Development Of A Simplified Finite Element Approach For

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Development Of A Simplified Finite Element Approach For Frp Development Of A Simplified Finite Element Approach For Frp

Bridge Decks. Bridge Decks.

Jignesh Vyas University of Central Florida

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DEVELOPMENT OF A SIMPLIFIED FINITE ELEMENT APPROACH FOR FRP BRIDGE DECKS

by

JIGNESH SUDHIR VYAS B.S.C.E. Karmaveer Bhaurao Patil College of Engineering, 2003

A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science

in the Department of Civil and Environmental Engineering in the College of Engineering and Computer Science

at the University of Central Florida Orlando, Florida

Fall Term 2006

ii

© 2006 Jignesh Sudhir Vyas

iii

ABSTRACT

Moveable bridges in Florida typically use open steel grid decks due to the weight

limitations. However, these decks present rideability, environmental, and maintenance problems,

for they are typically less skid resistant than a solid riding surface, create loud noises, and allow

debris to fall through the grids. Replacing open steel grid decks that are commonly used in

moveable bridges with a low-profile FRP deck can improve rider safety and reduce maintenance

costs, while satisfying the strict weight requirement for such bridges. The performance of the

new deck system, which includes fatigue and failure tests were performed on full-size panels in a

two-span configuration. The deck has successfully passed the preliminary strength and fatigue

tests per AASHTO requirements. It has also demonstrated that it can be quickly installed and that

its top plate bonds well with the wear surface.

The thesis also describes the analytical investigation of a simplified finite element

approach to simulate the load-deformation behavior of the deck system for both configurations.

The finite element model may be used as a future design tool for similar deck systems. Loadings

that were consistent with the actual experimental loadings were applied on the decks and the

stresses, strains, and the displacements were monitored and studied. The results from the finite

element model showed good correlation with the deflection and strain values measured during

the experiments. A significant portion of the deck deflection under the prescribed loads is

induced by vertical shear. This thesis presents the results from the experiments, descriptions of

the finite element model and the comparison of the experimental results with the results from the

analysis of the model.

iv

This thesis is dedicated to my family: Sudhir C. Vyas (my father), Kokila S. Vyas (my mother),

and Shraddha S. Vyas (my sister) for their prayers and continuous support throughout this work.

v

ACKNOWLEDGMENTS

The author would like to give his most sincerely appreciation to the following:

Dr. Lei Zhao, author’s advisor, for the opportunity to work for him on this project and for

his infinite patience during the last two years. None of the accomplishment gotten from this

research would have been possible without him.

Dr. Necati Çatbaş and Dr. Manoj Chopra for reviewing this thesis and helping to improve

it with their findings and corrections.

Melih Susoy, Jun Xia and Zachary Haber for sharing their knowledge in several phases

of the project.

Mike Olka, and Kevin Francoforte, for their comments and suggestions that help greatly

to the success of this research work.

My family and friends for their encouragement and support at all time during the writing

of this thesis.

vi

TABLE OF CONTENTS

LIST OF FIGURES ........................................................................................................................ x

LIST OF TABLES....................................................................................................................... xiii

CHAPTER 1 INTRODUCTION ................................................................................................... 1

1.1 Introduction........................................................................................................................... 1

1.1.1 Experimental Investigations and Field Applications ..................................................... 1

1.1.2 Analytical Investigations of FRP decks......................................................................... 4

1.2 Structural Characteristics for FRP Bridge Deck................................................................... 6

CHAPTER 2 DECK SYSTEM DESCRIPTION........................................................................... 7

2.1 Deck System Description...................................................................................................... 7

2.2 Advantages of the mechanically fastened FRP deck system................................................ 9

2.3 Potential technical challenges of mechanically fastened FRP deck system ......................... 9

2.4 Shape of core cells ................................................................................................................ 9

CHAPTER 3 TEST SETUP AND LOADING PROCEDURES................................................. 11

3.1 Assembly of the specimen .................................................................................................. 11

3.2 Loading Calculations .......................................................................................................... 13

3.2.1 Fatigue test ................................................................................................................... 13

3.2.2 Failure test.................................................................................................................... 16

3.3 Lifetime load cycle calculation........................................................................................... 18

3.4 Loading procedure .............................................................................................................. 18

3.4.1 Fatigue test ................................................................................................................... 19

3.4.2 Failure tests: ................................................................................................................. 19

vii

3.4.2.a FAIL 1 and FAIL 2 for Non-Skew Configuration ................................................ 19

3.4.2.b Fatigue, FAIL 1, and FAIL 2 Tests for Skew Configuration................................ 20

CHAPTER 4 TEST RESULTS ................................................................................................... 22

4.1 Non-Skew Results............................................................................................................... 22

4.1.1 Fatigue test ................................................................................................................... 22

4.1.2 Failure Test: ................................................................................................................. 23

4.1.2.a FAIL 1................................................................................................................... 23

4.1.2.b FAIL 2................................................................................................................... 23

4.1.3 Post-test failure analysis .............................................................................................. 26

4.2 Skew Results....................................................................................................................... 28

4.2.1 Fatigue test ................................................................................................................... 28

4.2.2 Failure Test: ................................................................................................................. 29

4.2.2.a FAIL 1................................................................................................................... 29

4.2.2.b FAIL 2.................................................................................................................. 30

4.2.3 Post-test failure analysis .............................................................................................. 32

CHAPTER 5 SYSTEM DESCRIPTIONS AND FINITE ELEMENT MODEL ........................ 34

5.1 Elements.............................................................................................................................. 35

5.1.a Shell Elements.............................................................................................................. 35

5.1.b Frame Element ............................................................................................................. 36

5.1.c Link Element................................................................................................................ 36

5.1.d Constraint..................................................................................................................... 36

5.1.e Supports........................................................................................................................ 37

5.2 Material Properties.............................................................................................................. 38

viii

5.2.1 Modulus of Elasticity................................................................................................... 38

5.2.2 Shear Modulus ............................................................................................................. 40

5.2.2.a Calculation of vertical shear G13 ........................................................................... 40

5.2.2.b Calculation of G23 ................................................................................................. 41

5.2.2.c Calculation of G12 ................................................................................................. 42

5.2.3 Poissons Ratio.............................................................................................................. 42

5.3 Effect of Shear Lag ............................................................................................................. 42

5.4 Loading for the Model ........................................................................................................ 43

5.5 Parametric Study................................................................................................................. 44

5.5.a Shear Moduli Effects.................................................................................................... 44

5.5.b Effects of Discontinuity ............................................................................................... 44

CHAPTER 6 VERIFICATIONS BY EXPERIMENTAL RESULTS......................................... 45

6.1 Summary of experimental results ....................................................................................... 45

6.2 Comparisons to Non-Skew Test Results............................................................................. 48

6.2.1 Service Level Load Displacement Distribution........................................................... 48

6.2.2 Service level Load Strain Distribution......................................................................... 49

6.2.3 Parametric study results ............................................................................................... 50

6.2.3.a Effect of the vertical shear modulus G13 ............................................................... 50

6.2.3.b Effect of deck transverse shear modulus G23........................................................ 51

6.2.4 FAIL 1 Displacement Distribution .............................................................................. 52

6.2.5 FAIL 1 Strain Distribution........................................................................................... 54

6.2.6 FAIL 2 Displacement Comparison .............................................................................. 54

6.2.7 FAIL 2 Strain Comparison........................................................................................... 55

ix

6.3 Comparisons to Skew Test Results..................................................................................... 56

6.3.1 Service Level Load Displacement Distribution........................................................... 57

6.3.2 Service level Load Strain Distribution......................................................................... 57

6.3.3 Parametric study results ............................................................................................... 58

6.3.3.a Effect of the vertical shear modulus G13 ............................................................... 58

6.3.3.b Effect of deck transverse shear modulus G23........................................................ 59


6.3.5 FAIL 1 strain distribution ............................................................................................ 62


6.3.7 Fail 2 Strain Distribution. ............................................................................................ 64

CHAPTER 7 CONCLUSIONS ................................................................................................... 65

CHAPTER 8 RECOMMENDATIONS....................................................................................... 68

REFERENCES ............................................................................................................................. 69

x

LIST OF FIGURES

Figure 1 Hillsboro Canal Bridge in Belle Glade, Florida ............................................................... 3

Figure 2 Pultruded Section.............................................................................................................. 7

Figure 3 Deck Assembly................................................................................................................. 8

Figure 4 Girder-deck connection concept..................................................................................... 12

Figure 5 Grouting connection between deck and girder............................................................... 12

Figure 6 Fatigue: Simultaneous loading in both pads................................................................... 14

Figure 7 Loading Cases ................................................................................................................ 15

Figure 8 Failure Tests: Loading Configurations........................................................................... 17

Figure 9 Non-Skew FAIL 1 test setup .......................................................................................... 20

Figure 10 Skew Fatigue test setup ................................................................................................ 21

Figure 11 Fatigue Progression – Non-skew................................................................................. 22

Figure 12 Load-Displacement and Load-Strain relation for FAIL 1 and FAIL 2 ........................ 24

Figure 13 Displacement and Strain Distribution Profiles – Non skew test .................................. 25

Figure 14 Crack on Wear Surface................................................................................................. 26

Figure 15 Post test inspection of the dissected specimen ............................................................. 27

