Citation
Response monitoring and modeling of constructed light rail bridges

Material Information

Title:
Response monitoring and modeling of constructed light rail bridges
Creator:
Liu, Lianjie ( author )
Language:
English
Physical Description:
1 electronic file (129 pages). : ;

Subjects

Subjects / Keywords:
Railroad bridges ( lcsh )
Live loads ( lcsh )
Bridges -- Live loads ( lcsh )
Bridges -- Live loads ( fast )
Live loads ( fast )
Railroad bridges ( fast )
Genre:
bibliography ( marcgt )
theses ( marcgt )
non-fiction ( marcgt )

Notes

Review:
Light rail bridge is an important part of the public transportation system. The current light rail bridges are designed by the exist codes. However codes are only specifying the design procedure of high way bridges and they are lack of guidance for design rails and light rail train load. This research evaluated the constructed five light rail bridges in Denver Colorado. The work includes testing and computer program modeling. The testing part includes lab test and field test. A steel rail s strain is tested on lab my simulated light rail train with different types of boundary conditions. The steel rail on Auraria Campus Station and five working light rail bridges are tested on this research. The five tested bridges are the Indiana Bridge Santa Fe Bridges 6th Ave Bridge Broadway Bridge and County Line Bridge. The strain change on the steel rail which is applied the light rail load is collected on the Auraria Campus Station and five light rail bridges and girder response of the five bridge also recorded on this project. The dynamic response of the five bridges is also monitored. The models of the five light rail bridges are built on the computer modeling programs of SAP 2000 and CSI Bridge to analysis the static and dynamic response of the light rail wheel load. The analysis by modeling of steel rail break gaps cuts the steel rail by the length of 1 2 and 3 inch respectively. The study also compares the dynamic load allowance DLA without and with rail break gaps in different length. Analysis of the thermal load on the light rail break is concluded on this research. It was shown that the current design code is conservative but acceptable used on the design of light rail bridge.
Thesis:
Thesis (M.S.)--University of Colorado Denver.
Bibliography:
Includes bibliographic references.
System Details:
System requirements: Adobe Reader.
General Note:
Department of Civil Engineering
Statement of Responsibility:
by Lianjie Liu.

Record Information

Source Institution:
|University of Colorado Denver
Holding Location:
Auraria Library
Rights Management:
All applicable rights reserved by the source institution and holding location.
Resource Identifier:
930370311 ( OCLC )
ocn930370311

Downloads

This item has the following downloads:


Full Text
RESPONSE MONITORING AND MODELING OF CONSTRUCTED LIGHT RAIL
BRIDGES
By
LIANJIE LIU
B.S., Northeast Forestry University, PR China, 2012
A thesis submitted to the
Faculty of the Graduate School of the
University of Colorado in partial fulfillment
of the requirements for the degree of
Master of Science
Civil Engineering
2015


This thesis for the Master of Science degree by
Lianjie Liu
has been approved for the
Civil Engineering program
By
Yail Jimmy Kim, Chair
Frederick Rutz
Chengyu Li
07/22/2015


Liu, Lianjie(M.S., Civil Engineering)
Response Monitoring and Modeling of Constructed Light Rail Bridges
Thesis directed by Associate Professor Yail Jimmy Kim
ABSTRACT
Light rail bridge is an important part of the public transportation system. The
current light rail bridges are designed by the exist codes. However, codes are only
specifying the design procedure of high way bridges, and they are lack of guidance
for design rails and light rail train load. This research evaluated the constructed five
light rail bridges in Denver, Colorado. The work includes testing and computer
program modeling.
The testing part includes lab test and field test. A steel rails strain is tested on lab
my simulated light rail train with different types of boundary conditions. The steel rail
on Auraria Campus Station and five working light rail bridges are tested on this
research. The five tested bridges are the Indiana Bridge, Santa Fe Bridges, 6th Ave
Bridge, Broadway Bridge, and County Line Bridge. The strain change on the steel rail
which is applied the light rail load is collected on the Auraria Campus Station and five
light rail bridges, and girder response of the five bridge also recorded on this project.
The dynamic response of the five bridges is also monitored.
The models of the five light rail bridges are built on the computer modeling
programs of SAP 2000 and CSI Bridge to analysis the static and dynamic response of
iii


the light rail wheel load. The analysis by modeling of steel rail break gaps cuts the
steel rail by the length of 1, 2, and 3 inch respectively. The study also compares the
dynamic load allowance (DLA) without and with rail break gaps in different length.
Analysis of the thermal load on the light rail break is concluded on this research. It
was shown that the current design code is conservative but acceptable used on the
design of light rail bridge.
The form and content of this abstract are approved. I recommend its publication.
Approved: Yail Jimmy Kim
IV


ACKNOWLEDGEMENTS
I wish to express my deep gratitude to my advisor, Dr. Yail Jimmy Kim, for his
invaluable instruction and multifaceted support during my graduate study, and
guidance of my research.
I wish to thank the faculty and staff of the Structural Engineering Department at
University of Colorado, Denver. I thank Dr. Chengyu Li and Dr. Frederick Rutz for
participating on my thesis committee. Thank are also extended to my partners of my
research team. I am grateful to acknowledge financial support provided by the
National Academy of Sciences.
I also wish to acknowledge my parents for their understanding and great support
throughout all the years of my educational pursuits.
v


TABLE OF CONTENTS
CHAPTER
I. INTRODUCTION........................................................1
Background.........................................................1
Objective..........................................................2
Research Significance..............................................3
Thesis Outline.....................................................4
II. LITERATURE REVIEW...................................................7
Bridge Types for Light-Rail Transportation.........................7
Concrete Girder Bridges........................................7
Prestressed Concrete Girder Bridges............................9
Steel Girder Bridges..........................................10
Loads Analysis....................................................10
Light-Rail Bridges Dynamic Analysis...............................12
Dynamic Behavior..............................................12
Mode Shape....................................................13
Dynamic Load Allowance........................................13
Thermal Load......................................................14
vi


Uniform Temperature Change
15
Gradient Temperature Change....................................16
AREMA design code..............................................17
Figures and Tables.................................................18
III. SITE WORK MONITORING OF LIGHT RAIL BRIDGE..........................27
Equipment of Test..................................................27
CR 5000 Data Logger............................................27
Other Equipment................................................28
Introduction of Tested Bridges.....................................28
Broadway Bridge................................................28
Indiana Bridge.................................................29
Santa Fe Bridge................................................29
County Line Bridge.............................................29
6th Avenue Bridge..............................................30
Testing Procedure..................................................30
Lab Test.......................................................30
Site Visit.....................................................31
Site Work Monitoring...........................................31
Dynamic Response Test..........................................34
vii


Temperature Effect On Train Rails
34
Tables and Figures...................................................36
IV. BRIDGE MODELING......................................................54
Property of Five Bridges Models......................................54
Section Properties...............................................54
Vehicular Loads..................................................55
Other Properties of Bridge Models................................55
Dynamic Response of Bridges..........................................56
Rail Break Gaps......................................................57
Thermal Load.........................................................58
Tables and Figures...................................................59
V. RESULTS AND ANALYSIS..................................................64
In-Situ Work Testing Results.........................................64
Wheel Load Analysis..............................................64
Girder Response..................................................67
Dynamic Response.................................................68
Temperature Effect on Train Rails................................69
Results From Simulation..............................................70
.70
viii
Dynamic Response Analysis


Rail Break Gaps...........................................71
Thermal Load and Frequency of Bridges.....................71
Analysis of Result............................................72
Natural Frequency.........................................72
Dynamic Response of Rail Break............................72
Temperature Change........................................72
Speed effect..............................................73
Tables And Figures............................................74
VI. CONCLUSION AND RECOMMENDATION..................................97
Conclusion....................................................97
Recommendation................................................98
REFERENCES........................................................100
APPENDIX..........................................................102
A. Modification of Bridge Model Example...........................102
IX


LIST OF FIGURES
FIGURE
2.1 Reinforced Concrete Beam.............................................19
2.2 The Behavior of Reinforced Concrete and Prestressed Concrete Beam Under Load
.........................................................................20
2.3 Light Rail Train and Truck Wheel Load ................................21
2.4 Forces Acting an the Mass ............................................21
2.5 Free Body Diagram of Two Degree of Freedom System....................21
2.6 Simply Supported Beam Subject to Thermal Load.........................22
2.7 Contour Maps..........................................................24
2.8 Solar Radiation Zones for The United States...........................25
2.9 Vertical Temperature Gradient.........................................25
3.1 CR 5000 Measurement and Control System................................36
3.2 Experimental Setup and Strain Gage Configurations for The Side ond Bottom of
the Rail..................................................................37
3.3 115RERail Subjected to Load With Continuous System....................37
3.4 Five Bridge Prepare to Test...........................................40
3.5 Broadway Bridge.......................................................42
x


3.6 Indiana Bridge........................................................43
3.7 Santa Fe Bridge.......................................................45
3.8 County Line Bridge....................................................48
3.9 6th Avenue Bridge.....................................................49
3.10 Typical Temperature Variation Of Track Rail, Broadway Bridge.........50
4.1 Section Properties of Bridge Deck and Girder: Indiana Bridge...........59
4.2 Models of Five Bridges...............................................62
4.3 Steel Rail Break on Models............................................63
4.4 Temperature Gradient of Five Bridges..................................63
5.1 Load-Strain Behavior at Bottom of Rail:................................74
5.2 Load-Strain Behavior on The Side of Continuous Rail....................74
5.3 Validation of Portable Data Comparison Acquisition System Using Rail Strain at
Bottom....................................................................75
5.4 Wheel Positioning Of Auraria West Station.............................75
5.5 Comparison Between In-Situ Test And Laboratory Test (Front Wheel Load).75
5.6 Measured Strains For Light Rail Train Wheel Load:.....................78
5.7 Fully-Loaded Design Axle Loads of The Light Rail Train Operated in Denver, CO
78
xi


5.8 Distribution of Measured Train Wheel Load
79
5.9 Flexural Response of Monitored Bridges:................................81
5.10 Deflection of Bridge Models..........................................84
5.11 Bending Moment Diagram of Bridges....................................86
5.12 Rail Break Model at Piered Location..................................87
5.13 Speed effect of five bridges.........................................89
xii


LIST OF TABLES
TABLE
1.1 Field Test Bridges..................................................6
2.1 Dynamic Load Allowance.............................................26
2.2 Ranges of Temperature In Procedure A...............................26
2.3 Basis for Temperature Gradients....................................26
3.1 Purpose of Equipment Used In Site Work.............................51
3.2 Summary of Five Tested Bridge Details..............................52
3.3 Maximum Temperature Variation of the Monitored Bridges.............53
5.1 Comparison Between Measured and Predicted Fundamental Frequencies..90
5.2 Assessment of Deflection Control...................................90
5.3 Maximum Temperature Variation of The Monitored Bridges.............91
5.4 Bridge Span and Span Length........................................92
5.5 Dynamic Response From Bending Moment at Piers......................93
5.6 Dynamic Response From Displacement at Mid-Span.....................93
5.7 Dimensions of Steel Rail...........................................93
5.8 Dynamic Response With Rail Break from Bending Moment At Piers......94
xiii


5.9 Dynamic Response With Rail Break from Displacement at Mid-Span........94
5.10 Natural Frequencies from Models......................................94
5.11 Thermal in Different Zone of Bridges From Models.....................95
5.12 Dynamic Load Allowance from Bending Moment............................95
5.13 Dynamic Load Allowance from Displacement..............................95
5.14 Thermal Load of Five Bridges from Calculation.........................96
5.15 Dynamic load allowance from moment with 20 mph speed..................96
5.16 Dynamic load allowance from moment with 40 mph speed..................96
xiv


CHAPTER I
INTRODUCTION
Background
Light rail system plays an important role in current United Stated public
transportation system. According to the report of American Public Transportation
Association, there are 27 areas in the United Stated have light rail transportation
system. Up to 2011, there are 436 million unlinked passenger trips and 2,203 million
passenger miles used by light rail. (APTA, 2013) Bridges are required in the light rail
system because the railways need to pass through urban roads and highways. The
light rail bridges safety is an important point for the light rail system. Light rail
bridges support static load and dynamic load, and the dynamic load varies in different
kinds of situation.
There are many old built light rail bridges in the United States. Steel rail breaks
gaps are cut on the bridges because the technology limit in this time. The rail break
makes interaction between the rail and light rail train. It means the dynamic load of
the light rail bridges are influenced by the rail gaps. The thermal load on the light rail
bridges is also not clear on the current design codes.
Due to the development of the bridge engineering, the light rail bridges may have
longer span and the light rail trains may run on the bridges with a higher speed in the
future. It is unknown that if the previously dynamic load allowance is meet the
1


requirement for the future light rail bridge. The analysis for the influence of dynamic
load allowance by different aspects of the bridges is necessary, and it is possible to do
with the finite element analysis software.
Objective
Girder bridges are the most widely used type on the light rail transportation
system, so the objective is to analysis the girder bridges used on the light rail
transportation system. There is no code specified with light rail bridge, so the
designers have to use different related design code on the design but conflict presents
on these codes. These make some problems on the design and maintain of light rail
bridges.
It is necessary to compare the results between site work test and model
calculation, so the first of all is to test the light rail bridges. Five light rail bridges are
selected in this test. For the finite element analysis, light rail bridges are modeled with
the CSI Bridge and SAP2000 with the five tested bridges, and some other programs
such as Matlab are used for calculation.
The dynamic load allowance also varies depends on the load case. The light rail
train load is differing with the common vehicles load. To model the light rail bridges,
the standard vehicle loads which are provided by AASHTO are not acceptable to be
used as vehicular load. In this case, the light rail train loads for the modeling are
defined manually according to the existing light rail train in the United States public
transportation system.
2


The objective is to find the response of light rail bridges from vehicular and
thermal load, and dynamic load allowance changing rules influenced by rail break.
The value changing trend of dynamic load allowance which are influenced by length
of rail break gaps are compared respectively.
Research Significance
The purpose of this research is to calibrate the dynamic load allowance for the
light rail girder bridges. This research will find the changing value of dynamic load
allowance based on the field test and modeling. This will help to estimate some
advices on design of light rail bridge.. Some light rail train may be improved in the
future, and if the train load changed, this research may have a reference value. In
additional, the rail break is concerned in this research to help the calibration of the
light rail bridges dynamic allowance factor especially for the light rail bridge with rail
break gaps.
Thesis Outline
Chapter 1 of the thesis introduces the background and objectives of this research
and this chapter also state the goals of this research. Chapter 2 reviews the different
types bridges used in the light rail public transportation system. A review of the light
rail train vehicular load is presented. This chapter also discusses the dynamic analysis
of structure and dynamic load allowance. A discussion of temperature change of
structure is concluded in this chapter.
3


Chapter 3 presents the site work light rail girder bridge deformation testing. The
tested bridges are shown on table 1.1. The testing equipment is introduced, and it
discusses the procedure of this test. The strain values of steel rail and girders on the
bridges are tested by strain gages when the light rail trains pass through the bridge.
The following part represents the translation of data from the bridge displacements
and bridge natural frequency by fast Fourier translation.
Chapter 4 describes the bridge models design and modeling. First of all, the
dimensions of girders are designed by following the AASHTO code. Finite element
analysis computer programs are used in building bridge models. Some general
assumptions such as boundary conditions are used for modeling. Using SAP2000 and
CSI Bridge to model the designed bridges, and make a collection for the calculated
light rail bridges data (such as moment, displacement, and frequencies). Secondly, a
discussion of rail break and thermal load is presented. Finally, modeling of thermal
load is provided.
Chapter 5 is the discussion on the testing and modeling result. The results of wheel
load, strain, temperature change, and dynamic response are analyzed from field test.
After that, the moment and displacement on modeling are compared with the data
without rail break to find the enhanced value of dynamic allowance. The comparison
of modeled and calculated thermal load is discussed.
Chapter 6 presents the conclusions of the dynamic load allowance which is
influenced by different factors. Continuously, the effect of rail break is discussed.
4


There is a comparison with the results between the site work results and the modeling
data in this chapter. At last, a direction for the future research about the dynamic load
allowance is provided.
5


Tablel.l Field Test Bridges
No. bridge
1 6th avenue bridge
2 Broadway bridge
3 County line bridge
4 Indiana bridge
5 Santa-fee bridge
6


CHAPTER II
LITERATURE REVIEW
This chapter introduces the concepts used in the finite element analysis in light
rail bridges, and introduces the typical type of bridges. This chapter also reviews the
dynamic behaviors of light rail bridges, especially the dynamic behaviors of rail break
gaps and thermal load influences.
Bridge Types for Light-Rail Transportation
Different types of bridges are used in the light rail transportation system. Bridges
can be subscribe as arch bridges, truss bridge, suspension bridges, cable stayed
bridges, and girder bridges. Most of the light rail bridges are girder bridges. This
research will mainly discuss girder bridges.
Concrete Girder Bridges
Concrete is consists of fine aggregate, coarse aggregate, Portland cement, and
water. Concrete is used as structural material for many centuries. The reinforced
concrete is also used for more than one hundred years in structure engineering.
Because the reinforced concrete can be shaped easily with high strength and the
economic efficiency of reinforced concrete is good, the reinforced concrete is widely
used all over the world.
Concrete is a kind of material with strong compression strength and weak tension
strength, so the tensile stresses which is from loads, temperature changes, and
7


restrained shrinkage cause cracks (Wight and MacGregor 2012). The load condition is
shown on figure 2.1. A simply support reinforced concrete beam is subjected to
vertical loads (figure 2.1 (a)). In figure 2.1 (b), point O is a point assumed on the
neutral axis. The part under the neutral axis is applied tensile stresses. As explained
previous, concretes tensile strength is much lower than the compressive strength,
then crack occurred. As a result, beam fails very suddenly and completely if the
concrete is unreinforced (Wight and MacGregor 2012). The reinforcing bars are
shown on figure 2.1 (c). These steel reinforcements embedded in the concrete are
supporting the tensile internal forces so that the concrete can work under the condition
of the tensile stress is beyond the concrete tensile strength but lower than the
reinforcing bars tensile stress.
The reinforced concrete of structures should use that not exceed the limit states.
James K. Wight indicate that the limit states of the reinforced concrete elements of
structures can be divided into the ultimate limit states, serviceability limit states, and
special limit state. The major ultimate limit states contain loss of equilibrium,
progressive collapse, rupture, instability, formation of a plastic mechanism, and
fatigue. Serviceability limit states include the excessive deflections, excessive crack
widths, and undesirable vibration. The special limit state is due to abnormal
conditions or loadings and physics damages.
The reinforced concrete girder bridges are widely used for short and medium
span highway and railway design. The superstructure of reinforced concrete girder
8


bridges is mainly consists of the reinforced concrete girders, bridge deck, barriers, and
pavements. The girders on the reinforced concrete bridges can be I girders, Tees, or
box girders.
Prestressed Concrete Girder Bridges
Prestressed concrete has developed rapidly in recent decades. The method of
prestressed concrete is improved from the reinforced concrete. As discussed
previously, the reinforced concrete cause micro cracks in the tension zone by service
loads. The concrete in the tension zone is not expected to support the tensile stresses,
so the reinforced concrete work with these crack and on exceed the limit states.
However, cracks cause the reinforcing bars expose on the air then corrosion occurred,
and cracks are looks unsafe.
Prestressed concrete element is more attractive and durable than reinforced concrete,
and it can possess higher strength (Naaman 2004). A comparison of reinforced
concrete and prestressed concrete beam is shown on figure 2.2. The prestressing steel
tendons are tensioned during or after the prestressed concrete beam casted. When the
prestressed concrete beam posted, beam itself only subject to dead load caused by
self-weight. The upper part is subjected to tensile force but no cracks, and the under
part is subjected to compressive force caused by the tensioned prestressing tendons.
Under the full service load applied on the beam, only steel tendons are subjected to
the tensile stress so the concrete on the tension zone are uncracked.
9


