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Stiffness Evaluation of Neoprene Bearing Pads under Long-Term Loads

Permanent Link: http://ufdc.ufl.edu/UFE0024062/00001

Material Information

Title: Stiffness Evaluation of Neoprene Bearing Pads under Long-Term Loads
Physical Description: 1 online resource (149 p.)
Language: english
Creator: Allen, Damon
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2008

Subjects

Subjects / Keywords: bearing, bridge, long, modulus, noeprene, rate, shear, strain, time
Civil and Coastal Engineering -- Dissertations, Academic -- UF
Genre: Civil Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: The objective of this research project was to evaluate the affect of shear strain rate on the shear modulus in steel reinforced neoprene bearing pads. Since neoprene is viscoelastic, it is possible that under strain rates typical in highway applications the shear modulus is less than what current product approval tests predict. The areas investigated were * Product approval strain rates vs. short-term field strain rates * Short-term field strain rates vs. long-term field strain rates * Reduction in shear modulus due to load cycles * Effects of compressive stress Forty-two tests were performed using test equipment designed to apply a shear-strain at various rates while maintaining a constant compression. Test results indicated * The shear modulus reduced on average 7% when tests were performed using the short- term field strain rates of 50% over 12 hours instead of the product approval strain rates of 50% over 30-60 seconds * There was essentially no reduction in shear modulus using long-term field loading rates of 50% over durations up to 90 days vs. short-term field strain rates. * Shear moduli for pads that had never been load cycled were approximately 12% higher than cycled pads (for 50 durometer hardness material). * The effect of compressive stress conforms to previous work; the shear modulus decreases with increased compression particularly for bearings with low shape factors. Based on the results of this study, the variation in shear strain rate, in highway applications has a negligible effect on shear modulus. However, it is recommended that upper and lower tolerance values for the shear modulus be used for calculations instead of a single value. Current product approval tests permit +15% to ? 15% of the specified shear modulus, however this range should be adjusted up by at least 5% to account for the net effects of the lack of cycling (+12%) and the reduced strain rates (-7%) that exist in the field. The recommended values are +20% and -20% of a specified shear modulus. Furthermore, with flat bearings, these values can be decreased due to dead load's effect on the shear modulus.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Damon Allen.
Thesis: Thesis (Ph.D.)--University of Florida, 2008.
Local: Adviser: Cook, Ronald A.
Local: Co-adviser: Hamilton, Homer R.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2008
System ID: UFE0024062:00001

Permanent Link: http://ufdc.ufl.edu/UFE0024062/00001

Material Information

Title: Stiffness Evaluation of Neoprene Bearing Pads under Long-Term Loads
Physical Description: 1 online resource (149 p.)
Language: english
Creator: Allen, Damon
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2008

Subjects

Subjects / Keywords: bearing, bridge, long, modulus, noeprene, rate, shear, strain, time
Civil and Coastal Engineering -- Dissertations, Academic -- UF
Genre: Civil Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: The objective of this research project was to evaluate the affect of shear strain rate on the shear modulus in steel reinforced neoprene bearing pads. Since neoprene is viscoelastic, it is possible that under strain rates typical in highway applications the shear modulus is less than what current product approval tests predict. The areas investigated were * Product approval strain rates vs. short-term field strain rates * Short-term field strain rates vs. long-term field strain rates * Reduction in shear modulus due to load cycles * Effects of compressive stress Forty-two tests were performed using test equipment designed to apply a shear-strain at various rates while maintaining a constant compression. Test results indicated * The shear modulus reduced on average 7% when tests were performed using the short- term field strain rates of 50% over 12 hours instead of the product approval strain rates of 50% over 30-60 seconds * There was essentially no reduction in shear modulus using long-term field loading rates of 50% over durations up to 90 days vs. short-term field strain rates. * Shear moduli for pads that had never been load cycled were approximately 12% higher than cycled pads (for 50 durometer hardness material). * The effect of compressive stress conforms to previous work; the shear modulus decreases with increased compression particularly for bearings with low shape factors. Based on the results of this study, the variation in shear strain rate, in highway applications has a negligible effect on shear modulus. However, it is recommended that upper and lower tolerance values for the shear modulus be used for calculations instead of a single value. Current product approval tests permit +15% to ? 15% of the specified shear modulus, however this range should be adjusted up by at least 5% to account for the net effects of the lack of cycling (+12%) and the reduced strain rates (-7%) that exist in the field. The recommended values are +20% and -20% of a specified shear modulus. Furthermore, with flat bearings, these values can be decreased due to dead load's effect on the shear modulus.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Damon Allen.
Thesis: Thesis (Ph.D.)--University of Florida, 2008.
Local: Adviser: Cook, Ronald A.
Local: Co-adviser: Hamilton, Homer R.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2008
System ID: UFE0024062:00001


