FINITE ELEMENT ANALYSES

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Nov 25, 2013 (3 years and 4 months ago)

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FINITE ELEMENT

ANALYS
E
S

OF

A

FULL
-
DEPTH

PRECAST
/PRESTRESSED

DECK PANEL
BRIDGE
S












APPROVED BY:

________________________________________ _______________

Dr. Michael Oliva

Date

Major

Advisor

Professor of Civil and Environmental Engineering

University of Wisconsin


Madison







ii







FINITE ELEMENT

ANALYS
E
S

OF

A

FULL
-
DEPTH

PRECAST
/PRESTRESSED DECK PANEL

BRIDGE
S



by
Sung

Je Chi











A thesis submitted in partial fulfillment of

th
e requirements for the degree of

Master of Science

(Civil Engineering)




a
t the

UNIVERSITY OF WISCONSIN
-
MADISON

200
7



iii

Acknowledgements

Many people have contributed in various ways to this project.

I would like to express my
sincere thanks and immeasurable

respect to

many individuals.

First,
I
offer a heartfelt thanks to
my advisor,
Professor
Michael G. Oliva

for all
your

comments and

suggestions as I worked on this thesis.

Without
your
support,
guidance
and

advice

this
project

would not be possible
. In pa
rticular, I would like to thank
my very
supportive

graduate committee

members,
Professor
Lawrence C. Bank

and

Professor
Jeffrey
S. Russell
,

who provided
alternate viewpoints, technical expertise

and
a delicate balance of
guidance
.

I

also want

to thank Scot
t Becker and Finn Hubbard from th
e
Wisconsin DOT,
Tom Strock from FHWA, and the Innovative Bridge Research and

Construction Program for
funding this research.

I would like to thank previous researchers, Scott M. Markowski and
Forrest Gregory
Ehmke
. Without

your successful and previous work this thesis

could not have been
completed.

I would like to t
hank you to my colleagues who have given me their
time to help
me and
friendship and

encouragement.

In particular I want to thank
Han

Ug Bae

and
Joseph
Hanus
. I
also would like to thank the members of a bridge meeting group,
P
aul

G
eorgieff,
A
ndrew

S
pottiswoode
,
Ajaya Malla

and
Pinar Okumus
.

I must thank my family. To my

future

wife,
Jimin,

you have always been there for

me.
Without your unquestioning love and supp
ort this journey would not have

been possible. To
express how much I love you would be impossible, just know

that it grows with each day. To
my brother and sister
thank you for your encouragement.

Finally
To my mother and father
who have always encouraged
me

and were never reticent to show their pride in me, I thank
you

and love you
.



iv

Abstract

T
he
purpose

of t
his
research is to evaluate
the
pre
-
stressing
needed across joints in

full
-
depth prefabricated
bridge
deck
s.

The structural analysis software was used
to perform the
finite element analyses.

T
hree different bridge
s

were
examined

to evaluate the
minimum

pre
-
stressing level needed to prevent
joint
opening between
the
precast deck
panels under
the
AASHTO standard
truck loading.

This thesis describes the fin
ite element analyses for the three different
bridges (
Culpeper
Bridge, Welland River Bridge and Door Creek Bridge) in terms of the
dimension

of each
bridge model, modeling assumptions, and AASHTO standard loading cases. Two full
-
depth
precast deck panel br
idges
(Culpeper Bridge and Welland River Bridge)

were previously
analyzed by other researchers. T
he accuracy of the
current
SAP model
ing method was
verified by comparing
the previously analyzed

results

with
the

result from the

SAP analys
e
s
.

The results fro
m the analys
e
s provide the r
e
-
evaluated
longitudinal
minimum
pre
-
stress
ing

levels

of the two previously analyzed bridges (
Culpeper Bridge and Welland River
Bridge
) and the required post
-
tensioning levels

at joints

across longitudinal and transverse
joints
in
the
Door Creek Bridge. Also the
analyses define

the overloading level

needed

to
cause joint opening with

a given

amount of pre
-
stressing or post
-
tensioning and
behavior
after

joint opening effect due to the overload

increas
ing toward the factored
streng
th

design
loads in
the
Door Creek Bridge.







v

Table of Contents

Chapter 1

Introduction

................................
................................
................................
...........

1

1.1

Introduction

................................
................................
................................
...........

1

1.2

Scope of the Research Project

................................
................................
...............

2

1.3

Scope of Finite Element Modeling (FEM) Analysis

................................
............

2

1.4

Research Objectives

................................
................................
..............................

3

1.4.1

Culpeper Bridge

................................
................................
............................

3

1.4.2

Welland River Bridge

................................
................................
...................

4

1.4.3

Door Creek Bridge

................................
................................
........................

4

Chapter 2

Literature Review

................................
................................
................................
..

5

2.1

Introduction

................................
................................
................................
...........

5

2.2

AASHTO Precast Deck Design Provisions

................................
..........................

5

2.3

Description of Bridge Model

................................
................................
................

6

2.3.1

Culpeper Bridge

................................
................................
............................

6

2.3.2

Welland River Bridge

................................
................................
...................

9

2.3.3

Door Creek Bridge

................................
................................
......................

11

2.4

Summ
ary

................................
................................
................................
.............

15

Chapter 3

Finite Element Modeling

................................
................................
....................

16

3.1

Introduction

................................
................................
................................
.........

16

3.2

Types and Sizes of Elements and Material Properties

................................
........

16

3.3

Testing the Nlink Element for Nonlinear Static Analysis

................................
..

19

3.4

De
scription of Bridge Models

................................
................................
.............

20

3.4.1

Culpeper Bridge Model

................................
................................
...............

20



vi

3.4.2

Welland River Bridge Model

................................
................................
......

25

3.4.3

Door Creek Bridge Model

................................
................................
..........

29

3.5

Summary

................................
................................
................................
.............

34

Chapter 4

Results

................................
................................
................................
.................

36

4.1

Objectives

................................
................................
................................
...........

36

4.2

Verification of Finite Element Modeling

................................
............................

36

4.2.1

Moment Equilibrium
Check

................................
................................
.......

37

4.2.2

Verification of Culpeper Bridge

................................
................................
.

38

4.2.3

Verification of Welland River Bridge

................................
.........................

40

4.2.4

Stress Analysis of Shear Studs

................................
................................
....

44

4.3

Results


Required Prestress

................................
................................
...............

46

4.3.1

Culpeper Bridg
e Model

................................
................................
...............

46

4.3.2

Welland River Bridge Model

................................
................................
......

48

4.3.3

Door Creek Bridge Model

................................
................................
..........

51

4.4

Overloading and Joint Opening Effect in Door Creek Bridge Model

................

54

Chapter 5

Summary, Conclusion and Recommendations

................................
...................

60

5.1

Introduction

................................
................................
................................
.........

60

5.2

Summary

................................
................................
................................
.............

60

5.2.1

Verification of Finite Element Modeling

................................
....................

60

5.2.2

Pre
-
stressing Level for Bridge Joints

................................
..........................

61

5.2.3

Overloading and Joint Opening Effect in the Door Creek Bridge Model

..

63

5.2.4

Summary

................................
................................
................................
.....

64

5.3

Conclusions

................................
................................
................................
.........

65



vii

5.4

Recommendations

................................
................................
...............................

66

References

................................
................................
................................
...............................

68

Appendix 1: Truck Loading Location (Culpeper Bridge)

................................
......................

70

Appendix 2: Single Truck Loading Lo
cation (Welland River Bridge)

................................
..