Prestressed concrete girder bridges can be classified by precast pretensioned
girders or posttensioned girders. Precast pretensioned girders are usually cast on the
labs or factories. The prestressed steel tendons are tensioned when the girder casted.
The tendons and concrete are bonded by friction. Posttensioned beam are apply
tensile stress after the concrete casted. Steel tendons are tensioned in the duct of
concrete and bond on boundary of the beam. The prestressed concrete girder bridge
can be up to 180 feet span length.
Steel Girder Bridges
Steel girder bridges are use steel girders to sustain loads, and concrete bridge
deck is usually used. The steel girders can be precast girders or consist of steel plates.
The precast beam can be I shape, T shape, rectangular hollow shape, L shape, and
some other shapes. The steel plate girders are built up from plate elements and
connected by high tensile strength bolts.
The steel plate girder can actually regard as deep beam (Salmon, Johnson and
Malhas 2009). Because steel plate girder is slender, local bucking should be
concerned. Stiffeners are used on steel plate girder to sustain shear force.
Loads Analysis
Load types due to highway bridge design can be classified dead loads, live loads,
pedestrian load, and vehicular dynamic load allowance. The AASHTO define the total
factored force effect as
10


Q= Iv iYiQi
(2.1)
Where r]t is the load modifier, Yi is the load factor, and Qt is force effects from
loads. For instance, the permanent load of component and attachments is taken load
factor as 0.9 to 1.25, and the load modifier is taken 1 for typical bridge.
The permanent load is consists of dead loads and earth loads. The live load is
consists of gravity loads, vehicular live load, fatigue load, dynamic load allowance,
centrifugal forces, braking force, and vehicular collision force. There are some kinds
of loads such as water loads and wind load.
The vehicular wheel load is the live load applied by the vehicles on the bridges.
For the general high way bridges, the AASHTO instruct to use designated HL-93
which is consist of the design truck or tandem and design lane load. From the
AASHTO LRFD bridge design specifications, the design truck is shown on figure 2.3,
and the design tandem is consist of two 25 kips axle loads with 4 feet spacing, and the
transverse spacing is 6 feet. The design lane load is a uniformly distributed
longitudinal load of 0.64 kips per foot. This uniformly distributed load is assumed
with a width of 10 feet.
The wheel load of the light rail trains is not represented from the AASHTO. In
this research, the design wheel load of light rail trains are taken from the RTD. The
light rail train wheel load used in Denver is shown in figure 2.4. The full train load
11


and empty train load are defined from the RTD. The full train load is used in this
research.
Light-Rail Bridges Dynamic Analysis
Dynamic Behavior
The single degree of freedom system (SDOF) is a simplified system of structures.
The SDOF system is idealized the mass of the structure is a point that supported by a
massless beam (Chopra 2012). The elastic modulus of the beam is constant. In the
linear system, the damping ratio of the structure is constant. The force of the vibration
{Fs} is related by the displacement of the mass {u} and the elastic modulus {k}.
(Equation 2.2) The damping ratio {c} relates the velocity {it} and damping force
{Fd}. (Equation 2.3) The mass of the structure {m} relates the acceleration {ii} and
inertia force {p}. (Equation 2.4)
Fs = ku (2.2)
II n (2.3)
P= mil (2.4)
Figure 2.4 show the forces acting on the single mass. The external force P(t) is
consist of the force of the vibration {Fs}, damping force {Fd}, and inertia force {p}.
Based on the Newton Second Law the equation of motion of the single degree of
freedom is given by equation 2.5.
(2.5)
P(t) = ku + cu + mil
12


In the bridge analysis of this research, a number of degree of freedom is used. As
a result, the multiple degree of freedom system (MDOF) is applied. For example, in
the two degree of freedom system, the values of the equation of motion are instead by
matrix as shown
\mi 1 { % + ( /di} + { fsi} = { Pl(t)}
L 0 m2i{ v 1 fD2> 1 fS2> 1 p2(t)j
(2.6)
Figure 2.5 shows the free body diagram of two degree of freedom system. The
external forces Pi(t) and p2(t) are subjected to two masses mx and m2
respectively (springs and viscous dampers are linear).
Mode shape
Vibration mode is defined by the natural frequency, mode shape and damping
value (Craig and Kurdila 2006). In the multiple degree of freedom system, the mode
shapes are depending on the number of degree of freedom. The relationship can be
describe as
kO=mOft2 (27)
where the matrix frequencies.
2.3.3Dynamic load allowance
Vibration cause bridges subjected to dynamic loads from vehicular traffic. A moving
vehicle on a bridge generates deflections and stresses that are generally greater than
those caused by the same vehicular loads applied statically. This is due to the dynamic
13


interaction between the bridge and the vehicle. This interaction is a problem of
considerable complexity and its solution is governed by both vehicle and bridge
dynamic characteristics.
From the AASHTO LRFD Bridge Design Specifications (2012), the static effects of
the design load shall be increased by the percentage specified for dynamic load
allowance (IM). There are two sources may attribute dynamic effects due to moving
vehicles. One source is the hammering effect, which is the dynamic response of the
wheel touch with the deck joints, cracks, potholes, and delamination. Another source
is the dynamic response of the bridges due to long undulations in the roadway
pavement. The AASHTO LRFD Bridge Design Specifications (2012) also indicate
that based on the date from the field tests, the dynamic component response is not
higher than 25 percent of the static response to vehicles, but the short and medium
span bridges specified live load which is a combination of the design truck and lane
load are at least 4/3 of the static response.
Unless the retaining walls subject to no vertical reactions from superstructure or
foundations components are lower than the ground level, the dynamic load allowance
need to be applied. Table 2.1 shows the dynamic load allowance except the buried
components and wood components.
Thermal Load
Most materials lengthen with increasing temperatures and shorten with
decreasing temperatures. Bridge is a kind of large scale structure so the volume
14


change caused by temperature cannot be neglected. There are two types of
temperature changes need to be considered in the analysis of the superstructure. One
is the temperature change where the superstructure changes temperature uniformly.
Another type of temperature change is the gradient temperature change of the
superstructure across the superstructures depth (Richard M. Barker and Jay A.
Puckett 2013). Figure 2.6 represents the difference of a simply supported beam
subject to these two types of thermal load. In type (a), beam temperature changes so
that volume of changes. In another word, the beam changes elongation. The beam in
the condition of type (b) changes curvature by non-uniform heating. For example, the
beam is subjected to sunshine, so the upper part of the beam heats more than the
under part. Bridges subject to thermal load as type (b) induce internal stress. In the
girder-type-bridge analysis bridge decks absorbs more heat than girder. Bridge is a
kind of spindly structure so the longitudinal change much more obviously that vertical
and horizontal.
Uniform Temperature Change
The calculation of movement from thermal load may be employed from
AASHTO LRFD Bridge Design Specifications (2012) Eq. 3.12.2.3-1 as
Aj~ Ct L ( TMns£)eslgn T^MinDesign) (2 8)
Where L is the expansion length and ais the coefficient of thermal expansion. The
AASHTO LRFD Bridge Design Specifications (2012) describes two ways to calculate
the uniform temperature change. One way called procedure A in AASHTO is
15


employed for all bridge types except deck bridges having concrete or steel girders.
The design maximum and minimum temperatures shall be taken as TMinDesign and
TMaxDesign m table 2.2. The AASHTO also notes that the moderate climate is the
freezing days of a year less than 14 days, and the freeing days are defined as the
average temperature is less than 32 F.
Procedure B is used for steel or concrete girder bridges with concrete deck. The
maximum and minimum design temperature in this part should be defined
respectively. Figure 2.7determines the maximum design temperature and minimum
design temperature for steel girder and concrete girder bridges.
Gradient Temperature Change
Temperature gradients are employed in design of bridges in case of the bridge
deck gain solar. The AASHTO LRFD Bridge Design Specifications (2012) prescribes
multilinear gradients of temperature change to aid the design of bridges. Bridges are
subjected to the temperature changes daily and seasonal. Based on the climate is quite
different in different zones in the US, the AASHTO divide four zones in the United
States (figure 2.7). Most of the western United States is in zone 1. The mid-west, part
of the northwest United States, and the southwest California are in zone 2. Zone 3
concludes the eastern United States, northwest United States and Hawaii. Alaska is
located in zone 4.
The gradients change of temperature is different in corresponding zones. Table 2.3
16
describes the AASHTO guide for vertical gradient of temperature in concrete girder


type and steel girder type bridge superstructures. AASHTO also notes that the
temperature is for calculating the change in temperature with the cross section depth
instead of the absolute temperature. Temperature may be taken positive. The negative
temperatures should multiple by -0.30 for the concrete deck or -0.20 for asphalt
overlay deck. The AASHTO LRFD Bridge Design Specifications (2012) exhibited
the positive vertical temperature gradient in figure 2.8. When the concrete
superstructures depth is 16 inch or more the dimension is taken as 12 inch, or take
actual depth minus 4 inch. For the steel superstructures, the dimension is taken 12
inch, and the distance is taken from the concrete deck depth.
AREMA Design code
The design code form American Railway Engineering and Maintenance of Way
Association (AREMA) specified the design guide of railway bridges. The concrete
girders common use slabs, tees, and boxes. The box sections are good for providing
deck suitable for ballasted track. For the steel girder bridges rolled or welded sections
are used. The AREMA design manual has no suggests for bridges used for light rail
transportation system. The designers should choose design code from the AASHTO
LRFD design code and AREMA design manual for the light rail bridge design.
17


Figures and Tables
(a)
(b)
18


(c)
Figure 2.1 Reinforced Concrete Beam (a) Beam and load (b) Stresses in concrete
beam (c) Stresses of reinforcing bars (Wight and MacGregor 2012).
Typical load
+ + I + + + + W + + I
Reinforced
Concrete
(RC)
'Reinforcing bars
Cracked with
deflection under
dead load and
full service load
(a)
Dead load
Prestressed
Concrete
(PC)
Prestressing tendons
Full service toad
X
m,
Uncracked with
likely camber
under dead load
and prestress
(b)
Figure2.2 The Behavior of Reinforced Concrete and Prestressed Concrete Beam
Under Load (a) reinforced concrete beam (b) prestressed concrete beam (Naaman
2004).
19


8,0 KIP
32.0 KIP
32.0 KIP
j I4,-Qm | H'-O" TO IQ'-O" |
(a)
^O.SMINTOl.ffMAX 28.ff TO 29.5TOC TRUCK
OF NEXT CAR
77.ff CAR LENGTH OVER CAR BODY ENDS
(b)
Figure 2.3 Light Rail Train and Truck Wheel Load (From RTD and AASHTO)
20


m
Figure 2.4 Forces Acting on the Mass (Chopra 2012)

I ^
^2
m 1 -G p,(t)


p2(r)
/ Friction-free surface
c2(ii2 i\)
cii
AV' P |(C
P2(0
Figure 2.5 Free Body Diagram of Two Degree of Freedom System (Chopra 2012)
21


aATL
(a)
\-
\
ft> ^ ^ ft. & ** t
9 t> t> P t P I* >

V/////
(b)
Figure 2.6 Simply Supported Beam Subject to Thermal Load (a) uniform
temperature change (b) gradient change. (Richard M. Barker and Jay A. Puckett
2013)
22


(c)
23


(d)
Figure 2.7 Contour Maps for (a) TMaxDesign for concrete girder bridges
(b) TMinDesign for concrete girder bridges (c) TMaxDesign for steel girder bridges (d)
TMinDesign for steel girder bridges (AASHTO)
Figure 2.8 Solar Radiation Zones for the United States (AASHTO)
24


Figure 2.9 Vertical Temperature Gradient (AASHTO)
25


Table 2.1 Dynamic Load Allowance (AASHTO)
Component IM
Deck JointsAll Limit States 75%
All Other Components:
Fatigue and Fracture Limit State 15%
All Other Limit States 33%
Table 2.2 Ranges of Temperature in Procedure A (AASHTO)
Climate Steel or Aluminum Concrete Wood
Moderate 0 to 10 to 10 to
120F 80F 75F
Cold -30 to 0 to 0 to
120F 80F 75F
Table 2.3 Basis for Temperature Gradients (AASHTO)
Zone T1 (F) T2 (F)
1 54 14
2 46 12
3 41 11
4 38 9
26


CHAPTER III
SITE WORK MONITORING OF LIGHT RATE BRIDGE
This chapter describes the site work includes lab testing and in-situ strain
measurement. The purpose of this test is to record the strain of light rail bridges
during the light rail train come through the bridges. The testing procedure details are
present in this chapter. This chapter also introduces the equipment and tools in this
chapter.
Equipment of Test
Some kinds of instrument and tools are used in this test. The parts being tested on
the bridge includes the rail on the bridges and bridge girders under the bridges. The
values of strain are read by strain gage and recorded by CR5000 data logger in the
in-situ work.
CR 5000 Data Logger
Figure 3.1 shows the CR 5000 data logger used in this testing. The CR 5000
measurement and control system can make measurement with 5000 Hertz. This
instrument has battery so that it can be used at in-situ test work, and the CR 5000 has
2 Mb SRAM memories to store data. The storage of CR 5000 is not enough to store
all data of the testing. In that case a laptop computer is used in the test to transport and
store data of the in-situ work. It has 20 testing channels to record the strain values
which are sufficient to this work.
27


Other Equipment
Other tools and consumables are used in the test. Table 3.1 present the detail of
these equipment.
Introduction of Tested Bridges
A total of five constructed bridges in Denver, CO, were monitored. Because most
of the light rail bridges are girder bridges, this site work is focus on the girder bridge.
Table 3.2 illustrates the details of five tested bridge. All five bridges are light rail
trains used only, and these light rail bridges are 2-rail-lanes except the Indiana Bridge
is one lane and two way use.
Broadway Bridge
The Broadway Bridge is comprised of 5 spans (2-span plus 3-span connected by
an expansion joint), including direct fixation tracks. The out-to-out deck width varies
from 34 ft to 42 ft with a typical thickness of 10 in. The depth and width of the steel
plates (AASHTO M-270 Grade 50) supporting the deck are approximately 5.5 ft and
2 ft, respectively. The 28-day compressive strength of the deck concrete is 4500 psi.
Indiana Bridge
The Indiana Bridge has no skew and consists of a hollow prestressed concrete
box girder with a direct fixation track. The depth and width of the box girder are 7 ft
and 20 ft, respectively, and the 28 day compressive strength of the girder concrete is
28


5800 psi. Post-tensioning was done with low-relaxation steel strands (Aps = 28.64 in2
and fpu = 270 ksi) at a jacking stress level of 75%fpu.
Santa Fe Bridge
The Santa Fe Bridge is a 2-span multi-cell prestressed concrete box girder bridge.
The bridge is approximately 28 ft wide and 10 ft deep and has a total length of 328 ft
(172 ft + 156 ft spans). Two train tracks are located on a ballast layer of 1.7 ft. The
28-day compressive strength of the box concrete was 6000 psi and low-relaxation
strands (Aps = 76 in2 and fpu = 270 ksi) were used for post-tensioning at a jacking
stress level of 75%fpu.
County Line Bridge
The County Line Bridge (L = 990 ft) consists of 4 prestressed concrete bulb
T-girders (Colorado BT84) for 7 spans varying from 114 ft to 160 ft. Each girder has
a depth of 7 ft with a girder spacing of 8.3 ft, and supports a deck slab (t = 8 in) with 2
direct-fixation tracks. All girders were connected by diaphragms cast on site (i.e. a
continuous system), except the fourth span where expansion joints were placed. Two
harping points were used for prestressing strands per girder (Ap = 5.2 in2 to 12.6 in2,
low-relaxation 270 ksi steel). A 28-day concrete strength of 8500 psi was used for the
girders.
29