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1 STIFFNESS EVALUATION OF NE OPRENE BEARING PADS UNDER LONG-TERM LOADS By DAMON ALLEN A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLOR IDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2008

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2 2008 Damon Allen

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3 To my wife: I would like to thank you for pu tting up with all of my nonsense and helping me through this difficult time. I love you honey.

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4 ACKNOWLEDGMENTS I would like to acknowledge the Florida Depa rtm ent of Transporta tion for providing the funding for this research projec t, and specifically thank Marc Ansley from FDOT. Special thanks are warranted for Dr. Ronald Cook, my a dvisor, and the members of my committee, Dr. Gary Consolazio, Dr. Kurtis Gurl ey, Dr. Trey Hamilton, and Dr. Bhavani Sankar for all of their help in completing this project. The success of th is project is also owed in large part to Chuck Broward at the University of Florida for his help with the instrumentati on. Finally, I would like to thank Dr. Cesar Fernandes, P.E. of Figg Engi neering, and Jerry Pfuntner, P.E. of the Finley Engineering Group for their assistan ce with current design practices and examples of their work.

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5 TABLE OF CONTENTS page ACKNOWLEDGMENTS ............................................................................................................... 4 LIST OF TABLES ...........................................................................................................................8 LIST OF FIGURES .........................................................................................................................9 LIST OF ABBREVIATIONS ........................................................................................................ 11 ABSTRACT ...................................................................................................................... .............12 CHAP TER 1 INTRODUCTION .................................................................................................................. 14 General Concept .....................................................................................................................14 Objectives .................................................................................................................... ...........14 2 LITERATURE REVIEW .......................................................................................................17 Codes, Specifications and Design Guidelines ........................................................................18 AASHTO Design Requirements ..................................................................................... 18 Shear Modulus Test AASHTO Designation: M 251-06 .................................................20 Shear Modulus Test ASTM D 4014 ANNEX-A ............................................................. 21 Florida Department of Transportation ............................................................................. 22 Applications in FDOT Projects ....................................................................................... 23 Reviewed Literature ................................................................................................................23 General Background on Elastomeric Bearings and Elastom ers ...................................... 24 Performance of elastomeric bearings: NCHRP report 298 ......................................24 Comparing the time and rate dependent m echanical properties of elastom ers ........ 26 Engineering with rubber ........................................................................................... 27 Neoprene elastomer bearings ten year s experience proves their im portance ........ 28 State-of-the-art elastomeri c bridge bearing design ..................................................29 Elastomeric bearing rese arch NCHRP report 109 ....................................................30 Additional design data based on full-size bridge bearing pads of neoprene ............ 32 Construction and design of prestressed concrete segm ental bridges ....................... 32 Design of elastomer bearings ................................................................................... 32 Summary of general background ............................................................................. 33 Test Methods for Elastomeric Bearings and Complications ...........................................33 Test method for determining the shear modulus of elastomeric bearings ................ 33 Elastomeric bridge bearings: recomme nded test m ethods: NCHRP report 449 ...... 34 On highly compressible helical springs and rubber rods, and their application for vibration-free m ountings ................................................................................. 34 Elastic stability of rubber compression springs ........................................................ 35

