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Structural analysis of cracked concrete piers and proposed rehabillitation using CFRP rods

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Title:
Structural analysis of cracked concrete piers and proposed rehabillitation using CFRP rods
Creator:
Mizyed, Samir ( author )
Language:
English
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1 electronic file (216 pages). : ;

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Subjects / Keywords:
Bridges -- Foundations and piers ( lcsh )
Carbon fiber-reinforced plastics ( lcsh )
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bibliography ( marcgt )
theses ( marcgt )
non-fiction ( marcgt )

Notes

Abstract:
All the concrete piers on 8th Avenue Viaduct, Denver, CO have shown an extensive amount of cracking, both vertically and diagonally. A pier by pier inspection performed in 2015 revealed that the cracks were expanding. Two bi-axial tilt-meters were installed on the fixed pier (Pier 11) to measure the rotation in both directions. A 3d model using ANSYS Mechanical APDL 16.0 software of the viaduct was built and calibrated using the field measurements. A separate fine model of pier 18, where cracks were expanding the most, was also constructed using the same software, which included the reinforcement detailing and the non-linear properties of the material. Dead, live and temperature loads were all applied on the general model under Strength I limit state and the resulting forces transferred to pier 18 were obtained and then applied onto the fine model of the pier, in order to perform non-linear finite element analysis. As expected, the model showed extensive cracking similar to the actual condition of the pier. A rehabilitation system of CFRP rods was proposed and tested on the model, showing very favorable results. The author of this thesis recommends this repair be used for all the piers on 8th Avenue Viaduct
Thesis:
Thesis (M.S.)--University of Colorado Denver.
Bibliography:
Includes bibliographic references.
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System requirements: Adobe Reader.
General Note:
Department of Civil Engineering
Statement of Responsibility:
by Samir Mizyed.

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University of Colorado Denver
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Auraria Library
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951981013 ( OCLC )
ocn951981013

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Full Text
STRUCTURAL ANALYSIS OF CRACKED CONCRETE PIERS AND PROPOSED
REHABILITATION USING CFRP RODS
By
SAMIR MIZYED
B.S., An-Najah National University, 2013
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
Masters of Science
Civil Engineering Program
2015


2015
SAMIR MIZYED
ALL RIGHTS RESERVED
11


This thesis for the Master of Science degree by
Samir Mizyed
Has been approved for the
Civil Engineering Program
By
Kevin L. Rens, Chair
Chengyu Li, Advisor
Frederick Rutz
m
20 November 2015


Mizyed, Samir (M.S., Civil Engineering)
Structural Analysis of Cracked Concrete Piers and Proposed Rehabilitation using CFRP
Rods
Thesis directed by Professor Keving L. Rens
ABSTRACT
All the concrete piers on 8th Avenue Viaduct, Denver, CO have shown an extensive
amount of cracking, both vertically and diagonally. A pier by pier inspection performed in
2015 revealed that the cracks were expanding. Two bi-axial tilt-meters were installed on
the fixed pier (Pier 11) to measure the rotation in both directions. A 3d model using ANSYS
Mechanical APDL 16.0 software of the viaduct was built and calibrated using the field
measurements. A separate fine model of pier 18, where cracks were expanding the most,
was also constructed using the same software, which included the reinforcement detailing
and the non-linear properties of the material. Dead, live and temperature loads were all
applied on the general model under Strength I limit state and the resulting forces transferred
to pier 18 were obtained and then applied onto the fine model of the pier, in order to
perform non-linear finite element analysis. As expected, the model showed extensive
cracking similar to the actual condition of the pier. A rehabilitation system of CFRP rods
was proposed and tested on the model, showing very favorable results. The author of this
thesis recommends this repair be used for all the piers on 8th Avenue Viaduct.
The format and content of the thesis are approved. I recommend its publication
Approved: Kevin L. Rens
IV


ACKNOWLEDGEMENTS
My sincerest thanks to my advisor, Dr. Kevin Rens, who on the very first time we
met offered me an internship with the City and County of Denver, through which I was
able to do this project. Not only that, but in the two years Ive been at UC Denver he never
failed to offer me guidance and advice whenever I needed it and encouraged me in my
pursuit of higher education.
Thank you, Dr. Cheng Li, for selecting me to take part in this project, which I am
extremely grateful for, for supervising my dissertation work and for all the classes that I
took with you, which played a vital role in preparing me for the work I needed to do for
this thesis. The knowledge and experience you brought both to your classes and this project
were immeasurable and no matter what problem I ran into you always had an answer for
it.
Thank you, Dr. Frederick Rutz for being a part of my committee and for preparing
me for the task of writing this thesis. It was through the reports I did for your class that I
truly learned how to follow code specifications and use ASCE standards of writing.
Thank you, Dick Miles for all the help you gave to this project, whether it be taking
the time to meet with us and offer us guidance or coming out to the field with us and finding
problems that we would have otherwise missed.
This project was a group effort and I couldnt have completed my work without a
really great team. Thank you, Brandon Zhou, for being a great team leader (and even
greater friend), and for always taking the initiative. Thank you, Juan Montenegro, for the
practical experience that you brought to this project, which we couldnt have done without.
v


And thank you, Lisa Wang; my colleague, teammate and best friend. Working on this
project with you has truly been an unforgettable experience.
vi


TABLE OF CONTENTS
CHAPTER
I. INTRODUCTION..................................................................1
Overview..................................................................1
The Substructure..........................................................6
Design Codes..............................................................9
II. LITERATURE REVIEW............................................................10
Concrete Cracking........................................................10
Concrete Crack Repair....................................................11
Carbon Fiber Reinforced Polymers.........................................12
FRP Design Considerations................................................17
ANSYS Modeling of FRP strengthened concrete..............................18
Steel Corrosion..........................................................19
III. EQUIPMENT INSTALLATION AND FIELD INSPECTION.................................20
Equipment Installation...................................................20
Pier Inspection..........................................................29
IV. GENERAL MODEL................................................................39
Program Used and Model Components........................................39
Geometry.................................................................45
Loads....................................................................47
Dead Load..............................................................47
Live Load..............................................................48
Temperature Load.......................................................52
Load Combinations........................................................53
Analysis.................................................................53
Check of Results.......................................................53
Impact of Guide Bar Removal............................................60
Temperature Effect.....................................................65
Load transferred to Pier 18............................................66
V. FINE MODEL...................................................................73
Pier 18..................................................................73
Model Detailing..........................................................76
vii


Materials.................................................................76
Element Type..............................................................79
Real Constants............................................................80
Constructing the Model....................................................80
Meshing...................................................................85
Loads and Boundary Conditions.............................................86
Solution Criteria.........................................................90
Analysis....................................................................91
Check of Results..........................................................91
Solution..................................................................96
VI. REPAIR USING CRFP RODS........................................................106
Method of Repair...........................................................106
Modeling of CFRP...........................................................107
Material Properties......................................................107
Steel Plate..............................................................108
Real Constant of CFRP Rods...............................................109
Creating CFRP Rods.......................................................109
Defining Pre-Stress Force................................................Ill
Analysis...................................................................Ill
Check of Results.........................................................Ill
Impact of CFRPs on cracking..............................................114
Method of Application......................................................128
CFRP Rods with Permanent Steel Plates....................................128
CFRP Rods Epoxied to the Concrete........................................130
Pre-Stressing Steel......................................................132
VII. CONCLUSIONS AND RECOMMENDATIONS...............................................133
Summary....................................................................133
Simplifications and Approximations.........................................135
General Model............................................................135
Fine Model...............................................................137
Recommendations for Further Research.......................................138
REFERENCES.........................................................................140
viii


APPENDIX
A. PIER AND ABUTMENT DETAILING..............................145
B. AN SYS (ODE FOR PIER 18..................................153
IX


LIST OF TABLES
TABLE
3.1. Readings from bi-axial tilt-meters on pier 11.......................................27
3.2. Length and thickness of cracks on pier 18 west face..................................35
3.3. Length and thickness of cracks on pier 18 north face.................................36
3.4. Length and thickness of cracks on pier 18 east face..................................37
3.5. Length and thickness of cracks on pier 18 south face.................................38
4.1. Superimposed dead load on Pier 16....................................................54
4.2. Self Weight of Pier 16...............................................................56
4.3. Average pressure on each bearing and resultant force two lane loaded case............71
4.4. Reactions at bottom of pier 18 two lane loaded case..................................71
4.5. Average pressure on each bearing and resultant force north lane loaded.............72
4.6. Reactions at bottom of pier 18 north lane loaded.....................................72
4.7. Average pressure on each bearing and resultant force south lane loaded.............72
4.8. Reactions at bottom of pier 18 south lane loaded.....................................72
5.1. Stress-strain data for concrete.....................................................77
5.2. Forces on bearing GW1..............................................................88
5.3. Forces on bearing GW2..............................................................88
5.4. Forces on bearing GW4..............................................................89
5.5. Forces on bearing GW5..............................................................89
x


LIST OF FIGURES
FIGURES
1.1. Satellite view of West 8th Avenue Viaduct.............................................2
1.2. General Layout of West 8th Avenue Viaduct (City and County of Denver 1993, used with
permission)................................................................................2
1.3. Side view of bridge at a horizontal curve.............................................3
1.4. Side view of bridge at a straight portion.............................................3
1.5. Steel box girders with I-girder in-between (from abutment 1 pier 6).................4
1.6. Steel box girders (from pier 6 abutment 20).........................................4
1.7. Guide bar of bearing removed..........................................................5
1.8. Cracking on one of the piers..........................................................6
1.9. Concrete Pier.........................................................................6
1.10. Piers 2-6 (City and County of Denver 2012, used with permission)......................7
1.11. Piers 7-19 (City and County of Denver 2012, used with permission).....................8
1.12. Abutment 1 (City and County of Denver 2012, used with permission).....................8
1.13. Abutment 20 (City and County of Denver 2012, used with permission)....................9
2.1. Application of FRP laminates (ACI 440.2R-08 Fig. 11.1, used with permission).........13
2.2. FRP Systems (ACI 440.2R-08 Fig 10.2, used with permission)...........................14
2.3. Typical stress-strain curve for CFRP.................................................15
2.4. Post-tensioned CFRP rods (Hughes Brothers Inc 2011, used with permission)............16
2.5. Mechanic anchorage of CFRP rods (Hughes Brothers Inc 2011, used with pennission)... 17
3.1. Distribution of strain gages and thermistors (stars represent strain gages, circles represent
thermistors)...............................................................................20
3.2. VW strain gage.......................................................................21
3.3. Thermistor...........................................................................21
xi


22
23
23
24
25
25
26
30
31
31
31
32
33
33
34
36
37
38
40
41
41
42
42
43
43
44
LVDT
Temperature gage....................................
Uni-axial tilt-meter................................
Bi-axial tilt-meter.................................
Multiplexer.........................................
Datalogger..........................................
Solar panel.........................................
Vertical and diagonal cracks........................
Horizontal cracks at base of pier...................
Hairline cracks.....................................
Crack 1/16 thick...................................
Crack extending from face to face of pier...........
Dormant crack.......................................
Active crack........................................
Cracking on pier 18 west face.......................
Cracking on pier 18 north face......................
Cracking on pier 18 east face.......................
Cracking on pier 18 south face......................
Pier................................................
Abutment............................................
Unguided bearing....................................
Guided bearing......................................
Bearings on top of pier.............................
Girders with diaphragms, diagonal bracing and stiffeners
Deck................................................
Span between two piers..............................
xii


45
49
49
50
50
50
51
52
55
56
59
61
62
63
64
65
66
67
68
68
69
69
70
74
74
Springs used to model the expansion joint at abutment 20.....................
Bridge span assuming simple supports and non-continuity......................
Moment influence line for simply supported single span at mid-span...........
Continuous spans under a concentrated load...................................
Deformation of continuous spans due to applied load..........................
Live load distribution to generate max moment at a certain span..............
Live load distribution to generate max reaction at a certain pier............
Application of temperature on south side of steel girders....................
Dimensions of pie 16 (simplified)............................................
Live load distribution to generate max reaction at pier 11...................
Displacement in the longitudinal direction at a section close to pier 6......
Stress in longitudinal direction on pier 19 with all guide bars present......
Stress in transverse direction on pier 19 with all guide bars present........
Stress in longitudinal direction on pier 19 with guide bars removed..........
Stress in transverse direction on pier 19 with guide bars removed............
Stress in transverse direction on pier 12 due to temperature.................
Stress in transverse direction on pier 18 due to temperature.................
Stress on pier 18 in transverse direction from case of two lane loaded.......
Contact pressure on bearing GW1..............................................
Contact pressure on bearing GW2..............................................
Contact pressure on bearing GW4..............................................
Contact pressure on bearing GW5..............................................
Contact friction stress on bearing GW5.......................................
Pier 18......................................................................
Plan view of pier 18 (City and Country of Denver 1993, used with permission)
xiii


5.3. Elevation view of pier 18 (City and Country of Denver 1993, used with permission and
some edits)................................................................................75
5.4. Reinforcement detailing of pier 18 (City and Country of Denver 1993, used with
permission)................................................................................75
5.5. Hammerhead cross-section reinforcement detailing of pier 18 (City and Country of Denver
1993, used with permission)................................................................76
5.6. Column cross-section reinforcement detailing of pier 18 (City and Country of Denver
1993, used with permission)................................................................76
5.7. Stress-strain relationship for concrete.............................................78
5.8. Stress-strain relationship for steel................................................79
5.9. Volume of pier 18...................................................................81
5.10. No. 4 bars..........................................................................82
5.11. No. 5 bars stirrups.................................................................82
5.12. No. 9 bars..........................................................................83
5.13. Front sectional view of reinforcement...............................................83
5.14. Baseplates on top on pier 18........................................................84
5.15. Meshing of pier 18..................................................................85
5.16. Meshing of pier 18 reinforcement....................................................86
5.17. Pier 18 with loads and B.C.s for two-lane-loaded case...............................90
5.18. Stress in steel reinforcement bars for test case..................................91
5.19. Location of section A-A.............................................................92
5.20. Reinforcement of cross section A-A..................................................92
5.21. Simplified force diagram of Pier 18.................................................94
5.22. Simplified bending moment diagram of Pier 18........................................95
5.23. Tensile stress in steel at specified section........................................96
5.24. Cracking/crushing of concrete under two lane loaded case............................97
xiv


5.25. Stress in steel reinforcement under two lane loaded case.............................97
5.26. Cracking/crushing of concrete under north lane loaded case...........................98
5.27. Stress in steel reinforcement under north lane loaded case...........................98
5.28. Cracking/crushing of concrete under south lane loaded case...........................99
5.29. Stress in steel reinforcement under south lane loaded case...........................99
5.30. Cracking in pier under two lane loaded case without longitudinal load...............101
5.31. Cracking in pier under two lane loaded case with all transverse forces creating tension in
pier (worst case scenario)................................................................102
5.32. Stress in steel reinforcement due to two lanes loaded worst case scenario...........102
5.33. Cracking/crushing of concrete due to north lane loaded worst case scenario..........103
5.34. Stress in steel reinforcement due to north lane loaded worst case scenario..........103
5.35. Cracking/crushing of concrete due to south lane loaded worst case scenario..........104
5.36. Stress in steel reinforcement due to south lane loaded worst case scenario..........104
6.1. Strengthening method for pier 18....................................................107
6.2. Stress-strain relationship for CFRP rod.............................................108
6.3. Modeling of steel plate............................................................109
6.4. CFRP rods connecting steel plates...................................................110
6.5. Model of pier 18 with CFRP rods.....................................................110
6.6. Stress in pier 18 in transverse direction under pre-stressed CFRP rods..............113
6.7. Stress at the test section in the transverse direction under pre-stressed CFRP rods.114
6.8. Cracking/crushing of concrete under two lane-loaded case with 4 No. 8 pre-stressed CFRP
rods and an initial strain of 0.007.......................................................115
6.9. Cracking/crushing of concrete under two lane-loaded case with 6 No. 8 pre-stressed CFRP
rods and an initial strain of 0.007.......................................................116
6.10. Cracking/crushing of concrete under two lane-loaded case with 6 No. 8 pre-stressed CFRP
rods and an initial strain of 0.009.......................................................117
xv


6.11. Pier 18 with refined brick meshing.................................................118
6.12. Distribution of 6 No. 8 CFRP rods for refined model of pier 18....................119
6.13. Cracking/crushing of pier 18 under two lane loaded case refined model.............120
6.14. Cracking/crushing at pier edge under two lane loaded case refined model...........120
6.15. Cracking at bottom of pier wireframe view.........................................121
6.16. Stress in steel plate longitudinal direction (x-component).........................122
6.17. Stress in steel plate vertical direction (y-component).............................122
6.18. Stress in steel reinforcement for pier 18 strengthened with 6 No. 8 CFRP bars strained to
0.007.....................................................................................123
6.19. New CFRP strengthening method......................................................124
6.20. Cross sectional view of selected CFRP strengthening method........................124
6.21. Steel plates with 12 No. 4 CFRP rods...............................................125
6.22. Cracking on pier 18 strengthened with 12 No. 4 CFRP rods strained to 0.009..126
6.23. Cracking on pier 18 strengthened with 12 No. 4 CFRP rods strained to 0.0076 (considering
all pre-stress losses)....................................................................127
6.24. Distribution of No. 4 CFRP rods spaced at 4 inches.................................128
6.25. Extension of CFRP 2 inches past steel plate........................................129
6.26. Near surface mounted CFRP rods.....................................................130
6.27. Example of NSM CFRP rods post-tensioned to different level.........................131
xvi


CHAPTERI
INTRODUCTION
Overview
West 8th Avenue Viaduct was constructed in 1985 and is located in Denver, CO
between Mariposa St (east end) and Tejon St (west end). The bridge measures 2372 feet in
length and crosses over light rails, railroads, a couple of streets and several parking lots
(including one belonging to Denver Water and another belonging to Union Pacific). It is a
steel and concrete bridge with an 8.5 inch concrete deck supported over twin steel box
girders. These girders run parallel to each other, though for the first five spans starting from
the east side of the bridge (abutment 1 to pier 6) the distance between them varies and there
is a steel I-girder centered between them with exterior diaphragms providing bracing
between the I-girder and the box girders. After Pier 6, the I-girder stops and the distance
between the box girders stays fixed at 10 feet, while the only exterior diaphragms that brace
the box girders are located directly above each pier, though there are still interior
diaphragms inside each of the box girders. This superstructure is supported on 18 piers and
2 abutments with pot type bearings connecting the superstructure to the substructure, with
the exception of the bearings on pier 11 which are fixed. All pot bearings are oriented
towards pier 11.
1


Figure 1.1: Satellite view of West 8th Avenue Viaduct
Figure 1.2: General layout of West 8th Avenue Viaduct (City and County
of Denver 1993, used with permission)
2


Figure 1.3: Side view of bridge at a horizontal curve
Figure 1.4: Side view of bridge at a straight portion
3


Figure 1.5: Steel box girders with I-girder in-between (from abutment 1 -
pier 6)
Figure 1.6: Steel box girders (from pier 6 abutment 20)
4


The bridge contains four horizontal and three vertical curves. It is these curves that
are the root of the many problems occurring on the bridge, as when it was designed the
effects of curvature were not considered and 8th Avenue Viaduct was treated as a straight
bridge. As such the transverse movement that occurred due to temperature effects was a
lot greater than expected, resulting in the fracture of several guide bars for the bearings as
well as the grinding of multiple others against the base plates. To relieve some of the stress
many guide bars were removed, changing the entire guide system of the bridge.
Figure 1.7: Guide bar of bearing removed
The problems dont stop at the bearings. Diagonal and horizontal cracks have been
observed on all the piers. Several inspections have been performed on the piers over the
years (most notably in 1998, 2008 and 2015) in order to measure the length of the cracks,
and in each of these inspections the cracks were observed to have grown. While the bridge
still remains safe to use the fact that year by year the cracks are continuing to expand
necessitates the rehabilitation of the bridge to prevent failure in the future.
5


. _____............ -
Figure 1.8: Cracking on one of the piers
As this thesis is on the substructure of the bridge the cracking of the piers will be
the main focus. However, a study on the bearings can be found in a paper by Wang, 2015.
The Substructure
Figure 1.9: Concrete Pier
6


All the piers of 8th Avenue Viaduct are hammerhead piers. The piers vary in height from
17 feet at the ends to 38 feet closer to the middle. All the piers are 3 feet in thickness with
the exception of pier 11, which is 7.5 feet thick. The width of the piers at the top is 30 feet
for piers 6-19, though it varies for piers 2-5. All the piers are supported on 4 foot thick
concrete foundations. The following Figures display the dimension detailing of the piers
(for more detailed info, see Appendix A):
Figure 1.10: Piers 2-6 (City and County of Denver 2012, used with
permission)
7


n'io %
Figure 1.11: Piers 7-19 (City and County of Denver 2012, used with
permission)
The abutments, meanwhile, are L-shaped. Their details are shown in the Figures
1.11 and 1.12 (more detailed info is in appendix A):
\El_EVATlOKJ
Figure 1.12: Abutment 1 (City and County of Denver 2012, used with
permission)
8


' <35
Figure 1.13: Abutment 20 (City and County of Denver 2012, used with
permission)
This paper will discuss the cause of cracks on the piers and their continued
expansion using both computer modeling and field measurements as well as propose
solutions for the rehabilitation of the piers and the prevention of future crack expansion.
While the bulk of the 8th Avenue Viaduct project was on modeling the bridge, it
was also necessary to go out to the field, both to install equipment that would give actual
physical data could be used to calibrate the model and to perform inspections on the piers,
bearings and superstructure.
Design Codes
Material properties, applied loads and load factors will all be based on the
AASHTO LRFD 2012 Bridge Design Specifications.
9


CHAPTER II
LITERATURE REVIEW
Concrete Cracking
Bridge engineering has seen a somewhat shift in focus from designing new bridges
to rehabilitating old ones, due to the fact that bridges are typically designed for a service
life of 50-75 years, meaning many bridges around today have met or exceeded their
expected life span (ASCE report card, 2009).
Concrete cracking, spalling and rebar corrosion are the most common forms of
deterioration in old structures. Cracks are especially common as concrete is weak in tension.
While they are expected to occur (one of the basic assumptions when designing a structure
is that concrete in tension will crack) they nonetheless can reduce both the durability and
capacity of the structure as well as allow water to leak into the structure (Kim et al. 2009)
thereby leading to the corrosion of the steel rebar.
Cracks have two stages: crack initiation, in which the cracks first form at the surface,
and then crack growth, in which they expand along both the surface and the depth of the
material (Schijve 2014). Their cause isnt necessarily structural; there are various other
reasons as to why they might form, such as the type of material used, damage to the
structure during construction or its service life and environmental factors, while the time
of formation of the cracks can give an idea as to what caused them (Kim et al. 2009).
Cracks can be grouped into two types: central cracks and shear cracks (Wang et al.
2013). The location, directions and density of the cracks provide important information as
10


to the type of failure that has occurred (Yang et al. 2015) and as such several different
techniques that offer more accurate and less labor intensive alternatives to the traditional
method of visual inspection have been proposed for crack detection (Abdel Qader I et al.
2003, Lee et al. 2013, Adhikari et al. 2014).
There have also been advances in how to model cracks. In 1999, Bolander Jr and
Le proposed a spring network model in order to predict how cracks would develop in
reinforced concrete (Boolander Jr. and Le 1999), an approach based on energetic fracture
mechanics for concrete (ACI committee 446, 1991) and a rigid-body-spring-model
developed by Kawai in the late seventies (Kawai 1978), while much research has been
done on using finite element modeling to analyze cracks (Saatci and Vecchio 2009; Wang
et al. 2013; Chen and Leung 2015).
Concrete Crack Repair
There are many different ways to repair cracked concrete. In a paper published in
2005, Thanoon and several others compared five different methods of concrete crack repair:
cement grout, epoxy injection, applying a ferrocement layer, using carbon fiber reinforced
polymer (CFRP) strips and enlarging the section. All these methods were used to repair
similar cracked concrete slabs. The first three methods were found to give the cracked slab
a similar strength to a non-cracked slab, while section enlargement and CFRP actually
made the cracked slab stronger (Thanoon et al. 2005). Because the purpose of this project
isnt just to repair the piers but also make sure they dont experience the same cracking
again in the near future, methods such as cement grout and epoxy injection wouldnt work
while enlarging the section would be very costly and require a significant amount of labor.
Therefore, in the case of this project, using FRP looks to be the best option for repair.
11


Carbon Fiber Reinforced Polymers
As the name implies, fiber reinforced polymers refers to polymers that are
reinforced with a matrix of numerous long thin fibers of various chemical origin oriented
parallel to each other (Plewako, 2015).
Fiber reinforced polymers are perhaps the most favored method of repairing
reinforced concrete structures and for good reason. They have a high strength but at the
same time are light weight, have great durability, are relatively easy to install and resist
corrosion (Clarke and Waldron 1996), though they also have a low fire safety (Verbruggen
et al. 2014). The most common types of FRPs are carbon fiber reinforced polymers (CFRP),
glass fiber reinforced polymers (GFRP) and aramid fiber reinforced polymers (AFRP).
CFRP and AFRP are typically preferred to GFRP as they have better resistance to creep
and alkaline environments (ACI 440.2R-08). This paper will be focused on CFRP as it
typically has the highest tensile strength (ACI 440.4R-04).
CFRPs can be applied onto the concrete in different ways. The most common is to
use laminates or sheets, which can be bonded to the concrete using epoxy resin, though the
disadvantage of that is that de-bonding failure can occur between the concrete and CFRP
before the CFRP strips can even reach their full capacity (ACI 440.2R-08). As such,
different types of CFRP anchors have been developed that can overcome this problem and
allow the CFRP sheets to reach their full strength (Kobayashi et al. 2001, Kim et al. 2014).
Modeling of CFRP sheets bonded to concrete has also been done using various methods to
simulate the interaction between them, such as non-linear spring elements (You et al. 2011;
Sun and Ghannoum 2015), traction-separation (Zidani et al. 2015) and even treating the
12


de-bonding failure that can occur between concrete and FRP as a dynamic rather than static
problem and using time integration to solve it (Chen et al. 2015).
Completely 3-sided 2 sides
wrapped "U-wrap"
Figure 2.1: Application of FRP laminates (ACI 440.2R-08 Fig. 11.1, used
with permission)
Due to issue of de-bonding failure, another method to apply CFRP is by near
surface mounting (NSM), where the CFRP is actually applied into a slot dug into the
surface of the concrete (ACI 440.2R-08). This method has shown to give a much stronger
bond between CFRP and concrete, better resistance to end peeling and improved fire safety,
though in does require more effort to carry out in the field (Taljsten 2002). As with CFRP
laminates, there have been different finite element models developed to study the behavior
of NSM CFRP, such as the one Almassri and others presented in a paper published in 2015,
which used the FEMIX computer code to develop a model that could accurately reflect a
reinforced concrete beam that was shear repaired with NSM CFRP rods (Almassri et al.
2015). The use ofNSM CFRP rods has been shown to give favorable results over externally
bonded CFRP laminates in both flexural and shear strengthening of RC members (De
Lorenzis and Nanni 2001; El-Hacha and Rizkalla 2004).
13


b j
df
d
or
dp
1
H- b
A$ of Ap

Af
dj
d
or
dp
As of Ap

_H__B__
\ /
(Tt) FRP Laminates
(b) NSM bars
Figure 2.2: FRP Systems (ACI 440.2R-08 Fig 10.2, used with permission)
Aside from the advantages of higher tensile strength and better resistance to
corrosion mentioned previously, CFRP rods differ from typical steel rods in that their
surface is smooth and that the relationships between stress and strain is linear up until the
point of failure (Benmokrane et al. 2000). Another difference is that unlike steel, CFRP
rods can have a wide range of tensile strengths that could go up to 1000 ksi (though 150-
500 ksi are the most commonly used), as well as significant variation in the modulus of
elasticity, from 10,000 ksi to as high as 70,000 ksi (fib Bulletin 55 and 56, 2012).
The biggest disadvantage in using external FRPs is that it reduces the ductility of
the member which could therefore lead to brittle failure (ACI 440.2R-08). One way to solve
this problem is to use CFRP rods embedded in the concrete, where instead of simply
placing the rods in grooves in the concrete, the surface of the concrete is actually removed
up to the level of the bottom reinforcement, where the CFRP rods are placed in between
the steel reinforcement; the steel reinforcement is then sandblasted and the surface of the
14


concrete is roughened and injected with epoxy before the new layer of concrete is cast,
reducing the risk of brittle failure (Morsy et al. 2015). The increased load capacity achieved
from embedding the CFRP rods in concrete is the reason why theres a recent favoring
towards using CFRP rods in place of traditional steel reinforcement (Puigvert et al. 2014).
Figure 2.3: Typical stress-strain curve for CFRP
The final method of repair using CFRPs is to use them as post-tensioned rods
anchored to the concrete (Bumingham et al. 2014). Due to the smoothness of the surface
of the CFRP rods there is a difficultly in clamping them down, which has led to the
development of different kinds of anchorage systems. These can be divided into two main
types: bonded anchorage, in which a resin or epoxy is used to anchor the rod, and
mechanical anchorage, which uses the friction created by compressing the inside surface
of the anchor against the rod (Schmidt et al. 2009, Schmidt et al. 2012). One of the most
popular types of mechanical anchors are the unibody clamp anchors; several generations
15


of these anchors have been developed, all of which use several bolts (number of bolts varies
depending on generation) to clamp down on the CFRP rod (Burningham et al. 2014). Tests
have shown that concrete beams repaired with post-tensioned CFRP rods show an increase
in load capacity and significantly less deflection than similar beams that are in perfect
condition but dont have CFRP rods (Burningham et al. 2015).
Figure 2.4: Post-tensioned CFRP rods (Hughes Brothers Inc 2011, used
with permission)
16


