Table Of ContentSTATE OF CALIFORNIA • DEPARTMENT OF TRANSPORTATION
ADA Notice
For individuals with sensory disabilities, this document is available in
TECHNICAL REPORT DOCUMENTATION PAGE alternate formats. For information call (916) 654-6410 or TDD (916) 654-
TR0003 (REV 10/98) 3880 or write Records and Forms Management, 1120 N Street, MS-89,
Sacramento, CA 95814.
1. Report Number 2. Government Accession Number 3. Recipient’s Catalog Number
CA13-2349
4. Title and Subtitle 5. Report Date
The Effect of Live Load on the Seismic Response of Bridges
May 2013
6. Performing Organization Code
7. Authors 8. Performing Organization Report Number
Hartanto Wibowo, Danielle M. Sanford, Ian G. Buckle, and CCEER 13-10
David H. Sanders
9. Performing Organization Name and Address 10. Work Unit Number
Center for Civil Engineering Earthquake Research
Department of Civil and Environmental Engineering 11. Contract or Grant Number
University of Nevada, Reno, MS 258, Reno, NV 89557 59A0695
12. Sponsoring Agency and Address 13. Type of Report and Period Covered
California Department of Transportation
14. Sponsoring Agency Code
Division of Research and Innovation, MS-83
P.O. Box 942873
Sacramento, CA 94273-0001.
15. Supplementary Notes
16. Abstract
With increasing congestion in major cities the occurrence of the design earthquake at
the same time as the design live load is crossing a bridge is now more likely than in the past.
But little is known about the effect of live load on seismic response and this report describes an
experimental and analytical project that investigates this behavior. The experimental work
included shake table testing of a 0.4-scale model of a three-span, horizontally curved, steel
girder bridge loaded with a series of representative trucks. The model spanned four shake
tables each synchronously excited with scaled ground motions from the 1994 Northridge
earthquake. Observations from the experimental work showed the presence of the live load had
a beneficial effect on performance of this bridge, but this effect diminished with increasing
amplitude of shaking. Parameters used to measure performance included column displacement,
abutment shear force, and degree of concrete spalling in the plastic hinge zones. Results
obtained from a SAP2000 analysis of a nonlinear finite element model of the bridge and trucks
confirmed this behavior, that live load reduces the dynamic response of the bridge. The most
likely explanation for this phenomenon is that the trucks act as a set of nonlinear tuned mass
dampers, which are known to be effective at controlling wind vibrations in buildings.
Preliminary parameter studies have also been conducted and show the above beneficial effect is
generally true for other earthquake ground motions, and vehicles with different dynamic
properties. Exceptions exist, but adverse effects are usually within 10% of the no-live load
case.
17. Key Words 18. Distribution Statement
seismic response, bridges, live load, shake No restriction. This Document is available to
table experiments, finite element modeling, the public through the Center for Civil
parameter studies Engineering Earthquake Research,
University of Nevada, Reno, NV, 89557.
19. Security Classification (of this Report) 20. Number of Pages 21. Cost of Report Charged
Unclassified 422
Reproduction of completed page authorized.
DISCLAIMER STATEMENT
This document is disseminated in the interest of information exchange. The contents of
this report reflect the views of the authors who are responsible for the facts and accuracy
of the data presented herein. The contents do not necessarily reflect the official views or
policies of the State of California or the Federal Highway Administration. This
publication does not constitute a standard, specification or regulation. This report does
not constitute an endorsement by the Department of any product described herein.
For individuals with sensory disabilities, this document is available in Braille, large print,
audiocassette, or compact disk. To obtain a copy of this document in one of these
alternate formats, please contact: the Division of Research and Innovation, MS-83,
California Department of Transportation, P.O. Box 942873, Sacramento, CA 94273-
0001.
Report No. CCEER 13-10
THE EFFECT OF LIVE LOAD ON THE
SEISMIC RESPONSE OF BRIDGES
Hartanto Wibowo
Danielle M. Sanford
Ian G. Buckle
David H. Sanders
A report to the California Department of Transportation
Contract No. 59A0695
Center for Civil Engineering Earthquake Research
University of Nevada, Reno
Department of Civil and Environmental Engineering, MS258
1664 N. Virginia St.
Reno, NV 89557
May 2013
ACKNOWLEDGMENTS
This project was principally funded by California Department of Transportation
(Caltrans) under contract number 59A0695. The Caltrans Program Manager was Dr.
