Transcript RESPONSE SPECTRUM

UNDERSTANDING
RESPONSE SPECTRUM
&
PROVISIONS OF BNBC-2014
OUTCOME
AT THE END OF THIS TRAINING/WORKSHOP/DISCUSSION YOU WILL
UNDERSTAND:

WHAT IS AN EARTHQUAKE RESPONSE SPECTRUM

RESPONSE SPECTRUM AS PER BNBC/14, AND

HAVE A DISCUSSION GROUP TO SHARE YOUR IDEAS
AND CONFUSIONS
CONTENT
PART – I
UNDERSTANDING EARTHQUAKE RESPONSE SPECTRUM
PART – II RESPONSE SPECTRUM PROVISION OF BNBC/2014
PART – III : GROUND MOTION SIMULATION
RECAP - STRUCTURAL DYNAMICS
EQUATION OF MOTION
Summing forces along the x-axis is p(t) - fS – fD –fI = 0
EQUATION OF MOTION (Earthquake Excitation)
Single-Degree-of-Freedom System
NATURAL PERIOD OF VIBRATION
n 
Tn 
k
m
2
n

fn  n
2
rads/sec
sec
cps (Hz)
DAMPED FREE VIBRATION
EFFECT OF DAMPING ON FREE VIBRATION
DAMPED FREE VIBRATION
EFFECT OF DAMPING ON THE NATURAL VIBRATION FREQUENCY
PART - I
UNDERSTANDING RESPONSE SPECTRUM
ORIGIN OF THE RESPONSE SPECTRUM METHOD
• Response Spectrum Method began in 1932, in the doctoral dissertation of M.A. Biot (1905–
1985)
• The RSM remained in the academic sphere of research for many years and did not gain
widespread engineering acceptance until the early 1970s.
• First, the computation of the response of structures to earthquake ground motion led
to “certain rather formidable difficulties” (Housner 1947), and,
• second, there were only a few well-recorded accelerograms that could be used for that
purpose.
• Then, in 1971, with the occurrence of the San Fernando, California, earthquake, the modern
era of RSM was launched. This earthquake was recorded by 241 accelerographs, and by
combining these data with all previous strong-motion records it became possible to
perform the first comprehensive empirical scaling analyses of response spectral amplitudes
(Lee 2002).
TIME HISTORY DATA
 THE MOST DIRECT DESCRIPTION OF AN EARTHQUAKE
MOTION IN TIME DOMAIN IS PROVIDED BY
ACCELEROGRAMS THAT ARE RECORDED BY INSTRUMENTS
CALLED STRONG MOTION ACCELEROGRAPHS.
 THE ACCELEROGRAPH RECORDS THREE ORTHOGONAL
COMPONENTS OF GROUND ACCELERATION AT A CERTAIN
LOCATION.
 THE PEAK GROUND ACCELERATION, DURATION, AND
FREQUENCY CONTENT OF EARTHQUAKE CAN BE OBTAINED
FROM AN ACCELEROGRAMS. AN ACCELEROGRAM CAN BE
INTEGRATED TO OBTAIN THE TIME VARIATIONS OF THE
GROUND VELOCITY AND GROUND DISPLACEMENT.
TIME HISTORY DATA
El Centro ground motion (N-S Component)
May 18, 1940
http://peer.berkeley.edu/smcat/
http://db.cosmos-eq.org/scripts/default.plx
Time, sec
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16
0.18
0.20
0.22
0.24
0.26
0.28
0.30
Acceleration, g
0.00630
0.00364
0.00099
0.00428
0.00758
0.01087
0.00682
0.00277
-0.00128
0.00368
0.00864
0.01360
0.00727
0.00094
0.00420
0.00221
TIME HISTORY DATA
0.4
ug,g
0.2
0
0
-0.2
2
4
6
8
10
12
14
Time, sec
16
18
20
22
24
26
28
30
-0.4
FOR EARTHQUAKE EXCITATION – i. ANALYTICAL SOLUTION IS NOT POSSIBLE; ii.
NUMERICAL METHODS ARE EMPLOYED TO FIND OTHER QUANTITIES LIKE a.
VELOCITY; b. DISPLACEMENT ETC. DIFFERENT NUMERICAL METHODS ARE:

CENTRAL DIFFERENCE METHOD

AVERAGE ACCELERATION METHOD

NEWMARK’S METHOD ETC.
32
TIME HISTORY DATA ANALYSIS
(Sa)2
Response Acceleartion
T1
T2,h1
T1,h1
Time
(b)
Acceleration
(a)
h0
h1
h2
T2
(c)
(Sa)3
Period(s)
T3
T3,h1
Peak Acceleration
(Sa)1
RESPONSE SPECTRUM
(d)
DEFORMATION RESPONSE SPECTRUM
VELOCITY RESPONSE SPECTRUM
Plot of V vs. TN
ACCELERATION RESPONSE SPECTRUM
 Plot of A vs. TN
COMBINED D-V-A SPECTRUM
A
 V  n D
n
Tn
2
A V 
D
Tn
2
RESPONSE SPECTRUM CHARACTERISTICS
Response spectrum ( = 0,2,5, and
10%) and peak values of ground
acceleration, ground velocity, and
ground displacement for El Centro
ground motion.
RESPONSE SPECTRUM CHARACTERISTICS
Response spectrum for El Centro
ground motion plotted with
normalized scale A/ϋgo , V/ůgo , and
D/ugo ;  = 0, 2 , 5 and 10%.
RESPONSE SPECTRUM CHARACTERISTICS
Response spectrum for El Centro
ground motion shown by a solid
line together with an idealized
version shown by a dashed line;  =
5%
ACCELERATION RESPONSE SPECTRUM
EL CENTRO EARTHQUAKE 5% DAMPING
 IT IS NOT PRACTICALLY
POSSIBLE TO CALCULATE
EXACT STRUCTURAL PERIOD
.
 SPECTRAL
ACCELERATION
FOR SHORT PERIOD IS VERY
IRREGULAR.
 FOR PRACTICAL USE IT HAS
TO MADE ‘SMOOTH’
DESIGN RESPONSE SPECTRUM
PART - II
RESPONSE SPECTRUM PROVISIONS OF BNBC/14
[PART 6, CHAPTER 2 – ARTICLE 2.5.6]
DEVELOPMENT HISTORY
EARTHQUAKE ZONING MAP OF BANGLADESH
EARTHQUAKE ZONING MAP 1972
Adopted from East Pakistan Map
DEVELOPED BY METROLOGICAL
DEPARTMENT OF BANGLADESH IN
1972
THE COUNTRY WAS DIVIDED IN FOUR ZONES
• ZONE 1 : Seismic factor 0.2g ~ 0.1g
• ZONE 2 : Seismic factor 0.1g ~ 0.067g
• ZONE 3 : Seismic factor 0.067g ~ 0.05g
• ZONE 4 : Seismic factor < 0.05g
ZONING MAP 1978
PREPARED
BY
GEOLOGICAL
SURVEY OF BANGLADESH
THE COUNTRY WAS DIVIDED IN THREE ZONES
• ZONE 1 : Seismic coefficient 0.08g
• ZONE 2 : Seismic coefficient 0.05g
• ZONE 3 : Seismic coefficient 0.04g
BNBC – 1993
Housing and Building Research Institute (HBRI)
FIRST
SCIENTIFIC
APPROACH
ADOPTED IN PREPARING SEISMIC
ZONING MAP
THE COUNTRY WAS DIVIDED IN THREE ZONES
• ZONE 1 : Seismic coefficient 0.2g
• ZONE 2 : Seismic coefficient 0.15g
• ZONE 3 : Seismic coefficient 0.075g
PROBABILITY OF EXCEEDANCE 20% IN 50 YEARS.
BNBC – 2014 being updated
Housing and Building Research Institute (HBRI)
SEISMIC ZONING MAP PREPARED
FOR 2475 YEARS HAZARD LEVEL
(PROBABILITY OF EXCEDENCE 2% IN
50 YEARS)
THE COUNTRY IS DIVIDED IN FOUR ZONES
• ZONE 1 : Seismic coefficient 0.36g
• ZONE 2 : Seismic coefficient 0.28g
• ZONE 3 : Seismic coefficient 0.20g
• ZONE 4 : Seismic coefficient 0.12g
EARTHQUAKES
1973-2013
http://earthquake.usgs.gov/
EARTHQUAKES
1973-2013
Historical earthquakes
of 1973~2013 (source
http://earthquake.usgs.gov/ea
rthquakes/search/)
superimposed
on
proposed on BNBC
seismic zoning map
BNBC/14 EARTHQUAKE DEFINITION
 2% Probability of Exceedence in 50 Years (2,475 Year Return
Period) – MAXIMUM CONSIDERED EARTHQUAKE (MCE)
 Design Ground Motion 2/3rd of MCE
 Design Ground Motions are Set at 2/3rd of MCE Ground Motion
Levels, With The Reasoning That Any Structure Designed With
The Provision Shall Have A Minimum Margin Against Collapse of