I . J
Figure 2.5: Mechanic anchorage of CFRP rods (Hughes Brothers Inc
2011, used with permission)
FRP Design Considerations
For FRP tendons the recommended stress level is between 40-65% of the ultimate
strength (Dolan et. al. 2000). For CFRP, when jacking the tendons it is not advised to stress
them more than the 65% limit of ultimate strength (ACI 440.4R-04 Table 3.3).
When using FRP for pre-stressing, it is important to consider the pre-stress losses
from various factors, such as the anchorage seating at transfer of pre-stress, the elastic
shortening, creep and shrinkage of concrete, and the relaxation of the FRP tendons; these
losses are calculated in a similar manner as for pre-stressed steel, though they are usually
smaller (ACI 440.4R-04).
For long term effects, both aramid and carbon fibers have shown strong resistance
to creep (fib Bulletin 40, 2007). CFRP, in particular, was tested under various applied loads
17


and through the use of creep rupture curves was found to retain 70% of its ultimate strength
capacity for a service life of 100 year (ACI 440.4R-04)
ANSYS Modeling of FRP strengthened concrete
In recent years, several studies have used ANSYS software in order to perform non-
linear finite element modeling of concrete strengthened with FRP (Hawileh 2012, Si Larbi
et al. 2012; Al-Rousan and Haddad 2013; Zidani et al. 2015). These studies all follow a
similar procedure in modeling: Concrete will be modeled using SOLID65 element which
allows for cracking; steel reinforcement will be modeled using LINK8 elements (or
LINK180 in the more recent versions of ANSYS); for FRP, it depends on what type is
being used (e.g. rods or laminates) but if FRP rods are being used then they can be modeled
using LINK8 elements as well. If there is a bond between the FRP and concrete then it can
be modeled using INTER205 interface elements to simulate the epoxy used for bonding.
Cracking of the SOLID65 element in concrete follows the smeared crack approach,
a method developed by Rashid in 1968 and Cervenka and Gerstlein in 1971 and 1972 in
which a crack is smeared along a finite element of the material with the material having
zero stiffness along the crack (Rashid 1968, Cervenka and Gerstlein 1971, 1972). This is
in contrast to the discrete approach developed by Saouma and Ingraffea, which attempts to
reflect in the model the discontinuities that would occur from a crack forming in the
material (Saouma and Ingraffea 1981). Although the later method is more accurate, it is
also much more time consuming as it would require the re-meshing of the model every
time a crack occurred, which is why in finite element modeling the smeared crack approach
is preferred (Larbi et. al. 2013).
18


Steel Corrosion
As mentioned previously, cracking can also lead to the corrosion of steel rebar,
which, like cracking, can lead to a loss of durability in the structure (Hobbs, 2001). Multiple
studies have been made to study the relationship between crack width and steel corrosion,
using the width of the cracks to predict how much corrosion there is in the steel (Schiessl
1997; Mohammed et al 2001; Vidal et al 2004; Oteino et al. 2010; Berrocal 2015).
19


CHAPTER HI
EQUIPMENT INSTALLATION AND FIELD INSPECTION
Equipment Installation
During the months of May and June, 2015, a team of four UC Denver graduate
students (Yang Zhou, Samir Mizyed, Wanting Wang and Juan Montenegro) went out to 8th
Avenue Viaduct to install the following equipment on the bridge:
1. Vibrating wire (VW) strain gages: These were used to measure both
strain and temperature. These were installed on the steel box girders at two different
locations: one directly above pier 14 and the other at the mid-span between piers
16 and 17. 10 sensors were installed at each location. Their distribution along each
section is shown in Figure 3.1. Due to the sensors heating up at a faster rate than
the steel box girders, it was necessary to cover all the sensors that could be exposed
to the sun.
Figure 3.1: Distribution of strain gages and thermistors (stars represent
strain gages, circles represent thermistors)
20


Figure 3.2: VW strain gage
2. Thermistors: These measure temperature only and were placed at
the same sections as the strain sensors with 4 sensors per section: two at the bottom
of the concrete deck close to the edges, one at south side of the concrete deck and
one at the top of the north concrete barrier. As with the strain sensors it was
necessary to cover the ones that would be in the sun.
Figure 3.3: Thermistor
21


3.
LVDTs: there are three of these, all of which were installed on
abutment 20. One is a spring sensor that can measure displacement up to 3 inches.
This was placed on the south side of the south box girder to measure its transverse
movement. The other two are ultrasonic displacement sensors and they can measure
displacement up to 15 inches. These were placed at the back of the two box girders
near their outer edge in order to measure the longitudinal movement of the bridge.
Figure 3.4: LVDT
4. Temperature gage: used to measure the ambient air temperate. This
was placed on top of the fence above abutment 20.
22


m
Figure 3.5: Temperature gage
5. Uni-axial tilt-meter: used to measure rotation. This was installed this
on the south side of the concrete deck above abutment 20.
Figure 3.6: Uni-axial tilt-meter
6. Bi-axial tilt-meters: similar to the uni-axial tilt-meter, only they can
be oriented in two directions. There are two of these, both of which were installed
23


at the top of pier 11 (the fixed pier) in order to measure the rotation in both
directions.
Figure 3.7: Bi-axial tilt-meter
7. Multiplexers: all the strain gages and thermistors were connected to
a multiplexer at each of the two locations where the gages were installed. These
multiplexers were connected with each other, while the west multiplexer (the one
at mid-span between pier 16 and 17) was also connected to the data logger.
24


Figure 3.8: Multiplexer
8. Data logger: All of the data the above mentioned equipment
collected was sent to the data logger, which was installed on abutment 20 and is
powered by an external battery. Using a USB cable, the data could then be
transferred to a regular laptop. This was done every week or so.
Figure 3.9: Data logger
25


9. Solar panel: was installed near abutment 20 in order to charge the
battery that powered the entire system.
Figure 3.10: Solar panel
The most important equipment for this dissertation are the bi-axial tilt-meters, as
they are the only devices that measure the movement of the substructure rather than the
superstructure.
The system first started running on June 19th, 2015, though the tilt-meters werent
properly calibrated until the 27th of the same month. Since then, several months of data
have been collected from the bi-axial tilt-meters, a small portion of which is represented in
Table 3.1.
26


Table 3.1: Readings from bi-axial tilt-meters on pier 11
TIMESTAMP RECORD Pll_Rotl_ Delta_Min Pll_Rot2_ Delta_Min Pll_Rotl_ temp_Min Pll_Rot2_ temp_Min Pll_Rotl_ Delta_Max Pll_Rot2_ Delta_Max Pll_Rotl_ temp_Max Pll_Rot2_ temp_Max Pll_Rotl_ Delta_Avg Pll_Rot2_ Delta_Avg
TS RN Deg_F Deg_F Deg_F Deg_F
Min Min Min Min Max Max Max Max Avg Avg
6/27/2015 13:00 214 -0.01 -0.004 78.87 78.96 0.001 0.005 81.2 81.3 -0.005 0.001
6/27/2015 14:00 215 -0.015 -0.007 81.2 81.3 -0.001 0.007 83.1 83.1 -0.007 0.001
6/27/2015 15:00 216 -0.019 -0.004 82.9 83 0.002 0.005 84.6 84.7 -0.008 0
6/27/2015 16:00 217 -0.017 -0.012 84.2 84.5 0.012 0.01 85.3 85.4 -0.008 -0.001
6/27/2015 17:00 218 -0.022 -0.004 84.8 85 -0.005 0.003 85.7 85.8 -0.009 -0.001
6/27/2015 18:00 219 -0.022 -0.009 84.1 84.3 0.009 0.003 85.7 85.9 -0.008 0
6/27/2015 19:00 220 -0.01 -0.004 83.1 83.4 -0.003 0.005 83.9 84.2 -0.007 0.001
6/27/2015 20:00 221 -0.022 -0.001 82.1 82.4 -0.004 0.01 83.2 83.4 -0.007 0.002
6/27/2015 21:00 222 -0.018 0 80.6 80.9 -0.001 0.009 82.1 82.4 -0.006 0.003
6/27/2015 22:00 223 -0.009 -0.001 80.1 80.4 -0.003 0.006 80.6 80.9 -0.005 0.003
6/27/2015 23:00 224 -0.013 -0.004 76.59 76.81 0 0.007 80.1 80.4 -0.004 0.004
6/28/2015 0:00 225 -0.002 0.005 74.36 74.56 0.009 0.014 76.49 76.69 0 0.007
6/28/2015 1:00 226 -0.008 0.005 73.42 73.76 0.006 0.014 74.6 74.8 0.002 0.007
6/28/2015 2:00 227 0.001 0.005 71.86 72.18 0.004 0.01 73.28 73.61 0.003 0.008
6/28/2015 3:00 228 -0.001 0.005 70.15 70.37 0.009 0.01 72.16 72.33 0.003 0.007
6/28/2015 4:00 229 0.003 0.007 69.41 69.53 0.006 0.009 70.06 70.28 0.005 0.008
6/28/2015 5:00 230 0 0.006 67.99 68.15 0.007 0.011 69.83 69.98 0.005 0.007
6/28/2015 6:00 231 0.005 0.005 67.5 67.67 0.007 0.009 68.06 68.25 0.006 0.007
6/28/2015 7:00 232 0.005 0.004 67.15 67.27 0.007 0.009 68.26 68.32 0.006 0.007
6/28/2015 8:00 233 0 0.001 68.12 68.31 0.007 0.008 71.34 71.54 0.004 0.005
6/28/2015 9:00 234 -0.008 -0.002 71.44 71.58 0.003 0.012 74.03 74.2 0.001 0.003
6/28/2015 10:00 235 -0.004 -0.017 73.88 74.08 0.004 0.006 75.38 75.51 0 0.003


In the table, PllRotl represents the bi-axial tilt-meter measuring the rotation in
the longitudinal direction of the bridge, while PI l_Rot2 is for the bi-axial tilt-meter thats
measuring the rotation in the transverse direction. The rotation (Delta) is measured in
degrees. The bi-axial tilt-meters also measure the temperature (temp), whose units are in
Fahrenheit.
Both tilt-meters take a reading every 90 seconds. This results in a massive amount
of raw data. Fortunately, the data logger also records the maximum and minimum values
measured from both tilt-meters for both the temperature and rotation, which is the data
represented in Table 3.1 (for a time period spanning 22 hours from 13:00 June 27th, 2015
to 10:00 June 28th, 2015). To make sure that the devices were recording values properly,
the temperature values were compared with the air temperature recorded at the same time
and found to give similar results.
The positive and negative signs for the rotational values represent the direction of
movement of the pier, with positive being clockwise and negative being counterclockwise
(measured from someone standing south of the pier for the longitudinal rotation and west
of the pier for the transverse rotation). In general the tilt-meter in the longitudinal direction
recorded larger values than the tilt-meter in the transverse direction which makes sense as
more movement in the longitudinal direction is expected.
As of the writing of this paper, the max rotation measured in the longitudinal
direction was recorded as 0.0891 degrees, while the max value in the transverse direction
was recorder as 0.043 degrees. Both tilt-meters were placed a foot below the top of the pier,
which is approximately 28.5 feet high at the mid-portion between the two girders where
the tilt-meters are located. The displacement can therefore be calculated as follow:
28


Displacement = height x sin(rotational angle)
Displacement in longitudinal direction = (28.5) x sin(0.089) = 0.0443 ft
Displacement in transverse direction = 28.5 x sin(0.043) = 0.0214 ft
These readings from the tilt-meters are the exception though, as most of the time
the rotation in both directions is less than 0.01 degrees.
Because the displacement of Pier 11 is generally very small, it can simply be
assumed that it is fixed. This is very important for the modeling of the bridge as it means
only half the bridge needs to be modeled at a time
Pier Inspection
Near the end of July, beginning of August, 2015, a two man team of Yang Zhou
and Samir Mizyed performed a pier by pier inspection of 8th Avenue Viaduct. This was
done on the following dates: Tuesday (July 28th), Thursday (July 30th) and Sunday (August
2nd). The objective of the inspection was to measure the cracks on the piers to see how
much they had expanded since previous inspections (the condition of the bearings and
superstructure above each of the piers was also checked).
All of the piers were inspected with the exception of piers 3 and 10 due to the former
being in-between two light rail tracks and the latter being on a median between two single
lane one-way streets, giving nowhere to park the bucket lift truck that was used for the
inspection.
Of the piers inspected, several different kinds of cracks were observed. The most
common were the vertical cracks (due to flexure) at the top of the piers towards the middle.
These were also the longest of the cracks with most of the cracks on the chamfer lines of
the piers (see Figure 3.18) extending all the way down to the bottom, though cracks at other
29


locations would range from a couple inches to 9 or 10 feet in length. These cracks extended
from one face of the pier to the other and would start off widest at the top (reaching up to
a 1/16 of an inch in thickness) before turning into hairline cracks as they went down. Also
at the top of the piers there were diagonal cracks (due to shear), though these were closer
to the edges. These diagonal cracks could reach up to several feet in length and like the
vertical cracks, they extended from one face of the pier to the other. Finally, there were
horizontal cracks at the bottom of a number of the piers, particularly those closer to the
edge of bridge (such as piers 16-18). Unlike the vertical and diagonal cracks, these were
always hairline cracks, though many of them would wrap around the base of the pier.
Figure 3.11: Vertical and diagonal cracks
30


Figure 3.12: Horizontal cracks at base of pier
Figure 3.14: Crack 1/16 thick
31


i
Figure 3.15: Crack extending from face to face of pier
While some of the cracks had remained dormant over the years, most of them were
still active and had expanded anywhere from 1 or 2 inches to several feet since previous
inspections. Because the rate of expansion could vary significantly from one crack to the
next on the very same pier it was difficult to make out a pattern, though in general the
farther away the pier was from pier 11, the faster the rate of expansion was. The exceptions
were the very end piers (2 and 19), where surprisingly most of the cracks hadnt expanded
significantly since 1998. This is likely due to a couple of reasons. First of all, piers 2 and
19 had two guide bars removed from the bearings above them, unlike all the other piers,
which had only one guide bar removed (the southern guide bar of the northern interior
bearing, GW4). This may have relieved a significant amount of the stress being transferred
from the superstructure through the bearings to the piers. An attempt to confirm this will
be done in the next chapter by comparing the stress transferred to pier 19 for two cases:
with all guide bars present and removing the two that are missing. Another possible reason
32


is that piers 2 and 19 are also by far the shortest of the piers, making them more stable than
the others.
Figure 3.16: Dormant crack
Figure 3.17: Active crack
Out of all the piers, pier 18 was the one where the cracks had expanded the most.
Figures 3.18 3.21 display the cracks on all four faces of that pier, while Tables 3.2 3.5
33


list the length and thickness of each crack as measured in 1998 and how much they have
expanded since then (note: a hairline crack refers to any crack that has a thickness less than
0.01 inch).
__________30'- NORTH I'-'d' SOUTH
Figure 3.18: Cracking on pier 18 west face
34


Table 3.2: Length and thickness of cracks on pier 18 west face
Crack # Length 1998 Expansion 2015 Maximum Size
2 4' -11" None 0.020"
3 O' 6 1/2" None 0.016"
4 O' 5 1/2" 2" 0.020"
5 1' -4" 8" 0.016"
6 1' -7" 7" 0.016"
7 5' -0" 16" 0.016"
8 7' -0" All the way to the bottom (chamfer line) hairline
10 4' -3" 20" 0.016"
11 4'- 7 1/2" 5" hairline
12 4' 2" 9" 0.016"
13 1' -4" 2" 0.020"
14 O' 8" None hairline
15 2'- 5 1/2" 2" hairline
15A O' -4" None hairline
16 (6A) 3' -9" 8" hairline
17 (6B) 2' -5" 3" hairline
18 (7A) 3' -1" 6" hairline
19 (9A) 2' 2" 8" hairline
20 (9B) 3' -1" All the way to the bottom (chamfer line) hairline
21 (10B) O' -11" 3" hairline
22 (11A) 1' -3" 8" hairline
23 (13B) 2' -10" None hairline
24 (14A) 3' -5" 4" hairline
25 2' -0" None hairline
26 1' 2" None hairline
27 9' -0" None hairline
35


1
8
3
4
6
7
2
5
NORTH FACE
Figure 3.19: Cracking on pier 18 north face
Table 3.3: Length and thickness of cracks on pier 18 north face
Crack # Length 1998 Expansion 2015 Maximum Size
1 Pier Width None hairline
2 O' 8" None hairline
3 1' -0" None hairline
4 1' -4" None hairline
5 O' -10" 8" hairline
6 O' -11" 7" hairline
7 1' -3" None hairline
8 Pier Width None hairline
36


NORTH
Figure 3.20: Cracking on pier 18 east face
Table 3.4: Length and thickness of cracks on pier 18 east face
Crack # Length Maximum Size
3 4' 4" 0.016"
4 1'- 1 1/2" Hairline
4A 1' 3 1/2" Hairline
5 3'- 9 1/2" Hairline
6 2' 2" Hairline
7 5' -4" Hairline
7A 2' -5" Hairline
7B 7' -10" Hairline
8 3' -2" Hairline
9 O' -3" Hairline
10 2' -6" Hairline
11 1'- 9 1/2" Hairline
12 3' -4" Hairline
13 0' -3" Hairline
17 Pier Width Hairline
18 Pier Width Hairline
19 Pier Width Hairline
20 Pier Width Hairline
21 Pier Width Hairline
22 Pier Width Hairline
23 Pier Width Hairline
24 Pier Width Hairline
37


SOUTH FACE
Figure 3.21: Cracking on pier 18 south face
Table 3.5: Length and thickness of cracks on pier 18 south face
Crack # Length Maximum Size
1 Pier Width Hairline
2 2' -9" Hairline
3 Pier Width Hairline
4 Pier Width Hairline
5 O' -9" Hairline
6 Pier Width Hairline
Due to the amount of expansion seen in the cracks on Pier 18, it will be taken as
the critical pier and the focus of much of the modeling that is discussed in the following
chapters.


CHAPTER IV
GENERAL MODEL
Program Used and Model Components
Due to the complexity of the bridge, a 3D model was necessary to reflect the
behavior of the bridge as accurately as possible. For this, the computer modeling program
ANSYS Mechanical APDL 16.0 was used. The program was selected because not only did
it have the capacity to run such a massive model with a total number of elements exceeding
half a million, but also because of its high accuracy and user friendly interface, which
allows a person to write commands in code on any program, such as Microsoft Word and
then copy and paste those commands onto ANSYS.
It is important to note that only half of the bridge was modeled (from pier 11-
abutment 20). The reason for that is because the main pier that is going to be analyzed is
pier 18 (with some analysis being done on pier 19 as well) and as the field data proved that
there is very little movement on Pier 11, it would be easier to simply take that pier as fixed,
especially because convergence of the solution is an important issue for a large complex
model and anything that can get the model to converge easier and faster will be taken into
account.
The general modeling for 8th Avenue Viaduct was done as a group effort by Yang
Zhou, Wanting Wang and Samir Mizyed.
39


Different types of elements were used to model the different components of the
bridge, which are as follows:
1) Foundation: Because the main concern here is structural, the
interaction between the bridge and the soil was neglected and the foundations were
modeled as fixed supports.
2) Piers and Abutments: These were modeled with 3D solid tetrahedral
elements.
Figure 4.1: Pier
40


Figure 4.2: Abutment
3) Bearings: The base plate, top plate and guide bars were modeled
with 3D solid elements, while contact elements were used to model the interaction
between the top and bottom plates, as well as the guide bars and base plate.
Figure 4.3: Unguided bearing
41


4) Girders: These were modeled using 2D shell elements, while the
diaphragms bracing them were modeled as ID beam elements, which were also
used for the diagonal bracing, while the stiffeners on the sides of the girders were
modeled with 2D shell elements.
42


Figure 4.6: Girders with diaphragms, diagonal bracing and stiffeners
Figure 4.7: Deck
43


Figure 4.8: Span between two piers
6) Expansion Joints: Linear spring elements were used to model their
behavior. The stiffness of each spring was calculated based on the stiffness of the
expansion joint (which was assumed to be linear) divided by the number of springs
used to represent said joint. The expansion joint at abutment 20 has a stiffness of
12.68 kips/ft which translates to 152160 Ibs/ft. 31 springs were used to model the
joint; therefore, the stiffness of each spring was 152160/31 = 4908.4 Ibs/ft.
44


Figure 4.9: Springs used to model the expansion joint at abutment 20
Two different types of materials were used: concrete for the piers, abutments and
deck; steel for the bearings and girders. For concrete a unit weight of 150 lbs/ft3, a Poissons
ratio of 0.2 and a modulus of elasticity of 5.25><108 lbs/ft2 were defined. For steel, the
defined values were: a unit weight of 490 lbs/ft3, a Poissons ratio of 0.3 and a modulus of
elasticity of 4.176><109 lbs/ft2 (note: because there are no units in ANSYS, it was critical
to make sure that all the values were inputted with the same units of measurement for length
and weight, which here were feet and pounds respectively). Both steel and concrete were
given a reference temperature of 70 degrees Fahrenheit (again, it was important to make
sure that all subsequent temperature values would be in Fahrenheit) with a thermal
expansion coefficient of 6x 10"6 for steel and 5.5x 10"6 for concrete.
Geometry
It is standard practice in structural engineering to design based on following the
load path. For the viaduct, the loads get transferred from the superstructure to the bearings
to the substructure; therefore, the design should start with the superstructure. However,
45


when the project for 8th Avenue first started the bearing detailing has yet to be secured.
Therefore, the substructure and the superstructure were designed separately and then when
the bearing details became available they were used to connect the two together.
The first thing needed in building the model was reference points from which to
build the piers, abutments, girders, etc. For the piers and abutments a point centered at the
base was selected as the reference point for each pier or abutment and using the as-built
bridge plans the x, y and z-coordinates of this point were found (in the global coordinate
system, x represents east(+)/west(-), z represents north(-)/south(+) and y represents the
elevation, while the zero-point of global coordinate system was at the east starting point of
the bridge with a reference elevation of 5200 ft). From each of these reference points the
corresponding pier or abutment was drawn.
Similarly for the girders, a reference point was established at the center of the two
box girders at the elevation of the top flange. A reference point was needed at every
location where there was a stiffener or diaphragm in the girder. Due to the large number of
stiffeners in the box girders a total of almost 400 reference points between pier 11 and
abutment 20 had to be established. Their coordinates were determined based on the vertical
and horizontal profile lines of the bridge. These reference points were used to draw the
superstructure (including the deck above the girders) in segments, which were then merged
together (although much of the bridge was curved, these segments were all drawn straight,
but because they were so small ranging from 1.75-6 ft the error was negligible).
For the bearings, a reference point for each bearing was set up at the top of the piers,
from which the base plate, top plate and guide bars were drawn. Because all the bearings
are oriented towards pier 11, the local coordinate system for each bearing reference point
46


had to be oriented in that direction. The top plate was then merged with the bottom of the
girders. The contact between the base plate and top plate/guide bars was modeled using
standard contact surface elements, allowing for both penetration and separation with a
friction coefficient of 0.08.
Loads
The loads applied on the structure were dead, live and temperature.
Dead Load
This includes the own weight of the structure (because the materials were defined
as density rather than mass, the acceleration was inputted either as 1 when checking the
normal capacity of the structure or 1.25 when considering the LRFD factors for ultimate
state design) as well as loads from non-structural components, which are as follows:
The asphalt wearing surface: 48 psf.
The concrete sidewalk: There is one sidewalk that is 6 10 wide on
the south side of the road which was assumed as 10 inches thick so the load
from the sidewalk will be equal to 10/12 150 = 125 psf.
The concrete barriers: There are two concrete barriers on either side
of the road, each of which was taken as 640 lbs/ft. Apply that load over 1 3
width translates to an area load of 640/1.25 = 512 psf.
Guard Rail: At the edge of the sidewalk there is a guard rail that is
estimate as 300 lbs/ft. Applying that over an 8 width gives an area 300 x 12/8
= 450 psf.
47


Live Load
An HL-93 load was applied following the AASHTO design code which is
comprised of a lane-load of 640 lbs/ft distributed over a width of 10 feet and an HS-20
design truck, which is 6 feet wide and has 6 axles: the two in the front carry a load of 4000
pounds each and the four in the back carry a load of 16000 pounds each (the spans are long,
so the design truck will control and not the design tandem). The spacing between the first
and second pair of axles is 14 feet and the spacing between the second and third pair ranges
from 14-30 feet (AASTHO LRFD 2012 Bridge Design Specifications 3.6.1.2.2-1).
Applying the live load was the hardest of all the loads due to it being a moving load.
All cases that would generate the maximum moment on the spans or the maximum reaction
force on the piers had to be considered. These cases were determined using the influence
line theory.
The influence line is based on drawing the moment, shear or deflection diagram of
a certain point resulting from a unit point load applied at various locations. For example, if
one of the spans of the bridge (span length is typically 127 feet) was assumed as simply
supported and non-continuous, then the influence line for the moment at the mid-point of
the span as shown in Figure 4.10 can be drawn based on simple static analysis. If a unit
load of 1 kip in placed at the center of the span the moment at that point will be PL/4 =
1*127/4 = 31.75 kip-ft. If the unit load is placed at either ends of the span the moment at
the center will be zero. Connecting these three points gives the influence line for the
moment, which will be a triangle with a maximum value at the center (31.75 kips-ft).
Therefore, if a point load from the HS-20 truck of 32 kips was applied 14 feet from the
center of the span then the moment value at the center of the span will be: 24.75 kips-ft
48


(the value obtained from the influence line) x 32 (ratio between the load applied and the
unit load) = 792 kips-ft. If a uniformly distributed lane load of 0.64 kips/ft was applied
along the entire length of the span then the moment at the center will be: 2016.125 kips-ft
(area under the influence line = 0.5x127x31.75) x 0.64 = 1290.32 kips-ft.
/

127'
_/
7
Figure 4.10: Bridge span assuming simple supports and non-continuity
Figure 4.11: Moment influence line for simply supported single span at
mid-span
This is an extremely simplified scenario though that cant really be applied to the
bridge. For an indeterminate structure, things are more complex. However, while drawing
an exact influence line is difficult its shape can still be predicted based on how the structure
is expected to deform under a load. For simplicity, the bridge can be taken as a 19
continuous span structure. As it is expected that the max moment for each span will occur
somewhere in the middle, the influence line for the mid-point of each span must be
determined.
49


As shown in Figure 4.13, applying a load on a certain span that will cause the entire
span to deflect downwards. Therefore the moment generated will be positive. However,
applying a load on an adjacent span causes the span being analyzed to deflect upwards,
therefore the moment generated from any load on an adjacent span will be negative.
Therefore, using the deflected shapes the influence line for the mid-point of the span under
analysis should be similar to the deflection curve shown in Figure 4.13.
TT
T
TE-
ur
Figure 4.12: Continuous spans under a concentrated load
Figure 4.13: Deformation of continuous spans due to applied load
Using the influence line, the maximum moment that can occur at any mid-span
point on the bridge will occur when applying the lane load on that span and every other
span from it while placing the truck at the center of the span.
NO ^1 (S3 IS 3 S) IS Cn £ C5> cs CNJ r\ n
l [ ' : i r I
SPAN
Figure 4.14: Live load distribution to generate max moment at a certain
span
50