Figure 16 Polymer concrete bonding to the plates........................................................................ 28

Figure 17 Fatigue Progression - Skew.......................................................................................... 29

Figure 18 Load-Displacement relations for FAIL 1 and FAIL 2.................................................. 30

Figure 19 Displacement and Strain Distribution Profiles – Skew test.......................................... 31

Figure 20 Fatigue Comparison...................................................................................................... 32

Figure 21 Deck Assembly............................................................................................................. 34

Figure 22 Finite Element Models ................................................................................................. 37

xi

Figure 23 Deck Orientation .......................................................................................................... 38

Figure 24 Typical Cross-section of the Deck ............................................................................... 39

Figure 25 Effective Height for Calculating Gweb .......................................................................... 40

Figure 26 Double Bending............................................................................................................ 41

Figure 27 Loading Configurations................................................................................................ 46

Figure 28 Location of Displacement and Strain Gages: Non-skew Configurations..................... 48

Figure 29 Service Level Displacement Distribution at Midspan.................................................. 49

Figure 30 Service Level Strain Distribution ................................................................................. 50

Figure 31 Effect of Shear Modulus G13 ........................................................................................ 51


Figure 33 FAIL 1 Displacement Distribution............................................................................... 53

Figure 34 FAIL 1 Load-Displacement Comparison ..................................................................... 53

Figure 35 FAIL 1 Strain Distribution ........................................................................................... 54

Figure 36 FAIL 2 Load Displacement Comparison ..................................................................... 55

Figure 37 FAIL 2 Load Strain Comparison.................................................................................. 56

Figure 38 Location of Displacement and Strain Gages: Skew Configurations ............................ 56

Figure 39 Service Level Displacement Distribution..................................................................... 57

Figure 40 Service Level Strain Distribution ................................................................................. 58

Figure 41 Effect of Shear Modulus G13 ....................................................................................... 59





xii




xiii

LIST OF TABLES

Table 1: Shell Elements Used ....................................................................................................... 36

Table 2: Manufacturer provided material properties .................................................................... 38

Table 3: Loads and Load Intensities ............................................................................................. 43

Table 4: Summary of Test results ................................................................................................. 47

Table 5: Recommended Material Properties................................................................................. 68

1

CHAPTER 1

INTRODUCTION

1.1 Introduction

1.1.1 Experimental Investigations and Field Applications

According to the US Federal Highways Administration, the most commonly cited

indicator of bridge condition in the US is the number of deficient bridges. Of the 591,707 bridges

in the inventory, 162,869 are classified as deficient (27.5 percent), either for structural or

functional causes. (FHWA, 2004) and are not suitable for current or projected traffic demands

(Zureick et al.1995).

The existing quality of the highway infrastructure has been on a decline, due to

insufficient maintenance, heavy loads, and unexpected or harsh environmental conditions. This

problem has created an urgent need for effective means of structural repair, rehabilitation, and

replacement. As a result, there are tremendous opportunities for the adoption of fiber reinforced

polymer bridge decks. FRP, not only has high strength, low density, fatigue resistance, corrosion

resistance, but also is easy to install on site, less time consuming and very easy to maintain.

Although FRP material costs are greater than traditional concrete and steel materials, they

have shown some promise in applications such as decks on moveable bridges, where the

advantages of FRP outweigh its high initial costs. Also an FRP bridge deck weighs

approximately 80% less than a concrete deck (Bin Mu et. al.2006). Reduction in dead load is

2

especially very beneficial for movable bridges where spans have to be lifted up for passage of

vessels.

Open steel grid decks are common on moveable bridges, which span across waterways

and may lift up or rotate out of the way to allow ships to pass. The weight limitation on the deck

of a moveable bridge is typically 1.2 kN/m2, which makes open steel grid deck, the only viable

option amongst conventional deck systems. However, these decks present rideability,

environmental, and maintenance problems, for they are typically less skid resistant than a solid

riding surface, create loud noises, and allow debris to fall through the grids. While the initial cost

of construction of a steel grid deck is low, maintenance cost is very high. FRP decks, in

comparison, are not only lightweight, which satisfy the strict weight requirement for moveable

bridges, but also provide a solid riding surface, which has the potential of improving driving

safety, reducing noise levels, and preventing falling debris. Also, the maintenance cost is

expected to be significantly lower.

There are more than a hundred bridges in Florida that use open steel grid decks, many of

which have the aforementioned problems. Therefore there is a need to investigate alternative

systems that are capable of replacing some of the problematic open steel grid decks.

In the past few years there have been numerous examples of new bridges using FRP

bridge decks or old bridge decks getting replaced by new FRP bridge decks.

An excellent example of an effective application with the FRP composite deck system

was the replacement of an existing conventional concrete deck on a 60-year old, Warren steel

truss, which was funded by the New York DOT. The 34.7 m simple span truss had a 12.7 metric

ton weight restriction. Replacing the deck with FRP composite deck panels reduced the

superstructure dead load from 830 kg/m2 to 171 kg/m2. The removal and replacement of the deck

3

system took less than a month to complete and the cost of the rehabilitation ($876,000) was

about one-third the cost of total replacement ($2.34 million) (Jerome S. et. al. 2000).

Other such examples are the construction of a new all composite cable-stayed bridge

spanning 137.2 m on I-5 in California, a new 3-span girder bridge, 52.1 m long on 53rd Avenue

over Crow Creek in Iowa, etc.(FHWA, 2004). Many experiments have been carried out on decks

with different FRP configurations.

Composite action between GFRP composite decks and steel girders was studied (Stiller,

W. B., 2006) and was found to work with good strain and displacement results.

The flexure, shear deflection, failure modes and overall performance of 16 FRP deck

panels supplied by various manufacturers was studied (Alagusundaramoorthy P., 2006) and

factors of safety were calculated after laboratory testing.

One of the alternatives under investigation is a low-profile FRP composite deck that has

mechanically fastened pultruded components. If proven successful by full-scale testing, the deck

system will be considered for use in a demonstration deck replacement project on the Hillsboro

Canal Bridge in Belle Glade, Florida, which has a deck that has been repeatedly damaged and

repaired (Figure 1).

Figure 1 Hillsboro Canal Bridge in Belle Glade, Florida

4

1.1.2 Analytical Investigations of FRP decks

Experimental and analytical work on FRP bridge decks with various material,

configurations, and connection detailing, etc., have been widely reported (Bakis C. E., 2002).

Examples of existing FRP deck designs include sandwich construction, slab-girder systems with

FRP deck fabricated by interlocking pultruded profiles, modular self-supported deck systems

with FRP shells, and the FRP-concrete hybrid deck.

Finite element analysis has been used as a tool to analyze these designs for their

performance under different loading conditions. Aref, et. al., (2005) used 4-node doubly curved

thin shell element, each node having six degrees of freedom to model the top and bottom surface,

and 4-node doubly curved thin shell element, each node having five degrees of freedom, to

model the web core.

Prachasaree, et. al., (2006) investigated the performance of FRP bridge deck under

torsion using simplified classical lamination theory and, the torsional rigidity, in-plane shear

modulus and strain of FRP structural member were predicted. Orthotropic shell elements, having

six degrees of freedom at each node, were used to model the deck system.

Zhang, et. al., (2006) compared the vehicular induced dynamic performance of FRP

bridge deck versus concrete slab bridges using orthotropic solid plate model. It was found that

the dynamic impact factors for conventional bridges can be applied to strength design of FRP

bridges, but the acceleration of FRP bridges was found to be significantly higher than that of

concrete bridges.

Alnahhal, et. al., (2006) used solid composite elements in a finite element model to

simulate the temporal thermal behavior and damage of FRP deck. Lamina thickness and fiber

5

orientation were modeled by using multiple layers and appropriate material property designation

for each layer in different directions. It was seen that FRP decks are sensitive to the effects of

elevated temperatures, and showed lower heat resistance when compared to steel, but showed

sufficient reserve capacity.

Karbhari et al. (2000) performed experimental study on the fatigue behavior of FRP

composite decks with pultruded cores, and then (Cheng and Karbhari, 2006) furthered the study

for steel-free FRP-concrete modular bridge deck system

Zhao and Karbhari, 2005 analyzed a composite bridge deck system with openings using

finite element analysis. Orthotropic shells elements were used individually for the flanges and

the web.

In a majority of the above-mentioned models, top and bottom flanges and webs of the

FRP deck panels are typically modeled separately with shell elements. The models are typically

time consuming to construct and are demanding on computational resources. A new simplified

FEA model is proposed in this paper. It uses one layer of thick shell elements to model the FRP

deck panels, which have top and bottom flanges and web. The equations for calculating the

equivalent properties of the thick shell are proposed in this paper. Due to the model’s simplicity,

it is anticipated that a typical bridge engineer will be able to use it for design.

The model is generic and not system specific and can be used for any FRP deck system

configuration as long as the equivalent material properties can be calculated. In the field, FRP

decks could be placed in a skewed configuration on beams. This method, which can be applied to

FRP deck systems with or without skew, has been successfully validated by two full-scale

laboratory tests, one with the principal direction of the deck panels perpendicular to the

supporting beams (non-skew) and the other is at the skew angle of 30°. Excellent agreements

6

between the test and the analytical results on deflection and strain were observed in both

configurations (non-skew and skew). The detailed descriptions of the laboratory testing of both

specimens of the deck system has been previously presented (Vyas and Zhao, 2007) and briefly

summarized in the next section of this paper.

