Bridge Rail Design Procedure

BRIDGE RAIL DESIGN PROCEDURE by EMAD BADIEE

Copyright

  • Copyright by Emad Badiee, 2014

ABSTRACT

  • The AASHTO Bridge Specifications recommend a yield line theory analysis to determine the structural capacity of concrete bridge railing based on static strength of concrete. However, this approach significantly underestimates the capacity of concrete bridge rails to withstand high-speed truck impacts.

  • Traditionally, the issue has been addressed by implementing artificial reductions in bridge rail design loads specified in the guidelines. Fear of legal action related to the failure of containment and redirecting an errant vehicle has rendered this policy unacceptable for most state highway agencies.

  • Existing barrier design guidelines contained in the Bridge Specifications are based upon the older NCHRP Report 350 which has been superseded by the Manual for Assessing Safety Hardware (MASH). The updated performance guidelines involve higher vehicles, impact angles, and in some instances, higher impact speeds.

  • Full-scale crash testing has demonstrated that the new testing criteria necessitate stronger and taller barriers. A study has proposed new height and design load requirements for incorporation into the updated Bridge Design Specifications, though the recommended load was found to be excessively high and was poorly received by AASHTO’s T7 committee on Guardrails and Bridge Rails.

  • Consequently, there exists a national need for a more thorough evaluation of bridge rail design loads and minimum barrier heights that align with MASH guidelines.

  • This thesis presents an improved method based on a modified Yield Line Theory and the dynamic strength of concrete to estimate the design impact loads to more realistic levels without adjustment of the underlying analysis technique. Applying this new method will ideally lead to significant reductions in the size and cost of bridge railings necessary to withstand these elevated loads.

Objectives of the Research

  1. Develop improved methods for estimating the structural capacity of bridge rails and cantilevered deck systems based on dynamic strength of concrete, considering factors such as deck overhang, moment of inertia of the barrier and deck sections, and the mass of the vehicle and barrier.

  2. Identify suitable design loads for the new methods that accurately reflect MASH-recommended crash test conditions TL-2 through TL-5.

Keywords

  • NCHRP, MASH, AASHTO, Bridge railing, Yield Line Theory, Moment of Inertia.

ACKNOWLEDGMENTS

  • Deep gratitude to Dr. Nasim Uddin for invaluable support, advice, and patience throughout the project.

  • Thanks to Dr. Dean L Sicking, Dr. Lee Moradi, and Dr. Ian Hosch for their cooperation and expertise.

  • Special appreciation to family for love and support throughout this journey.

  • Thankful to UAB for the opportunity and personal and professional growth.

TABLE OF CONTENTS

  • Abstract

  • Acknowledgments

  1. Introduction
       - 1.1 Background
       - 1.2 Problem Statement
       - 1.3 Objective

  2. Literature Review
       - 2.1 Guardrail Design
       - 2.2 Barrier Strength

  3. Work Method
       - 3.1 Objective
       - 3.2 Test Levels
       - 3.3 Modified Yield Line Method
          - 3.3.1 Unit Mass Velocity
          - 3.3.2 Distributed Impact Force
          - 3.3.3 Dynamic Increase Factor
          - 3.3.4 Moment of Inertia
             - 3.3.4.1 Barrier
             - 3.3.4.1.1 Segment I
             - 3.3.4.1.2 Segment II
             - 3.3.4.1.3 Segment III
             - 3.3.4.1.4 Barrier Section Moment of Inertia
             - 3.3.4.2 Deck Overhang
          - 3.3.5 Displacement
             - 3.3.5.1 Barrier
             - 3.3.5.2 Deck Overhang
             - 3.3.5.3 Superposition
          - 3.3.6 Strain Energy Absorption from Displacement
          - 3.3.7 Moment Capacity of the Barrier
             - 3.3.7.1 Vertical Moment Capacity, Mw
             - 3.3.7.2 Horizontal Moment Capacity, Mc
             - 3.3.7.3 Top Beam Moment Capacity
          - 3.3.8 Internal Virtual Work along Yield Line, Eyield
          - 3.3.9 External Virtual Work by Applied Load
          - 3.3.10 Critical Length of Yield-Line Failure Pattern, Lc
          - 3.3.11 Nominal Railing Resistance to Transverse Loads, Rw