6th Avenue Bridge
The 6th Avenue Bridge is comprised of 4 + 2 span prestressed concrete bulb
T-girders (BT42) connected by an arch bridge. The bridge has no skew and includes
two ballasted train tracks. A waterproofing membrane layer was placed in between
the deck concrete (t = 8 in) and the ballast. As in the case of the County Line Bridge
discussed above, all girders were connected on site to make a continuous system and
each girder had two harping points (Ap = 5.2 in2 with an effective steel stress of
56%fpu). The compressive strength of the girder concrete used was 9000 psi.
Testing Procedure
The testing work in this program includes lab test and in-situ testing. The lab test
collects the strain response with a simulative train load on the 115RE rail. The in-situ
testing includes the strain collection and dynamic response test with five operating
light rail bridges. The steel rail strain which is tested in the Auraria West Station also
includes making a comparison with lab test result.
Lab Test
A laboratory experiment was conducted to calibrate the response of an 115RE rail
subjected to mechanical load. A 128-inch long rail was received and tested with strain
gages, as shown in figure 3.2.
Two loading conditions were employed: simply-supported and continuous systems.
The simply-supported test is shown as figure 3.2, and the continuous system is shown
30


as figure 3.3. According to the RTD design manual (Sec. 2.4 LRV fleet and Sec. 6.4.2
Live load), the front wheel of a fully-loaded train weighs 12.2 kips, while that of an
empty train has 7.5 kips.
Site Visit
The research team studied the site condition of the five bridges to be monitored, as
shown in figure 3.4. The purposes of the site visit were to identify potential problems
that might hinder response monitoring and to confirm the engineering drawings
obtained from the RTD. The location of instrumentation was examined, including
vertical elevation. The bridges which the research team initial plan to test is Broadway
Bridge, Indiana Bridge, Santa Fe Bridge, County Line Bridge, and Cherry Creek
Bridge. All bridges were accessible without any problem except for the Cherry Creek
Bridge under which bike paths were paved. As a result, the 6th Ave Bridge replaces
the Cherry Creek Bridge.
Site Work Monitoring
The monitored span of the individual bridges was determined by the following
criteria as recommended by the Regional Transportation District (RTD) controlling all
light rail transit systems in Denver, CO: i) lowest superstructure elevation for safety,
and ii) accessibility to tracks with minimal disruption to train operation. This
subsection summarizes bridge details, in-situ data, and technical interpretation,
including statistical parameters which will be useful for developing design
recommendations. Typical field monitoring time was 12 hours (from 8:00 am to 8:00
31


pm) per bridge, while two days were spent for the 6th Avenue Bridge due to a strong
wind issue. The behavior of the bridges was converged from a statistics perspective,
which means there was no practical needed to extend to the monitoring time (i.e.,
sufficient data were obtained).
a) Broadway Bridg e
The behavior of the first span was monitored. Train speed was measured with a
digital speed gun confirmed by a portable global positioning system (GPS) inside
trains passing the bridge. (Figure 3.5, a) Instrumentation included
i) Eight strain gages bonded to the rail-side in order to measure in-situ train wheel
load. (Figure 3.5, b)
ii) One strain gage bonded in between the eight strain gage clusters for temperature
monitoring. (Figure 3.5, c)
iii) Three strain gages (one 4.7 in gage-length and two 0.2 in gage-length gages)
bonded to the bottom of each girder to monitor the flexural response of the bridge at
mid-span (i.e., bending and live load distribution). (Figure 3.5, d)
b) Indiana Bridge
The monitored span is 95 ft long and has expansion and fixed bearings at both
ends. (Figure 3.6, a) Strain gages were bonded to the side of the rail to measure train
wheel load and thermal deformation. (Figure 3.7, b) Unlike other bridges monitored
in this research program, one-way travel is allowed along a single track and light rail
32


trains are alternatively operated from Denver to Golden (east to west) and vice versa,
as shown in figure 3.7, c. Long and short gages (4.7 in and 0.2 in gage lengths,
respectively) were also bonded to the bottom of the prestressed concrete girder.
(Figure 3.7, d)
c) Santa Fe Bridge
The monitored span is 155 feet and 5 inch. (Figure 3.8, a) train gages were
bonded to the rail-side to measure train load and temperature (Figure 3.8 b and c) and
were bonded underneath each web member of the multi-cell girder. Scaffold is used in
Santa Fe Bridge test. (Figure 3.8 d)
d) County Line Bridge
The monitored span is 160 feet (Figure 3.9 a). Strain gages were bonded to the
rail (Figure 3.9 b) to measure light rail train load (Figure 3.9 c). Additional gages
were bonded to the bottom of each girder at mid-span to monitor flexural behavior
when loaded (Figure 3.9 d).
e) 6th Avenue Bridge
The 6th Avenue Bridge is connecting with arch bridge. Only the girder bridge
type part is tested in this program (Figure 3.10 a). Strain gages were bonded like other
bridges to measure the in-situ wheel load of light rail trains (Figure 3.10 b and c) and
the flexural response of the girders at midspan (Figure 3.10, d).
33


Dynamic Response Test
A non-contact interferometric radar technique called Image By Interferometric
Survey (IBIS hereafter) was employed. The IBIS system detects a phase-change in
reflected radar waves to identify the position of an object. Because Subtask 1
informed that the response of the light rail bridges was consistent, a nominal field
monitoring time of 5 hours was planned per bridge. Reflectors were installed along
the edge of the bridge deck at mid- and quarter-spans to measure the displacement and
frequency of the bridge. The monitored spans were identical to those of the previously
conducted field test in Subtask 1. The IBIS equipment was then set up using a tripod,
and its radar head was connected to a laptop computer.
A laser distance meter mounted to the radar head was used to uniquely link the
position of specific bridge members with a peak radar display. This process enabled
reviewing in-situ technical data at a later time for further data processing such as fast
Fourier transform (FFT) analysis. A sampling rate of 200Hz was used. Using the IBIS
system, the vibration and displacement data of all the five bridges were collected and
analyzed.
Temperature Effect on Train Rails
As mentioned in the Bridge details section, strain gages were bonded to measure
the effect of temperature on the behavior of track rails while monitoring train load.
The coefficient of thermal expansion (CTE) for steel (115RE) was taken as a = 6.5 x
10-6/F or 12 x 10-6/C (Okelo et al. 2011) and a rail temperature (T) was calculated
34


using the relationship between thermal strain (sth) and CTE (i.e., T = sth/a). The
maximum temperature variation range of each bridge is summarized in Table 2: the
maximum positive and negative temperatures indicate relative changes in temperature
against initial temperatures (e.g., the lower temperature bound of the Broadway
Bridge was -5.3F (-2.9C), which means that the maximum temperature drop was
-5.3F (-2.9C) from the initial temperature when the site work got started).
A net temperature variation for all the bridges monitored was in between 11.1F
(6.1C) and 25.0F (13.9C), excluding the temperature of the 6th Avenue Bridge
whose strain readings were influenced by strong wind blown for the two consecutive
days when the field work was conducted (further site monitoring for the 6th Avenue
Bridge was not carried out because the response of a bulb-tee superstructure was
already measured in the County Line Bridge). Train loading did not significantly
affect the temperature gage readings since the gage (horizontal direction) was bonded
at the centroid of the rail where flexural stress was none (even though some minor
effects were observed in the converted temperature spectra, as typically shown in Fig.
3.11).
35


Tables and figures
Figure 3.2 Experimental Setup and Strain Gage Configurations for the Side and
Bottom of the Rail
36


128
19 30 15 15 30 19
x^-------*-+--*----+-
P
37


(c)
38


(e)
Figure 3.4 Five Bridge Prepare to Test (a) County Line Bridge (b) Cheery Creek
Bridge (c) Broadway Bridge (d) Santa Fe Bridge (e)Indiana Bridge
39


I-
7*-tV IBF ABUT 1 TO 8f ABUT 61
(b)
40


r
(d)
Figure 3.5 Broadway Bridge (a) elevation view and girder cross section (b) Light
rail train operation on site and portable data acquisition system (c) Strain gages
bonded to rail (d) Strain gages bonded to girders at mid-span (Broadway Bridge)
41


42


(c)
(d)
Figure 3.6 Indiana Bridge (a) elevation view and typical cross section of girder (b)
Rail gage bonding (c) One-way train track (d) Girder gages
43


r-<7
x
(b)
44


(d)
Figure 3.7 Santa Fe Bridge (a) elevation view and typical cross section of girder (b)
rail strain gages bonding (c) Trains approaching (d) Girder gages
45


4^
On
(4J4J ajj offmow
MATCH LINE ST* 705TOO.00
E
SHE
s
3 !
?
!
*
4
it-
s
i
IF
i-E-r-Eg
4

p
so* ntr-------i
in iM* ro- - *
tea u/ t& Z, 1 Z ?
o/o m - i
* KO CU-----------
IF
l* w
i
S I
i
B
I
ft
*
*
I
t
OCATED me -+H
ip
f
'
Monitored span


(c)
(d)
Figure 3.8 County Line Bridge (a) elevation view and typical cross section of girder
(b) rail strain gages bonding (c) Trains approaching (d) Girder gages
47


(b)
48


(d)
Figure 3.9 6th Avenue Bridge (a) elevation view and typical cross section of girder (b)
rail strain gages bonding (c) Trains approaching (d) Girder gages
49


A7TF)
20 -
10 i
*<#N wWxwf
0 T 1000 2000 3000 f
-20
time (s)
8000 9000 10000
Fig. 3.10 Typical Temperature Variation of Track Rail Measured in the
Broadway Bridge
50


Table 3.1 Purpose of Equipment Used in Site Work
equipment purpose
strain gage read strain values on girders and rail
glue splice strain gage on bridge
wire connect strain gage and dada logger
laptop store data and do basic in-situ analysis
rubber tapes fix wire in workplace
tin solder connect strain gage and wire
welding torch melt solder fixed between gage and wire
51


Table 3.2 Summary of Five Tested Bridge Details
Bridge Type Typical cross Spans Materials
section modeled
Broadway Steel plate
bridge girder
nn
2 spans
(278 ft)
Indiana
bridge
Prestressed
concrete
box
5 spans
(628 ft)
Santa Fe Prestressed
bridge concrete
box
2 spans
(334 ft)
County Line bridge Prestressed concrete girders X M, ML TITT 4 spans (580 ft)
6th Ave bridge Prestressed concrete girders [1 5 5 5 1 1 n=n 4 spans (328 ft)
nnnnnr
Concrete deck:
f c = 4500 psi
Structural steel:
Fy = 36 ksi
Post-tensioned concrete:
f c = 5800 psi
Prestressing steel: fpu =
270 ksi
Post-tensioned concrete:
f c = 6000 psi
Prestressing steel: fpu =
270 ksi
All concrete: f c = 6000
psi
Prestressing steel: fpu =
270 ksi
Concrete deck: f c =
4500 psi
Post-tensioned concrete:
f c = 9000 psi
Prestressing steel: fpu =
270 ksi
52


Table 3.3 Maximum Temperature Variation of the Monitored Bridges
Bridge Maximum positive and negative temperatures Net temperature variation
Broadway -5.3F to 8.4F (-2.9C to 4.7C) 13.7F (7.6C)
Indiana Bridge -5.1F to 19.9F (-2.8C to 11.1C) 25.0F (13.9C)
Santa Fe Bridge -3.5F to 16.4F (-2.0C to 9.1C) 19.9F (11.1C)
County Line Bridge -8.0F to 3.1F (-4.4C to 1.7C) 11.1F (6.1C)
6th Avenue Bridge -23.5F to 9.7F (-13.1C to 5.4C)a 33.2F (18.5C)a
a: strong wind blew while the bridge was monitored for a two-day period so strain
reading was influenced
53


CHAPTER IV
BRIDGE MODELING
Models of the five tested are used in this research to aid the analysis. Modeling
computer program are used in the modeling part. The Santa Fe Bridge and Indiana
Bridge are modeled in SAP2000, and the Broadway Bridge, County Line Bridge, and
6th Ave Bridge are modeled in CSI Bridge. This chapter describes the conditions of
models based on the drawing of these five bridges. The models will analysis the
dynamic response of these five bridges. The thermal load and rail brake gaps are also
analyzed in this chapter. The general steps of modeling are shown on the appendix of
this paper.
Property of five bridges models
The research team built the models of five bridges base on the existed bridges and
drawings. Some details of the bridges are simplified in the model. This part will
describe the property of materials and sections, vehicular loads, and some other
details of the bridges.
Section Properties
The Broadway Bridge is steel plate girders bridge. The Indiana Bridge and Santa
Fe Bridge are prestress concrete box girders bridge. The County Line Bridge and 6th
Ave Bridge are prestress concrete precast girders bridge. The section of the deck and
girders are built on the computer program based on the drawing the five bridges.
54


Figure 4.1 (b) reveal the section property input on SAP2000 computer program
compare with the existing bridge (Figure 4.1 a), and the other four bridges sections
are built in the same way. The barriers and steel rails are also concerned in the model.
Reinforcement steel bars and prestress tendons with harp are used in the prestress
concrete bridge models.
Vehicular Loads
The full light rail train loads are employed in all of the five bridges which the
boundary wheel load is 24.375 kips and the middle wheel load is 16.25 kips for one
light rail train. The models use four trains as vehicular load on the bridge by the speed
of 60 mile per hour.
All bridge models are built by two lanes except the Indiana Bridge. The light rail
trains will go through the bridge in each side simultaneously on the two-lane models.
The axial wheel loads on the bridge models are two points with a width of 4.1 feet.
All axial wheel loads length is fixed after the leading load..
Other Properties Of Bridge Models
The five bridge models are multiple span girder bridges. The location of each
bent and abutment is simulated based on the draw of five bridges. The boundary
condition of piers and abutments is used as hinge and rollers. One of the abutments is
hinge, and the other abutment is roller in the other side. All piers are hinge type. The
hinge type bearing property is fixed with translation and rotation on each direction.
55


The roller type bearing property is fixed the vertical and longitudinal translation but
free to horizontal translation and all rotations. The piers and abutments are fixed with
the ground. The cross section of the abutment is simplified as 138 inch by 84 inch
rectangular section. The piers are used by rectangular section which the depth is 6
inch and the width is 48 inch.
Finite element method is employed by the calculation the computer program. The
bridge is simulated as amount of segments. The maximum segment length is 120 inch.
Bridge barriers and steel rails are connected with bridge deck as fixed link. The
models of five bridges are shown at figure 4.2.
Dynamic Response of Bridges
Dynamic response of the five bridge models is calculated by the maximum
longitudinal flexural moment at bridge pier and maximum displacement at the
mid-span. The dynamic load allowance (DLA) is calculated by
DLA= (Rdyn~Rstat ) x 100% (4.1)
Rstat
Where Rstat and Rdyn is the index of the dynamic and static response respectively.
The longitudinal flexural and maximum displacement is direct proportion to the
response, so the DLA due to moment is
DLA= (Mdyn~Mstat ) xl00% (4.2)
Mstat
And DLA due to displacement is
56


DLA= (:
) xlOO%
(4.3)
Sdyn Sstat
Sstat
Where M and S is moment and displacement.
The static and dynamic vehicular load is defined in the SAP2000 and CSI Bridge
computer programs as different kind on load cases. The static vehicular load is
multiple step static load which means the light rail trains locate on the bridges in
stable step by step. The dynamic load is the light rail trains time history load analysis
linearly. The simulated trains are moved on the bridge discretize load every 1.0
second.
Rail Break Gaps
The steel rails lays on the five exists bridges continuously, but rail break gaps are
simulated on the model. The rail break gaps is cut on the location of the maximum
negative bending moment which at pier on the bridges. The length of the rail break
gaps is simulated as 1,2, and 3 inch respectively. Dynamic load is calculate on this
research for calculate the increasing of DLA. The rail break gaps on the models are
shown on figure 2.3.
Calculation of the dynamic load allowance with rail breaks is similar to the
previous steps. The dynamic load allowance based on the bridges with steel rail break
gaps is
DLAbreaki= (Mbre^iMstat ) x 100% (4.4)
Mstat
DLAbreak,i= (Shre;kJ~Sstat ) x 100% (4.5)
^stat
57


Where the DLAbreaki is the dynamic load allowance with rail break gap, Mbreak,
and Sbreak i is the maximum negative bending moment at pier and displace at
mid-span of the bridges.
Thermal Load
Thermal load is simulated on the models in this research. The thermal load on the
five bridges is based on the temperature gradient method form the AASHTO LRFD
bridge design code.
The five bridges are located on zone 1 based on the AASHTO defined. However, the
thermal load on zone 1, 2, 3, and 4 are calculated by finite element method by SAP
2000 and CSI bridges on this research. The thermal load is built by an individual load
case on the computer program. The values of temperature change are the AASHTO
default shown on figure 2.4.
58


Tables and figures
TYPICAL SECTION
(a)
(b)
Figure4.1 Section Properties of Bridge Deck and Girder: Indiana Bridge (a)
Drawing (b) Modeling
59


(b)
60


(c)
(d)
61


(e)
Figure 4.2 Models of Five Bridges (a) Broadway Bridge (b) Indiana Bridge (c) Santa
Fe Bridge (d) County Line Bridge (e) 6th Avenue Bridge
Figure 4.3 Steel Rail Break on Models
62


- Temperature Gradient Name-
|btgli
- T emperature G radient Type----------------
^ AASHTO Default
Zone
Negative Temperature Multiplier
C Chinese JTG DGO Default
Overlay Type
Asphalt Thickness
Negative Temperature Multiplier
Use 0.7 Concerete-Masonry Arch Factor
C User
Type
- Temperature Difference Data-----------------
Number of Specified Distances
T his D istance I s A as S pecified in AAS H T 0
This Distance May Vary
Include These Temperature Difference Values
| Kip, in, F
T3
|-0.3
d1 |3.937 T1 Positive
d2 (a in AASHTO T2 Positive
d3 jMay Vary T3 Positive
d4 [7874
F
|d2
|d3
positive and Negative
[54
|TW
T1 Negative
T2 Negative
T3 Negative
|-16.2
j-4.212
. OX.:|
Figure 4.4 Temperature Gradient of Five Bridges
63


CHAPTER V
RESULTS AND ANALYSIS
The results contain the field work testing results and the results from computer
program modeling. This chapter also illustrates the bridge natural frequency translated
from strains with Fast Fourier Translation (FFT). The analysis of thermal load and
steel rail break is also discussed in this chapter.
In-situ Work Testing Results
The results of strain and displacements from the five tested bridges will be
analyzed in this part. This part also includes the result of lab test and the site work at
Auraira West Station.
Wheel Load Analysis
(a)Lab testing and Auraira West Station testing: Wheel load is simulated in the lab.
The 115RE rail is subjected to 16 kips and 12.2 kips load respectively. The strains
measured at the bottom of the rail where a maximum flexural effect takes place were
compared with those calculated by fundamental structural analysis formulas. The
strain values of the continuous rail were apparently less than those of the
simply-supported case (e.g., the measured strain of the continuous rail was 39% less
than that of the simply-supported counterpart at a load of 7.5 kips). This observation
indicates that the proposed test setup can adequately represent the response of
continuous rails supported by multiple sleepers on site.
64


Figure 5.1 exhibits the load-strain behavior of the 115RE rail. The response of the
strain gages boded to the side of the rail is given in Figure 5.2 The gages facing each
other in the diagonal direction showed similar behavior. Test data showed slight
discrepancy between the G1/G3 and G2/G4 groups. This result illustrates that the
applied principle stresses in these two diagonal directions (i.e., ol and o2) were not
the same. Linear curve-fitting equations were developed to establish relationships
between the strain and the applied load so that in-situ load would be measured based
on strain reading.
Figure 5.3 demonstrates the calibration of the portable data acquisition system using
the immovable laboratory data acquisition. At typical loads of 12 kips and 14 kips for
the continuous-rail test, the strain reading of these two systems was almost identical.
Such a calibration results corroborate that use of the portable data acquisition system
will be adequate to measure the in-situ behavior of the fiver bridges discussed in Site
visit.
The established load-strain relationships (Figure 5.2) were further validated with
actual train load on site as Figure 5.4. The front wheel of an empty stationary train
(7.5 kips) generated a maximum strain of 64.5 microstrain, as shown in Figure 5.4,
which agreed with the laboratory strain of 63.8 microstrain subjected to a load of 7.5
kips.
(b)In-situ wheel load of light rail trains: Figure 7 reveals typical strain responses
associated with the wheel load of light rail trains running on the bridges monitored.
65


