Introduction to Seismic Design

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ESDEP WG 17

SEISMIC DESIGN

Lecture 17.2: Introduction to Seismic

Design - Seismic Hazard and Seismic

Risk

OBJECTIVE/SCOPE

To give an introduction to seismicity, seismic hazard, seismic risk, and seismic measures.

PREREQUISITES

None.

RELATED LECTURES

None.

SUMMARY

The lecture introduces seismicity, explaining the origins of earthquakes and summarises theircharacteristics in both general and engineering terms. The need for probabilistic assessments is

demonstrated and the concept of response spectra is introduced. The basic approaches for design

against earthquakes and Eurocode 8[1] are presented.

1. INTRODUCTION

Among the natural phenomena that have worried human kind, earthquakes are without doubt themost distressing one. The fact that, so far, the occurrence of earthquakes has been unpredictable,

makes them especially feared by the common citizen, for he feels there is no way to assure aneffective preparedness.

The most feared effects of earthquakes are collapses of constructions, for they not only usuallyimply human casualties but represent huge losses for individuals as well as for the community.

Thus, although other consequences of earthquakes may include landslides, soil liquefaction and

tsunamis, it is the aim in this lecture to study seismic motion from the point of view of the

natural hazard it poses to construction, and particularly to steel structures.
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The fundamental goals of any structural design are safety, serviceability and economy.

Achieving these goals for design in seismic regions is especially important and difficult.

Uncertainty and unpredictability of when, where and how a seismic event will strike acommunity increases the overall difficulty. In addition, lack of understanding and ability to

estimate the performance of constructed facilities makes it difficult to achieve the above

mentioned goals.

The future occurrence of earthquakes can be regarded as a seismic hazard, whose consequences

represent what can be defined as seismic risk. The separate study of these two concepts isimportant. The first represents the action of nature and the second the effects on mankind and

man-made structures.

2. THE SEISMIC EVENT

2.1 General

The knowledge and study of past seismic events is an important way of predicting the potentialseismic hazard for the different zones of the earth. Earthquakes have been reported as far back as

during the Babylonian Empire or in 780 BC in China.

A region which has suffered large earthquakes (Figure 1) is the circum-Pacific belt includingNew Zealand, the Tonga and New-Hebrides Archipelagos, the Philippines, Taiwan, Japan, the

Kurile and Aleutian Isles, Alaska, the western coasts of Canada and the United States, Mexico,

all the countries in Central America and the western coast of South America from Colombia toChile. Other regions of the world that also have been subject to devastating earthquakes in the

past are the northern and eastern zones of China, northern India, Iran, the south of the Arabian

Peninsula, Turkey, all the southern part of Europe including Greece, Yugoslavia, Italy and

Portugal, the north of Africa and some of the Caribbean countries.


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Worldwide, the most devastating seismic event which has ever happened is believed to be the1556, January 23rd earthquake in the Shaanxi Province of China. That earthquake may have

caused more than half a million casualties. More recently, two other Chinese provinces, the

Ningxia province in 1920 and the Hebei province in 1976, were hit by earthquakes that may have

caused several hundreds of thousands of dead.

In Europe, earthquakes are reported as far back as 373 BC in Helice, Greece. Other catastrophic

earthquakes in Europe occurred in 365, 1455 and 1626 in Naples, 1531 and 1755 in Portugal,

1693 in Sicily, 1783 in Calabria and 1908 in Messina. Each one of these earthquakes is believed

to have caused between 30000 and 60000 deaths. Even if these figures are not totally reliable,

they give a dimension of the consequences or the risk that may result from the seismic hazard insome European countries.

These major earthquakes have each caused not only a large number of human casualties due to

the collapse of houses and other buildings, but also have caused huge economical losses which in

some cases took long periods to recover. The large losses, human and economic, that can beexpected from the occurrence of future earthquakes justify special attention being given to the

study of earthquake phenomena and the earthquake hazard.


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2.2 Origins of Earthquakes

Earthquakes have their origin in the sudden release of accumulated energy in some zones of theearth's crust and the resulting propagation of seismic waves.

Wegener introduced the concept of continental drift to explain the origin of the continents, andwhy the earth's crust is divided into interacting plates. The zones of the earth where most

earthquakes are generated are at the boundaries of the plates. Earthquakes occur in some casesdue to subduction movements between two plates, as is the case of the Pacific plate which moves

underneath the South American continent, and in other cases due to sliding movements between

the two plates, as is the case of San Andreas fault in California. In Southern Europe the boundarybetween the African and the Euroasiatic plates is responsible for some very large earthquakes, as

for example the 1755 earthquake that destroyed most of the city of Lisbon.