The finite element model, which accurately simulated the behavior of the deck system

under the test configurations, is being proposed for use as a design tool for a field deck

replacement project on a moveable bridge in Florida, which has a 28° skew.

1.2 Structural Characteristics for FRP Bridge Deck

The mechanical properties for a FRP bridge deck, which is anisotropic, vary with the

volume orientation of the fiber reinforcement and also their volume. The design strains for

structural FRP application are usually kept below 20% of ultimate capacity. (ACI 440.2R-

02) But bridge deck applications have been found to be typically stiffness-driven. This results in

service level strains well below the design strain level. Due to low levels of these strains, creep

as well as fatigue, as shown by the experiments carried out for this deck, play a rather small

part, when the FRP bridge deck is properly designed and fabricated.

Also it is seen that cracking and delamination of the overlay occurs due to wheel loads.

This could be avoided in presence of a deflection criterion. The AASHTO LRFD provision (for

orthotropic steel and timber desk) of deflection within L/300 to L/500 range gives us a small

indicator, but specific demarcating values have not been set for FRP bridge decks.

7

CHAPTER 2

DECK SYSTEM DESCRIPTION

2.1 Deck System Description

The deck system is composed of mechanically fastened pultruded FRP parts:

A bottom panel that included four T-sections and a bottom plate was first pultruded. (Fig. 2a)

These pultruded panels were placed side by side, with a small overlap in the “lip” area.

Stainless steel screws were used to mechanically fasten the lip area. (Fig. 3a)

(a) Exiting the pultrusion machine

203 203 203114 114838

5113

17114 13

13Unit: mm

(b) Dimensions

Figure 2 Pultruded Section

8

A pultruded top plate was then placed and mechanically fastened to the top flanges of the

bottom panel.

The center-to-center distance between the webs of the I-section is 203 mm. The total deck

thickness is 127 mm, which includes a 114-mm-deep bottom panel and a 13-mm-thick top

plate. (Fig. 3a)

Mechanical Fasteners

203 203203178

13

13 114

13

Unit: mm

a) Cross section of the deck system

b) Picture of the deck showing all components

Figure 3 Deck Assembly

While the majority of the FRP deck systems in US use adhesive bonding to assemble

pultruded components and face sheets, this deck system uses on-site mechanical fastening

instead which is a unique feature for this type of decks.


9

2.2 Advantages of the mechanically fastened FRP deck system

The FRP deck system investigated in this paper had the following advantages:

The fabrication cost was lower than most existing systems. This was due to the fact that the

deck was pultruded and hence there was no need for any bonding.

Using studs and grouting connections became significantly easy due to an open top.

Repair or replacement of these decks was comparatively easier. If damage occurred to the

deck during its service life, typically in the top plate or web, the top plate could potentially be

replaced or disassembled to allow repair.

2.3 Potential technical challenges of mechanically fastened FRP deck system

The system does, however, have a few potential challenges that will need to be further

studied and/or improved:

A quick way of drilling and fastening needs to be developed as there would be a need for

substantial on-site drilling and mechanical fastening to join various pieces together.

Extensive drilling may lead to hairline cracks or slightly bigger holes which could act as

open passages for moisture and salts to invade the laminates. This is a durability concern that

needs to be addressed.

Also presence of numerous holes could lead to stress concentration issues.

2.4 Shape of core cells

The geometries of the core of the FRP panels have a significant impact on the lateral load

transfer and distribution (perpendicular to the cells). Trapezoidal and triangular cores have been

widely adopted by manufacturers in most existing systems as they provide good lateral force

transfer. This in turn provides a larger area of the panel that can participate in carrying the wheel

10

load. Rectangular shaped cores, on the other hand, have very little capability of lateral force

transfer and distribution. A wheel load is mainly carried by the portion of the deck that is directly

under the loading points. The core of the FRP deck system being studied had a rectangular shape,

which was not effective in lateral load transfer and distribution.

11

CHAPTER 3

TEST SETUP AND LOADING PROCEDURES

3.1 Assembly of the specimen

Testing was performed on a deck specimen that was made of two pultruded panels and top

plates, and supported by three steel I-beams. The construction of the specimen involved the

following steps:

The three supporting beams (W10×15) were placed at 1.22-m spacing.

13-mm-dia. steel studs were welded on top of all three beams at locations corresponding to

every alternate cell of the deck (Figure 4)

To prepare for the pouring of a 13-mm-thick saddle between the beam and the deck, wood

formworks were built along the edges of the supporting I-beams.

76-mm-dia holes were drilled on the bottom of the pultruded deck panels to match the pattern

of the studs.

The deck panels were placed on the beams and then connected to the beams by inserting

studs through the holes. The deck panels were placed such that the lips of the panels

overlapped.

The lips of the deck were mechanically fastened by 6-mm-diameter stainless steel screws at a

spacing of 0.3 m.

Foam bricks were inserted through the open top of the panels to form a 254-mm-long grout

pocket around each stud (Fig. 4).

12

10-thick polymer wear surface

152 13-thick grout saddle

Grout filled to above the top of the stud

Panel joint overlap

Foamblock

Steelbeam

Unit: mm

Panel 1 Panel 2

Top FRP plate

Studs 13-dia.102-long every other cell 254

Figure 4 Girder-deck connection concept

Once the forms are sealed, both on the edges of the beams and in the core around the studs, a

low-shrinkage grout was manually mixed and poured in the first grout pocket above the beam

as shown in Fig. 5. The grout traveled along the saddle on top of the beam by gravity and

flowed into the next grout pocket.

Once the first pocket was full, additional grout was poured into the next grout pocket, until

all grout pockets were full.

Figure 5 Grouting connection between deck and girder

13

The grout was left to harden for one hour, before pultruded plates were placed on top of the

specimen along the beam direction.

Stainless steel fasteners were then used to secure the top plate to the top flanges of the panels

at a spacing of 0.3-m.

A polymer concrete wear surface is then installed on the top plate.

The assembled deck panels, prior to the installation of the wear surface, is shown in Figure 3b.

3.2 Loading Calculations

The loading for the test were calculated for the non-skew test. The magnitude of loading

was kept the same for the skew configuration.

3.2.1 Fatigue test

Loading pads used for the test were (254 mm × 508 mm) as per AASHTO 3.6.1.2.5. Two

loading pads were placed at a center to center distance of 1219.2 mm. 25.4 mm – 38.1 mm thick

elastomeric and steel plates were placed on top. (Fig. 6)

Load centeredbetween webs

Web LocationBeam

Top Plate 1 Top Plate 2 Top Plate 3

Pane

l 1Pa

nel 2

1.52

1.22

1.22

0.61

0.61 0.61

1.22

1.223.35

0.51 0.25

a) Non-Skew Configuration

14

Fatigue TestLocations

b) Skew Configuration

Figure 6 Fatigue: Simultaneous loading in both pads

The 1219.2 mm pad spacing was more critical than the design wheel spacing of 1828.8

mm (AASHTO 3.6.1.2.2) as the loads are at the mid-span which could give us a bigger

displacement and strain value.

A single 244.64 kN actuator was used with a spreader beam as the loading device to

properly distribute the fatigue load onto both the pads. Loading is adjusted so as to stop as soon

as failure is seen. The maximum number of fatigue cycles was set to 2 million cycles and the

frequency of loading cycles was set to 2 to 4 Hz. An upper load limit of 80.06 kN was calculated

as shown below. To prevent the pads from slipping or “walking”, a lower load limit was set as

2.22 kN.

Fatigue load upper target calculations

AASHTO fatigue load level: HS 20-44, fatigue load per wheel (AASHTO 3.6.1.4.1):

P f = γB 1 +IM100ffffffffffff g

BP = 61.4 kN

where γ = 0.75 load factor for fatigue (AASHTO Table 3.4.1-1)

15

IM = 15 impact allowance for fatigue (AASHTO Table 3.6.2.1-1)

P= 16 kips, load per wheel (AASHTO 3.6.1.2.2)

Magnification factor to account for multi-span loads

The two possible loading cases and the positive and negative bending moments on the

two span deck are shown in the figure 7. Case 1 is more critical on negative bending (M2= 0.187

PL); Case 2 is more critical on positive bending (M3=0.203 PL).

L L

P

P PCase 1.

Case 2.

M 3= 0.203 PL

M 4= 0.094 PL

M 2 = 0.187 PL

M 1= 0.156 PL

Figure 7 Loading Cases

The loading configure proposed for the fatigue test is that of Case 1. To ensure that the

maximum positive bending moment is simulated during the fatigue test, a magnifying factor of

Fm =M 3

M 1

ffffffffff= 0.2030.156ffffffffffffffffff g

= 1.30

16

should be applied to the fatigue load Pf calculated previously, i.e., the proposed fatigue load

after being magnified is:

P fm = FmBP f = 1.3B61.4 = 80 kN

It should be noted that this fatigue load will be over-loading the negative bending by 30%

(note Fm=1.30). The top flat sheet of the deck, which is secondarily connected to the rest of the

deck, happens to be in tension under negative moment and away from the loading pads, thus less

of a fatigue concern.