  4. Energy Method
       - 4.1 Objective
       - 4.2 Moving Vehicle Energy, IS
       - 4.3 Barrier Strain Energy
          - 4.3.1 Barrier Strain Energy Capacity in Elastic Region, E1
          - 4.3.2 Absorbed Energy by the Barrier, Δ1
       - 4.4 Absorbed Energy by Barrier in Plastic Region, Δ2
       - 4.5 Absorbed Energy by Vehicle Deformation, Δ3
       - 4.6 Deck Overhang Strain Energy
          - 4.6.1 Deck Overhang Strain Energy Capacity in Elastic Region, E4
          - 4.6.2 Absorbed Energy by Deck Overhang, Δ4

  5. LS-DYNA Simulation
       - 5.1 Implementation of LS-DYNA
       - 5.2 NCAC Model
          - 5.2.1 NCAC Single Unit Truck
          - 5.2.2 NCAC Rigid Barrier
          - 5.2.3 Objective of NCAC Model
       - 5.3 Proposed Model

  6. Results and Discussion
       - 6.1 Work Method
       - 6.2 Energy Method
       - 6.3 Results from Proposed Model

  7. Summary and Conclusion

  8. List of References

  9. Appendix A
       

INTRODUCTION

1.1 Background

  • The use of median barriers to divide highways and roadways has become essential in highway designs. Medians aim to provide recovery area for errant vehicles, allowing them to regain control without disrupting traffic flow.

  • Structures like bridge supports or piers close to the roadway can cause severe accidents, necessitating barriers positioned to minimize hazards and prevent collisions.

  • Barriers must be designed to prevent vehicles from penetrating and reaching critical roadway structures. Semi-rigid barriers undergo full-scale crash testing for placement in line with AASHTO standards.

  • AASHTO defines six test levels, varying based on vehicle type, impact angle and velocity with specifications for crash testing.

1.2 Problem Statement

  • The yield line method calculates external work done by applied loads as equal to internal work assessed through resisting moments along yield lines.

  • Full-scale testing has ascertained that external virtual work from vehicle impact must equal the internal virtual work established by barrier resisting moments. Calculated impact force via the yield line method tends to be conservative, failing to reflect real-world impact conditions accurately especially with respect to barriers positioned on deck overhang.

1.3 Objective

  • Propose a modified yield line method considering deck overhang through which vehicle impact is considered in energy assessments.

  • Implement an energy-based method accounting for energy absorption contributions from each component.

  • Create an LS-DYNA model for validating proposed methods, capable of simulating future variations on test levels and interactions between barriers and decks.

LITERATURE REVIEW

2.1 Guardrail Design

  • Overview of various guardrail types developed over time for collision energy absorption and controlled vehicle redirection.

  • Guardrail designs encompass geometric design alongside strength design, where geometric models dictate vehicle redirection post-collision, and strength design pertains to barrier material, size, and vehicle interaction specifics.

2.2 Barrier Strength

  • Analysis of barriers’ strength and methodology linked to yield line approaches, evaluating moment resistances across uniform thickness constructs.

WORK METHOD

3.1 Objective

  • Awareness of yield line theory as it pertains to calculating moment capacity in barrier designs under AASHTO standards.

3.2 Test Levels

  • Specification of six test levels captured under AASHTO standards defining vehicles, angles, and velocities guiding barrier designs specifically targeting TL-4 conditions (18 kips at 50 miles/hour, 15-degree impact angle).

3.3 Modified Yield Line Method

3.3.1 Unit Mass Velocity

  • Sequential use of conservation of momentum and energy demonstrates involvement of vehicle interaction dynamics post-collision.

3.3.2 Distributed Impact Force

  • Impulse distribution detailed for both vehicle and barrier interactions under chosen test levels, indicating the need for structured methodologies in impact summation across time intervals.

3.3.3 Dynamic Increase Factor

  • Investigation of concrete under varying strain rates, consolidated values and implications emanating from varying tensile strengths, rendering key differences in ductility and performance variables.

3.3.4 Moment of Inertia
3.3.4.1 Barrier

  • Determining moment of inertia across segments due to mechanical and structural dimensions, involving variances contributing to overall energy absorption during impacts.

3.3.4.1.1 Segment I

  • Analytical evaluations present moment characteristics based on rebar placements and geometrical distributions of thickness across longitudinal sections.