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6 An experimental study of elastome ric bridge bearings with design recomm endations .................................................................................................. 35 Slippage of neoprene bridge bearings ...................................................................... 37 Elastomeric bearings: background infor mation and field study ...............................37 Neoprene bearing pad slippage at Louisiana bridges ...............................................37 Summary of test methods and complications ........................................................... 37 General Background and Models of Viscoelastic Material ............................................. 38 Basic continuum models .......................................................................................... 38 Molecular theory ......................................................................................................38 An engineering theory of nonlinear vi scoelasticity with applications ..................... 38 Constitutive modeling of the large strain time-dependent behavior of elastom ers ............................................................................................................. 39 A three-dimensional constitutive model for the large stretch b ehavior of rubber elastic materials ....................................................................................................40 The behavior of rubberlike materials in m oderately large deformations ................. 40 Constitutive model for stretch-induced soft ening of stress-stretch behav ior of elastomeric materials ............................................................................................ 40 Nonlinear finite element analysis of elastom erstechnical paper ............................41 Summary of models of vi scoelastic m aterial ........................................................... 41 Possible Temperature Effects .......................................................................................... 41 Viscoelastic properties of polymers ......................................................................... 41 Low temperature behavior and acceptance criteria for elastomeric bridge bearings: NCHRP report 325 ................................................................................ 42 Performance of elastomeric bridge bearings at low tem peratures ...........................42 Summary of temperature .......................................................................................... 42 Summary of Literature Review ....................................................................................... 43 3 METHODOLOGY ................................................................................................................. 53 Developing the Samples ........................................................................................................ .53 Test Program ...........................................................................................................................54 Strain Rates ......................................................................................................................55 Mullins Effect ..................................................................................................................55 Multiple Compressive Stresses ........................................................................................ 56 Design of Test Apparatus .......................................................................................................57 Major Components of the Test Apparatus ..............................................................................58 Compression Mechanism ................................................................................................ 59 Long-Term Shear Loading Mechanism ........................................................................... 60 Short-Term Shear Loading Mechanism .......................................................................... 60 Instrumentation ............................................................................................................... .61 Procedure ..................................................................................................................... ...........61 Compression ................................................................................................................... .61 Shearing ...........................................................................................................................62 Temperature Factors ........................................................................................................... ....62

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7 4 TEST RESULTS ....................................................................................................................70 Sample Data ............................................................................................................................70 Determination of Shear Modulus ............................................................................................ 70 General Results .......................................................................................................................71 5 DISCUSSION OF RESULTS ................................................................................................76 Variations in Shear Modulus ..................................................................................................76 Initial Change due to Strain Rate .....................................................................................76 Changes due to Short Term Field Loading vs. Long Term Field Loading ..................... 76 Changes due to the Number of Loading Cycles ..............................................................77 Changes due to the Compressive Stress .......................................................................... 77 Temperature ................................................................................................................... ..79 Final Analysis of Strain Rate ........................................................................................... 79 Summary ....................................................................................................................... ..........81 6 CONCLUSION .................................................................................................................... ...88 APENDIX A RESEARCH DATA ................................................................................................90 APENDIX B ADDITIONAL LITERATURE REVIEW ............................................................132 Additional Literature Summary ............................................................................................ 132 Elastomeric bearings: state-of-the-art ............................................................................ 132 Effect of bearing pads on prestressed concrete bridges ................................................. 132 Restraint effect of bearings ............................................................................................133 Load-deformation characteristics of el astom eric bridge bearing pads .......................... 133 Rotational effects on elastomeric bearings .................................................................... 133 Influence of compression upon the shear properties of bonded rubber blocks ............. 134 Compression, bending, and shear of bonded rubber blocks ..........................................135 Behavior of elastomeric bridge bearings: com putational results ..................................136 The compression of bonded rubber blocks .................................................................... 136 Engineering with rubber ................................................................................................ 137 Stress analysis of rubber blocks under vertical loading and shear loading ................... 137 Hydrostatic tensile fracture of a polyurethane elastom er .............................................. 138 Steel bridge bearings ..................................................................................................... 138 Earthquake isolation ...................................................................................................... 138 Effects of axial load on elas tom eric isolation bearings .................................................138 Stability of elastomeric isolators: cr itical load tests and com putations ......................... 139 Evaluation of low-temperature test methods for elastom eric bridge bearings .............. 139 Parameters influencing performance of elastom eric bearings at low temperatures ...... 139 Elastomeric bearing design, c onstruction, and m aterials .............................................. 139 Natural rubber structural bearings ................................................................................. 140 LIST OF REFERENCES .............................................................................................................144 BIOGRAPHICAL SKETCH .......................................................................................................149