3.2.2 Failure test

The loading configuration for failure test is similar to that used for the fatigue test. The

only difference is that instead of two loading pads, a single loading pad was used. The loading

was displacement controlled and at a uniform rate. Failure test was performed for two conditions.

In the first configuration the load was applied on the west bay as shown in Fig. 8a, whereas for

the second configuration the load was applied on the east bay above a single web as shown in

Fig. 8b. The loading locations for skew configuration was as shown in Fig. 8c.


Beam

Pane

l 1Pa

nel 2


Beam

Pane

l 1Pa

nel 2

a) FAIL 1 Loading-West Span (Non-Skew) b) FAIL 2 Loading-East Span (Non-Skew)

17

Failure Test(Fail 2) Location


c) Skew Configuration

Figure 8 Failure Tests: Loading Configurations

Design wheel load

Preliminary test results from a simply-supported deck panel indicate that the failure is

caused by local crushing under the loading pads. Case 2 is anticipated to be more critical due to

larger positive bending moment. Thus it is recommended that the loading configuration of Case

2, which is loaded at one mid-span and yields the maximum positive bending moment at the

location of the load, is used to apply the failure load.

P f = γB 1 +IM100ffffffffffff g

BP design load for Strength I

P f = 1.75B 1 +33100ffffffffffff g

B16 = 165.5 kN

where γ = 1.75 load factor for Strength I (AASHTO Table 3.4.1-1)

IM = 33 impact allowance (AASHTO Table 3.6.2.1-1)

P= 16 kips, load per wheel (AASHTO 3.6.1.2.2)

18

3.3 Lifetime load cycle calculation

According to the available NBI data the current ADT (2000 est.) for the Hillsboro Canal

bridge is 19,800 and is expected to reach 34353 by 2022. Assuming the expected service life of

the deck to be 20 years (2007 – 2026), the traffic growth is calculated using linear extrapolation,

to be 30715. Using AASHTO 3.6.1.4.2 the average daily single-lane truck traffic was calculated

as 1306.

N = 365 (Nyear) n ADTTSL

= 365 (20) (2) 1306

=19.1 million cycles

where Nyear= 20 assumed in this study. Note the standard AASHTO for bridge is 75 years

n = 2.0 number of stress range per truck passage, (AASHTO Table 6.6.1.2.5-2

“Transverse member, spacing ≤20’)

Although the proposed fatigue test did not duplicate the fatigue behavior of the real

bridge, which is expected to be subjected to a much higher number of cycles, an extrapolation

from available results on a log-scale S-N curve help predict if the deck satisfies the fatigue load

requirement. It has been reported that a simply supported panel failed from local crushing at a

load of approximately 81 kips (McEntire and Nelson, 2006). This result provides a data point for

the graph: A (0, 81). This value will be compared with the values from the failure tests, carried

out after fatigue test, to evaluate the fatigue effect.

3.4 Loading procedure

Fatigue and failure tests were carried out for both, the skewed deck and the non-skewed

deck configuration. The prototype deck specimen was supported by three steel I-beams that were

19

1219 mm apart. A polymer-based wear surface was installed on the top plate of the deck.

Loading was applied with two (254 mm × 508 mm), 51-mm-thick elastomeric pads on the top

surface of the deck specimen.

3.4.1 Fatigue test

Fatigue loading, calculated in section 3.2.1, which simulated AASHTO truck loads, was

applied simultaneously at two locations as shown in Fig. 6. To apply equal amount of forces to

the two webs near the joint, the loading pads were centered on the joint between the two. A total

of two million cycles between 2 kN and 80 kN per loading pad was applied at a rate of 3 Hz. The

load-versus-deflection and load-versus-strain response of the specimen were monitored and

recorded at several intervals during the fatigue loading.

The failure tests were conducted in sequence on the same specimen at two different

locations, after the completion of the fatigue test.

3.4.2 Failure tests:

3.4.2.a FAIL 1 and FAIL 2 for Non-Skew Configuration

Failure loading is applied in the west span at the same location as that of the fatigue test

(Figure 8a). The AASHTO factored load demand is 164 kN. The test setup is as shown in Fig. 9.

FAIL 1 load was to terminate as soon as a load drop was observed, so that the deck in the east

span would not be too severely damaged or disturbed to allow for the FAIL 2 test.

20

The loading of FAIL 2 is applied directly above a web of the deck next to the panel-to-

panel joint (Figure 8b). Loading was to continue until failure or substantial damage to the

specimen. Even in FAIL 2 the deck had to demonstrate the capacity to satisfy the AASHTO

specified strength requirement of 164 kN.

Figure 9 Non-Skew FAIL 1 test setup

3.4.2.b Fatigue, FAIL 1, and FAIL 2 Tests for Skew Configuration

Similar loading procedure was followed for the skew test (Fig. 8c). The fatigue test setup

is shown in Fig. 10. While performing the FAIL 1 test for the skewed configuration, technical

difficulties prevented the recording of the load-deflection and load-strain data for the ascending

portion of the first loading cycle (333.6 kN). The loading was increased to 333.6 kN and then

was held constant for 5 minutes before unloading all the way back to zero. The data recording

was then started from the second loading cycle.

21

Figure 10 Skew Fatigue test setup

22

CHAPTER 4

TEST RESULTS

4.1 Non-Skew Results

4.1.1 Fatigue test

The deck specimen showed no signs of cracking, failure or stiffness reduction during the

fatigue test. The progression of the mid-span deflection of the deck showed a stable and largely

linear trend up to 2 million cycles on a log-scale plot shown in Figure 11. The mid-span

deflection of the deck stabilized after 1 million cycles except for one measurement location, D4,

where there was a rising trend after 1 million cycles. The maximum deflection under the fatigue

load (80 kN each loading pad) grew from 3.7 mm at the beginning of the fatigue loading to 5.2

mm after 2 million fatigue cycles. The long-term deflection growth, although not expected to

cause any safety concerns, needs to be further studied and monitored in the field.

0

1

2

3

4

5

1000 104 105 106

D4

Dis

plac

emen

t (m

m)

Number of Load Cycles (log scale)

D1

D2

D5D0

D3

Figure 11 Fatigue Progression – Non-skew

23

4.1.2 Failure Test:

4.1.2.a FAIL 1

The load-deflection and load-strain relations observed from FAIL1 were largely linear-

elastic up to the peak load of 370.5 kN, when a loud noise was heard, accompanied by a load

drop of approximately 25%. The mid-span displacement measured below the deck (D4 in Figure

12a) reached 23.3 mm. The strain readings from directly under the loading pad (S10 in Figure

12b) decreased slightly after the load peak, indicating a delamination in the panel. Loading was

terminated to avoid damage to the other span, which was to be tested in FAIL 2.

4.1.2.b FAIL 2

The load-deflection and load-strain relations observed from FAIL 2 were largely linear-

elastic up to 313.6 kN, when a loud noise was heard, accompanied by a load-drop of

approximately 12%. The mid-span displacement measured below the deck (D1 in Figure 12a)

reached 23.0 mm. The strain readings from directly under the loading pad (S2 in Figure 12b)

decreased slightly, indicating a delamination in the panel. In-test observation made from the end

of the cells of the deck specimen showed no sign of web buckling.

24

0 10 20 30 40 500

100

200

300

400

Load

(kN

)

Displacement (mm)

FAIL 1(D4)

FAIL 2(D1)

a) Load-Displacement

0 2000 4000 6000 80000

100

200

300

400

Strains ( 10-6 )

Load

(kN

)

FAIL 1(S10)

FAIL 2(S2)

b) Load Strain

Figure 12 Load-Displacement and Load-Strain relation for FAIL 1 and FAIL 2

When loading continued, the specimen was able to regain the load level of the first peak

and eventually failed from web buckling at a load of 396.8 kN and deflection of 48.9mm. The

system was able to achieve significant deflection after the first peak. The deflection at failure is

25

more than twice of that at the initial load-drop (23 mm). The transverse displacement and strain

profiles (Figures 13a and 13b) indicate that the load is not effectively transferred in the

transverse direction. The portions of the deck directly under the loading pad carried most of the

load.

0

5

10

15

20

25-600 -400 -200 0 200 400 6 00

Dis

plac

emen

t (m

m)

Location (mm )

0 % Peak

25 % Peak

50 % Peak

75 % Peak

Peak (368.5 kN )

0

10

20

30

40

50-600 -400 -200 0 200 400 600

0% Peak325% Peak350% Peak3Peak1 (313.5 kN )Peak2 (355.6 kN )Peak3 (396.9 kN )

Location (mm)

Dis

plac

emen

t (m

m)

0

1000

2000

3000

4000

5000-500 -250 0 250 500

Stra

ins

(mic

rostr

ains

)

Location (mm)

0 % Peak

25 % Peak

50 % Peak

75 % Peak

Peak (368.5 kN)

0

1000

2000

3000

4000

5000

6000

7000

8000-600 -400 -200 0 200 400 600

0% Peak325% Peak350% Peak3Peak1 (313.5 kN )Peak2 (355.6 kN )Peak3 (396.9 kN )

Stra

ins

(mic

rost

rain

s)

Location (mm) a) Test FAIL 1 b) Test FAIL 2

Figure 13 Displacement and Strain Distribution Profiles – Non skew test

Location (mm)

Location (mm) Location (mm)

Location (mm)

Stra

in (1

0-6)

Stra

in (1

0-6)

Dis

plac

emen

t (m

m)

26

The failure, even after the web buckling, was not catastrophic. The load drop was only

approximately 10% of the peak load. Loading was discontinued due to concerns of the stability

of the test setup after the deck had deflected by 49 mm.