The max reaction can be obtained based it on where a load will generate a
downwards or upwards pressure on the support (pier). If a load is applied on the adjacent
spans to a certain support, then it causes a downwards pressure on that support, but if it is
applied on the spans on either side after the adjacent ones, then that will result in an uplift
pressure on the support. Based on this, the max reaction on a pier will be when the truck is
directly above the pier and the land load is applied to the adjacent spans and every other
span from them.
c N S i
L L J ( i
PIER
Figure 4.15: Live load distribution to generate max reaction at a certain
pier
As there are 19 spans and 20 supports (2 abutments +18 piers) that means there are
a total of 39 different load cases that would have to be applied if the entire bridge was being
analyzed and thats ignoring cases of loading just one lane or the other. However, not only
is half the bridge being modeled but the focus of this paper is only on two piers (piers 18
and 19). Therefore, only cases that will result in maximum stress on those piers will be
considered. These cases include loading to generate maximum moment (e.g. placing the
truck in the middle of the span), loading to generate to max reaction (e.g. placing the truck
directly on the pier), loading the south lane only, loading the north lane only and loading
both lanes. One way to do so would be to apply these cases at different times while keeping
the Analysis Type Static to ignore dynamic effects. After running the model one can then
move through the different times while keeping track of which time corresponds to which
51


load case. However, as running so many different load cases on such a complex model
takes hours or days to complete, it would be easier to simply run one load case at a time.
When applying the live load all the factors specified in the AASHTO LRFD Bridge
Design Specification much be considered, including the load factor (for ultimate state
design), the dynamic impact factor and the multiple presence factor (AASHTO LRFD 2012
Bridge Design Specifications 3.6).
Temperature Load
This will be applied to the south side of the southern steel box girder (the side that
gets sunlight) and the concrete deck on top. While for more complex temperature analysis
various values would have to be applied to see how the bridge behaves under temperature
cycles for now the applied temperature will be a fixed vale of 120 F.
Figure 4.16: Application of temperature on south side of steel girders
52


Load Combinations
In the design, 8th Avenue Viaduct is taken as a bridge for basic vehicular use
without wind load. Therefore, based on the AASHTO LRFD 2012 Bridge Design
Specifications, the ultimate loading capacity will be based on the Strength I limit state
(AASHTO LRFD 2012 Bridge Design Specifications 3.4.1), which uses the following load
combination:
U = 1.25DL + 1.5DW + 1.75LL + 0.5/1.2T (From AASHTO 2012 LRFD Bridge
Design Specifications Table 3.4.1-1). As load combinations cant be inputted in ANSYS
the loads will be applied with their factors. Therefore all the dead loads mentioned
previously will be multiplied by 1.25, with the excpetion of the wearing surface and utilities
which will be factored by 1.5, and all live loads will be factored by 1.75 when designing
for Strength I Limit State (for service limit state loads will be un-factored).
Analysis
Check of Results
First off, it is important to check and make sure that the results from ANSYS make
sense. Hand calculations can be used to check the reactions on any of the piers by assuming
that each one will take half the load of the span on each side. Pier 16 will be used as an
example. Based on all of the components of the bridge (both structural and non-structural)
the total reaction from the superimposed dead load (SDL) can be calculated as shown in
Table 4.1.
53


Table 4.1: Superimposed dead load on 3ier 16
Concrete Component Thickness (ft) Width (ft) Weight Unit Total weight (Ibs/ft) Total weight (kips/ft)
Deck 0.7083 40.1667 150 pcf 4267.7083 4.2677
Sidewalk 0.8333 6.8333 150 pcf 854.1667 0.8542
Wearing surface 30 48 psf 1440 1.44
Fence 0.6667 600 psf 400 0.4
# of barriers
Barrier 2 640 Ibs/ft 1280 1.28

Steel Component Thickness (ft) Width (ft) # of components Density (pcf) Total weight (Ibs/ft) Total weight (kips/ft)
Top flange 0.1094 1.3333 4 490 285.8333 0.2858
Web 0.02604 4.25 4 490 216.9271 0.2169
Bottom flange 0.02604 10 2 490 255.2083 0.2552

Sum 8.9998
This means that each foot of span length weighs approximately 9 kips.
Pier 16 is between spans 15 and 16, each of which is 127 feet long. Therefore, the
total span length that will be carried by Pier 16 will be (127+127)/2 = 127 feet, from which
the total superimposed dead load transferred to Pier 16 can be calculated as follows:
SDL = span length x weight per ft
= 127 x 9 = 1143 kips
The own weight of the pier must also be considered. In ANSYS the pier dimensions
were simplified as shown in Figure 4.17.
54


Figure 4.17: Dimensions of pie 16 (simplified)
The thickness of the pier is constant at 3 feet. Therefore, the total volume of the
pier can be calculated as: Volume #3 (volume of a 30ftx30.82ftx3ft rectangular solid) -
Volume #2 Volume #1. The weight will be the volume multiplied by the density of the
concrete (150 pcf). The results are summarized in Table 4.2.
55


Table 4.2: Self Weight of Pier 16
Volume # Height (ft) Width (ft) Thickness (ft) Density (pcf) Weight (lbs) Weight (kips)
1 17.323 10.5 3 150 163701.56
2 10.5 10.5 3 150 38965.566
3 30.823 30 3 150 416109.38
Total weight 213442.25 213.442
The total un-factored dead load transferred to Pier 16 will be the summation of the
superimposed dead load and the self-weight of the pier:
DL = SDL + SW
= 1143 + 213.4 = 1356.4 kips
From ANSYS the total reaction at the bottom of pier 16 from the un-factored dead
load was 0.13508E+07 pounds which translates to 1350.8 kips. This is very close to the
values calculated by hand.
The next check will be for the live load. Theoretically, the case that will generate
the maximum live load on Pier 16 will be when both lanes are fully loaded and the
distribution is as shown in Figure 4.18.
14' 14
127' 127'
Figure 4.18: Live load distribution to generate max reaction at pier 11
56


The multiple presence factor, which depends on the number of lanes loaded must
also be considered. This can be obtained from the AASHTO LRFD 2012 Bridge Design
Specifications 3.6.1.1.2. Because the check here is for two lane loaded case, the multiple
presence factor will be 1, though for other cases when only one lane was loaded (either the
north or south lane) the multiple presence factor will be 1.2 (AASHTO LRFD 2012 Bridge
Design Specifications Table 3.6.1.1.2-1).
The truck must also be increased by a dynamic load allowance factor (IM) which
AASHTO specifies as follows:
IM = 33% (AASTHO LRFD 2012 Bridge Design Specification Table 3.6.2.1-1)
The un-factored live load from the trucks and lane loads (HL-93) transferred to Pier
16 will therefore be as follows:
Live load from HL-93 = ((Truck Load x (1+IM) + Lane Load x span-length) x #of
lanes x m
= ((32 + 32x113/127+8x113/127) x 1.33 + 0.64 x 127) x 2 x 1
= 344.9 kips
The pedestrian load must also be taken into account, which based on AASHTO
specifications will be taken as 75 psf (AASHTO LRFD 2012 Bridge Design Specifications
3.6.1.6). The sidewalk is 6 10 wide; therefore, the load transferred to pier 16 from the
pedestrian load can be calculated as follows:
Pedestrian load = 75psf x sidewalk width x span length
= 75/1000 x (6+10/12) x 127 = 65.1 kips
57


The total un-factored live load transferred to pier 16 will be the summation of the
HL-93 load and the pedestrian load:
LL = HL-93 + PL
= 344.9 + 65.1 = 410 kips
From ANSYS the total reaction at the bottom of pier 16 from the un-factored live
load was 0.46647E+06 which translates to 466.47 kips. This is higher then what was
calculated by hand but because live load is a moving load it was unrealistic to expect to get
the same level of accuracy as with the dead load. Therefore, a greater percentage of error
will be allowed.
The final load to check for is temperature. Theoretically, the displacement on a
point should be the longitudinal distance of that point from the fixed point of the bridge
(pier 11) multiplied by the coefficient of thermal expansion multiplied by the difference
between the applied temperature and the reference temperature (L x a x (T-Tr)). However,
the temperature was only applied on part of the model (the southern side of the south steel
box girder and the concrete deck), while there are also springs at the ends to resist
expansion. Therefore, in order to check the results the conditions of the model will be
changed so that the temperature of 120 degrees is applied to all components of the bridge.
Also, the check will be performed by running the code for the five spans east of pier 11
(this part is specific for the temperature check, the rest of the analysis will only be for the
spans west of pier 11) stopping just before pier 6, as the spans between pier 6 and 11 are
all of the same length (127 feet), while the bridge is straight near pier 6 running almost
parallel to the east-west direction. At this section, rather than connecting the girders to pier
58


6, springs in the vertical and transverse directions of the bridge will be used instead at this
end to keep the structure stable while at the same time allowing for free unrestrained
movement in the longitudinal direction (the stiffness of the springs in the transverse
direction will be the same as the stiffness of the springs at abutment 20; a stiffness 10 times
higher will be applied to the vertical springs). The reason springs were used instead of
merely fixing the section in the vertical and transverse directions is because all of the
contact areas defined for the bearings result in a model that takes many iterations to
converge and may not converge at all if the boundary conditions are too rigid. Therefore,
it is best to keep the model as flexible as possible.
With these new conditions defined the model is solved and the displacement at the
section near pier 6 is checked. The results are displayed in Figure 4.19.
Figure 4.19: Displacement in the longitudinal direction at a section close
to pier 6
59


Based on the results from the Figure, the girders moved 0.183 feet in the
longitudinal direction away from Pier 11. This result can be verified with hand calculations:
Deformation = L x a x (T-Tr)
= (5x127) x (6xl0'6) x (120-70) = 0.1905 ft
This value is very close to what ANSYS gave, which means that the model is
working properly.
Impact of Guide Bar Removal
Now the models accuracy has been verified the next step is to see what impact the
bearing system has on the piers. Even though this paper is on pier rehabilitation, the
bearings also need repair and any change done to them could have a major impact on the
stress transferred to the piers, whether positive or negative.
While initially the model was built reflecting the bridge as it was designed, the
current conditions of the bridge must now be taken into account. As mentioned in chapter
I, several guide bars on the bearing were removed to relieve some of the stress on the piers.
These guide bars were as follows:
The south guide bar of the northern interior bearing (GW4) for all the
piers and abutments.
The south guide bar of the southern interior bearing (GW2) for pier 2 and
both abutments.
The north guide bar of the southern interior bearing (GW2) for pier 19.
In the model these guide bars dont need to be deleted; instead the contact area
between them and the baseplates are removed.
60


First, the stress on pier 19 with all guide bars present under an applied temperature
of 120 degrees Fahrenheit on the concrete deck and south side of the south steel box girder
will be checked. For the case of both lanes loaded and the trucks placed directly above the
pier, the resulting stresses in the longitudinal and transverse directions are shown in Figures
4.20-4.21.
Figure 4.20: Stress in longitudinal direction on pier 19 with all guide
bars present
61


ELEMENT SOLUTION
STEP-1
SUB 1
TIME-1
SZ (NOAVG)
RSYS-0
DMX -.038963
SMN -9S2080
SMX -501970
DSYS-43
ANSYS
R16.0
OCT 26 2015
13:53:39
-952080 -628958 -305835 17286.8 340409
-790519 -467396 -144274 178848 501970
FULL MODEL OF 8TH AVENUE
Figure 4.21: Stress in transverse direction on pier 19 with all guide bars
present
Based on the results in the figures and ignoring a few small elements with uneven
mesh that resulted in some stress concentration, the maximum tensile stresses were:
124,000 psf in the longitudinal direction (0.861 ksi) and 210,000 psf at center top part of
the pier, which is 1.458 ksi. Both the normal longitudinal and transverse tensile stresses
are well above the tensile strength of concrete (0.4 ksi), which means that there will be
both vertical cracks at the top of the pier and horizontal cracks at the bottom. The max
compressive stresses meanwhile were found to be: -314,850 psf in the longitudinal
direction (-2.186 ksi) at the bottom of the pier on the opposite side to the max tension and
-144,000 psf in the transverse direction (-1 ksi) at the bottom of the hammer head portion
of the piers. Again, a few smaller elements with uneven meshing were ignored. Concrete
has a compressive strength of 4 ksi, so it is safe from crushing.
62


Next we the model is solved taking into consideration all the guide bars that were
removed. The resulting stresses in the longitudinal and transverse directions from the same
loading case (both lanes loaded, temperature applied to deck and south side of south girder)
are shown in Figure 4.22-4.23.
Figure 4.22: Stress in longitudinal direction on pier 19 with guide bars
removed
63


Figure 4.23: Stress in transverse direction on pier 19 with guide bars
removed
As observed in the figures, the max tensile stresses remain at the same locations for
the longitudinal and transverse directions; however the values reduced in both cases to
65,100 psf (0.452 ksi) in the longitudinal direction and 175,000 psf (1.215 ksi) in the
transverse direction. These values are still above the tensile limit but theyre not as bad as
when all the guide bars were present. Also, while the reaction at the bottom of the pier in
the vertical direction stayed the same the reactions in the transverse and longitudinal
directions decreased when the guide bars were removed.
Although more temperature cases would have to be checked and a finer model with
more uniform meshing of the pier would need to be constructed to get more accuracy, based
on the results obtained from this case, removing the guide bars helped relieve some of the
stress on pier 19, which could explain why the rate of crack expansion on pier 19 has
slowed down in recent years.
64


Therefore, from the results of both the model and the field inspection of the piers a
more flexible bearing system is recommended to reduce the stress transferred to the piers.
Temperature Effect
Based on the pier inspection performed, the stresses on the piers towards the ends
of the viaduct should be higher than the stresses on the piers near pier 11. Because the
vertical loads transferred to the piers from dead and live load cases shouldnt vary too much
from pier to pier, the difference in pier stresses should mainly come from the temperature
load. To prove that, a model with only the temperature loading case will be analyzed.
As expected, under temperature alone the stress increases the farther away the pier
is from the fixed pier, which explains why the piers closest to the edges had the most cracks.
A comparison between a pier close to pier 11 (pier 12) and a pier near the end (pier 18) is
shown in Figures 4.24 and 4.25.
Figure 4.24: Stress in transverse direction on pier 12 due to temperature
65


ELEMENT SOLUTION
ANSYS
R16.0
STEP=1
SUB =1
TIME=1
SZ (NOAVG)
RSYS=0
DMX =.049413
SMN =-69655.4
SMX =84159.6
OCT 16 2015
21:14:13
-69655.4 -35474.3 '"^1/^1293.17 32887.9 67069
-52564.8 -18383.7 15797.4 49978.5 84159.6
FULL MODEL OF 8TH AVENUE
Figure 4.25: Stress in transverse direction on pier 18 due to temperature
Load transferred to Pier 18
As Pier 18 is going to be checked for cracking/crushing the load that will be applied
is the service load rather than the ultimate load.
There are several cases that might control for Pier 18, all of which have to be
checked. Theres the case of both lanes loaded and the truck loads placed directly above
the pier, but there are also cases of the live load (both truck and lane) on only one lane,
either the north or south lane. For all of these cases the dead load (own weight + wearing
surface, barriers, fence and sidewalk) and temperature load (applying 120 degrees to south
side of south box girder and concrete deck) will be the same. The model will be analyzed
for the current condition of the bridge, taking into consideration the guide bars that were
removed.
66


The case that will be analyzed is when both lanes are loaded. From Figure 4.26 it
is observed that the stress in the transverse direction at the top part of the pier clearly
exceeds the tensile limit of concrete (0.43 0.73 ksi > 0.4 ksi), meaning cracking will occur
Figure 4.26: Stress on pier 18 in transverse direction from case of two
lane loaded
The resulting pressure on all of the four bearings is displayed in Figures 4.27-4.30.
To make sure that the contact is working properly the friction on bearing GW5 is also
checked, which is displayed in Figure 4.31.
67


ELEMENT SOLUTION
STEP=1
SUB =1
TIME=1
CONTPRES (NOAVG)
ANSYS
R16.0
OCT 16 2015
17:19:59
r~
192224 384448 576672 768896
96112 288336 480560 672784 865008
FULL MODEL OF 8TH AVENUE
Figure 4.28: Contact pressure on bearing GW2
68


69


Figure 4.31: Contact friction stress on bearing GW5
The max pressure found on bearing GW5 was 0.128xl07 psf. The max friction
value should therefore be the pressure value multiplied by the friction coefficient:
Friction = pressure x friction coefficient
= 0.127xl07 x 0.08 = 101600 psf
Checking this with the max pressure value from Figure 3.36, the results are nearly
identical.
The average pressure and friction values on each of the girders and the total force
obtained from them (force = pressure x area of baseplate) is summarized in Table 4.3.
These forces can be compared with the total reactions at the bottom of the pier, which are
summarized in Table 4.4.
70


Table 4.3: Average pressure on each bearing and resultant force two lane loaded case
Bearing Average Pressure (psf) Vertical Force (lbs)
GW1 266482 328579
GW2 315310 388785
GW4 333382 411069
GW5 391801 483101
1611534
Table 4.4: Reactions at bottom of pier 18 two lane loaded case
Reaction Value (lbs) Direction
Rx 122318 Longitudinal (west)
Ry 1740200 Vertical (upwards)
Rz 40788 Transverse (north)
The total force from the bearings is approximately 1611534 lbs (1612 kips). Adding
the weight of the pier to that value (140 kips approx.) will give approximately the total
reaction in the vertical direction, which is the Ry value (1740200 lbs = 1740 kips).
It is also observed that the reaction in the longitudinal direction (Rx) is
approximately 3 times the reaction in the transverse direction (Rz) which matches how the
bearing is oriented. Both Rx and Rz can be written in relation to the vertical load (without
the self-weight of the pier) in order to find an approximation of the ratio between the
friction force in both directions and the vertical force:
Transverse friction force/vertical force = 40788/1657842 = 0.0253
Longitudinal friction force/vertical force = 122318/1657842 = 0.0759
V(0.02532 + 0.07592) = 0.08, which is the friction coefficient
The pressure and reaction values for south lane and north lane loaded cases are
summarized in Tables 4.5-4.8. Under the two-lane loaded case it was observed that
bearings GW4 and GW5 on the north side of the pier had higher pressure values than
bearings GW1 and GW2 on the south side; therefore is expected that the north-lane loaded
71


case will be more critical than the south lane loaded case. This is also supported by field
evidence where it was observed that nearly all the cracks on the south side of the pier were
hairline cracks, whereas several cracks on the north side were 0.016 0.02 inches thick.
Table 4,5: Average pressure on each bearing and resultant force north lane loaded
Bearing Average Pressure (psf) Vertical Force (lbs)
GW1 208021 256495
GW2 215349 265530
GW4 275789 340055
GW5 424769 523750
1385831
Table 4,6: Reactions at bottom of pier 18 north lane loaded
Reaction Value (lbs) Direction
Rx 107044 Longitudinal (west)
Ry 1521878 Vertical (upwards)
Rz 35638 Transverse (north)
Table 4,7: Average pressure on each bearing and resultant force south lane loaded
Bearing Average Pressure (psf) Vertical Force (lbs)
GW1 288605 355857
GW2 312886 385796
GW4 273790 337590
GW5 287776 354836
1434079
Table 4,8: Reactions at bottom of pier 18 south lane loaded
Reaction Value (lbs) Direction
Rx 110149 Longitudinal (west)
Ry 1571157 Vertical (upwards)
Rz 36837 Transverse (north)
Because the sidewalk is on the south side of the bridge, the pedestrian load was
applied for the south lane loaded case but not for the north lane loaded case, which is why
the vertical reaction for the south lane loaded case is slightly higher.
72


CHAPTER V
FINE MODEL
Pier 18
Due to the size of the model it was necessary to simplify the piers or else it would
take too long for the model to run. Now that the loads transferred from the superstructure
to the piers have been obtained, however, it is possible to move on to the next step, which
is analyzing the piers in detail by building a more in-depth model of one of the piers,
complete with all reinforcement detailing and the non-linear properties of the materials.
This part is specific to this thesis, in contrast to the general modeling of the viaduct, which
was a group effort.
Because Pier 18 was in the worst condition as far as the rate of crack expansion
goes, it will be the pier to build a fine model for, and on which the proposed rehabilitation
will be tested out upon. If the cracking issue can be solved for this pier, then that solution
should work for the rest of the piers.
73


Figure 5.1: Pier 18
The dimensions of pier 18 are displayed in Figures 5.2-5.3, while Figures 5.4-5.6
display the reinforcement detailing.
Figure 5.2: Plan view of pier 18 (City and Country of Denver 1993, used
with permission)
74


Elv. 5229.07' Elv. 5229.11' Elv. 5229.01' Elv. 5228.94'
Figure 5.3: Elevation view of pier 18 (City and Country of Denver 1993,
used with permission and some edits)
Figure 5.4: Reinforcement detailing of pier 18 (City and Country of
Denver 1993, used with permission)
75


3'0* -
/fC* ,>V
| ./er

___£94/0/ 5>r
ff /* Ea. Face.
*5 Qe>vbfc 77cs
<54*
I_____£9^*' Spa.
££CTfON &i\
Ori^. Sca/t h,,r'Cr\^iJ
Figure 5.5: Hammerhead cross-section reinforcement detailing of pier 18
(City and Country of Denver 1993, used with permission)
SECTION (Ha*.
OriQ. Scole fe,mt:Q*\dJ
Figure 5.6: Column cross-section reinforcement detailing of pier 18 (City
and Country of Denver 1993, used with permission)
Model Detailing
Materials
Similar to the general model, both concrete and steel materials will be defined.
However, this time the materials will be given both linear and non-linear properties.
For concrete, the following properties will be inputted:
Elastic Modulus: the concrete is assumed to be normal weight concrete with
4,000 psi strength; therefore the modulus of elasticity will be defined as
3,605 ksi which is equivalent to 5.192x 108 lbs/ft2 (same as before).
76


Poissons ratio: Defined as 0.2 (same as before).
Density: Defined as 150 lbs/ft3 (same as before).
Ultimate uniaxial compressive strength: 4,000 psi strength is equivalent to
5.76x10s lbs/ft2
Ultimate uniaxial tensile strength: Also known as the modulus of rupture,
which is taken as ten percent of the compressive stress (5.76xl04 lbs/ft2).
Shear transfer coefficient: This has two components. First, there is the shear
transfer coefficient for open cracks which ranges from 0 (complete loss) to
1 (no loss). For the fine model a coefficient of 0.2 will be used (standard
value). Second, there is transfer coefficient for closed cracks, which will be
taken as 1, thereby neglecting any reduction in shear stiffness of the model.
Compressive uniaxial stress-strain relationship: In order to draw the
relationship between stress and strain for concrete several points must be
defined, which ANSYS will connect automatically. The data inputted is
summarized in Table 5.1 and the resulting stress-strain curve in displayed
in Figure 5.6.
Table 5.1: Stress-strain data for concrete
Strain Stress (lbs/ft2)
0.00055 2.86E+05
0.001083 4.54E+05
0.00174 5.59E+05
0.002 5.76E+05
0.003 5.76E+05
77


Figure 5.7: Stress-strain relationship for concrete
For steel, the following properties are inputted:
Elastic Modulus: the reinforcement used is grade-60 steel; therefore the
modulus of elasticity will be defined as 29,000 ksi which is equivalent to
4.176><109 lbs/ft2 (same as before).
Poissons ratio: Defined as 0.3 (same as before).
Yield stress: 60 ksi strength is equivalent to 8,64x106 lbs/ft2. By inputting
this value ANSYS will automatically draw the stress-strain curve for steel,
which is displayed in Figure 5.3 (note: if a more complex curve for steel
was desired, a tangent value could also be inputted, resulting in the straight
line segment curving upwards, but for this model the tangent will be kept
as zero).
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Figure 5.8: Stress-strain relationship for steel
Because the reinforcements weight will be relatively small compared to the other
loads being applied onto the pier, theres no need to input the density of the steel. However,
a third material is defined, which will also be steel, but with linear properties only. This is
done because aside from the reinforcement there are also the baseplates of the bearings,
which will be included in the model in order to apply the loads on (if the loads were applied
directly onto the concrete there would be issues of stress concentration). Because that will
be their only purpose in the model and no analysis will be performed on them, theres no
need to give them a yield stress.
Element Type
The following elements will be defined:
SOLID65: This is a 3D element type specific to concrete that allows
ANSYS to draw the potential cracking/crushing of the material.
LINK180: ID element used to model the steel reinforcement.
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SOLID 185: 3D element for modeling the baseplates (same as what was used
for modeling any volume in the general model).
Real Constants
For the link elements representing the steel reinforcement, real constants that
represent their cross sectional areas have to be defined. Therefore, each bar size will have
a different real constant. There are three different bar sizes for the reinforcement:
No. 4: Area = 0.196 in2 = 0.00136 ft2
No. 5: Area = 0.307 in2 = 0.00213 ft2
No. 9: Area = 0.994 in2 = 0.0069 ft
Constructing the Model
With the elements and materials defined, the model can now be built. The global
coordinate system will be set at the middle of the bottom of the pier with the x-axis
representing the longitudinal direction, the z-axis representing the transverse direction and
the y-axis representing the vertical direction (similar to the general model). All coordinates
will be inputted in the global system (unlike the general model, there is no need to create
any local coordinate systems because there is only one pier).
The pier volume is the first thing to create. Due to the symmetric properties of the
pier, the area of the pier that is displayed in Figure 5.3 is drawn and then extruded along
lines representing the thickness of the pier (because the thickness of the 3 foot wide center
portion of the column in the middle of the pier is 2 inches less than the 3 foot thickness of
the rest of the pier, it is extruded along a line slightly shorter than the others). The exterior
volume of the pier is displayed in Figure 5.9.
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Figure 5.9: Volume of pier 18
The next step is drawing the reinforcement. This can be accomplished by dividing
the exterior volume of the pier by a set of defined areas and work planes in order to create
interior lines, which are then grouped into components representing the different bar sizes
in order to make things easier for meshing and analyzing. This process will divide the
exterior volume into hundreds of blocks with the outside lines of the interior blocks
representing the reinforcement. In this way the steel will be attached to the concrete and
thus the stress can be transferred to it.
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Figure 5.10: No. 4 bars
Figure 5.11: No.
5 stirrups
82


Figure 5.12: No. 9 bars
Figure 5.13: Front sectional view of reinforcement
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The final components to construct are the baseplates. As noted previously, the
baseplates arent oriented parallel to pier 18 but towards the fixed pier (pier 11). While pier
11 could be included in the model and reference points towards it created from which to
construct the baseplates it would be easier to simply go back to the general model and
obtain the coordinates of the bottom four comer points of each baseplate in reference to the
local coordinate system at the bottom of the pier, which in the fine model is the global
coordinate system. With these points, the bottom area of each baseplate can be created. The
top areas of the pier can then be divided by these areas in order to let ANSYS know that
the bottom of the baseplate is attached to the top of the pier. The bottom baseplate areas
are then extruded by lines representing the thickness in order to create the baseplate
volumes.
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Full Text

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STRUCTURAL ANALYSIS OF CRACKED CONCRETE PIERS AND PROPOSED REHABILITATION USING CFRP RODS By SAMIR MIZYED B.S., An Najah National University, 2013 A thesis submitted to the Faculty of the Graduate School of the University of Colorado in partial ful fillment of the requirements for the degree of Masters of Science Civil Engineering Program 2015

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ii 2015 SAMIR MIZYED ALL RIGHTS RESERVED

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iii This thesis for the Master of Science degree by Samir Mizyed Has been approved for the Civil Eng ineering Program By Kevin L. Rens, Chair Chengyu Li Advisor Frederick Rutz 20 November 2015

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iv Mizyed, Samir (M.S., Civil E ngineering) Structural Analysis of Cracked Concrete Piers and Pro posed Rehabilitation using CFRP Rods Th esis directed by Professor Keving L. Rens ABSTRACT All the concrete piers on 8 th Avenue Viaduct, Denver, CO have shown an extensive amount of cracking, both v ertically and diagonally. A pier by pier inspection performed in 2015 revealed that the cracks were expanding. Two bi axial tilt meters were installed on the fixed pier (Pier 11) to measure the rotation in both directions. A 3d model using ANSYS Mechanical APDL 16.0 software of the viaduct was built and calibrated using the field measurem ents. A separate fine model of p ier 18, where cracks were expanding the most, was also constructed using the same softwar e, which included the reinforcement detailing and t he non linear properties of the material. Dead, live and t emperature loads were all applied on the general model under St r ength I limit state and the resulting forces transferred to pier 18 were obtained and then applied onto the fine model of the pier, in order to perform non linear finite element analysis. A s expected, the model showed extensive cracking similar to the actual condition of the pier. A rehabilitation system of CFRP rods was proposed a nd tested on the model, showing very favorable results. T he author of this thesis recommends this repair be used for all the piers on 8 th Avenue Viaduct. The format and content of the thesis are approved. I recommend its publication Approved: Kevin L. Rens

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v ACKNOWLEDGEMENTS My sincerest thank s to my advi sor, Dr. Kevin Rens who on the very first time we met offered me an internship with the City and County of Denver, through which I was able to do this project. faile d to offer me guidance and advic e whenever I needed it and encouraged me in my pursuit of higher education. Thank you, Dr. Cheng Li, for selecting me to take part in this project, which I am extremely grateful f or, for supervising my dissertation work and for all the classes th at I took with you, which played a vital role in preparing me for the work I needed to do for this thesis. The knowledge and experience you brought both to your classes and this project were immeasurable and no m atter what problem I ran into you always had an answer for it. Thank you, Dr. Frederick Rutz for being a part of my committee and for preparing me for the task of writing this thesis. It was through the reports I did for your class that I truly learned how to follow code specifications and use ASCE standards of writing. Thank you, Dick Miles for all the help you gave to this project, whether it be taking the time to meet with us and offer us guidance or coming out to the field with us and finding problems that we would have otherwise missed. This pro really great team. Thank you, Brandon Zhou, for being a great team leader (and even greater friend), and for always taking the initiative. Thank you, Juan Montenegro, for the practical experience t

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vi And thank you, Lisa Wang; my colleague, teammate and best friend. Work ing on this project with you has truly been an unforget t able experience.