74

Appendix 3: Double Truck Loading Location 1 (Welland River Bridge)

..............................

81

Appendix 4: Double Truck
Loading Location 2 (Welland River Bridge)

..............................

88

Appendix 5: Truck Loading Longitudinal Location (Door Creek Bridge)

.............................

95

Appendix 6:
Truck Loading Transverse Location (Door Creek Bridge)

..............................

100
































viii

List of Figures

Figure 2.1 Stress variation of the Culpeper Bridge along the Br
idge Length (Issa, 1998)

.......

7

Figure 2.2 Layout of the AASHTO Truck Loading in Welland River Bridge model (Issa,
1998)

................................
................................
................................
................................
.......

10

Figure 2.
3 Rotational Stiffness of Longitudinal Joint (Markowski, 2005)

.............................

13

Figure 2.4 Rotational Stiffness of Transverse Joint (Markowski, 2005)

................................

14

Figure 3.1 Rotational Stiffness for Two different Joints in Door Creek Bridge Model

.........

18

Figure 3.2 Example Modeling for Nonlinear Static Analysis

................................
.................

19

Figure 3.3 Rotational Stiffness of Nlink Element

................................
................................
...

19

Figure 3.4 Result from Nonlinear Static Analysis in SAP 2000

................................
.............

20

Figure 3.5 Typical Panel Layout for Culpeper Bridge Deck Panel (Ehmke, 2006)

...............

21

Figure 3.6 Three
-
Dimensional View of Culpeper Bridge Model

................................
...........

23

Figure 3.7 Truck Loading similar to Issa’s Truck Loading

................................
....................

24

Figure 3.8 AASHTO Truck Loading for Maximum Bending

................................
................

25

Figure 3.9 Three
-
Dimensional View of Welland River Bridge Model

................................
..

27

Figure 3.10 Double Truck Loading similar to Issa’s Truck Loading

................................
....

28

Figure 3.11 Single Truck Loading by AASHTO along Half of Bridge Length

....................

28

Figure 3.12 Typical Panel Layout for Door Creek Bridge (Plans by WisDOT)

...................

30

Figure 3.13 Three
-
Dimensional View of Door Creek Bridge Model

................................
....

31

Figure 3.14 Finding Critical Location of Truck Loading for Transverse Joi
nt

.....................

32

Figure 3.15 Critical Location of Truck Loading for Transverse Joint

................................
...

33

Figure 3.16 Critical Location of Truck Loading fo
r Longitudinal Joint

................................

34

Figure 4.1 Location of Moment Checking

................................
................................
.............

37



ix

Figure 4.2 Longitudinal Stress (ksi) on Top Surface

................................
.............................

39

Figure 4.3 Longitudinal Stresses along Bridge Length

................................
.........................

40

Figure 4.4 Longitudinal Stress (ksi) on Top Surface

................................
.............................

41

Figure 4.5 Longitudinal Stresses along Bridge Length

................................
.........................

42

Figure 4.6 Longitudinal Stresses in Transverse Joint along Bridge Width

...........................

42

Figure 4.7 Longitudinal Stress in Transverse Joint along Half of Bridge Length

.................

43

Figure 4.8 Internal Forces of Exterior Bridge Girder in Cul
peper Bridge Model

.................

44

Figure 4.9 Shear Studs Layout for Each Block
-
out (Plans by WISDOT)

.............................

45

Figure 4.10 Longitudinal Stress (k
si) on Top Surface along Bridge Length

.........................

46

Figure 4.11 Longitudinal Stress Variation along Bridge Length

................................
...........

47

Figure 4.12 Longitu
dinal Stress Variation along Bridge Length

................................
...........

48

Figure 4.13 Longitudinal Stress (ksi) on Top Surface along Half Bridge Length

.................

49

Figure 4.14 Longitudinal Stress in Transverse Joints along Half Bridge Length

..................

50

Figure 4.15 Longitudinal Stress (ksi) on Top Surface

................................
...........................

51

Figure 4.16 Longitudinal Stress Variation in Transverse Joint across Bridge Width

...........

52

Figure 4.17 Transverse Stress (ksi) on Top Surface

................................
..............................

53

Figure 4.18 Transverse Stress Variation in Longitudinal Joint across the Bridge Length

....

54

Figure 4.19 Longitudinal Bending Moment in Transverse Joint across Bridge Wi
dth

.........

55

Figure 4.20 Rotation about Transverse Axis in Transverse Joint across Bridge Width

........

56

Figure 4.21 Vertical Deflection a
t the critical section across Bridge Width

.........................

56

Figure 4.22 Rotation about longitudinal Axis in Longitudinal Joint along Bridge Length

...

57

Figure 4.23 Transverse Bending Moment in Longitudinal Joint along Bridge Length

.........

58

Figure 4.24 Vertical Deflection at the Longitudinal Joint along Span Length

......................

58



x

List of Tables

Table 2.1 Types of Elements for Structural Components used by Issa (1998)

........................

6

Table 3.1 Element Types for E
ach Structural Component (Ehmke’s thesis, 2006)

..............

17

Table 3.2 Number of Elements for Each Structural Component

................................
...........

18

Table 3.3 Sum
mary of the Finite Element Modeling

................................
............................

35

Table 4.1 Moment Check in the Culpeper Bridge

................................
................................
.

38

Table 4.2 Overloading Factor for Each
Joint

................................
................................
.........

54

Table 4.3 Load Factor of Overloading

................................
................................
...................

55

Table 4.4 Percent of Softened Transverse Joint to Deck Span

................................
..............

57

Table 4.5 Percent of Softened Longitudinal Joint to Bridge Span

................................
........

59

Table 5.1 Minimum Prestress in Joint

................................
................................
....................

63

Table 5.2 Comparison of the results from SAP and Issa

................................
.......................

65



1


Chapter 1

Introduction

1.1


Introduction

A

considerable

number of highway bridges in the United States
currently need
rehabilitation and replacement.

As
the
n
ation's bridges are aging and traffic demands are
increasing
, they
are functionally obsolete
and/
or
structurally
deficient
.

There are options to
select the most optimal
rehabilitation

and replacement. P
re
-
fabricated bridge

systems
,
especially prec
ast concrete deck panels
,

are

one of the innovative technologies

for
rehabilitation

and replacement because there are several advantages
that promise

a

high

payoff.


First,
impact on traffic in the form of delays

during b
ridge constructi
on
is

minimized

bec
ause

the u
s
e of

precast concrete deck panels

speeds the construction process
.

A second
adva
ntage is that construction work

zone

safety is improved. Because prefabrication moves
much of the bridge construction work off
-
site, the amount of time that workers
are required
to operate near
traffic is greatly d
ecreased
.

A third advantage is that construction is less
disruptive for the environment.
The u
s
e of

precast concrete deck panels
that are produced off
-
site reduces
the amount of time required for

bridge
cons
truction
.
A final advantage is that
increased quality and lower
maintenance

costs are realized.
U
sing p
refabricat
ed

systems
takes them out of the critical path of the project schedule: work can be done ahead of time,
using as much time as necessary, in a c
ontrolled environment. This reduces dependence on
weather and i
ncreases control of quality
and i
mproved quality
produce
s

lower life
-
cycle costs.

Taking the various advantages of the prefabricated systems,

a

full
-
depth precast concrete


2

bridge deck system wa
s applied to
a
deck replacement of the Door Creek Bridge on highway
I90
near

Madison, Wisconsin.