Allaoua Kartoum. The experimental work undertaken in this study was part of a larger
project on the seismic behavior of curved bridges funded by the Federal Highway
Administration (FHWA) under contract number DTFH61-C-00031. The FHWA Contract
Technical Representative was Dr. Wen-huei (Phillip) Yen. The authors therefore wish to
acknowledge both Caltrans and FHWA and their respective program managers for their
sponsorship and oversight of this project.
In particular the authors acknowledge FHWA for the construction and
instrumentation of the model as well as the following graduate students who worked on
various phases of this project: Nathan Harrison, Ebrahim Hormozaki, Michael Levi, Eric
Monzon, Ahmad Saad, Chunli Wei, and Joseph Wieser. In addition, valuable faculty
support was provided by Dr. Ahmad Itani and Dr. Gökhan Pekcan. The authors would
also like to express their gratitude to Dr. Koji Kinoshita (Visiting Professor), Dr. Arash
Esmaili Zaghi (Post-doctoral Scholar), and Moustafa Al-Ani (Visiting Researcher) for
their contribution to this project. Furthermore, the experimental work would not have
been possible without the skill and dedication of the laboratory staff including Kelly
Doyle, Dr. Sherif Elfass, Dr. Patrick Laplace, Robert Nelson, Mark Lattin, Chad Lyttle,
Todd Lyttle, Paul Lucas, as well as student workers including Kevin Boles and Joel
Heidema.
Finally, the authors acknowledge the National Science Foundation for the use of
the NEES Shake Table Array at the University of Nevada, Reno under a Shared-Use
Agreement with NEEScomm at Purdue University.
iv
TABLE OF CONTENTS
Acknowledgements, iv
Table of Contents, 1
Abstract, 5
Chapter 1 Introduction, 6
1.1. General, 6
1.2. Background, 6
1.3. Problem Statement, 7
1.4. Scope of Study, 7
1.5. Organization of Report,8
1.6. Summary, 8
Chapter 2 Literature Review, 10
2.1. General, 10
2.2. Previous Studies of the Impact Effects of Live Load on Bridges, 10
2.3. Previous Studies of Live Load Effects on the Seismic Response of Bridges, 14
2.3.1. Live Load Effects on the Seismic Response of Highway Bridges, 14
2.3.2. Live Load Effects on the Seismic Response of Railway Bridges, 16
2.4. Previous Studies on the Effects of Multiple Tuned-Mass Dampers and Nonlinear
Energy Sinks on Structure Response, 17
2.5. Vehicle Models, 18
2.5.1. Single Degree-of-Freedom Vehicle Models, 19
2.5.2. Multiple Degree-of-Freedom Vehicle Models, 19
2.6. Summary, 21
Chapter 3 Vehicle Selection and Characterization, 28
3.1. General, 28
3.2. Vehicle Selection, 28
3.2.1. Background and Rationale, 28
3.2.2. Basic Vehicle Data, 29
3.3. Single Truck Experiment Setup, 29
3.3.1. Outrigger Beam Design, 29
3.3.2. Experiment Configuration, 30
3.3.3. Experiment Logistics, 30
3.3.4. Experiment Protocol, 30
3.3.5. Instrumentation Plan, 31
1
3.4. Numerical Models, 31
3.4.1. Single-Axle Model, 32
3.4.2. Two-Axle Model, 32
3.5. Truck Properties in Vertical Direction, 33
3.5.1. Application of Snap Test Data to Determine Truck Properties, 33
3.5.2. Truck Vertical Properties without Tires, 35
3.5.2.1. Empty Truck, 35
3.5.2.2. Fully-Laden Truck, 35
3.5.3. Truck Vertical Properties with Tires, 35
3.6. Truck Properties in Longitudinal and Transverse Directions, 36
3.6.1. Truck Properties in Transverse Direction, 37
3.6.2. Truck Properties in Longitudinal Direction, 37
3.7. Vehicle Response during Earthquake Excitation, 37
3.7.1. Observed Vehicle Response, 37
3.7.1.1. Vertical Direction, 38
3.7.1.2. Transverse and Longitudinal Directions, 38
3.7.1.3. Empty and Fully-Laden Trucks, 39
3.7.2. Comparison of Numerical Model and Observed Responses, 39
3.8. Modal Properties of Truck, 40
3.9. Summary, 40
Chapter 4 Bridge Model and Experiment Setup, 61
4.1. General, 61
4.2. Prototype Bridge and Scaling Requirements, 61
4.2.1. Prototype Bridge Selection, 61
4.2.2. Seismic Hazard, 61
