CABLE-STAYED BRIDGE SEISMIC ANALYSIS USING ARTIFICIAL ACCELEROGRAMS Roman Guzeev, Ph.D. Institute...
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Transcript of CABLE-STAYED BRIDGE SEISMIC ANALYSIS USING ARTIFICIAL ACCELEROGRAMS Roman Guzeev, Ph.D. Institute...
CABLE-STAYED BRIDGE SEISMIC CABLE-STAYED BRIDGE SEISMIC ANALYSIS USING ARTIFICIAL ANALYSIS USING ARTIFICIAL
ACCELEROGRAMSACCELEROGRAMS
Roman Guzeev, Ph.D.Institute Giprostroymost-Saint-Petersburg
Russian Federationhttp://www.gpsm.ru
The Eastern Bosporus bridge, Vladivostok, RussiaThe Eastern Bosporus bridge, Vladivostok, Russia1
AASHTO LFRD
Bridge Design
Specification
EUROCODE
EN 1998-1:2004
Design of structures for
earthquake resistance
Design structures in
earthquake regions
(Russian code)
Presentation of the Response spectrum in national codesPresentation of the Response spectrum in national codes2
Disadvantages of Disadvantages of
the Response Spectrum Methodthe Response Spectrum Method
it is inapplicable for structures with anti-seismic devices, it is inapplicable for structures with anti-seismic devices, which make behavior of the structures nonlinearwhich make behavior of the structures nonlinear
It does not take into account seismic wave propagation It does not take into account seismic wave propagation
It considers mode shape vibration as statistically independentIt considers mode shape vibration as statistically independent
It uses approximate relations between response spectrum It uses approximate relations between response spectrum curves with different damping.curves with different damping.
3
Time history analysis using accelerograms.Time history analysis using accelerograms.Instrumentally recorded ground acceleration.Instrumentally recorded ground acceleration.
0 5 10 15 20 25 30 35 40 45 50 55 60-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Time T, sec
Sca
led
acc
eler
atio
n, m
/s2
1994, Northridge, Santa Monica, City Hall Grounds
0 5 10 15 20 25 30 35 40 45 50 55 60-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Sca
led
acc
eler
atio
n, m
/s2
Time T, sec
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 60
0.5
1
1.5
2
2.5
3
No
nd
imen
sio
nal
res
po
nse
Period T, sec
1940, El Centro Site
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 60
0.5
1
1.5
2
2.5
3
3.5
No
nd
imen
sio
nal
res
po
nse
Period T, sec
4
The main featuresThe main features
Instrumentally recorded earthquake acceleration is an Instrumentally recorded earthquake acceleration is an event of random processevent of random process
Every earthquake is unique and has its own peak Every earthquake is unique and has its own peak acceleration and spectral distributionacceleration and spectral distribution
Any earthquake Depends on ground conditionAny earthquake Depends on ground condition
Instrumentally recorded acceleration can be dangerous Instrumentally recorded acceleration can be dangerous to one type of structure and can be safe to anotherto one type of structure and can be safe to another
Instrumentally recorded ground acceleration ?Instrumentally recorded ground acceleration ?5
Artificial accelerogramsArtificial accelerograms
Artificial accelerogram should meet requirements of Artificial accelerogram should meet requirements of national codes:national codes:
1.1. There should be a peak value on accelerogram. The There should be a peak value on accelerogram. The peak value depends on the region seismic activity, peak value depends on the region seismic activity,
ground condition and period of exceedance. ground condition and period of exceedance.
2. Accelerogram response spectrum should match design 2. Accelerogram response spectrum should match design spectrum spectrum
6
Artificial accelerogram should meet physical Artificial accelerogram should meet physical requirements:requirements:
1.1. Acceleration, velocity and displacement should Acceleration, velocity and displacement should be equal to zero at the beginning and at the end be equal to zero at the beginning and at the end
of the earthquakeof the earthquake
2. Duration of the earthquake should not be less 2. Duration of the earthquake should not be less than 10 sec.than 10 sec.
Artificial accelerogramsArtificial accelerograms
7
The accelerogram generation algorithmThe accelerogram generation algorithm
Step 1. Step 1. Generating accelerogram with peak value equal to 1 Generating accelerogram with peak value equal to 1
Step 2.Step 2. Scaling accelerogram according to the design value Scaling accelerogram according to the design value
of ground acceleration.of ground acceleration.