The strains measured from the rail-side were converted to the wheel load of the trains
using the formulas developed in the laboratory test, which were also calibrated with
stationary light rail trains. The temperature effect discussed in the previous section
was compensated when interpreting train load. Provided that the primary interest of
the present site work was in detecting maximum train loads that would control the
response of the bridges (i.e., the light rail train has two design loads (fully loaded) for
six axles such as 24.375 kips and 16.25 kips, as shown in Fig. 8, and corresponding
wheel loads are 12.188 kips and 8.125 kips), maximum loads (or peak loads) detected
during each load cycle were acquired and summarized in Fig. 9. The number of
observation was not consistent for all bridges because some bridges were used by
multiple lines (there are 6 light rail lines in Denver); however, the mean wheel load
measured was almost consistent irrespective of the observation number. This fact
indicates that the measured load data are statistically stable.
The mean wheel load of the light rail trains varied from 6.2 kips to 6.9 kips. This
measured load range was reasonable because the articulated light rail train had a
nominal load range between 4.96 kips (empty train) and 12.19 kips (fully loaded train)
per train wheel. It is presumed that the passenger occupancy increased the train load
by 25% to 39%, including some dynamic effects. It illustrates a relationship between
the average train speed measured and the mean train wheel load. The regression line
indicates that the load has augmented with an increase in train speed. Although the
passenger load was not identical in individual trains (the number of passengers is
66


stochastic in nature), it appears to be reasonable to adopt the fitted equation because
the variation range of the wheel loads was not significant (i.e., 6.2 kips to 6.9 kips).
Girder Response
The flexural behavior of the monitored bridges is provided in Fig. 11 (only
selected cases are shown for brevity because superstructure responses were basically
repeated). The measured strains at midspan of each girder showed periodic spikes
when the light rail trains were passing, whose magnitude was a function of girder
types and geometric configurations. For instance, the response of the Broadway
Bridge (three steel plate I girders with a span length of 119 ft, Fig. 1) and the Indiana
Bridge (one large prestressed concrete box girder with a span length of 95 ft, Fig. 2)
had typical strains of approximately 100x 10-6 and 35 x 10-6, respectively, as shown
in Fig. 11(a) and (b). Some minor negative strains were detected in all cases because
the bridges were continuous and the behavior of the girders physically moved up and
down depending upon the location of train load, particularly noticeable for the
Broadway Bridge having relatively less flexural rigidity due to use of the slender steel
I plates [Fig. 11(a)], As discussed earlier, the strains of the 6th Avenue Bridge
significantly fluctuated because of the strong wind and close-up views were not
provided in Fig. 11(e).
67


Dynamic Response
Two dynamic modeling approaches were considered (i.e., mode superposition and
direct integration), while the mode superposition method was selected for the present
study because it is less sensitive to time steps (numerically stable) compared to the
direct integration and, consequently, generates accurate technical results with
reasonable computational effort, including modal analysis data. This was one of the
major concerns in the present research since the number of required simulations was
substantial. Constant modal damping was utilized in accordance with Art. 4.7
(Dynamic analysis) of the AASHTO LRFD Specifications and the train loading was
regarded as a transient parameter. First five modes and corresponding frequencies
were extracted using Eigenvector analysis. These modes were iteratively calculated
with the following convergence criterion:
^ Mi+1 ^
A+i
<1(T
(5.1)
where ^ is the eigenvalue relative frequency shift at the iteration. Provided that all
positive frequencies were predicted, it can be stated that the developed dynamic
bridge models were stable. Figure 6 illustrates a comparison between the measured
and predicted displacements at midspan of the individual bridges. For consistency, the
finite element models included two cases (i.e., empty train and fully-loaded train
loads) with inbound train-loading that was close to the reflector installed. The sign
convention used is as follows: positive and negative values indicate downward and
68


upward displacements, respectively. It should be noted that the direction of train
operation affected the positive and negative displacements of the monitored span in
continuous bridge systems (i.e., downward to upward deflections or upward to
downward deflections with time )
Temperature Effect on Train Rails
Temperature gradient was considered to address the non-uniform thermal exposure of
the bridge superstructure: thermal zones 1 to 4 (Art. 3.12.3 Temperature gradient).
The temperature-induced stress (CTr) may be obtained by a combination of axial strain
(St ) and curvature (tf/'r) (Ghali et al. 1989):
=72X4
Vt=jZ\
d,
i J
(5.2)
(5.3)
where A and Ai are the total cross-sectional area and the ith element area of the bridge
superstructure, respectively; Tai is the temperature at the element centroid; I and 1!
are the total moment of inertia and the moment of inertia of the section about its own
centroid, respectively; yi is the element centroidal axis; A7' is the temperature
difference from bottom to top of the element; and di is the element depth. The
temperature-induced distress was engaged with the aforementioned thermal zones of
the AASHTO LRFD. It is worth noting that such distress primarily contributes to
increasing internal stresses, rather than causing girder reactions when expansion joints
are appropriately designed.
69


Results from Simulation
This part presents the results calculation from the computer program models. A
summary of bridge spans and length of each spans is given on table 5.4. The results
include the dynamic load allowance of the light rail trains vehicular load. The
dynamic load allowance of the bridges with steel rail break gaps and thermal load is
also discussed on this part.
Dynamic Response Analysis
The deflection curve of five bridges applied by the light rail train vehicular load
is shown are shown on figure 5.11. The shape of deflection curve from the static and
dynamic load is similar. However, the displacement from dynamic load is higher than
the static load because of the stress caused by the interaction of the steel rail and light
rail train wheels, and the vibration of the bridges superstructure also increase the
maximum displacement.
The bending moment of the model is calculate. As predict, the dynamic effect
increase the bending moment. The bending moment diagrams of the five bridges are
shown on figure 5.12. Figure 5.12 indicates the moment at mid-span is positive and
the negative at pier, (i.e., the upper girder is subjected to tensile stress at pier and
compressive stress at mid-span.) This is conformed to the influence line of the
continuous bridge. The maximum bending moment and displacement is shown on
table 5.6 and 5.7.
70


Rail Break Gaps
The steel rail break gaps are given on figure 5.13.The steel rail is built on models.
The cross section is shown at table 5.8. The steel rails are fixed with the bridge. The
five bridges have four steel rails which is two wheels on each line except the Indiana
Bridge has 2 rails on the only one lane. The steel rail break gaps is simulated at the
pier which is the nearest to the field tested location. Dynamic load of light rail trains
vehicular is applied on the bridge models with steel rail break. The values of the
maximum bending moment and displacement based on the steel rail break are shown
on table 5.8 and 5.9.
Thermal Load and Frequency of Bridges
The natural frequency of five bridges model is show on table 5.10. The natural
frequency of bridge is not influenced by loads. The natural frequency changes when
the length of steel rail break gaps change. However, the difference of the bridges
natural frequency influenced by the rail break gaps change is relatively small, so this
difference is neglected. The thermal load based on 4 zones in given on table 5.11. The
thermal load decrease from zone 1 to zone 4. This illustrate that the thermal load is
decreasing by the value of temperature change decreasing.
Analysis of Result
The comparison of natural frequency between the finite element analysis and
field test is discussed in this part. The dynamic response which is influenced by the
71


steel rail break gaps is analyzed. The result of thermal load from modeling and
theoretical calculation is also included.
Natural Frequency
Both the natural frequency of the five bridges form the field test and from
modeling is agreed with the predict value. The natural frequency from test is floating
but the predict values are in the range of the tested value. The values of natural
frequency from computer program modeling have difference with the predicts, but the
difference is no more than 10 percent.
Dynamic Response of Rail Break
The dynamic load allowance of models is calculated. (Table 5.12 and 5.13) This
illustrates the DLA of bridges increases by the rail break gap, and the length of the
rail break gap influences the DLA of bridges. The DLA of bridges increase when the
length of the rail break gaps increase. The more of the rail break gaps extend the value
of DLA increases more obvious.
Temperature Change
The thermal is calculated by theoretical shown on table 5.14. The different
between the theoretical calculation and the modeling is calculated as
A=(RtheoRmode1) x j qqo/q (5 4)
Rtheo
72


Where A is the difference between the theoretical axial force and the finite element
analysis calculated value. The value of Rtheo ar|d Rmodei is the theoretical axial
force and finite element analysis calculated value.
Speed effect
The speed of vehicle is a function of the DLA. The dynamic load allowance of
low speed vehicular load is calculated by modeling in this research. The dynamic load
allowance of the vehicular speed 40 and 20 mile per hour is shown in table 5.15
respectively.
To compare with the maximum design speed which is 60 mile per hour, the
values of DLA decrease with the velocity light rail train of 20 and 40 mile per hour
(figure 5.13). This indicates that the DLA is decreasing when the speed of vehicle
decreasing. The dynamic load allowance is controlled by the maximum design train
speed for the light rail bridge design.
73


Tables and Figures
(a)
(b)
Figure 5.1 Load-Strain Behavior at Bottom of Rail: (a) simply-supported case; (b)
continuous case
Q.
o
CO
o
G1
Full train
Empty train
-0.0003 -0.0001 0.0001 0.0003
strain
Fig. 5.2 Load-Strain Behavior on the Side of Continuous Rail
74


Type of data acquisition system
Figure 5.3 Validation of Portable Data Comparison Acquisition System Using
Rail Strain at Bottom
Figure 5.4 Wheel Positioning of Auraria West Station
80
60
o
c 40
TO
55 20
0
Laboratory:
empty train \
----------

\

Measured:
empty train
W\H/-vy
0 50 100 150 200 250
Time (Sec)
Figure 5.5 Comparison Between In-Situ Test and Laboratory Test (Front Wheel
Load)
75


100
(a)
(b)
76


(c)
(d)
77


Time (sec) Time (sec)
(e)
Figure 5.6 Measured Strains for Light Rail Train Wheel Load: (a) Broadway
Bridge; (b) Indiana Bridge; (c) Santa Fe Bridge; (d) County Line Bridge; (e) 6th
Avenue Bridge.
Figure5.7 Fully-Loaded Design Axle Loads of the Light Rail Train Operated in
Denver, CO (the six axles loads of the articulated empty train consist of 14.869 k +
14.869 k + 9.913 k + 9.913 k + 14.869 k + 14.869)
78


1000
1000
§ 800 -l
£
0)
£ 600 -
o
400 H
200
li = 6.3 kips.
COV = 0.3L
5 = 23.4 mph.
_1 u-_
ITT
0 2 4 6 8 10 12
Train wheel load: Broadway Br (kip)
800
600 -
400 -
200
H = 6.2 kips.
COV = 0.30.
S = 40.4 mph.
0 2 4 6 8 10 12
Train wheel load: Indiana Br(kip)
(a)
(b)
c
.o
15
£
0)
to
-Q
o
1000
800
600
o
fc 400
xi
E
| 200
^ = 6.6 kips.
COV = 0.20.
S = 49.0 mph.
TTTT
IBs
H m i
0 2 4 6 8 10 12
Train wheel load: County Line Br (kip)
(c)
(d)
1000
800
600 -
400 -
200 -
0
ji = 6.2 kips
COV = 0.21
S = 32.9 mph
TTTTTT
n
0 2 4 6 8 10 12
Train wheel load: 6th Ave Br (kip)
15 i
"O
ro
S 10
5
c
'co 5

Design load (heavy wheel: full load)
Load = 0.0207(Speed) + 5.6293
-CLq
Design load (light wheel: empty train)
20 40 60
Average train speed (mph)
(e) (f)
Figure 5.8 Distribution of Measured Train Wheel Load (p = average; COV =
coefficient of variation; S = average train speed): (a) Broadway Bridge; (b) Indiana
Bridge; (c) Santa Fe Bridge; (d) County Line Bridge; (e) 6th Avenue Bridge; (f) mean
train load measured versus average train speed (heavy wheel = front and rear; light
wheel = middle)
79


iwcrosvwn ,
Microstrain > s , Microstrain
Time (Sec) Time (Sec)
(a)
(b)
80


Time (Sec) Time (Sec)
(c)
(e)
Figure 5.9 Flexural Response of Monitored Bridges: (a) Broadway Bridge (exterior
girder); (b) Indiana Bridge (exterior box web) (c) Santa Fe Bridge (2nd interior box
web); (d) County Line Bridge (interior girder); (e) 6th Avenue Bridge (interior girder)
81


(a)
(b)
82


(C)
(d)
83


(e)
Figure 5.10 Deflection of Bridge Models(a) Broadway Bridge (b) Indiana Bridge (c)
Santa Fe Bridge (d) County Line Bridge (e) 6th Avenue Bridge
(a)
84


(b)
(c)
85


L
(d)
Figure 5.11 Bending Moment Diagram of Bridges (a) Broadway Bridge (b) Indiana
Bridge (c) Santa Fe Bridge (d) County Line Bridge (e) 6th Avenue Bridge
86


Full Text

PAGE 1

RESPONSE MONITORING AND MODELING OF CONS TRUCTED LIGHT RAIL BRIDGES By LIANJIE LIU B.S., Northeast Forestry University, PR China, 2012 A thesis submitted to the Faculty of the Graduate School of the University of Colorado in partial fulfillment of the requirements for the degree of Master of Science Civil Engineering 2015

PAGE 2

ii This thesis for the Master of Science degree by Lianjie Liu has been approved for the Civil Engineering program By Yail Jimmy Kim Chair Frederick Rutz Chengyu Li 07/22 /2015

PAGE 3

iii Liu, Lianjie(M.S., Civil Engineering Response Monitoring and Modeling of Constructed Light Rail Bridges Thesis directed by Associate Professor Yail Jimmy Kim ABSTRACT Light rail bridge is an important part of the public transportation system. The current light rail bridges are designed by the exist codes. However, codes are only specifying the design procedure of high way bridges, and they are lack of guidance for design rails and light rail train load. This research evaluated the constructed five light rail bridges in Denver, Colorado. The work includes testing and computer program modeling. my simulated light rail train with different types of boundary conditions. The steel rail on Auraria Campus Station and five working light rail bridges are tested on this research. The five tested bridges are the Indiana Bridge, Santa Fe Bridges, 6th Ave Bridge, Broadway Bridge, and County Line Bridge. The strain change on the steel rail which is applied the light rail load is collected on the Auraria Campus Station and five light rail bridges, and girder response of the five bridge also recorded on this p roject. The dynamic response of the five bridges is also monitored. The models of the five light rail bridges are built on the computer modeling programs of SAP 2000 and CSI Bridge to analysis the static and dynamic response of

PAGE 4

iv the light rail wheel load. The analysis by modeling of steel rail break gaps cuts the steel rail by the length of 1, 2, and 3 inch respectively. The study also compares the dynamic load allowance (DLA) without and with rail break gaps in different length. Analysis of the thermal loa d on the light rail break is concluded on this research. It was shown that the current design code is conservative but acceptable used on the design of light rail bridge. The form and content of this abstract are approved. I recommend its publication. Approved: Yail Jimmy Kim

PAGE 5

v ACKNOWLEDGEMENTS I wish to express my deep gratitude to my advisor, Dr. Yail Jimmy Kim, for his invaluable instruction and multifaceted support during my graduate study, and guidance of my research. I wish to thank the faculty and staff of the Structural Engineering Department at University of Colorado, Denver. I thank Dr. Chengyu Li and Dr. Frederick Rutz for participating on my thesis committee. Thank are also extended to my partners of my research team. I am grateful to ackn owledge financial support provided by the National Academy of Sciences. I also wish to acknowledge my parents for their understanding and great support throughout all the years of my educational pursuits.

PAGE 6

vi TABLE OF CONTENTS CHAPTER I. INTRODUCTION ................................ ................................ ................................ ... 1 Background ................................ ................................ ................................ ........... 1 Objective ................................ ................................ ................................ ............... 2 Research Significance ................................ ................................ ........................... 3 Thesis Outline ................................ ................................ ................................ ....... 4 II. LITERATURE REVIEW ................................ ................................ ....................... 7 Bridge Types f or Light Rail Transportation ................................ ......................... 7 Concrete Girder Bridges ................................ ................................ ................ 7 Prestressed Concrete Girder Bridges ................................ ............................. 9 Steel Girder Bridges ................................ ................................ .................... 10 Loads Analysis ................................ ................................ ................................ ... 10 Light Rail Bridges Dynamic Analysis ................................ ............................... 12 Dynamic Behavior ................................ ................................ ...................... 12 Mode Shape ................................ ................................ ................................ 13 Dynamic Load Allowance ................................ ................................ ........... 13 Thermal Load ................................ ................................ ................................ ..... 14

PAGE 7

vii Uniform Temperature Change ................................ ................................ .... 15 Gradient Temperature Change ................................ ................................ .... 16 AREMA design code ................................ ................................ .................. 1 7 Figures a nd Tables ................................ ................................ .............................. 18 III. SITE WORK MONITORING OF LIGHT RAIL BRIDGE ................................ .. 27 Equipment o f Test ................................ ................................ .............................. 27 CR 5000 Data Logger ................................ ................................ ................. 27 Other Equipment ................................ ................................ ......................... 28 Introduction o f Tested Bridges ................................ ................................ ........... 28 Broadway Bridge ................................ ................................ ......................... 28 Indiana Bridge ................................ ................................ ............................. 29 Santa Fe Bridge ................................ ................................ ........................... 29 County Line Bridge ................................ ................................ ..................... 29 6th Avenue Bridge ................................ ................................ ...................... 30 Testing Procedure ................................ ................................ ............................... 30 Lab Test ................................ ................................ ................................ ....... 30 Site Visit ................................ ................................ ................................ ...... 31 Site Work Monitoring ................................ ................................ ................. 31 Dynamic Response Test ................................ ................................ .............. 34

PAGE 8

viii Temperature Effect On Train Rails ................................ ................................ .... 34 Tables a nd Figures ................................ ................................ .............................. 36 IV. BRIDGE MODELING ................................ ................................ .......................... 54 Property o f Five Bridges Models ................................ ................................ ........ 54 Section Properties ................................ ................................ ........................ 54 Vehicular Loads ................................ ................................ .......................... 55 Other Propert ies o f Bridge Models ................................ ............................. 55 Dynamic Response o f Bridges ................................ ................................ ........... 56 Rail Break Gaps ................................ ................................ ................................ .. 57 Thermal Load ................................ ................................ ................................ ..... 58 Tables a nd Figures ................................ ................................ .............................. 59 V. RESULTS AND ANALYSIS ................................ ................................ ................. 64 In Situ Work Testing Results ................................ ................................ ............. 64 Wheel Load Analysis ................................ ................................ .................. 64 Girder Response ................................ ................................ ......................... 67 Dynamic Response ................................ ................................ ...................... 68 Temperature Effect o n Train Rails ................................ .............................. 69 Results From Simulation ................................ ................................ .................... 70 Dynamic Response Analysis ................................ ................................ ....... 70