T
his research project is
part of the
Innovative Bridge Research and Construction

(
IBRC)
program

funded by the
Federal Highway Administration

(
FHWA
).
The
Univer
sity of
Wisconsin at Madison has joined with
the Wisconsin Department of Transportation

(WisDOT
) and
subcontracted

a private
design
company named
Alfred Benesch & Co.

to
design

the
precast

ful
l
-
depth concrete deck system for
the replacement of the Door Cre
ek
Bridge.

1.2


Scope of the Research Project

There are three phases for th
e IBRC

research project. The first phase is back ground
research and
preliminary

engineering, which is

related to

specific components of

the
prefabricated

deck system and
the
design pr
ocedure for the full
-
depth precast concrete deck
panel.

The
second

phase is the application and direct implementation of the full
-
depth precast
concrete deck panel system to the Door Creek Bridge, which is related to a
constructability

study of the full
-
de
pth precast bridge panel system compar
ed

with a conventional cast
-
in
-
place concrete deck system. The third phase is related to a finite element modeling (FEM)
analysis of the full
-
depth precast deck bridge to evaluate the minimum required pre
-
stressing
lev
el across joints and
the expected
structural behavior of the Door Creek Bridge. The first
two phases were performed by Scott Markowski (2005) and Greg Ehmke (2006). Th
e scope
of this research study includes

the FEM analyses of the full
-
depth precast deck
bridges.

1.3

Scope of Finite Element Modeling (FEM) Analysis



3

Three different bridges named
as the
Culpeper Bridge, Welland River Bridge and Door
Creek Bridge were modeled and analyzed by SAP 2000. Linear elastic analyses were
performed for
the
Culpeper and Wel
land River Bridge and both linear and non
-
linear elastic
analyses were performed for

the

Door Creek Bridge.
The
Culpeper and Welland River
Bridge models had been previously modeled and analyzed by Issa (1998).
T
hese two bridge
s

were re
-
analyzed in order to

verify the accuracy of the current SAP modeling method and
to
identify the
minimum required pre
-
stressing level across the joints

under
AASHTO
LRFD

(2007)

service loads

including impact. Then,
the
Door Creek Bridge w
as

analyzed to
evaluate the minimum req
uired pre
-
stressing level across the longitudinal joint
s

and
transverse joint
s

and
to predict

the structural behavior of the bridge under several
overloading cases.

1.4


Research Objectives

Research Objectives are
categorized

according to each bridge model in
the following
section
s

1.4.1
,
1.4.2

and
1.4.3
:
for the
Culpeper Bridge, Welland River Bridge and Door
Creek Bridge.

1.4.1

Culpeper Bridge

-

V
erify

the

accuracy of
current SAP

an
alys
e
s by comparing with stresses suggested
by Issa

s
previous paper

(1998)

-

Apply service loads
considering the dynamic allowance factor based on AASHTO
LRFD
(
2007
)

and
re
-
evaluate

stress levels
in the transverse joint.

-

Define a minimum prestress level re
quired to prevent joint opening between precast
panels



4

1.4.2

Welland River Bridge

-

V
erify

the

accuracy of
current SAP

analys
e
s by comparing with stresses suggested
by Issa’
s
previous
paper (
1998)
.

-

Apply service loads
considering the dynamic allowance factor based

on AASHTO
LRFD
(
2007
)

and
re
-
evaluate

stress levels
in the transverse joint.

-

Define a minimum prestress level

required to prevent joint opening between precast
panels.


1.4.3


Door Creek Bridge

-

Apply service loads
considering the dynamic allowance factor based

on AASHTO
LRFD
(2007)

and
re
-
evaluate

stress levels
in the transverse joint
s
.
Define joint
prestress level needed to prevent joint opening.

-

Determine
how large

an
overload would be required to cause joint opening with the
amount of
pre
-
stressing

level

tha
t actually exists in the bridge as constructed
.

-

S
imulate how joint opening

under

overload

would affect the overall performance of
the bridge and how loads are re
-
distributed as joints crack open when the loading is
increased slowly up toward the factored s
trength design loads.



5


Chapter 2

Literature Review

2.1


Introduction

Three different bridg
e models were created using SAP

2000
to perform FEM analyses.
In order to verify the accuracy of the current SAP modeling method, a publication was
carefully and
cautiously

refere
nced, which was Issa

s
article (
1998) published in PCI Journal
titled “Analysis of Full Depth Precast Concrete Bridge Deck

Panels”

This publication
provides the detailed description of the
two
selected bridges

(a simply supported bridge, the
Culpeper Bridg
e; a three
-
span continuous bridge, the Welland River Bridge) in terms of
modeling techniques,
material

properties and
recommendations for

minimum
pre
-
stressing

levels
across the transverse joint

to prevent panel joint opening
. In addition research papers
p
ublished by previous researchers (Scott
Mark
owski, 2005;
Greg Ehmke
,
2006
)

were
reviewed to create the finite element model
of
the Door Creek Bridge and perform the FEM
analyses using SAP 2000. The

following section will present
detail
ed information

on

pre
vious projects
.

2.2

AASHTO Precast Deck Design Provisions

Flexural
ly discontinuous precast decks
should be joined
together

by
shear keys
.
The
AASHTO LRFD Specificat
ion Section 9.7.5.3 recommends
that
a
minimum

post
-
tension
ing
level
of 250 psi

should be provide
d across the transverse

joint.

This post
-
tensioning level was
provided for the Door Creek Bridge
.





6

2.3

Description of Bridge Model

Issa

s

(1998)

a
nalytic models of

the

Culpeper Bridge

and
Welland

River Bridge
s

were
created using the finite element analysis pr
ogram, ALGOR. For the two selected bridge
models, five different types of element
s

corresponding to the types of structural components
were used to simulate the bridge geometry and materials.
Table
2
.
1

summarizes
the
elements
used

by Issa
. The Young

s moduli of elasticity were 30
×

10
6

psi for the reinforcing steel,
4.03
×

10
6

psi for the normal concrete

used in precast panels

and 5.1
×

10
6

psi for the
polymer concrete

used in transverse joints
. The
Poisson’s

ratios were

assumed to

be

0.3 for
the steel and 0.18 for the concrete
s
. The coefficients of thermal expansion were 6.5
×

10
-
6
per
°
F for the steel and 5.5
×

10
-
6
per
°
F for the concrete
s
.

Table
2
.
1


Types of Elements for Structur
al Components used by Issa (1998)

Types of Structural Components

Types of Finite Elements

Beams and Diaphragms

Plate elements (4
nodes
)

Precast Panels

Brick elements (6
nodes

and 8
nodes
)

Shear Connecting
Pockets

Brick elements (8
nodes
)

Transverse Joi
nts

Brick elements (8
nodes
)

Closure Pours

Brick elements (8
nodes
)

Parapets

Brick elements (8
nodes
)

Shear Connecting Studs

Brick elements (8
nodes
)

Reinforcement for Precast Panels

Truss elements

Reinforcement for Closure Pour

Truss elements

Post
-
t
ensioning Tendons

Truss elements


2.3.1


Culpeper Bridge

The Culpeper Bridge is a simply supported bridge 54.5
ft.

in
length

and 30
ft.

in width.
This bridge is located in
Virginia

and
maintain
ed by the Virginia D
epartment of
T
ransportation
.

Two exterior beams
are W33
×
125 with 3
ft.

deck
overhang
s

and the interior


7

beams are W33
×
132. All the finite elements corresponding to the structural components are
summarized in
Table
2
.
1
. For the Culpeper Bridge model, symmetry was imposed in
trans
verse direction.
A h
alf model was created

in order to provide faster and more efficient
FEM analyses.