The wear surface, which did not show any cracking during the fatigue and FAIL 1 tests,

showed a crack near the loading point (Figure 14).

Figure 14 Crack on Wear Surface

4.1.3 Post-test failure analysis

After the tests, the specimen was dissected for a failure mode analysis. As seen in Fig.15a

and 15b, delamination was observed between the web of the deck and the bottom plate. In

Fig.15b, where the loading was applied to a much further stage (in FAIL 2), a separation

between the lips of the two panels was observed. This indicated that the fastener connection has

failed, most likely from bearing failure on the FRP.

Among all the pieces (approximately 0.6m × 0.6 m each piece) dissected from the

specimen, delamination was found only at these two locations, both of which are near and

between the two loading points, where horizontal shear stress is expected to be the highest.

As seen in Fig.15c, web buckling was observed underneath the location where FAIL 2 loading

was applied.

27

It was also discovered that the joint between top plates is filled with resin and aggregate

seeping down from the wear surface (Figure 16). This resulted in continuity in the top plates,

which would have been otherwise simply bearing against each other.

No sign of wear surface debonding were found after careful examination of the cross-

section and the pieces.

(a) Bottom flange delamination (b) Lip separation

(c) Web buckling

Figure 15 Post test inspection of the dissected specimen

28

(a) Resin seeps through joint of top plates (b) Joint close-up

Figure 16 Polymer concrete bonding to the plates

4.2 Skew Results

4.2.1 Fatigue test

The deck specimen showed no signs of cracking, failure or stiffness reduction during the

fatigue test. The progression of the mid-span deflection showed a stable and largely linear trend

up to 2 million cycles on a log-scale plot shown in Figure 17. The mid-span deflection of the

deck stabilized after 1 million cycles except for two measurement locations, D8 and D4, where

there was a rising trend after 1 million cycles. The maximum deflection under the fatigue load

(80 kN each loading pad) grew from 4.2 mm at the beginning of the fatigue loading to 5.7 mm

after 2 million fatigue cycles for D4 and 4.9 mm at the beginning of the fatigue loading to 6.6

mm after 2 million fatigue cycles for D8.

29

0

1

2

3

4

5

6

7

8

1000 104 105 106 107

Dis

plac

emen

t (m

m)

Number of Cycles (Log Scale)

D8

D2

D6

D5

D7

D4

Figure 17 Fatigue Progression - Skew

4.2.2 Failure Test:

4.2.2.a FAIL 1

Due to technical difficulties the load-deflection relations was not measured for the

ascending portion of the first loading cycle. Hence, the curve for load-displacement had two

parts. The first part was the first loading cycle that was obtained during the descending portion of

the loading and the second curve was the load-displacement for the second loading cycle. The

load-deflection relation observed from FAIL1 was largely linear-elastic up to the peak load of

370 kN, when a loud noise was heard, accompanied by a load drop of approximately 27%. The

mid-span displacement measured below the deck (D3 in Figure 18) reached 27.5 mm. The

displacement reading showed effects of the softening due to load from the first loading cycle.

Loading was terminated to avoid damage to the other span, which was to be tested in FAIL 2.

30

4.2.2.b FAIL 2

The load-deflection relation observed from FAIL 2 was largely linear-elastic up to 390

kN, when a loud noise was heard, accompanied by a load-drop of approximately 13%. The mid-

span displacement measured below the deck (D9 in Figure 18) reached 26.5 mm. In-test

observation made from the end of the cells of the deck specimen showed no sign of web

buckling.

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60

FAIL1bFAIL2

Load

(kN

)

Displacement (mm)

FAIL 2

FAIL 1b

FAIL 1a

FAIL 1a

Figure 18 Load-Displacement relations for FAIL 1 and FAIL 2

When loading continued, the specimen eventually failed from web buckling at a load of

320 kN and a deflection of 52.5 mm. The deflection at failure is almost twice of that at the initial

load-drop (26.5 mm). The transverse displacement and strain profiles (Figures 19a and 19b)

indicate that the load is not effectively transferred in the transverse direction. The portions of the

deck directly under the loading pad carried most of the load.

31

D5 D4 D3 D2S5 S3 S2 S1S4

D10 D9 D8 D7S11 S9 S8S10S12 S7 S6

-30

-25

-20

-15

-10

-5

0

5

-600-400-20002004006008001000

0% Load25% LoadMax. Load (365 kN)75% Load50% Load

Dis

plac

emen

t (m

m)

Location (mm) -30

-25

-20

-15

-10

-5

0

5

-10 00-50 0050010 00

0 % Lo ad2 5% L o ad5 0% L o ad7 5% L o adM ax. Lo ad (388 .75 k N )

Dis

plac

emen

t (m

m)

Lo catio n (m m )

-7000

-6000

-5000

-4000

-3000

-2000

-1000

0

1000

-600-400-20002004006008001000

0% Load25% Load50% Load75% LoadMax. (365 kN)

Stra

in (m

icro

stra

ins)

Location (mm) -7000

-6000

-5000

-4000

-3000

-2000

-1000

0

1000

-1000-50005001000

0% Load25% Load50% Load75% LoadM ax. (388.75kN)

Stra

in (m

icro

stra

ins)

Location (mm)

a) Test FAIL 1b b) Test FAIL 2

Figure 19 Displacement and Strain Distribution Profiles – Skew test

It should be noted that even after the web buckling, the failure was not catastrophic. The

load drop was only approximately 15% of the peak load. Loading was discontinued due to

concerns of the stability of the test setup after the deck had deflected by 53 mm.

32

4.2.3 Post-test failure analysis

Post-test failure analysis gave results as those for the non-skew configuration.

Delamination was again seen at similar locations in the vicinity of the loading pads. Also

continuity between the top plates was maintained due to resin and aggregate seeping down from

the wear surface. The cross-sections of the dissected pieces were carefully examined and no sign

of wear surface debonding was found.

The design load is 37.2 kips after 19.1 million cycles: C (19.1x106, 37.2 kip).The

proposed failure tests after the fatigue test provided four data points: B (2x106, failure loads).

These strength values obtained from the FAIL1, FAIL2 tests of both skew and non-skew

configuration, are compared with the test results by McEntire and Nelson and then with the

AASHTO design load levels (Figure 20).

0

100

200

300

400

0.1 10 1000 105 107

Load

(kN

)

No. of Cycles (Log scale)

FAIL 2 Skew and Non-Skew

FAIL 1 Skew

Design Load

165.5 kips

19.1

mill

ion

cycl

esand Non-skew

Preliminary Testwithout fatigue

A B

C

Figure 20 Fatigue Comparison

From these two sets of test data, it was found that the deck did not show signs of strength

degradation, due to fatigue, upto 2 million loading cycles. The slightly higher strength of the

decks from this investigation, compared to the McEntire and Nelson, is likely due to different

33

boundary conditions of the test setup. The strength results from both investigations are more than

twice the AASHTO design load levels.

34

CHAPTER 5

SYSTEM DESCRIPTIONS AND FINITE ELEMENT MODEL

The prototype deck system, used for laboratory testing, was made of two pultruded

sections as shown in Figure 21.


203 203203178

13

13 114

13

Unit: mm

a) Cross section of the deck system

b) Picture of the deck showing all components

Figure 21 Deck Assembly

A top plate was mechanically fastened to the top of a bottom panel, which had four I-

sections. The whole pultruded deck assembly, which had a total thickness of 127 mm, was

supported by three steel I-beams that were 1.22 m apart.. A polymer concrete wear surface was

then installed on the top plate of the deck. The loading pads were placed on top of the wear

surface at a distance of 1.22 m center-to-center.

The finite element model simulated the deflection and strain behavior of the deck and

girders. The loading locations and loading magnitudes match those used for the laboratory tests.


35

A simplified finite element approach, which used a single layer shell elements for the FRP deck

system that is composed of flanges and webs, is used in this investigation. The key components

of this approach, which include selection of the elements, discretization, calculation of the

equivalent properties of the thick shell element, and surface load applications, is described in this

section.

5.1 Elements

While the deck system is made of top and bottom flanges, web, and a top plate, the

simplified model presented in this paper utilized a single layer of thick shell elements that had

the equivalent material properties of the deck. The finite element model also used frame

elements for the girders and link elements for the deck-to-girders connections.

5.1.a Shell Elements

A four node quadrilateral area section was used to model the deck. The area section was

defined as shell element which has translational and rotational degrees of freedom and is capable

of supporting forces and moments. Due to the short span length in the test configuration, which

the analysis is attempting to simulate, the vertical shear deformation in the web of the FRP deck

is expected to be significant when compared to the longitudinal flexural deformation. Hence the

use of a Mindlin / Reissner thick plate formulation, which includes the effects of transverse shear

deformation (CSI, 2005). The shell element was assigned a thickness of 127 mm, which was the

overall thickness of the actual test panels including the top plate, bottom plate and the I-section.

