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Strong Ground Motion and Concept of Response Spectrum
March 2013
Sudhir K Jain, IIT Gandhinagar
Sudhir K. Jain March 2013
EQ Ground Motions
Low Amplitude Vibrations
Long distance events
Usually displacements
Earth Scientists
0 200 400 600 800 1000 1200
Am
pli
tud
e
Time (s)
Teleseismic Earthquake Recording
P PP S Surface Waves
Sudhir K. Jain Slide 2 March 2013
2
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
Ac
cn
. (g
)
PGA=0.32g
Time (seconds)
EQ Ground Motions…
Sudhir K. Jain Slide 3 March 2013
Peak Ground Parameters
Acceleration (PGA)
Velocity (PGV)
Displacement (PGD)
Sudhir K. Jain Slide 4 March 2013
3
(Martinez-Pereira, 1999)
Maximum Recorded Motion
Sudhir K. Jain Slide 5 March 2013
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 6 March 2013
4
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.,. Attenuation with Distance
Fault
Fault
Characteristics
Sudhir K. Jain Slide 7 March 2013
Sudhir K. Jain March 2013 Slide 8
Accelerogram
During ground shaking, one can measure ground 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 called time history of ground motion)
5
Sudhir K. Jain March 2013 Slide 9
Typical Accelerograph
This is a typical analog instrument. These days, digital instruments are becoming popular (photo from Earthquakes by Bolt)
Typical Accelerograms
From Dynamics of Structures by A K Chopra, Prentice Hall
Time, sec
Sudhir K. Jain Slide 10 March 2013
6
Sudhir K. Jain March 2013 Slide 11
Response Spectrum (contd…)
If the ground moves as per the given accelerogram, what is the maximum response of a single degree of freedom (SDOF) system (of given natural period and damping)?
Response may mean any quantity of interest,
e.g., deformation, acceleration
T=2 sec,
Damping =2%
Ground motion time history Time, sec
a(t)/g
Sudhir K. Jain March 2013 Slide 12
Response Spectrum (contd…)
Using a computer, one can calculate the response of SDOF system with time (time history of response)
Can pick maximum response of this SDOF system (of given T and damping) from this response time history
See next slide
7
Sudhir K. Jain March 2013 Slide 13
Time, sec
a(t)/g
Response Spectrum (contd…)
Ground motion time history
Time History of Deformation (relative displacement of mass with respect to base) response
Maximum response = 7.47 in.
T=2 sec,
Damping =2%
Time, sec
d(t)
Sudhir K. Jain March 2013 Slide 14
Response Spectrum (contd…)
Repeat this exercise for different values of natural period.
For design, we usually need only the maximum response.
Hence, for future use, plot maximum response versus natural period (for a given value of damping).
Such a plot of maximum response versus natural period for a given accelerogram is called response spectrum.
8
Sudhir K. Jain March 2013 Slide 15
Time, sec
ag(t)/g
Response Spectrum (contd…)
Displacement Response Spectrum for the above time history
Time, sec
d(t)/g
d(t)/g
d(t)/g
T=0.5 sec =2%
T=1.0 sec =2%
T=2.0 sec =2%
dm
ax
T, sec Figure After Chopra, 2001
Sudhir K. Jain March 2013 Slide 16
Response Spectrum (contd…)
Response Spectrum is useful to obtain maximum response of any SDOF system for that accelerogram and for that value of damping.
See example on next slide
9
Sudhir K. Jain March 2013 Slide 17
Example
Ground Acceleration Time History
Acceleration Response Spectrum for the above accelerogram for 5% damping (Fig. from Seed and Idriss, 1982)
Mass = 10,000kg
Natural Period T=1 sec
Damping =5% of critical
From Response Spectrum:
Spectral Acceleration (for T=1sec) = 0.48 g
Max. Base Shear = Mass x Spectral Accln. =(10,000kg) x (0.48x9.81m/sec2) = 47,000 N = 47 kN
Max. Base Moment
=(47kN) x (3m) = 141 kN-m
3m
Undamped Natural Period T (sec)
Time (sec)
Maxim
um
Acc
ele
ration, g
Acc
ele
ration, g
Sudhir K. Jain March 2013 Slide 18
Response Spectrum (contd…)
May repeat the entire process for different values of damping
Velocity response spectra for N-S component of 1940 El Centro record (damping values of 0, 2, 5 and 10%)
Fig From Housner, 1970 Natural Period T (sec)
Maxim
um
Velo
city
, in
/sec
10
Sudhir K. Jain March 2013 Slide 19
Response Spectrum (contd…)
Unless otherwise mentioned, response spectrum is based on a linear elastic system
Sudhir K. Jain March 2013 Slide 20
Response Spectrum (contd…)
By response we may mean any response quantity of interest to us, for example: Absolute acceleration of the mass
Termed as Acceleration Response Spectrum
Relative velocity of the mass with respect to base
Termed as Velocity Response Spectrum
Relative displacement of the mass with respect to base
Termed as Displacement Response Spectrum
Word Spectra is used to denote plural of Spectrum.
11
Sudhir K. Jain March 2013 Slide 21
Response Spectrum (contd…)
Since SDOF system responds maximum to the waves of frequency near its own natural frequency,
Response spectrum is also a very good way to
characterize the strong ground motion from
engineering view point.