4.2.3. Scaling and Similitude Requirements, 62
4.3. Model Substructure Design and Instrumentation Plan, 63
4.3.1. Column, 63
4.3.2. Footing, 63
4.3.3. Bent Cap, 63
4.3.4. Additional Substructure Mass, 64
4.3.5. Instrumentation Plan, 64
4.4. Model Superstructure Design and Instrumentation Plan, 65
4.4.1. Girders, 66
4.4.2. Deck Slab, 66
4.4.3. Cross Frames, 67
4.4.4. Shear Keys, 67
4.4.5. Additional Superstructure Mass, 68
4.4.6. Instrumentation Plan, 68
4.5. Model Construction, 69
4.6. Live Load Vehicle, 69
4.6.1. Vehicle Placement, 70
4.6.2. Vehicle Instrumentation, 70
4.7. Ground Motion and Test Matrix, 71
2
4.7.1. Ground Motion, 71
4.7.2. Test Matrix, 72
4.8. Summary, 72
Chapter 5. Experimental Results, 117
5.1. General, 117
5.2. Material Properties, 121
5.2.1. Concrete, 117
5.2.2. Steel Reinforcement, 117
5.2.3. Section Analysis, 118
5.3. Shake Table Performance, 118
5.4. Bridge Dynamic Properties, 118
5.4.1. System Frequency, 119
5.4.2. System Damping, 119
5.5. Bridge Displacement, 120
5.6. Bridge Acceleration, 121
5.7. Bridge Forces and Moments, 121
5.7.1. Force and Moment Histories from Load Cells, 121
5.7.2. Calculation of Force and Moment at Bottom of the Bent, 122
5.7.3. Force vs. Displacement and Moment vs. Curvature Relationships, 124
5.8. Column Damage, 126
5.8.1. Cracking and Spalling, 126
5.8.2. Reinforcement Yield Strain, 127
5.8.3. Post-Experiment Torsional Stiffness, 127
5.9. Shear Key Performance, 128
5.10. Discussion, 128
5.11. Summary, 128
Chapter 6. Analysis Results and Validation of Numerical Model, 345
6.1. General, 345
6.2. Bridge Model and Input Motion, 345
6.2.1. Model Development, 345
6.2.2. Input Motion for Nonlinear Response History Analysis, 348
6.3. Vehicle Model, 348
6.3.1. Model Development, 348
6.3.2. Vehicle Properties, 348
6.4. Refinements to Analytical Model, 345
6.5. Structural Response and Comparison with Experimental Results, 349
6.5.1. Displacement, 349
6.5.2. Acceleration, 349
6.5.3. Forces and Moments, 350
6.6. Analysis of Bridge Model With and Without Live Load, 350
6.7. Discussion, 350
3
6.7. Summary, 350
Chapter 7. Preliminary Parameter Study, 371
7.1. General, 371
7.2. Parameters of Interest, 371
7.2.1. Live Load to Bridge Mass Ratio and Live Load Period, 371
7.2.2. Earthquake Ground Motion, 372
7.2.3. Number of Vehicles, 372
7.3. Numerical Models, 372
7.3.1. Stick Model, 372
7.3.2. Finite Element Model, 372
7.4. Parameter Study Results, 373
7.4.1. Effect of Live Load-to-Structure Mass Ratio, Vehicle Period, Damping
and Ground Motion, 373
7.4.2. Effect of Earthquake Ground Motion, 373
7.4.3. Effect of Number of Vehicles and Placement, 374
7.5. Discussion, 375
7.6. Summary, 375
Chapter 8 Observations and Recommendations, 391
8.1. Observations, 391
8.2 Recommendations / Future Work, 392
References, 393
Appendix A Basic Theory for Tuned Mass Dampers (TMD) and Multiple Tuned Mass
Dampers (MTMD), 405
A.1 General, 405
A.2 Undamped Structure and Undamped Tuned Mass Damper, 405
A.3 Undamped Structure and Damped Tuned Mass Damper, 407
A.4 Damped Structure and Damped Tuned Mass Damper, 409
A.5 Multiple Degree-of-Freedom System with Tuned Mass Damper, 410
A.6 System with Multiple Tuned Mass Dampers, 414
A.7 Summary, 414
4
ABSTRACT
With increasing congestion in major cities the occurrence of the design
earthquake at the same time as the design live load is crossing a bridge is now more
likely than in the past. But little is known about the effect of live load on seismic
response and this report describes an experimental and analytical project that investigates
this behavior. The experimental work included shake table testing of a 0.4-scale model of
a three-span, horizontally curved, steel girder bridge loaded with a series of
representative trucks. The model spanned four shake tables each synchronously excited
with scaled ground motions from the 1994 Northridge earthquake. Observations from the