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8 LIST OF TABLES Table page 2-1 Shear modulus AASHTO table 14.7.5.2-1 ..............................................................................50 2-2 Elastomer grade AASHTO table 14.7.5.2-2 ............................................................................50 2-3 Steel reinforced elastomer FDOT b earing pad dim ensions for AASHTO beams ................... 50 2-4 Neoprene properties FDOT .....................................................................................................50 2-5 Typical bearing pad properties ............................................................................................ ....51 2-6 Relaxation examples ....................................................................................................... .........51 2-7 Extended relaxation example ............................................................................................... ....51 2-8 Elastic constants ......................................................................................................................52 3-1 Sample physical dimensions ................................................................................................ ....68 3-2 Testing matrix ............................................................................................................ ..............68 3-3 Testing matrix: duration variation ...........................................................................................68 3-4 Testing matrix: with and without Mullins effect removed ...................................................... 69 3-5 Testing matrix: 12 hour compression variation ....................................................................... 69 3-6 Cylinder combinations (based on 1.6 ksi compressive stress) ................................................ 69 4-1 Shear moduli result table .........................................................................................................75 5-1 Initial shear modulus change due to reduced strain rate .......................................................... 86 5-2 Mullins effect change ..................................................................................................... .........86 5-3 Recovery of Mullins effect with time ...................................................................................... 87 5-4 Predicted compression adjusted shear m odulus vs. measures ................................................. 87 B-1 Effect of carbon black on shear modulus of neoprene .......................................................... 143 B-2 Coefficient table ....................................................................................................................143

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9 LIST OF FIGURES Figure page 1-1 Bearing pad in bridge ............................................................................................................16 2-1 Shape factor calculation example ..........................................................................................44 2-2 Inclined shear test setup ............................................................................................... ..........44 2-3 Shear creep test setup. ...........................................................................................................44 2-4 Test setup ASTM D 4014 ANNEX-A. ..................................................................................44 2-5 Example of ASTM D 4014 shear modulus determ ination from the sixth cycle ................... 45 2-6 Examples of model elements.. ............................................................................................ ...45 2-7 Four parameter viscoelastic model and pulse load. ............................................................... 45 2-8 Piecewise strain vs. time response. ..................................................................................... ...46 2-9 Superposition of strain vs. time response. ............................................................................. 46 2-10 Sample for relaxation testing NCHRP 109 ............................................................................ 47 2-11 Typical shear stress time graph constant 50% shear strain NCHRP 109 ........................... 47 2-12 Shear modulus (Gave) vs. stress relaxation per decade of time NCHRP 109 ......................... 47 2-13 Shear buckling .......................................................................................................................48 2-14 Standard linear model ............................................................................................................48 2-15 Maxwell element .......................................................................................................... .........48 2-16 Test data from constitutive modeling of th e large stra in time-dependent behavior of elastomers .................................................................................................................... ......49 2-17 Elastomer shear moduli vari ation with tem perature. .............................................................49 3-1 Pad design for shape factor of 24 (1 inch pad or SF-24 pad) ................................................ 63 3-2 Bearing deformation.. ............................................................................................................63 3-3 Test apparatus cross section ............................................................................................ ......64 3-4 Test apparatus photo ..............................................................................................................64

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10 3-5 Compression mechanism ................................................................................................... ....65 3-6 Hydraulic system diagram .....................................................................................................66 3-7 Long-term shear loading mechanism .................................................................................... 66 3-8 Short-term shear loading mechanism ..................................................................................... 67 3-9 Compressive stress losses during SF 12, 1.5 ksi, 12 hour test ............................................... 67 4-1 Displacement time history from 90 day test (SF = 16) ......................................................... 72 4-2 Load time history from 90 day test (SF = 16) .......................................................................72 4-3 Strain history from 90 day test (SF = 16) .............................................................................. 73 4-4 Stress history from 90 day test (SF = 16) .............................................................................. 73 4-5 Stress-strain history from 90 day test (SF = 16) .................................................................... 74 4-6 ASTM method shear modulus from 90 day test (SF = 16) ................................................... 74 5-1 Mullins removed shear moduli (45 sec and 12 hr) of 1 ksi com pression tests ...................... 83 5-2 Long-term modulus change with duration ............................................................................. 83 5-3 ASTM method 12 hr shear moduli vs. compression ............................................................. 84 5-4 Shear moduli vs. compression with predicted by Yura and Muscarella ............................... 84 5-5 Shear modulus vs. temperature ........................................................................................... ...85 5-6 Strain rate data summary ................................................................................................ .......85 B-1 Expansion restraint reduction in moment. ....................................................................... 141 B-2 Pad bulging under compression. ......................................................................................... 141 B-3 Pad in original position and in sheared position with shear st rain equal to a. ................. 141 B-4 Cross section of an infinite strip of an elastom er bulging under compression. .................. 142 B-5 Relationship between compressive strai n, shape factor and appa rent shear m odulus. ....... 142