The meshing for the shell elements used in the non-skew and skew configurations is shown in

Table 1 and Fig. 22.

36

Table 1: Shell Elements Used

Non-Skew Configuration

No. of Shell Elements

Skew Configuration

No. of Shell Elements

Per Row (Direction x) 66 120

Per Column (Direction y) 59 59

Total Number of Shell Elements 3894 7080

Area of each Shell Element 25.4 mm × 29.21 mm 25.4 mm × 29.21 mm

5.1.b Frame Element

Prismatic frame elements were used to model the girders supporting the deck. The

dimensions and the end supports for the frame element were matched to the experimental girder

dimensions and support. The frame elements were discretized to match the meshing pattern of

the shell element above.

5.1.c Link Element

Link elements were used to maintain constant distance between the nodes of the frame and

shell elements.

5.1.d Constraint

Beam constraints were assigned the same rotational degrees of freedom so that the nodes in

the frame and shell elements would move together, simulating a fixed beam-to-slab connection.

37

5.1.e Supports

The exterior beams were roller supported on their ends; the interior beam was simply

supported.

a) Finite Element Model for the Non-Skew Configuration

b) Finite Element Model for the Skew Configuration

Figure 22 Finite Element Models

38

5.2 Material Properties

The FRP bridge deck is orthotropic. The values for all the material properties of the shell

elements were calculated based upon the equivalent cross-sectional moment of inertia, EI, and

the shear moduli, G, for all three principal directions of the FRP deck. The global coordinate

system (x-y) and the materials coordinate system (Directions 1 and 2) are defined as shown in

Fig. 23. The equivalent properties used for the shell elements were calculated as follows:

5.2.1 Modulus of Elasticity

The values of Modulus of Elasticity for different components of the deck system provided by the

FRP deck system manufacturer are shown in Table 2.

Table 2: Manufacturer provided material properties

Top Flat Face sheet I Section Bottom Flat Face Sheet

Transverse (Direction 2) 20.685 GPa 6.895 GPa 20.685 GPa

Longitudinal (Direction 1) 6.895 GPa 27.580 GPa 6.895 GPa

Transverse(Dir 2)

Longitudinal(Dir 1)

Transverse(Dir 2)

Longitudinal(Dir 1)

X

Y

X

Y

Figure 23 Deck Orientation

39

The typical cross-section of the FRP deck under investigation is shown in Fig. 24. The

equivalent properties of the shell element are calculated for a unit width of 203 mm of the deck

panel. The equivalence is based on the same flexural and shear stiffness values, i.e., the EI and

GA values.

127 mm

83% Flange Widths Used

Actual Section Equivalent Section

127 mm

203 mm 203 mm

E × I = 1.197×1012 N × mm2 E11 =EBIbBd3

12ffffffffffffffffffffffffffffffffffffff

Figure 24 Typical Cross-section of the Deck

Due to the effects of the shear lag phenomenon, the effective width of the top flange was

calculated to be 83%, based on the approach described in (Hughes, 1988). This reduced width of

top and bottom flanges was used to calculate the EI of the deck panel per unit width (203 mm).

Equivalent shell element modulus of elasticity, E11, was then calculated for the FEA model. The

equivalent “E×I” value per unit width was calculated as 1.197 × 1012 N×mm2, and the moment of

inertia for a 127 mm thick plate was calculated to be I=1.43×108 mm4. Then the equivalent

Young’s modulus in Direction 1 (stronger) was calculated as E11 =EBII eq

ffffffffffffffff

E11 =EBIbBd3

12ffffffffffffffffffffffffffffffffffffffff= 1.197B1012

1.43B108fffffffffffffffffffffffffffffffffffffff= 8.37 GPa.

40

Similar procedure was followed for the other direction and the value calculated was

E22=4.67 GPa. The value for E33 was taken as 10.34 GPa.

5.2.2 Shear Modulus

Calculation of the equivalent shear moduli in all three orthogonal directions of the deck are

described as follows:

5.2.2.a Calculation of vertical shear G13

The fibers in the FRP deck were pultruded in a pattern as shown in Fig. 25. Due to this

alignment of fibers and the curvature at the web-to-flange joints, the portion of the web that is

effective in resisting shear is assumed to be

Effective ht = Total ht@ top & bottom plate@ top & bottom flange@ 2B 13ffff gBRadius

Effective ht = 127@ 3B12.7` a

@ 4.32@ 2B13fffB12.7

f g

= 76.2 mm

In calculating the shear modulus for the shell elements, the difference between the web

thickness (12.7 mm) and the unit section width (203 mm) was also taken into account.

PultrudedFibers .

Effective Ht. forGweb Calculation

Figure 25 Effective Height for Calculating Gweb

41

The Classical Lamination Theory of was used to calculate the in-plane shear modulus of

the web Gweb (4640 MPa), which was then used to calculate the equivalent shell shear modulus

(G13) as

G13 = GwebBEffective Height

Total Heightffffffffffffffffffffffffffffffffffffffffffffffffffff

BWeb thickness

Unit widthffffffffffffffffffffffffffffffffffffffffffff

= 4640.34B 76.2127fffffffffffffff g

B12.7203.2ffffffffffffffffff g

= 174.01 MPa

5.2.2.b Calculation of G23

The rectangular configuration of the cell of the deck panels is ineffective in resisting

shear deformation. When a unit width of the cell is subjected to a unit shear force, P, the

rectangular cell will deform as shown in Fig. 26. The deflection Δ can be calculated based on the

double bending in the top and bottom flanges.

Δγ

127 mm

C / C Distance betweenWebs = 203.2 mm

P

Figure 26 Double Bending

The equivalent shear strain

γ =ΔLfffff where, L = center to center (c/c) distance between webs = 203.2 mm

42

Then average shear stress is τ =PAfffff

Finally the equivalent shear modulus of the shell element was calculated as

G23 =τγffff= 12.3 MPa

5.2.2.c Calculation of G12

The in-plane shear modulus G12 in the shell element is only provided by the top and

bottom flanges. It was assumed that the top and the bottom plates have the same shear modulus

value as the web laminate. The total thickness for the top and the bottom plate combined is 25.4

mm; the thickness of the deck section is 127 mm.

Shear modulus (G12) as

G12 = Web Laminate ShearBTop plate thickness + Bottom plate thicknessDeck thickness

fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff

= 4640.34B 25.4127ffffffffffffff g

= 928.068 MPa

5.2.3 Poissons Ratio

The poissons ratio value was assumed to be 0.3 for the deck in all three directions.

5.3 Effect of Shear Lag

The Simple beam theory assumes that plane cross section remains plane, thus points at

the same elevation have the same stress. But in reality the stress at locations closer to the web is

higher than that away from the web. This phenomenon is known as shear lag.

43

In the principal direction of this deck system, which is composed of webs and flanges,

shear lag is expected. Based on the procedure described in (Hughes, 1988), the effective width of

the top and bottom flanges was calculated to be 83% of the actual unit width.

Since the web in–plane shear plays a major role in deflection, the reduction in flexural

moment of inertia, due to shear lag, did not significantly affect the, but increased the stress by

more than 10%.

5.4 Loading for the Model

For each test configuration, three load cases were considered: Service (up to Fatigue level

used in the test) , Fail 1 and Fail 2. The loads were applied as pressure uniformly across an area

of 254mm×508mm on the mid-surface of the shell elements. The direction of loading was

specified in the direction of gravity (negative Z-direction) in the global coordinate system. The

load intensities, which were defined as force per unit area, were obtained by dividing the

required load levels by the loading areas. The load levels and the loading configurations for all

three load cases for both skew and non-skew configuration are summarized in Table 3 and

Figures 27a, 27b, 27c respectively.

Table 3: Loads and Load Intensities

Load Case Load (kN) Intensity (MPa)

Service (Each Pad) 457.2 3.54

FAIL 1 914.4 7.08

FAIL 2 914.4 7.08

44

5.5 Parametric Study

5.5.a Shear Moduli Effects

While analyzing the FEA model, it was seen that vertical shear played a major part and the

area element showed deflection only under the loading location. That meant the load was not

transferred to the neighbouring girders. Also it was seen that the shear modulus values,

especially the vertical and transverse shear modulus values, G13 and G23, had a major impact on

the deflection results. Two parametric studies, of the effects of G12 and G23 on the deflection,

were performed:

(1) Values of G23 varied from 3.5 MPa to 20.7 MPa, while G13 remained constant at 174.01 MPa;

(2) Values of G13 from 69 MPa to 689.7 MPa, while G23 constant at 12.3 MPa. The results of

these parametric studies are shown under results section of this paper.

5.5.b Effects of Discontinuity

When the top plate for the deck was laid out for the experimental test, it had three pieces

that were joined together to form the complete deck surface. To study the localized softening

effect on the global stiffness of the deck system, two strips of FEA shell elements, at the exact

location as the joints during experiments, were given only 50% stiffness values. The results

showed that having a joint at the specified locations did not affect the displacement or strain

values in the deck.

45

CHAPTER 6

VERIFICATIONS BY EXPERIMENTAL RESULTS

6.1 Summary of experimental results

The FRP deck tests used for the validation of the model for both non-skew and skew

configurations, underwent fatigue and failure tests, the results of which are briefly summarized

in this section. Detailed explanation of these two tests results has been previously presented in

(Vyas and Zhao, 2007). The loading configurations used by the non-skew and skew tests for

laboratory experiments are shown in Fig. 27. In both tests, the deck panels are supported by

three steel I-beams spaced 1.2-m apart.

