response spectrum skj
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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)
Sudhir K. Jain Slide 4February 2012
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(Martinez-Pereira, 1999)
Maximum Recorded Motion
Sudhir K. Jain Slide 5February 2012
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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
Sudhir K. Jain Slide 6February 2012
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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
Sudhir K. Jain Slide 7February 2012
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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)
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9/42Sudhir K. Jain February 2012 Slide 9
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
Sudhir K. Jain Slide 10February 2012
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12/42Sudhir K. Jain February 2012 Slide 12
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
Response Spectrum (contd)
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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Sudhir K. Jain February 2012 Slide 16
Response Spectrum (contd)
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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Sudhir K. Jain February 2012 Slide 18
Response Spectrum (contd)
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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Sudhir K. Jain February 2012 Slide 19
Response Spectrum (contd)
Unless otherwise mentioned, response spectrumis based on a linear elastic system
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Sudhir K. Jain February 2012 Slide 20
Response Spectrum (contd)
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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Sudhir K. Jain February 2012 Slide 21
Response Spectrum (contd)
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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Sudhir K. Jain February 2012 Slide 22
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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Sudhir K. Jain February 2012 Slide 23
Response Spectrum (contd)
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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Sudhir K. Jain February 2012 Slide 24
Response Spectrum (contd)
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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Sudhir K. Jain February 2012 Slide 25
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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Sudhir K. Jain February 2012 Slide 26
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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Sudhir K. Jain February 2012 Slide 27
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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Sudhir K. Jain February 2012 Slide 28
Ground Acceleration
ZPA stands for Zero Period Acceleration.
Implies max acceleration experienced by astructure having zero natural period (T=0).
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Sudhir K. Jain February 2012 Slide 29
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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Sudhir K. Jain February 2012 Slide 30
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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Sudhir K. Jain February 2012 Slide 31
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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Sudhir K. Jain February 2012 Slide 32
What is Design Spectrum
Seismic Design Force can be specified in termsof Response Spectrum:
Termed as Design Spectrum
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Sudhir K. Jain February 2012 Slide 33
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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Sudhir K. Jain February 2012 Slide 36
Design Spectrum (contd)
Natural vibration period Tn, sec
SpectralAccelera
tion,g
Fig. from Dynamics of Structures by Chopra, 2001
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Sudhir K. Jain February 2012 Slide 37
Design Spectrum (contd)
Design Spectrum is a design specification It must take into account any issues that have
bearing on seismic safety.
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Sudhir K. Jain February 2012 Slide 38
Design Spectrum (contd)
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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Sudhir K. Jain February 2012 Slide 40
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