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11 LIST OF ABBREVIATIONS AASHTO American Association of State Highway and Trans portation Officials ASCE American Society of Civil Engineers FDOT Florida Department of Transportation LVDT Linear Variable Differential Transformer NCHRP National Cooperative Highway Research Program POT Potentiometer SF Shape factor (defined in Chapter 2)

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12 Abstract of Dissertation Pres ented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy STIFFNESS EVALUATION OF NE OPRENE BEARING PADS UNDER LONG-TERM LOADS By Damon Allen December 2008 Chair: Ronald A. Cook Cochair: H. R. Hamilton III Major: Civil Engineering The objective of this research project was to ev aluate the affect of shear strain rate on the shear modulus in steel reinforced neoprene bear ing pads. Since neoprene is viscoelastic, it is possible that under strain rates t ypical in highway applications the shear modulus is less than what current product approval tests pred ict. The areas investigated were: Product approval strain rates vs. short-term field strain rates Short-term field strain rates vs. long-term field strain rates Reduction in shear modulus due to load cycles Effects of compressive stress Forty-two tests were performed using test e quipment designed to apply a shear-strain at various rates while maintaining a constant compression. Test results indicated: The shear modulus reduced on average 7% when tests were performed using the shortterm field strain rates of 50% over 12 hours in stead of the product appr oval strain rates of 50% over 30-60 seconds There was essentially no reduction in shear modulus using long-term field loading rates of 50% over durations up to 90 days vs short-term field strain rates. Shear moduli for pads that had never been load cycled were approximately 12% higher than cycled pads (for 50 dur ometer hardness material). The effect of compressive stress conforms to previous work; the shear modulus decreases with increased compression particularly fo r bearings with low shape factors.

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13 Based on the results of this study, the variation in shear strain rate, in highway applications has a negligible effect on shear modulus. However, it is recomme nded that upper and lower tolerance values for the shear modulus be used fo r calculations instead of a single value. Current product approval tests permit +15% to 15% of th e specified shear modulus, however this range should be adjusted up by at least 5% to account fo r the net effects of the lack of cycling (+12%) and the reduced strain rates (-7%) that exist in the field. The recommended values are +20% and -20% of a specified shear modulus. Furthermore, with flat bearings these values can be decreased due to dead loads effect on the shear modulus.

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14 CHAPTER 1 INTRODUCTION Highway bridges are supported on bearings th at reduce the fo rces in the substructure caused by translations due to creep, shrinkage, a nd uniform temperature change of the bridge superstructure. Different types of bearings are available for this function ranging from metal rocker and roller bearings to neoprene and PTFE (Teflon) bearings. Neoprene, invented in 1930 by the DuPont Company, became a popular type of bearing material in the 1950s when steel reinforced neoprene bearings were introduced. Due in part to th e reduced need for maintenance, neoprene bearing pads are now often used in the support of bridge superstructures. Unlike idealized roller bearings which are used for simplifying structural calculations, most real bearings, including neoprene bearing pads, exert a latera l force as a reaction to lateral movement in the system (see Figure 1-1). The ma gnitude of this force directly impacts both the design of the substructure of a bridge and the design of the superstructure. General Concept Vulcanized elas tomeric material, specifically neoprene, has a tendency to creep over time under a sustained load. For displa cements that are applied at a re latively slow rate, it is thought that the resulting reactions would be lower than if they had been applied faster. This is particularly the case with neoprene since it is m odeled as elastic material that has properties based on material tests conducted at a rapid displ acement rate. The implications of this means that the forces induced in bri dge structures due to translat ions from creep, shrinkage, and uniform temperature change are not really as high as they are cu rrently predicted. Objectives Currently, the shear m odulus of neoprene is meas ured with a short-term test and the strain rate of this testing is closer to the strain rate due to a braking car than the strain rate due to daily