Other zones where earthquakes occur are at the faults in the intraplate regions, due to the

accumulation of strains caused by the pressures in the plate's boundaries. Most of the Chinese

earthquakes are generated in the intraplate region. In Europe a similar region is involved for mostof the southern part of the continent but also for some other central and northern areas.

The point or the zone at which the earthquake slip first occurs is commonly designated as the

focus or hypocentre. The earthquake focus is usually at a certain depth, known as the focal depth.

The intersection of a vertical line through the focus with the ground surface is known as theepicentre (Figure 2). Obviously the most affected zones are the ones closer to the focus, showing

that distance to the epicentre (or hypocentre) is a significant factor of seismic hazard.


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The sudden release of energy at the focus generates seismic waves that propagate through therock and soil layers. There are three basic types of seismic waves; P waves, S waves and surface

waves which include the Love and Rayleigh waves. The difference of velocity between the P and

the S waves allows, by means of the difference in the arrival time, the determination of the

hypocentral distance. Typical velocities of P and S waves vary from 100m/sec for S waves inunconsolidated soils (300m/sec for P waves) to 4000m/sec for S waves in igneous rocks

(7500m/sec for P waves).

2.3 Earthquake Characteristic

The "size" of the earthquake or what could be seen as a seismic scale is a very important factor

for a correct characterization of its potential hazard. Intensity and magnitude are two different

means of "measuring" an earthquake which are often confused by the media.

The concept of magnitude which was first introduced by Richter and which still carries his name,

represents a measure of the earthquake that is supposed to be independent of the location at

which the measurement is obtained. It is related to the amplitude of the seismic waves corrected

with respect to distance. It represents a universal measure of the size of the earthquake,


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independently of its effects. Although there is no maximum value for the magnitude of an

earthquake, the two largest magnitudes ever observed correspond to the 1906 earthquake off the

coast of Ecuador and the 1933 earthquake off the Sanriku coast in Japan with magnitudes of 8,9.The 1755 earthquake, off the coast of Portugal, is believed to have been the largest earthquake in

Europe with a magnitude of 8,6.

The magnitude of an earthquake can be related to other physical measures of earthquakes such as

the total released energy, the length of the fault rupture, the fault rupture area and the fault

slippage or relative displacement suffered between the two sides of the fault. Severalrelationships have been proposed by different authors. The ones presented here are merely an

indication of the types of relationships. More accurate expressions can probably be presented for

different seismic zones. Approximate relationships between magnitude (M), total energy (E inergs), fault rupture length (L in meters), fault rupture area (A in Km

2) and fault slippage

displacement (D in meters) are:

Log E = 9,9 + 1,9 M - 0,024 M2

M = 1,61 + 1,182 log L

M = 4,15 + log A

M = 6,75 + 1,197 log D

The relationship between energy and magnitude shows that an earthquake of magnitude 8

releases as much as about 37 times the energy released by a magnitude 7 earthquake. The sameobservation can be made for the relationships between magnitude and measures of the fault,

showing that an increase of one degree in the Richter scale corresponds to a considerable

increase in terms of seismic hazard.

A different way of measuring an earthquake, has been adopted, based on a scale initiallyproposed by Mercalli and later modified, known as the Modified Mercalli Intensity (MMI).

According to this scale (Table 1), which varies between I and XII, the intensity of an earthquake

is dependent on the observed effects on landscape, structures and people at a given site. Thus, theintensity is variable from place to place and relies on a subjective appreciation of the earthquake

consequences. An approximate correspondence between MMI and ground acceleration, a

parameter which will be further discussed, is presented in Table 1.

Table 1 Modified Mercalli Intensity (MMI) Scale Peak ground acceleration

(m sec-2

)

I Not felt by people. < 2,5 x 10-3

2,5 x 10-3

- 0,005II Felt only be a few persons at rest, especially on upper floors of buildings.

III Felt indoors by many people. Feels like the vibration of a light truck passing by. Hanging objects swing. May notbe recognised as an earthquake.

