaccele

(modified from Faccioli, 2005)

Tn=0.15 sE.g building 2 floors

Tn=0.8 sE.g CA building 8-9 floors

Tn=2 sE.g CA building 25 floors

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For too flexible structures: nT

Notes:

Mass is not affected by soil displacement

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( ) ( ) ( ) ( ) ( ) 0y t u t , y t u t , x t =& & &&

0max max

t t tlim D s , limV v , lim A

= = =

For too rigid structures:

0n

T

( ) ( ) ( ) ( )0y t y t , x t u t= & && &&

0 maxD V , A a= = =

Soil max acceleration

No mass-soil relative displacement

Approximation not valid for flexible structures0

PSV=


Notes:

Velocity response spectrum with no damping represents the upper limit of theF i l ti t th th t t i t l h th

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Fourier acceleration spectrum, thus these two spectra approximately show thepeaks at the same frequencies. The meaning of the abscissa is different:

oscillator natural period Tn,in the first case, period Tof the single harmonic of

the signal in the second one

(From Faccioli, 2005)

S

pectralvelocity

Velocity response spectrum 5%

Fourier spectrumVelocity response spectrum 0%

S

pectralvelocity

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D, PSV, PSA Three-log representation

22log PSA log log D

= +

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2

2

n

n

log PSA log log DT

log PSV log log DT

= +

= +

VEL

OCITY:

PERIOD:

( )2

2

n

n

Tlog PSV log PSA log

Tlog PSV log D log

= +

=

Lines with inclination +1 are points

location with constant acceleration

Lines with inclination -1 are pointslocation with constant displacement


Design elastic response spectra:

In the practice, especially for normative aims, envelope spectra from statisticalanalyses are used

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analyses are used

Eurocode 8 (EC8):

Earthquake motion is represented by an elastic acceleration response spectrumTwo shapes are prescribed for two levels of seismic action:

Type 1: no collapse Type 2: damage limitation requirements

Two horizontal components are assumed independent and represented by thesame response spectrum; a different form is prescribed for the verticalcomponent


EC8 elastic acceleration response spectrum for horizontal components:

( ) ( )1 2 5 1 0T

S T a S T T

= +

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( ) ( )

( )

( )

1 2 5 1 0

2 5

2 5

e g B

B

e g B C

Ce g C D

C D

S T a S . T T T

S T a S . T T T

TS T a S . T T T T

T T

= +

=

=

=

coefficient of importanceI

:

2e g T

g

B C

D

T :

a :

T ,T :

T :

S :

:

vibration period of a linear SDOF system

design ground acceleration on ground of type A ( )

lower and upper limits of the period of the constant spectra acceleration branch

value defining the beginning of the constant displacement response range

soil factor to take into account non-linear soil response effects

damping (=1 for 5% viscous damping)

With:

Depend on ground type

g I gr a a=

acceleration on type A groundgr


Local geological-geomorphological-geotechnical conditions modify thecharacteristics of ground motion

Local site effects:

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characteristics of ground motion

Local site effects include:

- Lithostratigrafic amplification

- Topographic amplification

Path

Source

Soil layers

Bedrock

Surface morphology


Lithostratigrafic amplificationH

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Impedance effect Seismic Impedance depend on shear-wave velocity and density, which increase with

increasing depth

Seismic waves are amplified by impedance effects as they travel to the surface

Amplification due to impedance effects is frequency dependent

- ,increases with increasing frequency

Resonance effects Trapped waves reverberate due to multiple reflections

Constructive interference causes resonance, which depends on thickness of layersand elastic properties

Resonance can occur even if there are not discontinuities in seismic impedances

Resonance frequency for one layer over bedrock: f=Vs/4H Basin effects

Basins are filled by sediments, within body waves are trapped

Surface waves are generated at basin edges

Duration of shaking in basins is greatly increased

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Effects due to abrupt variations of earth surface

Topographic amplification

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Surface morphologies as slopes, trenches, ridges, crests and canyons can influencewaves propagation path and induce relevant amplifications of the seismic motion

Focalization/de-focalization of the trajectories ofpropagation of seismic waves due to reflection of

free surface in the proximity of crests

Interaction between the incident wave field and the

refracted one by the topographic irregularity


Ground types:used to account for local ground conditions

30

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30

1

30

S ,i

i ,N i

Vh

v=

=

i ih , v :Thickness and shear wave velocity of

with:

ayer n a o a o n e op m.