Issa did not provide clear description
, however,

of the critical location of the AASHTO
truck loading

used in the analysis
. The truck loading location in

longitudinal direction was
shown in
a

figure

of Issa

s paper

that shows stress variation along

the

bridge length for the
Culpeper Bridge.
This figure is reproduced here in

Figure
2
.
1
.


Figure
2
.
1

Stress variation of the Culpeper Bridge along the Bridge Length (Issa, 1998)


As shown in
Figure
2
.
1
,

one small peak and two large peaks clearly represent the
location of the 3 axles of
the
HS20
-
44

truck loading u
sed by Issa
.

T
he spacing between the


8

two axles of
the
HS20
-
44 is approximately 10 ft. However, this 10
ft.

spacing is shorter than
the typical spacing (14
ft.
) between the two axles of

the HL
-
93 design truck
based on
AA
SHTO LRFD Design Specifications
(2007)

or the HS20
-
44 truck from the AASHTO
Standard Specifications(1996)
.


As shown in
Figure
2
.
1

of the longitudinal stress variation on the bottom layer along the
bridge span
in Issa’
s article (1998), the maximum tensile stress value

was 100 psi near
midspan under the service loading only.

Furthermore
, as described
in Ehmke’
s thesis

(2006),
there

appeared to be

an

inconsistency between
the
construction sequence and the finite element modeling method
described in Issa

s article.
Issa
describe
s

the
deck
panels
a
s

stressed

in

the

longitudinal
direction
before grouting

the
haunches

and shear connector pockets, which means that since
the deck panels are entirely
separated

from the girder

when the deck panels are stressed,
the
stress would
be

carried by the panels alone
. Issa

s description of the finite element model
shows that the deck panels are compositely connected to the girders using beam elements
modeling shear studs and brick elements modeling the grout in the shear studs pocket. Iss
a
used temperature change on the truss element corresponding to the post
-
tensioning tendons to
simulate

post
-
tensioning force.
Th
is modeling method

impl
ies that the composite action was
achieved

prior to applying the post
-
tensioning force and

the post
-
tens
ioning force was
applied to a composite section.

Thus, since the post
-
tensioning force should be applied to the
deck panels alone in a non
-
composite state, Issa

s modeling method to apply the post
-
tensioning force
does

not

appear

consistent with the constr
uction sequence that
was

described.

Issa

s results also showed that the truck loading caused 100 psi of tension stress in the
transverse

joints. When 200 psi of compressive post
-
tensioning was applied, the truck load


9

tension was only reduced by 75 psi rat
her than 200 psi. This contradiction would be natural if
Issa

s model was composite, since a portion
of the

post
-
tensioning would be absorbed by the
girders.

Issa
recomm
e
n
d
s

tha
t
a

minimum 200 psi longitudinal post
-
tensioning

stress
i
s
requir
ed

for

the Cul
peper Bridge
, even though this does not fully eliminate the truck induced tension,

considering all the residual stresses in the concrete including creep and shrinkage effects.

2.3.2


Welland River Bridge

The Welland River Bridge

carrying two southbound lanes
is
located near the City of
Niagara Falls and

maintained by the Ontario Ministry of Transportation.
As described by Issa,
the bridge consist
s

of 18 continuous spans 48
ft.

long and 43.5
ft.

wide. Only 3 spans were
constructed using the precast concrete deck p
anels with 8.85 inches depth. The deck is
supported by four lines of steel bridge girders with sizes of W33X125 for the exterior girders
and W33X150 for the interior girders. All the finite elements
used by Issa
corresponding to
the structural components a
re summarized in
Table
2
.
1
. For the Welland Bridge model,
symmetry is imposed again in both
the
transverse and longitudinal direction
s
. A quarter
model was created in order to provide faster and more efficient way for the FEM anal
yses.

As described by Issa,
a

double truck loading w
as

applied along the bridge span. Issa
presented

a figure of

the layout of
the
AASHTO truck loading which shows the location of
the AASHTO truck loading to cause the maximum negative moment over the pier
.

This
figure is reproduced here in
Figure
2
.
2
.

However Issa did not provide a detailed description
related to the critical location of the truck loading. Four axles were shown in
Figure
2
.
2
,
which consist
ed of one complete HS20
-
44

truck

and one axle of another HS20
-
44

truck
. Issa


10

describes that the loads (shears and moments) produced by the rest of the one axle of the
second truck predetermined and superimposed
on one edge of his a quarter bridge model to
simulate actual loads
.


Thus the loading used by Issa actually appears to simulate the effect of having 2 or more
design trucks on the three
-
span bridge with a spacing
of approximately

24 feet between truck
axles. This is not a standard design loading used

in either the AASHTO Standard
Specifications or the LRFD specifications.


Figure
2
.
2

Layout of the AASHTO Truck Load
ing

in Welland River Bridge
model

(Issa, 1998)


Issa

s modeling is further thrown into do
ubt when he notes that the magnitude of
compressive stress in joints is greater than in the panels because the joint material is

stiffer.


11

This conclusion ignore
s the basic requirement of
equilibrium:

Static force balance must exist
between the joint materi
al and the deck material.

For the Welland
R
iver Bridge model, Issa used again temperature change on the truss
element corresponding to the post
-
tensioning tendons to
simulate

post
-
tensioning force. As
mentioned in

2.3.1
, there
was the inconsistency between construction sequence and the finite
element modeling method described in Issa

s article (1998).

In addition Issa did not provide dimensions in the figure of the layout of AASHTO truck
loading. It is observed that the spacing

between the two trucks is approximately 24
ft.

based
on the relative
dimension
s comparing with
other

elements in the figure. However, AASHTO
LRFD Specifications

(2007)

have a

specified
50
ft.

spacing between a rear axle of the first
truck and a front axle

of the second truck. In Issa

s double truck loading case, the
longitudinal stress level
may

be too conservative
compared to that obtained using truck
spacing of
the AASHTO LRFD Specifications

(2007)
.

Issa
recomm
e
n
d
s

tha
t
a

minimum 200 psi longitudinal pos
t
-
tensioning

stress level
i
s
requir
ed
near midspan
of girders
at the bottom layer in the positive bending region

of the
deck. T
he minimum

of

450 psi post
-
tensioning level is required to avoid tension in the
transverse joint over the interior
pier
supports
at the top layer in the
negative bending region

of the girders.

2.3.3


Door Creek Bridge

Information describing the Door Creek Bridge was
provided in

Mark
owski’
s thesis
(
2005
) and Ehmke

s thesis (2006). The Door Creek Bridge is a single span bridge located
on
In
terstate I
-
90 near the city of McFarland, Wisconsin
. In 2006 the bridge was reconstructed


12

to replace existing
decking

and widen
ed

to
accommodate

an additional lane. T
wo

bridge
s
were actually involved on the divided freeway.

As described in
Mark
owski’
s the
sis (
2005
)
and Ehmke

s
thesis (2006), taking advantage

of prefabricat
ion, a

full
-
depth precast deck
panel

system was utilized
in

the
westbound

bridge. A conventional cast in place steel
reinforced concrete deck system was utilized
in

the eastbound bridge i
n order to compare the
differences

between the two different systems with respect to
constructability
, performance
and durability. This research study is focused on the westbound bridge
with

the full
-
depth
precast deck panel system.