IV Felt indoors by most people and outdoors by a few. Feels like the vibration of a heavy truck passing by. Hangingobjects swing noticeably. Standing automobiles rock. Windows, dishes, and doors rattle; glasses and crockery


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clink. Some wood walls and frames creak. 0,005 - 0,010

0,010 - 0,025

0,025 - 0,05

V Felt by most people indoors and outdoors; sleepers awaken. Liquids disturbed, with some spillage. Small objectsdisplaced or upset; some dishes and glassware broken. Doors swing; pendulum clocks may stop. Trees and poles

may shake.

VI Felt by everyone. Many people are frightened; some run outdoors. People move unsteadily. Dishes, glassware, andsome windows break. Small objects fall off shelves; pictures fall off walls. Furniture may move. Weak plaster andmasonry D cracks. Church and school bells ring. Trees and bushes shake visibly.

0,05 - 0,10

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, corners, unbraced parapets, and architecturalornaments fall from buildings. Damage to masonry D; some cracks in masonry C. Waves seen on ponds. Smallslides along sand or gravel banks. Large bells ring. Concrete irrigation ditches damaged.

0,10 - 0,25

VIII General fright; signs of panic. Steering of vehicles is affected. Stucco falls; some masonry walls fall. Sometwisting and falling of chimneys, factory stacks, monuments, towers, and elevated tanks. Frame houses move onfoundations if not bolted down. Heavy damage to masonry D; damage and partial collapse on masonry C. Somedamage to masonry B, none to masonry A. Decayed piles break off. Branches break from trees. Flow ortemperature of water in springs and wells may change. Cracks appear in wet ground and on steep slopes.

0,25 - 0,5

IX General panic. Damage to well-built structures; much interior damage. Frame structures are racked and, if notbolted down, shift off foundations. Masonry D destroyed; heavy damage to masonry C, sometime with completecollapse; masonry B seriously damaged. Damage to foundations, serious damage to reservoirs; underground pipesbroken. Conspicuous cracks in the ground. In alluvial soil, sand and mud is ejected; earthquake fountains occur andsand craters are formed.

0,5 - 1,0

X Most masonry and frame structures destroyed with their foundations. Some well-built wooden structures andbridges destroyed. Serous damage to dams, dikes, and embankments. Large landslides. Water is thrown on banksof canals, rivers, and lakes. Sand and mud are shifted horizontally on beaches and flat land. Rails bent slightly.

1,0 - 2,5

XI Most masonry and wood structures collapse. Some bridges destroyed. Large fissures appear in the ground.Underground pipelines completely out of service. Rails badly bent.

2,5 - 5,0

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

5,0 - 10,0

1. At intensity I there may be effects from very large earthquakes at considerable distance in the form of long-period motion. These effectsinclude disturbed birds and animals, swaying of hanging objects, and slow swinging of doors, although people will not feel the shaking and willnot recognize the effects as being caused by an earthquake.

2. Each earthquake effect is listed in the table at the level of intensity at which it appears frequently. It may be found less frequently or lessstrongly at the preceding (lower) level and more frequently and more strongly at higher levels.

3. The quality of masonry or brick construction was categorized by Richter (1956) as follows:

Masonry AGood workmanship, mortar, and design; reinforced, especially laterally, and bound together by using steel, concrete, etc: designed to resistlateral forces.

Masonry BGood workmanship and mortar; reinforced, but not designed in detail to resist lateral forces.

Masonry COrdinary workmanship and mortar; no extreme weaknesses like failing to tie in at corners, but neither reinforced nor designed againsthorizontal forces.

Masonry DWeak materials, such as adobe; poor mortar; low standards of workmanship; weak horizontally.


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Figure 3 represents a map of the maximum observed intensities in Europe, which is based on the

recollection of the effects of past earthquakes, and thus can already be looked at as a measure of

seismic risk.

The duration of ground motion is another parameter of great interest when assessing the seismic

hazard for a given seismic environment. Although there is no single definition for the duration of

an earthquake, all the most commonly used definitions agree as a rule that the duration of an

earthquake at a given site increases with the magnitude, epicentral distance, and the depth of thesoil above bed-rock. The duration of an earthquake is a very important parameter especially


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when assessing the non-linear response of structures. The accumulation of structural damage,

which is related to the non-linear behaviour of the structure and may lead to structural failure,

can be highly affected by the total time a structure is subjected to strong ground motion. Anearthquake with a given magnitude may represent a smaller hazard than an earthquake with a

smaller magnitude but larger duration or even than a series of smaller magnitude earthquakes.