Fatigue Test Location Failure Test(Fail 2) Location

Failure Test(Fail 1) LocationWest Bay East Bay

a) Non-Skew Fatigue b) Non-Skew Failure

46


Fatigue TestLocation


West Bay

East Bay

Boundary of FEA Model

Boundary ofFEA Model

c) Skew Fatigue and Failure

Figure 27 Loading Configurations

Each test included a fatigue test and two failure tests, all of which were used in the

validation of the finite element models. For both configurations the deck system displayed no

noticeable signs of degradation after 2 million fatigue cycles.

Similar results were seen for the skewed configuration, where the specimen did not show

any signs of degradation after 2 million fatigue cycles and substantially exceeded the AASHTO

required capacities.

47

Table 4: Summary of Test results

Configuration Non-Skew Skew

Test FAIL 1 FAIL 2 FAIL 1 FAIL 2

First Peak Load (kN) 370.5 313.6 370 390

Deflection at first peak load (mm) 23.3 23.0 27.5 26.5

Final Failure Load (kN) NA 396.8 NA 320

Deflection at final peak load (mm) NA 48.9 NA 52.5

During the ascending portion of the first loading cycle (up to 333.6 kN) of the Fail 1 test

in the skewed configuration, technical difficulties prevented the recording of load-deflection and

load-strain data. The data was recorded for the peak load of the first loading cycle and then the

ascending portion of the second loading cycle.

Post-test inspection revealed that, in both the non-skew and skew configurations, failure

was initiated by delamination between the web and the bottom flange of the deck but the final

failure occurred due to web buckling.

The displacements and the strains obtained from the FEA model were compared with

those from the two full-scale tests. An excellent agreement between the test and analytical results

was observed in the deflection and strain response.

48

6.2 Comparisons to Non-Skew Test Results

Results of deflection and strain at the midspan, obtained from the finite element analysis,

are compared with those measured from the test at service, FAIL1, and FAIL2 load levels. They

are summarized in this chapter. The locations of strain gages and the displacement gages that

were used for the laboratory tests for non-skew configuration are shown in Fig. 28.

a) Fatigue Test b) Failure Test

Fatigue Test LocationFailure Test(Fail 2) Location


D4

D3

D5

D0

D1

D2

S6S7S8S9S10S11S12S13

S0S1S2S3S4S5

D4

D3

D5

D0

D1

D2

S6S7S8S9S10S11S12S13

S0S1S2S3S4S5

Figure 28 Location of Displacement and Strain Gages: Non-skew Configurations

6.2.1 Service Level Load Displacement Distribution

The mid-span displacement distribution curves from tests and the FEA analysis are shown

in Fig. 29. The experimental data followed the general trend of the FEA results. The maximum

displacement from both west and east bay were 4.25 mm and 2.9 mm respectively, while the

FEA result was 4.4 mm. The percentage error between the experimental results and FEA was

3.5% and 52% in the two corresponding spans in this load case.

49

-5

-4

-3

-2

-1

0

-800 -600 -400 -200 0 200 400 600 800

FEA WBTest WBFEA EBTest EB

Dis

plac

emen

t (m

m)

Location (mm)

Figure 29 Service Level Displacement Distribution at Midspan

6.2.2 Service level Load Strain Distribution

The mid-span strain distribution curves from tests and the FEA analysis are shown in

Fig.30. The experimental data followed the general trend of the FEA results. The maximum

recorded strain from both west and east bay were 700 με and 490 με respectively, while the FEA

result was 770 με. The test strain values gave a good match when compared to the FEA strain

values at those locations.

50

-800

-700

-600

-500

-400

-300

-200

-100

0

-40 -30 -20 -10 0 10 20 30


Stra

in (m

icro

stra

ins)

Location (mm)

Figure 30 Service Level Strain Distribution

6.2.3 Parametric study results

6.2.3.a Effect of the vertical shear modulus G13

A parametric study was carried out on the initial loading up to the service load to

examine the effects of the vertical shear modulus, G13, which is determined by the in-plane shear

modulus of the webs. Fig. 31 indicated that as G13 varies from 69 MPa to 689.7 MPa, the

maximum deflection changed from 7.3 mm to 2.4 mm. At the theoretical value of G13= 175 MPa,

a good agreement on the maximum deflection between the test (West Bay response) and

analytical results was observed (4.4 mm versus 4.35 mm). The figure demonstrated that the total

deflection in the deck (4.4 mm), due to its short shear span, is significantly affected by the shear

51

deformation in the web. The flexural deformation, obtained asymptotically when a large G13

value was used, is only 2.2 mm, or one-half of the total deflection.

0

1

2

3

4

5

6

7

8

0 100 200 300 400 500 600 700

13

WB DisplacementEB Displacement

Dis

plac

emen

t (m

m)

G13

(MPa)

Figure 31 Effect of Shear Modulus G13

6.2.3.b Effect of deck transverse shear modulus G23

A parametric study was performed to investigate the effects of shear modulus G23 on non

skew decks. As shown in Fig. 32, the maximum displacement value decreased from 5.2 mm to

3.85 mm as G23 increased from 3.5 MPa to 20.7 MPa. At the theoretical value of G23= 12.3 MPa,

a good agreement on the maximum deflection between the test (West Bay response) and

analytical results was observed (4.4 mm versus 4.37 mm at the mid point).

52

0

1

2

3

4

5

6

0 5 10 15 20 25

23

Max. Center Displacement

Dis

plac

emen

t (m

m)

G23

(MPa)


The parametric study validated the approach for calculating the equivalent shear moduli

of the deck.

6.2.4 FAIL 1 Displacement Distribution

As seen from Fig. 33 the maximum displacement value from the FEA was 9.2 mm, only a

3% over estimate of the test result (8.9 mm). Displacement on the non-loading bay was much

smaller and not compared here. The proximity of the test and analysis readings can be seen even

from the load-displacement comparison graph for FAIL 1 test (Fig. 34)

53

-10

-8

-6

-4

-2

0

-800 -600 -400 -200 0 200 400 600 800

FEA WBTest

Dis

plac

emen

t (m

m)

Location (mm)

Figure 33 FAIL 1 Displacement Distribution

0

50

100

150

200

0 2 4 6 8 10

TestFEA

Load

(kN

)

Displacement (mm)

Figure 34 FAIL 1 Load-Displacement Comparison

54

6.2.5 FAIL 1 Strain Distribution



recorded strain from west bay was 1657 με, while the FEA result was 1800 με. The test strain

value gave a good match when compared to the FEA strain value of 1663 με at that location.

Strain on the non-loading bay was much smaller and not compared here.

-2000

-1500

-1000

-500

0

-800 -600 -400 -200 0 200 400 600 800

FEA WBTest

Stra

in (M

icro

stra

ins)

Location (mm)

Figure 35 FAIL 1 Strain Distribution

6.2.6 FAIL 2 Displacement Comparison

The deck used in the laboratory test had undergone 2 million cycles of fatigue loading and

a failure test loading, which had a softening effect on the deck. This showed when the Fail2 test

was performed on the east bay. The maximum displacement recorded during the test was 9.8

55

mm, whereas the FEA model gave a displacement value of approximately 9.1 mm (<10% error),

as seen in Fig. 36.

0

50

100

150

200

TestFEA

0 2 4 6 8 10

Load

(kN

)

Displacement (mm)

Figure 36 FAIL 2 Load Displacement Comparison

6.2.7 FAIL 2 Strain Comparison

The strain values showed a similar trend as displacement values, and gave a value of

approximately 1800 με from the tests. When compared to the FEA model strain value of 1480

με, it shows the effects of softening. (Fig. 37)

56

0

50

100

150

200

0 500 1000 1500 2000

TestFEA

Load

(kN

)

Strain (microstrains) Figure 37 FAIL 2 Load Strain Comparison

6.3 Comparisons to Skew Test Results

The locations of strain gages and the displacement gages that were used for the laboratory

tests for skew configuration are shown in Fig. 38.

D1

D2

D3

D4

D5

D7

D8

D9

D11D6

D10

S1S2

S3

S4

S5

S6

S7

S8S9

S10

S11

S12

FATIGUETest

FAIL 1Test

FAIL 2Test

Figure 38 Location of Displacement and Strain Gages: Skew Configurations

57

6.3.1 Service Level Load Displacement Distribution

The mid-span displacement distribution curves from tests and the FEA analysis are shown

in Fig. 39. The experimental data followed the general trend of the FEA results. The maximum

displacement from both west and east bay were 5.1 mm and 5.2 mm respectively, while the FEA

result was 4.7 mm for both bays. The percentage error between the experimental results and FEA

was 7.9% and 8% in the two corresponding spans in this load case.

-6

-5

-4

-3

-2

-1

0

1

-1000-50005001000


Dis

plac

emen

t (m

m)

Location (mm)

Figure 39 Service Level Displacement Distribution

6.3.2 Service level Load Strain Distribution



recorded strain from both west and east bay were 850 με and 850 με respectively, while the FEA

58

result was 785 με. The test strain values gave a good match when compared to the FEA strain

values at those locations. Hence, the FEA value is only an 8% over estimate of the test result.