The accelerogram to be found is presented as trigonometric series:The accelerogram to be found is presented as trigonometric series:
1
2 2( ) sin cos
N
i ii ii
a t a t b tT T
-sought coefficients,
-natural period of mode i,
,i i
i
a b
T
N -number of considered modes
We take into account the modes which contribute to effective modal mass in the earthquake direction
8
1
2 2max sin cos 1
N
i ii ii
a t b tT T
The accelerogram constraintsThe accelerogram constraints
Peak value nonlinear constraint:Peak value nonlinear constraint:
Acceleration, velocity and displacement linear constraints:Acceleration, velocity and displacement linear constraints:
At the beginning t=0 At the end t=Ts
9
1
1
2 2
2 21
2 2cos sin 0,
2 2
2 2sin cos 0,
2 2sin cos 0,
4 4
Ni i
i s i si ii
N
i s i si ii
Ni i
i s i si ii
T Ta T b T
T T
a T b TT T
T Ta T b T
T T
2
21
1
0,
0,4
0,2
N
ii
Ni
ii
Ni
ii
b
Tb
Ta
Generated accelerogram response spectrumGenerated accelerogram response spectrum
1
( ) max ( ) ( ) ( ) 0N
s сi i i i s
i
T a t a y t b y t t T
( ), ( ) 0s сi i sy t y t t T
is the solution of differential equation of motion for one DOF oscillator on sine and cosine base excitation.
2
2
2 2 2( ) 2 sin , (0) 0, (0) 0,
2 2 2( ) 2 cos , (0) 0, (0) 0
s s s s si d i i i i
c c c c ci d i i i i
y t y y t y yT T T
y t y y t y yT T T
d - damping ratio of design response spectrum
Where,
10
The coefficient of series terms to be found The coefficient of series terms to be found ссan be determined an be determined by means of the least square method with linear and nonlinear by means of the least square method with linear and nonlinear
constraintsconstraints
We minimize the sum square of differences between We minimize the sum square of differences between accelerogram response spectrum and the design response accelerogram response spectrum and the design response
spectrum spectrum
{ ( ) ( )} { ( ) ( )}Tj d j j d jF T T W T T
F – object sum square function
[W] – diagonal matrix of weight factors
{ ( ) ( )}j d jT T
accelerogram response spectrum and the design response spectrum
– vector of differences between the
11
Recommendation on analysis using artificial acelerogramRecommendation on analysis using artificial acelerogram
Terms of series should contain natural frequencies of Terms of series should contain natural frequencies of structures. It lead to resonance excitation.structures. It lead to resonance excitation.
We should take into account the modes which contribute We should take into account the modes which contribute to effective modal mass in the earthquake directionto effective modal mass in the earthquake direction
For the closest match to design response spectrum we For the closest match to design response spectrum we can add extra terms into the seriescan add extra terms into the series
We have to generate more than one design accelerogram. We have to generate more than one design accelerogram. We can do it by varying the number of terms and considered We can do it by varying the number of terms and considered modesmodes
For every strain-stress state parameter we have to built For every strain-stress state parameter we have to built an envelope caused by action generated accelerogramsan envelope caused by action generated accelerograms
12
30580 mm
33270 mm
30580 mm
33300 mm
3330
mm
331
2 m
m
Concrete deck
Steel deck
Golden Horn Bay cable-stayed bridge, Vladivostok, RussiaGolden Horn Bay cable-stayed bridge, Vladivostok, Russia
m
m mm
13
Elastic response spectrum
Seismic action input dataSeismic action input data
1( , ) ( , )d i el iS T S T K
( , )d iS T - design spectrum
( , )el iS T - elastic spectrum
1 0.25K - ductility factor
( , ) (0.08, )el i elS T S T
(0.08, )elS T - elastic spectrum
with 0.08 damping ratio
0.08
i
- dumping correction factor
i - modal damping ratio
0 1 2 3 4 5 60
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
5.5
6
Natural Period T, sec
S
Peak ground acceleration
0.107gA g
Return period is 5000 years.
14
GTSTRUDL ModelGTSTRUDL Model15
Mode
Natural period /
frequency
Effective modal mass
Mode shape
1T=4.88s
f=0.205 Hz
X: 0%
Y: 0%
Z: 10.0%
lateral
2T=4.36s
f=0.229 Hz
X: 0%
Y: 6.5%
Z: 0%
vertical
vertical
3T=3.62s
f=0.276 Hz
X: 28.4%
Y: 0%
Z: 0%
longitudinal
16
ModeNatural period /
frequency
Effective modal mass
Mode shape
4T=2.84s
f=0.352 Hz
X: 45.8%
Y: 0%
Z: 0%
longitudinal
and lateral
6T=2.78s
f=0.358 Hz
X: 0%
Y: 0%
Z: 17.8%
lateral
17
Stiffness weighted average dampingStiffness weighted average damping
Structural element
Damping ratio
Steel deck 0.02
Concrete deck 0.02
Pylon 0.025
Cables 0.00096
Concrete piers 0.05
CONSTANT MODAL DAMPING PROPORTIONAL TO STIFFNESS 0.025 GROUP 'PYLON'MODAL DAMPING PROPORTIONAL TO STIFFNESS 0.02 GROUP 'DECK'MODAL DAMPING PROPORTIONAL TO STIFFNESS 0.05 GROUP 'SUPP'MODAL DAMPING PROPORTIONAL TO STIFFNESS 0.00096 GROUP 'CABLE'DYNAMIC PARAMETERS RESPONSE DAMPING STIFFNESS 1.0END OF DYNAMIC PARAMETERSCOMPUTE MODAL DAMPING RATIOS AVERAGE
18
0 4 8 12 16 20-1.1-1-0.8-0.6-0.4-0.2
00.20.40.60.8
11.1
Time t, s
acce
lera
tio
n, m
/s2
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50
0.5
1
1.5
2
2.5
3
Period T, s
resp
on
se s
pec
tru
m
0 4 8 12 16 20-0.06
-0.04
-0.02
0
0.02
0.04
0.06
Time t, s
velo
sity
m/s
0 4 8 12 16 20-0.03
-0.02
-0.01
0
0.01
0.02
0.03
Time t, s
dis
pla
cem
ent
m/s
natural period
Accelerogram generation resultsAccelerogram generation results 19
Response spectrum analysisResponse spectrum analysis.. GTSTRUDL statement GTSTRUDL statement..