PAGE 9

ix Rail Break Gaps ................................ ................................ .......................... 71 Thermal Load a nd Frequency o f Bridges ................................ .................... 71 Analysis o f Result ................................ ................................ ............................... 72 Natural Frequency ................................ ................................ ....................... 72 Dynamic Response o f Rail Break ................................ ............................... 72 Temperature Change ................................ ................................ ................... 72 Speed effect ................................ ................................ ................................ 7 3 Tables And Figures ................................ ................................ ............................. 7 4 VI. CONCLUSION AND RECOMMENDATION ................................ .................... 9 7 Conclusion ................................ ................................ ................................ .......... 9 7 Recommendation ................................ ................................ ................................ 9 8 REFERENCES ................................ ................................ ................................ .......... 100 APPENDIX ................................ ................................ ................................ ................ 102 A. Modification of B ridge M odel E xampl e ................................ .............................. 102

PAGE 10

x LIST OF FIGURES FIGURE 2.1 Reinforced Concrete Beam ................................ ................................ ............................ 19 2.2 The Behavior o f Reinforced Concrete a nd Prestressed Concrete Beam Under Load ................................ ................................ ................................ ................................ ................. 20 2.3 Light Rail Train a nd Truck Wheel Load ................................ ................................ ... 21 2.4 Forces Acting a n t he Mass ................................ ................................ .......................... 21 2. 5 Free Body Diagram o f Two Degree o f Freedom System ................................ .......... 21 2. 6 Simply Supported Beam Subject t o Thermal Load ................................ ............... 22 2. 7 Contour Maps ................................ ................................ ................................ .................. 24 2. 8 Solar Radiation Zones f or The United States ................................ .............................. 25 2. 9 Vertical Temperature Gradient ................................ ................................ ..................... 25 3.1 CR 5000 Measurement a nd Control System ................................ ............................... 36 3.2 Experimental Setup a nd Strain Gage Configurations f or The Side o nd Bottom o f t he Rail ................................ ................................ ................................ ................................ .... 37 3.3 115RE R ail Subjected t o Load With Continuous System ................................ ......... 37 3.4 Five Bridge Prepare t o Test ................................ ................................ ........................... 40 3.5 Broadway Bridge ................................ ................................ ................................ ............ 42

PAGE 11

xi 3. 6 Indiana Bridge ................................ ................................ ................................ ................. 43 3. 7 Santa Fe Bridge ................................ ................................ ................................ ............... 45 3. 8 County Line Bridge ................................ ................................ ................................ ........ 48 3. 9 6 th Avenue Bridge ................................ ................................ ................................ ........... 49 3. 10 Typical Temp erature Variation Of Track Rail Broadway Bridge ........................ 50 4.1 Section Properties o f Bridge Deck a nd Girder: Indiana Bridge ............................... 59 4.2 Models o f Five Bridges ................................ ................................ ................................ .. 62 4.3 Steel Rail Break o n Models ................................ ................................ ........................... 63 4.4 Temperature Gradient o f Five Bridge s ................................ ................................ ........ 63 5.1 Load Strain Behavior a t Bottom o f Rail: ................................ ................................ .... 7 4 5.2 Load Strain Behavior o n The Side o f Continuous Rail ................................ ............. 74 5.3 Validation o f Portable Data Comparison Acquis ition System Using Rail Strain a t Bottom ................................ ................................ ................................ ................................ .... 7 5 5.4 Wheel Positioning Of Auraria West Station ................................ ............................... 7 5 5.5 Comparison B etween In Situ Test And Laboratory Test (Front Wheel Load) ...... 7 5 5.6 Measured Strains For Light Rail Train Wheel Load:. ................................ ............... 7 8 5.7 Fully Loaded Design Axle Loads o f The Light Rail Train Operated i n Denver, CO ................................ ................................ ................................ ................................ ................. 7 8

PAGE 12

xii 5.8 Distribution o f Measured Train Wheel Load ................................ .............................. 79 5.9 Flexural Response o f Monitored Bridges: ................................ ................................ ... 8 1 5.1 0 Deflection o f Bridge Models ................................ ................................ ....................... 8 4 5.1 1 Bending Moment Diagram o f Bridges ................................ ................................ ....... 86 5 .1 2 Rail Break Model a t Piered Location ................................ ................................ ......... 87 5 .1 3 Speed effect of five bridges ................................ ................................ ......................... 8 9

PAGE 13

xiii LIST OF TABLES TABLE 1.1 Field Test Bridges ................................ ................................ ................................ .... 6 2.1 Dynamic Load Allowance ................................ ................................ ..................... 26 2.2 Ranges o f Temperature In Procedure A ................................ ................................ 26 2.3 Basis f or Temperature Gradients ................................ ................................ ........... 26 3.1 Purpose o f Equipment Used In Site Work ................................ ............................. 51 3.2 Summary o f Five Tested Bridge Details ................................ ................................ 52 3. 3 Maximum Temperature Variation o f t he Monitored B ridges ................................ 53 5.1 Comparison Between Measured a nd Predicted Fundamental Frequencies ........... 90 5.2 Assessment o f Deflection Control ................................ ................................ ......... 90 5.3 Maximum Temperature Variation o f The Monitored Bridges .............................. 91 5.4 Bridge Span a nd Span Length ................................ ................................ ................ 92 5.5 Dynamic Response From Bending Moment a t Piers ................................ ............. 9 3 5.6 Dynamic Response From Displacement a t Mid Span ................................ ........... 9 3 5.7 Dimensions o f Steel Rail ................................ ................................ ....................... 9 3 5.8 Dynamic Response With Rail Break f rom Bending Moment At Piers ................. 9 4

PAGE 14

xiv 5.9 Dynamic Response With Rail Break f rom Displacement a t Mid Span ................. 9 4 5.10 Natural Frequencies f rom Models ................................ ................................ ....... 9 4 5.11 Thermal i n Different Zone o f Bridges From Models ................................ ........... 9 5 5.12 Dynamic Load Allowance f rom Bending Moment ................................ ............. 9 5 5.13 Dynamic Load Allowance f rom Displacement ................................ .................... 9 5 5.14 Thermal Load o f Five Bridges f rom Calculat ion ................................ ................. 9 6 5.15 Dynamic load allowance from moment with 20 mph speed ................................ 9 6 5.16 Dynamic load allowance from moment with 4 0 mph speed ................................ 9 6

PAGE 15

1 CHAPTER I INTRODUCTION Background Light rail system plays an important role in current United Stated public transportation system. According to the report of American Public Transportation Association, there are 27 areas in the United Stated have light rail transportation system. Up to 2011, there a re 436 million unlinked passenger trips and 2,203 million passenger miles used by light rail. ( APTA, 2013) Bridges are required in the light rail system because the railways need to pass through urban roads and highways. The light rail bridges safety is a n important point for the light rail system. Light rail bridges support static load and dynamic load, and the dynamic load varies in different kinds of situation There are many old built light rail bridges in the United States. S teel rail breaks gaps are cut on the bridges because the technology limit in this time The rail break makes interaction between the rail and light rail train. It means the dynamic load of the light rail bridges are influenced by the rail gaps. The thermal load on the lig ht rail bridges is also not clear on the current design codes. Due to the development of the bridge engineering, the light rail bridges may have longer span and the light rail trains may run on the bridges with a higher speed in the future. It is unknown that if the previously dynamic load allowance is meet the

PAGE 16

2 requirement for the future light rail bridge. The analysis for the influence of dynamic load allowance by different aspects of the bridges is necessary, and it is possible to do with the finite elem ent analysis software. Objective Girder bridges are the most widely used type on the light rail transportation system, so the objective is to analysis the girder bridges used on the light rail transportation system. There is no code specified with light r ail bridge, so the designers have to use different related design code on the design but conflict presents on these codes. These make some problems on the design and maintain of light rail bridges. It is necessary to compare the results between site work test and model calculation, so the first of all is to test the light rail bridges. Five light rail bridges are selected in this test. For the finite element analysis, light rail bridges are modeled with the CSI Bridge and SAP2000 with the five tested bridg e s and some other programs such as Matlab are used for calculation. The dynamic load allowance also varies depends on the load case. The light rail the standard vehi cle loads which are provided by AASHTO are not acceptable to be used as vehicular load. In this case, the light rail train loads for the modeling are defined manually according to the existing light rail train in the United States public transportation sys tem.

PAGE 17

3 The objective is to find the response of light rail bridges from vehicular and thermal load, and dynamic load allowance changing rules influenced by rail break The value changing trend of dynamic load allowance which are influenced by length of rail break gaps are compared respectively. Research S ignificance The purpose of this research is to calibrate the dynamic load allowance for the light rail girder bridges. This research will find the changing value of dynamic load allowance based on the field test and modeling This will help to estimate some advices on design of light rail bridge. Some light rail train may be improved in the future, and if the train load changed, this research may have a reference value. In additional, the rail break is concerned in this research to help the calibration of the light rail bridges dynamic allowance factor especially for the light rail bridge with rail break gaps. Thesis O utline Chapter 1 of the thesis introduces the background and objectives of this resea rch and this chapter also state the goals of this research. Chapter 2 reviews the different types bridges used in the light rail public transportation system. A review of the light rail train vehicular load is presented. This chapter also discusses the dynamic analysis of structure and dynamic load allowance. A discussion of temperature change of structure is conclude d in t his chapter

PAGE 18

4 Chapter 3 presents the site work light rail girder bridge deformation testing. The tested bridges are shown on table 1.1. The testing equipment is introduced, and it discusses the procedure of this test. The strain values of steel rail and girders on the bridges are tested by strain gages when the light rail trains pass through the b ridge. The following part represents the translation of data from the bridge displacements and bridge natural frequency by fast Fourier translation Chapter 4 describes the bridge models design and modeling. First of all, the dimensions of girders are des igned by following the AASHTO code. F inite element analysis computer programs are used in building bridge models. Some general assumptions such as boundary conditions are used for modeling. Using SAP2000 and CSI Bridge to model the designed bridges, and ma ke a collection for the calculated light rail bridges data (such as moment, displacement, and frequencies). Secondly, a discussion of rail break and thermal load is presented. Finally, modeling of thermal load is provided. Chapter 5 is the discussion on t he testing and modeling result. The results of wheel load, strain, temperature change, and dynamic response are analyzed from field test. After that, the moment and displacement on modeling are compared with the data without rail break to find the enhanced value of dynamic allowance. The comparison of modeled and calculated thermal load is discussed. Chapter 6 presents the conclusions of the dynamic load allowance which is influenced by different factors. Continuously, the effect of rail break is discussed

PAGE 19

5 There is a comparison with the results between the site work results and the modeling data in this chapter. At last, a direction for the future research about the dynamic load allowance is provided.

PAGE 20

6 Table1 .1 Field Test Bridges No. bridge 1 6th avenue bridge 2 Broadway bridge 3 County line bridge 4 Indiana bridge 5 Santa fee bridge

PAGE 21

7 CHAPTER II LITERATURE REVIEW This chapter introduces the concepts used in the finite element analysis in light rail bridges, and introduces the typical type of bridges. This chapter also reviews the dynamic behaviors of light rail bridges, especially the dynamic behaviors of rail break gaps and thermal load influences. Bridge Types for Light Rail Transportation Different types of bridges are used in the light ra il transportation system. Bridges can be subscribe as arch bridges, truss bridge, suspension bridges, cable stayed bridges, and girder bridges. Most of the light rail bridges are girder bridges. This research will mainly discuss girder bridges. Concrete Girder Bridges Concrete is consists of fine aggregate, coarse aggregate, Portland cement, and water. Concrete is used as structural material for many centuries. The reinforced concrete is also used for more than one hundred years in structure engineering. Because the reinforced concrete can be shaped easily with high strength and the economic efficiency of reinforced concrete is good, the reinforced concrete is widely used all over the world. Concrete is a kind of material with strong compression strength and weak tension strength, so the tensile stresses which is from loads, temperature changes, and

PAGE 22

8 re strained shrinkage cause cracks Wight and MacGregor 2012 The load condition is shown on figure 2.1. A simply support reinforced concrete beam is subjecte d to vertical loads figure 2.1 (a I n figure 2.1 (b), point O is a point assumed on the neutral axis. The part under the neutral axis is applied tensile stresses. As explained strength, then crack occurred. As a result, beam fails very suddenly and completely if the concre te is unreinforced Wight and MacGregor 2012 The reinforcing bars are shown on figure 2.1 (c). These steel reinforcements embedded in the concrete are suppor ting the tensile internal forces so that the concrete can work under the condition of the tensile stress is beyond the concrete tensile strength but lower than the The reinforced concrete of structures should use that no t exceed the limit states. James K. Wight indicate that the limit states of the reinforced concrete elements of structures can be divided into the ultimate limit states, serviceability limit states, and special limit state. The major ultimate limit states contain loss of equilibrium, progressive collapse, rupture, instability, formation of a plastic mechanism, and fatigue. Serviceability limit states include the excessive deflections, excessive crack widths, and undesirable vibration. The special limit stat e is due to abnormal conditions or loadings and physics damages. The reinforced concrete girder bridges are widely used for short and medium span highway and railway design. The superstructure of reinforced concrete girder

PAGE 23

9 bridges is mainly consists of th e reinforced concrete girders, bridge deck, barriers, and pavements. The girders on the reinforced concrete bridges can be I girders, Tees, or box girders. Prestressed Concrete Girder Bridges Prestressed concrete has developed rapidly in recent decades. T he method of prestressed concrete is improved from the reinforced concrete. As discussed previously, the reinforced concrete cause micro cracks in the tension zone by service loads. The concrete in the tension zone is not expected to support the tensile st resses, so the reinforced concrete work with these crack and on exceed the limit states. However, cracks cause the reinforcing bars expose on the air then corrosion occurred, and cracks are looks unsafe. Prestressed concrete element is more attractive and durable than reinforced concrete, and it can possess higher strength Naaman 2004 A comparison of reinforced concrete and prestressed concrete beam is shown on figure 2.2. The prestressing steel tendons are tensioned during or after the prestressed conc rete beam casted. When the prestressed concrete beam posted, beam itself only subject to dead load caused by self weight. The upper part is subjected to tensile force but no cracks, and the under part is subjected to compressive force caused by the tension ed prestressing tendons. Under the full service load applied on the beam, only steel tendons are subjected to the tensile stress so the concrete on the tension zone are uncracked

PAGE 24

10 Prestressed concrete girder bridges can be classified by precast pretension ed girders or posttensioned girders. Precast pretensioned girders are usually cast on the labs or factories. The prestressed steel tendons are tensioned when the girder casted. The tendons and concrete are bonded by friction. Posttensioned beam are apply t ensile stress after the concrete casted. Steel tendons are tensioned in the duct of concrete and bond on boundary of the beam. The prestressed concrete girder bridge can be up to 180 feet span length. Steel Girder Bridges Steel girder bridges are use stee l girders to sustain loads, and concrete bridge deck is usually used. The steel girders can be precast girders or consist of steel plates. The precast beam can be I shape, T shape, rectangular hollow shape, L shape, and some other shapes. The steel plate g irders are built up from plate elements and connected by high tensile strength bolts. The steel plate girder ca n actually regard as deep beam (Salmon, Johnson and Malhas 2009) Because steel plate girder is slender, local bucking should be concerned. Stiffeners are used on steel plate girder to sustain shear force. Loads Analysis Load types due to highway bridge design can be classified dead loads, live loads, pedestrian load, and vehicular dynamic load allowance. The AASHTO define the total factored force effect as

PAGE 25

11 Q= (2.1) Where is the load modifier, is the load factor, and is force effects from loads. For instance, the permanent load of component and attachments is taken load factor as 0.9 to 1.25, and the load modifier is taken 1 for typical bridge. The permanent load is consists of dead loads and earth loads. The live lo ad is consists of gravity loads, vehicular live load, fatigue load, dynamic load allowance, centrifugal forces, braking force, and vehicular collision force. There are some kinds of loads such as water loads and wind load. The vehicular wheel load is the live load applied by the vehicles on the bridges. For the general high way bridges, the AASHTO instruct to use designated HL 93 which is consist of the design truck or tandem and design lane load. From the AASHTO LRFD bridge design specifications, the desi gn truck is shown on figure 2.3, and the design tandem is consist of two 25 kips axle loads with 4 feet spacing, and the transverse spacing is 6 feet. The design lane load is a uniformly distributed longitudinal load of 0.64 kips per foot. This uniformly d istributed load is assumed with a width of 10 feet. The wheel load of the light rail trains is not represented from the AASHTO. In this research, the design wheel load of light rail trains are taken from the RTD. The light rail train wheel load used in De nver is shown in figure 2.4. The full train load

PAGE 26

12 and empty train load are defined from the RTD. The full train load is used in this research. Light Rail Bridges Dynamic Analy sis Dynamic B ehavior The single degree of freedom system (SDOF) is a simplified system of structures. The SDOF system is idealized the mass of the structure is a point th at supported by a massless beam (Chopra 2012). The elastic modulus of the beam is constant. In the linear system, the damping ratio of the structure is constant. The force of the vibration { } is related by the displacement of the mass {u} and the elastic modulus {k}. (Equation 2. 2 ) The damping ratio {c} relates the velocity { } and damping force { }. (Equation 2. 3 ) The mass of the structure {m} relates the acce leration { } and inertia force {p}. (Equation 2. 4 rL (2. 2 rL (2. 3 P= m (2. 4 Figure 2. 4 show the forces acting on the single mass. The external force Pt) is consist of the force of the vibration { }, damping force { }, and inertia force {p}. Based on the Newton Second Law the equation of motion of the single degree of freedom is given by equation 2. 5 P(t) = rE + m (2. 5

PAGE 27

13 In the bridge analysis of this research, a number of degree of freedom is used. As a result, the multiple degree of freedom system (MDOF) is applied. For example, in the two degree of freedom system, the values of the equation of motion are instead by matrix as shown [ ] { } + { } + { } = { } (2. 6 Figure 2. 5 shows the free body diagram of two degree of freedom system. The external forces and are subjected to two masses and respectively (springs and viscous dampers are linear) Mode shape Vibration mode is defined by the natural frequency, mode shape and damping v alue (Craig and Kurdila 2006) In the multiple degree of freedom system, the mode shapes are depending on the number of degree of freedom. The relationship can be describe as k = (2. 7 where the matrix is model matrix, and the matrix is diagonal matrix with frequencies. 2.3.3Dynamic load allowance Vibration cause bridges subjected to dynamic loads from vehicular traffic. A moving vehicle on a bridge generates deflections a nd stresses that are generally greater than those caused by the same vehicular loads applied statically. This is due to the dynamic