-800

-600

-400

-200

0

-1000-50005001000


Stra

in (m

icro

stra

ins)

Location (mm)

Figure 40 Service Level Strain Distribution

6.3.3 Parametric study results

6.3.3.a Effect of the vertical shear modulus G13

A parametric study was also carried out for the skew configuration on the initial loading

up to the service load to examine the effects of the vertical shear modulus, G13, which is

determined by the in-plane shear modulus of the webs. Fig. 41 indicated that as G13 varies from

69 MPa to 689.7 MPa, the maximum deflection changed from 7.6 mm to 2.5 mm. At the

theoretical value of G13= 175 MPa , a good agreement on the maximum deflection between the

59

test and analytical results was observed (4.7 mm versus 4.65 mm). The figure demonstrated that

the total deflection in the deck (4.7 mm), due to its short shear span, is significantly affected by

the shear deformation in the web. The flexural deformation along, obtained asymptotically when

a large G13 value was used, is only 2.1 mm, or approximately one-half of the total deflection.

0

1

2

3

4

5

6

7

8

0 100 200 300 400 500 600 700

WB DisplacementEB Displacement

Dis

plac

emen

t (m

m)

G13

(MPa)


6.3.3.b Effect of deck transverse shear modulus G23

A parametric study was performed to investigate the effects of shear modulus G23 on

skew decks. As shown in Fig. 42, the maximum displacement value decreased from 5.4 mm to

4.2 mm as G23 increased from 3.5 MPa to 20.7 MPa. At the theoretical value of G23= 12.3 MPa ,

a good agreement on the maximum deflection between the test and analytical results was

observed (4.7mm versus 4.6 mm at the mid point).

60

0

1

2

3

4

5

6

0 5 10 15 20 25

Max. Displacement

Dis

plac

emen

t (m

m)

G23

(MPa)


Due to aforementioned technical difficulty, the comparisons used in this paper for skew

configuration failure test results are from

(1) The peak load of the first loading cycle, and

(2) The ascending portion of the second load cycle.

The sustained load at the first peak of 333.6 kN for 5 minutes had slightly softened the specimen.


The displacement for the FAIL 1a test was measured by approximating its value for the

ascending part of the first loading. The value of 9.7mm, as seen in Fig. 43 gave almost an exact

match to the test displacement. The third load-displacement curve is from FAIL test 1b, which

recorded the displacement for the second loading excursion. As expected the softening during the

first loading cycle affected the displacement recorded during the second cycle, giving a

61

maximum displacement value of 12.0 mm. The proximity of the test and analysis readings can be

seen even from the load-displacement comparison graph for FAIL 1 test (Fig. 44)

-12

-10

-8

-6

-4

-2

0

-1000-50005001000

FEATest 1bTest 1a

Dis

plac

emen

t (m

m)

Location (mm)


0

50

100

150

200

0 2 4 6 8 10 12 14

FEAFAIL1 1aFAIL1 1b

Load

(kN

)

Displacement (mm)


62

6.3.5 FAIL 1 strain distribution

The strain calculated by the FEA model was approximately 1800 με (Fig. 45). The

maximum strain at the midspan during the first loading cycle was not recorded during the

laboratory test. Hence, Fig. 45 shows the strain graph from the second loading cycle. This

loading cycle gave a higher strain value due to softening effect from the first loading cycle. Also,

strain during the laboratory test was not measured exactly below the loading, but was measured

at two locations very close to the center. The proximity of those values to the FEA model values

and the overall curve of the strain graphs shows that the FEA model gave a pretty good match to

the strain values obtained from the laboratory tests.

-2000

-1500

-1000

-500

0

-800-600-400-2000200400600800

FEATest 1b

Stra

in (m

icro

stra

ins)

Location (mm)


63


FAIL2 test was not affected by FAIL1 test due to its location, i.e., damage sustained from

Fail 1 did not propagate to the loading point of Fail 2. Hence the displacement results from

FAIL2 exactly match those from the test. As seen in Fig. 46 the value of 9.8mm from the

analysis almost matches the test result (9.7 mm), giving us less than 2% error. The proximity of

the test and analysis readings can be seen even from the load-displacement comparison graph for

FAIL 2 test (Fig. 47)

-10

-8

-6

-4

-2

0

-1000-50005001000

FEATest 1bD

ispl

acem

ent (

mm

)

Location (mm)


64

0

50

100

150

200

0 2 4 6 8 10

FEAFAIL2

Load

(kN

)

Displacement (mm)


6.3.7 Fail 2 Strain Distribution.

As seen from Fig. 48, the maximum strain observed from the test (2350 με) is 30.6%

higher than the analytical value (1800 με).

-2500

-2000

-1500

-1000

-500

0

-5000500

FEATest 1b

Stra

in (m

icro

stra

ins)

Location (mm)


65

CHAPTER 7

CONCLUSIONS

7.1 Experimental Investigation

The following conclusions can be drawn from the experimental investigation of this low-

profile FRP composite deck system:

• The assembly of the system is easy and quick except that the procedure for drilling and

fastening of the top plate still needs to be improved.

• The deck system displayed no noticeable signs of degradation after 2 million fatigue cycles

for both, non-skew as well as skew configurations. The progression of the mid-span

deflection of the deck showed a stable and largely linear trend up to 2 million cycles on a

log-scale.

• The peak loads measured from the FAIL 1 and FAIL 2 tests were 370.5 kN and 396.8 kN,

which are 2.3 and 2.4 times the AASHTO strength requirement (164 kN) for non-skew

configuration and 370 kN and 390 kN, which are 2.3 and 2.4 times the AASHTO strength

requirement (164 kN) for skew configuration, respectively.

• In FAIL 2, the deck system showed significant deflection capability beyond the first load

drop caused by the delamination. This failure mechanism allowed for substantial ductility

and warning prior to the web failure. The ductile failure mode is a unique and valuable

attribute, which was not observed from most other existing FRP deck systems.

• Delamination appeared to have been concentrated near and between loading points, where

horizontal shear stress is the highest.

66

• No visible sign of degradation or debonding was observed on the wear surface after the

fatigue test.

• The web buckling in FAIL 2 did not lead to a catastrophic failure. The load drop was

minimal.

• The deck showed excellent strength at shear stud connections.

• The lower initial strength observed from the FAIL 2 test could be attributed to:

The delamination that occurred during FAIL 1 test may have propagated into the other span,

causing a pre-existing weak spot in the east span. In FAIL 2, the load was applied on only one

web of the deck, as oppose to two (equally) in FAIL 1.

The propagation of the deck deflection during fatigue loading, which may not be directly

related to the strength of the deck, needs to be further studied and monitored in the field.

7.2 Finite Element Analysis

A simplified FEM approach, which uses a single layer of thick shell elements to simulate

a FRP deck, that has top and bottom face sheets and web, was proposed in this thesis. Equations

for calculating the equivalent properties for the shell elements are presented. The results from the

FEA were compared with two full-scale deck tests, one non-skew and the other skew. An

excellent agreement between the analytical and experimental results, both in terms of deflection

and strain values and their patterns of distribution, were obtained.

The results from a parametric study using the FEA approach indicated that the shear

deformation in the web of the FRP deck contributed significantly to the overall deflection. This

conclusion identified an important design parameter that deserves special consideration. It also

67

presented an excellent opportunity to use this approach to optimize the design of the pultruded

sections.

Due to the simplicity of the model, constructing the model is easy and quick. It may be used

by engineers as a design tool for bridges using this or similar FRP decks.

1. The model can reasonably predict the deflection as well as strain.

2. The model can capture the general trend of displacement and strain distribution at mid

span.

3. Deflection distribution measured from FAIL 2 tests, which were conducted after Fail 1 in

the other span, still reasonably conform with the values given by the finite element

model. However, strain distribution is affected due to softening by FAIL 1 test loading,

thus giving us a higher percentage error when compared with the values from the finite

element model.

4. The average percentage error for maximumn deflection for undamaged section (Fatigue

and Fail 1 tests for both non-skew and skew configurations) is approximately 4% and for

maximum strain is approximately 15%.

5. The average percentage error for maximumn deflection for damaged section (Fail 2 tests

for both non-skew and skew configurations) is approximately 8% and for maximum

strain is approximately 25%.

68

CHAPTER 8

RECOMMENDATIONS

1) Future research needs to be carried out to study the debond mechanism, both between the

bottom plate and the I-section and between the lips of two panels.

Different repair mechanisms like resin injection, fasteners etc. need to be studied. Also

the number of fasteners or studs required for a particular section of a deck need to have a proper

calculation technique. Further research is also required for material characterization of the deck

properties.

2) In the absence of further data, engineers could consider using the following values for the

equivalent material properties for the deck design described in this thesis.

Table 5: Recommended Material Properties

Equivalent Material properties

E11

(GPa)

E22

(GPa)

E33

(GPa)

G13

(MPa)

G23

(MPa)

G12

(MPa)

ν12 ν23 ν13

8.37 4.67 10.34 174.01 12.3 928.1 0.3 0.3 0.3

3) Effects of shear deformation are considered in FEA by using thick shell elements.

69

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Documents

Development Of A Simplified Finite Element Approach For