1.5
PEAK GROUND ACCELERATION (PGA)
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, PEAK GROUND ACCELERATION REPRESENTS STRUCTURAL RESPONSE OF
A STRUCTURE OF ZERO PERIOD
PARAMETERS DEFINING ELASTIC RESPONSE SPECTRUM
ACCELERATION RESPONSE SPECTRUM
TB
= Lower limit of the period of the
constant spectral acceleration branch as a
function of site class (Table 2.5.4 )
TC
= Upper limit of the period of the
constant spectral acceleration branch as a
function of site class (Table 2.5.4 )
TD = Lower limit of the period of the constant
spectral displacement branch as a function of
site class (Table 2.5.4 ).
PARAMETERS DEFINING ELASTIC RESPONSE SPECTRUM
Table 2.5.4: Site dependent soil factor and other parameters defining
elastic response spectrum
MAY BE THIS VALUE IS
Soil type
S
SA
WRONG !!!!!!!!!!!!
TB(s)
TC(s)
TD(s)
1.00
0.15
0.4
2.0
SB
1.20
0.15
0.5
2.0
SC
1.15
0.20
0.6
2.0
SD
1.35
0.20
0.8
2.0
SE
1.40
0.15
0.5
2.0
ELASTIC RESPONSE COEFFICIENT, CS
• SOIL TYPE = SA (ROCK)
• DAMPING = 5%
• ZONE = DHAKA (0.2g)
DESIGN RESPONSE SPECTRUM
STRUCTURE IMPORTANCE FACTOR, AS DEFINED IN SECTION 2.5.7.1
Table 2.5.5 Importance Factors for Buildings and Structures for
Earthquake design
OCCUPANCY IMPORTANCE
CATEGORY
FACTOR, I
I OR II
1.0
III
1.25
IV
1.5
RESPONSE REDUCTION FACTOR
AN EXAMPLE
Table 2.5.4: Site dependent soil factor and other
parameters defining elastic response spectrum
Soil type
S
TB(s)
TC(s)
TD(s)
SA
1.00
0.15
0.4
2.0
SB
1.20
0.15
0.5
2.0
SC
1.15
0.20
0.6
2.0
SD
1.35
0.20
0.8
2.0
SE
1.40
0.15
0.5
2.0
AN EXAMPLE - Continued
• ELASTIC SEISMIC RESPONSE COEFFICIENT FOR “0” PERIOD (PGA FOR THE SITE)
• ELASTIC SEISMIC RESPONSE FOR SHORT PERIOD
• ELASTIC SEISMIC RESPONSE COEFFICIENT FOR CONSTANT ACCELERATION ZONE
• ELASTIC SEISMIC RESPONSE COEFFICIENT FOR VELOCITY SENSITIVE ZONE
• ELASTIC SEISMIC RESPONSE COEFFICIENT FOR DISPLACEMENT SENSITIVE ZONE
AN EXAMPLE - Continued
T
TD = 2 sec
TC = 0.6 sec
TB = 0.2 sec
ELASTIC RESPONSE COEFFICIENT, CS
CS
0.000
0.100
0.150
0.200
0.300
0.400
0.500
0.600
0.700
0.800
0.900
1.000
1.100
1.200
1.300
1.400
1.500
1.600
1.700
1.800
1.900
2.000
1.150
2.013
2.444
2.875
2.875
2.875
2.875
2.875
2.464
2.156
1.917
1.725
1.568
1.438
1.327
1.232
1.150
1.078
1.015
0.958
0.908
0.863
AN EXAMPLE - Continued
DESIGN RESPONSE SPECTRUM, Sa
0.450
0.400
Amplified for Soil Type
SPECTRAL ACCELERATION, Sa
0.350
0.300
0.250
Original on Rock
0.200
Reduced by Response
Reduction Factor, R
0.150
0.100
0.050
0.000
0.0
0.5
1.0
1.5
2.0
PERIOD T, SEC
2.5
3.0
3.5
4.0
Soil
Original
Design, Sa
T
Amplicatio
(Rock site)
(Reduced by R)
n
0.153
0.031
0.000 0.133
0.268
0.054
0.100 0.267
0.326
0.065
0.150 0.333
0.383
0.077
0.200 0.333
0.383
0.077
0.300 0.333
0.383
0.077
0.400 0.333
0.383
0.077
0.500 0.267
0.383
0.077
0.600 0.222
0.329
0.066
0.700 0.190
0.288
0.058
0.800 0.167
0.256
0.051
0.900 0.148
0.230
0.046
1.000 0.133
0.209
0.042
1.100 0.121
0.192
0.038
1.200 0.111
0.177
0.035
1.300 0.103
0.164
0.033
1.400 0.095
0.153
0.031
1.500 0.089
PART - III
GROUND MOTION SIMULATION
SEISMIC INSTRUMENTATION ERA, BANGLADESH