3.3.4.1.2 Segment II
3.3.4.1.3 Segment III
3.3.4.1.4 Barrier Section Moment of Inertia
3.3.4.2 Deck Overhang

  • Emphasis on the analysis of moment of inertia within deck overhang margins, alongside impact resistance dynamics.

3.3.5 Displacement
3.3.5.1 Barrier

  • Horizontal displacement computed as a result of impact forces, characterized within the bounds of cantilever beam definitions under dynamic loading.

3.3.5.2 Deck Overhang
3.3.5.3 Superposition
3.3.6 Strain Energy Absorption from Displacement
3.3.7 Moment Capacity of the Barrier
3.3.7.1 Vertical Moment Capacity, Mw
3.3.7.2 Horizontal Moment Capacity, Mc
3.3.7.3 Top Beam Moment Capacity
3.3.8 Internal Virtual Work along Yield Line, Eyield
3.3.9 External Virtual Work by Applied Load
3.3.10 Critical Length of Yield-Line Failure Pattern, Lc
3.3.11 Nominal Railing Resistance to Transverse Loads, Rw

ENERGY METHOD

4.1 Objective

  • Adopt a conservation of energy method to analyze impacts thoroughly across barriers and measure performances under TL-4 conditions.

4.2 Moving Vehicle Energy, IS

  • Kinetic energy as influenced by vehicle mass and crash velocity, determining the interactive effects on structures involved.

4.3 Barrier Strain Energy

4.3.1 Barrier Strain Energy Capacity in Elastic Region, E1
4.3.2 Absorbed Energy by the Barrier, Δ1

4.4 Absorbed Energy by Barrier in Plastic Region, Δ2

4.5 Absorbed Energy by Vehicle Deformation, Δ3

4.6 Deck Overhang Strain Energy

4.6.1 Deck Overhang Strain Energy Capacity in Elastic Region, E4
4.6.2 Absorbed Energy by Deck Overhang, Δ4

LS-DYNA SIMULATION

5.1 Implementation of LS-DYNA

  • Detailed accounting of the dynamics present in the simulation environment using LS-DYNA for barrier responses.

5.2 NCAC Model

5.2.1 NCAC Single Unit Truck
5.2.2 NCAC Rigid Barrier
5.2.3 Objective of NCAC Model

5.3 Proposed Model

RESULTS AND DISCUSSION

6.1 Work Method

  • Analysis derived from work methodology indicates the conservativism of the current designs necessitating reevaluation of standards for efficiency and effectiveness, derived from specified AASHTO guidelines.

6.2 Energy Method

  • Values corroborated against energy dynamics highlight non-exceedance of failure criteria for both barriers and decks across designed conditions.

6.3 Results from Proposed Model

SUMMARY AND CONCLUSION

7.1 Work Method

  • Evaluation of alignment of results against AASHTO guidelines indicate further opportunities for economization through verified methodologies.

7.2 Energy Method

  • Ancillary studies confirm both energy dynamics underpinning safe barrier performance under severe conditions which align with conventional metrics.

7.3 LS-DYNA Model

  • Provides validation for analytical conclusions drawn, reinforcing current engineering standards while emphasizing opportunities for improvement.

7.4 Recommendations for Future Studies

Recommendations

  1. Conduct field tests with various test level impacts for validation of simulation results.

  2. Reassess section sizing to improve cost efficiency without compromising safety.

  3. Redesign evaluations for new testing specifications ensuring ongoing safety in innovative barrier techniques.

APPENDIX A

NCAC MODEL KINETIC ENERGY OUTPUTS

  • Time stamps with respective kinetic energy values, demonstrating methodical iterations of energy absorption related links, reinforcing the practical evaluations.

LIST OF REFERENCES

  1. AASHTO (2010). LRFD Bridge Design Specifications, 5th ed., American Association of State Highway and Transportation Officials, Washington, DC.

  2. Barker, R., & Puckett, J. (2013). Concrete Barrier Strength and Deck Design. In “Design of highway bridges an LRFD approach (3rd ed.).” Hoboken, N.J.: John Wiley & Sons.

  3. National Crash Analysis Center. (2008, November 3). Finite Element Model Archive. Retrieved from http://www.ncac.gwu.edu/vml/models.html
     

LIST OF TABLES

  • Summary of metrics summarized in tabulated formats throughout sections, emphasizing structure and efficiency of design principles analyzed.