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i

FINITE-ELEMENT MODELING OF HYBRID COMPOSITE BEAM

BRIDGE IN VIRGINIA: TIDES MILL STREAM BRIDGE

Haozhe Yi

ABSTRACT

The Hybrid Composite Beam (HCB), an innovative composite shell/reinforced

concrete beam, was used as part of the replacement of the superstructure of the Tides Mill

Stream Bridge on Route 205 in Colonial Beach, Virginia. A series of load tests were

conducted on the completed replacement structure in order to validate the design

assumptions and to characterize the overall structural response of the bridge. A detailed

finite element model of the bridge was developed in order to further understand the

behavior of this unique bridge. Finite element modeling has been widely used to conduct

structural analysis on bridges for many years. However, because of the novelty of the HCB,

finite element modeling has only been used in limited analyses on HCB bridges (Myers,

2015). This study aimed to develop a rational finite element model to simulate the behavior

of the Tides Mill Stream Bridge under static and dynamic loads. Results from a laboratory

study conducted at Virginia Tech (Ahsan, 2012) were used to calibrate a finite element

model of the HCB beam. A three beam/concrete deck bridge system, also tested at Virginia

Tech, was used to calibrate a finite element model of the tested bridge system. A full finite

element model of the Tides Mill Stream Bridge was developed. Results from field testing

conducted on the completed Tides Mill Stream Bridge, by the University of Virginia, were

used as benchmarks to adjust the full finite element bridge model. The proposed finite

element model developed in this study was able to predict the behavior of the Tides Mill

ii

Stream Bridge with acceptable accuracy. This finite element model can be used as a

reference for future analyses on the Tides Mill Stream Bridge.

iii

ACKNOWLEDGEMENT

I would like to thank Dr. Jose Gomez, Dr. Devin Harris, and Dr. Osman Ozbulut

for serving as the committee members of my defense.

I deeply appreciate the opportunity to be involved in the research of Dr. Devin

Harris and receiving the guidance and support from Dr. Devin Harris and Dr. Jose Gomez

during my stay at the University of Virginia. I would like to greatly thank Dr. Jose

Gomez for accepting me as his student, and for his input, patience and endless support.

iv

Table of Content

1 Introduction ................................................................................................................. 1

1.1 Project Description and Overview ...................................................................... 1

1.2 Thesis Objective.................................................................................................. 2

1.3 Thesis Outline ..................................................................................................... 2

2 Literature Review ....................................................................................................... 4

2.1 Previous Studies on Modeling Bridge Components made of FRP or GFRP ...... 5

2.2 Previous Studies on Modeling Hybrid Composite Beam Bridges ...................... 6

2.3 Previous Studies on HCB Bridges ...................................................................... 8

2.4 Summary ........................................................................................................... 10

3 Initial Model Development ....................................................................................... 11

3.1 Summary of Experimental Program ................................................................. 11

3.2 Geometry of Model ........................................................................................... 16

3.3 Materials Properties of the Model .................................................................... 18

3.4 Model Construction and Analysis ..................................................................... 20

3.4.1 HCB Model without Arch ........................................................................... 21

3.4.2 Full HCB Model ......................................................................................... 24

3.4.3 Three Beam/Composite Deck Model.......................................................... 39

3.4.4 Model of Tides Mill Stream Bridge ............................................................ 47

4 Results and Discussion ............................................................................................. 59

v

4.1 HCB Model without Arch ................................................................................. 59

4.2 Full HCB Model ............................................................................................... 63

4.2.1 Discussion about Contact Conditions ......................................................... 63

4.2.2 Refinement of HCB Model ......................................................................... 63

4.2.3 Results of Full HCB Model ........................................................................ 66

4.3 Three Beam/Composite Deck Model................................................................ 72

4.4 Model of Tides Mill Stream Bridge .................................................................. 79

4.4.1 Simplifications ............................................................................................ 79

4.4.2 Modification on Open Deflection Joints ..................................................... 79

4.4.3 Refinement on Semi-Integral Backwalls .................................................... 79

4.4.4 Accuracy of Bridge Model.......................................................................... 81

4.4.5 Load Case A ................................................................................................ 81

4.4.6 Load Case B ................................................................................................ 84

4.4.7 Load Case C ................................................................................................ 87

4.4.8 Load Case D ................................................................................................ 90

4.4.9 Load Case E ................................................................................................ 93

4.4.10 Load Case F ................................................................................................ 95

4.4.11 Comparison of Frequencies of First Modes ................................................ 97

5 Conclusions and Recommendations ......................................................................... 98

5.1 Conclusions ....................................................................................................... 98

vi

5.2 Recommendations ............................................................................................. 99

vii

List of Tables

Table 3-1 Dimension of Main Components (Slade & Eriksson, 2012) ............................ 17

Table 3-2 Material Properties of FRP (Slade & Eriksson, 2012) ..................................... 18

Table 3-3 Material Properties of Other Components (Ahsan, 2012) ................................ 19

Table 3-4 Paths of HCB Model ........................................................................................ 30

Table 3-5 Paths of Three HCBs System Model ................................................................ 42

Table 3-6 Paths of Bridge Model ...................................................................................... 53

Table 4-1 Mid-Span Deflection for HCB without Arch ................................................... 60

Table 4-2 Mid-Span Strains for Tests 7 (HCB without Arch) .......................................... 61

Table 4-3 Quarter Strains for Tests 7 (HCB without Arch) .............................................. 62

Table 4-4 Strains of Model, Refined Model, and VT’s Tests ........................................... 65

Table 4-5 Promotion of HCB Model after Refinement .................................................... 65

Table 4-6 Mid-Span Deflection for Point Load Tests ...................................................... 66

Table 4-7 Mid-Span Deflection for Quarter Point Load Tests ......................................... 67

Table 4-8 Mid-Span Strain for Point Load Tests .............................................................. 68

Table 4-9 Quarter Point Strains for Quarter Point Load Tests ......................................... 69

Table 4-10 Mid-Span Strains in Top-Arch for Point Load Tests ..................................... 70

Table 4-11 Mid-Span Strain in Top-Arch for Quarter Point Load Tests .......................... 71

Table 4-12 Maximum FRP Strain in Bottom Flange ........................................................ 72

Table 4-13 Deflections of Three HCBs at Bottom Flange ............................................... 74

Table 4-14 Maximum Arch Strains of Three HCBs ......................................................... 76

Table 4-15 Promotion of Bridge Model after Refinement................................................ 79

Table 4-16 Average Deviation of Strain at Mid-Span ...................................................... 81

viii

Table 4-17 Mid-Span Strains at Tension Level ................................................................ 81

Table 4-18 Mid-Span Strains through Bridge Depth ........................................................ 82











Table 4-29 Natural Frequencies of First Five Modes ....................................................... 97

ix

List of Figures

Figure 1-1 HCB Design (Harris, Civitillo, & Gheitasi, 2016) ............................................ 1

Figure 2-1 Comparison of the B0439 Deflections Measured at the Field and Predicted by

ANSYS, SAP2000, and Theoretical Calculations (Myers, 2015) ...................................... 7

Figure 2-2 Typical Cross Section of Bridge B0439 (Myers, 2015) .................................... 8

Figure 3-1 Instrumentation of HCB (Ahsan, 2012) .......................................................... 12

Figure 3-2 Uniform Load on HCB without Arch (Ahsan, 2012) ..................................... 12

Figure 3-3 Load Cases of Full HCB Tests (Ahsan, 2012) ................................................ 13

Figure 3-4 Load Cases of Three HCB/Composite Deck System Tests (Ahsan, 2012) .... 14

Figure 3-5 Instrumentation of Tides Mill Stream Bridge ................................................. 15

Figure 3-6 Load Cases of Tests on Tides Mill Stream Bridge ......................................... 15

Figure 3-7 Typical Section of Bridge Model .................................................................... 16

Figure 3-8 Plan View of HCBs Model ............................................................................. 16

Figure 3-9 Shell and Bottom Strands ................................................................................ 21

Figure 3-10 Distributed Load of 2125 pounds .................................................................. 22

Figure 3-11 Concentrated Load of 250 pounds at Mid-Span ........................................... 23

Figure 3-12 Model of HCB ............................................................................................... 24

Figure 3-13 Model of Arch ............................................................................................... 25

Figure 3-14 Model of Bottom Strands .............................................................................. 26

Figure 3-15 Model of Embedded Strands in Arch ............................................................ 26

Figure 3-16 Model of Shear Connectors ........................................................................... 27

Figure 3-17 Model of Shell ............................................................................................... 27

Figure 3-18 Model of Added Surface ............................................................................... 29

x

Figure 3-19 Details of Cross Sections .............................................................................. 29

Figure 3-20 Plan View of Paths on HCB Model .............................................................. 30

Figure 3-21 Locations of Paths on HCB Model (Side Elevation View)........................... 31

Figure 3-22 Mesh Result of Full HCB Beam ................................................................... 34

Figure 3-23 Details of “Patch Conforming Method” ........................................................ 35

Figure 3-24 Details of “Mesh” .......................................................................................... 35

Figure 3-25 Concentrated Load of 15 kips at Mid-Span .................................................. 37

Figure 3-26 Concentrated Load of 25 kips at quarter spans ............................................. 37

Figure 3-27 Separated Bottom Shell ................................................................................. 38

Figure 3-28 Model of Three HCBs System ...................................................................... 39

Figure 3-29 Deck Setback 7 Inches for Framework ......................................................... 40

Figure 3-30 Model of Deck on Three HCBs .................................................................... 41

Figure 3-31 Model of Added Surfaces.............................................................................. 42

Figure 3-32 Locations of Paths on Three HCBs System Model (Side Elevation View) .. 43

Figure 3-33 Paths of Three HCBs System Model ............................................................ 43

Figure 3-34 Eight Load Cases of Three HCBs System Model ......................................... 45

Figure 3-35 Load Case Configurations of Three HCBs System....................................... 46

Figure 3-36 Model of Tides Mill Stream Bridge .............................................................. 47

Figure 3-37 Model of Bridge Deck ................................................................................... 48

Figure 3-38 Model of Bridge Parapets.............................................................................. 49

Figure 3-39 Model of Bridge Backwalls .......................................................................... 49

Figure 3-40 Illustration of HCB Beam (G5) Embedded into Backwalls .......................... 50

Figure 3-41 Model of Added Surfaces on Bridge ............................................................. 51

xi

Figure 3-42 Parapet with Open Deflection Joints ............................................................. 52

Figure 3-43 Open Deflection Joint ................................................................................... 52

Figure 3-44 Paths of Bridge Model .................................................................................. 54

Figure 3-45 Locations of Paths on Bridge Model (West Side Elevation View) ............... 54

Figure 3-46 Simply Supported Support at Western Backwall (Bottom View) ................ 55

Figure 3-47 Displacement Support at Eastern Backwall (Bottom View) ......................... 55

Figure 3-48 Six Load Cases of Bridge Model .................................................................. 56

Figure 3-49 Load Case Configurations of Tides Mill Stream Bridge .............................. 57

