response spectrum skj

7/31/2019 Response Spectrum SKJ

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1

Strong Ground Motion and Conceptof Response Spectrum

February 2012

Sudhir K Jain, IIT Gandhinagar

Sudhir K. Jain February 2012


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Strong Ground Motions Near-field ground motions

Usually accelerations

Engineers

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0 10 20 30 40 50 60 70 80

Acc

n.

(g)

PGA=0.32g

Time (seconds)

EQ Ground Motions

Sudhir K. Jain Slide 3February 2012


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Peak Ground Parameters

Acceleration (PGA) Velocity (PGV)

Displacement (PGD)



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(Martinez-Pereira, 1999)

Maximum Recorded Motion



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Parameters

Duration of Significant Shaking Frequency Content

0 10 20 30 40 50 60

0.5g

Time (sec)

1985 Mexico Earthquake (SCT 1A; N90E)

1940 Imperial Valley Earthquake (El Centro; S00E)

1971 San Fernando Earthquake (Pacoima Dam; N76W)

1991 Uttarkashi Earthquake (Uttarkashi, N75E)

Characteristics



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Influence of Magnitude of EQ

Source mechanism

Type of faulting

Distance from source

Soil/rock medium along travel path

Local soil site, geology, topology, etc.,. Attenuationwith Distance

Fault

Fault

Characteristics



8/42Sudhir K. Jain February 2012 Slide 8

Accelerogram

During ground shaking, one can measureground acceleration versus time (accelerogram)using an accelerograph

Accelerograph is the instrument

Accelerogram is the record obtained from it Accelerogram is the variation of ground acceleration with

time (also calledtime history of ground motion)



Typical Accelerograph

This is a typical analog instrument. These days, digital instruments arebecoming popular (photo from Earthquakesby Bolt)


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TypicalAccelerograms

From Dynamics of Structuresby A K Chopra, Prentice Hall

Time, sec



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Response Spectrum (contd)

Using a computer, one can calculate theresponse of SDOF system with time (timehistory of response)

Can pickmaximum response of this SDOF

system (of given T and damping) from thisresponse time history

See next slide


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Sudhir K. Jain February 2012 Slide 14


Repeat this exercise for different values ofnatural period.

For design, we usually need only the maximumresponse.

Hence, for future use, plot maximum responseversus natural period (for a given value ofdamping).

Such a plot of maximum response versusnatural period for a given accelerogram is calledresponse spectrum.


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Response Spectrum is useful to obtain maximumresponse of any SDOF system for thataccelerogram and for that value of damping.

See example on next slide


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May repeat the entire process for different values ofdamping

Velocity response spectrafor N-S component of 1940El Centro record (dampingvalues of 0, 2, 5 and 10%)

Fig From Housner, 1970Natural Period T (sec)

MaximumV

elocity,in/sec


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Unless otherwise mentioned, response spectrumis based on a linear elastic system


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By response we may mean any responsequantity of interest to us, for example: Absolute acceleration of the mass

Termed asAcceleration Response Spectrum

Relative velocity of the mass with respect tobase Termed asVelocity Response Spectrum

Relative displacement of the mass with respectto base Termed asDisplacement Response Spectrum

Word Spectra is used to denote plural ofSpectrum.


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Since SDOF system responds maximum to thewaves of frequency near its own naturalfrequency,

Response spectrum is also a very good way to

characterize the strong ground motion fromengineering view point.

For instance, relative strength of low frequency versus highfrequency waves

See example on next slide


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Example: Velocity spectra from two accelerograms

Note that the two response spectra above show very different frequency content. Groundmotion B has more energy at low periods. An expert may be able to make out from thesespectra that B is recorded at a short distance (say 15km) from a small earthquake, while Ais recorded from a large earthquake at a large distance (say 100km) (Fig. edited fromHousner, 1970)

Natural Period T (sec)

Velocity,

ft/sec


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Response spectrum is a very powerful tool. Uses of response spectrum:

To obtain maximum response of a SDOF system(to the original accelerogram using which

response spectrum was obtained) To obtain maximum response in a particular

mode of vibration of a multi degree of freedom(MDOF) system

It tells about the characteristics of the groundmotion (accelerogram)


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Different terms used in IS:1893 Design Acceleration Spectrum (clause 3.5)

Response Spectrum (clause 3.27)

Acceleration Response Spectrum (used in cl.