experimental work show the presence of the live load had a beneficial effect on
performance of this bridge, but this effect diminished with increasing amplitude of
shaking. Parameters used to measure performance included column displacement,
abutment shear force, and degree of concrete spalling in the plastic hinge zones. Results
obtained from a SAP2000 analysis of a nonlinear finite element model of the bridge and
trucks confirm this behavior, that live load reduces the dynamic response of the bridge.
The most likely explanation for this phenomenon is that the trucks act as a set of
nonlinear tuned mass dampers, which are known to be effective at controlling wind
vibrations in buildings. Preliminary parameter studies have also been conducted and
show the above beneficial effect is generally true for other earthquake ground motions,
and vehicles with different dynamic properties. Exceptions exist, but adverse effects are
usually within 10% of the no-live load case.
5
CHAPTER 1. INTRODUCTION,
1.6. General
An experimental and analytical study on the effect of live load on the seismic
response of ordinary bridges has been conducted. The experimental study featured a
series of shake table tests on a large-scale model of a 3-span bridge loaded with six
representative trucks. The experiment was used to gain insight into the effect of trucks on
seismic response and to validate a computer model of the bridge-vehicle system. This
report presents the findings from the study and shows that live load changes the behavior
of bridge during an earthquake and, in this case, in a beneficial way.
1.2. Background
Dynamic interaction between vehicles and bridges has long been studied, but
mainly in regard to the impact effect of live load due to surface roughness and vehicle
speed and not the dynamic effect of sprung live load on seismic behavior. Consequently
the effect of vehicle-bridge interaction on the seismic response is not well understood.
Bridge design specifications have few requirements concerning the inclusion of
live load in the seismic design of bridges for perhaps two reasons. The likelihood of the
full design live load occurring at the same time as the design earthquake is judged to be
negligible, and adverse behavior due to live load in an earthquake has not been observed
in practice. But traffic congestion has become a common situation in major cities and the
occurrence of significant live load at the time of a major earthquake is much more likely
than previously thought possible. It is clear that live load not only provides additional
gravity load but also dynamic force effects due to its sprung nature. However, the
significance of these effects on the seismic response of a bridge is not very obvious.
The live load project described in this report was undertaken to investigate this
question. It was able to take advantage of a separate study being conducted on the seismic
response of curved bridges at the University of Nevada, Reno. Funded by the Federal
Highway Administration (FHWA), this study involved a series of shake table
experiments on a 0.4-scale model of three-span steel girder bridge with a high degree of
horizontal curvature, as shown in Figure 1.2.1. This series included a conventional bridge
with and without abutment pounding, and an isolated bridge with full, hybrid, and
rocking isolation systems, as shown in Table 1.2.1.
For the purpose of the live load project described in this report six trucks were
placed on the conventional bridge and performance compared with the no-live load case.
Experimental studies on curved bridges have been done previously with either static
testing (Clarke, 1966; Culver and Christiano, 1969) or dynamic testing (Williams and
Godden, 1979; Kawashima and Penzien, 1979). However, those studies were done at a
6
