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Bentley RM Bridge Seismic Design and Analysis

Bentley RM Bridge Seismic Design and Analysis. Alexander Mabrich, PE, Msc. AGENDA. Kobe, Japan (1995). AGENDA. Loma Prieta, California (1989). RM Bridge Seismic Design and Analysis. Critical infrastructures require: Sophisticated design methods

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Bentley RM Bridge Seismic Design and Analysis

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  1. Bentley RM Bridge Seismic Design and Analysis Alexander Mabrich, PE, Msc

  2. AGENDA Kobe, Japan (1995)

  3. AGENDA Loma Prieta, California (1989)

  4. RM Bridge Seismic Design and Analysis • Critical infrastructures require: • Sophisticated design methods • Withstand collapse in earthquake occurrences

  5. RM Bridge Seismic Design and Analysis • AASTHO, Simple Seismic Load • Basic concepts for Dynamic Analysis: - Eigenvalues - Eigenshapes • Two non-linear dynamic options: - Response Spectrum - Time-History

  6. AASHTO Bridge Design Specifications • 7% probability of exceedence in 75years • Seismic Design Categories • Soil • Site / location • Importance • Earthquake Resistant System • Demand/Capacity

  7. AASHTO Bridge Design Specifications • Site Location

  8. AASHTO Bridge Design Specifications • Type of Seismic Analysis Required

  9. Static Seismic Load

  10. Equivalent Static Analysis • Uniform Load Analysis • Orthogonal Displacements • Simultaneously • Fundamental mode

  11. Equivalent Static Analysis • Direction, Factor

  12. Fundamental Mode

  13. Results

  14. Basic Concepts used in Dynamic Analysis

  15. Basic Concepts • Vibration of Systems with one or more DOF • Eigen values and Eigen modes • Forced Vibration • Harmonic and Stochastic Simulation • Linear and Non-linear behavior of the structure

  16. Dynamic Vibration

  17. Damped Vibration

  18. damping constant c spring constant k mass m x amplitude x(t) F external Force F(t) Single Mass Oscillator EQUILIBRIUM EQUATION OF MOTION

  19. Damping Ratio c0:

  20. Free Vibration …no damping…and dividing by m… But.. • Solution:

  21. Multi Degree of Freedom System

  22. Numerical Methods for Dynamic Analysis • Calculation of Eigen frequency • Modal Analysis • Direct Time integration, linear and non-linear

  23. Modal Analysis • System of dynamic equations : • Free vibration motion: • Non trivial solution:

  24. Eigen Calculation • Eigen values • Eigen shapes • Unique nature • Differential equations

  25. Eigen Shapes

  26. MASS PARTICIPATION FACTORS [%] MODE phi*M*phi X Y Z SUM-X SUM-Y SUM-Z HERTZ ------------------------------------------------------------------------- 1 0.3768E+04 88.33 0.00 3.14 88.33 0.00 3.14 0.905 2 0.1653E+04 2.35 0.00 71.45 90.68 0.00 74.59 1.704 3 0.8292E+03 0.00 5.03 0.04 90.68 5.03 74.63 3.111 4 0.1770E+04 1.14 0.01 0.05 91.82 5.04 74.68 3.809 5 0.1055E+04 0.28 0.01 0.01 92.10 5.05 74.69 5.425 6 0.1101E+04 0.00 57.35 0.01 92.10 62.40 74.69 6.300 7 0.1675E+04 0.43 0.01 7.31 92.54 62.41 82.00 7.145 8 0.9072E+03 0.17 0.00 0.05 92.70 62.41 82.05 9.656 9 0.5307E+04 0.13 0.04 3.98 92.83 62.45 86.03 10.042 10 0.1038E+04 0.06 0.01 0.04 92.90 62.46 86.08 11.795 11 0.1405E+04 0.13 0.01 0.00 93.02 62.47 86.08 11.830 12 0.1671E+04 0.74 0.01 0.03 93.77 62.48 86.10 13.265 13 0.4010E+03 1.74 0.00 0.04 95.51 62.49 86.14 13.321 14 0.8892E+03 0.00 0.43 0.05 95.51 62.92 86.20 13.890 15 0.5452E+04 0.01 0.03 0.25 95.52 62.95 86.45 14.077 16 0.1986E+04 0.08 0.03 0.87 95.59 62.97 87.32 16.719 17 0.6586E+03 0.03 5.91 0.03 95.63 68.88 87.35 16.936 18 0.6484E+03 0.09 3.54 0.00 95.72 72.42 87.35 16.961 19 0.1086E+04 0.00 7.02 0.00 95.72 79.44 87.35 17.275 20 0.1866E+04 0.02 0.01 0.00 95.74 79.45 87.35 18.408 21 0.1310E+04 0.11 0.00 3.47 95.85 79.45 90.82 21.221 22 0.2060E+04 0.06 0.00 0.00 95.91 79.45 90.82 22.277 23 0.1474E+04 0.06 0.00 0.00 95.97 79.45 90.83 24.414 24 0.2324E+04 0.04 0.00 0.00 96.00 79.45 90.83 24.983 25 0.1613E+04 0.00 0.00 0.00 96.01 79.45 90.83 26.843

  27. Response Spectrum Modal Decomposition

  28. Response Spectrum • Combination of natural modes • One mass oscillator • Oscillating loads • Intensity factor • Single contribution • Synchronization by Stochastic Calculation Rules: ABS,SRSS,CQC, etc

  29. Spectral Response Acceleration AASHTO Definition

  30. Solution in Frequency Domain • Solution by combining the contributions of the eigenvectors • Superposition of eigenvectors • Loading has lost information about correlation during conversion • Solution has no information on phase differences between the contributions of different eigenvectorsUse Stochastic methodology • Use Stochastic methodology

  31. Combination Rules • Max/Min results with different rules available: • ABS – Rule (Sum of absolute values) • SRSS – Rule (Square root of sum of sqaures) • DSC – Rule (Newmark/Rosenblueth) • CQC – Rule (Complete quadratic combination) • GENERAL : a lot of other rules exist

  32. Earthquake Load

  33. Response Spectrum in RM Bridge

  34. Time-History Time Integration

  35. Time History • Direct Time Integration • Linear and Non-Linear analysis • Standard event is defined: time-histories of ground acceleration are site specific • Probability of bearable damage • Most accurate method to evaluate structure response under earthquake event.

  36. What Can Be Non-Linear in RM Bridge? Structure-stiffness - Springs - Connections - Materials - Interaction between the substructure and bridge - Large deformations - Cables Mass of structure - Moving vehicle traffic Structure-damping - Raleigh damping effect - Viscous damping Load dependent on time - Change of position, intensity or direction - Time delay of structural elements

  37. Comparison MODAL ANALYSIS • Solution of uncoupled differential equations • Each eigenmode as single mass oscillator • Coupled system of differential equations • Time domain approximated • Static starting condition • Analysis of secondary systems: vehicles, equipment, extra bridge features • All Non-Linearities possible TIME-HISTORY

  38. Element 105 Element 110 Element 125 Element 131 Element 118 40 m 60 m 40 m Application Example

  39. Bentley RM Bridge Seismic Analysis Conclusions

  40. Kobe, Japan (1995)

  41. Akashi-Kaikyo – “Pearl Bridge”

  42. RM Bridge Benefits • Bentley BrIM vision • Bentley portfolio • Intuitive step-by-step calculation • One tool for all: static, modal, time-history • Integrated reports and drawings

  43. Bentley RM Bridge Seismic Design and Analysis Questions

  44. Thank you for your attention! Alex.Mabrich@bentley.com

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