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vii TABLE OF CONTENTS CHAPTER I. INTRODUCTION ................................ ................................ ................................ ................... 1 Overview ................................ ................................ ................................ ............................ 1 The Substructure ................................ ................................ ................................ ................ 6 Design Codes ................................ ................................ ................................ ..................... 9 II. LITERATURE REVIEW ................................ ................................ ................................ ....... 10 Concrete Cracking ................................ ................................ ................................ ........... 10 Concrete Crack Repair ................................ ................................ ................................ ..... 1 1 Carbon Fiber Reinforced Polymers ................................ ................................ .................. 12 FRP Design Considerations ................................ ................................ ............................. 17 ANSYS Modeling of FRP strengthened concrete ................................ ............................ 18 Steel Corrosion ................................ ................................ ................................ ................. 19 III. EQUIPMENT INSTALLATION AND FIELD INSPECTION ................................ ............ 20 Equipment Installation ................................ ................................ ................................ ..... 20 Pier Inspection ................................ ................................ ................................ ................. 29 IV. GENERAL MODEL ................................ ................................ ................................ ............. 39 Program U sed and Model Components ................................ ................................ ........... 39 Geometry ................................ ................................ ................................ .......................... 45 Loads ................................ ................................ ................................ ................................ 47 Dead Load ................................ ................................ ................................ .................... 47 Live Load ................................ ................................ ................................ ..................... 48 Temperature Load ................................ ................................ ................................ ........ 52 Loa d Combinations ................................ ................................ ................................ .......... 53 Analysis ................................ ................................ ................................ ............................ 53 Check of Results ................................ ................................ ................................ .......... 53 Impact of Guide Bar Removal ................................ ................................ ..................... 60 Temperature Effect ................................ ................................ ................................ ...... 65 Load transferred to Pier 18 ................................ ................................ .......................... 66 V. FINE MODEL ................................ ................................ ................................ ........................ 73 Pier 18 ................................ ................................ ................................ .............................. 73 Model Detailing ................................ ................................ ................................ ................ 76

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viii Materials ................................ ................................ ................................ ...................... 76 Element Type ................................ ................................ ................................ ............... 79 Real Constants ................................ ................................ ................................ ............. 80 Constructing the Model ................................ ................................ ................................ 80 Meshing ................................ ................................ ................................ ........................ 85 Loads and Boundary Conditions ................................ ................................ .................. 86 Solution Criteria ................................ ................................ ................................ ........... 90 Analysis ................................ ................................ ................................ ............................ 91 Check of Results ................................ ................................ ................................ .......... 91 Solution ................................ ................................ ................................ ........................ 96 VI. REPAIR USING CRFP RODS ................................ ................................ ........................... 106 Method of Repair ................................ ................................ ................................ ........... 106 Modeling of CFRP ................................ ................................ ................................ ......... 107 Material Properties ................................ ................................ ................................ ..... 107 Steel Pla te ................................ ................................ ................................ ................... 108 Real Constant of CFRP Rods ................................ ................................ ..................... 109 Creating CFRP Rods ................................ ................................ ................................ .. 109 Defining Pre Stress Force ................................ ................................ .......................... 111 Analysis ................................ ................................ ................................ .......................... 111 Check of Results ................................ ................................ ................................ ........ 111 Impact of CFRPs on cracking ................................ ................................ .................... 114 Method of Application ................................ ................................ ................................ ... 128 CFRP Rods with Permanent Steel Pl ates ................................ ................................ ... 128 CFRP Rods Epoxied to the Concrete ................................ ................................ ......... 130 Pre Stressing Steel ................................ ................................ ................................ ..... 132 VII. CONCLUSIONS AND RECOMMENDATIONS ................................ .............................. 133 Summary ................................ ................................ ................................ ........................ 133 Simplifications and Approximations ................................ ................................ ............. 135 General Model ................................ ................................ ................................ ........... 135 Fine Model ................................ ................................ ................................ ................. 137 Recommendations for Furth er Research ................................ ................................ ........ 138 REFERENCES ................................ ................................ ................................ ............................ 140

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ix APPENDIX A. PIER AND ABUTMENT DETAILING ................................ ................................ ............. 145 B. ANSYS CODE FOR PIER 18 ................................ ................................ ............................ 153

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x LIST OF TABLE S TABLE 3.1. Readings from bi axial tilt meters on pier 11 ................................ ................................ ..... 27 3.2. Length and t hickness of cracks on pier 18 west face ................................ .......................... 35 3.3. Length and thickness of cracks on pier 18 north face ................................ ......................... 36 3.4. Length and th ickness of cracks on pier 18 east face ................................ ........................... 37 3.5. Length and thickness of cracks on pier 18 south face ................................ ......................... 38 4.1. Superimposed d ead load on Pier 16 ................................ ................................ .................... 54 4.2. Self Weight of Pier 16 ................................ ................................ ................................ ......... 56 4.3. Average pressure on each bearing and resultant force two lane l oaded case ...................... 71 4.4. Reactions at bottom of pier 18 two lane loaded case ................................ .......................... 71 4.5. Average pressure on each bearing and result ant force north lane loaded ........................... 72 4.6. Reactions at bottom of pier 18 north lane loaded ................................ ............................... 72 4.7. Average pressure on each bear ing and resultant force south lane loaded ........................... 72 4.8. Reactions at bottom of pier 18 south lane loaded ................................ ............................... 72 5.1. Stress strain d ata for concrete ................................ ................................ ............................. 77 5.2. Forces on bearing GW1 ................................ ................................ ................................ ...... 88 5.3. Forces on bearing GW2 ................................ ................................ ................................ ...... 88 5.4. Forces on bearing GW4 ................................ ................................ ................................ ...... 89 5.5. Forces on bearing GW5 ................................ ................................ ................................ ...... 89

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xi LIST OF FIGURE S FIGURE S 1.1 Satellite view of West 8 th Avenue Viaduct ................................ ................................ ........... 2 1.2 General Layout of West 8 th Avenue Viaduct (City and County of Denver 1993, used with permission) ................................ ................................ ................................ ................................ ....... 2 1.3 Side view of bridge at a horizontal curve ................................ ................................ ............. 3 1.4 Side view of bridge at a straight portion ................................ ................................ ............... 3 1.5 Steel box girders with I girder in between (from abutment 1 pier 6) ................................ 4 1.6 Steel box girders (from pier 6 abutment 20) ................................ ................................ ...... 4 1.7 Guide bar of bearing removed ................................ ................................ .............................. 5 1.8 Cracking on one of the piers ................................ ................................ ................................ 6 1.9 Concrete Pier ................................ ................................ ................................ ......................... 6 1.10 Piers 2 6 (City and County of Denver 2012, used with permission) ................................ .... 7 1.11 Piers 7 19 (City and County of Denver 2012, used with permission) ................................ .. 8 1.12 Abutment 1 (City and County of Denver 2012, used with permission) ................................ 8 1.13 Abutm ent 20 (City and County of Denver 2012, used with permission) .............................. 9 2.1 Application of FRP laminates (ACI 440.2R 08 Fig. 11.1, used with permission) ............. 13 2.2 FRP Systems (ACI 440.2R 08 Fig 10.2, used with permission) ................................ ........ 14 2.3 Typical stress strain curve for CFRP ................................ ................................ .................. 15 2.4 Post tensioned CFRP rods (Hughes Brothers Inc 2011, used with permission) ................. 16 2.5 Mechanic anchorage of CFRP rods (Hughes Brothers Inc 2011, used with permission) ... 17 3.1 Distribution of strain gages and thermistors (stars represent strain gages, circles represent thermistors) ................................ ................................ ................................ ................................ .... 20 3.2 VW strain gage ................................ ................................ ................................ ................... 21 3.3 Thermistor ................................ ................................ ................................ ........................... 21

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xii 3.4 LVDT ................................ ................................ ................................ ................................ .. 22 3.5 Tem perature gage ................................ ................................ ................................ ................ 23 3.6 Uni axial tilt meter ................................ ................................ ................................ .............. 23 3.7 Bi axial tilt meter ................................ ................................ ................................ ................ 24 3.8 Multiplexer ................................ ................................ ................................ .......................... 25 3.9 Data logger ................................ ................................ ................................ .......................... 25 3.10 Solar panel ................................ ................................ ................................ .......................... 26 3.11 Vertical and diagonal cracks ................................ ................................ ............................... 30 3.12 Horizontal cracks at base of pier ................................ ................................ ......................... 31 3.13 Hairline cracks ................................ ................................ ................................ .................... 31 3.14 ................................ ................................ ................................ ................ 31 3.15 Crack extending from face to face of pier ................................ ................................ ........... 32 3.16 Dormant crack ................................ ................................ ................................ ..................... 33 3.17 Active crack ................................ ................................ ................................ ........................ 33 3.18 Cracking on pier 18 west face ................................ ................................ ............................. 34 3.19 Cracking on pier 18 north face ................................ ................................ ............................ 36 3.20 Cracking on pier 18 east face ................................ ................................ .............................. 37 3.21 Cracking on pier 18 south face ................................ ................................ ........................... 38 4.1 Pier ................................ ................................ ................................ ................................ ...... 40 4.2 Abutment ................................ ................................ ................................ ............................ 41 4.3 Unguided bearing ................................ ................................ ................................ ................ 41 4.4 Guided bearing ................................ ................................ ................................ .................... 42 4.5 Bearings on top of pier ................................ ................................ ................................ ........ 42 4.6 Girders with diaphragms, diagonal bracing and stiffeners ................................ .................. 43 4.7 Deck ................................ ................................ ................................ ................................ .... 43 4.8 Span between two piers ................................ ................................ ................................ ...... 44

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xiii 4.9 Springs used to model the expansion joint at abutment 20 ................................ ................. 45 4.10 Bridge span assuming simple supp orts and non continuity ................................ ................ 49 4.11 Moment influence line for simply supported single span at mid span ............................... 49 4.12 Continuous spans under a concentrated load ................................ ................................ ...... 50 4.13 Deformation of continuous spans due to applied load ................................ ........................ 50 4.14 Live load distribution to gene rate max moment at a certain span ................................ ....... 50 4.15 Live load distribution to generate max reaction at a certain pier ................................ ........ 51 4.16 Applicat ion of temperature on south side of steel girders ................................ ................... 52 4.17 Dimensions of pie 16 (simplified) ................................ ................................ ...................... 55 4.18 Live load distribution t o generate max reaction at pier 11 ................................ .................. 56 4.19 Displacement in the longitudinal direction at a section close to pier 6 ............................... 59 4.20 S tress in longitudinal direction on pier 19 with all guide bars present ............................... 61 4.21 Stress in transverse direction on pier 19 with all guide bars present ................................ .. 62 4.22 Stress in longitudinal direction on pier 19 with guide bars removed ................................ .. 63 4.23 Stress in transverse direction on pier 19 with guide bars removed ................................ ..... 64 4.24 Stress in transverse direction on pier 12 due to temperature ................................ .............. 65 4.25 Stress in transverse direction on pier 18 due to temperature ................................ .............. 66 4.26 Stress on pier 18 in transverse direction from case of two lane loaded .............................. 67 4.27 Contact pressure on bearing GW1 ................................ ................................ ...................... 68 4.28 Contact pressure on bearing GW2 ................................ ................................ ...................... 68 4.29 Contact pressure on bearing GW4 ................................ ................................ ...................... 69 4.30 Contact pressure on bearing GW5 ................................ ................................ ...................... 69 4.31 Contact friction stress on bearing GW5 ................................ ................................ .............. 70 5.1 Pier 18 ................................ ................................ ................................ ................................ 74 5.2 Plan view of pier 18 (City and Country of Denver 1993, used with permission) ............... 74

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x iv 5.3 Elevation view of pier 18 (City a nd Country of Denver 1993, used with permission and some edits) ................................ ................................ ................................ ................................ ..... 75 5.4 Reinforcement detailing of pier 18 (City and Country of Denver 1993, used with permission) ................................ ................................ ................................ ................................ ..... 75 5.5 Hammerhead cross section reinforcement detailing of pier 18 (City and Country of Denver 1993, used with permission) ................................ ................................ ................................ .......... 76 5.6 Column cross sec tion reinforcement detailing of pier 18 (City and Country of Denver 1993, used with permission) ................................ ................................ ................................ .......... 76 5.7 Stress strain relationship for concrete ................................ ................................ ................. 78 5.8 Stress strain relationship for steel ................................ ................................ ....................... 79 5.9 Volume of pier 18 ................................ ................................ ................................ ............... 81 5.10 No. 4 bars ................................ ................................ ................................ ............................ 82 5.11 No. 5 bars stirrups ................................ ................................ ................................ ............... 82 5.12 No. 9 bars ................................ ................................ ................................ ............................ 83 5.13 Front sectiona l view of reinforcement ................................ ................................ ................ 83 5.14 Baseplates on top on pier 18 ................................ ................................ ............................... 84 5.15 Meshing of pier 18 ................................ ................................ ................................ .............. 85 5.16 Meshing of pier 18 reinforcement ................................ ................................ ....................... 86 5.17 Pier 18 with loads and B.C.s for two lane loaded case ................................ ....................... 90 5.18 Stress in steel reinforcement bars for test case ................................ ................................ ... 91 5.19 Location of section A A ................................ ................................ ................................ ...... 92 5.20 Reinforcement of c ross section A A ................................ ................................ ................... 92 5.21 Simplified force diagram of Pier 18 ................................ ................................ .................... 94 5.22 Simplified bending moment diagram of Pier 18 ................................ ................................ 95 5.23 Tensile stress in steel at specified section ................................ ................................ ........... 96 5.24 Cracking/crushing of concrete under two lane loaded case ................................ ................ 97

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xv 5.25 Stress in steel reinforcement under two lane loaded case ................................ ................... 97 5.26 Cracking/crushing of concrete under north lane loaded case ................................ .............. 98 5.27 Stress in steel reinforcement under north lane loaded case ................................ ................. 98 5.28 Cracking/crushing of concrete under south lane loaded cas e ................................ ............. 99 5.29 Stress in steel reinforcement under south lane loaded case ................................ ................ 99 5.30 Cracking in pier under two lane loaded case wit hout longitudinal load ........................... 101 5.31 Cracking in pier under two lane loaded case with all transverse forces creating tension in pier (worst case scenario) ................................ ................................ ................................ ............. 102 5.32 Stress in steel reinforcement due to two lanes loaded worst case scenario ....................... 102 5.33 Cracking/crushing of concrete due to north lane loaded worst case scenar io ................... 103 5.34 Stress in steel reinforcement due to north lane loaded worst case scenario ...................... 103 5.35 Cracking/crushing of concret e due to south lane loaded worst case scenario .................. 104 5.36 Stress in steel reinforcement due to south lane loaded worst case scenario ..................... 104 6.1 Strengthening method for pier 18 ................................ ................................ ..................... 107 6.2 Stress strain relationship for CFRP rod ................................ ................................ ............ 108 6.3 Modeling of st eel plate ................................ ................................ ................................ ...... 109 6.4 CFRP rods connecting steel plates ................................ ................................ .................... 110 6.5 Model of pier 18 with CFRP rods ................................ ................................ ..................... 110 6.6 Stress in pier 18 in transverse direction under pre stressed CFRP rods ............................ 113 6.7 Stress at the test section in the transverse direction under pre stressed CFRP rods ......... 114 6.8 Cracking/crushing of concrete under two lane loaded case with 4 No. 8 pre stressed CFRP rods and an init i al strain of 0.007 ................................ ................................ ................................ 115 6.9 Cracking/crushing of concrete under two lane loaded case with 6 No. 8 pre stressed CFRP rods and an initial strain of 0.007 ................................ ................................ ................................ 116 6.10 Cracking/crush ing of concrete under two lane loaded case with 6 No. 8 pre stressed CFRP rods and an initial strain of 0.009 ................................ ................................ ................................ 117

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xvi 6.11 Pier 18 with refined brick meshing ................................ ................................ ................... 118 6.12 Distribution of 6 No. 8 CFRP rods for refined model of pier 18 ................................ ...... 119 6.13 Cracking/crushing of pier 18 under two lane loaded case refined model ......................... 120 6.14 Cracking/crushing at pier edge under two lane loaded case refined model ...................... 120 6.15 Cracking at bottom of pier wireframe view ................................ ................................ ...... 121 6.16 Stress in steel plate longitudinal direction (x component) ................................ ................ 122 6.17 Stress in steel plate vertical direction (y comp onent) ................................ ....................... 122 6.18 Stress in steel reinforcement for pier 18 strengthened with 6 No. 8 CFRP bars strained to 0.007 ................................ ................................ ................................ ................................ ............ 123 6.19 New CFRP strengthening method ................................ ................................ .................... 124 6.20 Cross sectional view of selected CFRP strengthening method ................................ ......... 124 6.21 Steel plates with 12 No. 4 CFRP rods ................................ ................................ ............... 125 6.22 Cracking on pier 18 strengthened with 12 No. 4 CFRP rods strained to 0.009 ................ 126 6.23 Cracking on pi er 18 strengthened with 12 No 4 CFRP rods strained to 0.0076 (considering all pre stress losses) ................................ ................................ ................................ ..................... 127 6.24 Distribution of No. 4 CFRP rods spaced at 4 inches ................................ ......................... 128 6.25 Extension of CFRP 2 inches past steel plate ................................ ................................ ..... 129 6.26 Near surface mounted CFRP rods ................................ ................................ ..................... 130 6.27 Example of NSM CFRP rods post tensioned to different level ................................ ........ 131

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1 C HAPTER I INTRODUCTION Overview West 8 th Avenue Viaduct was constructed in 1985 and is located in Denver, CO between Mariposa St (east end) and Tejon St (west end). The bridge measure s 2372 feet in length and crosses over light rails, railroads, a couple of streets and several parking lots (including one belonging to Denver Water and another belonging to Union P acific). It is a steel and concrete bridge with an 8.5 inch concrete deck supported over twin steel box girders. These girders run parallel to each other though for the first five spans starting from the east side of the bridge (abutment 1 to pier 6) the distance between them varies and th ere is a steel I girder centered between them with exterior diaphragms providing bracing between the I girder and the box girders. After Pier 6, the I girder stops and the distance between the box girders stays fi xed at 10 feet, while the only exterior dia phragms that brace the box girders are located directly above each pier, though there are still interior diaphragms inside each of the box girders. This superstructure is supported on 18 piers and 2 abutments with pot type bearings connecting the superstru cture to the substructure, with the exception of the bearings on pier 11 which are fixed. All pot bearings are oriented towards pier 11.

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2 Figure 1.1: Satellite view of West 8 th Avenue Viaduct Figure 1.2 : General l ayout of West 8 th Avenue Viaduct (City and County of Denver 1993, used with permission)

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3 Figure 1.3 : Side view of bridge at a horizontal curve Figure 1.4 : Side view of bridge at a straight portion

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4 Figure 1. 5 : Steel box girders with I girder in between (from abutment 1 pier 6) Fig ure 1.6 : Steel box girders (from pier 6 abutment 20)

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5 The bridge contains four horizontal and three vertical curves. It is these curves that are the root of the many problems occurring on the bridge, as when it was designed the effects of curvature were not considered and 8 th Avenue Viaduct was treated as a straight bridge. As such the transverse movement that occurred due to temperature effects was a lot greater than expected, resulting in the fracture of several guide bars for the bearings as well as t he grinding of multiple others against the base plates. To relieve some of the stress many guide bars were removed, changing the entire guide system of the bridge. Figure 1.7 : Guide bar of bearing removed t stop at the bearings. Diagona l and horizontal cracks have been observed on all the piers Several inspections have been performed on the piers over the years (most notably in 1998, 2008 and 2015) in order to measure the length of the cracks, and in each of these inspections the cracks were observed to have grown. While the bridge still remains safe to use the fact that year by year the cracks are continuing to expan d necessitates the rehabilitation of the bridge to prevent failure in the future.

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6 Figure 1.8 : Cracking on one of the pie rs As this thes is is on the substructure of the bridge the cracking of the piers will be the main focus. However, a study on the bearings can be found in a paper by Wang, 2015. The Substructure Figure 1.9 : Concrete Pier

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7 All the piers of 8 th Avenue Viadu ct are hammerhead piers. The piers vary in height from 17 feet at the ends to 38 feet closer to the middle. All the piers are 3 feet in thickness with the exception of pier 11, which is 7.5 feet thick. The width of the piers at the top is 30 feet for piers 6 19, though it varies for piers 2 5. A ll the piers are supported on 4 foot thick concrete foundations. The following Figure s display the dimension detailing of the piers (for more detailed info, see Appendix A) : Figure 1.10 : Piers 2 6 (City and County of Denver 2012, used with permission)

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8 Figure 1.11 : Piers 7 19 (City and County of Denver 2012, used with permission) The abutments, meanwhile, are L shaped. Their details are shown in the Figure s 1.11 and 1.12 (more detailed info is in appendix A): Fig ure 1.12 : Abutment 1 (City and County of Denver 2012, used with permission)

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9 Figure 1.13 : Abutment 20 (City and County of Denver 2012, used with permission) This paper will discuss the cause of cracks on the pier s and their continued expa nsion using both computer modeling and field measurements as well as propose solutions for the rehabilitation of the piers and the prevention of future crack expansion While the bulk of the 8 th Avenue Viaduct project was on modeling the bridge, it was also necessary to go out to the field, both to insta ll equipment that would give actual physical data could be use d to calibrate the model and to perform inspections on the piers, bearings and superstructure. Design Codes Material properties, applied loads and load factors w ill all be based on the AASHTO LRFD 2012 Bridge Design Specifications.

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10 CHAPTER II LITERATURE REVIEW Concrete Cracking Bridge engineering has seen a somewhat shift in focus from designing new bridges to rehabilitating old ones, due to the fact that brid ges are typically designed for a service life of 50 75 years, meaning many bridges around today have met or exceeded their expected life span (ASCE report card, 2009). Concrete cracking, spalling and rebar corrosion are the most common forms of deteriorat ion in old structures. Cracks are especially common as concr ete is weak in tension. While they are expect ed to occur (one of the basic assumptions when designing a structure is that concrete in tension will cr ack ) they nonetheless can reduce both the durab ility and capacity of the structure as well as allow water to leak into the structure (Kim et al. 2009) thereby leading to the corrosion of the steel rebar. Cracks have two stages: crack initiation, in which the cracks first form at the surface, and then c rack growth, in which they expand along both the surface and the depth of th e material (Schijve 2014). Their reasons as to why they might form, such as the type of material used, damage to the str ucture during construction or its service life and environmental factors, while the time of for mation of the cracks can give an idea as to what caused them (Kim et al. 2009). Cracks can be grouped into two types: central cracks and shear cracks ( Wang et al. 2013). The location, directions and density of the cracks provide important information as

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11 to the type of failure that has occurred (Yang et al. 2015) and as such several different techniques that offer more accurate and less labor intensive alternati ves to the traditional method of visual inspection have been proposed for crack detection (Abdel Qader I et al. 2003, Lee et al. 2013, Adhikari et al. 2014). There have also been a dvances in how to model cracks. In 1999, Bolander Jr and Le proposed a sprin g network model in order to predict how cracks would develop in reinforced concrete (Boolander Jr. and Le 1999) an approach based on energetic fracture mechanics for concrete (ACI committee 446, 1991) and a rigid body spring model developed by Kawai in th e late seventies (Kawai 1978) while much research has been done on using finite element modeling to an alyze cracks (Saatci and Vecchio 2009; Wang et al. 2013; Chen and Leung 2015). Concrete Crack Repair There are many different ways to repair cracked con crete. In a paper published in 2005 Thanoon and several others compared five different methods of concrete crack repair: cement grout, epoxy injection, applying a ferrocement layer, using carbon fiber reinforced polymer (CFRP) strips and enlarging the sec tion A ll these methods were used to repair similar cracked concrete slabs. The first three methods were found to give the cracked slab a similar strength to a non cracked slab, while section enlargement and CFRP actually made the cracked slab stronger (Th anoon et al. 2005 ) Because the purpose of this project again in the near future while enlarging the s ection would be very costly and require a significant amount of labor Therefore, in the case of this project, using FRP looks to be the best option for repair.

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12 Carbon Fiber Reinforced Polymers As the name implies, fiber reinforced polymers refers to polym ers that are reinforced with a matrix of numerous long thin fibers of various chemical origin oriented parallel to each other (Plewako, 2015). Fiber reinforced polymers are perhaps the most favored method of repairing reinforced concrete structures and f or good reason. They have a high strength but at the same time are light weight, have great durability, are relatively easy to install and resist corrosion (Clarke and Waldron 1996), though they also have a low fire safety (Verbruggen et al. 2014). The mos t common types of FRPs are c arbon fiber reinforced p olymers (CFRP), glass f iber reinfo rced polymers (GFRP) and aramid fiber reinforced polymers (AFRP). CFRP and AFRP are typically preferred to GFRP as they have better resistance to creep and alkaline envir onments (ACI 440.2R 08). This paper will be focused on CFRP as it typically has the highest tensile strength (ACI 440.4R 04). CFRPs can be applied onto the concrete in different ways. The most com mon is to use laminates or sheets, which can be bonded to th e concrete using epoxy resin, though the disadvantage of that is that de bonding failure can occur between the concrete and CFRP before the CFRP strips can even reach their full capacity (ACI 440.2R 08). As such, different types of CFRP anchors have been d eveloped that can overcome this problem and allow the CFRP sheets to reach their full strength (Kobayashi et al. 2001, Kim et al. 2014) Modeling of CFRP sheets bonded to concrete has also been done using various methods to simulate the interaction between them, such as non linear spring elements ( You et al. 2011; Sun and Ghannoum 2015), traction separation (Zidani et al. 2015) and even treating the

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13 de bonding failure that can occur between concrete and FRP as a dynamic rather than static problem and using time integration to solve it (Chen et al. 2015). Figure 2.1 : Application of FRP laminates ( ACI 440.2R 08 Fig. 11. 1 used with permission ) Due to issue of de bonding failure, another method to apply CFRP is by near surface mounting (NSM), where the CFRP is actually applied into a slot dug into the surface of the concrete (ACI 440.2R 08). This method has shown to give a much stronger bond between CFRP and concrete, better resistance to end peeling and improved fire safety, though in does require more effor t to carry out in the field (Tljsten 2002). As with CFRP laminates, there have been different finite element models developed to study the behavior of NSM CFRP, suc h as the one Almassri and others presented in a paper published in 2015, which used the FEM IX computer code to develop a model that could accurately reflect a reinforced concrete beam that was shear repaired with NSM CFRP rods (Almassri et al. 2015). The use of NSM CFRP rods has been shown to give favorable results over externally bonded CFRP la minates in both flexural and shear strengthening of RC members (De Lorenzis and Nanni 2001; El Hacha and Rizkalla 2004).