ForS1andS2special studies are required


Type 1 (Ms> 5.5)

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Type 2 (Ms< 5.5)

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Maximum ordinates concentrated ina narrow band at low periods

Higher values of Sfor classes B-Edue to lesser cyclic deformation(lower M), thus a more linear

dynamic response

Type 2 with respect to type 1:


( ) ( )1 3 0 1 0T

S T a T T

+

EC8 elastic acceleration response spectrum for vertical component:

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( ) ( )

( )

( )

1 3 0 1 0

3 0

3 0

ve vg B

B

ve vg B C

Cve vg C D

S T a . T T T

S T a . T T T

TS T a . T T T

T

= +

=

=

( ) 23 0 4

C Dve vg D

S T a . T T sT

=


STShould be taken into account for important structures (I> 1.0)

STis considered independent of the fundamental period of vibration, hence, multiply as ali f h di f h l i d i

EC8 topographic amplification factors ST:

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constant scaling factor the ordinates of the elastic design response spectrum

ST should be applied when the slopes belong to two-dimensional topographicirregularities, such as long ridges and cliffs of height greater than about 30 m.

STis recommended for slope angles >15o:

a)isolated cliffs and slopes: ST> 1.2 for sites near the top edge

b)ridges with crest width significantly less than the base width: ST> 1.4 near the top ofthe slopes for average slope angles greater then 30o, ST> 1,2 for smaller slope

angles

c)presence of a loose surface layer: STgiven in a) and b) increased by at least 20%

d)spatial variation of amplification factor: STmay be assumed to decrease as a linearfunction of the height above the base of the cliff or ridge, and to be unity at the base

In general, seismic amplification also decreases rapidly with depth within the ridge.Therefore, topographic effects to be reckoned with in stability analyses are largest andmostly superficial along ridge crests, and much smaller on deep seated landslides wherethe failure surface passes near to the base


( ) ( )2

2De e E

TS T S T T T

=

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( ) ( )

( )

2

0 025 2 5 1 2 5

0 025

EDe g C D E F

F E

De g C D F

T TS T . a ST T . . T T T

T TS T . a ST T T T

= +

= >

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Illustrative Example

Comparison of the time history analyses of an elastic and an inelastic SDOF system

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Where:

Ry=fel/fy : Force reduction factor (Ry in USA codes and q in EU codes)fel : Maximum restoring force that the elastic SDOF system reaches over the course

of elastic exitationfy : Yield force of the inelastic SDOF system=xm/xy : Displacement ductility

xm : Maximum displacement that the inelastic SDOF system reaches over the courseof elastic exitationxy : Yield displacement of the inelastic SDOF system

Results:

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Comparison:

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We could define an inelastic response spectrum integrating the equation of motion of an SDOFsystem that is inelastic instead of being elastic. But we would rather define rules to pass fromthe elastic spectrum to the inelastic one, since for an Engineer the starting point is the elasticresponse spectrum of the design codes.

Seismic behaviour equations:

For seismic collapse prevention, the following approximate relationship applies:

qualityof seismic behaviour strength ductility

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q y g y

To survive an earthquake different combination of strength and ductility are possible:

More realistic representation of the decision possibilities

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If the strength of the structure reduces, the stiffness typically reduces too; If the masses do not change significantly (which is typically the case), the fundamental

period T of the softer structure is longer; Structures with a longer fundamental period T are typically subjected to larger deformations,

i.e., the deformation demand is larger.