PAGE 28

14 interaction between the bridge and the vehicle. This interaction is a problem of considerable complexity and its solution is governed by both vehicle and bridge dynamic characteristics. From the AASHTO LRFD Bridge Design Specifications (2012), the static effects of the design load shall be increased by the percentage specified for dynamic load allowance IM). There are two sou rces may attribute dynamic effects due to moving vehicles. One source is the hammering effect, which is the dynamic response of the wheel touch with the deck joints, cracks, potholes, and delamination. Another source is the dynamic response of the bridges due to long undulations in the roadway pavement. The AASHTO LRFD Bridge Design Specifications (2012) also indicate that based on the date from the field tests, the dynamic component response is not higher than 25 percent of the static response to vehicles, but the short and medium load are at least 4/3 of the static response. Unless the retaining walls subject to no vertical reactions from superstructure or foundations co mponents are lower than the ground level, the dynamic load allowance need to be applied. Table 2.1 shows the dynamic load allowance except the buried components and wood components. Thermal L oad Most materials lengthen with increasing temperatures and shorten with decreasing temperatures. Bridge is a kind of large scale structure so the volume

PAGE 29

15 change caused by temperature cannot be neglected. There are two types of temperature changes need to be c onsidered in the analysis of the superstructure. One is the temperature change where the superstructure changes temperature uniformly. Another type of temperature change is the gradient temperature change of the superstructure ac epth (Richard M. Barker and Jay A. P uckett 2013) Figure 2. 6 represents the difference of a simply supported beam subject to these two types of thermal load. In type (a), beam temperature changes so that volume of changes. In another word, the beam changes elongation. The beam in the condition of type (b) changes curvature by non uniform heating. For example, the beam is subjected to sunshine, so the upper part of the beam heats more than the under part. Bridges subject to thermal load as type (b) induce in ternal stress. In the girder type bridge analysis bridge decks absorbs more heat than girder. Bridge is a kind of spindly structure so the longitudinal change much more obviously that vertical and horizontal. Uniform Temperature Change The calculation of movement from thermal load may be employed from AASHTO LRFD Bridge Design Specifications (2012) Eq. 3.12.2.3 1 as (2. 8 Where L is the expansion length and is the coefficient of thermal expansion. The AASHTO LRFD Bridge Design Specifications (2012) describes two ways to calculate the uniform temperature change. One way called procedure A in AASHTO is

PAGE 30

16 employed for all bridge types except deck bridges having co ncrete or steel girders. The design maximum and minimum temperatures shall be taken as and in table 2.2. The AASHTO also notes that the moderate climate is the freezing days of a year less than 14 days, and the fre eing days are defined as the average temperature is less than F. Procedure B is used for steel or concrete girder bridges with concrete deck. The maximum and minimum design temperature in this part should be defined respectively. Figure 2. 7 determines the maximum design temperature and minimum design temperature for steel girder and concrete girder bridges. Gradient Temperature Change Temperature gradients are employed in design of bridges in case of the bridge deck gain solar. The AASHTO LRFD Bridge D esign Specifications (2012) prescribes multilinear gradients of temperature change to aid the design of bridges. Bridges are subjected to the temperature changes daily and seasonal. Based on the climate is quite different in different zones in the US, the AASHTO divide four zones in the United States (figure 2. 7 ). Most of the western United States is in zone 1. The mid west, part of the northwest United States, and the southwest California are in zone 2. Zone 3 concludes the eastern United States, northwest United States and Hawaii. Alaska is located in zone 4. The gradients change of temperature is different in corresponding zones. Table 2.3 describes the AASHTO guide for vertical gradient of temperature in concrete girder

PAGE 31

17 type and steel girder type bridge superstructures. AASHTO also notes that the temperature is for calculating the change in temperature with the cross section depth instead of the absolute temperature. Temperature may be taken positive. The negative temperatures should multiple by 0.30 for the concrete deck or 0.20 for asphalt overlay deck. The AASHTO LRFD Bridge Design Specifications (2012) exhibited the positive vertical temperature gradient in figure 2. 8 When the concrete as 12 inch, or take actual depth minus 4 inch. For the steel superstructures, the dimension is taken 12 inch, and the distance is taken from the concrete deck depth. AREMA Design code The design code form American Railway Engineering and Maintenance of Way Association (AREMA) specified the design guide of railway bridges. The concrete girders common use slabs, tees, and boxes. The box sections are good for providing deck suitable for ba llasted track. For the steel girder bridges rolled or welded sections are used. The AREMA design manual has no suggests for bridges used for light rail transportation system. The designers should choose design code from the AASHTO LRFD design code and AREM A design manual for the light rail bridge design.

PAGE 32

18 Figures and T ables (a (b)

PAGE 33

19 (c Figure 2.1 Reinforced Concrete Beam a) Beam and load (b) Stresses in concrete beam (c) Stresses of reinforcing bars Wight and MacGregor 2012 (a (b) Figure2 .2 The Behavior o f Reinforced Concrete a nd Prestressed Concrete Beam Under Load (a) reinforced concrete bea m (b) prestressed concrete beam Naaman 2004

PAGE 34

20 (a (b) Figure 2.3 Light Rail Train a nd Truck Wheel Load (From RTD and AASHTO

PAGE 35

21 Figure 2.4 Forces Acting o n t he Mass (Chopra 2012) Figure 2. 5 Free Body Diagram o f Two Degree o f Freedom System (Chopra 2012)

PAGE 36

22 (a (b) Figure 2. 6 Simply Supported Beam Subject t o Thermal Load (a) uniform temperature change (b) gradient change. (Richard M. Barker and Jay A. P uckett 2013)

PAGE 37

23 (b) (c

PAGE 38

24 (d) Figure 2. 7 Contour Maps for (a for concrete girder bridges (b) for concrete girder bridges (c) for steel girder bridges (d) for steel girder bridges AASHTO Figure 2. 8 Solar Radiation Zones for the United States (AASHTO

PAGE 39

25 Figure 2. 9 Vertical Temperature Gradient AASHTO

PAGE 40

26 Table 2.1 Dyna mic Load Allowance (AASHTO Component IM Deck Joints All Limit States 75% All Other Components: 15% 33% Table 2.2 Ranges o f Temperature in Procedure A (AASHTO) Climate Steel or Aluminum Concrete Wood Moderate to 120F to F to F Cold to 120F to F to F Table 2.3 Basis for Temperature Gradients (AASHTO Zone TF TF 1 54 14 2 46 12 3 41 11 4 38 9

PAGE 41

27 CHAPTER III SITE WORK MONITORING OF LIGHT RAIL BRIDGE This chapter describes the site work includes lab testing and in situ strain measurement. The purpose of this test is to record the strain of light rail bridges during the light rail train come through the bridges. The testing procedure details are present in this chapter. This chapter also introduces the equipment and tools in this chapter. Equipment of T est Some kinds of instrument and tools are used in this test. The parts being tested on the bridge includes the rail on the bridges and bridge girders under the bridges. The values of strain are read by strain gage and recorded by CR5000 data logger in the in situ work. CR 5000 D ata L ogger Figure 3.1 shows the CR 5000 data logger used in this testing. The CR 5000 measurement and control system can make measurement with 5000 Hertz. This instrument has bat tery so that it can be used at in situ test work, and the CR 5000 has 2 Mb SRAM memories to store data. The storage of CR 5000 is not enough to store all data of the testing. In that case a laptop computer is used in the test to transport and store data of the in situ work. It has 20 testing channels to record the strain values which are sufficient to this work.

PAGE 42

28 Other Equipment Other tools and consumables are used in the test. Table 3.1 present the detail of these equipment. Introduction of T ested B ridge s A total of five constructed bridges in Denver, CO, were monitored. Because most of the light rail bridges are girder bridges, this site work is focus on the girder bridge. Table 3.2 illustrates the details of five tested bridge. All five bridges are lig ht rail trains used only, and these light rail bridges are 2 rail lanes except the Indiana Bridge is one lane and two way use. Broadway Bridge The Broadway Bridge is comprised of 5 spans (2 span plus 3 span connected by an expansion joint), including direc t fixation tracks. The out to out deck width varies from 34 ft to 42 ft with a typical thickness of 10 in. The depth and width of the steel plates (AASHTO M 270 Grade 50) supporting the deck are approximately 5.5 ft and 2 ft, respectively. The 28 day compr essive strength of the deck concrete is 4500 psi. Indiana Bridge The Indiana Bridge has no skew and consists of a hollow prestressed concrete box girder with a direct fixation track. The depth and width of the box girder are 7 ft and 20 ft, respectively, and the 28 day compressive strength of the girder concrete is

PAGE 43

29 5800 psi. Post tensioning was done with low relaxation steel strands (Aps = 28.64 in2 and fpu = 270 ksi) at a jacking stress level of 75%fpu. Santa Fe Bridge The Santa Fe Bridge is a 2 span multi cell prestressed concrete box girder bridge. The bridge is appro ximately 28 ft wide and 10 ft deep and has a total length of 328 ft (172 ft + 156 ft spans). Two train tracks are located on a ballast layer of 1.7 ft. The 28 day compressive strength of the box concrete was 6000 psi and low relaxation strands (Aps = 76 in 2 and fpu = 270 ksi) were used for post tensioning at a jacking stress level of 75%fpu. County Line Bridge The County Line Bridge L = 990 ft) consists of 4 prestressed concrete bulb T girders (Colorado BT84) for 7 spans varying from 114 ft to 160 ft. Each girder has a depth of 7 ft with a girder spacing of 8.3 ft, and supports a deck slab (t = 8 in) with 2 direct fixation tracks. All girders were connected by diaphragms cast on site (i.e. a continuous system), except the fourth span where expansion joints were placed. Two harping points were used for prestressing strands per girder (Ap = 5.2 in2 to 12.6 in2, low relaxation 270 ksi steel). A 28 day concrete strength of 8500 psi was used for the girders.

PAGE 44

30 6th Avenue Bridge The 6th Avenue Bridge is comprised of 4 + 2 span prestressed concrete bulb T girders (BT42) connected by an arch bridge. The bridge has no skew and includes two ballasted train tracks. A waterproofing membrane layer was placed in between the deck concrete (t = 8 in) and the ballast. As in t he case of the County Line Bridge discussed above, all girders were connected on site to make a continuous system and each girder had two harping points (Ap = 5.2 in2 with an effective steel stress of 56%fpu). The compressive strength of the girder concret e used was 9000 psi. Testing Procedure The testing work in this program includes lab test and in situ testing. The lab test collects the strain response with a simulative train load on the 115RE rail. The in situ testing includes the strain collection and dynamic response test with five operating light rail bridges. The steel rail strain which is test ed in the Auraria West Station also includes making a comparison with lab test result. Lab Test A laboratory experiment was conducted to calibrate the response of an 115RE rail subjected to mechanical load. A 128 inch long rail was received and tested with strain gages, as shown in figure 3.2. Two loading conditions were employed: simply supported a nd continuous systems. The simply supported test is shown as figure 3.2, and the continuous system is shown

PAGE 45

31 as figure 3.3. According to the RTD design manual (Sec. 2.4 LRV fleet and Sec. 6.4.2 Live load), the front wheel of a fully loaded train weighs 12.2 kips, while that of an empty train has 7.5 kips. Site Visit The research team studied the site condition of the five bridges to be monitored, as shown in figure 3.4. The purposes of the site visit were to identify potential problems that might hinder response monitoring and to confirm the engineering drawings obtained from the RTD. The location of instrumentation was examined, including vertical elevation. The bridges which the research team initial plan to test is Broadway Bridge, Indiana Bridge, Sant a Fe Bridge, County Line Bridge, and Cherry Creek Bridge. All bridges were accessible without any problem except for the Cherry Creek Bridge under which bike paths were paved. As a result, the 6th Ave Bridge re places the Cherry Creek Bridge. Site Work Moni toring The monitored span of the individual bridges was determined by the following criteria as recommended by the Regional Transportation District (RTD) controlling all light rail transit systems in Denver, CO: i) lowest superstructure elevation for safet y, and ii) accessibility to tracks with minimal disruption to train operation. This subsection summarizes bridge details, in situ data, and technical interpretation, including statistical parameters which will be useful for developing design recommendation s. Typical field monitoring time was 12 hours (from 8:00 am to 8:00

PAGE 46

32 pm) per bridge, while two days were spent for the 6th Avenue Bridge due to a strong wind issue. The behavior of the bridges was converged from a statistics perspective, which means there w as no practical needed to extend to the monitoring time (i.e., sufficient data were obtained). a) Broadway Bridg e The behavior of the first span was monitored. Train speed was measured with a digital speed gun confirmed by a portable global positioning sy stem (GPS) inside trains passing the bridge. (Figure 3. 5, a ) Instrumentation included i) Eight strain gages bonded to the rail side in order to measure in situ train wheel load. (Figure 3. 5, b ) ii) One strain gage bonded in between the eight strain gage clusters for tem perature monitoring. (Figure 3. 5, c ) iii) Three strain gages (one 4.7 in gage length and two 0.2 in gage length gages) bonded to the bottom of each girder to monitor the flexural response of the bridge at mid span (i.e., bending and live load distribution). (Figure 3.5 d b) Indiana Bridge The monitored span is 95 ft long and has expansion and fixed bearings at both ends. (Figure 3.6 a ) Strain gages were bonded to the side of the rail to measure train wheel load and thermal deformation. Figure 3.7 b ) Unlike other bridges monitored in this research program, one way travel is allowed along a single track and light rail

PAGE 47

33 trains are alternatively operated from Denver to Golden (east to west) and vice versa, as shown i n figure 3. 7, c Long an d short gages (4.7 in and 0.2 in gage lengths, respectively) were also bonded to the bottom of the prestres sed concrete girder. (Figure 3. 7, d c) Santa Fe Bridge The monitored span is 155 feet and 5 inch. (Figure 3. 8, a ) train gages were bonded to the rai l side to measure train load and temperature (Figure 3. 8 b and c ) and were bonded underneath each web member of the multi cell girder. Scaffold is used in Santa Fe Bridge test. (Figure 3. 8 d ) d) County Line Bridge The monitored span is 160 feet (Figure 3. 9 a ). Strain gages were bonded to the rail (Figure 3. 9 b ) to measure light rail train load (Figure 3. 9 c ). Additional gages were bonded to the bottom of each girder at mid span to monitor flexural behavior when loaded ( Figure 3. 9 d ). e) 6th Avenue Bridge The 6th Avenue Bridge is connecting with arch bridge. Only the girder bridge type part is tested in this program (Figure 3.1 0 a ). Strain gages were bonded like other bridges to measure the in situ wheel load of light rai l trains (Figure 3.1 0 b and c ) and the flexural response of the girders at midspan (Figure 3. 10, d ).

PAGE 48

34 Dynamic Response Tes t A non contact interferometric radar technique called Image By Interferometric Survey IBIS hereafter) was employed. The IBIS system detects a phase change in reflected radar waves to identify the position of an object. Because Subtask 1 informed that the response of the light rail bridges was consistent, a nominal field monitoring time of 5 hours was planned per bridge. Reflectors wer e installed along the edge of the bridge deck at mid and quarter spans to measure the displacement and frequency of the bridge. The monitored spans were identical to those of the previously conducted field test in Subtask 1. The IBIS equipment was then se t up using a tripod, and its radar head was connected to a laptop computer. A laser distance meter mounted to the radar head was used to uniquely link the position of specific bridge members with a peak radar display. This process enabled reviewing in sit u technical data at a later time for further data processing such as fast Fourier transform (FFT) analysis. A sampling rate of 200Hz was used. Using the IBIS system, the vibration and displacement data of all the five bridges were collected and analyzed. T emperature Effect on Train Rails As mentioned in the Bridge details section, strain gages were bonded to measure the effect of temperature on the behavior of track rails while monitoring train load. The coefficient of thermal expansion (CTE) for steel (115 10 F or 12 10 C (Okelo et al. 2011) and a rail temperature (T) was calculated

PAGE 49

35 maximum temperature variation range of each bridge is summarized in Table 2: the maximum positive and negative temperatures indicate relative changes in temperature against initial temperatures (e.g., the lower temperature bound of the Broadway Bridge was 5.3F ( 2.9C), which means that the maximum temperature drop was 5.3F ( 2.9C) from the initial temperature when the site work got started). A net temperature variation for all the bridges monitored was in between 11.1F (6.1C) and 25.0F (13.9C), excluding the temperature of the 6th Avenue Bridge whose strain readings were influenced by strong wind blown for the two consecutive days when the field work was conducted ( further site monitoring for the 6th Avenue Bridge was not carried out because the response of a bulb tee superstructure was already measured in the County Line Bridge). Train loading did not significantly affect the temperature gage readings since the gage (horizontal direction) was bonded at the centroid of the rail where flexural stress was none (even though some minor effects were observed in the converted temperature spectra, as typically shown in Fig. 3.11 ).