Figure 4-1 Mid-Span Deflection for HCB without Arch .................................................. 60

Figure 4-2 Mid-Span Strains for Tests 7 (HCB without Arch) ........................................ 61

Figure 4-3 Quarter Strains for Tests 7 (HCB without Arch) ............................................ 62

Figure 4-4 Change of Modulus of Elasticity in Bottom Flange........................................ 64

Figure 4-5 Comparison of Strains through HCB Depth ................................................... 64

Figure 4-6 Mid-Span Deflection for Point Load Tests ..................................................... 66

Figure 4-7 Mid-Span Deflection for Quarter Point Load Tests ........................................ 67

Figure 4-8 Mid-Span Strain for Point Load Tests ............................................................ 68

Figure 4-9 Quarter Point Strain for Quarter Point Load Tests.......................................... 69

Figure 4-10 Mid-Span Strain in Top-Arch for Point Load Tests...................................... 70

Figure 4-11 Mid-Span Strain in Top-Arch for Quarter Point Load Tests ........................ 71

Figure 4-13 Maximum FRP Strain in Bottom Flange ...................................................... 73

Figure 4-14 Deflections of Three HCBs at Bottom Flange .............................................. 75

Figure 4-15 Maximum Arch Strains of Three HCBs (inconsistent values not shown) .... 77

xii

Figure 4-16 Comparison of Performance of Bridge Model before and after Placement of

Semi-Integral Backwalls ................................................................................................... 80

Figure 4-17 Plan View of Total Deflection for Load Case A ........................................... 81

Figure 4-18 Mid-Span Strains at Tension Level ............................................................... 82

Figure 4-19 Mid-Span Strains through Bridge Depth in G5 (upper left), G7 (upper right),

and G8 (bottom) ................................................................................................................ 83

Figure 4-20 Plan View of Total Deflection for Load Case B ........................................... 84



and G8 (bottom) ................................................................................................................ 86

Figure 4-23 Plan View of Total Deflection for Load Case C ........................................... 87



and G8 (bottom) ................................................................................................................ 89

Figure 4-26 Plan View of Total Deflection for Load Case D ........................................... 90



and G8 (bottom) ................................................................................................................ 92

Figure 4-29 Plan View of Total Deflection for Load Case E ........................................... 93



and G8 (bottom) ................................................................................................................ 94

Figure 4-32 Plan View of Total Deflection for Load Case F ........................................... 95

xiii



and G8 (bottom) ................................................................................................................ 96

Figure 4-35 First Five Mode Shapes ................................................................................. 97

1

1 Introduction

1.1 Project Description and Overview

The Tides Mill Stream Bridge is located on Route 205 in Colonial Beach,

Virginia. The bridge superstructure was replaced in March 2013 with eight Hybrid

Composite Beams (HCB) (Figure 1-1), and a standard 8-inch reinforced concrete deck.

Figure 1-1 HCB Design (Harris, Civitillo, & Gheitasi, 2016)

The bridge is skewed at an angle of 45 degrees with the acute angles at the

northwest and southeast corners. The HCB is a unique beam system, consisting of a fiber

reinforced polymer (FRP) shell encapsulating a steel reinforced concrete arch. The

concrete arch was formed by placing self-consolidating concrete into an arch profile

which was shaped by inserted forms (Hillman, Product Application of a Hybrid-

Composite Beam System., 2008). The concrete is cast after the beams are placed on the

bridge sub-structure, thereby alleviating the need for heavy construction equipment

normally required to place heavier steel or prestressed concrete beams. Steel strands,

placed inside the FRP shell, provide tension reinforcement to the concrete arch. Shear

2

reinforcement is also in place prior to casting of the concrete arch. The shear

reinforcement extends through the top of the HCB to provide horizontal shear transfer

between the cast-in-place deck and the HCB beams, thus insuring composite action

between the HCB beams and the bridge deck. Internal sensors were installed inside the

bridge during the fabrication for research purpose.

This study depended on previous researches conducted by Virginia Tech and the

University of Virginia. To build a rational bridge model, the results from experimental

testing at Virginia Tech and the collected data from field testing by the University of

Virginia were used as benchmarks to validate the accuracy of models in this study.

1.2 Thesis Objective

The goal of this study was to develop a detailed finite element model of the Tides

Mill Stream Bridge. A detailed finite element model of the HCB beam was first

developed and calibrated from results reported by Virginia Tech on full-scale structural

testing of the individual HCB beam. Next a three beam/composite concrete deck finite

element model was developed and calibrated using results from a full-scale test, again

conducted at Virginia Tech (Ahsan, 2012). Finally, a finite element model of the Tides

Mill Stream Bridge was developed and calibrated, using results from static and dynamic

field testing on the completed Tides Mill Stream Bridge, conducted by the University of

Virginia.

1.3 Thesis Outline

Chapter 2 presents a summary and review of literature relevant to this thesis.

Chapter 3 provides details of the methodological approach to the development of the

finite element model of the Tides Mill Stream Bridge. Chapter 4 presents comparisons of

3

the finite element models to experimental results. Chapter 5 concludes with a summary

and recommendations for further study.

4

2 Literature Review

Fiber reinforced polymer (FRP) composite materials are progressively used in

civil engineering projects (Cai, Oghumu, & Meggers, 2009). The HCB is an efficient

combination of glass fiber reinforced polymer and conventional materials such as

concrete and steel (Hillman, Product Application of a Hybrid-Composite Beam System.,

2008). This new type of beam was designed to provide necessary strength and stiffness

with a lighter self-weight compared with concrete and steel beams of similar size and

load carrying capacity. The light weight results from the reduced quantity of concrete

required to meet the design strength and stiffness, which is both economical and

environmentally friendly. Also the shipping costs may be reduced based on the fact of

lighter weight, especially when the beams are shipped before placement of the concrete

arch. Another advantage of the light weight of the HCB is that existing abutments can be

reused for bridge replacement. The HCB is able to support its self-weight and the weight

of the uncured concrete. Thus it can be placed on the abutments prior to placing of the

arch concrete and no shoring is needed during the construction (Hillman, Investigation of

a Hybrid-Composite Beam System, 2003). An HCB bridge structure can be easily

constructed by state forces using typical state force equipment (no need to rent

large/high-cost cranes). Furthermore, the FRP shell is able to protect the internal

components from corrosion and damage and potentially extend the lifespan to

approximately 100 years versus approximately 75 years for the conventional concrete

beams (Civitillo, 2014). The FRP composite material also weathers marine environments.

5

2.1 Previous Studies on Modeling Bridge Components made of FRP or

GFRP

Machado et al. studied a finite element modeling technique for honeycomb FRP

bridge decks which have been used for rehabilitating highway bridges in the United

States. The complex geometry of honeycomb FRP decks and computational limits

prevented modeling the decks in detail. To solve this problem, the proposed modeling

technique provided a workable tool to model the complicated geometry of honeycomb

FRP bridge decks. The modeling of other components of the bridges were also introduced

in this study.

Tuwair et al. developed analytical models of glass fiber-reinforced polymer

(GFRP) bridge deck panels, and conducted finite element analyses on these models. The

deck panels were composed of two GFRP sheets and trapezoidal-shaped low-density

polyurethane foam segments separated by webs made of E-glass-woven fabric. These

panels shown better performance than regular sandwich panels on flexural stiffness,

strength, and shear stiffness. The critical sheet winkling of the panels was predicted using

analytical models. A 3D model was constructed to analyze the panel system under four-

point static loading. The behavior of the finite element model agreed with that of the

experimental testing in a good manner. The flexural strength of the sandwich panel was

predicted using a flexural beam theory. The effects of the deck panel components were

evaluated by conducting a parametric study.

Cai et al. developed equivalent properties for a complicated sandwich panel

utilizing the finite element modeling techniques. The sandwich panel were used for FRP

bridge decks to meet the necessary stiffness and to reduce the self-weight at the same

6

time. The hollowed sandwich panel can be transformed into a solid orthotropic plate

which has equivalent properties with the original sandwich panel. The deflection limits

can be evaluated and designed by analyzing the equivalent plate. The in-plane axial

properties of the sandwich core was first been developed, then the out-of-plane panel

properties for bending behavior of the panel was established. The contribution of wearing

surface to the stiffness of bridges with FRP panels was investigated. In the conventional

design of bridges with traditional deck systems, the contribution of wearing surface was

not usually counted in.

2.2 Previous Studies on Modeling Hybrid Composite Beam Bridges

Myers et al. modeled the Bridge B0439, a three-span hybrid composite beam

bridge completed in November 2011 in Missouri, using two commercial finite element

analysis (FEA) packages (ANSYS and SAP2000), and examined the accuracy of linear

FEA in predicting the static behavior of the HCB under service loads. Load testing was

performed on the bridge, and the deflections of the HCB beams were measured at

different locations. The transformed area method was used to theoretically calculate the

deflections of HCB beams. The measured deflections and the theoretical calculations

were compared with the predicted deflections of the finite element models.

7

e

Figure 2-1 Comparison of the B0439 Deflections Measured at the Field and Predicted by

ANSYS, SAP2000, and Theoretical Calculations (Myers, 2015)

As can be seen in Figure 2-1, the deflections of two finite element models were

close to the measured deflections, whereas the deflections from theoretical calculation

were generally larger than the measured deflections. The comparison proved that the

FEA can predict the behavior of the HCB Bridge with acceptable accuracy.

8

Figure 2-2 Typical Cross Section of Bridge B0439 (Myers, 2015)

2.3 Previous Studies on HCB Bridges

Harris et al. investigated the Tides Mill Stream Bridge located on Route 205 in

Colonial Beach, Virginia. The in-service performance of this bridge was evaluated by

acquiring data from a series of internal and external strain gauges. Tandem axle dump

trucks were used to perform both quasi-static and dynamic tests. Lateral load distribution,

internal load-sharing behavior, and dynamic load allowance were determined in the

experimental investigation. The HCB system performed close to the beam-type bridges

described in the AASHTO specifications when considering the live load performance, but

this system also reflected some features of a flexible system when considering the

dynamic response. The internal load-sharing behavior was found to be noncomposite and

even nonlinear, which indicating that the components within the HCB system can behave

independently. Local arch bending and slide between the tension strands and the resin

matrix could be the reasons of this phenomena.

Ahsan introduced the evaluation of HCB for use in the Tides Mill Stream Bridge.

An individual HCB and a three-HCB-system was tested and examined at Virginia Tech

to validate the current design methodology and the simplifying assumptions used in

HCB. The experimental results of the FRP shell and the tension strands were consistent

with the predicted behavior. The arch was found to be easily affected by local bending so

9

that it can performed in a very different way from the predicted behavior. In general, the

HCB behaved linearly. Small non-linear behavior happened in the beams under the

design live load. The distribution factors from AASHTO were conservative for exterior

girders compared with those from testing, but were not conservative for interior girders.

The distribution factors from Hillman’s model were conservative for both exterior and

interior girders. The current design methodology was shown to be good at predicting the

behavior of FRP shell and strands. However, the arch behaved far differently from the

prediction.

