1. CABLE-STAYED BRIDGE SEISMIC ANALYSIS USING ARTIFICIAL ACCELEROGRAMS
Roman Guzeev, Ph.D.
Institute Giprostroymost-Saint-Petersburg
Russian Federation

2. The Eastern Bosporus bridge, Vladivostok, Russia1
The Eastern Bosporus bridge, Vladivostok, Russia

3. Presentation of the Response spectrum in national codes AASHTO LFRD 2
Presentation of the Response spectrum in national codes
AASHTO LFRD
Bridge Design
Specification
EUROCODE
EN :2004
Design of structures for
earthquake resistance
Design structures in
earthquake regions
(Russian code)

4. the Response Spectrum Method3
Disadvantages of
the Response Spectrum Method
it is inapplicable for structures with anti-seismic devices, which make behavior of the structures nonlinear
It does not take into account seismic wave propagation
It considers mode shape vibration as statistically independent
It uses approximate relations between response spectrum curves with different damping.

5. Time history analysis using accelerograms. 4
Time history analysis using accelerograms.
Instrumentally recorded ground acceleration.
1994, Northridge, Santa Monica, City Hall Grounds
1940, El Centro Site

6. Instrumentally recorded ground acceleration ?5
Instrumentally recorded ground acceleration ?
The main features
Instrumentally recorded earthquake acceleration is an event of random process
Every earthquake is unique and has its own peak acceleration and spectral distribution
Any earthquake Depends on ground condition
Instrumentally recorded acceleration can be dangerous to one type of structure and can be safe to another

7. Artificial accelerograms6
Artificial accelerograms
Artificial accelerogram should meet requirements of national codes:
There should be a peak value on accelerogram. The peak value depends on the region seismic activity, ground condition and period of exceedance.
2. Accelerogram response spectrum should match design spectrum

8. Artificial accelerograms7
Artificial accelerograms
Artificial accelerogram should meet physical requirements:
Acceleration, velocity and displacement should be equal to zero at the beginning and at the end of the earthquake
2. Duration of the earthquake should not be less than 10 sec.

9. The accelerogram generation algorithm8
The accelerogram generation algorithm
Step Generating accelerogram with peak value equal to 1
Step Scaling accelerogram according to the design value
of ground acceleration.
The accelerogram to be found is presented as trigonometric series:
sought coefficients,
natural period of mode i,
number of considered modes
We take into account the modes which contribute to effective modal mass in the earthquake direction

10. The accelerogram constraints9
The accelerogram constraints
Peak value nonlinear constraint:
Acceleration, velocity and displacement linear constraints:
At the beginning t=0
At the end t=Ts

11. Generated accelerogram response spectrum10
Generated accelerogram response spectrum
Where,
is the solution of differential equation of motion for one DOF oscillator on sine and cosine base excitation.
- damping ratio of design response spectrum

12. F – object sum square function [W] – diagonal matrix of weight factors11
The coefficient of series terms to be found сan be determined by means of the least square method with linear and nonlinear constraints
We minimize the sum square of differences between accelerogram response spectrum and the design response spectrum
F – object sum square function
[W] – diagonal matrix of weight factors
– vector of differences between the
accelerogram response spectrum and the design response spectrum

13. Recommendation on analysis using artificial acelerogram12
Recommendation on analysis using artificial acelerogram
Terms of series should contain natural frequencies of structures. It lead to resonance excitation.
We should take into account the modes which contribute to effective modal mass in the earthquake direction
For the closest match to design response spectrum we can add extra terms into the series
We have to generate more than one design accelerogram. We can do it by varying the number of terms and considered modes
For every strain-stress state parameter we have to built an envelope caused by action generated accelerograms

14. Golden Horn Bay cable-stayed bridge, Vladivostok, Russia13
Golden Horn Bay cable-stayed bridge, Vladivostok, Russia
Concrete deck
Steel deck

15. Seismic action input data14
Seismic action input data
Elastic response spectrum
- design spectrum
- elastic spectrum
- ductility factor
- elastic spectrum
Peak ground acceleration
with 0.08 damping ratio
Return period is 5000 years.
- dumping correction factor
- modal damping ratio