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14 Figure 2.2: FRP Systems ( ACI 440.2R 08 Fig 10.2 used with permission ) Aside from the advantages of hig her tensile strength and bet ter resistance to corrosion mentioned previously, CFRP rods differ from typical steel rods in that their surface is smooth and that the relationships between stress and strain is linear up until the point of failure (Benmokrane et al. 2000). Another differ ence is that unlike steel, CFRP rods can have a wide range of tensile strengths that c ould go up to 1000 ksi (though 1 50 500 ksi are the most commonly used), as well as significant variation in the modulus of elasticity, from 10 ,000 ksi to as high as 70,00 0 k si (fib Bulletin 55 and 56 2012). The biggest disadvantage in using exter nal FRPs is that it reduces the ductility of the member which could therefore lead to brittle failure (ACI 440.2R 08). One way to solve this proble m is to use CFRP rods embedded in the concrete, where instead of simply placing the rods in gr o oves in the concrete, the surface of the concrete is actually removed up to the level of the bottom reinforcement, where the CFRP rods are placed in between the steel reinforcement; the steel reinforcement is then sandblasted and the surface of the

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15 concrete is roughened and injected with epoxy before the new layer of concrete is cast, reducing the risk of brittle failure (Morsy et al. 2015). Th e increased load capacity achieved from embedding t he CFRP towards using CFRP rods in place of traditional steel reinforcement (Puigvert et al. 2014). Figure 2.3: Typical stress strain curve for CFRP The final method of repair using CFRPs is to use them as post tensioned rods anchored to the concrete (Burningham et al. 2014). Due to the smoothness of the surface of the CFRP rods there is a difficultly in clamping them down, which has led to the development of different kinds of anchorage systems These can be divided into two main types : bonded anchorage, in which a resin or epoxy is used to anchor the rod, and mechanical anchorage, which uses the friction created by compressing the inside surface of the anchor against the rod (Schmidt et al. 200 9, Schmidt et al. 2012). One of the most popular types of mechanical anchors are the unibody clamp anchors; several generations

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16 of these anchors have been developed, all of which use several bolts (number of bolts varies depending on generation) to clamp d own on the CFRP rod (Burningham et al. 2014). Tests have shown that concrete beams repaired with post tensioned CFRP rods show an increase in load capacity and significantly less deflection than similar beams that are in perfect RP rods (Burningham et al. 2015). Figure 2.4: Post tensioned CFRP rods (Hughes Brothers Inc 2011, used with permission)

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17 Figure 2.5: Mechanic a nchorage of CFRP rods (Hughes Brothers Inc 2011, used with permission) FRP Design Considerations For FRP ten dons the recommended stress level is between 40 65% of the ultimate strength (Dolan et. al. 2000). For CFRP, when jacking the tendons it is not advised to stress them more tha n the 65% limit of ultimate strength (ACI 440.4R 04 Table 3.3). When using FRP f or pre stressing, it is important to consider the pre stress losses from various factors, such as the anchorage seating at transfer of pre stress, the elastic shortening, creep and shrinkage of concrete, and the relaxation of the FRP tendons; these losses are calculated in a similar manner as for pre stressed steel, though they are usually smaller (ACI 440.4R 04). F or long term effects, both aramid and carbon fibers have shown strong resistance to creep (fib Bulletin 40, 2007). CFRP, in particular, was tes ted under various applied loads

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18 and through the use of creep rupture curves was found to retain 70% of its ultimate strength capacity for a service life of 100 year (ACI 440.4R 04) ANSYS Modeling of FRP strengthened concrete In recent years, several studi es have used ANSYS software in order to perform non linear finite element modeling of concrete st rengthened with FRP ( Hawileh 2012, Si Larbi et al. 2012; Al Rousan and Haddad 2013; Zidani et al. 2015). These studies all follow a similar procedure in model ing: Concrete will be modeled using SOLID65 element which allows for crack ing ; s teel reinforcement will b e modeled using LINK8 elements (or LINK180 in the more recent version s of ANSYS); f or FRP, it depends on what type is being used (e.g. rods or laminate s) but if FRP rods are being used then they can be modeled using LINK8 elements as well. If there is a bond between the FRP and concrete then it can be modeled using INTER205 interface elements to simulate the epoxy used for bonding. Cracking of the SOLID6 5 element in concrete follows the smeared crack approach, a method developed by Rashid in 1968 in in 1971 and 1972 in which a crack is smeared along a finite element of the material with the material having zero stiffness along the crack (Rashid 1968 ). This is in contrast to the discrete approach developed by Saouma and Ingraffea, which attempts to reflect in the model the discontinuities that would occur from a crack forming in the material (Saouma and Ingraffea 1981) Although the later method is more accurate, it is also much more time consuming as it would require the re meshing of the model every time a crack occurred, which is why in finite element modeling the smeared crack approach is preferr ed (Larbi et. al. 2013).

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19 Steel Corrosion As mentioned previously, cracking can also lead t o the corrosion o f steel rebar, which, like cracking, can lead to a loss of du rability in the structure ( Hobbs, 2001). Multiple studies have been made to study th e relationship between crack width and steel corrosion, using the width of the cracks to predict how much corrosion there is in the steel (Schiessl 1997; Mohammed et al 2001; Vidal et al 2004 ; Oteino et al. 2010; Berrocal 2015)

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20 CHAPTER III EQUIPMENT IN STALLATION AND FIELD INSPECTION Equipment Installation During the months of May and June, 2015, a team of four UC Denver graduate students (Yang Zhou, Samir Mizyed Wanting Wang and Juan Montenegro ) went out to 8 th Avenue Viaduct to install the following e quipment on the bridge: 1. Vibrating wire (VW) strain gages : These were used to measure both strain and temperature. T hese were installed on the steel box girders at two different locations: one directly above pier 14 and the other at the mid span between pie rs 16 and 17. 10 sensors were installed at each location. Their distribution along each section is shown in Figure 3.1 Due to the sensors heat ing up at a faster rate than the steel box girders it was necessary to cover all the sensors that could be expos ed to the sun. Figure 3.1: Distribution of strain gages and thermistors (stars represent strain gages, circles represent thermistors)

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21 Figure 3.2: VW strain gage 2. Thermistors : These measu re temperature only and were placed at th e same sections as the st rain sensors with 4 sensors per secti on: two at the bottom of the con crete deck close to the edges, one at south side of the concrete deck and one at the top of the north concrete barrier. As with the strain sensors it was necessary to cover the ones that would be in the sun. Figure 3.3: Thermistor

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22 3. LVDTs: there are three of these, all of which we re in stalled on abutment 20. O ne is a s pring sensor that can measure displacement up to 3 inches. Thi s was place d on the south side of the south box girder to mea sure its transverse movement. The other two are ultrasoni c displacement sensors and they can measure displacemen t up to 15 inches. These were placed at the back of the two box girders near their outer edge in order to measure the longitudinal movement of t he bridge Figure 3.4: LVDT 4. Temperature gage: used to measure the ambient air temperate. This was placed on top of the fence above abutment 20.

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23 Figure 3.5: Temperature gage 5. Uni axial tilt met er: used to measure rotation. This was installed this on the south side of the concrete deck above abutment 20. Figure 3.6: Uni axial tilt meter 6. Bi axial tilt meters: simi lar to the uni axial tilt meter, only they can be oriented in two directions. There are two of these both of which we re installed

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24 at the top o f pier 11 (the fixed pier) in order to measure the rotation in both directions. Figure 3.7: Bi axial tilt meter 7. Multiplexers: all the strain gages and thermistors were connected to a multiplexer at each of the two locations where the gages were installed These multiplexers we re connected with each other, while the west multiplexer (the one at mid span between pier 16 and 17) was also connected to the data logger.

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25 Figure 3.8: Multiplexer 8. Data l ogger: All of the data the above mentioned equipment collect ed was sent to the data logger, which was installed on abutment 20 and is powered by an external b attery. Using a USB cable the data could then be transferred to a regular laptop This was done every week or so Figure 3.9: Data l ogger

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26 9. Solar p anel: wa s installed near abutment 20 in order to charge the battery that powered the entire system Figure 3.10: Solar p anel The most important equipment for this dissertation are the bi axial tilt meters as they are the only devices that measure the movement o f the substructure rather than the superstructure. The system first started running on June 19 th 2015, though the tilt properly calibrated until the 27 th of the same month. Since then several months of dat a have been collected from the bi axial tilt meters, a small port ion of which is represented in Table 3.1.

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27 Table 3.1: Readings from bi axial tilt meters on pier 11 TIMESTAMP RECORD P11_Rot1_ Delta_Min P11_Rot2_ Delta_Min P11_Rot1_ temp_Min P11_Rot2_ temp_Min P11_Rot1_ Delta_Max P11_Rot2_ Delta_Max P11_Rot1_ temp_Max P11_Rot2_ temp _Max P11_Rot1_ Delta_Avg P11_Rot2_ Delta_Avg TS RN Deg_F Deg_F Deg_F Deg_F Min Min Min Min Max Max Max Max Avg Avg 6/27/2015 13:00 214 0.01 0.004 78.87 78.96 0.001 0.005 81.2 81.3 0.005 0.001 6/27/2015 14:00 215 0.015 0.007 81.2 81 .3 0.001 0.007 83.1 83.1 0.007 0.001 6/27/2015 15:00 216 0.019 0.004 82.9 83 0.002 0.005 84.6 84.7 0.008 0 6/27/2015 16:00 217 0.017 0.012 84.2 84.5 0.012 0.01 85.3 85.4 0.008 0.001 6/27/2015 17:00 218 0.022 0.004 84.8 85 0.005 0.003 85.7 85 .8 0.009 0.001 6/27/2015 18:00 219 0.022 0.009 84.1 84.3 0.009 0.003 85.7 85.9 0.008 0 6/27/2015 19:00 220 0.01 0.004 83.1 83.4 0.003 0.005 83.9 84.2 0.007 0.001 6/27/2015 20:00 221 0.022 0.001 82.1 82.4 0.004 0.01 83.2 83.4 0.007 0.002 6/ 27/2015 21:00 222 0.018 0 80.6 80.9 0.001 0.009 82.1 82.4 0.006 0.003 6/27/2015 22:00 223 0.009 0.001 80.1 80.4 0.003 0.006 80.6 80.9 0.005 0.003 6/27/2015 23:00 224 0.013 0.004 76.59 76.81 0 0.007 80.1 80.4 0.004 0.004 6/28/2015 0:00 225 0.0 02 0.005 74.36 74.56 0.009 0.014 76.49 76.69 0 0.007 6/28/2015 1:00 226 0.008 0.005 73.42 73.76 0.006 0.014 74.6 74.8 0.002 0.007 6/28/2015 2:00 227 0.001 0.005 71.86 72.18 0.004 0.01 73.28 73.61 0.003 0.008 6/28/2015 3:00 228 0.001 0.005 70.15 70.37 0.009 0.01 72.16 72.33 0.003 0.007 6/28/2015 4:00 229 0.003 0.007 69.41 69.53 0.006 0.009 70.06 70.28 0.005 0.008 6/28/2015 5:00 230 0 0.006 67.99 68.15 0.007 0.011 69.83 69.98 0.005 0.007 6/28/2015 6:00 231 0.005 0.005 67.5 67.67 0.007 0.009 68.06 68.2 5 0.006 0.007 6/28/2015 7:00 232 0.005 0.004 67.15 67.27 0.007 0.009 68.26 68.32 0.006 0.007 6/28/2015 8:00 233 0 0.001 68.12 68.31 0.007 0.008 71.34 71.54 0.004 0.005 6/28/2015 9:00 234 0.008 0.002 71.44 71.58 0.003 0.012 74.03 74.2 0.001 0.003 6/28 /2015 10:00 235 0.004 0.017 73.88 74.08 0.004 0.006 75.38 75.51 0 0.003

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28 In the table P11_Rot1 represents the bi axial tilt meter measuring the rotation in the longitudinal direction of the bridge, while P11_Rot2 is for the bi axial tilt measuring the rotation in the transverse direction. The rotation (Delta) is measured in degree s The bi axial tilt meters also measure the temperature (temp), whose units are in Fahrenheit. Both tilt meters take a rea ding every 90 seconds. This results in a massive amount of raw data. Fortunately, the data logger also records the max imum and min imum values measured from both tilt meters for both the temperature and rotation, which is the data represented in Table 3.1 ( for a time period spanning 22 hours from 13:00 June 27 th 2015 to 10:00 June 28 th 2015). To make sure that the devices were recording values properly, the temperature values were compared with the air temperature recorded at the same time and found to giv e similar results. The positive and negative signs for the rotational values represent the direction of movement of the pier, with positive being clockwise and negative being counterclockwise (measured from someone standing south of the pier for the longi tudinal rotation and west of the pi er for the transverse rotation). In general the tilt meter in the longitudinal direction recorded larger values than the tilt meter in the transverse direction which makes sense as more movement in the longitudinal direct ion is expected As of the writing of this paper, the max rotation measured in the longitudina l direction was recorded as 0.089 1 degrees, while the max value in the transverse direction was recorder as 0.043 degrees. Both tilt meters were placed a foot be low the top of the pier, which is approximately 28.5 feet high at the mid portion between the two girders where the tilt meters are located. The displacement can therefore be calculated as follow:

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29 Displacement = height sin(rotational angle) Displacement in longitudinal dir ection = (28.5 ) sin(0.089 ) = 0.0443 ft Displacemen t in transverse direction = 28 .5 sin(0.043) = 0. 0214 ft These readings from the tilt meters are the exception though, as most of the time the rotation in both direction s is less than 0.01 degrees. Because the displacement of Pi er 11 is generally very small it can simply be assumed that it is fixed This is very important for the modeling o f the bridge as it means only half the bridge needs to be modeled at a time Pier Inspection Nea r the end of July, beginning of August, 2015, a two man team of Yang Zhou and Samir Mizyed performed a pier by pier inspection of 8 th Avenue Viaduct. This was done on the following dates: Tuesday (July 28 th ), Thursday (July 30 th ) and Sunday (August 2 nd ). T he objective of the inspection was to measure the cracks on the piers to see how much they had expanded since previ ous inspections ( the condition of the bearings and superstructure above each of the piers was also checked). A ll of the piers were inspected with the exception of piers 3 and 10 due to the former being in between two light rail tracks and the latter being on a median between two single lane one way streets givi ng nowhere to pa rk the bucket lift truck that was used for the inspection. Of the p iers inspected, several different kinds of cracks were observed The most common were the vertical cracks (due to flexure) at the top of the piers towards the middle. These were also the longest of the cracks with most of the cracks on the chamfer lines of the piers (see Figure 3.18) extending all the way down to the bottom, though cracks at other

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30 locations would range f rom a couple inches to 9 or 10 fee t in length. These cracks extended from one face of the pier to the other and would start off widest at t he top (reaching up to a 1/16 of an inch in thickness) before turning into hairline cracks as they went down. Als o at the top of the piers there were diagonal cra cks (due to shear ), though these were close r to the edges. These diagonal cracks could reach u p to several feet in length and like the vertical cracks, they extended from one face of the pi er to the other. Finally, there were horizontal cracks at the bottom of a number of the piers particularly those closer to the edge of bridge (such as piers 16 18 ). Unlike the vertical and diagonal cracks, these were always hairline cracks, though many of them would wrap around the base of the pier. Figure 3.11: Vertical and diagonal cracks

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31 Figure 3.12: Horizontal cracks at base of pier Figure 3.1 3 : Hairlin e crack s Figure

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32 Figure 3.15 : Crack extending from face to face of pier While some of the cracks had remained dormant over the years, most of them were still active and had expanded anywhere from 1 or 2 inches to several feet sin ce previous in spections. Because the rate of expansion could vary significantly from one crack to the next on the very same pier it was difficult to make out a pattern though in general the farther away the pier was from pier 11, the faster the rate of ex pansion was. The exceptions were the very end piers (2 and 19), whe significantly since 1998. This is likely due to a couple of reason s F irst of all, pier s 2 and 19 had two guide bars removed from the bear ings above them, unlike all the other piers, which had only one guide bar removed (the southern guide bar of the northern interior bearing, GW 4). This may have relieved a significant amount of the stress being transferred from the superstructure through th e bearings to the piers. An attempt to confirm this will be done in the next chapter by comparing the stress transferred to pier 19 for two cases: with all guide bars present and removing the two that are missing. Another possible reason

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33 is that piers 2 an d 19 are also by far the shortest of the piers, making them more s t able than the others. Figure 3.16 : Dormant crack Figure 3.17 : Active crack Out of all the piers, pier 18 was the one where the cracks had expanded the most. Figure s 3.18 3.21 display the cracks on all fo u r faces of that pier, while Table s 3.2 3.5

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34 list the length and thickness of each crack as measured in 1998 and how much t hey have expanded since then (note: a hairline crack refers to any crack that has a thickness less than 0.01 in ch). Figure 3.18: Crack ing o n pier 18 west face

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35 Table 3.2 : Length and thickness of cracks on pier 18 west face Crack # Length 1998 Expansion 2015 Maximum Size 2 4' 11" None 0.020" 3 0' 6 1/2 None 0.016" 4 0' 5 1/2 2" 0.02 0" 5 1' 4" 8" 0.016" 6 1' 7" 7" 0.016" 7 5' 0" 16" 0.016" 8 7' 0" All the way to the bottom (chamfer line) hairline 10 4' 3" 20" 0.016" 11 4' 7 1/2 5" hairline 12 4' 2" 9" 0.016" 13 1' 4" 2" 0.020" 14 0' 8" None hairline 15 2' 5 1/2 2" hairline 15A 0' 4" None hairline 16 (6A) 3' 9" 8" hairline 17 (6B) 2' 5" 3" hairline 18 (7A) 3' 1" 6" hairline 19 (9A) 2' 2" 8" hairline 20 (9B) 3' 1" All the way to the bottom (chamfer line) hairline 21 (10B) 0' 11" 3" hai rline 22 (11A) 1' 3" 8" hairline 23 (13B) 2' 10" None hairline 24 (14A) 3' 5" 4" hairline 25 2' 0" None hairline 26 1' 2" None hairline 27 9' 0" None hairline

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36 Figure 3.19: Cracking on pier 18 north face Table 3.3 : Length and thickness of cracks on pier 18 north face Crack # Length 1998 Expansion 2015 Maximum Size 1 Pier Width None hairline 2 0' 8" None hairline 3 1' 0" None hairline 4 1' 4" None hairline 5 0' 10" 8" hairline 6 0' 11" 7" hairline 7 1' 3" None hairli ne 8 Pier Width None hairline

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37 Figure 3.20: Cracking on pier 18 east face Table 3.4 : Length and th ickness of cracks on pier 18 eas t face Crack # Length Maximum Size 3 4' 4" 0.016" 4 1' 1 1/2 H airline 4A 1' 3 1/2 H airline 5 3' 9 1/2 H ai rline 6 2' 2" H airline 7 5' 4" H airline 7A 2' 5" H airline 7B 7' 10" H airline 8 3' 2" H airline 9 0' 3" H airline 10 2' 6" H airline 11 1' 9 1/2 H airline 12 3' 4" H airline 13 0' 3" H airline 17 Pier Width H airline 18 Pier Width H airline 19 Pier Width H airline 20 Pier Width H airline 21 Pier Width H airline 22 Pier Width H airline 23 Pier Width H airline 24 Pier Width H airline

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38 Figure 3.21: Cracking on pier 18 south face Table 3. 5 : Length and thickness of cracks on pier 18 sou th face Crack # Length Maximum Size 1 Pier Width H airline 2 2' 9" H airline 3 Pier Width H airline 4 Pier Width H airline 5 0' 9" H airline 6 Pier Width H airline Due to the amount of expansion seen in the cracks on Pier 18, it will be taken as the critical pier and the focus of much of the modeling that is dis cussed in the following chapter s

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39 CHAPTER IV GENERAL MODEL Program U sed and Model Components Due to the complexity of the bridge, a 3D model was necessary to reflect the behavior of the bridge as accurately as possible. For this, the computer modeling pr ogram ANSYS Mechanical APDL 16.0 was used. The program was selected because not only did it have the capacity to run such a massive model with a total number of elements exceeding half a m illion, but also because of its high accuracy and user friendly interface, which allows a person to write commands in code on any program, such as Microsoft Word and then copy and paste those commands onto ANSYS. It is important to note that only half of t he bridge was modeled (from pier 11 abutment 20). The reason for that is because the main pier that is going to be analyzed is pier 18 (with some analysis being done on pier 19 as well) and as the field data proved that there is very little movement on P ier 11, it would be easier to simply take that pier as fixed, especially because convergence of the solution is an important issue for a large complex model and anything that can get the model to converge easier and faster will be taken into account. The general modeling for 8 th Avenue Viaduct was d one as a group effort by Yang Zhou Wanting Wang and Samir Mizyed.

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40 Different types of elements were used to model the different components of the bridge, which are as follows: 1) Foundation: Because the main con cern here is structural, the interaction between the bridge and the soil was neglected and the foundations were modeled as fixed supports. 2) Piers and Abutments: These were modeled with 3D solid tetrahedral elements. Figure 4.1: Pier

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41 Figure 4.2: Abutmen t 3) Bearings: The base plate, top plat e and guide bars were modeled with 3D solid elements, while contact elements were used to model the interaction between the top and bottom plates, as well as the guide bars and base plate. Figure 4.3 : Unguided bearing

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42 Figure 4.4 : Guided bearing Figure 4.5 : Bearings on top of pier 4) Girders: These were modeled using 2D shell elements, while the diaphragms bracin g them were modeled as 1D beam elements which were also use d for the diagonal bracing while the stiffeners on the sides o f the girders were modeled with 2D shell elements.

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43 Figure 4.6 : Girders with diaphragms, diagonal bracing and stiffeners 5) Deck: Modeled with 2D shell elements. Figure 4.7 : Deck

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44 Figure 4.8 : Span between two piers 6) Expansion Joints: Linear s pring elements were used to model their behavior. The stiffness of each spring was calculated based on the stiffness of the expansion joint (which was assumed to be linear) divided by the number of springs used to repr esent said joint. T he expansion joint at abutment 20 has a stiffness of 12 .68 kips/ft which translates to 152160 Ibs/ft. 31 springs were used to model the joint ; there fore, the stiffness of each spring was 152160/31 = 4908.4 Ibs/ft.

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45 Figure 4.9 : Springs used to model the expansion joint at ab utment 20 T wo different types of materials were used : concrete for the piers, abutments and deck; steel for the beari ngs and girders. For concrete a unit weight of 150 l bs/ft 3 ratio of 0.2 and a modulus of elasticity of 5.25 10 8 l bs/ft 2 were d efined. For steel, the defined values were: a unit weight of 490 lbs/ft 3 and a modulus of elasticity of 4.176 10 9 l bs/ft 2 (note: because the re are no units in ANSYS, it was critical to make sure that all the values were inputted w ith the same unit s of measurement for length and weight, which here were feet and pounds respectively) Both steel and concrete were given a reference temperature of 70 degrees Fahrenheit (again, it was important to make sure that all subsequent temperatur e values would be in Fahrenheit) with a ther mal expansion coefficient of 6 10 6 for steel and 5.5 10 6 for concrete. Geometry It is standard practice in s tructural engineering to design based o n following the load path. For the viaduct, the loads get trans ferred from the superstructure to the beari ngs to the substructure; therefore, the design should start with the superstructure. However,

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46 when the project for 8 th Avenue fi rst started the bearing detailing has yet to be secured Therefore, the substructure and the superstructure were designed separately and then when the bearing details became available they were used to connect the two together. The first thing needed in building the model was reference points from which to build the piers, abutments, girde rs, etc. For the piers and abutments a point centered at the base was selected as the referen ce point for each pier or abutment and using the as built bridge plans the x, y and z coordinates of this point were found (in the global coordinate system, x repr esents east (+) /west ( ) z represents north ( ) /south (+) and y represents the elevation while the zero point of global coordinate system was at the east start ing point of the bridge with a reference elevation of 5200 ft). From each of these reference points the corresponding pier or abutment was drawn. Similarly for the girders a reference point was established at the center of the two box girders at the elevation of the top flange. A refer ence point was needed at every location where there was a stiffener or diaphragm in the girder. Due to the large number of stiffeners in the box girders a total of almost 4 00 reference points between pier 11 and abutment 20 had to be establish ed. Their coordinates were determined based on the vertical and horizontal profil e lines of the bridge. These reference points were used to draw the superstructure (including the deck above the girders) in segments, which were then merged together (although much of the bridge was curved, these segments we re all drawn straight, but beca use they were so small ranging from 1.75 6 ft the error was negligible). For the bearings, a reference point for each bearing was set up at the top of the piers, from which the base plate, top plate and guide bars were drawn. Because all the bearings a re oriented towards pier 11 the local coordinate system for each bearing reference point

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47 had to be oriented in that direction. The top plate was then merged with the bottom of the girders The contact between the base plate and top plate/guide bars was mo deled using standard contact surface elements, allowing for b oth penetration and separation with a friction coefficient of 0.08. Loads The loads applied on the structure were dead, live and tem perature. Dead Load This includes the own we ight of the structu re (because the materials were defined as density rather than mass, the acceleration was inputted either as 1 when checking the normal capacity of th e structure or 1.25 when considering the LRFD factors for ultimate state design) as well as loads from non structural components which are as follows : The asphalt wearing surface: 48 psf. T he concrete sidewalk : There is one sidewalk on the south side of the road which was assumed a s 10 inches thick so the load from the sidewalk will be equa l to 10/12 150 = 125 psf. T he concrete barriers : There are two concrete barriers on either side of the road, each of which was take n as 640 l bs/ft. A pply width translates to an area load of 640/1.25 = 512 psf. Guard Rail: At the edge of the sidewalk there is a guard rail that is estim ate as 300 l 12/8 = 450 psf.

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48 Live Load An HL 93 load was applied following the AASHTO design code which is comprised of a lane load of 640 lb s/ft distributed over a width of 10 f ee t and an HS 20 design truck, whi ch is 6 f ee t wide and has 6 axles: the two in th e front carry a load of 4000 pounds each and the four in the back carry a load of 16000 pounds each ( the spans are long so the design tr uck will control and not the design tandem). The spacing between the first and second pair of axles is 14 f eet and the spacing between the second and third pair ranges from 14 30 f ee t (AASTHO LRFD 2012 Bridge Design Specifications 3.6.1.2.2 1 ). Applying th e live load was the hardest of all the loads due to it being a moving load. All cases that would generate the maximum moment on the spans or the maximum reaction force on the piers had to be considered. These cases were determined using the influence line theory. The influence line is based on drawing the moment, shear or deflection diagram of a certain point resulting from a unit point load applied at various locations For example, if one of the spans of the bridge (span l ength is typically 127 feet) was assumed as simply supported and non continuous then the influence line for the moment at the mid point of the span as shown in Figure 4.10 can be drawn based on simple static analysis. If a unit load of 1 kip in placed at the center of the span the moment at that point will be PL/4 = 1*12 7 /4 = 3 1.75 kip ft. If the unit load is place d at either ends of the span the moment a t the center will be zero. Connecting these three points gives the influence line for the moment, which will be a triangle with a max imu m value at the center (31.75 kips ft). Therefore if a point load from the HS 20 truck of 32 kips was applied 14 f ee t from the center of the span the n the moment value at t he center of the span will be: 24 7 5 kips ft

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49 (the value obtained from the influence line) 32 (ratio between the load a pplied and the unit lo ad) = 792 kips ft. If a uniformly distributed lane load of 0 .64 kips/ft was applied along the entire length of the span then the moment at the center will be: 2016.125 kips ft (area under the influe nce line = 0.5 127 31.75) 0 .64 = 129 0 .32 kips ft. Figure 4.10 : Bridge span assuming simple supports and non continuity Figure 4.11 : Moment i nfluence line for simply supported single span at mid span This is an extremely simplified scenario though tha t bridge For an indeterminate structure thing s are more complex. However, while drawing an exact influence line is difficult its shape can still be predicted based on how the structure is expected to deform under a load. Fo r simplicity, the bridge can be taken as a 19 continuous s pan stru cture. As it is expect ed that the max moment for each span will occur som ewhere in the middle, the influence line for the mid point of each span must be determined.