Thomas Snape et al. reported the testing of the HCB for the Knickerbocker

Bridge. The Maine Department of Transportation (MDOT) intended to replace the

Knickerbocker Bridge utilizing the HCB system in 2009. A full-scale HCB manufactured

by Harbor Technologies, Inc. was tested in AEWC laboratory. The test program was

consisted of fabricating one beam unit, placing it in the AEWC lab, pouring the SCC in

the arch, and casting a concrete deck on it. The composite HCB behaved well through the

important period of filling the arch concrete. The initial deflections caused by the fluid

load of the concrete of the arch and the deck generally agreed with the design

calculations except that the beam experienced a negative camber of approximately 1 3/8

inches at mid-span immediately prior to static testing. The HCB is linear-elastic under the

design loading, and John Hillman’s analytical model is accurate in predicting behavior of

beam under service loads. The fatigue tests showed that no deterioration or degradation

was investigated in the HCB under service load and following 2,000,000 fatigue bending

cycles. Almost all of the measured mechanical properties increased after the weathering

treatment.

10

2.4 Summary

Numerous studies have been conducted on modeling regular type of bridges, and

a number of studies have been performed on modeling bridge components consisting of

FRP or GFRP composite materials. Because of the novelty of the HCB, however, limited

studies have been developed on modeling HCB bridges.

This study aimed to develop a rational finite element model to simulate the

behavior of the Tides Mill Stream Bridge. The results from laboratory testing at Virginia

Tech and field testing of the completed bridge by the University of Virginia were used as

benchmarks to calibrate the models in this study.

11

3 Initial Model Development

3.1 Summary of Experimental Program

The individual HCB without concrete arch was tested at Virginia Tech before the

testing of the full individual HCB. A system consisted of the shell and the bottom strands

was tested to better understand the behavior of these two components. The FRP lid was

not attached prior to shipping to Virginia Tech to facilitate the placement of

instrumentation prior to testing. The instrumentation of the test HCB is shown in Figure

3-1. The lid was attached to the FRP box with epoxy and screws after the instrumentation

was placed. Pin and roller supports were placed at 6 inches from the beam ends at a clear

span of 43 feet in order to simulate the span length of the Tides Mill Stream Bridge. Steel

angles (each weighing 25 pounds) were placed on the top of the HCB to provide a

uniform load across the span. Three HCBs, designated HCB1, HCB2, and HCB3 were

tested. For HCB1, a total of 85 steel angles, were evenly placed across the span length

resulting in a uniform load of 2125 pounds. For HCB2 and HCB3, the 85 steel angles

were placed 2.5 feet apart (Figure 3-2). In addition, 10 steel angles equivalent to a

concentrated load of 250 pounds were placed at mid-span of each HCB to perform point

load tests. Photos were taken for the photogrammetry analysis throughout the testing

process.

12

Figure 3-1 Instrumentation of HCB (Ahsan, 2012)

Figure 3-2 Uniform Load on HCB without Arch (Ahsan, 2012)

13

The full HCBs were tested at Virginia Tech after the concrete arch and shear

connectors were placed and 28 days were given for the concrete to cure. This test was

designed to investigate the behavior of the individual HCB. The same layout of strain

gages and pin and roller supports used in this test. Each HCB was tested twice under each

of the two load cases. The first load case was a 15 kips concentrated load at mid-span,

and the second load case was two 12.5 kips concentrated loads (in total 25 kips) at

quarter points (Figure 3-3).

Figure 3-3 Load Cases of Full HCB Tests (Ahsan, 2012)

The three HCB/composite deck system was tested at Virginia Tech after the tests

of the individual HCB. A 7.5 inch thick concrete deck was placed on the top of three

HCBs on a forty-five-degree skew. Two diaphragms were placed at the ends of the three

HCB/composite deck system to alleviate lateral-torsional displacements. A total of 17

tests were performed based on 8 load cases after the concrete achieved adequate strength.

For tests 1-12, a load of four representative tire patches representing the rear axles of a

HL-93 truck was applied on the top of the concrete deck. The tire patches were in 9 in. *

18 in., and they were spaced at 14 feet * 6 feet (Figure 3-35). The load evenly distributed

14

on the four tire patches was 85.12 kips which is the result of the weight of the two rear

axles of a HL-93 truck (64 kips) multiplied by the Dynamic Load Factor 1.33. For the

tests 13-17, a load representing the one wheel line was applied over the centerline of the

deck (Figure 3-4).

Figure 3-4 Load Cases of Three HCB/Composite Deck System Tests (Ahsan, 2012)

The field testing of the Tides Mill Stream Bridge was conducted by the University

of Virginia. The field testing included three main parts with different instrumentation

plans (Figure 3-5). A static truck load test was performed using exterior strain gages

instrumented on the bridge and internal vibrating wire gages. The truck traversed the

bridge along paths predefined in six load cases at a crawl speed (no impact) and parked at

mid-span for a period of time. Strains were recorded during the entire loading time. A

dynamic truck load test was performed after the static truck load test. . A truck was

driven along paths predefined in two load cases for multiple times. The load cases of

static and dynamic truck load tests is shown in Figure 3-6. Strains were recorded

throughout the testing process. Vibration tests were performed for a set period of time.

Ambient vibrations were recorded by the external accelerometers and the internal

vibrating wire gages. Figure 3-5 and Figure 3-6 come from the field testing plan of the

recent field testing conducted by the University of Virginia.

15

Figure 3-5 Instrumentation of Tides Mill Stream Bridge

Figure 3-6 Load Cases of Tests on Tides Mill Stream Bridge

16

3.2 Geometry of Model

The full model of Tides Mill Stream Bridge consisted of the eight HCB beams,

the reinforced concrete deck, the parapets, and the semi-integral backwalls. Each HCB

was composed of three components, FRP shell, SCC concrete, and tension reinforcement.

The HCBs were placed from north to south skewed at 45 degrees to the roadway (Figure

3-8), and named as G1 to G8 from north to south. The details and dimensions of the main

components are shown in Table 3-1.

Figure 3-7 Typical Section of Bridge Model

Figure 3-8 Plan View of HCBs Model

17

Table 3-1 Dimension of Main Components (Slade & Eriksson, 2012)

Component Dimension Description

Beam

21.33in Height of hybrid composite beam (HCB)

24in Width of HCB shell

34in Length of End Chimney (Must at least the Length of

Bearing Pad)

4in Average Width of Concrete Fin

2 Number of Webs

Shell

0.072in Q64 GFRP laminate thickness

6 Equivalent number of Q64 GFRP layers in the top

flange

1.53 Equivalent number of Q64 GFRP layers in the

bottom flange

1.53 Equivalent number of Q64 GFRP layers in the web

Arch

4in Thickness of arch concrete in HCB

22.5in Width of the Compression Arch Reinforcement

4in Width of "fin" that connects arch to CIP slab

Shear

Reinforcement

5 Stirrup Size for Shear Connectors

45deg Angle of inclination of shear connectors

4in Height of the stirrup above the HCB top flange

Arch

Reinforcement 2

Number of Additional Strands placed in the

compression reinforcing

Slab 7.5in Thickness of CIP slab above HCB

Span 48ft+8in Overall length of section

44ft+4in Design span of section

Bridge

4ft+1in Beam spacing

8 Number of precast sections in bridge cross section

32.5ft Overall width of bridge

30ft Curb to curb width of bridge

15in Width of Barrier

45deg Skew of Bridge

6in Overhang length from CL of Exterior beam

18

3.3 Materials Properties of the Model

The material properties of the fiber-reinforced polymer came from the

manufacturer’s description, the thesis (Ahsan, 2012), and the Engineering Report of

Tides Mill Stream Bridge (Slade & Eriksson, 2012). As shown in Table 3-2. E11 and E22

represented the moduli of elasticity of directions parallel (0°) and perpendicular (90°) to

the roadway. Instead of the value provided by the manufacturer, a limit of 7.5 ksi for

ultimate shear stress was used in this study. This limit was obtained from previous study

(Hillman, Investigation of a Hybrid-Composite Beam System, 2003).

Table 3-2 Material Properties of FRP (Slade & Eriksson, 2012)

Material Properties of Fiber-Reinforced Polymer (Web and Flange)

Laminate Weight 1.47 lb/ft²

E11 3100 ksi

E22 2300 ksi

G12 1010 ksi

υ12 0.3

υ21 0.26

Tensile Ultimate Stress (0°) 27.8 ksi

Tensile Ultimate Stress (90°) 20.6 ksi

Compressive Ultimate Stress (0°) 27.8 ksi

Compressive Ultimate Stress (90°) 20.6 ksi

τallow 7.5 ksi

The material properties of arch, deck, strand, and shear connector are shown in

Table 3-3. The material properties of arch concrete and deck concrete came from the

concrete cylinder testing. The material properties of strands came from the prestressing

19

strand calibration. The material properties of shear connectors are shown as rebar in

Table 3-3.

Table 3-3 Material Properties of Other Components (Ahsan, 2012)

Component

HCB and Three-beam System Model of Bridge

Compressive

Strength

(psi)

Tensile

Strength

(psi)

Modulus

of

Elasticity

(ksi)

Compressive

Strength

(psi)

Tensile

Strength

(psi)

Modulus

of

Elasticity

(ksi)

Arch 4870 545 5250 4000 460 3640

Deck 4010 483 4670 4000 460 3640

Strand 33660 33660

Rebar 27500 27500

20

3.4 Model Construction and Analysis

The software used for building and analyzing the models was ANSYS

Workbench 18.1. The computer-aided design (CAD) software was Design Modeler

which is a built-in module of ANSYS Workbench 18.1.

After establishing the models by the built-in CAD tool Design Modeler, the

analysis was commenced in the analytical tool (Mechanical). There were three

components in Mechanical: Model, Static Structural, and Solution. The analysis settings

were included in these sections and will be introduced in each of the three phases.

Three models were developed in this study. Section 3.4.1 and section 3.4.2 focus

on a detailed model of a single HCB beam. Section 3.4.3 includes three HCB beams with

a composite concrete deck. Section 3.4.4 is the development of the full Tides Mill Stream

Bridge.

21

3.4.1 HCB Model without Arch

3.4.1.1 Geometry

The HCB model without arch included two components: the shell and the bottom

strands. This HCB beam was first tested at Virginia Tech to better understand its

behavior without the arch. The finite element of the HCB beam was fully developed to

include the shell, concrete arch, strands, and shear connectors. The full beam model

development will be discussed in sections 3.4.1 and 3.4.2. In section 3.4.1, concrete arch,

strands embedded in the arch, and shear connectors were suppressed.

Figure 3-9 Shell and Bottom Strands

To conduct this analysis, the command “Suppress” in Geometry was used to

suppress the components such as arch, strands embedded in the arch, and shear

connectors. Consequently, the software would only consider the unsuppressed

components (shell and bottom strands) into analysis. In this case, the other settings based

on the suppressed components would be suppressed as well, and this may cause

22

inaccuracy of the solution. For example, the settings in Construction Geometry,

Coordinate Systems, Connections, and Mesh would be suppressed if the based

geometries were suppressed. Therefore, the construction geometries and coordinate

systems should depend on the components that would not be suppressed through the

analysis process. When performing the analysis of the full HCB, the command

“Unsuppress” was applied on the suppressed components to involve them in the analysis.