Both bridges have the s
ame dimensions. Each bridge is a simply supported structure with
8.5


deck
thickness, 83


bridge

span and 30
°

skew angle.
The existing bridges originally
were 40’
-
2” wide,

however,
the bridges were widened to
64’
-
6”.

Each
bri
dge originall
y ha
d

five 60” dee
p steel

plate girders spaced at 8’
-
10”
on center with the supporting top

flange
measuring 12” wide
. T
hree additional gi
rders
with
7’
-
6”
spacing on

center

were added to each
bridge

to

accommodate the widening
.

The

existing steel plate girders are constructed

from grade ASTM A36 steel

and
consist
of a 1¼”

×

16” bottom flange, a 3/8”
×

60” web, and

5/8”
×

12” top flange; the additional
new girders are constructed from ASTM

A709 Grade 36 steel and consist of a 1”
×

16”
bottom flange, a 7/16”
×

60” web, and ¾”
×

12” top flange. The haunch between the

girders
and the bridge deck varies between 1” to 3” to adjust for camber in the

girders.
H
eaded shear
studs
are
utilize
d

to
obtain

composite beam action

for both bridges
. Parapets

for each
structure are
the typical W
i
s
DOT

LF

constructed from conventionally

formed steel
reinforced concrete.



13

2.3.3.1

Longitudinal Joint

The Door Creek Bridge was constructed in stages in order
to
keep

two lanes of
traffic

flow during the
construction
.

A l
ongitudi
nal joint exist
s

between
stage

1 and

stage

2
construction.

As described in
Mark
owski’
s thesis (
2005
), three full
-
scale longitudinal joint
tests were performed to determine the amount of post
-
tensioning stress
needed

across the
longitudinal joints under
service level vehicle loads

considering

impact loads based on
AASHTO Standard
Specification (
1996)
.

The design level
f
or

transverse

post
-
tensioning
in the deck panels

on the Door Creek
Bridge was 370 psi. Half of th
at

post
-
tensioning
existed

across the longitudinal joint
between

stage 1

and st
age 2

construction.
Figure
2
.
3

shows the
moment

per foot

versus
rotation

relationship
measured
from the longitudinal joint test with 360 psi post
-
tensioning level
a
s
performed by
Mark
owski

(2005). This test result will be used as

the rotational stiffness of the
longitudinal joints considering half
as much

post
-
tensioning
existed

(185 psi) and the joint
spacing in the finite element model.

0
50
100
150
200
250
0.000
0.002
0.004
0.006
0.008
0.010
0.012
0.014
Rotation (rad)
Moment (k-in / ft)
360 psi prestress
Softening Moment

Figure
2
.
3

Rotational Stiffness of Longitud
inal Joint (Markowski, 2005)



14

2.3.3.2

Transverse Joint

Transverse joints exist between the precast panels
during
both
stage
s

of

construction. As
described in
Mark
owski’
s thesis (
2005
), one full
-
scale transverse joint test was performed to
determine the amount of po
st
-
tensioning stress level
needed
across the transverse joints under
service level vehicle loads

considering impact loads based on AASHTO Standard
Specification

(1996)
.

The design level longitudinal post
-
tensioning used on the Door Creek Bridge was 250 psi

in order to keep the transverse joints tight under the service loads.
Figure
2
.
4

shows the
moment

per foot
versus
rotation

relationship from the transverse joint test with

a

154 psi
post
-
tensioning level
from

Mark
owski

(2005). Th
is test result will be used as the rotational
stiffness of the transverse joints considering the post
-
tensioning level (250 psi) across the
transverse joints and the joint spacing in the finite element model.

0
10
20
30
40
50
60
70
80
90
100
-0.002
0
0.002
0.004
0.006
0.008
0.01
0.012
Rotation (rad)
Moment (k-in/ft)
154 psi prestress
Softening Moment

Figure
2
.
4

Rotational Stiffness of Transverse Joint (
Mark
owski
,
2005
)




15

2.4

Summary

In this chapter descriptions were provided for the
AASHTO design prestress level
,
p
restress

level s
uggested by Issa
, p
otential errors in Issa

s results
,
Markowski data used i
n
later modeling
.



16


Chapter 3

Finite Element
Modeling


3.1

Introduction

SAP 2000 was used to create the three
sets
of thr
ee
-
dimensional bridge models which are
named Culpeper Bridge, Welland River Bridge and Door Creek Bridge. Prior to the bridge
modeling, a simple model

was created to check whether the Nlink element behave
d

correctly
or not.

Two bridge models: the

Culpeper Bridge and Welland River Bridge, were created to
verify the accuracy of the SAP modeling by comparing result
s

with previous analyses
published by Iss
a (1998, PCI Journal). The primary objective of the finite element modeling
was to estimate the tension stresses in the joint due to bending as a means of selecting the
pre
-
stressing level needed in the three different bridge
s

to prevent joint opening. In

addition,
the bridge model of
the
Door Creek Bridge was created
to examine the
deck

behavior under
over
load

with non
-
linear analysis. The following section provides a detailed description of
the three different bridge models with respect to element types
,

element
sizes, material
properties, and modeling techniques.

3.2

Types and Sizes of Elements and Material Properties

Six different elements were prepared to simulate the bridge geometry and materials.
E
lement type
s,
material
s and number of ele
ments equivalent

to each structural component
w
ere selected in the bridge
models, which are

shown
in
Table
3
.
1

and

Table
3
.
2
.

Distinct d
ifference
s

can be found between the current SAP models and the previous
models creat
ed by Issa (1998). Issa included the mild reinforcing steel, post
tensioning

tendons and used solid elements for the
precast
concrete
panel

and the panel joint. In order to


17

apply post
-
tensioning force, Issa applied temperature difference
s

to the post
-
tensi
oning
tendon elements. The post
-
tensioning tendons and any mild reinforcing steel were not
explicitly modeled in the current SAP models. It was assumed that the
effect

of the mild
reinforcing steel and prestressing strand in developing added stress is insi
gnificant as long as
the deck panels remain uncracked.

Table
3
.
1


Element Types for
Each
Structural Component

(
Ehmke

s thesis, 2006)

Structural

Component

Element Type

Precast
Deck Panel

Thin shell with appr
opriate deck thickness

Closure Pour

Thin shell with appropriate deck thickness

Parapet

Thin shell area in correct geometric orientation,

but with negligible thickness (0.01 inches)

Girder

Frame element located at a distance below the
deck area elements
equal to half the girder
height plus half the deck thickness

Shear Stud

Stiff element connecting girders to deck at
discrete points spaced at the shear stud block
-
out spacing from the actual bridge

Panel Joints

N Link elements, all degrees of freedom
ass
igned fixed condition except
longitudinal

axial and longitudinal bridge bending direction

T
he material properties were
the
same as the values that Issa reported for the Culpeper
and Welland River Bridges. The Young

s modulus of
elasticity
was 4.03 x 10
6

p
si
for the
closure pour and parapets, 5.1x10
6

psi for the deck panels and 29x10
6

psi for the steel girders
in those bridges. Poisson

s ratios were 0.3 for the steel girder and 0.18 for the deck panels,
closure pours and parapets.

Issa used eight
-
node brick

elements to simulate the transverse joints. In the current model,
transverse joints between the panels were modeled as SAP Nlink elements to simulate either
linear or non
-
linear springs. For the Nlink elements, all degrees of freedom were fixed except
for

axial extension across the joint and bending across the joint. It was assumed that the shear
stiffness of the keyed joint remained high under small joint openings.