PAGE 50

36 Tables and figures Figure 3.1 CR 5000 Measurement and Control System Figure 3.2 Experimental Setup and Strain Gage Configurations for t he Side a nd Bottom o f t he Rail

PAGE 51

37 Figure 3.3 115RE Rail Subjected t o Load with Continuous System (a

PAGE 52

38 (b) (c

PAGE 53

39 (d) (e Figure 3.4 Five Bridge Prepare t o Test a) County Line Bridge (b) Cheery Creek Bridge (c) Broadway Bridge (d) Santa Fe Bridge eIndiana Bridge

PAGE 54

40 (a (b) Monitored span

PAGE 55

41 (c (d) Figure 3.5 Broadway Bridge (a) elevation view and girder cross section (b) Light rail train operation on site and portable data acquisition system (c) Strain gages bonded to rail (d) Strain gages bonded to girders at mid span (Broadway Bridge

PAGE 56

42 (a (b) Monitored span

PAGE 57

43 (c (d) Figure 3. 6 Indiana Bridge (a) elevation view and typical cross section of girder (b) Rail gage bonding (c) One way train track (d) Girder gages

PAGE 58

44 (a (b) Monitored span

PAGE 59

45 (c (d) Figure 3. 7 Santa Fe Bridge (a) elevation view and typical cross section of girder (b) rail strain gages bonding (c) Trains approaching (d) Girder gages

PAGE 60

46 (a (b) Monitored span

PAGE 61

47 (c (d) Figure 3. 8 County Line Bridge (a) elevation view and typical cross section of girder (b) rail strain gages bonding (c) Trains approaching (d) Girder gages

PAGE 62

48 (a (b) Monitored span

PAGE 63

49 (c (d) Figure 3. 9 6 th Avenue Bridge (a) elevation view and typical cross section of girder (b) rail strain gages bonding (c) Trains approaching (d Girder gages

PAGE 64

50 Fig 3.1 0 Typical Temperature Variation of Track Rail Measured i n the Broadway Bridge

PAGE 65

51 Table 3.1 Purpose of Equipment Used i n Site Work equipment purpose strain gage read strain values on girders and rail glue splice strain gage on bridge wire connect strain gage and dada logger laptop store data and do basic in situ analysis rubber tapes fix wire in workplace tin solder connect strain gage and wire welding torch melt solder fixed between gage and wire

PAGE 66

52 Table 3.2 Summary of Five Tested Bridge Details Bridge Type Typical cross section Spans modeled Materials Broadway bridge Steel plate girder 2 spans (278 ft) Fy = 36 ksi Indiana bridge Prestressed concrete box 5 spans (628 ft) tensioned concrete: 270 ksi Santa Fe bridge Prestressed concrete box 2 spans (334 ft) tensioned concrete: g steel: fpu = 270 ksi County Line bridge Prestressed concrete girders 4 spans (580 ft) psi 270 ksi 6th Ave bridge Prestressed concrete girders 4 spans (328 ft) 4500 psi tensioned concrete: 270 ksi

PAGE 67

53 Table 3. 3 Maximum Temperature Variation of the Monitored Bridges Bridge Maximum positive and negative temperatures Net temperature variation Broadway 5.3F to 8.4F 2.9C to 4.7C 13.7F (7.6C Indiana Bridge 5.1F to 19.9F 2.8C to 11.1C 25.0F (13.9C Santa Fe Bridge 3.5F to 16.4F 2.0C to 9.1C 19.9F (11.1C County Line Bridge 8.0F to 3.1F 4.4C to 1.7C 11.1F (6.1C 6th Avenue Bridge 23.5F to 9.7F 13.1C to 5.4C 33.2F (18.5C)a a: strong wind blew while the bridge was monitored for a two day period so strain reading was influenced

PAGE 68

54 CHAPTER IV BRIDGE MODELING Models of the five tested are used in this research to aid the analysis. Modeling computer program are used in the modeling part. The Santa Fe Bridge and Indiana Bridge are modeled in SAP2000, and the Broadway Bridge, County Line Bridge, and 6th Ave Bridge are modeled in CSI Bridge. This chapter describes the conditio ns of models based on the drawing of these five bridges. The models will analysis the dynamic response of these five bridges. The thermal load and rail brake gaps are also analyzed in this chapter. The general steps of modeling are shown on the appendix of this paper. Property of five bridges models The research team built the models of five bridges base on the existed bridges and drawings. Some details of the bridges are simplified in the model. This part will describe the property of materials and sectio ns, vehicular loads, and some other details of the bridges. Se ction Properties The Broadway Bridge is steel plate girders bridge. The Indiana Bridge and Santa Fe Bridge are prestress concrete box girders bridge. The County Line Bridge and 6th Ave Bridge are prestress concrete precast girders bridge. The section of the deck and girder s are built on the computer program based on the drawing the five bridges.

PAGE 69

55 Figure 4.1 (b) reveal the section property input on SAP2000 computer program compare with the existing bridge (Figure 4.1 a), and the other four bridges sections are built in the sa me way. The barriers and steel rails are also concerned in the model. Reinforcement steel bars and prestress tendons with harp are used in the prestress concrete bridge models. Vehicular Loads The full light rail train loads are employed in all of the fiv e bridges which the boundary wheel load is 24.375 kips and the middle wheel load is 16.25 kips for one light rail train. The models use four trains as vehicular load on the bridge by the speed of 60 mile per hour. All bridge models are built by two lanes except the Indiana Bridge. The light rail trains will go through the bridge in each side simultaneously on the two lane models. The axial wheel loads on the bridge models are two points with a width of 4.1 feet. All axial wheel loads length is fixed after the leading load. Other Properties Of Bridge Models The five bridge models are multiple span girder bridges. The location of each bent and abutment is simulated based on the draw of five bridges. The boundary condition of piers and abutments is used as hinge and rollers. One of the abutments is hinge, and the other abutment is roller in the other side. All piers are hinge type. The hinge type bearing property is fixed with translation and rotation on each direction.

PAGE 70

56 The roller type bearing property is fi xed the vertical and longitudinal translation but free to horizontal translation and all rotations. The piers and abutments are fixed with the ground. The cross section of the abutment is simplified as 138 inch by 84 inch rectangular section. The piers are used by rectangular section which the depth is 6 inch and the width is 48 inch. Finite element method is employed by the calculation the computer program. The bridge is simulated as amount of segments. The maximum segment length is 120 inch. Bridge barri ers and steel rails are connected with bridge deck as fixed link. The models of five bridges are shown at figure 4.2. Dynamic Response of Bridges Dynamic response of the five bridge models is calculated by the maximum longitudinal flexural moment at bridg e pier and maximum displacement at the mid span. The dynamic load allowance (DLA) is calculated by DLA= ( fZfofd fifjfWfj fifjfWfj 100% 4 .1) Where and is the index of the dynamic and static response respectively. The longitudinal flexural and maximum displacement is direct proportion to the response, so the DLA due to moment is DLA= ( fZfofd fifjfWfj fifjfWfj 100% 4 .2) And DLA due to displacement is

PAGE 71

57 DLA= ( fZfofd fifjfWfj fifjfWfj 100% (4.3) Where M and S is moment and displacement. The static and dynamic vehicular load is defined in the SAP2000 and CSI Bridge computer programs as different kind on load cases. The static vehicular loa d is multiple step static load which means the light rail trains locate on the bridges in stable step by step. The dynamic load is the light rail trains time history load analysis linearly. The simulated trains are moved on the bridge discretize load every 1.0 second. Rail Break Gaps The steel rails lays on the five exists bridges continuously, but rail break gaps are simulated on the model. The rail break gaps is cut on the location of the maximum negative bending moment which at pier on the bridges. The length of the rail break gaps is simulated as 1, 2, and 3 inch respectively. Dynamic load is calculate on this research for calculate the increasing of DLA. The rail break gaps on the models are shown on figure 2.3. Calculation of the dynamic load allowa nce with rail breaks is similar to the previous steps. The dynamic load allowance based on the bridges with steel rail break gaps is = ( fXfhf[fWfa f_ fifjfWfj fifjfWfj 100% 4 4 = ( fXfhf[fWfa f_ fifjfWfj fifjfWfj 100% 4 5

PAGE 72

58 Where the is the dynamic load allowance with rail break gap, and is the maximum negative bending moment at pier and displace at mid span of the bridges. Thermal L oad Thermal load is simulated on the models in this research. Th e thermal load on the five bridges is based on the temperature gradient method form the AASHTO LRFD bridge design code. The five bridges are located on zone 1 based on the AASHTO defined. However, the thermal load on zone 1, 2, 3, and 4 are calculated by f inite element method by SAP 2000 and CSI bridges on this research. The thermal load is built by an individual load case on the computer program. The values of temperature change are the AASHTO default shown on figure 2.4.

PAGE 73

59 Tables and figures (a (b) Figure4 .1 Section Properties of Bridge Deck and Girder : Indiana Bridge (a Drawing (b) Modeling

PAGE 74

60 (a (b)

PAGE 75

61 (c (d)

PAGE 76

62 (e Figure 4.2 Models of Five Bridges (a) Broadway Bridge (b) Indiana Bridge (c) Santa Fe Bridge (d) County Line Bridge (e) 6th Avenue Bridge Figure 4.3 Steel Rail Break on Models

PAGE 77

63 Figure 4.4 Temperature Gradient of Five Bridge s

PAGE 78

64 CHAPTER V RESULTS AND ANALYSIS The results contain the field work testing results and the results from computer program modeling. This chapter also illustrates the bridge natural frequency translated from strains with Fast Fourier Translation (FFT). The analysis of thermal load and steel rail break is also discussed in this chapter. In situ W ork T esting Results The results of strain and displacements from the five tested bridges will be analyzed in this part. This part also includes the result of lab test and the site work at Auraira West Station. Wheel Load Analysis (aLab testing and Auraira West Station testing: Wheel load is simulated in the lab. The 115RE rail is subjected to 16 kips and 12.2 kips load respectively. The strains measured at the bottom of the rail where a maximum flexural effect takes place were compared with those calculated by fundamental structural analysis formulas. The strain v alues of the continuous rail were apparently less than those of the simply supported case (e.g., the measured strain of the continuous rail was 39% less than that of the simply supported counterpart at a load of 7.5 kips). This observation indicates that t he proposed test setup can adequately represent the response of continuous rails supported by multiple sleepers on site.

PAGE 79

65 Figure 5.1 exhibits the load strain behavior of the 115RE rail. The response of the strain gages boded to the side of the rail is given in Figure 5.2 The gages facing each other in the diagonal direction showed similar behavior. Test data showed slight discrepancy between the G1/G3 and G2/G4 groups. This result illustrates that the applied principle stresses in these two diagonal directio the same. Linear curve fitting equations were developed to establish relationships between the strain and the applied load so that in situ load would be measured based on strain reading. Figure 5.3 demonstrates the calibration of the portable data acquisition system using the immovable laboratory data acquisition. At typical loads of 12 kips and 14 kips for the continuous rail test, the strain reading of these two systems was almost identical. Such a calibration results corrobo rate that use of the portable data acquisition system will be adequate to measure the in situ behavior of the fiver bridges discussed in Site visit. The established load strain relationships (Figure 5.2) were further validated with actual train load on si te as Figure 5.4. The front wheel of an empty stationary train (7.5 kips) generated a maximum strain of 64.5 microstrain, as shown in Figure 5.4, which agreed with the laboratory strain of 63.8 microstrain subjected to a load of 7.5 kips. (b)In situ wheel load of light rail trains: Figure 7 reveals typical strain responses associated with the wheel load of light rail trains running on the bridges monitored.

PAGE 80

66 The strains measured from the rail side were converted to the wheel load of the trains using the form ulas developed in the laboratory test, which were also calibrated with stationary light rail trains. The temperature effect discussed in the previous section was compensated when interpreting train load. Provided that the primary interest of the present si te work was in detecting maximum train loads that would control the response of the bridges (i.e., the light rail train has two design loads (fully loaded) for six axles such as 24.375 kips and 16.25 kips, as shown in Fig. 8, and corresponding wheel loads are 12.188 kips and 8.125 kips), maximum loads (or peak loads) detected during each load cycle were acquired and summarized in Fig. 9. The number of observation was not consistent for all bridges because some bridges were used by multiple lines (there are 6 light rail lines in Denver); however, the mean wheel load measured was almost consistent irrespective of the observation number. This fact indicates that the measured load data are statistically stable. The mean wheel load of the light rail trains varied from 6.2 kips to 6.9 kips. This measured load range was reasonable because the articulated light rail train had a nominal load range between 4.96 kips (empty train) and 12.19 kips fully loaded train) per train wheel. It is presumed that the passenger occ upancy increased the train load by 25% to 39%, including some dynamic effects. It illustrates a relationship between the average train speed measured and the mean train wheel load. The regression line indicates that the load has augmented with an increase in train speed. Although the passenger load was not identical in individual trains (the number of passengers is

PAGE 81

67 stochastic in nature), it appears to be reasonable to adopt the fitted equation because the variation range of the wheel loads was not significa nt (i.e., 6.2 kips to 6.9 kips). Girder Response The flexural behavior of the monitored bridges is provided in Fig. 11 (only selected cases are shown for brevity because superstructure responses were basically repeated). The measured strains at midspan of each girder showed periodic spikes when the light rail trains were passing, whose magnitude was a function of girder types and geometric configurations. For instance, the response of the Broadway Bridge (three steel plate I girders with a span length of 11 9 ft, Fig. 1) and the Indiana Bridge (one large prestressed concrete box girder with a span length of 95 ft, Fig. 2) had typical strains of approximately 100 10 6 and 35 10 6, respectively, as shown in Fig. 11(a) and (b). Some minor negative strains were detected in all cases because the bridges were continuous and the behavior of the girders physically moved up and down depending upon the location of train load, particularly noticeable for the Broadway Bridge havi ng relatively less flexural rigidity due to use of the slender steel I plates [Fig. 11(a)]. As discussed earlier, the strains of the 6th Avenue Bridge significantly fluctuated because of the strong wind and close up views were not provided in Fig. 11(e).

PAGE 82

68 Dynamic Response Two dynamic modeling approaches were considered (i.e., mode superposition and direct integration), while the mode superposition method was selected for the present study because it is less sensitive to time steps (numerically stable) comp ared to the direct integration and, consequently, generates accurate technical results with reasonable computational effort, including modal analysis data. This was one of the major concerns in the present research since the number of required simulations was substantial. Constant modal damping was utilized in accordance with Art. 4.7 (Dynamic analysis) of the AASHTO LRFD Specifications and the train loading was regarded as a transient parameter. First five modes and corresponding frequencies were extracted using Eigenvector analysis. These modes were iteratively calculated with the following convergence criterion: 5. 1) where is the eigenvalue relative frequency shi ft at the iteration. Provided that all positive frequencies were predicted, it can be stated that the developed dynamic bridge models were stable. Figure 6 illustrates a comparison between the measured and predicted displacements at midspan of the individu al bridges. For consistency, the finite element models included two cases (i.e., empty train and fully loaded train loads) with inbound train loading that was close to the reflector installed. The sign convention used is as follows: positive and negative v alues indicate downward and

PAGE 83

69 upward displacements, respectively. It should be noted that the direction of train operation affected the positive and negative displacements of the monitored span in continuous bridge systems (i.e., downward to upward deflectio ns or upward to d ownward deflections with time Temperature Effect on Train Rails Temperature gradient was considered to address the non uniform thermal exposure of the bridge superstructure: thermal zones 1 to 4 (Art. 3.12.3 Temperature gradient). The temperature induced stress ( ) may be obtained by a combination of axial strain ) and curvature ( ) (Ghali et al. 1989): (5.2) (5.3) where A and Ai are the total cross sectional area and the ith element area of the bridge superstructure, respectively; Tai is the temperature at the element centroid; I and are the total moment of inertia and the moment of inertia of the section about its own centroid, respectively; is the element centroidal axis; is the temperature difference from bottom to top of the element; and di is the element depth. The temperature induced distress wa s engaged with the aforementioned thermal zones of the AASHTO LRFD. It is worth noting that such distress primarily contributes to increasing internal stresses, rather than causing girder reactions when expansion joints are appropriately designed.

PAGE 84

70 Result s from Simulation This part presents the results calculation from the computer program models. A summary of bridge spans and length of each spans is given on table 5.4. The results include the dynamic load allowance of the light rail trains vehicular load. The dynamic load allowance of the bridges with steel rail break gaps and thermal load is also discussed on this part. Dynamic Response Analysis The deflection curve of five bridges applied by the light rail train vehicular load is shown are shown on figure 5.11. The shape of deflection curve from the static and dynamic load is similar. However, the displacement from dynamic load is higher than the static load because of the stress caused by the interaction of the steel rail and light rail train wheel s, and the vibration of the bridges superstructure also increase the maximum displacement. The bending moment of the model is calculate. As predict, the dynamic effect increase the bending moment. The bending moment diagrams of the five bridges are shown on figure 5.12. Figure 5.12 indicates the moment at mid span is positive and the negative at pier. (i.e., the upper girder is subjected to tensile stress at pier and compressive stress at mid span.) This is conformed to the influence line of the continuou s bridge. The maximum bending moment and displacement is shown on table 5.6 and 5.7.

PAGE 85

71 Rail Break Gaps The steel rail break gaps are given on figure 5.13.The steel rail is built on models. The cross section is shown at table 5.8. The steel rails are fixed w ith the bridge. The five bridges have four steel rails which is two wheels on each line except the Indiana Bridge has 2 rails on the only one lane. The steel rail break gaps is simulated at the pier which is the nearest to the field tested location. Dynami c load of light rail trains vehicular is applied on the bridge models with steel rail break. The values of the maximum bending moment and displacement based on the steel rail break are shown on table 5. 8 and 5. 9 Thermal Load and Frequency of Bridges The natural frequency of five bridges model is show on table 5.1 0 The natural frequency of bridge is not influenced by loads. The natural frequency changes when natural freque ncy influenced by the rail break gaps change is relatively small, so this difference is neglected. The thermal load based on 4 zones in given on table 5.1 1 The thermal load decrease from zone 1 to zone 4. This illustrate that the thermal load is decreasin g by the value of temperature change decreasing. Analysis of Result The comparison of natural frequency between the finite element analysis and field test is discussed in this part. The dynamic response which is influenced by the

PAGE 86

72 steel rail break gaps is analyzed. The result of thermal load from modeling and theoretical calculation is also included. Natural Frequency Both the natural frequency of the five bridges form the field test and from modeling is agreed with the predict value. The natural frequenc y from test is floating but the predict values are in the range of the tested value. The values of natural frequency from computer program modeling have difference with the predicts, but the difference is no more than 10 percent. Dynamic Response of Rail B reak The dynamic load allowance of models is calculated. (Table 5.1 2 and 5.1 3 This illustrates the DLA of bridges increases by the rail break gap, and the length of the rail break gap influences the DLA of bridges. The DLA of bridges increase when the le ngth of the rail break gaps increase. The more of the rail break gaps extend the value of DLA increases more obvious. Temperature Change The thermal is calculated by theoretical shown on table 5.14. The different between the theoretical calculation and th e modeling is calculated as fjf^f[fe fcfefZf[fb fjf^f[fe 100% (5.4)

PAGE 87

73 analysis calculated value. The value of and is the theoretical axial force and finite element analysis calculated value. Speed effect The speed of vehicle is a function of the DLA. The dynamic load allowance of low speed vehicular load is calculated by modeling in this research. The dynamic load a llowance of the vehicular speed 40 and 20 mile per hour is shown in table 5.15 respectively. To compare with the maximum design speed which is 60 mile per hour, the values of DLA decrease with the velocity light rail train of 20 and 40 mile per hour (fig ure 5.1 3 ). This indicates that the DLA is decreasing when the speed of vehicle decreasing. The dynamic load allowance is controlled by the maximum design train speed for the light rail bridge design.