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50 As shown in Figure 4.13 apply ing a load on a certain span that will cause the entire span to deflect downwards. Therefore the moment generated wil l be positive. However, a pply ing a load on an adjacent span causes the span being analyzed to deflect upwards, therefore the moment g enerated from any load on an adjacent span will be negative. Therefore, usin g the deflected shapes the influence line for the mid p oint of the span under analysis should be simil ar to the deflection curve shown in Figure 4.13 Figure 4.12 : Continuous spa ns under a concentrated load Figure 4.13 : Deformation of continuous spans due to applied load Usi ng the influence line, the max imum moment that can oc cur at any mid span point on the bridge will occur when applying the lane load on that span and every ot her span from it while placing the truck at the cent er of the span. Figure 4.14 : Live load distribution to generate max moment at a certain span

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51 T he max reaction can be obtained base d it on where a load will generate a downwards or upwards pressure on th e support (pier) If a load is applied on the adjacent spans to a certain support, then it cause s a downwards pressure on that support but if it is applied on the span s on either side after the adjacent ones, then that will result in an uplift pressure on the support. Based on thi s, the max reaction on a pier will be when the truck is directly above the pier and the land load is applie d to the adjacent spans and every other span from them. Figure 4.15 : Live load distribution to generate max reaction at a certain pier As there are 19 spans and 20 supp orts (2 abutments + 18 piers) that means there are a total of 39 different load cases that would have to be applied if the entire bridge was being analyzed the other However, not only is half the bridge being modeled but the focus of this paper is only on two piers (piers 18 and 19). T herefore, only cases that will result in maximum stress on those piers will be considered These cases include loading to ge nerate maximum moment (e.g. placing the truck in the middle of the span), loading to generate to max reaction (e.g. placing the truck directly on the pier), loading the south lane only, loading the north lane only and loading both lanes. One way to do so w ould be to apply these cases at different times while keeping the Analysis Type Static to ignore dynamic effects After running the model one can then move through the different times while keeping track of which time corresponds to which

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52 load case. Howeve r, as running so many diff erent load cases on such a complex model takes hours or days to compl ete it would be easier to simply run one load case at a time. When applying the live load all the factors specified in the AASHTO LRFD Bridge Design Specifica ti on much be considered, including the load factor (for ultimate state design), the dynamic impact factor a nd the multiple presence factor (AASHTO LRFD 2012 Bridge Design Specifications 3.6 ). Temperature Load This will be applied to the south side of the southern steel box gird er (the side that gets sunlight) and the concrete deck on top While for more complex temperature analysis various values would have to be applied to see how the bridge behaves under temperat ure cycles for now the applied tem perature will be a fixed vale of 120 o F. Figure 4.16 : Application of temperature on south side of steel girders

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53 Load Combinations In the design, 8 th Avenue Viaduct is taken as a bridge for basic vehicular use without wind load. Therefore, b ased on the AA SHTO LRFD 2012 Bridge Design S pecifications the ultimate loading capacity will be based on the Strength I limit state (AASHTO LRFD 2012 Bridge Des ign Specifications 3.4.1), which uses the following load combination: U = 1.25DL + 1.5DW + 1.75LL + 0.5/1.2 T (From AASHTO 2012 LRFD Bridge Design Specifications Table 3.4.1 1) As load combinations the loads will be applied with their factors Therefore all the dead loads mentioned previously will be multiplied by 1.25 with the excpeti on of the wearing surface and utilities which will be factored by 1.5, and all live loads will be factored by 1.75 when designing for Strength I Limit State (for service limit state loads will be un factored). Analysis Check of Results First off, it is im portant to check and make sure that the results from ANSYS make sense. Hand calculations can be used to check the reactions on an y of the piers by assuming that each one will take half the load o f the span on each side. Pier 16 will be used as an example. Based on all of the components of the bridge (both structural and non structural) the total reaction from the superimposed dead load (SDL) can be calculated as shown in Table 4.1

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54 Table 4.1: Superimposed dead load on Pier 16 Concrete Component Thickness (ft) Width (ft) Weight Unit Total weight (Ibs/ft) Total weight (kips/ft) Deck 0.7083 40.1667 150 pcf 4267.7083 4.2677 Sidewalk 0.8333 6.8333 150 pcf 854.166 7 0.8542 Wearing surface 30 48 psf 1440 1.44 Fence 0.6667 600 psf 400 0.4 # of barriers Barrier 2 640 Ibs/ft 1280 1.28 Steel Component Thickness (ft) Width (ft) # of components Density (pcf) Total weight (Ibs/ft) Total weight (kips/ft) Top flange 0.1094 1.3333 4 490 285.8333 0.2858 Web 0.02604 4.25 4 490 216.9271 0.2169 Bottom flange 0.02604 10 2 490 255.2083 0.2552 Sum 8.9998 This means that each foot of span length weighs approximately 9 kips. Pier 16 is between spans 15 and 16, each of which is 127 feet long. Therefore, the total sp an length that will be carried by Pier 16 will be (127+127)/2 = 127 f ee t, from which the total superimposed dead load transferred to Pier 16 can be calculated as follows: SDL = span length weight per ft = 127 9 = 1143 kips T he own weight of th e pier must also be considered In ANSYS the pier dimensions were simplified as show n in Figure 4.17

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55 Figure 4.17 : Dimensions of pie 16 (simplified) The thickness of the pier is constant at 3 feet. Therefore, the total volume of the pier can be calculate d as: Volume #3 (volume of a 30ft30.82ft3ft rectangular solid) Volume #2 Volume #1. The weight will be the volume multiplied by the density of the concrete (150 pcf). The resu lts are summarized in Table 4.2.

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56 Table 4.2: Self Weight of Pier 16 Volu me # Height (ft) Width (ft) Thickness (ft) Density (pcf) Weight (Ibs) Weight (kips) 1 17.323 10.5 3 150 163701.56 2 10.5 10.5 3 150 38965.566 3 30.823 30 3 150 416109.38 Total weight 213442.25 213.442 The total un factored dead load tr ansferred to Pier 16 will be the summation of the superimposed dead load and the self weight of the pier: DL = SDL + SW = 1143 + 213.4 = 1356.4 kips From ANSYS the total reaction at the bottom of pier 16 from the un factored dead load was 0.13508E + 0 7 pound s which translates to 1350.8 kip s. This is very close to the values calculated by hand. The next check will be for the live load. Theoretically, the case that will generate the maximum live load on Pier 16 will be w hen both lanes are fully loaded a nd the distribution is as shown in Figure 4.18 Figure 4.18 : Live load distribution to generate max reaction at pier 11

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57 T he multiple presence factor, which depends on the number of lanes loaded must also be considered. This can be obtain ed from the AAS HTO LRFD 2012 Bridge Design Specification s 3.6.1.1.2 Because the check here is for two lane loaded case the multiple presence factor will be 1, though for other cases when only one lane was loaded (either the north or south lane) the multiple presence fa ctor will be 1.2 (AASHTO LRFD 2012 Bridge Design Specification s Table 3.6.1.1.2 1) Th e truck must also be increased by a dynamic load allowance factor (IM) which AASHTO specifies as follows: IM = 33% (AASTHO LR FD 2012 Bridge Design Specification Table 3.6 .2.1 1) The un factored live load from the trucks and lane loads (HL 93) transferred to Pier 16 will therefore be as follows: Live load from HL 93 = ((T ruck L oad (1+IM ) + L ane L oad span length) #of lanes m = ((32 + 32113/127 + 8113/127) 1.33 + 0.64 127) 2 1 = 344.9 kips T he pedestrian load must also be taken into account which based on AASHTO speci fications will be take n as 75 psf (AASHTO LRFD 2012 Bridge Design Specification s 3.6.1.6). The sidewalk i th erefore, the load transferred to pie r 16 from the pedestrian load can be calculated as follows: Pedestrian load = 75psf sidewalk width span length = 75 /1000 (6+10/12) 127 = 65.1 kips

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58 The total un factored live load transferred to pier 16 will be the summation of the HL 93 load and the pedestrian load: LL = HL 93 + PL = 344.9 + 65.1 = 410 kips From ANSYS the total reaction at the bottom of pier 16 from the un factored live loa d was 0.46647E+06 which t ranslates to 466.47 kips. This is hig her then what was calculated by hand but because live load is a moving load it was unrealistic to expect to get the sa me level of accuracy as with the de ad load. Therefore, a greater percentage of error will be allowed The final load to check for is temperature. Theoretically, the displacement on a point should be the longitudinal distance of that point from the fixed point of the bridge (pier 11) multiplied by the coefficient of thermal expansion multiplied by the diff erence between the applied temperature and the r T R )). However, the temperature was only applied on part of the model (the southern side of the south steel box girder and the concrete deck ), while there are also springs at the ends to resist expansion. Therefore, in order to c heck the results the conditions of the model will be changed so that the temperature of 120 degrees is applied to all components of the bridge Also, the check will be performed by running the code for the five spans east of pie r 11 (this part is spec ific for the temperature check, the rest of the analysis will only be for the spans west of pier 11) stopping just befor e pier 6, as the spans between p ier 6 and 11 are all of the sa me length (127 feet), while the bridge is straight near p ier 6 running alm ost parallel to the east west direction At this section, rather than connecting the girders to pier

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59 6, springs in the vertical and transverse directions of the bridge will be used instead at this end to keep th e structure s t able while at the same time all owing for free unrestrained movement in the longitudinal direction (the stiffness of the springs in the transverse direction will be the same as the stiffness of the springs at abutment 20; a stiffness 10 times higher will be applied to the vertical s pring s). The reason springs were used instead of merely fixing the section in the vertical and transverse directions is beca use all of the contact areas defined for the bearings result in a model that takes many iterations to converge and may not converge at al l if the boundary conditions are too rigid. Therefore, it is best to keep the model as flexible as possible. With these new conditions defined the model is solved and the displacement at the section near pier 6 is checked The resu lts are displayed in Figu re 4.19 Figure 4.19 : Displacement in the longitudinal direction at a section close to pier 6

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60 Based on the results from the Figure the girders moved 0.183 feet in the longitudinal direction away from Pier 11. This result can be verified with hand calcul ations: T R ) = (5127) (610 6 ) (120 70) = 0.1905 ft This value is very close to what ANSYS gave, which means that the model is working properly. Impact of Guide Bar Removal ed the next step is to see what impact the bearing system has on the piers. Even though this paper is on pier rehabilitation, the bearings also need repair and any change done to them could have a major impact on the stress transferred to the piers, whethe r positive or negative. While initially the model was built reflecting the bridge as it w as designed, the current conditions of the bridge must now be taken into account As mentioned in chapter I several guide bars on the bearing were removed to relieve some of the stress on the piers. These guide bars were as follows: The south guide bar of the northern interior bearing (GW4) for all the piers and abutments. The south guide bar of the southern interior bearing (GW2 ) for pier 2 and both abutments. The nor th guide bar of the southern interior bearing (GW2) for pier 19. In the model these guide bars the contact area between them and the baseplates are removed.

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61 First, the stress on pier 19 with all guide bars present under an applied temperature of 120 degrees Fahrenheit on the concrete deck and south side of the south steel box girder will be checked For the case of both lanes loaded and the trucks placed directly above the pier, t he resulting stress es in the longitudinal an d transverse direction s are shown in Figure s 4.20 4.21 Figure 4.20 : Stress in longitudinal direction on pier 19 with all guide bars present

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62 Figure 4.21 : Stress in transverse direction on pier 19 with all guide bars present Based on the results in the f igure s and ignoring a few small elements with uneven mesh that resulted in some stress concentration the maximum tensile stresses were: 124 000 psf in t he longitudinal direction (0.861 ksi) and 210 000 psf at center top part of the pier, which is 1.458 k si. B oth the normal longitudinal and tr ansverse tensile stress es are well above the tensile stre ngth of concrete (0.4 ksi), which means that there will be both vertical cracks at the top of the pier and horizontal cracks at the bottom The max compressive stress es meanwhile were found to be : 314 850 psf in the longitudinal direction ( 2.186 ksi) at the bottom of the pier on the opp o site side to the max tension and 144 000 psf in the transverse direction ( 1 ksi) at the bottom of the hammer head portion of the piers Again, a few smaller elements with uneven meshing were ignored C oncrete has a compressive strength of 4 ksi so it is safe from crushing

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63 Next we the model is solved taking into consideration all the guide bars that were removed. The resulting stress es in the longitudinal and transverse direction s from the same loading case (both lanes load ed temperature applied to deck an d south side of south girder) are shown in Figure 4.22 4.23 Figure 4.22 : Stress in longitudinal direction on pier 19 wit h guide bars removed

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64 Figure 4.23 : Stress in transverse direction on pier 19 with guide bars removed As observed in the f igure s t he max tensile stresses remain at the same locations for the longitudinal and transverse directions; however the values reduc ed in both cases to 65 100 psf (0.452 ksi) in the longitudinal direction and 175 000 psf (1.215 ksi) in the transverse when all the guide bar s were present. Also, while the reaction at the bottom of the pier in the vertical direction stayed the same the reactions in the transverse and longitudinal directions decreased when the guide bars were removed. Although more temperature cases would have to be checked and a finer model with more uniform meshing of the pier would need to be constructed to get more accuracy based on the results obtained from this case removing the guide bars helped relieve some of the stress on pier 19, which could explain why the rate of crack expansio n on pier 19 has slowed down in recent years.

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65 Therefore, from the results of both the model and the field inspection of the piers a more flexible bearing system is recommended to reduce the stress transferred to the piers. Temperature E ffect Based on the pier inspection performed, the stress es on the piers towards the ends of the viaduct should be higher than the stresses on the piers near pier 11. Because the fro m pier to pier the difference in pier stresses should mainly come from the temperature load. To prove that, a model with only the temperature loading case will be analyzed As expected, under temperature alone the stress increases the farth er away the p ier is from the fixed pier, which explains why the piers closest to the edges had the most cracks. A comparison between a pier close to pier 11 (pier 12) and a pier near the end (p ier 18) is shown in Figure s 4.24 and 4.25 Figure 4.24: Stress in transve rse direction on pier 12 due to temperature

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66 Figure 4.25: Stress in transverse direction on pier 18 due to temperature Load transferred to Pier 18 As Pier 18 is going to be checked for cracking/crushing the load that will be applied is the service load ra ther than the ultimate load. There are several cases that might contr ol for Pier 18, all of which have to be check ed Ther the pier, but there are also cases of the live load (both truck and lane) on only one lane either the north or south lane. For all of the s e cases the dead load (own weight + wearing surface, barriers, fence and sidewalk) and temperature load (applying 120 degrees to south side of south box girder and concrete de ck) will be the sa me. T he model will be analyzed for the current condition of the bridge, taking into consideration the guide bars that were removed.

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67 T he case that will be analyzed is when both lanes are loaded. From Figure 4.26 it is observed that the s tress in the transverse direction at the top part of the pier clearly exceeds the tensile limit of concrete (0.43 0.73 ksi > 0.4 ksi), meaning cracking will occur Figure 4.26 : Stress on pier 18 in transverse direction from case of two lane loaded The resulting pressure on all of the four bearings i s displayed in Figure s 4.27 4.30 To ma ke sure that the contact is work ing properly the frict ion on bearing GW5 is also checked, which is displayed in Figure 4.31.

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68 Figure 4.27 : Contact pressure on bearing G W1 Figure 4.28 : Contact pressure on bearing GW2

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69 Figure 4.29 : Contact pressure on bearing GW4 Figure 4.30 : Contact pressure on bearing GW5

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70 Figure 4.31 : Contact friction stress on bearing GW5 The m ax pressure found on bearing GW5 was 0.12810 7 psf The max friction value should therefore be the pressure value multiplied by the friction coefficient: Friction = pressure friction coefficient = 0. 127 10 7 0.08 = 1016 00 psf C heck ing this with the max pressure valu e from Figure 3.36, the results are nearly identical. The average pressure and friction values on each of the girders and the total force obtain ed from them (force = pressure area of baseplate) is summarized in Table 4.3. These forces can be compared with the total reactions at the bottom of the pier, which are summarized in Table 4.4.

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71 Table 4 .3 : Average pressure on each bearing and resultant force two lane loaded case Bearing Average Pressure (psf) Vertical Force (Ibs) GW1 266482 328579 GW2 315310 388785 GW4 333382 411069 GW5 391801 483101 1611534 Table 4.4: Reactions at bottom of pier 18 two lane loaded case Reaction Value (Ibs) Direction Rx 122318 Longitudinal (west) Ry 1740200 Vertical (upwards) Rz 40788 Transverse (north) T he total force from the bearings i s approximately 1611534 Ibs ( 1612 kips). Adding the weigh t of the pier to that value ( 140 kips approx.) will give approximately the total reaction in the vertical dir ection which is the Ry value (174 0200 Ibs = 1 7 4 0 kips). It is also observed that the reac tion in the longitudinal direction (Rx) is approximately 3 times the reaction in the transverse direction (Rz) which matches how the bearing is oriented. Both Rx and Rz can be written in relation to the vertica l load (without the self weight of the pier) i n order to find an approximation of the ratio between the friction force in both directions and the vertical force: Transverse fri ction force/vertical force = 407 88/1657842 = 0.0253 Longitudinal fri ction force/vertical force = 122318 /1657842 = 0.0759 253 2 + 0.0759 2 ) = 0.08, which is the friction coefficient The pressure and reaction values for south lane and north lane loaded cases ar e summarized in Table s 4.5 4.8. U nder the two lane loaded case it was observed that bearings GW4 and GW5 on the north side of the pier had higher pressure values than bearings G W1 and GW2 on the south side; therefore is expect ed that the north lane loaded

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72 case will be more critical than the south lane loaded case. This is also supporte d by field evidence where it was obse rved that nearly all the cracks on the south side of the pier were hairline cracks, whereas several cracks on the north side were 0.016 0.02 inches thick. Table 4.5: Average pressure on each bearing and resultant force north lane loaded Bearing Average P ressure (psf) Vertical Force (Ibs) GW1 208021 256495 GW2 215349 265530 GW4 275789 340055 GW5 424769 523750 1385831 Table 4.6: Reactions at bottom of pier 18 north lane loaded Reaction Value (Ibs) Direction Rx 107044 Longitudinal (west) Ry 1521 878 Vertical (upwards) Rz 35638 Transverse (north) Table 4.7: Average pressure on each bearing and resultant force south lane loaded Bearing Average Pressure (psf) Vertical Force (Ibs) GW1 288605 355857 GW2 312886 385796 GW4 273790 337590 GW5 287776 354836 1434079 Table 4.8: Reactions at bottom of pier 18 south lane loaded Reaction Value (Ibs) Direction Rx 110149 Longitudinal (west) Ry 1571157 Vertical (upwards) Rz 36837 Transverse (north) Because the sidewalk is on the sou th side of the bridge, the pedestrian load was applied for the south lane loaded case but not for the north lane loaded case, which is why the vertical reaction for the south lane loaded case is slightly higher

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73 CHAPTER V FINE MODEL Pier 18 Due to the size of the model it was necessary to simplify the piers or else it would take too long for the mod el to run. Now that the loads transferred from the superstructure to the piers have been obtained however, it is possible to move on to the next step, which is analyzing the piers in detail by building a more in depth model of one of the piers, complete with all reinforcement detailing and the non linear propertie s of the materials. This part is specific to this thesis, in contrast to the general modeling of the viaduct, whic h was a group effort. Because Pier 18 was in the worst condition as far as the rate of crack expansion goes, it will be the pier to build a fine model for and on which the proposed rehabilitation will be tested out upon If the cracking issue can be solv ed for this pier, then that solution should work for the rest of the piers.

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74 Figure 5.1: Pier 18 The dimensions of pier 18 are displayed in Figure s 5.2 5.3, while Figure s 5.4 5.6 display the reinforcement detailing. Figure 5.2: Plan view of pier 18 (Ci ty and Country of Denver 1993, used with permission)

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75 Figure 5.3 : Elevation view of p ier 18 (City and Country of Denver 1993, used with permission and some edits ) Figure 5.4: Reinforcement detailing of pier 18 (City and Country of Denver 1993, use d with permission )

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76 Figure 5.5: Hammerhead cross section reinforcement detailing of pier 18 (City and Country of Denver 1993, used with permission) Figure 5.6: Column cross section reinforcement detailing of pier 18 (City and Country of Denver 1993, used wit h permission) Model Detailing Materials Similar to th e general model, both concrete and steel materials will be defined However, this time the materials will be given both linear and non linear properties. For concrete, the following properties will be i nputted : E lastic Modulus: the concrete is assumed to be normal weight concrete with 4,000 psi strength; therefore the modulus of elasticity will be defined as 3 605 ksi which is equivalent to 5.19210 8 l bs/ft 2 (same as before).

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77 0.2 (same as before). Density: Defined as 150 l bs/ft 3 (same as before). Ultimate uniaxial compressive strength: 4 000 psi strength is equivalent to 5.7610 5 l bs/ft 2 Ultimate uniaxial tensile strength: Also known as the m odulus of rupture, which is taken a s ten percent of the compressive stress (5.7610 4 l bs/ft 2 ). Shea r transfer coefficient: T his has two components. First, there is the shear transfer coefficient for open cracks which ranges from 0 (complete loss) to 1 (no loss). For the fine model a coeffic ient of 0.2 will be used (standard value). Second, the re is transfer coeffici ent for closed cracks, which will be take n as 1, thereby neglecting any reduction in shear stiffness of the model. Compressive uniaxial stress strain relationship: In order to dr aw the relationship between stress and st rain for concrete several points must be defined which ANSYS will con nect automatically. The data inputted is summarized in Table 5.1 and the resulting stress strain curve in displayed in Figure 5.6. Table 5.1: Str ess strain data for concrete Strain Stress (Ibs/ft 2 ) 0.00055 2.86E+05 0.001083 4.54E+05 0.00174 5.59E+05 0.002 5.76E+05 0.003 5.76E+05

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78 Figure 5. 7 : Stress strain relationship for concrete For steel, the following properties are inputted : E lastic M odulus: t he reinforcement used is grade 60 steel; therefore the modulus of elasticity will be defined as 29 000 ksi which is equivalent to 4.17610 9 l bs/ft 2 (same as before). Yield stress: 60 ksi strength i s equivalent to 8.6410 6 l bs/ft 2 By inputting this value ANSYS will automatically draw the stress strain curve for steel, which is disp layed in Figure 5.3 (note: if a mor e complex curve for steel was desired, a tangent value could also be inputted result ing in the straight line segm ent curving upwards, but for this model the tangent will be kept as zero).

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79 Figure 5. 8 : Stress strain relationship for steel Because loads being applied onto the pier e steel. However, a third material is defined which will also be steel, but with linear properties only. This is done because aside fro m the reinforcement there are also the baseplates of the beari ng s which will be include d in the model in order to apply t he loads on (if the loads were applied directly onto the concrete there would be issues of stress concentration). Because that will be t heir only purpose in the model and no analysis will be perfo rmed on them need to give them a yield stress. Element Type The following elements will be defined: SOLID 65 : This is a 3D element type specific to co ncrete that allows ANSYS to draw the potential cracking/crushing of the material. LINK180: 1D element used to model the steel reinforcement.

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80 SOLID185: 3D element for modeling the baseplates (same as what was used for modeling any volume in the general model). Real Constants For the link elements representing the stee l reinforcement real constants that represent their cross sectional area s have to be defined Therefore, each bar size will have a d ifferent real constant. There are three different bar sizes for the reinforcement: No. 4: Area = 0.196 in 2 = 0.00136 ft 2 No. 5: Area = 0.307 in 2 = 0.00213 ft 2 No. 9: Area = 0.994 in 2 = 0.0069 ft Constructing the Model With the elements and material s defined, the mod el can now be built. T he global coordinate system will be set at the middle of the bottom of the pier with the x axis representing the longitudin al direction, the z axis representing the transverse direction and the y axis representing the vertical direction (similar to the general model). All coordinates will be inputted in the global system (unlike the general model, there is no need to create an y local coord inate systems because there is only one pier). T he pier volume is the first thing to create. Due to the symmetric properties of the pier, the area of the pier that is displayed in Figure 5.3 is drawn and then extrude d along lines representing the thickness of th e pier (because the thickness of the 3 foot wide center portion of the column in the middle of the pier is 2 inches less than the 3 foot thickness of the rest of the pier it is extrude d along a line slightly shorter than the others ) Th e exterior volume of the pier is displayed in Figure 5.9

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81 Figure 5.9: Volume of p ier 18 T he next step is drawing the reinforcement. This can be accomplished by dividing the exterior volume of the pier by a set of defined areas and work planes in order to crea te interior lines, which are then group ed into components representing the different bar sizes in order to make things easier for meshing and analyzing. This process will divide the exterior volume into hundreds of blocks with the outside lines of t he interior blocks representing the reinforcement. In this way the steel will be attached to the concrete and thus the stress can be transferred to it.