All the possible measures of an earthquake that have been presented so far, are of limited interest

from the engineering point of view. The relationships that have been established between the

different parameters are not deterministic and involve a great amount of uncertainty andvariability. On the other hand, they relate more to the physical aspects of the seismic source and,

except for the Mercalli Intensity which is determined based on subjective judgement, do not take

into account the site characteristics and the hypocentral or epicentral distance.

The need for an engineering characterization of the seismic motion, justifies the use ofalternative parameters, such as the maximum ground acceleration or peak ground acceleration

(ag) observed during the ground motion at a given site. The maximum acceleration has been

observed to be statistically dependent on the magnitude of the earthquake. Hence it is dependenton the severity of the seismic source, and is also highly dependent on the distance to theepicentre and on the soil characteristics and other local site conditions. Figure 4 shows the type

of relationship that exists between agand distance for different earthquake magnitudes.


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Approximate relationships exist between the Richter Magnitude, the Modified Mercalli Intensity

and agobserved in the epicentral zone. However these relationships are very dependent on

several other parameters such as the local soil conditions and even on the type of seismic source.

Instruments are available that measure the movements of the ground due to earthquakes. Some

instruments measure the ground displacements and are called seismographs. To measure theground accelerations, other type of device exist, called accelerographs. The accelerographs

register the accelerations of the soil and the record obtained is called an accelerogram. A typical

accelerogram is represented in Figure 5, showing the peak ground acceleration (ag).

Knowing, for a given earthquake and site, the accelerations in three orthogonal directions, it is

possible to evaluate the response of a structure when subjected to that specific earthquake.

But for a given site, there may be more than one potential seismic source and from a given

source earthquakes with different magnitudes, durations and peak ground accelerations mayoccur. In addition, even for the same earthquake, accelerograms obtained in different locations

may vary substantially, depending on the local site conditions. The geometry and properties of

the soil have been shown in past earthquakes to have a large influence on the characteristics ofthe accelerogams obtained. Thus, the accelerograms obtained from past earthquakes have to be

used with special care. They may not correctly represent the ground accelerations of future

events.

The knowledge of the seismic ground motion is an essential aspect of the characterization of the

seismic hazard. Access to accelerograms from different earthquakes, in different seismicenvironments, for several magnitudes and epicentral distances, in different soil conditions gives a

unique basis for characterizing the ground motion and determining its most influential parameter.

Arrays of strong ground motion accelerographs have been used in the last decade allowing amore reliable estimate of the earthquake motion. Thus a probabilistic assessment of the

earthquake input is obtained for use in engineering applications.


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Among the aspects that are investigated with arrays of ground motion accelerographs are the

influence of the type of seismic action, hypocentral distance, wave propagation path, orientation

of the site with respect to the fault line, local soil conditions and local topography.

During the lifetime of a structure there is a certain probability that it may be subjected to one or

more earthquakes. The probability depends on the seismic environment and on the period forwhich the structure is to function. The probability that an earthquake with a large magnitude, and

consequently with large agvalues, occurs during the lifetime of a structure, is smaller than the

probability of occurrence of smaller earthquakes. The number of earthquakes (N) having amagnitude (M) or greater per year, can be estimated by means of recurrence formulae of the

type.

log N = a - b M

where a and b are parameters depending on local conditions.

For each seismic zone, and based on past seismic events, recurrence formulae can be obtained,giving the annual probability of occurrence of earthquakes with a certain magnitude, or the

return period of occurrence of an earthquake with a given magnitude. As the magnitude can be

related with ag, these types of relationship give the return period of occurrence of a certain level

of ground acceleration. According to the time period to be adopted, which depends on the levelof risk to be accepted, the corresponding agvalue can be determined. This agvalue, is the peak

ground acceleration that will be exceeded with a given probability, necessarily very small, and

thus assuming a certain level of seismic risk.

Differences between past and future ground accelerations will exist not only in terms of themaximum observed values (ag) but also in terms of the frequency content. Thus, another aspect

that has to be examined in any study of seismic hazard, is the frequency content of theearthquake records. The fourier transform, the spectral density function or power spectrum and

the response spectrum are different ways to characterize an accelerogram in the frequencydomain. It should be noted that Eurocode 8 recommendations allow the use of accelerograms,

power spectra or response spectra to define the seismic motion for structural analysis purposes.

The last approach will be discussed here because it is the simplest approach of those available

which have direct application to structural analysis.