18

Table
3
.
2


Number of Elements for Each Struc
tural Component

Structural
Component

Element
Type

Number of Elements

Culpeper
Bridge

Welland
Bridge

Door Creek
Bridge

Deck Panel

Shell

504

2592

5120

Closure Pour

Shell

72

-

-

Parapet

Shell

43

108

712

Bridge
Girder

Frame

2

6

8

Shear Stud

Frame

132

1
08

176

Transverse

Joint

Nlink

91

425

594

Longitudinal

Joint

Nlink

-

-

90

Size of a Shell element

1.667
ft.
2

1.2303
ft.
2

1.1041
ft.
2


For linear elastic analysis, the joint axial stiffness was calculated using the equation AE/L
and
AE/L
and the rotational stiffn
ess wa
s calculated using the equation EI/L.

A


is the area of the
the transverse joint computed as the spacing (b) of the link elements multiplied by the thickness
thickness (h) of
the
deck panels,

E


is Young

s modulus of elasticity for the grout, I is the
moment ine
rtia computed using the equation bh
3
/12 and

L


is the
thickness

of the transverse
joint taken as 1.5 inches. For nonlinear inelastic analysis, the axial stiffness is assumed as
infinite and the rotational stiffness is based on the test result in Markowski

s thesis (2005).

Figure
3
.
1

shows the rotational stiffness
used
for the longitudinal and transverse joint
s

in
the model of
the
Door Creek Bridge.

95.3
143.6
45.8
101.1
0
25
50
75
100
125
150
0
0.002
0.004
0.006
0.008
0.01
0.012
0.014
Rotation (rad)
Moment (k-in/ft)
Transverse Joint
Longitudinal Joint

Figure
3
.
1

R
otational Stiffness f
or Two different Joints in Door Creek Bridge Model



19

3.3

Testing the Nlink Element
for Nonlinear Static Analysis

A two
-
dimensional simple model was developed to check the input technique and
behavior of the Nlink element in SAP 2000. The model was a cantilever s
tructure shown in
Figure
3
.
2

and supported at the left end
. The beam was modeled as a frame element 10

ft.

long. A very short Nlink element
modeling

a nonlinear joint was placed between the support
and left end of the beam to chec
k the behavior of the Nlink element under load. The
boundary condition
s

of the cantilever

structure were

appli
ed

at the support location by
assigning joint restraints all fixed in both
axes
.


Figure
3
.
2

E
xample Modeling for Nonlinear Static Analysis

Figure
3
.
3

shows the plot of the rotational stiffness assigned as the material property to
simulate the desired nonlinearity of the Nlink element. The ultimate joint load, 2.21
kips

wa
s
assigned at the right end of the frame in the vertical direction to cause an ultimate moment in
the structure.

265.32
176.19
0
50
100
150
200
250
300
0
0.002
0.004
0.006
0.008
0.01
0.012
Rotation (rad)
Moment (k-in)

Figure
3
.
3

Rotational Stiffness of Nlink Element

Nlink

element



20


The rotational
displacement
s

in the Nlink
element w
ere

then monitored in multiple
load
steps to verify whether the Nlink element behave
d

as expected.
Figure
3
.
4

shows the moment
versus rotation plot resulting from the nonlinear static analysis in multiple steps. The resul
t
shows that the behavior of the Nlink element is entirely dependent on the
material’
s
rotational stiffness and did provide the response as expected in
Figure
3
.
4
.

27
53
80
106
133
159
172
265
239
212
0
50
100
150
200
250
300
0.000
0.002
0.004
0.006
0.008
0.010
0.012
Rotation (rad)
Moment (k-in)
SAP Output

Figure
3
.
4

Resul
t from Nonlinear Static
Analysis

in SAP

2000


3.4

Description of Bridge Models

Three
sets
of three
-
dimensional bridge mo
dels were created using SAP
. They are
simulating the
Culpeper

Bridge,
Door Creek Bridge
and

Welland River Bridge
. With these
models
, three d
ifferent bridge types were
simulated
:
a

simply
supported

bridge, the simply
supported bridge with 30 degree skew angle and a three
-
span continuous bridge

respectively
.

3.4.1

Culpeper Bridge

Model

Information describing this bridge was obtained from Issa

s articl
e published in the PCI
Journal (
1998). The Culpeper Bridge is
own
ed by the Virginia Department of Transportation.


21

As described by Issa, the bridge is a simply supported structure 54.5
ft.

in
length

and 30
ft.

in
width.
T
he girder spacing is 6.25
ft.

center

to center with a 3
ft.

deck overhang at the sides.
The two steel exterior beams are W33X125 and the interior beams are W33X132. As
described in Ehmke

s thesis (2006), the length of overhang was modified to 2.5

ft.

in the
model

in order to maintain the sta
ted deck width and

girder spacing
and W33X130 was
assigned

to all of the girder sections due to the
lack of these older sections in the program
library. This approximation is not expected to affect the deck behavior significantly.
Figure
3
.
5

shows the plan view of an individual precast deck panel for half of the bridge width.



Figure
3
.
5

Typical Panel Layout for Culpeper Bridge

Deck Pane
l

(Ehmke, 2006)


The bridge deck was modeled
w
ith

shell elements and
an

appropriate size of shell
elements w
as

selected so that the location of their corner node
s

was matched to the location


22

of the composite shear connector installed between the deck panel and the girder.

Each
element was 16 inches al
ong one side and 15 inches on the other.

In order to connect these
shell elements to the frame elements
modeling

the bridge girders, very stiff
beam
elements
between the girder and the deck were used at the discrete locations of shear connectors.
T
he
spaci
ng of the shear connector was 16 inches. It is assumed that the force is
transfer
red from
the deck to the girder by very stiff elements in the actual bridge.
Local shear deformation in
the girder web is ignored.
Thus, the composite action was obtained betw
een the deck panels
and the bridge girders.

Taking advantage of the bridge

s symmetry in the transverse direction, half of the

simply
supported

bridge width was modeled in order to provide a faster and more efficient
method
of

performing the FEM analysis.

Thus under loading the model simulated equal trucks
positioned on the two sides of the bridge.

The appropriate boundary conditions were applied
to simulate the simply supported condition at the supports and special boundary condition
along the bridge cente
rline of symmetry. To simulate the simply supported condition,
longitudinal, transverse, and vertical restraints were assigned at one end of the bridge girders
and
transverse

and vertical restraints assigned at the other end. To create the half
-
sized model

with symmetry in the transverse direction, transverse displacement and rotation about

the
longitudinal axis were restrained

at all of the nodes located in the deck elements on the
longitudinal axis of symmetry. This procedure is valid if
transversely

symm
etrical loading
acts on

the bridge structure. All of the section properties of the bridge girder along the line of
symmetry were modified to half of their actual section properties. In order to prevent frame
racking, lateral support conditions were applied

at

the

bottom of the deck
over both ends of
the girders by
assigning

transverse restraints.
Figure
3
.
6

shows

a three dimensional view of



23

the
Culpeper Bridge model with the line of symmetry at the left and the guard barrier at the

right.


Figure
3
.
6

Three
-
Dimensional View of Culpeper Bridge Model


A standard AASHTO H
L
-
93

truck

loading

was applied on the bridge deck. The three
axles were spaced at 14.0
ft.

and
the

two wheel locations
across the width of the truck were
spaced at 6 ft. Two case
s

of the truck loading
are

applied. One is similar to the truck loading
case that Issa (1998)
described
, which is named Truck Loading Case 1. The other is the truck
loading case with dynamic load a
llowance factors based on AASHTO LRFD
(
2007
)
, which
is named Truck Loading Case 2.

