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TRANSCRIPT
Rail-Structure Interaction using MIDAS
Sean McAuley, P.E.
Scott Henning, P.E.
CA HSR CP2-3
• 65.5 miles of HSR infrastructure
– 18 HST Bridges
– 32 Roadway Overpasses
• 25 kV a.c. Electrification
• Design Speed:
• 250 mph/400km/hrCP 2-3
Track Structure Interaction Analysis
• Goals– Ensure passenger comfort, safety, and track serviceability
• Investigations– Frequency
• Vertical, Longitudinal, Transverse, Torsional
– Serviceability• Deflections in all directions
– Rail Structure Interaction (Focus of this presentation)
– Dynamic Modeling• Dynamic Impact Factor
• Deck Acceleration
Rail Structure InteractionAnalysis Goals
• Investigate Rail Stress
• Investigate Relative Displacements at Expansion Joints
– Investigate and Limit Rail Stress and Relative Displacements to prevent rail fracture
Modeling Requirements
• Generating Geometry of the Track
Ballasted Track
CW Rail
TieTop of Rail
Centroid of Superstructure
Modeling Requirements• Assign Properties
– Rail elements as beams• Only concerned with axial stress, bending stress
controlled by displacements and rotations
– Linear springs vertically and transverse• Vertical spring modeled as fully elastic for ballasted
structures, uplift only checked for direct fixation fasteners
– Bi-linear springs longitudinally • Captures fastener “slip”
Modeling Requirements
Modeling Requirements
• Assign Properties
– Foundation stiffness
• 6 DOF spring for foundation elements
– Approach embankment stiffness
• 6 DOF spring for approach– For rail stress and relative displacement calculations a “fixed”
embankment spring can be conservatively used
– For total displacement checks or for calculating rail-structure interaction forces (forces imposed on the bridge by a continuously welded rail) compare fixed condition and a lower bound embankment stiffness
Loads and Load Case Requirements
• Construction Stages
– Capture rail installation timeframe
• Consider/Investigate Creep and Shrinkage
• Generate non-linear load combinations
1. LL2 + LF ± Temp (±40⁰ F)
2. LL1 + LF ± 0.5 Temp + Operation Based EQ (OBE)
• LF includes Braking/Traction for Load Case 1
• LF includes only Braking for Load Case 2
Live Loads
• Modified Cooper E-50 Loading
– Deflections and Rail Stress
• High Speed Rail Trainsets
– Dynamic Analysis
Thermal Loads
• ±40⁰ F Temperature Differential
– Temperature applied to the Bridge
• Simulates the effect of restraining movement of the rail due to the bridge expanding/contracting
– Thermal rail stress controlled by limiting thermal length
Analysis Types
Analysis Types• Non-linear Static Analysis
– Covers non-seismic load combination
– Elastic Multi-Linear Link
Analysis Types• Non-linear time-history analysis
– Covers seismic load combinations
– General Link (Force-Type-Hysteretic)
Analysis Types
Rail Structure Interaction in MIDAS• Example Structure:
– CIP PT Box Girder
– 90’-120’-90’ span configuration
– Integral connection to superstructure
– Founded on pile group foundation
Rail Structure InteractionModel Features
• Superstructure using Beam Elements
• Rail using single beam to represent 2-rail track
• Bi-linear Springs to represent fasteners– Multi-linear Elastic Links for
nonlinear Static Analysis
– General Link for Nonlinear Time History Analysis
• Rail Extension to capture approach embankment– Point Spring Boundary Spring
Rail Structure InteractionModel Features
Elastic Links(linear and bi-linear)
Rigid Elastic Links
Rail Structure InteractionModel Features
• Construction Stage Implementation
– Rail Installation Timeframe
• Coordinate schedule
– Allows for time-dependent effects on rail to begin at proper time
Figure 2: Rail Installation at 2 years Figure 1: Completion of post-tensioning
Rail Structure InteractionModel Features
• Non-linear load case development
– Combination of static load cases into single case
– Cannot implement moving loads with non-linear analysis
• Non-Linear Time History Analysis
– Review Development of Analysis Model
Rail Structure Interaction Analysis Results
• Review Rail Stress Results
– Maximums at Expansion Joints, as expected
Figure 3: Group 4 Stress Results
Rail Structure Interaction Analysis Results
• Expansion displacement within limits
Figure 3: Group 4 Stress Results
Conclusions
• Lessons Learned and Troubleshooting
– Linear superposition (static + time history)
– Verify Bi-linear Link Behavior
Expansion Jt
Conclusions
• Lessons Learned and Troubleshooting– Creation of Critical Live Load
• Generates wheel loads to specified max force
• Write text file for static load to MCT Command shell
Thanks
Acknowledgement
California High Speed Rail Authority
MIDAS
Contacts
Questions: [email protected]
Compliments: [email protected]