General definition of ductility

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Comments The ductility capacity is a property of the structural member; The ductility demand is a result of the seismic excitation and also a function of the

dynamic properties of the structure;

A structural member survives the earthquake if: Ductility capacity Ductility demand; The structural member collapse when locally the deformation capacity of the structural

materials (i.e., their strain capacities) are reached and exceeded. The ductility capacity istherefore exhausted.

Types of ductility

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Inleastic Responce Spectra

Inelastic responce spectra

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Force reduction factor Ry

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Suitable in the long period range Suitable in the short period range

In the equal displacement principle and the equal energy principle there are historicalRy, -Tn relationships. Also in recent years a lot of research has been done to come upwith more accurate relationships.Ry, -Tn relationships lead to the definition of behaviour factor (Ry in US codes and q inEuropean codes)

Inelastic design spectra in D (displacement) - V(velocity) A (acceleration):

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If xy

is the yield displacement:

Dy= xy; Vy=n xy; Ay=n2 xy

Newmarks inelastic design spectra (NH82):

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Maximum displacement of inelastic SDOF system:

xm = Dy

Yeld strenght of the inelastic SDOF system:fy = m Ay

Construction of the Ry, -Tn relationships:

Ay =Sa, inelastic = Sa, elastic/Ry

D =Sd, inelastic = Sd, elastic/Ry

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It should be noted that:

Sa, inelastic 2

Sd, inelastic

Ry, -Tn relationships according to NH82:

( )

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( )

principle)ntdisplaceme(equalTT cn

Inelastic design spectra according to NH82:

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Ry, -Tn relationships according to VFF94:

( )

TT1T

1 n

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( )

>

+=

principle)ntdisplaceme(equalTT

TT1T

1R

0n

0n

0

n

y

T0 = 0.65 0.3 TcTc

Tc corner period between constant Sa, elastic region and constant Sv, elastic region

Inelastic design spectra according to VFF94:

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Inelastic design spectra in ADRS format (Acceleration Displacement Response Spectra):

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Determining the response of an inelastic SDOF system by means of inelastic designspectra in ADRS format

In this section the response of two example inelastic SDOF systems is determined bymeans of inelastic design spectra in ADRS-format:

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SDOF system 1 with Tn = 0.9 s

SDOF system 2 with Tn = 0.3 s Ry, -Tn relationships according to [VFF94] will be used T = 0.5 sec

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Representation of the inelastic SDOF system 1 in the inelastic design spectrum inADRS-format:

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If the force-deformation relationship of the inelastic SDOF system is divided by its massm, the capacity curve is obtained, which can be plotted on top of the spectrum inADRS-format

The capacity curve and the inelastic spectrum intersect in the performance point

SDOF system 2

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kN471f

m011.0S

sec/m71.4S

sec3.043865

1002k

m2T

2systemSDOFelastictheofsponceRe

el

d

2a

n

=

=

=

===In this second example two differentinelastic SDOF systems will be considered:(a) a SDOF system with a rather low fy(b) a SDOF system with a rather high fy

( ) ( )n

cy

c0

y

ely

88.513.0

5.0193.31

T

T1R

sec5.0TTthatlargesois93.3ffR

a2systemSDOFinelastictheofsponceRe

=+=+=

====

( ) yc

3.0

n

c0

y

ely

1.73R1T65.0

T1

sec5.0TThencesmall,is57.1ffR

b2systemSDOFinelastictheofsponceRe

==+

=

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dym

c0.3

c3.0

0

c0

S0.0160.002788.5xx

Tsec553.05.05.8865.0T65.0T

TTifcheck

>===

>===

>

dym

c0.3

c3.0

0

c0

S0.0120.006873.1xx

Tsec383.05.01.7365.0T65.0T

TTifcheck

>===

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Design spectra are very useful tools to design structures for the expected seismicdemand. Design spectra represent the average effect of an earthquake with designintensity