ONE ANALOGUE SEISMOGRAPH WAS INSTALLED IN 1954 IN BALU-BAGAN
CHITTAGONG.

INSTRUMENTATION ERA STARTED BY INSTRUMENTATION OF JAMUNA BRIDGE.
JAMUNA MULTIPURPOSE BRIDGE AUTHORITY COMPLETED THE INSTRUMENTATION
WORK IN 2003.

SIXTY MORE ACCELEROGRAPHS WERE OBTAINED FROM SAFER CITIES PROJECT
OF COSMOS—WSSI TO DEPLOY IN THE FREE-FIELD AT DIFFERENT LOCATION OF
BANGLADESH.

THIRTY FOUR (34) STRONG MOTION ACCELEROGRAPHS (SMA) ARE INSTALLED IN
DIFFERENT LOCATIONS OF PWD OFFICE AND BUET CAMPUS IN 2006.

NO TIME HISTORY DATA AVAILABLE
BANGLADESH STRONG MOTION DATA
at Station ID: ALTUS S/N 2928 Channel 1: EW 07/05/2008 16:55:52 (GMT) – AT NATORE
GROUND MOTION SIMULATION
SPECTRUM COMPATIBLE TIME HISTORY DATA GENERATION
• STANDARD PROCEDURES AVAILABLE
 Linear scaling
 Frequency content modification
 Frequency domain techniques
 Time domain techniques
• COMPUTER ROUTINE NEEDED TO CALCULATE THE MATCHING. COMMONLY
AVAILABLE SOFTWARE ARE
 RspMatch
 SeismoMatch
 SIMQKE
 SYNTH
 EZ-FRISK
GROUND MOTION SIMULATION
1. LINEAR SCALING OF A KNOWN STRONG MOTION DATA
EL-CENTRO EARTHQUAKE STRONG MOTION DATA HAS BEEN SCALED DOWN BY A
FACTOR OF 0.41716 TO MAKE MAXIMUM ACCELERATION OF 0.133g
RESPONSE SPECTRUM OF THE SCALED STRONG MOTION DATA
COMPARISON OF SCALED DATA – BNBC/14 SPECTRUM
STRONG MOTION SIMULATION
2. SPECTRA MATCHING IN FREQUENCY DOMAIN TECHNIQUES
EL-CENTRO
SPECTRUM PLANNED
TO MATCH WITH THE
BNBC SPECTRUM
SPECTRUM MATCHED
COMPARES OF THE SPECTRUMS
MATCHED TIME HISTORY GRAPH
THANKS
&
WELCOME TO OPEN DISCUSSION