PAGE 88

74 Tables and Figures a b) Figure 5.1 Load Strain Behavior a t Bottom o f Rail : (a) simply supported case; (b) continuous case Fig. 5.2 Load Strain Behavior o n t he Side o f Continuous Rail

PAGE 89

75 Figure 5.3 Validation of Portable Data Comparison Acquisition System Using Rail Strain at Bottom Figure 5.4 Wheel Positioning o f Auraria West Station Figure 5.5 C omparison Between In Situ Test a nd Laboratory Test (Front Wheel Load

PAGE 90

76 (a b)

PAGE 91

77 (c (d)

PAGE 92

78 (e Figure 5.6 Measured Strains f or Light Rail Train Wheel Load : (a) Broadway Bridge; (b) Indiana Bridge; (c) Santa Fe Bridge; (d) County Line Bridge; (e 6th Avenue Bridge. Figure5 .7 Fully Loaded Design Axle Loads o f t he Light Rail Train Operated i n Denver CO (the six axles loads of the articulated empty train consist of 14.869 k + 14.869 k + 9.91 3 k + 9.913 k + 14.869 k + 14.869

PAGE 93

79 (a) (b) (c) (d) (e) (f Figure 5.8 Distribution o f Measured Train Wheel Load coefficient of variation; S = average train speed): (a) Broadway Bridge; (b Indiana Bridge; (c) Santa Fe Bridge; (d) County Line Bridge; (e) 6th Avenue Bridge; (f) mean train load measured versus average train speed (heavy wheel = front and rear; light wheel = middle

PAGE 94

80 (a (b)

PAGE 95

81 (c (d) (e Figure 5.9 Flexural Response o f Monitored Bridges : (a) Broadway Bridge (exterior girder); (b) Indiana Bridge (exterior box web) (c) Santa Fe Bridge (2nd interior box web); (d) County Line Bridge (interior girder); (e) 6th Avenue Bridge (interior girder)

PAGE 96

82 (a (b)

PAGE 97

83 (c (d)

PAGE 98

84 (e Figure 5.1 0 Deflection of Brid ge Models (a) Broadway Bridge (b) Indiana Bridge (c) Santa Fe Bridge (d) County Line Bridge (e) 6th Avenue Bridge (a

PAGE 99

85 (b) (c

PAGE 100

86 (d) (e Figure 5.1 1 Bending Moment Diagram o f Bridges (a) Broadway Bridge (b) Indiana Bridge (c) Santa Fe Bridge (d) County Line Bridge (e) 6th Avenue Bridge

PAGE 101

87 Figure 5.1 2 R ail Break Model at Piered Location

PAGE 102

88 (a (b)

PAGE 103

89 (c (d) (e Figure 5.1 3 Speed effect of five bridges (a Santa Fe Bridge (b) Indiana Bridge (c) 6th Avenue Bridge (d) Broadway Bridge (e County Line Bridge

PAGE 104

90 Table 5.1 Comparison between Measured and Predicted Fundamental Frequencies Bridge Fundamental frequency Measured Predicted Broadway Bridge 1.72 0.42 Hz 1.99 Hz Indiana Bridge 1.76 0.50 Hz 1.95 Hz Santa Fe Bridge 1.84 0.13 Hz 1.70 Hz County Line Bridge 2.22 0.85 Hz 2.95 Hz 6th Avenue Bridge 1.31 0.11 Hz 1.32 Hz Table 5.2 Assessment of Deflection Control Bridge Type Monitored span Test service load average Broadway Steel plate girder 119 ft 0.365 in L/3910 Indiana Bridge PC box girder 95 ft 0.040 in L/28500 Santa Fe Bridge PC box girder 155 ft 0.224 in L/8300 County Line Bridge PC I girder 160 ft 0.250 in L/7680 6th Avenue Bridge PC I girder 80 ft 0.066 in L/14550

PAGE 105

91 Table 5.3 Maximum Temperature Variation of the Monitored Bridges Bridge Maximum positive and negative temperatures Net temperature variation Broadway Bridge 5.3F to 8.4F 2.9C to 4.7C 13.7F(7.6C Indiana Bridge 5.1F to 19.9F 2.8C to 11.1C 25.0F(13.9C Santa Fe Bridge 3.5F to 16.4F 2.0C to 9.1C 19.9F(11.1C County Line Bridge 8.0F to 3.1F 4.4C to 1.7C 11.1F(6.1C 6th Avenue Bridge 23.5F to 9.7F 13.1C to 5.4C)a 33.2F(18.5C)a a: strong wind blew while the bridge was monitored for a two day period so strain reading was influenced

PAGE 106

92 Table 5.4 Bridge Span and Span Length Brid ge span 1(feet) span 2(feet) span 3(feet) span 4(feet) span 5(feet) Broadway Bridge 95 230 365 517 628 Indiana Bridge 172.6 334 Santa Fe Bridge 119 238 County Line Bridge 114.25 274.25 434.25 580.25 6th Avenue Bridge 80 160 240 320

PAGE 107

93 Table 5.5 Dynamic Response from Bending Moment at Piers Bridge Bending moment (kips*ft) static + static dynamic + dynamic Santa Fe Bridge 2639 3312 2656 3452 Indiana Bridge 1612 2392 1680 2487 6th Avenue Bridge 805 987 820 1030 Broadway Bridge 2910 4704 2930 4897 County Line Bridge 2431 3381 2532 3513 Table 5.6 Dynamic Response from Displacement at Mid Span Bridge Displacement(inch static dynamic Santa Fe Bridge 0.457 0.476 Indiana Bridge 0.375 0.394 6th Avenue Bridge 0.611 0.651 Broadway Bridge 0.883 0.939 County Line Bridge 1.102 1.155 Table 5.7 Dimensions of Steel Rail dimensions value (inch outside height 7.06 top flange width 2.8 top flange thickness 1.4 web thickness 0.625 bottom flange width 5.5 bottom flange thickness 0.78

PAGE 108

94 T able 5. 8 Dynamic Response with Rail Break f rom Bending Moment at Piers Bridge moment of dynamic load with rail break (kips*ft) 1 inch + 1 inch 2 inch + 2 inch 3 inch + 3 inch Santa Fe Bridge 2656 3465 2657 3471 2657 3487 Indiana Bridge 1680 2498 1680 2504 1682 2506 6th Avenue Bridge 821 1034 823 1041 826 1046 Broadway Bridge 2931 4920 2932 4978 2932 4992 County Line Bridge 2533 3532 2536 3548 2537 3565 Table 5.9 Dynamic Response with Rail Break from Displacement at Mid Span Bridge maximum displacement with rail break (inch 1 inch 2 inch 3inch Santa Fe Bridge 0.481 0.487 0.489 Indiana Bridge 0.397 0.398 0.401 6th Avenue Bridge 0.66 0.662 0.664 Broadway Bridge 0.933 0.934 0.937 County Line Bridge 1.156 1.163 1.171 Table 5.10 Natural Frequencies from Models Bridge frequency (Hz Broadway Bridge 2.23 Indiana Bridge 1.57 Santa Fe Bridge 1.75 County Line Bridge 2.8 6th Avenue Bridge 1.34

PAGE 109

95 Table 5.11 Thermal in Different Zone Of Bridges from Models Bridge Loading zone 1 2 3 4 Santa Fe Bridge 586 495 449 393 Indiana Bridge 881 686 623 545 6th Avenue Bridge 654 554 503 438 Broadway Bridge 795 619 562 497 County L ine Bridge 562 469 428 382 Table 5.12 Dynamic Load Allowance from Bending Moment bridge no rail break 1 inch break 2 inch break 3 inch break Santa Fe Bridge 4.15 5.25 6.56 7.00 Indiana Bridge 5.06 5.86 6.13 6.93 6th Avenue Bridge 6.54 8.0 2 8.34 8.67 Broadway Bridge 6.34 5.66 5.77 6.11 County L ine Bridge 4.8 1 4.90 5.53 6.26 Table 5.13 Dynamic Load Allowance from Displacement bridge no rail break 1 inch break 2 inch break 3 inch break Santa Fe Bridge 4.2 2 4.633 4.79 5.2 9 Indiana Bridge 3.9 8 4.41 4.67 4.75 6th Avenue Bridge 4.35 4.70 5.50 5.99 Broadway Bridge 4.09 4.59 5.82 6.12 County L ine Bridge 3.88 4.46 4.93 5.43

PAGE 110

96 Table 5.14 Thermal Load of Five Bridges from Calculation Bridge axial force(kips) zone 1 zone 2 zone 3 zone 4 Santa Fe Bridge 613 518 472 41 5 Indiana Bridge 926 724 662 575 6th Avenue Bridge 689 5817 532 465 Broadway Bridge 837 658 602 534 Countyline Bridge 590 500 454 398 Table 5.1 5 Dynamic load allowance from moment with 20 mph speed (% bridge no rail break 1 inch break 2 inch break 3 inch break Santa Fe Bridge 4.01 4.41 4.56 5.03 Indiana Bridge 3.76 4.18 4.42 4.51 6th Avenue Bridge 4.12 4.45 5.21 5.67 Broadway Bridge 3.89 4.37 5.53 5.82 County L ine Bridge 3.68 4.25 4.68 5.1 Table 5.1 6 Dynamic load allowance from moment with 4 0 mp h (% bridge no rail break 1 inch break 2 inch break 3 inch break Santa Fe Bridge 3.20 3.51 3.61 4.02 Indiana Bridge 3.03 3.39 3.57 3.63 6th Avenue Bridge 3.31 3.583 4.18 4.56 Broadway Bridge 3.12 3.48 4.43 4.65 Countyline Bridge 2.94 3.37 3.74 4.14

PAGE 111

97 CHAPTER V I CONCLUSION AND RECOMMENDATION The following conclusion and recommendation are made from field testing and computer program finite element modeling of the constructed five light rail bridges in this research. Co nclusion The conclusions from this research are show below: 1. The critical sec tion of multiple span light rail bridges is determined. The maximum positive bending moment of light rail bridges is located on the mid span and the maximum negative bending moment is on the pier. 2. The field test is influenced by strong wind, then wind c ause errors of the testing result by directly blowing to instruments use for testing. The influence factor of wind for field test is not only the wind load applied on bridge but also wind influence instruments. 3. The dynamic load allowance is determined. The dynamic load allowance of light rail bridges is about 2% 7%. Depends on the shape of girders, the dynamic load allowance may be different calculate by the maximum flexural bending moment and displacement. 4. The steel rail break gap causes increasing to the dynamic load. The rail break gaps should avoid cutting on the critical section which is the pier on bridges. The steel rail

PAGE 112

98 break gaps cannot be neglected on designing of dynamic load allowance for the light rail bridges. 5. The increasing of dynami c load allowance caused by the rail break gap is affected by the length of break gap. Longer break gap causes the increasing of dynamic load allowance higher. 6. Fast Fourier translation is acceptable to determine to natural frequency of bridge by testing time step displacement of bridge. 7. Thermal load cannot be neglected by designing of light rail bridge. Recommendation There are recommendations for future research: 1. Calibration of wind load and centrifugal forces influence the value of dynamic load allowance. 2. Study the relationship between natural frequency and dynamic load allowance. 3. Dynamic response of arch light rail bridges. Arch bridges are also used on light rail transportation system. The concrete or steel arch should be analyzed for cal ibration of dynamic load allowance. 4. Study the response of the single span light rail bridges. 5. The speed of light rail train is an important factor on calculation the dynamic load allowance of light rail bridges. The light rail trains may be have high er maximum

PAGE 113

99 speed in the future. The increasing of dynamic load allowance by the light rail train speed increase should be concerned on strengthening and repairing the light rail bridges. 6. Rails and crosstie should be concerned to use the temperature grad ient method from AASHTO. The temperature gradient method is generally used for highway bridges. The effect of steel rails and crosstie covered on bridges may cause the temperature change different from highway bridges.

PAGE 114

100 REFERENCE S American A ssocitition S tste H ighway and T ransportation O fficals. 2012 ). AASHTO LRFD B ridge D esign S pecifications. American A ssocitition S tste H ighway and T ransportation O fficals Neff, John. Dickens, Matthew (20 13 ). Public Transportation Fact B ook. American Public Transporta tion Association. Backer M. Richard, Puckett and Jay A. (20 13 ). Design of Highway B ridges an LRFD A pproach. JohnWiley & Sons, Inc. Black Alan. 1993 The R ecent P opularity of L ight R ail T American Public Transportation Association Chopra K. Anlk. (20 12 ). Dynamics of structures. Prentice Hall Gullers Per. Andersson Lars. (20 08 ). High frequency Vertical Wheel rail Contact Forces Field Measurements and Influence of Track Irregularities. Elsevier B.V. Heerah Arden. (20 09 F ie ld I ncestagration of F undamental F requency of B ridges U sing A mbient B ibration M easurements. Ju Shen Haw. Lin Hung Ta. (20 06 A Finite Element Model of Vehicle bridge Interaction Considering Braking and Acceleration. Kassa Elias (20 06 Vehicle System D ynamics: International Journal of Vehicle Mechanics and Mobility. Lin Yiching Lin Kuo lung. 1997 Transient impac t R esponse of B ridge I girders wi th of w ithout F laws. MacDougal Colin Mark F. Green and Scott Shilinglaw. (20 06 Fatigue D amage of S teel B ridge D ue to D ynamic V ehicule L oad." Naaman Antoine E. (20 04 Restressed Concrete Analysis and Design Quality Books,Inc. Okelo Roman Olabimtan Afisu. (20 11 Nonlinear Rail Structure Interaction Analysis Elevated Skewed Steel Guideway. Pugi Luca. (20 07 Modelling the Longitudinal Dynamics of Long Freight Trains During the Braking Phase. Regional Transportation District, Denver CO. (20 13 Comprehensive Annual financial R eport. Regional Transportation District

PAGE 115

101 Remennikov M. Alex and Kaewunruen Sakdirat. (20 07 A Review of Loading Conditions for railway Track Structure to Train and Track Vertical Interaction John Wiley & Sons, Ltd. 10.1002/stc.227 Roeder Charles. (20 03 Proposed Design Method for Thermal Bridge Movements. Salmon, Charles G., John E. Johnson and Faris A. Malhas. (20 09 Steel structures design and behavior. Pearson Prentice Hall. Saurahb, Kumar (20 06 A study of rail degradations process. Division of Operation and Maintenance Engineering S chellingR .D., Galdos H.N. and Sahin M. 1993 Evaluation of Impact Factors for Horizontally Currved Steel Box Bridges. Senthilvasan, J G. Thambiratnam. (20 02 Dynamic R esponse of a C urved B ridge U nder M oving T ruck L oad. Engineering Structures 24 1283 1293 Toth J., Ruge P. (20 00 Spectral Assessment of Mesh Adaptations for the Alalysis of the Dynamical longitudinal Behavior of Railway Bridges. Wight, James K. and James G. MacGregor. (20 12 Reinforced Concrete Mechanics and Design. Pearson. Ze inS. Ahmed, Gassman GassmanS arah. (20 10 ). Frequency Spectrum Analysis of Impact echo W aveforms for T beam.

PAGE 116

102 APPENDIX A. Modification of B ridge M odel E xample Introduction The models of five bridges are built on the computer program of SAP 2000 and CSI Bridge. These two programs have similar interface. SAP 2000 is used on this example to instruct modify the model of Santa Fe Bridge. Review of M odel This model is built as shown on figure A.1. The model can be built by the Bridge Wizard prov ided on this program. Figure A .1 Model of Santa Fe Bridge Built o n SAP 2000 (a Click the Bridge tab on the menu bar, then choose the Bridge Wizard under to Bridge tab.(The Bridge Wizard has a friendly interface to build a general bridge model step by step, users can also build the bridge model by using to tab on menu

PAGE 117

103 bar by themselve s.) (b) Double click each step on the Summary Table tab, and then the labels of each step will be opened. Figure A.2 Bridge Modeler Wizard Add rails on the bridge deck The steel rail is an important part of the light rail bridges. The rail is not provided on the Bridge Wizard which means it should be added from other tabs. This example shows how to add rails on the bridge model. A.3.1 Define the material, section property, and link of the rail. (a Choose Define Material on the menu bar, and click the tab Add A New Material

PAGE 118

104 Quickly. (b) Choose the needed material. (c Choose Define Section Properties Frame Sections. Add a new property, and (d) Type the dimension of the rail. Figure A .3 Define Materials Figure A.4 Quick Material Def inition

PAGE 119

105 Figure A.5 Frame Properties Figure A .6 Frame Section Property

PAGE 120

106 Figure A .7 I Section Property (e Open Define Section Properties Link/ support properties. (f) Add a new property, and input the properties of link. Figure A .8 Link Property

PAGE 121

107 Figure A .9 Link Data Draw rails on the models (a) Find the coordinate of the rail centroid of y and z axial. Note that it is an easy to find this by using a 2D view. (b) Click the Draw Draw Frame on the menu bar, and choose the defined section. Draw the frame on t he corresponding coordinate. The finite element analysis divides the bridge to elements. The elements on this example are 10 feet on the layout line, and then draw the rail as a beam on 10 feet. (I.e. If the coordinate of the rail centroid is located on (x ,0,0), draw rail form (0,0,0) to (10,0,0).)

PAGE 122

108 (c) Draw the rest rails on corresponding location. User can draw these rails on the same way, or click the Edit replicate to do this. (d) Click Edit replicate to repeat the rail on the lanes of the bridge. (e)Cl ick Draw Draw 2 Joint Link to fix the rail on bridge deck. The link should connect the boundary of the rail and the bridge deck perpendicular to z axial. (f) Repeat the rest of the links on each boundary of the rail elements. Figure A .10 2D View Of Model Figure A .11 Rail Property Label

PAGE 123

109 Figure A .12 Link Property Label Figure A.13 Replicate

PAGE 124

110 Figure A .14 Rail Frame on Model Cutting rail break gaps (a) Choose the links where the nearest to the rail break gap located. (b) Click Edit Replicate, and calculate the distance from the chosen links and the location of the rail break gap. For example, the chosen link is located at (100,0,0), and the location of rail break gap is from (110,0,0) to (110.25,0,0). Click Edit Replicate and input 10 and 10.25 at the dx label on the increment respectively. (c) Delate the steel rail beam already added on the location of break gaps. Delate the whole rail break link which is going through the rail break gaps, and draw the rail element between the nearest link and each side of the break gap.

PAGE 125

111 Figure A .15 Original Link

PAGE 126

112 Figure A .16 Link on Each Side of Break Figure A .17 Rail Break Gaps Thermal load Adding on model (a) Click Define Load Pattern to add a new load pattern for thermal load. (b) Click Bridge Bridge Temper ature Gradient to add a temperature gradient on the bridge model. Zone of bridges can be defined, and the detail of the temperature change on different depth of bridges can also be modified on the temperature difference data interface. (c) Open Bridge Brid ge Object to define this temperature gradient on the bridge object.

PAGE 127

113 (d) Copy this temperature gradient on each span of the bridge. Figure A .18 Load Pa tt ern Figure A .19 Temperature Gradient

PAGE 128

114 Figure A .20 Bridge Object

PAGE 129

115 Figure A .21 Temperature Load