,demand for a certain period range

This characteristic of design spectra should be considered when designing structures:The seismic design should aim at structures that are as robust as possible

Linear Equivalent Elastic SDOF System

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Where:

The equivalent elastic system in red is used in conjunction to the behaviour factor Ry in force

based design methods

The equivalent system in green is used in conjunction to the equivalent viscous damping eqin displacement based design methods

References[IG79] Iwan W.D., Gates N.C.: Estimating Earthquake Response of Simple Hysteretic Structures. ASCE,Journal of the Engineering Mechanics Division, Vol. 105, EM3, June 1979.[Jac60] Jacobsen L.S.: Damping in composite structures. Proceedings of the 2nd World Conference inEarthquake Engineering. Vol. 2. Tokio and Kyoto, Japan, 1960.[Jen68] Jennings P.C.: Equivalent Viscous Damping for Yielding Structures. ASCE, Journal of theEngineering Mechanics Division, Vol. 94, No. EM1, February 1968.

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Engineering Mechanics Division, Vol. 94, No. EM1, February 1968.[Mir01] Miranda E.: Estimation of inelastic defromation demands of SDOF Systems. ASCE, Journal of

structural engineering, Vol. 127, No. 9, 2001.[New59] Newmark N.M.: A Method of Computation for Structural Dynamics. ASCE, Journal of theEngineering Mechanics Division, Vol. 85, No. 3, July 1959.

Newmark N.M., Hall W.J.: Earthquake Spectra and Design. Earthquake Engineering ResearchInstitute (www.eeri.org), 1982.[PCK07] Priestley M.J.N., Calvi G.M., Kowalsky M.J.: Displacement-Based Seismic Design of Structures.

IUSS Press, 2007.[SS81] Saiidi A., Sozen M.: Simple Nonlinear Seismic Analysis of R/C Structures. ASCE, Journal of theStructural Division, Vol. 107, No. 5, May 1981.[SS76] Shibata A., Sozen M.: Substitute Structure Method for Seismic Design in R/C. ASCE, Journal of theStructural Division, Vol. 102, No. 1, January 1976.[TF99] Tolis S.V., Faccioli E.: Displacement design spectra. Journal of Earthquake Engineering vol. 3, No. 1,

1999.[TSN70] Takeda T., Sozen M.A., Nielsen N.N.: Reinforced Concrete Response to Simulated Earthquakes.ASCE, Journal of Structural Engineering, Vol. 96, No. 12, December 1970.[VFF94] Vidic T., Fajfar P., Fischinger M.: Consistent inelastic design spectra: strength and displacement.Earthquake Engineering and Structural Dynamics 23(5) 507-521. 1994.

Conceptual Seismic Design S D B S D D

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Postgraduated course Seismic Design of Building Structures - Dr. Alessandro Dazio

Uncertainty of the seismic action

Earthquakescharacteristics

Structuralresponse

Free

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Site effect

field

2

Consequences

Structuralresponse

Damage

Seismicsource

Wave

propagation

seismic

input

General characteristics of the buildings

It is almost impossible to exactly predict which seismic action a structure will undergoduring its life time. For this reason the structure should be conceived to allowsignificant variations of the loading function without failing

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significant variations of the loading function without failing.

To ensure a good seismic performance, a building should be ductile and easilytransfer the lateral forces to the ground without reaching excessive deformations.

The conceptual design is crucialin earthquake engineering

General characteristics of the buildings

Structural simplicity

easier to understand, predict and build

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Regularity, symmetry and continuity

in plan and elevation

Flexural strength and stiffness along two orthogonal directions

Torsional strength and stiffness

In-plane strength and stiffness of the floors

Adequate foundation

A good seismic building has to be robust!

Adequate structural systems

Moment resisting frames

System comprising beams rigidly connected to columns. Applicable to steeland reinforced concrete structures.