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82 Figure 5.10: No. 4 bars Figure 5.11: No. 5 stirrups

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83 Figure 5.12 : No. 9 bars Figure 5.13: Front s ectional view of reinforcement

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84 T he final components to construct are the bas eplates. As noted previously, the e fixed pier (pier 11). While pier 11 could be included in the model and reference po ints towards it created from which to construct the basepla tes it would be easier to simply go back to the general model and obtain the coordinates of the bottom four corner points of each baseplate in reference to the local coordinate system at the bottom of the pier, which in the fine model is the global coordinate system. With these points the bottom area of each baseplate can be created T he top areas of the pier can then be divided by these areas in order to let ANSYS know that the bottom of the basep late is attached to the to p of the pier. T he bottom baseplate areas are then extruded by lines representing the thickness in order to create the baseplate volumes. Figure 5 .14 : Baseplates on top on pier 18

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85 Meshing Now that the geometry of the model ha s been completed the attributes of all the different components are assigned and then the model is meshed (note: it is critical to give the baseplates the same mesh size as they had in the general model in order to make the next step after meshing easier) The resulting mesh for the pier and basep l ates is displayed in Figure 5.15 while the mesh of the reinforce ment is displayed in Figure 5.16 Figure 5.15 : Meshing of pier 18

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86 Figure 5.16 : Meshing of pier 18 reinforcement Loads and Boundary Conditions A s in t he general model, the foundation is replaced with fixed supports at the bottom of the pier The loads, as mentioned previously, will be applied onto the top of the baseplate with a force being placed upon each node. First off will be to apply a test load of 35 kips vertic ally downwards per node. Every baseplate has 12 nodes at the top surface, which means the total load on each baseplate will be 12 35 = 420 kips. This is just a simplified case though. As observed in the previous chapter, the pressur e on each bearing is not uniform. Therefore, in order to apply the load more accurately, the load transferred from the top plate and guide bars to each node of t he contact areas of the baseplates on pier 18 in the general model is taken and then applied to the corresponding node in the fine model (this is why it was important to make sure that the

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87 baseplates in the fine model would get the same meshing and therefore the same node distribution as the baseplates in the general model ) The vertical load in eac h nod e is determined by assuming that all the node s take the same amount of area. As there are twelve nodes for the contact area of each bearing, the area a single no de will take will be the total bearing area (177.5 in 2 = 1.233 ft 2 ) divided by twelve. The force can then be calculated by multiplying the pressure reading at that node by the node area: Force at node = Pressure at node node area = Pressure 1.233/12 This simplifies things so mewhat due to the assumptions that every nod e take s the same area and that the pressure at each node represents the aver age pressure of that area. Because a dozen nodes were taken for each contact area, however, the error is negligible. The longitudinal and transverse loads are determined by multip lying each vertical force by the coefficients determined in the previous chapter (0.759 and 0.253 respectively). F or the case of both lanes being loaded, the pressure readings and loads transferred to each node on the contact areas of the baseplates ar e summ arized in Table s 5.2 5.5 For vertica l forces, a negative value means a downwards force, a positive value means upwards force. For transverse and longitudinal forces, the positi ve values are in the south and we st directions and the negative values are in the north and east directions respectively

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88 Table 5.2: Forces on bearing GW1 Node # Pressure (psf) Corresponding Node # Vertical Force (Ibs) Friction Force longitudinal (Ibs) Friction Force transverse (Ibs) 314127 533031 4559 54770 4157 13 86 314128 197010 4552 20243 1536 512 314129 0 4560 0 0 0 314132 22121 4565 2273 173 58 314133 349297 4566 35891 2724 908 314136 592802 4553 60912 4623 1541 314137 3063 4570 315 24 8 314140 280825 4554 28855 2190 730 314143 226000 4579 23222 1763 588 314144 353410 4580 36314 2756 919 314145 278147 4577 28580 2169 723 314146 362173 4578 37214 2825 942 Sum 328589 24940 8313 Table 5.3: Forces on bearing GW2 Node # Pressure (psf) Corresponding Node # Vertical Fo rce (Ibs) Friction Force longitudinal (Ibs) Friction Force transverse (Ibs) 314198 251900 4507 25883 1965 655 314199 411713 4525 42304 3211 1070 314200 148086 4536 15216 1155 385 314209 43365 4505 4456 338 113 314210 455423 4508 46796 35 52 1184 314214 1080042 4521 110977 8423 2808 314215 75333 4522 7741 588 196 314218 527526 4527 54204 4114 1371 314224 172130 4544 17687 1342 447 314225 136791 4545 14056 1067 356 314226 296726 4546 30489 2314 771 314227 235581 454 7 24206 1837 612 Sum 394015 29906 9969

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89 Table 5.4: Forces on bearing GW4 Node # Pressure (psf) Corresponding Node # Vertical Force (Ibs) Friction Force longitudinal (Ibs) Friction Force transverse (Ibs) 314376 668375 4476 68677 5213 17 38 314377 344311 4460 35379 2685 895 314378 236437 4477 24294 1844 615 314387 434826 4481 44679 3391 1130 314388 255397 4483 26243 1992 664 314392 871168 4462 89514 6794 2265 314393 112712 4492 11581 879 293 314396 453999 4463 466 49 3541 1180 314402 87466 4501 8987 682 227 314403 171959 4502 17669 1341 447 314404 172471 4499 17722 1345 448 314405 194147 4500 19949 1514 505 Sum 411344 31221 10407 Table 5.5: Forces on bearing GW5 Node # Pressure (psf) Corr esponding Node # Vertical Force (Ibs) Friction Force longitudinal (Ibs) Friction Force transverse (Ibs) 314541 561577 4431 57703 4380 1460 314542 490184 4443 50367 3823 1274 314543 76960 4448 7908 600 200 314546 104420 4430 10729 814 271 3 14547 574537 4432 59035 4481 1494 314550 384613 4437 39520 3000 1000 314551 352042 4438 36173 2746 915 314554 1032687 4444 106111 8054 2685 314557 350514 4455 36016 2734 911 314558 178383 4456 18329 1391 464 314559 405800 4457 4169 7 3165 1055 314560 173570 4458 17835 1354 451 Sum 481423 36540 12180

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90 The pier with all the loading and B.C.s for the two lane loaded case is displayed in Figure 5.17 Figure 5.17 : Pier 18 with loads and B.C.s for two lane loaded cas e Solution Criteria Beca use the analysis is non linear, a convergence criteria must be set before solving the model. As loads are being applied the criteria will be Force F. The default tolerance in ANSYS is 0.001. T his is a very tight tolerance, however which makes it very difficult for the solution to converge once cracks start forming. Th erefore the tolerance will be relaxed to 0.05. Also, because the Solid65 element of concrete gives better results when the load is applied gradually, the time step w ill be broken into five sub steps; the load will start at zero and at each sub step it will increase by a fifth of the total value. Only the final sub step will be written (when the total load is applied), as

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91 Analysis Check of Results As with the gen eral model the first part of analysis is to make sure that the model is working properly. Ther efore, the test load of 420 kips will be the first load case to solve the mode for The resulting tensile stress in the s teel bars is disp layed in Figure 5.18 Figure 5.1 8 : Stress in steel reinforcement bars for test case From the f igure the maximum tensile stress is 0.597E+07 psf which is approximately 41.5 ksi, which is below the yield limit of steel. T he stress at one particular secti on will be analyzed : the start of the hammerhead portion of the reinforcement, which begins 2 inches away from the 9 foot column section of t he pier, as shown in Figure 5.19 The reinforcement detailing of that s ection is shown in Figure 5.20

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92 Figure 5.1 9 : Location of section A A Figure 5.20 : Reinforcement of cross section A A

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93 In order to calculate the moment c apacity of this section the first step is to figure out how much of the section is in tension and how much is in compression. In order to do s o, an assumption must first be made, which in this case will be that all of the No. 4 and No. 9 bars are in tension. Because there are several layer s of bars, their centroid must be calculated, which will be measured from the top steel tension fiber : = A ll the No. 9 b ars are at the same level of the reference point which means their y value will be zero, which lea ves only the No. 4 bars. There are two bars every foot; therefore, the total y can be calculated as follows: y = 2 (0 .3+1.3+2.3+3.3+4. 3+5.3+6.3+7.3+8.3+9.3+10.3) = 11 6.6 ft Therefore: = = 1.6 5 ft From this the depth d can be calculated : d = 11.55 1.6 5 = 9.9 ft The depth from the bottom of the compression zon e to the neutral axis (c) can be calculated as follows: 0.85 c b a = A s y 0.85 4 (312) a = (10(9/8) 2 + 22(4/8) 2 a = 7 in 1 1 = 0.85: c = 7/0.85 = 8.22 in

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94 This means that t he compression zone includes none of the No. 4 bars therefore the assumption is correct. With the depth of the tension and compression zones known the nominal flexural strength of the section can be determined as follows: M n = A s y (d a/2) = (10(9/8) 2 + 22( 4/8) 2 3. 5 /12) M n = 8 220 kips ft This is the tot al moment capacity, which can be use d to calculate the tensile stress in the steel under the applied moment. To calculate the a pplied moment, the pier will be simplified into a 1D beam with t he 9 foot wide column in the middle of the pier acting as the fixed support as shown in Figure 5.21 The resulting moment diagram is shown in Figure 5.22 Figure 5.21 : Simplified force diagram of Pier 18

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95 Figure 5.22 : Simplified bending moment diagram o f Pier 18 Fro m Figure 5.22 the applied momen t on the section under analysis is approximately 4 560 kips ft. The tensile stress on the steel at this section can be calculated as follows: s = M u /M n y = 4560 /8 220 60 s = 3 3 3 ksi T his can be checked with the tensile strength in the steel at the same section in the model, as shown in Figure 5.23

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96 Figure 5.23 : Tensile stress in steel at specified section While in the hand calculations it was assumed that the stress would be evenly distributed among t he steel bars in ANSYS However, averaging ou t the stress gives a value of approximately 35 k si, which is close enough to the value calculated by hand. Solution For all the differe nt load cases, the cracking/crushing of concrete as wel l as the tensile stress in the steel reinforcement will be checked For the case of two lane s loaded t he result s are dis played in Figure s 5.24 5.25 (note: in ANSYS red marks mean cracking while green mark s mean crushing).

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97 Figure 5.24 : Cracking/crushing of concrete under two lane loaded case Figure 5.25 : S tress in steel reinforcement under two lane loaded case

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98 Figure 5.26: Cracking/crushing of concrete under north lane loaded case Figure 5.27: S tress in steel reinforcement under north lane loaded ca se

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99 Figure 5.28: Cracking/crushing of concrete under south lane loaded case Figure 5.29: S tress in steel reinforcement under south lane loaded case

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100 As expected, under the various applied loads, the pier model shows extensive cracking, while for the case s of two lane and north lane loaded the steel reinforcement yield s near the north side of the column section of the pier while the highest value for the south lane loaded case is around 45 ksi for the top steel reinfor cement While there is more cracking i n the two lane loaded case, the north lane loaded case had the most amount of steel yielding due to the load being concentrated on one side. The high stress and large amount of cracking on the north side of the pier matches with what was observed in realit y, where as mentioned previously, the cracks on that side had a thic kness up to 0.02 inches, while most of the cracks on the south side were only hairline. In orde r to understand how much of the cracking is from the vertical and transverse loads and how much is from the lon gitudinal loads, the model will also be solved without the forces in the longitudinal direction for the two lane loaded case W hile there is still a lot of cracking at the top, t he bottom of the pier is now free of cracks, as shown in F igure 5.30

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101 Figure 5.30 : Cracking in pier under two lane loaded case without longitudinal load One thing to note in this analysis is that based on the results of the general model the forces in the tr ansverse direction were all in the same direction th ereby creating tension on one side of the pier (north side) and compression on the other side (south side) which would work to prevent cracking at that side However, in practice that may not always be t he case. Therefore, a worst case scenario will be tak en by assuming that all of the forces in the transverse direction are creating tension in the pier. T he cracking in the concrete and stress in steel will be checked once more:

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102 Figure 5.31: Cracking in pier under two lane loaded case with all transverse f orces creating tension in pier (worst case scenario) Figure 5.32 : S tress in steel reinforc ement due to two lanes loaded worst case scenario

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103 Figure 5.33 : C racking/crushing of concrete due to north lane loaded worst case scenario Figure 5.34 : S tress i n steel reinforcement due to north lane loaded worst case scenario

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104 Figure 5.3 5 : C racking/crushing of concrete due to south lane loaded worst case scenario Figure 5.36 : S tress in steel reinforcement due to south lane loaded worst case scenario

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105 While crac cracking of the south side became worse. The maximum stress in steel for the cases of two lane and north lane loaded still remains on the north side of the pier (once again there is yieldin g), though for south lane loaded the max stress moved towards the south side of the pier and increased slightly to 46.5 ksi. While it would seem unlikely that the two steel box girders would move in different directions in the field it was noticed that at some locations the diaphragm bracing the two girders directly above the pier had buckled, suggesting that the g i r ders were moving towards each other, which means it is also possible for them to move away from each other as well, causing tension on both th e north and south sides of the pier. This is something that would have to be confirmed by applying a temperature cycle on the bridge. Based on the amount of cracking the pier is clearly not well suited against the applied loads, which necessitates the des ign of a strengthening method, which will be discussed in the next chapter.

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106 CHAPTER VI REPAIR USING CRFP RODS Method of Repair Based on both the field observation of the continuing expansion of the cracks and the result s from the fine model of pier 18 itself needs strengthening and one of the more popular methods to do so would be the use of CFRP rods. As mentioned in the literature review, CFRP rods vary in both their elastic modulus and their tensile st rength. They can also be applied in a slot in the concrete and bonded to it using epoxy or simply placed above the concrete. The second method is what this paper will focus on as it is less labor intensive. In order to apply the CFRP rods to the pier a st eel plate will be placed at each side of the pier. Due to the smo othness of the rod surface a mechanical anchor will be used to connect each end of each rod to the steel plate. This anchor also allows for the CFRP rods to be post tensioned. Four CFRP rods will be applied to the pier, two on each side. Their location is shown in Figure 6.1. The optimal bar size and pre stress force will be determined through finite element modeling.

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107 Figure 6.1: Strengthening method for pier 18 Modeling of CFRP Material Properties For CFRP, the following data is inputted : Elastic Mo dulus: A value of 2175 0 ksi (typical) for CFRP will be used which is equivalent to 3.132 10 9 psf Multilinear Isotropic s tress strain relations hip: Because the relationship between stress and strain for CFRP is linear up until the fa ilure point only the failure point needs to be defined which in this case will be at a stress of 300 ksi (4.32 10 7 psf ) and a strain of 0.013793 (Stress/Modulus of E lasticity). The resulting stress strain relationship is displayed in Figure 6.2.

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108 Figure 6.2 : Stress strain relationship for CFRP rod Steel Plate As the properties of steel have already been defined another materi al for the plat e. However, because the plate ca n be taken as a shell, an additional element type of SHELL181 will be defined Each 4 high starting from the bottom of each side of the hammerhead pier (see Figure 6.1), which are approximately the s For the width of the plate an additional 2 inches is added on either side so that when the CFRP bars are drawn and meshed nodes of the pier, which runs the risk of two nodes being directly on top of each other and therefore possibly getting m erged together. A preliminary section of 1.5 inch thickness for the plate will be defined (to be adjusted if stress on plate exceeds yielding limit) The resulting steel plate is displaye d in Figure 6.3.

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109 Figure 6.3 : Modeling of steel plate Real Constant of CFRP Rods Like the steel reinforcement, the CFRP rods will be modeled as 1D LINK180 ele ments, so a real constant representing the cross section area must be defined. Because the opti mal rod size needs to be determined different bar sizes will be tested to see which one gives the best results 2 / 144 = 0.00545). Creating CFRP Rods Each CFRP rod is created by simply drawing a line between the two steel plates and then assign ing the appropriate attributes to it (element ty pe, material and real constant ) before meshing it. The meshed CFRP rods and steel plates are shown in Figure 6.4.

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110 Figure 6.4: CFRP rods connecting steel plate s Figure 6.5 : Model of pier 18 with CFRP rods

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111 Defining Pre Stress Force There are several diff erent ways in ANSYS a pre stress force can be applied. It can simply be applied as a regular force value at each node of the CFRP rods or a temperature value to the CFRP rods that will create a shrinkage effect can be applied instead (though a temperature expansion coefficient for the material would have to be defined first). The most common way to apply a pre stress force, however, is to define an initial state cond ition for the CFRP material. This initial state can be a stress or a strain value. In this case, a n initial strain in the CFRP rods will be defined While theoretically the strain value could be as high 0.0138 in practice it would not be advisable to apply a strain that is close to the ultimate strain as CFRP fails suddenly. The preferable range would be 40 65% of the ultimate strain (Dolan et. al. 2000) Therefore a s train of 0.007 (approximately half the ult imate strain value) will be defined in all rod s Analysis Check of Results As always, the first step in analysis is to make sure that the ANSYS model is working proper ly. To do so, the model will first be solved without any loa ds in order to see how it will react under the pre stress force from the CF RP rods ( in this way, it can also be mad e sure that stress force in cases of lower loads, The stress in the concrete under pre ten sioning can be calculated as follows: Where P is the pre stress force from the CFRP rods

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112 T he strain, area and modulus of elasticity of the steel rods are known; therefore, the force in each rod can be calculated as follows: ess = strain modulus of elasticity) Therefore: 119.5 kips per rod T here are a total of four rods; therefore: P Total = 4 119.5 = 478 kips As the cross section of t he concrete varies, the cross section at the very end of the south side of the pier will be taken The width at that location is 3 feet and the height is 3 feet + 7/8 inches Because this is a simple rectangular section, the area (A), distance from the top fiber to the centroid (y) and moment of inertia ( I) will be as follows: A = b h = (312) (312 + 7/8) = 1327.5 in y = h/2 = (312 + 7/8)/2 = 18.4375 in I = b h 3 /12 = (312) (312 + 7/8) 3 /12 = 150424 in 4 T he bars are place d in two layers (2 bars per layer) which means there will be two values of eccentricity (e): e 1 = 0.5 ft = 6 in e 2 = 1.5 ft = 18 in As A, y and I will all stay the same the total moment from the eccentricity (Pe) can be calculated and then applied it into the equation: Pe total = P 1 e 1 + P 2 e 2 = 2 (119.56 + 119.518) = 5736 ki ps in

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113 The total stress at the top concrete fiber will therefore be as follows: top = = = 1.02 ksi (compression) The total stress at the bottom concrete fiber will be similar, only because the eccentricity will create tension the sign of t he second term will be positive. bottom = = 0.3 ksi (tension) Both of these values are below the limit s which means the section is safe from both crack ing and crushing From ANSYS, the stress distribution in the transverse direction of the pier is shown in Figure 6.6 : Figure 6.6 : Stress in pier 18 in transverse direction under pre stressed CFRP rods As observed from the f igure the str ess is distributed in the way one would expect The to p part of the pier is in compression while e verything else is in tension The

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114 deformation is also wha t would be expect ed under the pre stressing force, as the ends of the pier have risen slightly. Actual values are obtained by zoom ing in and click ing on either the top or bottom nodes of the section that the stress was calculated for. While the values var y from node to node, averaging them out gives a compressive stress of 0.94 ksi at the top and a tensile stress of 0.32 ksi at the bottom. Both of these are very close to what was calculated by hand, which gives confidence that the model is running properly Figure 6.7 : Stress at the test section in the transverse direction under pre stressed CFRP rods Impact of CFRPs on cracking Now that the CFRP rods are determined to be working properly the next step is to run model again, th is time with the applied loa ds. T he first case that will be analyzed is the one that generated the maximum amount of cracking on the pier : when both lanes are fully loaded.

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115 A fter running the model, the cracking/crushing of the concrete is checked, the results of which are displayed i n Figure 6.8 Figure 6. 8 : Cracking/crushing of concrete under two lane loaded case with 4 No. 8 pre stressed CFRP rods and a n initial strain of 0.007 As see n from the Figure the crackin g has reduced significantly compared to the case of no CFRP rods ; ho wever, there are still some cracks remaining, which means a bigger pre stressing force must be given to the rods. This can be done either by increasing the bar size number of bars or the initial strain For starters a third layer of CFRP rods is placed o ne feet below the second layer so that there are now 3 No. 8 rods on each side The resulting cracking/cru shing is displayed in Figure 6.9

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116 Figure 6.9 : Cracking/crushing of concrete under two lane loaded case with 6 No. 8 pre stressed CFRP rods and a n in itial strain of 0.007 Again, the cracking has been reduced but not eliminated. Therefore, another adjustment must be made this time by increasing the ini t i al strain to 0.009 (this is approximately 65% of the t otal strain, which is just within the range re commended by ACI 440.4R 04 ). As before, the concrete cracking/crushi ng is plotted, as is shown in Figure 6.10

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117 Figure 6.10 : Cracking/crushing of concrete under two lane loaded case with 6 No. 8 pre stressed CFRP rods and a n initial strain of 0.0 09 In thi s case the cracks on the top part of the pier have almost been completely eliminated The exception s are near the bearing s due to the connection between the base plate and the concrete resulting in some uneven mesh that results in stress concentration as well as at t he edges, which may be due to the increased pre st ress force applied. This suggest that use as much tension on the pier ends must be found However, after running several different distributio ns of CFRP rods, it was observed that cracking at the ends always occurred, while theoretically, it should have been prevented for cases such as 3 No. 8 bars on each side, because they were oriented about the neutral axis at the end so as to create minimum eccentricity. This means that the stress force from the rods but with the mesh of the piers at the

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118 edges, which like the mesh near the baseplates is uneven, resulting is stress concentration. Therefore, the mesh needs to be re fined in order to get more accurate results. The most accurate type of mesh for concrete is brick meshing. This will be used instead of the tetrahedral mesh used previously, though due to the shape of the pier and the orientation of the bearings there will nonetheless remain a few spots of uneven meshing though as shown in Figure 6.11 they have been significantly reduced. The CFRP rods, meanwhile will remain No. 8 rods with an initial strain of 0.009 with three on each side of the pier. Figure 6.11 : Pi er 18 with refined brick meshing

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119 Figure 6.12: D istribution of 6 No. 8 CFRP rods for refined model of pier 18 After r unning this new model, the concrete is once again checked for cracking and this time it has almost been completely prevented at the top portion of the pier ( Figure 6.13), including the edges as shown in Figure 6.14. The exception once again remains at the few spots of uneven meshing near the bearings, but in this case they are small enough to be neglected.

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120 Figure 6.13: Cracking /crushing of pier 18 under two lane loaded case refined model Figure 6.14: Cracking /crushing at pier edge under two lane loaded case refined model

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121 There are still cracks at the bottom of the pier d ue to the forces in the longitudinal direction. vented by the CFRP rod s at the top, but CFRP laminates could be wrapped around the bottom of the pier as a repair measure. However, in the field these cracks were only h airline so the cracks at the top of the pier (even in the mo del the cracks at the bottom are mainly on the surface). Figure 6.15: Cracking at bottom of pier wireframe view With the concrete being safe from cracking the next step is to check both the steel plates and the steel reinforcement to make sure that non e of it has yielded. Figure s 6.16 and 6.17 display the stress in the steel plate in the x and y directions respectively, while Figure 6.18 displays the stress in the steel reinforcement.

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122 Figure 6.1 6 : Stress in steel plate longitudinal direction (x compon ent) Figure 6.17: Stress in steel plate vertical direction (y component)

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123 Figure 6.18: Stress in steel reinforcement for pier 18 strengthened with 6 No. 8 CFRP bars strained to 0.007 As seen from the figures for both the steel plate and the steel reinf orcement the stress is below the yield limit (60 ksi = 0.864E+08 psf). This means that both the CFRP rods and steel plates selected are appropriate to prevent cracking f or the case of two lane loaded. T his solution is tested out for the remaining loading c ases and is found to work for all of them. However, as mentioned in the previous chapter, many of the transverse forces were creating compression on the pier, wh ich helped reduce the tensile stress Therefore the worst case scenario of reversing all the fo rces in the transverse direction that are creating compression will also be tested out ; however, due to the additional 310 kips (approx.) of compression forces by the two new CFRP bars the concrete pier remains safe from cracking, and while the stress in steel increases it remains well below the yield limit

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124 for all cases. Therefore, the use of 6 No. 8 CFRP rods with two 3 plates should prevent cracking not only on pier 18 but for all other piers. Figure 6.19 : New CFRP strengthening method Figure 6.20: Cross sectional view of selected CFRP strengthening method

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125 All of this design so far is based on using CFRP rods of 1 inch diameter (No. 8). However, in reality it may be difficult to finds rods of that size, especially with the requi red tensile strength. Many companies only manufacture quarter to half inch diameter rods. Taking that into co nsideration an appropriate number and distribution of No. 4 CFRP rods that can be used in place of the No. 8 bars will be determined. For started, the initial strain will be taken as 0.009. This will result in a pre stress force of approximately 4 0 kips in each bar, which is 1/4 of the pre stress force generated in the No. 8 bars strained to 0.009 Theoretically, this wo uld mean the number of bars w ould have to be quadrupled on each side; however, this number can be reduced by placing most of the bars close to the top of the pier. The top layer of rods will remain at 3 f ee t from the bottom of the steel plate but there will be s ix rods on each side spaced at 4 inches (see Figure 6.21) Unde r this new condition the model is solved for the case of two lanes loaded and then check ed for cracking, which is shown in Figure 6.22. Figure 6.21 : Steel plates with 12 No. 4 CFRP rods

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126 o Figure 6.22: Cracking on pier 18 strengthened with 12 No. 4 CFRP rods strained to 0.009 While there is some cracking at the middle of the pier it is minor enough that it can T he cases of south lane and north lane loaded are also checked, which give similar results. Therefore, in the event 4 bars initially strained to 0.009 (stress = 195 ksi) spaced at 4 inch with the top layer 3 f ee t from the bottom of the s teel plate can act as a replacement to prevent the cracks in the pier from expanding. Unfortunately, this has been neglecting the pre stress losses Taking into account both the short term (elastic shortening of concrete, anchorage seating loss, etc.) and long term losses (creep and shrinkage of concrete) the pre stressing force will likely end up 10 20% less than the applied jacking force (fib Bulletin 14, 2001). For this case a total pre

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127 stress loss of 15% is assumed, resulting in a final pre stress leve l in the tendons of approximately 55% of the ultimate strength. This translates to a strain level of around 0.0076. While it is possible in ANSYS to do a time dependent analysis, in this case this final strain will simply be applied as an initial strain fo r both the solution of No. 8 and No. 4 bars in order to see how the pier would behave in the long term. For the solution of 6 No. 8 bars there was enough additional extra strength provided that reducing the strain from 0.009 to 0.0076 only saw a very smal l amount of cracking on a few select surface elements that could be neglected However, for the case of 12 No. 4 bars there was already some cracking occurring and it increased to the point that it is hard to neglect. Therefore, it is recommended to add an other layer of CFRP rods giving a total of 7 CFRP rods on each side (spacing remains the same), which is checked and verified in ANSYS. Figure 6.23: Cracking on pier 18 strengthened with 12 No 4 CFRP rods strained to 0.0076 (considering all pre stress losses)

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128 Figure 6.24 : Distribution of No. 4 CFRP rods spaced at 4 inches Method of Application CFRP Rods with Permanent Steel Plates Before applying the CFRP rods to the piers there are a few preliminary steps that must be taken. First off, because the cracking in the piers has been occurring for almost two decades there is a good possibility that corrosion in the steel rebar at the top of the piers has already occurred. While, there were no noticeable signs of corrosion observed from the outside, non de structive corrosion testing should still be performed. If it is found that corrosion in the steel rebar is occurring, then protective measure s must be taken to keep the corrosion from getting worse or else the use of post tension ed external reinforcement will only work as a temporary solution.

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129 The next step would be to close the cracks with epoxy. It is preferable to do this before applying the post tensioned reinforcement rather than after. There are many different kinds of sealant s and epoxies that can k eep water from seeping into the pier and offer a compressive strength greater than even that of concrete. Once the c racks have been sealed and the epoxy has dried, the CFRP rods can finally be applied. Typically, the manufacturing company will attach the m echanical anchors to the rods in the factory before shipping them to the site (a machine will install the anchors at the rod ends, which use compressive force to clamp down on the rod). The rods can then be bolted to the steel plates through the mechanical anchors. By having the CFRP rods extend a couple inches past the steel plate they can then be post tensioned. Figure 6.2 5 : Extension of CFRP rods 2 inches past steel plate

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130 There are a few downsides to this method. First of all, because the steel plates are going to be there permanently they must be protected against corrosion. Second of all, not only are the CFRP rods going to be placed above the conc rete surface, but as noted previous ly there is going to be a couple inches of each rod sticking out fro m the steel plates. This makes this method of repair very eye catching and runs the risk of vandalism, especially at the end piers, which are very short, meaning it would be very easy for someone to get to the CFRP rods and try to uninstall them. CFRP Rod s Epoxied to the Concrete Figure 6.26 : Near surface mounted CFRP rods An alternative method would be to use near surface mounting (NSM). In this method, the CFRP rods would be placed in slots grouted into the concrete (for a No. 4 CFRP rods the preferred depth of the slo t would be 5/8 1 inch. Because t he concrete cover is at least 2 inches steel reinforcement). Similar to the previous method, the CFRP rods would be anchored to steel plates and post tensioned. H owever, epoxy would be applied afterwards to the slots,

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131 fixing the CFRP rods to the concrete. Once the epoxy dries the CFRP rods would be released or cut from the steel plates a nd the epoxy would keep them in place, transferring their tensile force to the concrete. This method can be done in several stages, starting with epoxying the mid portion of the rods and then performing multiple cycles of post tensioning the CFRP rods and adding more epoxy, reducing the post tension force with e ach cycle thereby resulting in a lower force at the ends Figure 6.27 : Example of NSM CFRP rods post tensioned to different level s While this method is the most labor intensive, it is also the most effective Not only does it solve the issue of corrosio n due to the fact that the steel plates would only be s also far more unassum ing due to the CFRP rods being embedded in the concrete.