The location of the AASHTO truck loading causing the largest longitudinal moment was
f
ound by using the PCBRIDGE program (1990).

To study wheel load effects on the deck
joint,
the middle

truck

axle was located on the
transverse
panel joint
at the

center of the
bridge to cause the maximum bending effect
in that
joint. For the transverse position, the


24

wheel is centered between the bridge girders to cause the maximum bending

effect in the
deck panel. Since symmetry was used in the modeling it is assumed that the same truck
loading exists on the other half of the bridge.
E
ach wheel load was applied as a uniform
pressure on the shell elements which are modeling the deck panel.

The size of one shell
elements used in the Culpeper Bridge model is 15 in.
×

16 in.
Figure
3
.
7

and
Figure
3
.
8

shows the two cases of truck loading location
assigned

to the deck panel.


Figure
3
.
7

Truck Loading
s
imilar to Issa

s Truck Loading

(
Culpeper Bridge
Model, Truck L
oading
C
ase
1)




25


Figure
3
.
8

AASHTO Truck Loading for
Maximum

Bending

(Culpeper Bri
dge Model, Truck Loading Case
2
)

3.4.2

Welland River Bridge

Model

Information describing this bridge was again obtained from Issa

s article published in the
PCI
Journal

(1998). The Welland River Bridge is located near the City of Niagara Falls and
maintained by
the Ontario Ministry of Transportation. As described by Issa, the bridge
consist
s

of 18 continuous spans 48 ft
.

long and 43.5
ft.

wide. Only 3 spans were constructed
using precast concrete deck panels that were 8.85 inches deep. The deck is supported by fo
ur
lines of
older
steel bridge girders with sizes of W33X125 for the exterior girders and
W33X150 for the interior girders. In the SAP modeling, W33X130 was
assigned

to the
exterior girders and W33X152 was assigned to the interior girders due to the limite
d library
6
0


1
35


1
43


3
19


4
79




26

of girders in SAP.

This slight variation in girder properties will not significantly affect the
deck stresses.

The girder spacing was assumed to be 12.03
ft.

with

a 3.7
ft.

overhang.

The bridge deck was modeled using shell elements and the sizes
of shell elements were
selected so that the loca
tion of their corner node was matched to the location of the shear
connector.
The size of

each
element used in the Welland River Bridge model is 1
6

in
ches

×

1
1.1

in
ches
.
In order to connect these shell eleme
nts to the frame elements modeling the
bridge girders, very stiff elements were used at the discrete locations of shear connectors.
The spacing of the shear connector
s

was 16 inches. It is assumed that the force is
transfer
red
from the deck to the girder b
y very stiff elements in the real

bridge. Thus, the composite
action was obtained between the deck panels and the bridge girders.

No information was given

by Issa (1998) with respect to the deck panel joint location
in
relat
ion

to the pier location. Since
it is expected that the negative bending moment region
over a pier
is a critical section

for transverse crack opening
, it is assumed that the transverse
joint could exist directly over the pier. This means that the most critical location of the
transverse
joint was considered in the modeling, regardless of where the
panels

were located
in the actual bridge.

Taking advantage of bridge symmetry in the transverse direction, half of the bridge width
was modeled in order to provide a faster and more efficient w
ay
of
performing the analysis.
Again the appropriate boundary conditions were applied to simulate the support condition of
the three
-
span continuous bridge and the symmetrical half modeling. To simulate the support
conditions, longitudinal, transverse, and

vertical displacement restraints were assigned at one
end of the bridge girders and
transverse

and vertical restraints were

assigned over the pier
and at the other end of the bridge girder.

Other features used in the modeling were similar to


27

those used fo
r the Culpeper Bridge model.
Figure
3
.
9

shows a three
-
dimensional view of the
Welland River Bridge Model

including three spans, centerline at left and
guard

barrier at
right.


Figure
3
.
9

Three
-
Dimensional View of
Welland River
B
ridge Model


A standard AASHTO H
L
-
93

truck

loading

was applied to this bridge as in the Culpeper
Bridge. Two case
s

of truck loading we
re

applied. One is a double truck loading case similar
to the loading case

with the trucks spaced close
together

(but not including a dynamic
allowance)

that Issa described, named
Truck Loading Case
3
. The other is the single truck
loading case with dynamic load allowance factors based on AASHTO LRFD
(
2007
)
, named
Truck Loading
Case
4
.
The AASHTO LRFD double truck case did not control since the
trucks were spaced at 50 ft. while the bridge span was only 48 feet.
The critical location of
the AASHTO truck loading was again
f
ound by using the PCBRIDGE program. The


28

longitudinal posit
ion was selected to cause the maximum negative bending effect over a pier.
For the transverse position, one wheel line is centered between the bridge girders to cause the
maximum bending effect in the deck panel. Since the half sized symmetric model was
c
reated, it is assumed that the same truck loading exists on the other half of the bridge.
E
ach
wheel load was a
pplie
d as a uniform pressure on the
deck
shell elements which
were
16

inches by
11.1

inches
.

Figure
3
.
10

and
Figure
3
.
11

show the locations of the truck loading
case 3 and 4.


Figure
3
.
10


Double Truck Loading similar to Issa

s Truck Loading

(Welland River Bridge Model, Truck Loadi
ng Case 3)


Figure
3
.
11


Single Truck Loading by AASHT
O along Half of Bridge Length

(Welland River Bridge Model, Truck Loading Case 4)



29

3.4.3

Door Creek Bridge Model

A model of the Door Creek
Bridge

was
built

using

SAP 2000, based on the bridge data
provided in Ehmke

s thesis (2006). The Door Creek
Bridge

is owned by is owned by the
Wisconsin Department of Transportation and is a simply supported structure with 84.0
ft.

length
, 64.5

ft.

width and a 30
°

skew angle.
T
he full
-
depth precast bridge deck
was

const
ructed
in stages

in order to
maintain

the
traffic

flow

with

two lanes on the roadway at all
times.

Thus, longitudinal joint w
as

required to
accommodate

staged construction.
The
longitudinal
joint w
as

located betwe
en

the bridge

girders
to
avoid possible

ingress of salt
solutions and

leakage along
a

joint
directly above a girder
and
to

improve the durability of
the deck.

Stage 1

panels
were

34

ft.

-

7
11
/
16

in.

long
, 6
ft.

-

10
7
/
8

in.
wi
de and

8
3
/
4

in.

deep
.
Stage 2 pa
nels
wer
e 39

ft.

-

10
1
/
16

in.

long, 6

ft.

-

10
7
/
8

in.

wide

and
8
3
/
4

in.

deep
.

Five existing steel bridge girders and three new girders were used to support the bridge
deck.
The existing steel plate girders
we
re constructed from grade ASTM A36 steel and

co
nsist of a 1¼

in.

x 16

in.

(32 x 406 mm) bottom flange, a 3/8

in.

x 60

in.

(10 x 1,524 mm)
web, and

5/8

in.

x 12

in
.

(16 x 305 mm) top flange; the additional new girders
we
re
constructed from ASTM

A709 Grade 36 steel and consist of a 1

in
.

x 16

in
.

(25 x 4
06 mm)
bottom flange, a 7/16

in
.

x

60

in
.
(11 x 1,524 mm) web, and ¾

in
.

x 12

in
.

(19 x 305 mm) top
flange.

The girder spacing was 8
ft.
-
10 in. for the existing girders and 7
ft.
-
6

in. for the new
girders with deck overhang of 3
ft.