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System with single or coupled walls The horizontal forces are totally carried by reinforced concrete or masonry

(reinforced!) walls. Other structural elements carry vertical loads only.

5

Dual systems

Reinforced concrete frames coupled with reinforced concrete or masonry(reinforced!) walls. The horizontal forces are shared by the different structuralelements.

Trusses with centric or eccentric braces

Popular for tall steel structures

Example of moment resisting frames

x3.3

5m

T7

6

5

5 m 5 m 5 m 5 m

5m

5.5m 0.60x060

0.65x0.400.62x0.35

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7

x

43

2

5.5

5.5m

Columns Beams

No. story = 1 - 3: bxh > ca. 40x40 cm Span 6x6 m: hxb = ca. 50x35 cm

No. story = 3 - 6: bxh > ca. 50x50 cm Span 8x8 m: hxb = ca. 75x40 cm

No. story = 6 - 10: bxh > ca. 60x60 cm h including the floor

6 x 5.5 m = 33 m 4 x 5.0 m = 20 m

4m

PT

15.5m

0.43x0.300.50x0.35

U. Yazgan Example of moment resisting frames

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7

H. Bachmann H. Bachmann

8 x 6m =48m

Example of system with single or coupled walls

Dimensions

Coupling beamsh = ~ 60-100cm

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6m=

48

m

2.8m

28.9m tw = 0.25 0.40 m

8x

4m

8.2m

4m

6m6.5m2

.5m

5.0m 5.0m1.0m

0.6

3.7m

5.0m 5.0m

1.0m

w w .

Foundation!!!


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H. Bachmann


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Seismic retrofit of the childrens hospital in Aarau (ag=0.1g) using RC coupled walls with

diagonal reinforcement in the coupling beams

M. Koller

Dual systems

Tube in Tube system

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ElevationClassic dual system

Plan

9.2

m

9.2m

7 frames + 2 wallswall transversalframes

secundary beamslongitudinalframes

Trusses with centric or eccentric braces

Childrens hospital in Brig (ag=0.2g)Seismic retrofit using ductile steel trusses.

P. Tissiers

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12Eccentric joint with shear connectors

Use compact plan configurations!

Unfavorable better

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13

BWG

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Avoid eccentric bracing systems!

Past earthquakes have shown that structureswith eccentric bracing systems perfom poorly,however ...

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BWG

T. Wenk

... structures with eccentric bracing

systems keep being built!

Avoid ground soft-storey!

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!!! MOST POPULAR CAUSE OF SEISMIC FAILURE !!!The structural system is reduced at the ground floor to increase use friendliness of

commercial spaces.

BWG

Avoid ground soft-storey!

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P. Lestuzzi, K. Thiele

T. Wenk

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Avoid soft-storey!

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BWG BWG

BWG

Avoid irregular systems in elevation

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BWG BWG

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Pay attention to masonry infills!

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Structural or non-structural infills?

Design of the frames!

BWG


Strong frame weak infill

Weak frame Strong infill

Structural infills

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BWG

BWG


Flexible joint10 - 40mm

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Non-structural infills=

Non structural elements

BWG

Proper design of non-structural elements

Non-structural elements are expensive and can be damaged very easily

Because of the seismic acceleration

Because of the seismic deformations

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The failure of non-structural elements can be dangerous

Mechanical effects

Emissions

Indirect consequences

Damage due to acceleration

Ceilings

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Facades Parapets BWG

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Fasten installations and equipment

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BWG

Design installationson time

No! BWG

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31

No!

No!

Ni

Important structures

can be isolated

Salt Lake City

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Separate the building

from the ground

Dynamic Model for 2-DoF Isolated System

ks2s ====

Frequencies

Naeim F., Kelly J.: Design of Seismic Isolated Structures.John Wiley & Sons, 1999.