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132 Pre Stressing Steel The final method would be to use high strength pre stressed steel inst ead of CFRP rods. T he application of this method can be done in a similar way to either the first or second method with the only difference being that the steel will be placed in a condui t in order to prevent corrosion. Due to pre stressed steel being mo re widely available than CFRP, this method is the m methods, as even with the conduit corrosion in the ste el could still eventually occur, which is why it is preferred to embed the pre stress steel in the concrete rather than apply it as external reinforcement though due to the concrete cover being a mere 2 inches of thickness from the steel stirrups it is hard to offer much cover for the pre stressing strands. O ne thing to ta ke into consideration in support of a more economical but not as long lasting method is that the bridge was designed for a service life of 75 years and it has already completed 30 of those years, meaning that it only has around 40 years left of expected se rvice life so even if the steel may eventually corrode it will likely be at a rate

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133 CHAPTER VII CONCLUSION S AND RECOMMENDATIONS Summary This research was done in three sta ges: field inspections and equipment installation, constructing a general model of 8 th Avenue Viaduct, and construc ting a fine model of one of the piers Through field inspection, it was found that not only were all the piers showing extensive cracking but that the cracks were expanding at various rates, with the expansion noticeably higher at piers close to either ends of the viaduct. Based on the inspections of all but two of the piers (piers 3 and 10), Pier 18 was judged to be the worst in terms of crack expansion rate, which was why it was selected for fine modeling. Also, through the installation of tilt meters on pier 11, it was observed that there was very little movement at th at pier. P ier 11 could therefore be taken as a fixed point and thus only h alf the bridge had to be modeled for this study. Because pier 18 was the critical pier the half of the bridge that was modeled was the part from pier 11 to abutment 20. The model was built using ANSYS Mechanical APDL 16.0, a program selected because it all ows for complex three dimensional finite element analysis of structures. The loads that were applied on the model were dead, live and temperature. Both the steel and concrete materials defined for the general model were given linear elastic properties. Aft er using basic hand calculations to make sure that the model was working properly analysis was done on both the impact of removing some of the guide bars from

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134 the bearings and the effect of temperature. By comparing the case of removing guide bar s on pier 19 to the case when all guide bars were present it was observed that guide bar removal resulted in lower stresses in the transverse and longitudinal directions on the pier, while the effect of temperature increased the farther away the pier was from the f ixed pier (pier 11). Both of these results match with what was observed in the field. S everal loading cases that would generate maximum stress on pier 18 were then tested out For each case the forces that were transferred from the superstructure to the p ot bearings on top of pier 18 (both from the p ressure and the friction ) were recorded in order to be used for the fine model analysis. The fine model of pier 18 differed from the general model in that the steel reinforcement of the pier was included and th e materials were defined as non linear. After running a test load on the model to make sure that it was working properly, the forces on each bearing that were obt ained from the general model were applied onto pier 18 for all of the different loading cases. As expected, each of the cases resulted in heavy cracking of the pier, though the amount and location of the cracks varied from case to case. The worst case scenario was when both lanes above pier 18 were loaded using HL 93 live load specified in AASHTO ( AASTHTO LRFD 2012 Bridge Design Specifications). Based on the amount of cracking, it was necessary to find a method of strengthening the pier. D ue to the advantages CFRP has in terms of strength and non corrosiveness, 4 CFRP rods were initially selected w hich would be connected by mechanical anchors to 1.5 inch thick steel plates at either ends of the pier. After several trials of different bar sizes and pre stress levels, an appropriate design was selected of 3 No. 8 CFRP rods on each side of the pier of 300 ksi tensile strength an d a modulus of elasticity of 21, 75 0 k si initially

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135 strained to 0 .009 (stress = 195 ksi) With this strengthening method the pier was tested under the different loading cases and in all cases both the vertical and diagonal cracks a t the top of the pier were prevented and the steel reinforcement was well below the yield the yield limit, so the selected thickness was judged to be appropriate. Therefore it was concluded that 3 No. 8 bars on each side would prevent cracking; however, due to the difficult y in finding a company that can manufacture bars of such sizes another design of CFRP rods was introduced, this time wi th 12 No. 4 bars (6 on e ach side) at 4 inch spacing strained to 0.009 (stress = 195 ksi) U nlike the use of 3 No. 8 CFRP rods on each side this new method resulted in some minor cracks at the middle of the pier, but they were small enough considered critical. H owever, while this method offers enough strengthening for the short term, the cracks were found to grow more numerous when considering long term pre stress losses due to shrinkage and creep. Therefore it is recommended to add another layer of No. 4 CFRP ro ds resulting in 7 bars on each side. Simplifications and Approximations General Model While the general model was constructed to reflect the details and behavior of the bridge as much as possible, no model can be completely accurate. There were a number of simplifications, which were as follows: I. Foundation: Because the focus of this research was structural the interaction between the soil and structure was neglected and the foundation s were simply replaced with fixed supports at the bottom of each pier.

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136 II. G eometry simplifications: Due to the model being three dimensional, much of the detailing such as all the interior and exterior stiffeners and bracing of the girders was successf ully modeled; however, n ot all of the geometry details were accurately reflecte d. The curves of the superstructure were approximated as multiple short straight line segments while the top surfaces of both the piers and the deck were modeled as flat, neglecting the tilt for dra inage and traffic purposes because again, the focus here i s structural. The piers in particular wer e simplified because a fine model of one of them wa s going to be constructed though this meant that the analysis done on pier 19 was not very accurate. III. Temperature load: In the model the parts of the superstructur e that were facing the sun (the deck and the south side of the south steel box girder) were given a temperature of 120 degrees Fahrenheit (the max temperature they would likely be under), while the parts that would be shade d were given a temperature of 70 degrees Fahrenheit. In reality, temperature effects are far more complex. Not only does temperature change throughout the day but the superstructure does not heat up so uniformly. For example, the deck overhang means a certain portion of the south side of the girder will be shaded and that amount varies with position of the sun. While one would assume that applying the max temperature would create the worst case on the piers in the general model it actually resulted in some compressive forces on the pier, m eaning that applying a temperature gradient could

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137 create higher tensile stresses even if none of the values are as high as the max temperature. IV. as brick meshing. This also effects the accuracy of the contact elements, which used areas on the 3d volumes of the bearings. Fine Model While the fine model of pier 18 was much more detailed than the piers in the general model, it to I. Foundation: As in the general model fixed supports instead of the foundation were placed at the bottom of the pier. II. Steel and concrete bond: for simplicity, it was assumed that the concrete and steel reinforcement had a perfect bond. III. Uneven meshing: The solid65 elements used to model concrete are highly sensitive to the type of mesh used. Brick mesh ing would be the most accurate; unfortunately, due to the shape of the pier and the bearings on top of it being angled not all portions of the pier could be modeled with bricks and despit e best attempts to refine the mesh as much as possible there were still a few small portions of the pier where free tetrahedral mesh had to used, which is much less accurate than brick meshing. IV. Tolerance: In order to get the model to converge at loads high enough to create cracking the tolerance criteria had to be loosened from its default value of 0.001 to a higher value of 0.05.

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138 V. Pre stress losses: These were not calculated in detail but rather the total loss from all the different factors (anchorage, cr eep, shrinkage, relaxation, etc.) was approximated as 15% which was deducted from the initial strain while keeping the analysis static. Recommendations for Further Research As mentioned previously the general model used a simplified temperature loading case. For a more detailed analysis a pplying a temperatu re cycle on the model and observing how that would affect both the superstructure and substructure is recommended The design for CFRP strengthening was done for the as built conditions of the viaduct However, if a new design for the bearings is selected that could change the loads transferred to the piers, something that has to be taken under consideration when selecting a new bearing system for the viaduct. Based on both the field observations and t he results from the general model a more flexible bearing system that allows for more relative movement between the superstructure and substructure is recommended in order to reduce the stress on the substructure. The expansion joints of 8 th Avenue Viaduc t may also be replaced and as such the behavior of the superstructure under a new expansion joint system and how that would affect the piers should be studied, though like the bearings, it is highly likely that a more flexible system will relieve some of t he stress transferred to the piers and abutments. While all the cracks at the bottom of the piers are hairline cracks that are to be expected as a result of concrete being weak in tension

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139 the time being, if in subsequent ins pections of the piers it is ob served that these cracks are expanding then it is recommended to investigate the use of CRFP laminates wrapped around the bottom of the pier as a method of strengthening. A time dependent analysis that not only considers the effects of temperature cycles mentioned previously but also creep and shrinkage is recommended.

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140 REFERENCES AASHTO LRFD 2012 Bridge design S pecification s 6th edition. The American Association of State Highway and Transportation Officials, Washi ngton, D.C.,2012. ACI 440.2R 08 (2008). Guide for the d esign and construction of externally bonded FRP systems for strengthening concrete structures American Concrete Institute (ACI), Farmington Hills, MI (USA). ACI 440.4 R 0 4 (2004 ). Prestressing concre te structures with FRP tendons American Concrete Institute (ACI), Farmington Hills, MI (USA). City and County of Denver, Department of Public Works, Design Engineering Division (1993) Project No.B83 050 West 8 th Avenue Viaduct Between Mariposa and Vall ejo Streets Denver, Colorado ASCE (2009). American Society of Civil Engineers, Reston VA. ACI Committee 446 (1991). Fracture mechanics of concrete: concepts, models and determination of material properties Ame rican Concrete Institute, Detroit, MI. re Behavior of Precracked Conc rete Beams Retrofitted with FRP J. Compos. Constr. 2(3), 138 144. Kim, Y.M., Kim, C.K., Lee, J.C. (2009) determination of reinforced concrete structures Advances in Engineering So ftware 40, 202 211 limit of specimens and structures International Journal of Fatigue 61, 39 45. ion analysis of an aging RC girder bridge using FE crack analysis and simple capacity evaluation equations Engineering Fracture Mechanics 108, 209 221. concrete bridge pier test using Advances in Engineering Software 83, 99 108.

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141 Abdel Detection J. Comput. Civ. Eng. 17(4), 2 55 263. image processing technique for Struct Infrastruct Eng 9(6), 567 77. based retri eval of concrete crack Autom Construct 39, 180 94. st Construction and Building Materials 13, 23 31. Nucl Eng Des 8, 207 229. Saatci, S., Nonlinear finite element modeling of reinforced concrete structures under impact l oads ACI Structural Journal 106(5), 717 725. Chen, E. and Leung, C. (2015). "Finite element modeling of concrete cover cracking due to no n uniform steel corrosion." Engineering Fracture Mechanics 134, 61 78. structural performance of initially cracked reinforced concrete slabs Construction and Building M aterials 19, 595 603. Plewako, Z. (2005) Improvement of Buildings Structural Quality by New Technologies 4, 213 218. Clarke, J.K., Waldron, P. (1996) vanced Struct Eng 74(17), 283 288. reinforced concrete beams: An experimental study of the cracking behavior. Engineering Structures 77, 49 56. Kobayashi, K. wrapping system with cf anchor 5 th International symposium on fiber reinforced polymer (FRP) reinforcement for concrete structures Cambridge, U K, 379 388. gthening of reinforced concrete T ACI Struct J 111(5), 1027 1036. dimensional nonlinear finite element J Compos Constr 15(6), 896 907.

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142 concrete Construction and Building Materials 85, 144 156. Zidani, M.B., Belakhdar, K., Tounsi, A., Bedia, E.A.A. (2015). Finite element analysis of initially damaged beams repaired with FRP plates Composite Structures 134, 429 439. t modeling of debonding failures in FRP strengthened RC beams: A dynamic approach Computers and Structures 158, 167 183. Strengthened Concrete Structures strengthened with near surface mounted CFRP laminates Proc. 3 Int. Co nf. on Composites in Infrastructure, 10 12, San Francisco. based model to study the behaviour of corroded RC beams shear repaired by NSM CFRP rods technique Composite Structures ,1 31, 731 741. Shear strengthening of reinforced concrete beams with near surface mounted fiber reinforced polymer rods ACI Structural Journal 98(1), 60 68. El Near surface mounted f iber reinforced polymer reinforcements for flexural strengthening of concrete structures 101(5), 717 726 Benmokrane, B., Zhang, B., Chennouf behaviour of AFRP and CFRP rods for grouted anchor applications Co nstruction and Building Materials 17, 157 170. Fdratio n Internationale du Betn (2012) Model Code 2010 First complete draft vol. 1 and 2. Bulletins 55 and 5 6, International Federation for Structural Concret e, Lausanne, Switzerland. Morsy, A.M., El Tony, E.T.M. Mohamed El repair/strengthening of pre damaged R.C. beams using embedded CFRP rods Article in press Alexandria Engineering Journal xxx, xxx xxx. sis of adhesively bonded anchorages for CFRP tendons Construction and Building Materials 61, 206 215. for posttensioning carbon fiber reinforced polymer rods PCI J, 59 (1), 103 13.

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143 Schmidt, J.W., Tljsten, B. Bennitz, A., Pedersen, H. FRP tendon anchorage in post tensioned concrete structures Concrete Repair, Rehabilitation and Retrofitting 1181 1186. Schmidt, J.W., Bennitz A., Tljsten, B.; Goltermann, P ., Pedersen, H. (2012) Mechanical anchorage of FRP tendons A literature review Construction and Building Materials 32, 110 121. concrete beams with damaged steel tend ons using post tensioned carbon fiberreinforced polymer rods ACI Struct J 111(2), 387 95. deep beams using post tensioned CFRP rods Composite Structures ,125, 25 6 265. Dolan, C. W., Hamilton, H. R., Bakis, C. E., Nanni, A. ( 2000 for Concrete Structures Prestressed with FRP Tendons, Final Report. Civil and Architectural Engineering Report DTFH61 96 C 00019, University of Wy oming, Laramie, Wyo., May, 113 pp Fdratio n Internationale du Betn. (2007 ). FRP reinforcement in RC structures. Bulletin 40 Lausane: FIB; Technical Report. Hawileh R. A. (2012) Nonlinear finite element modeling of RC beams strengthened with NSM FRP rods Construction and Building Materials ; 27; 461 471 Si Larbi A, Agbossou A, Ferrier E, Michel L. (2012) composite fiber cement plate rein forced by prestressed FRP rods: experimental and Composite Structures 94, 830 8. Al Rousan, R., Haddad R. (2013) NLFEA sulfate damage reinforced concrete beams strengthened with FRP composites Composite Structures ; 96; 433 445 R ashid, Y.R. (1968). Ultimate Srength Analysis of Pre stressed Concrete Pressure Vessels, Nuclear Engineering and Design Vol. 7, pp.334 344. a, V., Gerstle, K., (1971, 1972). Inelastic Analysis of Reinforced Concrete Panels: Part I. Theory, Part II : Experimental Verification IABSE, Zurich, Part I: Vol.31, pp. 32 45, Part II: Vol. 32, pp. 26 39. Saouma, V .E., and Ingraffea, A.R. (1981). Fracture Mechanics Analysis of Discrete Cracking, Proc. IABSE Coll. in Advanced Mechanics of Reinforced Concrete Delft, June 1981, pp. 393 416.

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144 investigations about textile reinforced concrete and hybrid solutions for repairing and/or strengthening reinforced concrete beams Composit e Structures 99, 152 162. Int. Mater. Rev. 46 (3), 117 144. of crack width o n chloride induced corrosion of steel in concrete ACI Mater. J. 94 (1), 56 61. J. Mater. Civ. Eng. 13(3), 194 201. V idal, T., Castel, A., Franois R. (2004). Analyzing crack width to predict corrosion in reinforced concrete Cement and Concrete Research 34, 165 174. Otieno, M., Alexander, M., Beushausen, H. uncracked concrete i nfluence of crack width, concrete quality and crack reopening Mag. Concr. Res. 62 (6), pp. 393 404 Berrocal C.G., Lfgren, I., Lundgren, K. Tang, L. (2015). Corrosion initiation in cracked fibre reinforced concrete: Influence of crack width, fibre t ype and loading conditions Corrosion Science 98, 128 139. Fdration Internationale du Betn. (2001). Externally bonded FRP reinforcement for RC structu res. Bulletin 14. Lausane: FIB; Technical Report.

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145 APPENDIX A PIER AND ABUTMENT DETAILING Design er: Diana Horner (Eng.) Co: Meheen Engineering As built Drawings City and County of Denver 1993, used with permission

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153 APPENDIX B ANSYS CODE FOR PIER 18 /PREP7

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189 ASEL,,,,ars+5,ars+9,4 ASEL,a,,,ars+18,ars+30,12 ASEL,a,,,ars+52,ars+100,48 NUMSTR,LINE,lnn+100 NUMSTR,KP,kpn+100 !Create steel plate plthght=3 K,,th ck/2,g+r+plthght,totalwdth/2

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190 K,, thck/2,g+r+plthght,totalwdth/2 K,,thck/2,g+r+plthght, totalwdth/2 K,, thck/2,g+r+plthght, totalwdth/2 LSTR,kpn+100,kpn+101 LSTR,kpn+102,kpn+103 ASBL,all,lnn+100 ASBL,all,lnn+101 NUMSTR,KP,kpn+200 epltwdth=2/12 frpsp=1 K, ,thck/2+epltwdth,g+r+plthght,totalwdth/2 K,,thck/2+epltwdth,g+r+plthght frpsp,totalwdth/2 K,,thck/2+epltwdth,g+r+plthght 2*frpsp,totalwdth/2 K,,thck/2+epltwdth,g+r,totalwdth/2 K,,thck/2+epltwdth,g+r+plthght, totalwdth/2 K,,thck/2+epltwdth,g+r+plthght frps p, totalwdth/2 K,,thck/2+epltwdth,g+r+plthght 2*frpsp, totalwdth/2 K,,thck/2+epltwdth,g+r, totalwdth/2 K,, thck/2 epltwdth,g+r+plthght,totalwdth/2 K,, thck/2 epltwdth,g+r+plthght frpsp,totalwdth/2 K,, thck/2 epltwdth,g+r+plthght 2*frpsp,totalwdth/2 K,, th ck/2 epltwdth,g+r,totalwdth/2 K,, thck/2 epltwdth,g+r+plthght, totalwdth/2 K,, thck/2 epltwdth,g+r+plthght frpsp, totalwdth/2 K,, thck/2 epltwdth,g+r+plthght 2*frpsp, totalwdth/2 K,, thck/2 epltwdth,g+r, totalwdth/2 NUMSTR,LINE,lnn+200 LSTR,kpn+100,kpn+2 00 LSTR,kpn+200,kpn+201 LSTR,kpn+201,kpn+202 LSTR,kpn+202,kpn+203 LSTR,kpn+203,kps+16 LSTR,kpn+102,kpn+204 LSTR,kpn+204,kpn+205 LSTR,kpn+205,kpn+206 LSTR,kpn+206,kpn+207

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191 LSTR,kpn+207,kps+4 LSTR,kpn+101,kpn+208 LSTR,kpn+208,kpn+209 LSTR,kpn+209,kpn+210 LS TR,kpn+210,kpn+211 LSTR,kpn+211,kps+41 LSTR,kpn+103,kpn+212 LSTR,kpn+212,kpn+213 LSTR,kpn+213,kpn+214 LSTR,kpn+214,kpn+215 LSTR,kpn+215, kps+27 NUMSTR,AREA,arn+100 AL,lnn+110,lnn+200,lnn+201,lnn+202,lnn+203,lnn+204 AL,lnn+117,lnn+205,lnn+206,lnn+207,lnn+ 208,lnn+209 AL,lnn+105,lnn+210,lnn+211,lnn+212,lnn+213,lnn+214 AL,lnn+100,lnn+215,lnn+216,lnn+217,lnn+218,lnn+219 VSLA,, VATT,1,10,2 AATT,2,,4,,1 LESIZE,ALL,1 AMESH,ALL NUMSTR,LINE,lnn+300 LSTR,kpn+200,kpn+204 LSTR,kpn+201,kpn+205 LSTR,kpn+208,kpn+212 LSTR,kpn+209,kpn+213 LSEL,,,,lnn+300,lnn+307 LESIZE,ALL,,,1 LATT,4,12,1 LMESH,all ESLL,,, NUMSTR,KP,kpn+400 NUMSTR,LINE,lnn+400 NUMSTR,AREA,arn+400

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192 K,,THCK/2+clz,g+r+j,TOTALWDTH/2 K,, THCK/2 clz,g+r+j,TOTALWDTH/2 LSTR,lnn+200,lnn+400 LSTR,lnn+400,lns+ 15 LSTR,lnn+208,lnn+401 LSTR,lnn+401,lns+40 AL,lnn+200,lnn+400,lnn+401,lnn+107 AL,lnn+210,lnn+402,lnn+403,lnn+102 K,,THCK/2+clz,g+r+h, TOTALWDTH/2 K,, THCK/2 clz,g+r+h, TOTALWDTH/2 LSTR,lnn+204,lnn+402 LSTR,lnn+402,lns+5 LSTR,lnn+212,lnn+403 LSTR,lnn+ 403,lns+28 AL,lnn+205,lnn+404,lnn+405,lnn+120 AL,lnn+215,lnn+406,lnn+407,lnn+115 ASEL,,,,lnn+400,lnn+403 AATT,2,,4,,1 LSEL,,,,lnn+400,lnn+407 LESIZE,ALL,1 AESIZE,ALL,1 AMESH,ALL !Set initial strain Inistate,set,dtyp,epel Inistate,set,mat,4 Inistate,def i,,,,,0.007 7 !Assign Loads (Two Lanes) !GW1 nstr=4500 fcx=0.0759 fcz=0.0253 N1=54770

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193 N2= 20243 N3=0 N4=2273 N5=35981 N6=60912 N7=315 N8=28855 N9=23222 N10=36314 N11=28580 N12=37214 Nx1=fcx*N1 Nx2=fcx*N2 Nx3=fcx*N3 Nx4=fcx*N4 Nx5=fcx*N5 Nx6=fcx*N6 Nx7=fc x*N7 Nx8=fcx*N8 Nx9=fcx*N9 Nx10=fcx*N10 Nx11=fcx*N11 Nx12=fcx*N12 Nz1= fcz*N1 Nz2= fcz*N2 Nz3= fcz*N3 Nz4= fcz*N4 Nz5= fcz*N5 Nz6= fcz*N6 Nz7= fcz*N7 Nz8= fcz*N8 Nz9= fcz*N9 Nz10= fcz*N10 Nz11= fcz*N11 Nz12= fcz*N12 F,nstr+59,FY, N1 F,nstr+59,FX, Nx1 F, nstr+59,FZ,Nz1 F,nstr+52,FY, N2 F,nstr+52,FX, Nx2 F,nstr+52,FZ,Nz2 F,nstr+60,FY, N3

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194 F,nstr+60,FX, Nx3 F,nstr+60,FZ,Nz3 F,nstr+65,FY, N4 F,nstr+65,FX, Nx4 F,nstr+65,FZ,Nz4 F,nstr+66,FY, N5 F,nstr+66,FX, Nx5 F,nstr+66,FZ,Nz5 F,nstr+53,FY, N6 F,nstr+53,F X, Nx6 F,nstr+53,FZ,Nz6 F,nstr+70,FY, N7 F,nstr+70,FX, Nx7 F,nstr+70,FZ,Nz7 F,nstr+54,FY, N8 F,nstr+54,FX, Nx8 F,nstr+54,FZ,Nz8 F,nstr+79,FY, N9 F,nstr+79,FX, Nx9 F,nstr+79,FZ,Nz9 F,nstr+80,FY, N10 F,nstr+80,FX, Nx10 F,nstr+80,FZ,Nz10 F,nstr+77,FY, N1 1 F,nstr+77,FX, Nx11 F,nstr+77,FZ,Nz11 F,nstr+78,FY, N12 F,nstr+78,FX, Nx12 F,nstr+78,FZ,Nz12 !GW2 nstr=4500 N1=25883 N2= 42304 N3=15216 N4=4456

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195 N5=46796 N6=110977 N7=7741 N8=54204 N9=17687 N10=14056 N11=30489 N12=24206 Nx1=fcx*N1 Nx2=fcx*N2 Nx3=fcx*N 3 Nx4=fcx*N4 Nx5=fcx*N5 Nx6=fcx*N6 Nx7=fcx*N7 Nx8=fcx*N8 Nx9=fcx*N9 Nx10=fcx*N10 Nx11=fcx*N11 Nx12=fcx*N12 Nz1= fcz*N1 Nz2= fcz*N2 Nz3= fcz*N3 Nz4= fcz*N4 Nz5= fcz*N5 Nz6= fcz*N6 Nz7= fcz*N7 Nz8= fcz*N8 Nz9= fcz*N9 Nz10= fcz*N10 Nz11= fcz*N11 Nz12= fcz*N1 2 F,nstr+7,FY, N1 F,nstr+7,FX, Nx1 F,nstr+7,FZ,Nz1 F,nstr+25,FY, N2 F,nstr+25,FX, Nx2 F,nstr+25,FZ,Nz2 F,nstr+36,FY, N3 F,nstr+36,FX, Nx3 F,nstr+36,FZ,Nz3

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196 F,nstr+5,FY, N4 F,nstr+5,FX, Nx4 F,nstr+5,FZ,Nz4 F,nstr+8,FY, N5 F,nstr+8,FX, Nx5 F,nstr+8,FZ,Nz5 F,nstr+21,FY, N6 F,nstr+21,FX, Nx6 F,nstr+21,FZ,Nz6 F,nstr+22,FY, N7 F,nstr+22,FX, Nx7 F,nstr+22,FZ,Nz7 F,nstr+27,FY, N8 F,nstr+27,FX, Nx8 F,nstr+27,FZ,Nz8 F,nstr+44,FY, N9 F,nstr+44,FX, Nx9 F,nstr+44,FZ,Nz9 F,nstr+45,FY, N10 F,nstr+45 ,FX, Nx10 F,nstr+45,FZ,Nz10 F,nstr+46,FY, N11 F,nstr+46,FX, Nx11 F,nstr+46,FZ,Nz11 F,nstr+47,FY, N12 F,nstr+47,FX, Nx12 F,nstr+47,FZ,Nz12 !GW4 nstr=4400 N1=68677 N2=35379 N3=24294 N4=44679 N5=26243 N6=89514 N7=11581 N8=46649

PAGE 213

197 N9=8987 N10=17669 N11=1772 2 N12=19949 Nx1=fcx*N1 Nx2=fcx*N2 Nx3=fcx*N3 Nx4=fcx*N4 Nx5=fcx*N5 Nx6=fcx*N6 Nx7=fcx*N7 Nx8=fcx*N8 Nx9=fcx*N9 Nx10=fcx*N10 Nx11=fcx*N11 Nx12=fcx*N12 Nz1= fcz*N1 Nz2= fcz*N2 Nz3= fcz*N3 Nz4= fcz*N4 Nz5= fcz*N5 Nz6= fcz*N6 Nz7= fcz*N7 Nz8= fcz*N8 Nz9= fc z*N9 Nz10= fcz*N10 Nz11= fcz*N11 Nz12= fcz*N12 F,nstr+76,FY, N1 F,nstr+76,FX, Nx1 F,nstr+76,FZ,Nz1 F,nstr+60,FY, N2 F,nstr+60,FX, Nx2 F,nstr+60,FZ,Nz2 F,nstr+77,FY, N3 F,nstr+77,FX, Nx3 F,nstr+77,FZ,Nz3 F,nstr+81,FY, N4 F,nstr+81,FX, Nx4 F,nstr+81,FZ,N z4

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198 F,nstr+83,FY, N5 F,nstr+83,FX, Nx5 F,nstr+83,FZ,Nz5 F,nstr+62,FY, N6 F,nstr+62,FX, Nx6 F,nstr+62,FZ,Nz6 F,nstr+92,FY, N7 F,nstr+92,FX, Nx7 F,nstr+92,FZ,Nz7 F,nstr+63,FY, N8 F,nstr+63,FX, Nx8 F,nstr+63,FZ,Nz8 F,nstr+101,FY, N9 F,nstr+101,FX, Nx9 F ,nstr+101,FZ,Nz9 F,nstr+102,FY, N10 F,nstr+102,FX, Nx10 F,nstr+102,FZ,Nz10 F,nstr+99,FY, N11 F,nstr+99,FX, Nx11 F,nstr+99,FZ,Nz11 F,nstr+100,FY, N12 F,nstr+100,FX, Nx12 F,nstr+100,FZ,Nz12 !GW5 nstr=4400 N1=57703 N2=50367 N3=7908 N4=10729 N5=59035 N6=3 9520 N7=36173 N8=106111 N9=36016 N10=18329 N11=41697

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199 N12=17835 Nx1=fcx*N1 Nx2=fcx*N2 Nx3=fcx*N3 Nx4=fcx*N4 Nx5=fcx*N5 Nx6=fcx*N6 Nx7=fcx*N7 Nx8=fcx*N8 Nx9=fcx*N9 Nx10=fcx*N10 Nx11=fcx*N11 Nx12=fcx*N12 Nz1= fcz*N1 Nz2= fcz*N2 Nz3= fcz*N3 Nz4= fcz*N4 Nz5= fcz*N5 Nz6= fcz*N6 Nz7= fcz*N7 Nz8= fcz*N8 Nz9= fcz*N9 Nz10= fcz*N10 Nz11= fcz*N11 Nz12= fcz*N12 F,nstr+31,FY, N1 F,nstr+31,FX, Nx1 F,nstr+31,FZ,Nz1 F,nstr+43,FY, N2 F,nstr+43,FX, Nx2 F,nstr+43,FZ,Nz2 F,nstr+48,FY, N3 F,nstr+48,FX, Nx3 F,nstr+48,FZ,Nz3 F,nstr+30,FY, N4 F,nstr+30,FX, Nx4 F,nstr+30,FZ,Nz4 F,nstr+32,FY, N5 F,nstr+32,FX, Nx5

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200 F,nstr+32,FZ,Nz5 F,nstr+37,FY, N6 F,nstr+37,FX, Nx6 F,nstr+37,FZ,Nz6 F,nstr+38,FY, N7 F,nstr+38,FX, Nx7 F,nstr+38,FZ,Nz7 F,nstr+44,FY, N8 F,nstr+44,FX, Nx8 F,nstr+ 44,FZ,Nz8 F,nstr+55,FY, N9 F,nstr+55,FX, Nx9 F,nstr+55,FZ,Nz9 F,nstr+56,FY, N10 F,nstr+56,FX, Nx10 F,nstr+56,FZ,Nz10 F,nstr+57,FY, N11 F,nstr+57,FX, Nx11 F,nstr+57,FZ,Nz11 F,nstr+58,FY, N12 F,nstr+58,FX, Nx12 F,nstr+58,FZ,Nz12 /SOLU