16. 15
GTSTRUDL Model

17. Natural period / frequency16
Mode
Natural period / frequency
Effective modal mass
Mode shape 1
T=4.88s
f=0.205 Hz
X: 0%
Y: 0%
Z: 10.0%
lateral 2
T=4.36s
f=0.229 Hz
Y: 6.5%
Z: 0%
vertical 3
T=3.62s
f=0.276 Hz
X: 28.4%
longitudinal

18. Natural period / frequency17
Mode
Natural period / frequency
Effective modal mass
Mode shape 4
T=2.84s
f=0.352 Hz
X: 45.8%
Y: 0%
Z: 0%
longitudinal
and lateral 6
T=2.78s
f=0.358 Hz
X: 0%
Z: 17.8%
lateral

19. Stiffness weighted average damping18
Stiffness weighted average damping
Structural element
Damping ratio
Steel deck
0.02
Concrete deck
Pylon
0.025
Cables
Concrete piers
0.05
CONSTANT
MODAL DAMPING PROPORTIONAL TO STIFFNESS 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 GROUP 'CABLE'
DYNAMIC PARAMETERS
RESPONSE DAMPING STIFFNESS 1.0
END OF DYNAMIC PARAMETERS
COMPUTE MODAL DAMPING RATIOS AVERAGE

20. Accelerogram generation results19
Accelerogram generation results

21. Response spectrum analysis. GTSTRUDL statement.20
Response spectrum analysis. GTSTRUDL statement.
STORE RESPONSE SPECTRA ACCELERATION LINEAR vs -
NATURAL PERIOD LINEAR 'SEYSM‘ DAMPING RATIO 0.02 FACTOR
…………………………………………………………………………………………
END OF RESPONSE SPECTRA
RESPONSE SPECTRA LOADING 'RSP' 'response'
SUPPORT ACCELERATION
TRANS X FILE 'SEYSM'
END RESPONSE SPECTRUM LOAD
LOAD LIST 'RSP'
ACTIVE MODES ALL
PERFORM MODE SUPERPOSITION ANALYSIS
COMPUTE RESPONSE SPECTRA FORCES MODAL COMBINATION RMS MEM ALLCOMPUTE RESPONSE SPECTRA DISPL MODAL COMBINATION RMS JOINTS ALL

22. Time history analysis. GTSTRUDL statement.21
Time history analysis. GTSTRUDL statement.
STORE TIME HISTORY ACCELERATION TRANSLATION –
'EARTHQ' FACTOR
…………………………………………………………………………………………
TRANSIENT LOADING 1
SUPPORT ACCELERATION
TRANSLATION X FILE 'EARTHQ'
INTEGRATION FROM 0.0 TO 25.0 AT 0.01
ACTIVE MODES ALL
DYNAMIC ANALYSIS MODAL
STORE TIME HISTORY ACCELERATION TRANSLATION –
'EARTHQ' FACTOR
…………………………………………………………………………………………
TRANSIENT LOADING 1
SUPPORT ACCELERATION
TRANSLATION X FILE 'EARTHQ'
INTEGRATION FROM 0.0 TO 25.0 AT 0.01
ACTIVE MODES ALL
DYNAMIC ANALYSIS MODAL

23. The time history analysis results22
The time history analysis results

24. Time history analysis record23
Time history analysis record

25. Pylon leg bending moment Pylon top displacement24
The 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 force
302 mton
363 mton
Pylon top displacement
0.127 m
0.116 m

26. this analysis can take into account seismic wave propagation;25
Conclusion
Time history analysis using artificial accelerograms overcome weaknesses of the response spectrum method:
this analysis is applicable for structures with anti-seismic devices, which make behavior of the structures nonlinear;
this analysis can take into account seismic wave propagation;
this analysis does not consider mode shape vibration as statistically independent;
this analysis uses exact methods of taking into account structural damping.
2. Time history analysis using artificial acelerograms does not contradict with national codes.
3. Time history analysis using artificial acelerograms usually gives higher value of forces and displacements.

27. Thank you for your attention