-
7 in.
Figure
3
.
12

shows the
skewed
panel

layout for the
Door Creek Bridge with th
e supports at left and right.



30


Figure
3
.
12


Typical Panel Layout for
Door Creek Bridge

(Plans by W
is
DOT)

The bridge deck

was modeled with

shell elements
having

a
trapezoidal shape selected to
accommodate a 30º skew angle of th
e
bridge
. The size of shell element
s

was selected so that
the location of their corner node was matched to the location of the shear connector.

Each
e
lement was
12

inches along one side and
13.3

inches on the other.

In order to connect these
shell elements to the girder elements, very stiff links were used at the discrete locations of
composite shear connectors
. The spacing of the shear connector was 4
feet. It is assumed that
the force is
transferred

from th
e deck to the girder by very stiff elements in the real bridge.
Thus, the composite action was obtained between the deck panels and the bridge girders. For
both the longitudinal and transverse joints
, Nlink elements were used between the bridge
deck panels with approximately 1
ft.

spacing between
adjacent

links along the joint length.

A full model of the bridge was created in order to perform the FEM analysis

since the
longitudinal joint eliminated the

possibility of using transverse symmetry. To simulate the
simply supported condition, longitudinal, transverse, and vertical displacement restraints


31

were assigned at one end of the bridge girders and
transverse

and vertical restraints assigned
at the othe
r end of the bridge girders.
In
order

to prevent frame racking, lateral support
conditions were applied at

the

bottom of the deck
at both

end
s

of the girders by
assigning

transverse restraints.

Figure
3
.
13

shows a three dimensiona
l view of

the

Door Creek Bridge
model with supports at top and bottom and guard barriers at left and right. The heavy lines
indicated deck panel joints
.


Figure
3
.
13

Three
-
Dimensional View of
Door Creek Bri
dge
Model

A standard AASHTO H
L
-
93

truck

loading

was applied to the bridge

with dynamic load
allowance factor
, 1.33

based on AASHTO LRFD (2007)
. The three axles were spaced at 14.0
ft.

and
the

wheel lines were spaced at 6 ft.
E
ach wheel load was applied as
a uniform pressure
on the shell elements.

An initial possible location of the truck for maximum joint moment was
f
ound by using
the PCBRIDGE program. Since the result
s

from the PCBRIDGE program
provide

only the
location of the truck loading for a linear be
am and this bridge has a 30
°
skew angle, several
transverse and longitudinal locations of truck loading were applied in order to find the critical
location of the truck loading causing the
maximum

bending
effect

at both transverse and
longitudinal joints.



32

A

basic location of the front axle in the longitudinal direction was selected with the aid
of PCBRIDGE and iterations were used to find the truck loading location causing the
maximum bending effect in the transverse joints. The transverse wheel location was

constrained by AASHTO LRFD 3.6.1.3; center of the wheel is not closer than 1.0

ft.

from the
face of railing. The truck loading location was moved by small increments transversely and
longitudinally while monitoring the increment of moment value in the tra
nsverse joints for
each case.
Figure
3
.
14

shows this process to find the critical location of the truck loading
with the arrows showing how wheel lines and axle location were changed.


Figure
3
.
14


Finding Critical Location of Truck Loading for Transverse Joint

In the same way, the basic location of the right wheel line in the transverse direction and
the truck loading location in the longitudinal direction causing the maximum bendin
g effect
in the longitudinal joints
were

located. The truck loading location was again moved by small
increments transversely and longitudinally while monitoring the increment of moment value


33

in the longitudinal joints for each case.
Figure
3
.
15

and
Figure
3
.
16

show the critical location
of the truck loading
assigned

to the deck panel.



Figure
3
.
15


Critical Location of
Truck Loading for Transverse Joint

(Door Creek Bridge, Truck Loading Case 5)

3
29


1
69


1
69


5
99



78




34


Figure
3
.
16


Critical Location of Truck Loading for Longitudinal Joint

(Door Creek Bridge, Truck Loading Case 6)

3.5

Summary

In
this
chapter

descriptions
we
re provided for the
three

different bridge models created
by using SAP.
The m
ain objectives of the modeling are to verify the accuracy of the bridge
modeling technique by comparison with other results, to
establish a minimum amo
unt of pre
-
stressing needed to limit joint

openin
g by examining bridges under a standard AASHTO
truck loading and
to
examine the joint

behavior under load
s that cause joint opening. Prior to
the bridge modeling, a simple model was created to check whether
the Nlink element
behave
d

correctly or not.

The Culpeper and Welland River

bridges were both chosen as

bas
es

to compare
modeling techniques and results with those of other researchers to validate our methods.

The
Culpeper Bridge was a single span simply su
pported structure
.
The Welland River Bridge
9
9


1
68


1
69


7
8


2
84




35

was a three

span continuous

structure.

The Door Creek Bridge was a single span simply
supported structure
with a

30
°

skew angle.

Linear elastic analysis
will
be performed
on

the single span Culpeper Bridge in Vir
ginia,
and

the multi
-
span Welland River Bridge in Ontario, Canada
. Both linear elastic and
nonlinear inelastic
analyses are

intended to be performed
on

the Door Creek Bridge in

Wisconsin
.
Table
3
.
3

shows

the summary of the finite
element modeling with respect to
types of analysis, load cases and objectives.
The results of the

FEM
analysis w
ill be
discussed in
Chapter

4
.

Table
3
.
3

Summary of the Finite Element
Modeling

Bridge
Model

Typ
e of Analysis

Load
Case

Objectives

Culpeper

Linear,
Elastic

Service

(Issa)

Verification of Accuracy

Service + Impact

Pre
-
stressing

L
evel

Welland

River

Linear
Elastic

Service

(Issa)

Verification of Accuracy

Service + Impact

Pre
-
stressing

L
evel

Door

Creek

L
inear
Elastic

Service + Impact

Joint
S
tress
C
heck

Overload

Joint Opening Check

Nonlinear
,
Inelastic

Overload

Effect of Joint Opening

Note: Both the Culpeper and Welland River bridges were examined with AASHTO HL
-
93 loading and an alternate tr
uck load case



36


Chapter 4


Results

4.1

Objectives

The Primary objective of the FEM analys
e
s is to evaluate the stress level in either the
transverse joint or the longitudinal joint under service loading conditions for the three
different bridges, considering the dynamic

load allowance factor
and design truck

based on
the
A
A
SHTO LRFD
Bridge Design Specifications (2007)
. To achieve th
is

primary objective,
it was
first necessary

to verify the accuracy of the finite element modeling by comparison
with Issa

s
previous publish
ed
results for the Culpeper and Welland River Bridges. The
secondary
objective

is to determine how much overloading would be required to cause joint
opening with the amount of pre
-
stress that actually exists in the Door Creek Bridge.
T
he third
objective wa
s to

examine

how the joint opening would affect the overall performance of the
bridge and how
the
loads are redistributed as joints crack open
while

the loading is increased
slowly toward the factored strength design loads.

The following section
s

provide t
he results
with respect to the verification of the modeling accuracy and results of the finite element
analysis for each bridge.

4.2

Verification of Finite Element Modeling

The results for the
Culpeper

and Welland River Bridges were compared with the result
s

t
hat Issa

described.

Maximum longitudinal tension stresses in the tran
s
verse joint were
examine
d.
The sign convention used for all plots
is

that a positive value

corresponds to a
tensile stress.



37

4.2.1

Moment Equilibrium Check

Since the Culpeper Bridge is a simply

supported, statically determinate structure, it was