Similarly, the suppressed settings were unsuppressed in the meantime.

3.4.1.2 Loading

A distributed load and a point load (Figure 3-10 and Figure 3-11) were applied on

the system consisted of shell and bottom strands in the experimental testing at Virginia

Tech. To simulate the two load scenarios in the model, a -2125 pounds distributed load

was applied on the top flange in Y coordinate, leaving the X and Z coordinates zeros, and

a -250 pounds concentrated load were applied on the edges of top flange at mid-span in Y

coordinate, leaving the X and Z coordinates zeros.

Figure 3-10 Distributed Load of 2125 pounds

23

Figure 3-11 Concentrated Load of 250 pounds at Mid-Span

24

3.4.2 Full HCB Model

3.4.2.1 Geometry

The individual HCB beam model (Figure 3-12) included five components:

concrete arch, bottom strands, strands embedded in the arch, shear connectors, and shell.

To accurately simulate the boundary conditions, extra geometries were added to the

model. Considering the purpose of simplification, some assumptions and changes were

made in the model.

Figure 3-12 Model of HCB

The arch (Figure 3-13) was constructed prior to the other components. The name

of element used in arch was SOLID187. SOLID187, a higher order 3D ANSYS element

including 10 nodes, has quadratic displacement behavior and is able to model irregular

meshes. Each node of the element has three degrees of freedom. SOLID187 is capable to

deal with conditions of plasticity, hyperelasticity, creep, stress stiffening, and large strain.

25

It can also be used to simulate deformations of almost incompressible elastoplastic

materials and entirely incompressible hyperelastic materials (ANSYS 18.1).

Figure 3-13 Model of Arch

The element used in bottom strands (Figure 3-14), embedded strands (Figure

3-15), and shear connectors (Figure 3-16) was BEAM188. BEAM188 is a two-node 3D

element. Each node has six or seven degrees of freedom including translations in the x, y,

and z directions, rotations about x, y, and z directions, and warping magnitude (optional).

The high degrees of freedom allow the element to have linear, quadratic, or cubic

behavior. BEAM188 is good for dealing with linear, large rotation, and/or large strain

nonlinear conditions (ANSYS 18.1).

26

Figure 3-14 Model of Bottom Strands

Figure 3-15 Model of Embedded Strands in Arch

27

Figure 3-16 Model of Shear Connectors

Figure 3-17 Model of Shell

The model of shell is shown in Figure 3-17. The lid was separately extruded to

define a different thickness.

28

In the testing conducted by Virginia Tech, to better simulate the movement of the

HCB under the loading, pin and roller supports were placed 6 inches from the edges of

the beam ends and were perpendicular to the longitudinal direction of the beam. (Figure

3-18). Due to the effect of the supports, the span length was reduced to 43ft, equal to the

span length of the Tides Mill Stream Bridge. To simulate the pin and roller supports, two

surfaces were attached to the bottom face of the shell at 6 inches from the end edges. The

length of the surfaces was equal to the width of the bottom shell, and the width of the

surfaces were equal to the width of the supports. The thickness of the surfaces was 0.01

inch and the material was the same as the shell. Therefore, the two surfaces would have

very limited influence on the stiffness of the HCB model. The reason for introducing

surfaces to the model was that the simply supported condition can only be assigned to a

surface or line of nodes in 3D simulation in Mechanical (the analytical module of

ANSYS). Adding surfaces is an efficient way to simulate the supports setup in the testing

at Virginia Tech.

The top face of the flange of the HCB beam model was divided into four equal

parts for the convenience of assigning the loads on the edges at mid-span or quarter-span.

29

Figure 3-18 Model of Added Surface

3.4.2.2 Cross Sections

Two circular cross sections (Figure 3-19) were applied to strands (Circular 2) and

shear connecters (Circular 3).

Figure 3-19 Details of Cross Sections

3.4.2.3 Construction Geometry

Construction geometry was designed to choose particular points, lines, faces, or

volume by defining paths, surfaces, or solids in the model, with the final purpose of

obtaining the analytical results at interested locations. By applying the construction

30

geometries, the user is able to screen and obtain the results of interested nodes accurately

and rapidly. The model of HCB consisted of ten paths, corresponding to the locations of

the gauges in the testing at Virginia Tech. The detailed locations are shown in Table 3-4,

Figure 3-20, and Figure 3-21.

Table 3-4 Paths of HCB Model

Path Location Start End

1 Top Flange East North South

2 Top Flange West North South

3 Top Web East North South

4 Top Web West North South

5 Bottom Web East North South

6 Bottom Web West North South

7 Bottom Flange East North South

8 Bottom Flange West North South

9 Top Arch North South

10 Bottom Flange North South

Figure 3-20 Plan View of Paths on HCB Model

31

Figure 3-21 Locations of Paths on HCB Model (Side Elevation View)

3.4.2.4 Coordinate Systems

Construction geometries depend on coordinate systems. Two Cartesian coordinate

systems (the global coordinate system and a new coordinate system) were set up in this

model.

3.4.2.5 Component Connections

The components in the model were connected by defining the contact types

between them. There were five available contact types for various problems: bonded, no

separation, frictionless, rough, and frictional. The following descriptions of these five

contacts are based on the Help Manual of ANSYS 18.1.

The bonded contact applies to all contact regions including solids, surfaces, faces,

lines, and edges. It is the default contact type. Bonded contact does not allow sliding or

separation between faces or edges. The contact region can be imagined as glued (ANSYS

18.1). The length or the area of the contact region do not change under the application of

32

the load, so bonded contact allows for a linear solution. In the calculation of

mathematical model, any gaps between contact bodies will be closed automatically, and

any initial penetration will be disregarded. In this model, most of the type of contact

regions were defined as bonded.

The no separation contact applies to faces between 3D solids or edges on 2D

plates. It does not allow separation between the geometries in contact.

The frictionless contact allows a gap to exist between geometries depending on

the applied load. When the separation occurs, the normal pressure equals to zero. Free

sliding is allowed in this type of contact, because the coefficient of friction is assumed as

zero.

The rough contact prevents sliding from happening between the contact

geometries. It only applies to faces of solids in 3D simulations or edges of plates in 2D

simulations. For this contact type, the gaps between contact geometries will not be closed

automatically.

The frictional contact allows the contact geometries keep a no sliding status

before the shear stress between the two contact geometries exceeds a certain value which

can be defined by users. Once this defined shear stress is exceeded, the contact

geometries are allowed to have relative sliding.

3.4.2.6 Contact Conditions

Six contact conditions were used in the finite element model development and

will be introduced in this section. The connection between the shell and the arch was

defined as no separation, because the connection between them was weak, according to

33

the experimental testing at Virginia Tech. This will be discussed further in Chapter Four

(section 4.2.1).

The contact type between the top flange and deck was originally defined as

bonded in section 3.4.3. This contact type was later modified to reflect better

comparisons to the experimental results and will be further discussed in Chapter Four

(section 4.2.1).

The bottom strands were connected to the shell by infusing vinyl-ester into the

mold where strands had been placed prior to the infusion. According to the experimental

testing at Virginia Tech, the strain of bottom shell at mid-span was 812 με, while the

average strain of bottom strands at mid-span was 740 με. The small difference of 72 με

shown that composite condition of bottom shell and bottom strands was strong.

Therefore, the contact condition was defined as bonded.

The main function of strands embedded in arch was anchoring the shear

connectors. They were fabricated into the concrete arch, and it assumed no relative

sliding occurred. Hence, the contact type between them was defined as bonded.

The function of the shear connectors was to insure composite action between the

HCBs and the bridge deck. The lower parts were embedded into the concrete arch, and

attached to the embedded strands. There was no sliding allowed between the shear

connectors and the concrete arch. Hence, the contact type between them was defined as

bonded.

As described in section 3.4.2.10, the bottom shell was separated from the whole

shell to allow adjustment of its material property. Ultimately, these two parts were

integrated in the beam, acting as a whole shell. Sliding and separation were not allowed

34

between them. Hence, the contact type between the shell and bottom shell in the model

was defined as bonded.

The surfaces were designed for defining the supports. The supports were applied

on the surfaces, and the surfaces were bonded to the bottom face of the shell.

3.4.2.7 Mesh

The accuracy of any finite element model requires refinement or discretization of

surface and body structures into smaller, compatible elements. A model needs to be

refined such that numerical accuracy is achieved within a reasonable processing time.

Details of “Mesh” are shown in Figure 3-24. The physics preference for this model was

determined to be “Mechanical”.

The method for arch, deck, and shell was “Tetrahedrons”; the algorithm for them

was “Patch Conforming”. The other components used the method of “Automatic”.

Figure 3-22 Mesh Result of Full HCB Beam

35

Figure 3-23 Details of “Patch Conforming Method”

Figure 3-24 Details of “Mesh”

36

3.4.2.8 Supports

A simply supported support and a displacement support were used to simulate the

pin and roller in the Virginia Tech’s test. The following descriptions of the supports were

based on the Help Manual of ANSYS 18.1.

The moving or deforming of straight and curved edges or vertices are constrained

by simply supported boundary condition. However, rotations are free. (ANSYS 18.1).

Simply supported boundary condition can only be applied on surface and line body.

When simply supported boundary condition is required on a solid body, forming a

surface or a line body to simulate the boundary condition is a reasonable methodology. In

the model of HCB, a simply supported condition was assigned on the added surface at

one end of the bottom flange.

A displacement boundary condition (commonly referred as a roller support)

allows body, including flat or curved faces or edges or vertices, to displace from their

original locations to new locations by defining the three components of a displacement

vector based on the world coordinate system or local coordinate systems (ANSYS 18.1).

It is supported by geometries for solid, surface/shell, and wire body/line body/beam. In

this model, a displacement boundary condition was assigned on the surface at the other

end of the bottom flange.

3.4.2.9 Loading

Two point loads (Figure 3-25 and Figure 3-26) were applied on the full HCB in

the experimental testing at Virginia Tech. To simulate the two load scenarios in the

model of HCB, a 15 kips load was assigned on the edges of top flange at mid-span in Y

coordinate, leaving the X and Z coordinates zeros, and a 25 kips load was applied on the

37

edges of the top flange at two quarter spans in Y coordinate (12.5 kips on each quarter

span), leaving the X and Z coordinates zeros.

When testing the model under one of the load scenarios, the other loads were

suppressed. The coordinate system used in all load settings was global coordinate system.

Figure 3-25 Concentrated Load of 15 kips at Mid-Span

Figure 3-26 Concentrated Load of 25 kips at quarter spans

3.4.2.10 Refinement of HCB Model

A consistent discrepancy occurred in the results from the behavior of the HCB

model and the test results conducted on the single HCB beam at Virginia Tech. The

tension strains in the bottom flange of the model were consistently lower than those

measured during the Virginia Tech’s testing. Consistent with this discrepancy was

accompanying differences in the compression strains in the top flange of the HCB beam.