3.30) Design Spectrum (title of cl. 6.4)

Structural Response Factor

Average response acceleration coefficient (seeterminology of Sa/g on p. 11)

Title of Fig. 2: Response Spectra for .

It is better if the code uses the termconsistently.


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Smooth Response Spectrum

Real spectrum has somewhat irregular shapewith local peaks and valleys

For design purpose, local peaks and valleysshould be ignored

Since natural period cannot be calculated withthat much accuracy.

Hence, smooth response spectrum used fordesign purposes

For developing design spectra, one also needsto consider other issues We will discuss this later.


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Smooth Response Spectrum (contd)

Acceleration Spectra Velocity Spectra Displacement Spectra

Shown here are typical smooth spectra used in designfor different values of damping

(Fig. from Housner, 1970)

Period (sec)Period (sec) Period (sec)


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Ground Acceleration (contd...)

Note the term Peak Ground Acceleration(PGA) is max acceleration of ground.

Because of deformation in the structure, themotion of its base and the superstructure will be

different Max acceleration experienced by mass of the

structure will be different from the PGA (except ifthe structure is rigid)


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Ground Acceleration

ZPA stands for Zero Period Acceleration.

Implies max acceleration experienced by astructure having zero natural period (T=0).


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Zero Period Acceleration

An infinitely rigid structure Has zero natural period (T=0)

Does not deform:

No relative motion between its mass and its base

Mass has same acceleration as of the ground

Hence, ZPA is same as Peak GroundAcceleration

For very low values of period, acceleration

spectrum tends to be equal to PGA.

We should be able to read the value of PGAfrom an acceleration spectrum.


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Peak Ground Acceleration (contd)

Average shape of acceleration responsespectrum for 5% damping (Fig. on next slide) Ordinate at 0.1 to 0.3 sec ~ 2.5 times the PGA

There can be a stray peak in the ground motion;

i.e., unusually large peak. Such a peak does not affect most of the

response spectrum and needs to be ignored.

Effective Peak Ground Acceleration

(EPGA) defined as 0.40 times the spectralacceleration in 0.1 to 0.3 sec range (cl. 3.11) There are also other definitions of EPGA, but we

will not concern ourselves with those.


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Typical shape of acceleration spectrum

Typical shape of acceleration response spectrum

Spectral acceleration at zero period (T=0) gives PGA

Value at 0.1-0.3 sec is ~ 2.5 times PGA value (for 5% damping)

PGA = 0.6g0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

1.60

1.80

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5

Period (sec)

Sp

ectralAcceleration(g)


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What is Design Spectrum

Seismic Design Force can be specified in termsof Response Spectrum:

Termed as Design Spectrum


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Response Spectrum versus Design Spectrum

Consider the Acceleration Response Spectrum Notice the region of red circle marked: a slight

change in natural period can lead to largevariation in maximum acceleration

Undamped Natural Period T (sec)SpectralAcceleration,g


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Design Spectrum (contd)

Natural vibration period Tn, sec

SpectralAccelera

tion,g

Fig. from Dynamics of Structures by Chopra, 2001


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Design Spectrum is a design specification It must take into account any issues that have

bearing on seismic safety.


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Design Spectrum must be accompanied by:

Load factors or permissible stresses that must beused

Different choice of load factors will give different seismicsafety to the structure

Damping to be used in design Variation in the value of damping used will affect the design

force.

Method of calculation of natural period

Depending on modeling assumptions, one can get differentvalues of natural period.

Type of detailing for ductility

Design force can be lowered if structure has higher ductility.


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Soil Effect (contd)

This variation in ground motion characteristic fordifferent sites is now accounted for through differentshapes of response spectrum for three types of sites.

SpectralAccele

rationCoefficient(S

a/g)

Period(s)

Fig. fromIS:1893-2002


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Design Spectrum for Stiff Structures

For very stiff structures (T < 0.1sec), ductility is not helpful in

reducing the design force.

Actual shape of response spectrum(may be used for higher modes only)

T(seconds)

S

pectralacceleration

Design spectrum assumes peakextends to T=0

Concept sometimes used by the codes forresponse spectrum in low period range.

As a stiff structure getsdamaged during theshaking, its periodelongates i.e., during the same

ground shaking, a verystiff structure may rideup the ascending partof the graph.

Codes tend todisallow the reduction

in force in the periodrange of T < 0.1sec

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