Bentley RM Bridge Seismic Design and Analysis

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Bentley RM Bridge Seismic Design and Analysis

• Alexander Mabrich, PE, Msc

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(No Transcript)
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AGENDA
Kobe, Japan (1995)
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AGENDA
Loma Prieta, California (1989)
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RM Bridge Seismic Design and Analysis

• Critical infrastructures require
• Sophisticated design methods
• Withstand collapse in earthquake occurrences

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RM Bridge Seismic Design and Analysis

1. The Bentley BrIM vision
2. RM Bridge Seismic Design Methods
3. Earthquake simulations in Bentley RM Bridge

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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

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AASHTO Bridge Design Specifications

• 7 probability of exceedence in 75years
• Seismic Design Categories
• Soil
• Site / location
• Importance
• Earthquake Resistant System
• Demand/Capacity

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AASHTO Bridge Design Specifications

• Site Location

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AASHTO Bridge Design Specifications

• Type of Seismic Analysis Required

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Static Seismic Load
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Equivalent Static Analysis

• Uniform Load Analysis
• Orthogonal Displacements
• Simultaneously
• Fundamental mode

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Equivalent Static Analysis

• Direction, Factor

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Fundamental Mode
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Results
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Basic Concepts used in Dynamic Analysis
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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

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Dynamic Vibration
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Damped Vibration
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Rayleigh Damping

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Single Mass Oscillator
EQUILIBRIUM
EQUATION OF MOTION
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Damping Ratio
c?0

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Free Vibration
no dampingand dividing by m
But..

• Solution

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Multi Degree of Freedom System

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Numerical Methods for Dynamic Analysis

• Calculation of Eigen frequency
• Modal Analysis
• Direct Time integration, linear and non-linear

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Modal Analysis

• System of dynamic equations

• Free vibration motion

• Non trivial solution

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Eigen Calculation

• Eigen values
• Eigen shapes
• Unique nature
• Differential equations

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Eigen Shapes
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MASS PARTICIPATION FACTORS

• MODE phiMphi X Y Z
  SUM-X SUM-Y SUM-Z HERTZ
• ----------------------------------------
  ---------------------------------
• 1 0.3768E04 88.33 0.00 3.14
  88.33 0.00 3.14 0.905
• 2 0.1653E04 2.35 0.00 71.45
  90.68 0.00 74.59 1.704
• 3 0.8292E03 0.00 5.03 0.04
  90.68 5.03 74.63 3.111
• 4 0.1770E04 1.14 0.01 0.05
  91.82 5.04 74.68 3.809
• 5 0.1055E04 0.28 0.01 0.01
  92.10 5.05 74.69 5.425
• 6 0.1101E04 0.00 57.35 0.01
  92.10 62.40 74.69 6.300
• 7 0.1675E04 0.43 0.01 7.31
  92.54 62.41 82.00 7.145
• 8 0.9072E03 0.17 0.00 0.05
  92.70 62.41 82.05 9.656
• 9 0.5307E04 0.13 0.04 3.98
  92.83 62.45 86.03 10.042
• 10 0.1038E04 0.06 0.01 0.04
  92.90 62.46 86.08 11.795
• 11 0.1405E04 0.13 0.01 0.00
  93.02 62.47 86.08 11.830
• 12 0.1671E04 0.74 0.01 0.03
  93.77 62.48 86.10 13.265
• 13 0.4010E03 1.74 0.00 0.04
  95.51 62.49 86.14 13.321
• 14 0.8892E03 0.00 0.43 0.05
  95.51 62.92 86.20 13.890
• 15 0.5452E04 0.01 0.03 0.25
  95.52 62.95 86.45 14.077
• 16 0.1986E04 0.08 0.03 0.87
  95.59 62.97 87.32 16.719
• 17 0.6586E03 0.03 5.91 0.03
  95.63 68.88 87.35 16.936

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Response Spectrum

• Modal Decomposition

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Response Spectrum

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

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Spectral Response Acceleration
AASHTO Definition
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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

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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

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CQC-RULE

• More complex theory, modelling the correlation
  between different eigenfrequencies

• Good results if the duration of the event is 5
  times higher than the longest considered period
  of vibration
• AASHTO preferred by art. 4.7.4.3.3

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ABS-RULE

• Total response computed by adding the absolute
  values of all individual contributions

• Full correlation between the different
  eigenfrequencies
• All maxima are reached at the same time

• ABS-rule is suitable for structures where
  relevant eigenvalues are situated close to each
  other

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SRSS-RULE

• Individual eigenfrequencies are completely
  uncorrelated

• Eigenfrequencies are added in Pythagorean manner

• Good results if considered eigenfrequencies are
  over a wide range
• They are not situated too close one to each other

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DSC-RULE

• Correlation between the contributions of
  individual eigenfrequencies must exist

• Different damping for different eigenfrequencies
  can be taken into account
• Additional information specifiying the frequency
  dependency of damping must be available

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Earthquake Load

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Response Spectrum in RM Bridge
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Time-History

• Time Integration

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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.

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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

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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
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Application Example
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Bentley RM Bridge Seismic Analysis

• Conclusions

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Kobe, Japan (1995)
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Akashi-Kaikyo Pearl Bridge
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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

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Bentley RM Bridge Seismic Design and Analysis

• Questions

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Thank you for your attention!

• Alex.Mabrich_at_bentley.com