To resolve this problem, the bottom shell was separated from the whole shell

(Figure 3-27), and its material properties were redefined. The bottom strands were

removed from the HCB model. The modulus of elasticity of the bottom shell was set to

32100 ksi which was the summation of the modulus of elasticity of the steel and the FRP

material. This modification better simulated the composite condition between the bottom

strands and the bottom flange, resulting in increased tension strain in the bottom flange.

Further details will be discussed in Chapter Four.

38

Figure 3-27 Separated Bottom Shell

39

3.4.3 Three Beam/Composite Deck Model

3.4.3.1 Geometry

Figure 3-28 Model of Three HCBs System

The three-girder bridge model (Figure 3-28) was developed in this section. The

HCB model developed in section 3.4.2 was triplicated and a concrete deck model was

added. The three HCB beams and deck were skewed at 45 degrees to further replicate the

system that was tested at Virginia Tech.

A reinforced concrete deck 7.5 in thick (Figure 3-30) was formed and placed on

the top flanges of the three HCBs. The deck was set back 7 inches along the length of the

girders to allow space for the formwork and as such, the deck in the model was set back

the same distance along the span (Figure 3-29). ANSYS SOLID187 element was used to

model the bridge deck. The reinforcement was not modeled in the deck. All loads applied

on this model were assumed to be in the linear elastic range of the constituent materials.

Hence, the assumption of linear strain compatibility between rebar and concrete was

40

assumed with no concrete cracking. Also, full composite action between the deck and the

HCB beams was assumed in this model, which means that all concrete was in

compression and further detailed finite element modeling of the reinforced concrete deck

was considered to be beyond the scope of this thesis. (Biggs, Barton, Gomez, Massarelli,

& McKeel, 2000). The focus of detailed modeling was on the HCB beam.

Figure 3-29 Deck Setback 7 Inches for Framework

41

Figure 3-30 Model of Deck on Three HCBs

In the experimental testing at Virginia Tech, a total of seventeen tests were

conducted based on eight load configurations simulating eight locations of a HL-93 truck

on the deck. The truck’s load was transferred through four representative tire footprints (9

inches by 18 inches) to the deck. Four footprints represent the load of a truck, and were

arranged at 6 feet transversely and 14 feet longitudinally. To simulate the eight load

configurations, a total of twenty-eight surfaces (Figure 3-31) were attached to the top face

of the deck. These surfaces followed the size and the locations of the tire footprints in the

eight load configurations. To make less influence to the stiffness of the model, the

thickness of the surfaces was defined as 0.01 inch and the material was the same as that

of the deck.

42

Figure 3-31 Model of Added Surfaces


Nine paths (Figure 3-33) were set up in this model. The locations of them were

shown in Table 3-5, Figure 3-32 and Figure 3-33.

Table 3-5 Paths of Three HCBs System Model


1 Bottom Flange 1 North South



4 Top Arch 1 North South



7 Bottom Arch 1 North South



43

Figure 3-32 Locations of Paths on Three HCBs System Model (Side Elevation View)

Figure 3-33 Paths of Three HCBs System Model

3.4.3.3 Connections

Shear connectors were used to insure composite action between the deck and

HCB beams. The shear connectors were tightly aligned and were anchored into both the

arch and the deck, which insured none or very limited separation or relative sliding would

occur between the deck and HCBs. Therefore, the contact type between the deck and

three shells was bonded. The contact type between the deck and shear connectors was

also bonded.

44

3.4.3.4 Supports

In Virginia Tech’s testing, pin supports and roller supports were used, similar to

the testing of the single HCB beam tests. Therefore, simply supported supports and

displacement supports were set up on each of the three HCB models, the configuration

followed that used in section 3.4.2.

In Virginia Tech’s testing, diaphragms were placed at the ends of beams to

prevent the beams from lateral translations and rotations about the global X-axis. In this

model, the function of the diaphragms was achieved by restraining the beams from

moving in the global Z axis and rotating about the global X axis.

45

3.4.3.5 Loads

There were seventeen tests based on eight load cases in Virginia Tech’s testing.

The first six load cases simulated a load of 85.12 kips (85 kips in testing), which is the

combined two rear axle loads (32 kips/axle) of a HL-93 truck (64 kips) multiplied by the

Dynamic Load Factor of 1.33. The last two load cases simulated the condition that only

two wheels from the same side were on the deck, and the load was reduced to 43 kips.

Each red rectangle in Figure 3-34 represented a footprint of the truck. The loads were

evenly distributed on all the footprints. The configurations of load cases were shown in

Figure 3-35.

Figure 3-34 Eight Load Cases of Three HCBs System Model

46

Figure 3-35 Load Case Configurations of Three HCBs System

The dimensions in Figure 3-35 are in inches.

47

3.4.4 Model of Tides Mill Stream Bridge

3.4.4.1 Geometry

The content of section 3.4.4 was establishing the bridge model of the Tides Mill

Stream Bridge (Figure 3-36). The HCB beam developed in section 3.4.2 was replicated 7

times and all eight HCBs were placed at a forty-five-degree skew. A deck (Figure 3-37)

of 7.5 inches thickness, 51ft-9.5in in length, and 32ft-6in in width was placed on the top

flanges of the HCBs. The parapet used in Tides Mill Stream Bridge was VDOT Kansas

corral, BCR-2 type and placed on the top of the reinforced concrete deck (Figure 3-31).

Figure 3-36 Model of Tides Mill Stream Bridge

A semi-integral abutment design was used in this bridge. A semi-integral

abutment is one in which the bridge superstructure (both deck and beams) is directly

connected to the backwall portion of the substructure. The superstructure is not

continuous with the abutments. Conventional bearings, connecting the integral backwall

to the supporting abutment, are used to allow for the horizontal movements between

48

superstructure and abutment. The advantage of semi-integral bridges is the removal of

expansion joints at the ends of the bridge, thus alleviating a maintenance issue. The

flexural rigidity of the imbedded beams is influenced by the torsional stiffness of the

backwall structure. In order to simulate this behavior, the eight HCBs were embedded

into the backwalls at both ends of the bridge. The model of backwalls is shown in Figure

3-39 and Figure 3-40.

SOLID187 elements were used in the deck, the parapets, and the backwalls.

Figure 3-37 Model of Bridge Deck

49

Figure 3-38 Model of Bridge Parapets

Figure 3-39 Model of Bridge Backwalls

50

Figure 3-40 Illustration of HCB Beam (G5) Embedded into Backwalls

To accurately apply the loads to the deck, a series of surfaces (Figure 3-41) were

introduced on the top face of the bridge deck. Again, the thickness of the surface was

defined as 0.01 in, and the material was identical to the deck. In the field testing

conducted by the University of Virginia, the tire footprints of the two trucks were

13inches by 10inches (130 square inches’ area) and 13inches by 11inches (143 square

inches’ area). To simulate the loads of the trucks and simplify the model at the same time,

the whole surface was divided to 1500 squares with size 12 inches by 12 inches (142

square inches’ area). There were six load configurations of the testing. The detailed

configurations were shown in Figure 3-48 and Figure 3-49. The surface can be cut into

even smaller squares to achieve additional accuracy.

51

Figure 3-41 Model of Added Surfaces on Bridge

There were open deflection joints of 1ft-9in deep (Figure 3-43) on the parapets of

Tides Mill Stream Bridge at the center line of posts. The joints were modified in the

bridge model to be continuous to better reflect the behavior observed in the load tests and

will be discussed further in Chapter Four (section 4.4.2).

52

Figure 3-42 Parapet with Open Deflection Joints

Figure 3-43 Open Deflection Joint

53


Thirty paths were set up in the model of Tides Mill Stream Bridge. The paths

went through the length of the HCBs, and were parallel to the roadway direction. The

details are shown in Table 3-6, Figure 3-44, and Figure 3-45.

Table 3-6 Paths of Bridge Model










9 Top Flange 1 North South








17 Mid Deck 1 North South








25 Lower Arch 5 North South



28 Upper Web 5 North South



54

Figure 3-44 Paths of Bridge Model

Figure 3-45 Locations of Paths on Bridge Model (West Side Elevation View)

3.4.4.3 Connections

The contact conditions of HCB remained the same as in previous discussions.

Five new contact conditions established in the bridge model were all defined as bonded.

They were connections of parapets to deck, deck to HCBs, deck to shear connectors, deck

to backwalls, and backwalls to HCBs.

55

3.4.4.4 Supports

In this model, a simple support was assigned on the inward longitudinal edge of

the bottom surface on the western backwall (Figure 3-46), and a displacement support

was assigned on the inward longitudinal edge of the bottom face on the eastern backwall

(Figure 3-47). The eastern backwall was defined as free in the X direction (the

longitudinal direction of the span). All supports were fixed in the Y and Z directions.

Figure 3-46 Simply Supported Support at Western Backwall (Bottom View)

Figure 3-47 Displacement Support at Eastern Backwall (Bottom View)

56

3.4.4.5 Loading

Six load cases (Figure 3-48) were applied in the field testing by the University of

Virginia. A load of 46 kips were applied evenly on the six footprints to represent the

truck’s load in the field testing. One truck was used in load case A, B, C and D, and two

trucks were used in load case E and F. The loads were placed at mid-span in all load

cases.

Figure 3-48 Six Load Cases of Bridge Model

57

Figure 3-49 Load Case Configurations of Tides Mill Stream Bridge

58

3.4.4.6 Refinement of Semi-Integral Backwalls

The semi-integral backwalls significantly influenced the performance the bridge

model, especially the performance of the girders at the two sides (girder G1 and G8). The

configuration of the semi-integral backwalls was introduced in section 3.4.4.1. This will

be discussed further in Chapter Four (section 4.4.3).

59

4 Results and Discussion

The results from the three models of this study were compared with the results

from the thesis of Virginia Tech’s student Ahsan (2012) and the results from the field

testing by the University of Virginia. All results were collected from the modified model

as discussed in section 3.4.2.10 and section 4.2.2 (material of bottom shell was redefined

and bottom strands were removed).

The results from models of this study were labeled as “Model” in tables and

figures. Similarly, the results from the experimental testing at Virginia Tech and the

University of Virginia were labeled as “VT” and “UVA” in tables and figures.

4.1 HCB Model without Arch

In the testing at Virginia Tech, eight tests were conducted on three HCBs. For

HCB 2 and HCB 3, two distributed load tests and a concentrated load test were

conducted. For HCB 1, one distributed load test and one concentrated load test were

conducted.

The comparison of mid-span deflections for HCB model without the concrete

arch is shown in Table 4-1 and Figure 4-1. The deflections of the model under distributed

loads were generally smaller than those of the Virginia Tech tests. The deflections of the

model under concentrated loads were closer to the test results.