2.4 Response Spectrum

The response spectrum of a given earthquake record is the representation of some maximum

response quantity of a damped, linear, single degree of freedom system as a function of thenatural frequency of that system.


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For example, for the system shown in Figure 6, with mass m, stiffness k, (velocity dependent)

damping c, ground displacement dg, and displacement of the mass relative to the ground d r, theequation of motion can be written in the form

m (dg'' + dr'') + cdr'' + kdr= 0

or

mdr'' + cdr' + kdr= - mdg''

This equation of relative displacement is the same as that for a mass with fixed base subjected to

a horizontal force -mdg''. Introduction of the natural frequency of the undamped system =

, the natural period of the undamped system T = 2/, and the damping ratio = c/2m,gives

dr'' + 2dr' + 2dr= -dg''

with the solution

dr = -exp (-p,t)/D dg''() exp [D(t - )] sin D(t - ) d,

di= exp (-Dt)/D dg() exp [D(t - )] sin D(t - ) d,

where

D= (1 - 2) is the natural frequency of the damped system.


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=1 corresponds to the critical damping ccr= 2 .

For a given accelerogram, i.e. given dg'', the maximum of dr, for a given value of , can bedetermined for each D. Usually the value = 0,05 is used as a reference value and a correctionfactor for damping ratios different from 5% is introduced.

A typical acceleration response spectrum for three damping ratio values is shown in Figure 7.

The two parameters that most influence the shape of the response spectrum, or its frequency

content, are the type of earthquake and the local soil conditions. The influence of these twoparameters on the shape of the spectrum arises from the phenomenon of resonance. In reality the

fact that a certain earthquake has a predominance of energy centred in a given frequency range

will cause the response spectrum to have larger amplitudes in that same frequency range. Twoaspects that may lead to different spectra are the distance of the site to the seismic source and the

characteristics of the local soil. Large hypocentral distances tend to diminish the high frequency

components of the local ground motion. Soft soils also tend to amplify the low frequency

components of the ground motion, whereas for hard soils the high frequency components areamplified.

In the past, it has been observed that similar structures subjected to the same earthquakes show a

quite different seismic behaviour because of the local soil conditions. In the 1967 Caracas,

Venezuela earthquake, it was observed that damage to buildings was not uniform throughout thecity. Tall buildings with foundations on soft thick soil layers showed much more damage than

the same type of building with foundations on stiffer soils. The opposite was observed for low-

rise buildings; they showed more damage for foundations on the stiffer soils. This observation

showed that the same earthquake motion can be filtered in a different way by two distinct soils.


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Thus the seismic input into a structure may vary according to the local soil conditions. The

interaction between the ground motion and the structural characteristics is thus of great

importance in the evaluation of the seismic response of structures and the associated seismic risk.

3. EARTHQUAKE INPUT FOR STRUCTURAL DESIGN

The fact that, for a given earthquake source and site, there have been no observed earthquakes

with a magnitude, intensity, or peak ground acceleration larger than certain values, does notmean that larger values will not be observed in future. Thus, the maximum possible or probable

values have to be derived using a probabilistic approach. Furthermore, if one derives

probabilistic maximum values for earthquakes that may occur during a certain future period oftime, the values will differ from the ones relating to a different period of time. The return period

of an earthquake with given characteristics, can be defined as the inverse of the annual

probability of occurrence of that event. The larger the seismic event, the larger the corresponding

return period as shown by the recurrence formulae already presented.

If the earthquake for which the structure has to be designed and its return period are known, andif the period for which the structure is designed is also known, the probability of the structure

being subjected to the earthquake during its lifetime can be determined. Evaluating this

probability is a matter of assessing a parameter of seismic risk. To evaluate the global seismicrisk, one should combine this type of information with the information regarding the single

probability of collapse or malfunctioning of the structure if designed according to certain levels

and standards of resistance and ductility.

Different earthquakes lead to dissimilar response spectra. Not only different maximum values ofthe ground acceleration (ag) lead to different maximum spectrum values, but also different

accelerograms will result in dissimilar shapes of spectra even with the same ag. So, the use of

response spectra to characterize a certain potential seismic event, has to take into account theinfluence of important aspects such as the nature and distance of the seismic source and thecharacteristics of the soil.