For instance, relative strength of low frequency versus high frequency waves
See example on next slide
Sudhir K. Jain March 2013 Slide 22
Example: Velocity spectra from two accelerograms
Note that the two response spectra above show very different frequency content. Ground motion B has more energy at low periods. An expert may be able to make out from these spectra that B is recorded at a short distance (say 15km) from a small earthquake, while A is recorded from a large earthquake at a large distance (say 100km) (Fig. edited from Housner, 1970)
Natural Period T (sec)
Velo
city
, ft
/sec
12
Sudhir K. Jain March 2013 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 ground
motion (accelerogram)
Sudhir K. Jain March 2013 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 (see terminology of Sa/g on p. 11)
Title of Fig. 2: Response Spectra for ….
It is better if the code uses the term consistently.
13
Sudhir K. Jain March 2013 Slide 25
Smooth Response Spectrum
Real spectrum has somewhat irregular shape with local peaks and valleys
For design purpose, local peaks and valleys should be ignored Since natural period cannot be calculated with
that much accuracy.
Hence, smooth response spectrum used for design purposes
For developing design spectra, one also needs to consider other issues We will discuss this later.
Sudhir K. Jain March 2013 Slide 26
Smooth Response Spectrum (contd…)
Acceleration Spectra Velocity Spectra Displacement Spectra
Shown here are typical smooth spectra used in design for different values of damping
(Fig. from Housner, 1970)
Period (sec) Period (sec) Period (sec)
14
Sudhir K. Jain March 2013 Slide 27
Ground Acceleration (contd...)
Note the term Peak Ground Acceleration
(PGA) is max acceleration of ground.
Because of deformation in the structure, the
motion of its base and the superstructure will be
different
Max acceleration experienced by mass of the
structure will be different from the PGA (except if
the structure is rigid)
Sudhir K. Jain March 2013 Slide 28
Ground Acceleration
ZPA stands for Zero Period Acceleration.
Implies max acceleration experienced by a
structure having zero natural period (T=0).
15
Sudhir K. Jain March 2013 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 Ground Acceleration
For very low values of period, acceleration
spectrum tends to be equal to PGA.
We should be able to read the value of PGA
from an acceleration spectrum.
Sudhir K. Jain March 2013 Slide 30
Peak Ground Acceleration (contd…)
Average shape of acceleration response spectrum 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 spectral acceleration 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.
16
Sudhir K. Jain March 2013 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 = 0.6g 0.00
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)
Spectr
al A
ccele
ration (
g)
Sudhir K. Jain March 2013 Slide 32
What is Design Spectrum
Seismic Design Force can be specified in terms of Response Spectrum:
Termed as Design Spectrum
17
Sudhir K. Jain March 2013 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 large variation in maximum acceleration
Undamped Natural Period T (sec)
Spect
ral Acc
ele
ration, g
Sudhir K. Jain March 2013 Slide 34
Response Spectrum versus Design Spectrum (contd…)
Natural period of a civil engineering structure cannot be calculated precisely
Design specification should not very sensitive to a small change in natural period.
Hence, design spectrum is a smooth or average shape without local peaks and valleys you see in the response spectrum
18
Sudhir K. Jain March 2013 Slide 35
Design Spectrum
Since some damage is expected and accepted in the structure during strong shaking, design spectrum is developed considering the overstrength, redundancy, and ductility in the structure.
The site may be prone to shaking from large but distant earthquakes as well as from medium but nearby earthquakes: design spectrum may account for these as well.
See Fig. next slide.
Sudhir K. Jain March 2013 Slide 36
Design Spectrum (contd…)
Natural vibration period Tn, sec
Sp
ectr
al A
ccel
erat
ion
, g
Fig. from Dynamics of Structures by Chopra, 2001
19
Sudhir K. Jain March 2013 Slide 37
Design Spectrum (contd…)
Design Spectrum is a design specification
It must take into account any issues that have bearing on seismic safety.
Sudhir K. Jain March 2013 Slide 38
Design Spectrum (contd…)
Design Spectrum must be accompanied by:
Load factors or permissible stresses that must be
used
Different choice of load factors will give different seismic safety 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 different values of natural period.
Type of detailing for ductility
Design force can be lowered if structure has higher ductility.
20
Sudhir K. Jain March 2013 Slide 39
Soil Effect
Recorded earthquake motions show that response spectrum shape differs for different type of soil profile at the site
Period (sec)
Fig. from Geotechnical Earthquake Engineering, by Kramer, 1996
Sudhir K. Jain March 2013 Slide 40
Soil Effect (contd…)
This variation in ground motion characteristic for different sites is now accounted for through different shapes of response spectrum for three types of sites.
Sp
ectr
al A
ccel
erat
ion
Coef
fici
ent
(Sa /
g)
Period(s)
Fig. from IS:1893-2002
21
Sudhir K. Jain March 2013 Slide 41
Shape of Design Spectrum
The three curves in Fig. 2 have been drawn based on general trends of average response spectra shapes.
In recent years, the US codes (UBC, NEHRP and IBC) have provided more sophistication wherein the shape of design spectrum varies from area to area depending on the ground motion characteristics expected.
Sudhir K. Jain March 2013 Slide 42
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)
Sp
ectr
al a
ccel
erat
ion
Design spectrum assumes peak extends to T=0
Concept sometimes used by the codes for response spectrum in low period range.
As a stiff structure gets damaged during the shaking, its period elongates
i.e., during the same ground shaking, a very stiff structure may ride up the ascending part of the graph.
Codes tend to
disallow the reduction
in force in the period
range of T < 0.1sec