60

Table 4-1 Mid-Span Deflection for HCB without Arch

Test

Number HCB Loading (lb)

Deflection of

Model (in)

Deflection of VT's

tests (in) Ratio

1 3 Distributed 2125 0.25 0.33 0.76

2 3 Distributed 2125 0.25 0.33 0.76

3 3 Concentrated 250 0.052 0.06 0.87

4 2 Distributed 2125 0.25 0.29 0.86

5 2 Distributed 2125 0.25 0.29 0.86

6 2 Concentrated 250 0.052 0.05 1.04

7 1 Distributed 2125 0.25 0.33 0.76

8 1 Concentrated 250 0.052 0.05 1.04

Figure 4-1 Mid-Span Deflection for HCB without Arch

61

The comparison of mid-span strains for test 7 are shown in Table 4-2 and Figure

4-2. Test 7 was performed on HCB 1 under a uniformly distributed load of 2125 lb/ft.

Table 4-2 Mid-Span Strains for Tests 7 (HCB without Arch)

Location Strain (µƐ)

Ratio Model VT's Test

Top Flange E. -76.27 -136.00 0.56

Top Flange W. -76.50 -89.00 0.86

Top of Web E. -25.65 -40.00 0.64

Top of Web W. -23.68 -81.00 0.29

Bottom Web E. 19.92 0.00 0.00

Bottom Web W. 24.22 -5.00 -4.84

Bottom Flange E. 65.75 81.00 0.81

Bottom Flange W. 65.14 71.00 0.92

Figure 4-2 Mid-Span Strains for Tests 7 (HCB without Arch)

62

The comparison of quarter point strains for test 7 are shown in Table 4-3 and

Figure 4-3. The top flange and top web compressed not as much as those parts in the real

shell.

Table 4-3 Quarter Strains for Tests 7 (HCB without Arch)

Location Strain (µƐ)

Ratio Model VT's Test

Top Flange E. -56.93 -146 0.39

Top Flange W. -55.81 -116 0.48

Top of Web E. -17.514 -77 0.23

Top of Web W. -18.636 -91 0.20

Bottom Web E. 15.972 23 0.69

Bottom Web W. 14.673 11 1.33

Bottom Flange E. 48.67 -26 -1.87

Bottom Flange W. 48.757 36 1.35

Figure 4-3 Quarter Strains for Tests 7 (HCB without Arch)

There were discrepancies of the magnitudes of strains between the results from

the model and the Virginia Tech’s testing. The strain profiles were basically correct, and

the location of the natural axes were close. The focus was on the behavior of the full

HCB model and the three beam/composite deck model.

63

4.2 Full HCB Model

4.2.1 Discussion about Contact Conditions

As mentioned in section 3.4.2.6, the contact type between the shell and the arch

was defined as no separation because the connection between them was weak. According

to the results from Virginia Tech’s test, the strain at the top shell at mid-span was -530

με, while the strain of the top arch at mid-span was only -164 με. The significant

difference between these two contact regions indicated the composite condition between

them was weak. Thus, the appropriate contact type should be a condition between no-

separation and bonded. Similarly, the contact type between the top flange and deck was

defined as bonded, even the real contact condition between them should be a contact type

between no-separation and bonded. By defining the contact type between the top shell

and the arch as no-separation and defining the contact type between the top shell and the

deck as bonded, the model of the bridge was better able to simulate the performance of

the bridge. Hence, these contact types were kept in use.

4.2.2 Refinement of HCB Model

As mentioned in section 3.4.2.10, the material properties of the bottom shell were

redefined. Figure 4-4 shows the mid-span strain at top and bottom flanges in the test

conducted on the HCB model without arch. As can be seen, the strains of HCB model

without arch were closer to the experimental results when the modulus of elasticity was

defined as 32100ksi.

64

Figure 4-4 Change of Modulus of Elasticity in Bottom Flange

As can be seen in Figure 4-5, the strains through HCB depth in the test conducted

on the full HCB model were improved by this refinement. The performance of the refined

HCB model increased 33% on average compared with the initial model (Table 4-5).

Figure 4-5 Comparison of Strains through HCB Depth

65

Table 4-4 Strains of Model, Refined Model, and VT’s Tests

Location

Strain (µƐ)

Model Refined Model VT's Tests

Top Flange E. -211.01 -407.76 -518.00

Top Flange W. -207.26 -416.56 -541.00

Top of Web E. 42.07 78.45 82.00

Top of Web W. 39.28 112.62 155.00

Bottom Web E. 291.83 462.69 406.00

Bottom Web W. 279.69 541.02 466.00

Bottom Flange E. 546.27 852.90 793.00

Bottom Flange W. 544.83 840.53 830.00

Table 4-5 Promotion of HCB Model after Refinement

Location

Comparison of Strain

Model/VT's Tests Refined

Model/VT's Tests

Increased Accuracy

(Average: 33%)

Top Flange E. 41% 79% 38%

Top Flange W. 38% 77% 39%

Top of Web E. 51% 96% 44%

Top of Web W. 25% 73% 47%

Bottom Web E. 72% 114% 14%

Bottom Web W. 60% 116% 24%

Bottom Flange E. 69% 108% 24%

Bottom Flange W. 66% 101% 33%

66

4.2.3 Results of Full HCB Model

The comparison of mid-span deflection for point load tests are shown in Table 4-6

and Error! Reference source not found.. The deflections of the model were generally l

arger than those from test results.

Table 4-6 Mid-Span Deflection for Point Load Tests

Test


Model

(in)

Virginia Tech's

Test (in)

Ratio

Avg.(1.40)

- 1 Midspan Point Load 15000

2.23

1.56 1.43

1 1 Midspan Point Load 15000 1.54 1.45






Average for All Beams 1.59 1.40

Figure 4-6 Mid-Span Deflection for Point Load Tests

67

The comparison of mid-span deflection for quarter point load tests are shown in

Table 4-7 and Error! Reference source not found.. The deflections of the model were

generally larger than those from the test results.

Table 4-7 Mid-Span Deflection for Quarter Point Load Tests

Test


Model

(in)

Virginia Tech's

Test (in)

Ratio

Avg.(1.40)

- 1 Quarter Point Load 12500

2.49

1.77 1.41

3 1 Quarter Point Load 12500 1.71 1.46




- 3 Quarter Point Load 12500 1.82 1.37



Average for All Beams 1.77 1.41

Figure 4-7 Mid-Span Deflection for Quarter Point Load Tests

68

The comparison of mid-span strain for point load tests are shown in Table 4-8 and

Figure 4-8. Strains along the depth of the beam model were close to those from Virginia

Tech’s tests.

Table 4-8 Mid-Span Strain for Point Load Tests

Location Strain (µƐ) Ratio

Avg.(0.95) Model VT's Tests

Top Flange E. -407.76 -518.00 0.79

Top Flange W. -416.56 -541.00 0.77

Top of Web E. 78.45 82.00 0.96

Top of Web W. 112.62 155.00 0.73

Bottom Web E. 462.69 406.00 1.14

Bottom Web W. 541.02 466.00 1.16

Bottom Flange E. 852.90 793.00 1.08

Bottom Flange W. 840.53 830.00 1.01

Figure 4-8 Mid-Span Strain for Point Load Tests

69

The comparison of quarter point strains for quarter point load test are shown in

Table 4-9 and Figure 4-9. Strains along the depth of the beam model were close to those

from Virginia Tech’s tests.

Table 4-9 Quarter Point Strains for Quarter Point Load Tests

Location Strain (µƐ) Ratio


Top Flange E. -734.32 -686.00 1.07

Top Flange W. -706.91 -830.00 0.85

Top of Web E. -77.79 -130.00 0.60

Top of Web W. -141.73 -80.00 1.77

Bottom Web E. 343.29 309.00 1.11

Bottom Web W. 286.45 307.00 0.93

Bottom Flange E. 726.52 659.00 1.10

Bottom Flange W. 723.34 694.00 1.04

Figure 4-9 Quarter Point Strain for Quarter Point Load Tests

The deflections of model consistently had an average 40% discrepancy, indicating

that the model was less stiff than the actual HCB beam. This is likely from the estimates

from the modification of the HCB beam. The deflections could have been adjusted to be

closer to the test results, but the strain profiles were much closer to the test results (on

average 5%-6% discrepancies).

70

The comparison of mid-span strains in top-arch for point load tests are shown in

Table 4-10 and Error! Reference source not found..

Table 4-10 Mid-Span Strains in Top-Arch for Point Load Tests

Test HCB Loading (lb) Strain (µƐ) Ratio


1 1 Midspan Point Load 15000

-206.00

-168.00 1.23

2 1 Midspan Point Load 15000 -129.00 1.60





Average for All Beams -164.00 1.26

Figure 4-10 Mid-Span Strain in Top-Arch for Point Load Tests

71

The comparison of mid-span strain in top-arch for quarter point load tests are

shown in Table 4-11 and Error! Reference source not found..

Table 4-11 Mid-Span Strain in Top-Arch for Quarter Point Load Tests

Test HCB Loading (lb) Strain (µƐ) Ratio


3 1 Quarter Point Load 12500

-186.28

-136.00 1.37

4 1 Quarter Point Load 12500 -136.00 1.37

7 2 Quarter Point Load 12500 N/A N/A




Average for All Beams -146.00 1.28

Figure 4-11 Mid-Span Strain in Top-Arch for Quarter Point Load Tests

There were discrepancies between the results of the six tests conducted on three

HCB beams at Virginia Tech. The model’s results for beam 2 were close to the test

results (on average 8%-11% discrepancies).

In summary, the full HCB beam model behaved with reasonable accuracy when

compared to test results. Thus the HCB beam model was considered to be complete. The

beam model was then used to produce the 3-beam/full composite deck model for

comparison to the next series of tests conducted at Virginia Tech.

72

4.3 Three Beam/Composite Deck Model

Seventeen tests were performed in Virginia Tech’s testing based on eight load

cases. The comparison of maximum FRP strain in bottom flange is shown in Table 4-12.

The comparison of deflections is shown in Table 4-13. The comparison of maximum

strain in the concrete arch is shown in Table 4-14.