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ms

M

m

mm

m

b

====++++

==== 2s

2b

====

b

b2b

mm

k

++++====

Important Ratios:

Example masonry bldgPostgraduated course Seismic Design of BuildingStructuresDr. Alessandro Dazio

Building

Modal mass 893 t

Mass basement 250 t

Stiffness ks 130589 kN/m

Period T1 0.52 s (f1=1.92Hz)

= 0.78

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Dampers:

40 pieces: 30x30x10 cm

Stiffness kb 36000kN/m

0.2

Damping b 0.10Damping cb 1281 t/s

Acceleration spectra ( = 0.8 , = 0.2)

3.0

4.0

rationSa

[m/s2

]EarthquakeBase shear coefficient

Earthquake for TH

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2.0

ler

0.0

1.0

0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00

Period Ts[s]

Spectra

lAcce

Displacement spectra ( = 0.8 , = 0.2)

0.10

0.15

cem

entSd[m] Earthquake

Relative displacement Damper

Relative displacement Building

Earthquake for TH

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lac

T=0.52s

36

0.00

0.05

0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00

Period Ts [s]

SpectralDisp

8.7mm

16.4mm23.5mm

42mm

0.01

0.02

0.03

men

t[m]

Building no damperBuilding with damper

Damper

Time-history analysis (SAP2000)

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m

-0.03

-0.02

-0.01

0 5 10 15 20

Time [s]

Displac

400

500

600

700

arF

[kN]

Building

Pushover curve of the masonry building

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a

0

100

200

300

0.000 0.005 0.010 0.015 0.020 0.025

Displacement [m]

Ba

seSh

F

Capacity spectrum method

2.0

3.0

4.0

lera

tionSa

[m/s

2] Earthquake

Demand on the isolated buildingCapacity of the Building

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el

0.0

1.0

0.00 0.05 0.10 0.15

Spectral Displacement [m]

SpectralAc

Fajfar P.: CAPACITY SPECTRUM METHOD BASED ON INELASTIC DEMAND SPECTRA.Earthquake Engng. Struct. Dyn. 28, 979-993 (1999)

The masonry building would clearly fail

under the design earthquake?The isolated masonry building would survive thedesign earthquake experiencing only minor damage

Close collaboration between Architect and engineerfrom the earliest planning stage!

The seismic behavior of structures is extremely complex (cyclic, non-linear, dynamic) and the

forces in play are huge!

Even the most sophisticated design methods cant compensate for conceptual mistakes!

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Even the most sophisticated design methods can t compensate for conceptual mistakes!

Capacity design and displacement based design principle cant be use on conceptually wrong

structures!

The serial design is typically inefficient because it yields unsatisfactory solutions (structural

and non-structural) at extra costs!

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IntroductionThere are 2 philosophy for seismic analysis:

Force-based design methods Force-based procedures are currently the most used design methods in practice, and

corresponding provisions are widely available in almost all design codes worldwide. For this reason in most of this section force-based procedures are discussed in order to

ensure their meaningful application in design practice. However, force-based procedures are affected by several drawbacks that should beknown in order to avoid serious mistakes

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known in order to avoid serious mistakes.

Displacement-based design methods The intensive development of displacement-based design procedures started about 10 to

15 years ago. Such procedures are very promising, however they are still mostly confined to the

academic environment. In many cases the use of displacement-based design procedures in practice require the

engineer to deviate from current code provisions and take full responsibility for that.

However, in the near future they will find more and more space in design codes. Hence itis important to be aware of some principles of displacement based design method andthey will be given in this lecture

Force Based Design Method

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Force Based Design Method

Overview of Force Based Design MethodEquivalentlateral forcemethod

Responsespectrummethod

Non linearstatic analysis

Non lineal timehistoryanalysis

DynamicModel

Linear SDOFsystem

Linear MDOFsystem

Non linear SDOFsystem

Non linearMDOF system

Material Model Linear Linear Non linear Non linear

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---vibrationconsidered

mode only mode only

Considerationof material nonlinearities

Q-factor Q-factor Non lineal model Non linear model

Seismic action Design spectrum Design spectrum Design spectrum Time history

Typicalapplication

Design Design Assessment Design/Assessment

Effort Low Medium Medium High

Overview of Structural Dynamic

SDOF Systemua absolute displacementu relative displacementug ground displacementk stiffness

c dampingm mass

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umkuucum0kuucum ga &&&&&&&&

=++=++

The equilibrium equation is:

Relative equations Effective earthquake force

This equation is a second order inhomogeneous differential equation and can be solved

analytically for simple excitations (harmonic). For seismic excitation, it is typically solvednumerically either solving the Duhamel integral or integrating with a numerical method theequation of motion

MDOF System

M mass matrixK stiffness matrixC damping matrix (usually defined as a combination of M and K)1 unitary vector

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uuif gg &&&&&&&&&&&&&&

1MKuuCuM1uu0KuuCuM aa =+++==++

The equilibrium equation is:

Background on mode of vibrationFree vibration of non dissipative MDOF systems:

0KuuM =+&&

Let us express the solution as:

n..1i(t)q)t(u ii ==

Substitutin in the e uation of motion:

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Substitutin in the e uation of motion:

0)t(q)t(q)t(q

)t(qgsinpo

)t(q

)t(q)t(q)t(q

22 =+=

==+

&&&&

&&&& KM0KM

The solution like for the SDOF system is of the type:

)t(sinR)t(q +=

Substituting in the equation of motion:

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Important outcome!

The equation of motion of the original system is transformed in n equation of motion ofSDOF systems, with n the number of degree of freedom of the MDOF system

If the system is dissipative, but tC is diagonal (this is certainly the case when C isexpressed as C=M+K) what is true for the non dissipative MDOF system is valid also forthe dissipative one

n can be less than the number of degree of freedom of the system, because if n is big

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enough, the modes above n do not contribute to the response of the system

Modal equation of motion:

gii2iiiii

facorionpartecipatalmod

g

iti

ti

i2iiiii uqq2quqq2q

iti

ti

i

&&&&&&&&&& =++

=++

=

M

1MM1M

If we define the effective modal mass like:

systemtheofmasstotalmmmmn

itot

*

enoughbigisnif

*2i

*

effi,ieffi,= =

Criterion toselectthe n of vibrationmodes toconsider

Equivalent lateral forces

It is a simple linear static analysis method allowed by almost all design codes worldwide. The dynamic action of the earthquake on the structure is replaced by lateral static forces

called equivalent lateral forces. The methods can be applied to structural systems which can be represented by two 2D

structural models, and which behaviour is not substantially influenced by higher modes of

vibration. Criteria for regularity shall be met

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Higher vibration modes are neglected. The fundamental period of vibration of the building can be estimated by means of simple

equations or by means of a proper structural model. The second option is recommended.

Torsional effects are taken into account in an approximate way (e.i. increasing the forces toaccount for torsion)

The inelastic behaviour of the structure is also taken into account in an approximate waythrough inelastic design spectra.

F = mtot Sa (T1,, q, f)total equivalent lateral force

mtot : total mass of the buildingSa : spectral value taken from the design acceleration spectrum at the fundamental period ofthe building T1; the spectrum is computed assuming a damping ratio and a behaviour factorq. Additional parameters, like e.g. the importance factor f can be taken into account whilecomputing the spectral ordinate : Correction factor ranging between 0.85 and 1.0. Some codes (e.g. EC8) use to account

for the fact that in buildings with at least three storeys and translational degrees of freedom ineach horizontal direction, the effective modal mass is about 85% of the total mass.

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F shall be distributed along the building height ( )

=

=

=ni

1j

jj

ii'ni

hm

hmFFF

Fi , mi, hi: equivalent lateral force, mass andheight on floor iFn: special single force acting at the top of thebuilding. Some codes use this force to increase

the shear force in the upper storeys and thebending moment at the base

Modeling issues

1) Substitute beam

The simplest structural mod

Modulus 1

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