For these reasons, the evaluation of response spectra for design purposes must include a

probabilistic study of the seismic occurrences. The study will define the maximum ground

acceleration and the shape of the spectra to be considered, for each seismic source and eachdifferent kind of soil. This definition is usually obtained by statistical means. The spectra used

for design purposes, and the spectra presented in regulations are usually the smoothed graphs of

the maximum credible values of the corresponding spectra, for a certain level of risk acceptance,

in terms of seismic origin and local soil conditions, obtained for different earthquakes.

The different levels of risk acceptance are also related to the importance of the structure to be

designed. The catastrophic consequences arising as a result of collapse or malfunctioning of

important buildings and other structures, such as hospitals, fire stations, power plants, schools,

dams, main bridges, etc. requires design to a lower level of risk than for normal structures. Thislower level is achieved by designing these structures to a larger earthquake return period and

consequently to higher values of seismic input. This approach corresponds to designing them to a

lower probability of damage and collapse in the event of future earthquakes.


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Similarly, different levels of probability of occurrence of earthquakes can also be used for

different design philosophies. For regular structures, the choice of an earthquake level with a

very low probability of being exceeded is usually associated with a design aimed at avoidingstructural collapse, and thus human casualties, even if the structure undergoes major damage and

has to be rebuilt. For earthquake levels with higher probability of occurrence, and that may thus

occur more often during the lifetime of the structure, the design goal is not to avoid collapse butrather to guarantee that no substantial damage occurs and that the structure maintains itsserviceability.

Usually, the response spectra are presented in normalized form, as is the case of the normalized

elastic response spectrum of Eurocode 8. It is normalized to the peak ground acceleration (a g),

i.e. it is independent of agand so can be used for different values of the maximum expectedacceleration for the site. This approach allows for the use of the same spectra for different

conditions of severity of the ground motion. In other words, it enables the consideration of

earthquakes corresponding to different return periods and thus to different acceptance of seismic

risk.

According to Eurocode 8 and other national regulations, the elastic response spectrum to be usedfor design purposes depends on several parameters such as the seismic zone, the type of seismic

action, the local soil conditions and the viscous damping ratio of the structure.

The seismic zone can be characterized by means of the severity of the seismic action. This

characterization is accomplished by normalizing the response spectra to a certain level of a g.Usually, the response spectrum for the vertical motion is defined as a percentage of the response

spectrum for the two orthogonal horizontal directions. In Eurocode 8 the suggested percentage is

70%.

The maximum acceleration to be used in each region in Europe is defined according tomicrozonation studies for each zone, depending on the local seismic hazard parameters. It is the

responsibility of the National Authorities.

The normalized elastic response spectrum e(T) (Figure 8) is defined by means of fourparameters, o, T1T2and k, according to the following expressions:

0 < T < T1e(T) = 1 + T/T1(o- 1)

T1< T < T2e(T) = o

T2< T e(T) = (T2/T)k

o

where

T is the natural vibration period of the structure, or the inverse of the natural frequency (Hz)

ois the maximum value of the normalised spectral value assumed constant for periods betweenT1and T2


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k is an exponent which influences the shape of the response spectrum for vibration periods larger

than T2.

The values of the transition periods T1and T2, also known as the inverses of the corner

frequencies, depend essentially on the magnitude of the earthquake and on the ratios between the

maximum ground acceleration, ground velocity and ground displacement.

The basic values presented in Eurocode 8 [1] apply to the ground motion at bedrock or in firm

soil conditions. If the soil characteristics differ from the ones considered, other values for theparameters can be chosen in such a way that the shape of the response spectrum is modified

accordingly. Eurocode 8 considers three different soil profiles (A, B and C). For each soil profile

different parameters (o, T1T2and k) apply. The local response spectrum, s(T), can beobtained, correcting the elastic response spectrum by a soil parameter S, which is also dependent

on the soil profile.

s(T) = S e(T)

Although the basic form of the response spectrum is uniform, and is common to the designers in

every European Community country, the parameters that define the response spectrum are also

the responsibility of each National Authority. The parameters can vary from region to region


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even in a single country. This variation is due to the fact that each European region has different

seismicity.

The ovalue is the maximum spectral amplification. It is dependent on the selected probabilityof being exceeded for the considered peak ground acceleration, on the damping ratio, on the

duration of the ground motion, and on its frequency content. According to Eurocode 8, for a 20to 30 second earthquake and 5% damping, the value of o= 2,5 corresponds to a probability ofnot being exceeded of between 70 and 80% [1].