Table 4-12 Maximum FRP Strain in Bottom Flange

ST1 623.00 1.19

ST2 620.00 1.20

Model ST1&ST2 741.03 -

ST3 580.00 1.34

ST4 576.00 1.35


ST5 559.00 1.30

ST6 555.00 1.31


ST7 388.00 1.26

ST8 386.00 1.27


ST9 401.00 1.29

ST10 401.00 1.29

Model ST9&ST10 517.03 -

ST11 421.00 1.50

ST12 545.00 1.16

Model ST11&ST12 630.12 -

ST13 162.00 1.34

ST14 160.00 1.36

Model ST13&ST14 217.00 -

ST15 276.00 1.42

ST16 275.00 1.42

Model ST15&ST16 391.01 -

Test NumberStrain

(µƐ)

Ratio (Avg. 1.31)

(Model/VT)

Beam Experiencing

Max Strain in VT's

1

1

1

1

2

2

2

1

2

2

2

1

1

1

Data Source

VT's Tests

VT's Tests

VT's Tests

VT's Tests

VT's Tests

VT's Tests

VT's Tests

VT's Tests

1

2

2

2

2

2

2

1

1

1

73

Figure 4-12 Maximum FRP Strain in Bottom Flange

74

Table 4-13 Deflections of Three HCBs at Bottom Flange

N. Qtr. Mid S. Qtr. N. Qtr. Mid S. Qtr. N. Qtr. Mid S. Qtr.

ST1 SL 85 0.42 0.79 0.61 0.48 0.71 0.47 0.51 0.67 0.44 1.03

ST2 SL 85 0.41 0.77 0.58 0.47 0.69 0.44 0.50 0.65 0.43 1.06

Model ST1&ST2 SL 85 0.41 0.82 0.61 0.47 0.79 0.49 0.55 0.76 0.40 -

ST3 SL 85 0.36 0.69 0.51 0.44 0.67 0.43 0.53 0.70 0.46 1.08

ST4 SL 85 0.35 0.66 0.47 0.45 0.63 0.48 0.48 0.65 0.40 1.13

Model ST3&ST4 SL 85 0.36 0.75 0.58 0.44 0.78 0.50 0.57 0.80 0.44 -

ST5 SL 85 0.32 0.60 0.43 0.42 0.63 0.36 0.52 0.70 0.43 1.22

ST6 SL 85 0.33 0.61 0.44 0.42 0.63 0.36 0.52 0.70 0.43 1.21

Model ST5&ST6 SL 85 0.36 0.73 0.56 0.46 0.80 0.51 0.62 0.87 0.47 -

ST7 SL 85 0.22 0.45 0.26 0.26 0.44 0.25 0.32 0.45 0.30 1.04

ST8 SL 85 0.21 0.42 0.33 0.24 0.41 0.23 0.30 0.43 0.29 1.06

Model ST7&ST8 SL 85 0.18 0.40 0.39 0.22 0.45 0.33 0.29 0.49 0.30 -

ST9 SL 85 0.23 0.45 0.36 0.29 0.48 0.29 0.35 0.54 0.38 0.95

ST10 SL 85 0.20 0.40 0.33 0.25 0.44 0.26 0.33 0.50 0.35 1.05

Model ST9&ST10 SL 85 0.17 0.40 0.38 0.23 0.47 0.36 0.32 0.55 0.34 -

ST11 SL 85 0.18 0.35 0.30 0.24 0.42 0.28 0.34 0.54 0.38 1.14

ST12 SL 85 0.17 0.33 0.27 0.22 0.39 0.24 0.31 0.50 0.35 1.25

Model ST11&ST12 SL 85 0.17 0.40 0.38 0.24 0.51 0.40 0.36 0.63 0.41 -

ST13 WL 43 0.17 0.17 0.13 0.11 0.19 0.08 0.16 0.21 0.15 1.03

ST14 WL 43 0.06 0.14 0.10 0.08 0.16 0.04 0.13 0.18 0.12 1.53

Model ST13&ST14 WL 43 0.07 0.16 0.16 0.09 0.20 0.16 0.13 0.23 0.15 -

ST15 WL 43 0.19 0.29 0.21 0.19 0.28 0.13 0.23 0.31 0.17 1.33

ST16 WL 43 0.15 0.29 0.19 0.19 0.28 0.18 0.23 0.29 0.17 1.32

Model ST15&ST16 WL 43 0.18 0.37 0.29 0.22 0.39 0.26 0.28 0.40 0.22 -

VT's Tests

VT's Tests

VT's Tests

VT's Tests

VT's Tests

VT's Tests

VT's Tests

Test NumberLoad

Pattern

Load

Magnitud

e (kips)

Deflection (in)

HCB 1 HCB 2 HCB 3 Ratio (Avg 1.15)

(Model/VT)

VT's Tests

Data Source

75

Figure 4-13 Deflections of Three HCBs at Bottom Flange

76

Table 4-14 Maximum Arch Strains of Three HCBs

The bold values were greater than cracking strain of 152 µƐ. These values were not consistent with the other values.

HCB 1 HCB 2 HCB 3 HCB 1 HCB 2 HCB 3 HCB 1 HCB 2 HCB 3

ST1 129.00 114.00 107.00 0.98 1578.00 N/A 403.00 - -64.00 -28.00 -14.00 -1.71

ST2 129.00 113.00 106.00 0.99 N/A N/A 402.00 - -64.00 -28.00 -13.00 -1.84

Model ST1&ST2 132.06 108.44 103.08 - 14.51 -4.43 -9.30 - -65.41 25.31 73.37 -

ST3 114.00 110.00 109.00 0.99 N/A N/A 469.00 - -44.00 -23.00 -15.00 -1.30

ST4 112.00 107.00 106.00 1.01 N/A N/A 429.00 - -46.00 -30.00 -16.00 -1.15

Model ST3&ST4 113.31 113.33 102.91 - 16.03 1.45 -6.98 - -49.32 21.15 61.31 -

ST5 103.00 108.00 110.00 0.99 N/A N/A 446.00 - 0.00 -27.00 -21.00 -1.63

ST6 101.00 106.00 108.00 1.01 N/A N/A 411.00 - -29.00 -26.00 -20.00 -0.66

Model ST5&ST6 106.89 104.94 106.83 - 15.40 0.50 -10.90 - -41.75 18.01 54.42 -

ST7 57.00 97.00 100.00 0.64 830.00 N/A 440.00 - -20.00 -14.00 -13.00 -1.28

ST8 56.00 97.00 101.00 0.64 828.00 N/A 437.00 - -20.00 -13.00 -13.00 -1.31

Model ST7&ST8 30.04 53.96 82.64 - 27.18 9.25 1.60 - -9.27 18.34 38.80 -

ST9 57.00 98.00 119.00 0.60 830.00 N/A 589.00 - -12.00 -5.00 -19.00 -1.53

ST10 56.00 97.00 119.00 0.61 N/A N/A 594.00 - -12.00 -5.00 -18.00 -1.56

Model ST9&ST10 29.83 53.49 88.69 - 26.50 12.17 3.18 - -4.80 16.59 31.91 -

ST11 45.00 72.00 110.00 0.77 902.00 N/A 537.00 - -12.00 5.00 -18.00 0.54

ST12 44.00 71.00 110.00 0.78 819.00 N/A 523.00 - -11.00 4.00 -18.00 0.79

Model ST11&ST12 30.15 53.95 97.46 - 26.29 15.26 4.89 - 1.19 15.18 23.88 -

ST13 25.00 35.00 50.00 0.55 340.00 129.00 155.00 - -6.00 6.00 -5.00 -0.18

ST14 24.00 35.00 48.00 0.57 333.00 128.00 152.00 - -6.00 5.00 -4.00 -0.30

Model ST13&ST14 10.86 18.80 33.88 - 11.36 7.19 2.76 - -2.60 11.14 14.19 -

ST15 57.00 52.00 56.00 1.00 439.00 157.00 126.00 - -16.00 -17.00 -7.00 -1.17

ST16 57.00 51.00 54.00 1.02 446.00 162.00 133.00 - -17.00 -17.00 -6.00 -1.45

Model ST15&ST16 52.26 59.13 52.94 - 7.91 2.90 -2.79 - -23.90 9.12 31.32 -

Test NumberMidspan Strains (µƐ) Ratio (avg 0.82)

(Model/VT)

Quarter Point Strains (µƐ)-

Support Strains (µƐ)Data Source

VT's Tests

VT's Tests

VT's Tests

VT's Tests

VT's Tests

VT's Tests

VT's Tests

VT's Tests

Ratio (avg -0.98)

(Model/VT)

77

Figure 4-14 Maximum Arch Strains of Three HCBs (inconsistent values not shown)

The model’s maximum FRP strains at bottom flanges were 31% on average higher than

the results from Virginia Tech’s tests. The deflections of the model at bottom flange were 15%

on average higher than the results from Virginia Tech’s tests. The maximum arch strains at mid-

span were 18% on average lower than the experimental results. The maximum arch strains at

supports shown much discrepancies, which might because of the idealized boundary condition

78

used in this model could not well simulate the boundary condition of the real structure, and the

diaphragms of the real structure were not involved in this model.

As shown above, the three-beam/composite deck model basically agreed with the testing

results from Virginia Tech’s tests. However, it may not be a good representation of the Tides

Mill Stream Bridge because of the following reasons. First, the Tides Mill Stream Bridge has

eight girders, thus the load distribution characteristics are significantly different than the three

girder system. Second, the parapets and semi-integral backwalls have significant influence on the

overall bridge stiffness, however these components were not developed in the three-

beam/composite deck model.

79

4.4 Model of Tides Mill Stream Bridge

Twelve tests were performed on the finite element model of the full bridge, based on six

load cases conducted by the University of Virginia on the completed Tides Mill Stream Bridge.

A modal analysis was also conducted on the full model and natural frequencies were compared

to those experimentally obtained from the field tests.

4.4.1 Simplifications

Two details were not modelled for simplification. First, the cross-slopes of 0.02 F/F from

the center line of the bridge to the parapets were neglected in the model construction. Second, the

small elevation difference between the northwestern and the southeastern corners of the deck

were neglected. It was felt that both details would have little or no influence on the behavior of

the model.

4.4.2 Modification on Open Deflection Joints

As mentioned in section 3.4.4.1, the open deflection joints were reflected on the initial

model of the parapets. However, these open deflection joints dramatically reduced the bending

stiffness of the parapets, thus reducing their influence on overall bridge stiffness. Hence, these

joints were removed from the final bridge model.

4.4.3 Refinement on Semi-Integral Backwalls

The performance of the bridge model increased 50% on average by refining the semi-

integral backwalls (Table 4-15).

Table 4-15 Promotion of Bridge Model after Refinement

Load Case

A B C D E F Average

72% 46% 49% 63% 41% 28% 50%

80

Figure 4-15 Comparison of Performance of Bridge Model before and after Placement of Semi-

Integral Backwalls

81

4.4.4 Accuracy of Bridge Model

Compared with the test results from the University of Virginia, the model’s average strain

deviation at mid-span was 9.84 µƐ, which indicated that it could be a reasonably accurate model.

Table 4-16 Average Deviation of Strain at Mid-Span

Average Deviation of Strain at Mid-Span (µƐ)

Load Case A B C D E F Average

Difference 10.50 7.84 7.01 8.06 11.77 13.88 9.84

4.4.5 Load Case A

Figure 4-16 the total deflection of the bridge model under load case A.

Figure 4-16 Plan View of Total Deflection for Load Case A

4.4.5.1 Comparison of Mid-Span Strains at Tension Level

Table 4-17 and Figure 4-17 show the comparison of mid-span strains at tension level.

Table 4-17 Mid-Span Strains at Tension Level

Gauge Test year G1 G2 G3 G4 G5 G6 G7 G8

Model - 45.91 53.27 58.49 50.73 31.18 18.63 13.70 13.08

BDI 2017 43.28 67.98 49.53 32.93 21.60 11.04 11.29 3.72

2013 34.65 69.58 47.45 29.32 16.03 10.65 10.22 4.75

VWG 2017 - - - - 5.71 - 5.37 6.51

2013 - - - - 8.40 - 7.07 8.12

82

Figure 4-17 Mid-Span Strains at Tension Level

4.4.5.2 Comparison of Mid-Span Strain Profile through Bridge Depth

The comparison of mid-span strain profiles through bridge depth are shown in Table 4-18

and Figure 4-18.