STORE RESPONSE SPECTRA ACCELERATION LINEAR vs - NATURAL PERIOD LINEAR 'SEYSM‘ DAMPING RATIO 0.02 FACTOR 0.26242……………………………………………………………………………………………………………………………………………………………………………………END OF RESPONSE SPECTRA RESPONSE SPECTRA LOADING 'RSP' 'response'SUPPORT ACCELERATION TRANS X FILE 'SEYSM'END RESPONSE SPECTRUM LOADLOAD LIST 'RSP'ACTIVE MODES ALLPERFORM MODE SUPERPOSITION ANALYSISCOMPUTE RESPONSE SPECTRA FORCES MODAL COMBINATION RMS MEM ALLCOMPUTE RESPONSE SPECTRA DISPL MODAL COMBINATION RMS JOINTS ALL
20
STORE TIME HISTORY ACCELERATION TRANSLATION – 'EARTHQ' FACTOR 0.262310.0000000 0.0000000-0.0441006 0.0100000-0.0805970 0.0200000……………………………………………………………………………………………………………………………………………………………………………………TRANSIENT LOADING 1SUPPORT ACCELERATION TRANSLATION X FILE 'EARTHQ'INTEGRATION FROM 0.0 TO 25.0 AT 0.01ACTIVE MODES ALLDYNAMIC ANALYSIS MODAL
STORE TIME HISTORY ACCELERATION TRANSLATION – 'EARTHQ' FACTOR 0.262310.0000000 0.0000000-0.0441006 0.0100000-0.0805970 0.0200000……………………………………………………………………………………………………………………………………………………………………………………TRANSIENT LOADING 1SUPPORT ACCELERATION TRANSLATION X FILE 'EARTHQ'INTEGRATION FROM 0.0 TO 25.0 AT 0.01ACTIVE MODES ALLDYNAMIC ANALYSIS MODAL
Time history analysisTime history analysis.. GTSTRUDL statement GTSTRUDL statement..21
0 5 10 15 20 25-6
-4
-2
0
2
4
6x 10
4
Time t, s
Pyl
on
leg
mo
me
nt,
mto
n x
m
0 5 10 15 20 25-6000
-4000
-2000
0
2000
4000
6000
Time t, s
Pie
re m
om
ent,
mto
n x
m
0 5 10 15 20 25-400-300-200-100
0100200300400
Time t, s
ST
U f
orc
e, m
ton
0 5 10 15 20 25-0.15
-0.1
-0.05
0
0.05
0.1
0.15
Time t, s
Pyl
on
to
p d
isp
lace
men
t, m
The time history analysis resultsThe time history analysis results 22
Time history analysis recordTime history analysis record23
The Result comparisonThe Result comparison
Parameter Response spectrum Time history
Pylon leg bending moment
49990 mton x m 57300 mton x m
Pier bending moment
4767 mton x m 5074 mton x m
Shock-transmitter
unit force302 mton 363 mton
Pylon top displacement
0.127 m 0.116 m
24
ConclusionConclusion1.1. Time history analysis using artificial accelerograms Time history analysis using artificial accelerograms
overcome weaknesses of the response spectrum method:overcome weaknesses of the response spectrum method:
a)a) this analysis is applicable for structures with anti-seismic this analysis is applicable for structures with anti-seismic devices, which make behavior of the structures nonlinear;devices, which make behavior of the structures nonlinear;
b)b) this analysis can take into account seismic wave this analysis can take into account seismic wave propagation;propagation;
c)c) this analysis does not consider mode shape vibration as this analysis does not consider mode shape vibration as statistically independent;statistically independent;
d)d) this analysis uses exact methods of taking into account this analysis uses exact methods of taking into account structural damping. structural damping.
2. Time history analysis using artificial acelerograms does not 2. Time history analysis using artificial acelerograms does not contradict with national codes.contradict with national codes.
3. Time history analysis using artificial acelerograms usually 3. Time history analysis using artificial acelerograms usually gives higher value of forces and displacements.gives higher value of forces and displacements.
25
Thank you for your attentionThank you for your attention