The exponent k is dependent on the frequency content and the selected probability of being

exceeded. It describes the shape of the response spectrum for the higher periods (lowerfrequencies).

The use of the elastic response spectrum, simultaneously with linear elastic design, does not take

into account the capability of a structure to resist seismic actions beyond the elastic limit. If it

can be assumed that the structure will behave linearly for small earthquakes, for larger

earthquakes it would be almost impossible and non-economical to design structures based on theassumption of linear behaviour. For larger earthquakes it should be assumed that the structure

has a certain capacity to dissipate the energy input by the earthquake by means of non-linear

behaviour, even if that implies the existence of structural damage although guaranteeing thatcollapse is avoided.

Thus, for design purposes, and to avoid the necessity of performing non-linear analysis, the

concept of structural behaviour factor (q) is introduced, to correct the results obtained by linear

analysis and obtain an estimate of the non-linear response. These behaviour factors, which will

be presented in more detail in other lectures, take into account the energy dissipation capacitythrough ductile behaviour. Thus they are dependent on the materials, type and characteristics of

the structural system and the assumed ductility levels. Eurocode 8 defines the q values to beadopted in the case of steel structures according to criteria that will be presented in later lectures.

Based on the q factors, it is possible to define the linear analysis design response spectra that canbe used for design purposes by means of linear analysis.

The linear analysis design response spectra is defined in Eurocode 8 as follows:

0 < T < T1(T) = S [1 + T/T1(o/q - 1)]

T1< T < T2(T) = S o/q

T2< T (T) = (T2/T)kS o/q

where

T, o, T1, T2and k have the same meaning as above.

is the ratio of the peak ground acceleration to the acceleration of gravity.


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earthquakes may be used. There are several alternative methodologies for generating artificial

earthquakes. The only constraint is that the generated histories shall be consistent with the

response spectrum corresponding to the case under study. The same applies to the use of powerspectra to represent the seismic action.

As a final observation on the characterization of the seismic motion, the effects of the spatialvariability of the seismic motion should be considered. The seismic input may be different from

support to support. The differences are due to several factors such as the overall dimensions of

the structure, the large distances between two supports of the same structure, or the fact that astructure may have different foundation conditions, both in terms of soil or foundation types. In

this case a spatial model of the seismic action has to be used, taking into account a model of the

wave propagation.

4. FINAL REMARKS

The social consequences of earthquakes, in terms of human casualties and injuries and direct and

indirect economic losses justify the need to be prepared for earthquakes. Earthquakes are stilldifficult to predict and, even if they could become predictable, would pose a threat to buildings

and other structures. Thus, being prepared for earthquakes consists mainly in proper structural

design procedures for seismic loading. To achieve a correct design procedure and thus diminishthe seismic risk, it is necessary in the first place, to have a correct knowledge of the seismic

input, or the seismic hazard. Simultaneously with the study of the behaviour of structures when

subject to seismic loading it is thus fundamental to study the seismic motion, its origin, and the

parameters that most influence the characteristics of the motion.

5. CONCLUDING SUMMARY

Earthquakes are natural phenomena that have caused tremendous losses of lives andgoods worldwide including in some large areas of Europe.

To design structures that can resist earthquakes requires an understanding of the seismichazard.

"Measuring" the earthquake can be achieved by means of different parameters such asmagnitude, intensity, peak ground acceleration, power spectrum and response spectrum.Parameters that influence the characteristics of the earthquake motion and its response

spectrum are the duration and frequency content of the motion and the local soil

conditions.

The response spectrum approach presented in Eurocode 8 which can be used forstructural design takes into account a probabilistic approach of the definition of the

seismic motion [1].

6. REFERENCES

[1] Eurocode 8: "Structures in Seismic Regions - design", Commission of the European

Communities, Report EUR 12266, 1989.


20/20

7. ADDITIONAL READING

1. Clough, R. W. and Penzien, J., Dynamics of Structures,

McGraw-Hill - International Student Edition, 1975.

2. Gere, J. M. and Shah, H. C., Terra Non Firma - Understanding and preparing for

earthquakes, Stanford Alumni Association, Stanford, USA, 1984.

3. Catalogue of European earthquakes with intensities higher than 4,

Commission of the European Communities, Report EUR 13406, 1991.

4. Dowrick, D. J., Earthquake Resistant Design, Wiley and Sons, 1987.

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Introduction to Seismic Design

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