Table 4-18 Mid-Span Strains through Bridge Depth

Data Source Location Test year Strain (µɛ)

Depth (cm) G5 G7 G8

Model

Deck - 0.18 2.75 4.70 12.20

Lower arch - 12.20 0.65 0.46 32.76

Upper web - 12.38 6.65 7.98 37.84

Bot. flange - 31.18 13.70 13.08 73.40

BDI

Upper web 2017 6.04 1.62 -2.81 33.49

2013 7.41 4.85 4.39 33.49

Bot. flange 2017 21.60 11.29 3.72 72.39

2013 16.03 10.22 4.75 72.39

VWG

Deck 2017 -5.47 -1.54 0.05 10.79

2013 -9.18 -1.76 -0.74 10.79

Lower arch 2017 15.93 2.14 1.43 29.99

2013 9.68 4.00 2.85 29.99

Tension Strand 2017 5.71 5.37 6.51 71.76

2013 8.40 7.07 8.12 71.76

83

Figure 4-18 Mid-Span Strains through Bridge Depth in G5 (upper left), G7 (upper right), and G8

(bottom)

84

4.4.6 Load Case B

Figure 4-19 shows the total deflection of the bridge model under load case B.

Figure 4-19 Plan View of Total Deflection for Load Case B




Gauge Test year G1 G2 G3 G4 G5 G6 G7 G8

Model - 27.55 37.58 47.43 55.67 52.19 33.63 19.83 14.60

BDI 2017 21.26 40.03 47.97 59.10 37.54 18.36 20.72 5.86

2013 16.94 44.66 43.12 45.29 31.90 21.01 19.06 7.43

VWG 2017 - - - - 7.53 7.91 9.63

2013 - - - - 14.83 13.61 14.72

85



The comparison of mid-span strain profiles through bridge depth is shown in Table 4-20

and Figure 4-21.



Depth (cm) G5 G7 G8

Model

Deck - 0.39 2.42 4.49 12.20

Lower arch - 5.63 1.32 0.58 32.76

Upper web - 23.35 8.82 8.53 37.84

Bot. flange - 52.19 19.83 14.60 73.40

BDI

Upper web 2017 12.54 5.14 6.10 33.49

2013 19.23 7.77 6.42 33.49

Bot. flange 2017 37.54 20.72 5.86 72.39

2013 31.90 19.06 7.43 72.39

VWG

Deck 2017 -4.27 -1.91 -0.03 10.79

2013 -16.34 -2.56 -0.55 10.79

Lower arch 2017 31.78 2.98 2.45 29.99

2013 24.95 8.06 5.58 29.99

Tension Strand 2017 7.53 7.91 9.63 71.76

2013 14.83 13.61 14.72 71.76

86


(bottom)

87

4.4.7 Load Case C

Figure 4-22 shows the total deflection of the bridge model under load case C

Figure 4-22 Plan View of Total Deflection for Load Case C




Data

Source Test year G1 G2 G3 G4 G5 G6 G7 G8

Model - 16.09 18.36 26.36 37.73 46.61 54.07 47.93 29.89

BDI 2017 8.24 15.61 22.09 41.15 56.34 40.68 46.94 12.43

2013 8.35 22.31 24.91 33.51 38.82 42.56 43.64 18.56

VWG 2017 - - - - 18.02 26.79 24.18

2013 - - - - 14.66 31.40 31.05

88




and Figure 4-24.



Depth (cm) G5 G7 G8

Model

Deck - -0.62 2.82 4.96 12.20

Lower arch - 2.18 4.65 1.85 32.76

Upper web - 17.62 21.77 15.81 37.84

Bot. flange - 46.61 47.93 29.89 73.40

BDI

Upper web 2017 26.72 10.75 5.45 33.49

2013 20.71 19.94 14.07 33.49

Bot. flange 2017 56.34 46.94 12.43 72.39

2013 38.82 43.64 18.56 72.39

VWG

Deck 2017 -9.13 -3.40 0.64 10.79

2013 -10.92 -6.12 -0.51 10.79

Lower arch 2017 101.63 6.76 5.62 29.99

2013 10.67 20.53 12.49 29.99

Tension Strand 2017 18.02 26.79 24.18 71.76

2013 14.66 31.40 31.05 71.76

89


(bottom)

90

4.4.8 Load Case D

Figure 4-25 shows the total deflection of the bridge model under load case D.

Figure 4-25 Plan View of Total Deflection for Load Case D




Data


Model - 14.45 14.11 16.72 24.22 36.71 48.88 59.83 55.68

BDI 2017 5.12 8.29 11.71 20.56 35.64 42.21 80.01 30.78

2013 5.10 12.57 13.74 19.09 25.74 41.00 65.57 46.91

VWG 2017 - - - - 7.59 49.66 56.51

2013 - - - - 10.65 49.08 66.93

91




and Figure 4-27.



Depth (cm) G5 G7 G8

Model

Deck - 0.64 2.12 7.88 12.20

Lower arch - 2.51 4.09 4.13 32.76

Upper web - 15.95 27.81 30.75 37.84

Bot. flange - 36.71 59.83 55.68 73.40

BDI

Upper web 2017 7.66 21.92 17.17 33.49

2013 10.60 31.31 28.29 33.49

Bot. flange 2017 35.64 80.01 30.78 72.39

2013 25.74 65.57 46.91 72.39

VWG

Deck 2017 -4.24 -8.84 -0.51 10.79

2013 -8.09 -6.97 -4.89 10.79

Lower arch 2017 10.42 23.07 14.91 29.99

2013 9.24 27.65 32.81 29.99

Tension Strand 2017 7.59 49.66 56.51 71.76

2013 10.65 49.08 66.93 71.76

92


(bottom)

93

4.4.9 Load Case E

The total deflection of the bridge model under load case E is shown in Figure 4-28.

Figure 4-28 Plan View of Total Deflection for Load Case E



Data


Model - 62.70 73.26 87.81 90.88 79.76 72.85 57.20 39.21

BDI 2017 59.76 96.87 87.11 96.64 83.33 45.94 51.32 14.39

VWG 2017 - - - - 28.32 28.29 26.73


94



Data Source Location Test year Strain (µƐ)

Depth (cm) G5 G7 G8

Model

Deck - -0.34 5.63 9.43 12.20

Lower arch - 5.27 4.88 1.96 32.76

Upper web - 30.97 26.15 21.87 37.84

Bot. flange - 79.76 57.20 39.21 73.40

BDI Upper web

2017 37.02 11.55 12.35 33.49

Bot. flange 83.33 51.32 14.39 72.39

VWG

Deck

2017

-19.43 -4.09 -0.40 10.79

Lower arch 127.97 6.99 5.83 29.99

Tension Strand 28.32 28.29 26.73 71.76


(bottom)

95

4.4.10 Load Case F

The total deflection of the bridge model under load case F is shown in Figure 4-31.

Figure 4-31 Plan View of Total Deflection for Load Case F



Data


Model - 42.22 52.28 65.63 82.60 91.41 84.35 79.07 64.47

BDI 2017 33.96 60.87 73.64 99.82 96.89 68.08 87.25 25.49

VWG 2017 - - - - 32.61 - 51.43 48.58


96



Data Source Location Test year Strain (µƐ)

Depth (cm) G5 G7 G8

Model

Deck - 0.66 4.67 11.49 12.20

Lower arch - 7.94 6.14 4.32 32.76

Upper web - 39.06 37.46 35.63 37.84

Bot. flange - 91.41 79.07 64.47 73.40

BDI Upper web

2017 38.74 21.61 15.97 33.49

Bot. flange 96.89 87.25 25.49 72.39

VWG

Deck

2017

-21.50 -6.54 0.10 10.79

Lower arch 132.58 12.85 9.77 29.99

Tension Strand 32.61 51.43 48.58 71.76


(bottom)

97

4.4.11 Comparison of Frequencies of First Modes

The natural frequencies of first five modes from the model and field testing of Tides Mill

Stream Bridge are shown in Table 4-29. The modal shapes of the first five modes can be seen in

Figure 4-34.

Table 4-29 Natural Frequencies of First Five Modes

Mode Frequencies (Hz) from Model Frequencies (Hz) from

Calculation

Mode 1 8.3036 8.929

Mode 2 10.716 10.896

Mode 3 14.198 14.232

Mode 4 19.866 19.798

Mode 5 20.833 32.102

Figure 4-34 First Five Mode Shapes

98

5 Conclusions and Recommendations

5.1 Conclusions

The full HCB beam model behaved with reasonable accuracy when compared to Virginia

Tech’s test results. The strain profiles were close to the test results (on average 5%-6%

discrepancies). However, the deflections of the model consistently averaged 40% higher,

indicating that the model was less stiff than the actual HCB beam. Because strain data, and not

deflection data, were available from the Tides Mill bridge field testing, it was determined to

proceed with the HCB model without further refinement for the development of the full Tides

Mill bridge model.

The model of Tides Mill Stream Bridge is a reasonably accurate model compared with

the test results from the University of Virginia. The model’s average strain deviation at mid-span

was 9.84 µƐ. A means of determining accuracy of finite element models of complex systems is

to compare natural frequencies of the model, obtained from a modal analysis, to those

frequencies determine experimentally. The natural frequencies of a physical system are a

function of the square root of the system’s global stiffness to its mass. Mass is fairly simple to

obtain. All one needs to know are system geometries and constituent material densities. The

difficult is in determining a system’s global stiffness. The natural frequencies of the Tides Mill

finite element model compare very favorably to those obtained from experimentation. Thus

indicating, at least to some degree quantitatively, the closeness of the global model stiffness to

that of the actual bridge structure. The close natural frequencies of the first four modes indicated

that the bridge model could be a rational simulation of the Tides Mill Stream Bridge.

99

5.2 Recommendations

Improvements to the HCB beam model may result from better understanding of the

complex surface connection conditions between the composite material shell and the concrete

arch and the bottom flange of the shell and the steel strands. This would require significant mesh

refinement and the need to conduct non-linear analyses. Both would represent significant

requirements of computational resources. A second recommendation is to focus a study on

simplifying the HCB model by developing a detailed “transformed section” methodology. The

simplified HCB model could then be used to create another model of the Tides Mill Stream

Bridge. From this transformed section model, it is recommended to conduct a series of load tests

to determine its accuracy to the field test data. This could lead to a simplified design approach

for the enhanced use of this novel beam. Additionally, the simplified model could be used by

bridge management personnel to better assess in-service condition states for maintenance

decisions. It is recommended to conduct a thermal load analysis of the Tides Mill model, to

include backfill soil characteristics, in order to better understand soil/structure interaction of the

semi-integral bridge design. Finally, a series of moving load tests should be conducted and

results compared to the dynamic load tests conducted by the University of Virginia to better

understand load distribution and dynamic load factor for this novel bridge system.

100

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),1,7( (/(0(17 02'(/,1* 2) +

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