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15 temperature change in most bridges. Results ba sed on this short-term testing are supposed to be used by designers to calculate the stiffness for a ll loads, short and long te rm alike. Since most shear loads that bridge substructures experience due to these bearings are applied more slowly than the current test rate (whi ch ranges from 50% stain in 30 to 60 seconds) a relationship between shear stiffness and rate of loading (i.e., ra te of shear strain) needs to be determined. The objective of this project is to quantify the relationship between shear stiffness and the rate of shear strain for steel reinfor ced neoprene bearing pads.

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16 Figure 1-1 Bearing pad in bridge

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17 CHAPTER 2 LITERATURE REVIEW This chapter covers inform ation found during the background review into neoprene bearing pads and serves as a basis of understandi ng for this project. It contains what was found in codes, design guides, literature, and in formation obtained from design professionals. In order to provide some understanding into th e subject mater of this chapter and neoprene an introduction to the concept of viscoelasticity is necessary. Viscoelastic behavior in the broadest sense is a combination of both elasti c behavior and viscous behavior. Stress in a viscoelastic material is dependant on both strain and the rate that strain is applied. Additionally, it is important to discuss some terminology at this point. The shape factor (denoted as SF in this dissertat ion) is used in the American Association of State Highway and Transportation Officials[1,2] (AASHTO) bearing design spec ifications, FDOT specifications[3,4] and is found in many other studies on elastomeric bearing pads. Because of its prevalent use in code and research, the defin ition is presented here. The shape factor is used to describe the geomet ric characteristics of a layer of an elastomer used in a bridge bearing. Thes e bearings are essentia lly stub columns made of a flexible material that is expected to undergo large horizontal strains. Since elasto mers have a Poissons ratio of nearly 0.5, under compressive loading they experi ence significant transverse straining. With substantial compressive loads on a material with a low Youngs modulus the typically neglected effects of end restraint on tr ansverse straining become an important consideration when calculating the compressive deflection and capacity of these materials. The shape factor is a ratio of restrained surface area to the unrestrained surface areas and is used to account for the end restraint effect. In practice, the shape factor is us ed to try to capture the effect of the geometry of

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18 the elastomeric layer on the compression strai n, shear strain and both compression, and shear capacity of a bearing pad. The shape factor is calculated by dividing the pl an area by the area free to bulge in a layer. As an example, a 1 inch thick unreinforced pad that is 12 inch x 12 inch has a SF of 3, and a 2 inch thick unreinforced pad that is 18 inch x 36 inch also has a SF of 3. The shape factor is calculated for each individual layer for reinforced pa ds, i.e. a pad that consists of two layers 12 inch x 12 inch x 1 inch with a reinforcing plate between them would still have a SF of 3. An example calculation is shown below in Figure 2-1. For bearings with multiple layers the shape factor of the thickest layer controls. Codes, Specifications and Design Guidelines AASHTO Design Requirements The Am erican Association of State Highway and Transportation Officials (AASHTO) publishes guidelines for the design of highways th at include design specifications for bridge bearing pads. The sections of the AAS HTO LRFD Bridge De sign Specifications[1] on elastomeric bearing pads treat elastomers as a homogeneous material but a llow for bearings that are designed to act in a compos ite manor. Composite pads, also known as reinforced pads, are made by bonding layers of an el astomeric material with layers of reinforcement typically consisting of either fiberglass, cotton-duck (cotton canvas), or thin steel plates. The reinforced pads that carry the greatest ver tical loads are typically designed with steel reinforcement. There are two methods that can be used to desi gn steel reinforced el astomeric bearings in AASHTO Specifications; these are referred to as Method A and Me thod B. Of the two, Method B is the method most recently added to the sp ecifications. The Commentary of the AASHTO Specifications states that Met hod B typically results in a high er bearing capacity as well as smaller horizontal forces. These smaller horizonta l forces result from a reduced shear stiffness

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19 due to the reduction in size of the pads from the higher allowed compression capacity permitted by Method B. This higher compression capacity is only allowed with additional testing and quality control of the bearings. The alternative and more conser vative approach, Method A, can be used for all types of reinforced and unreinforced elastomeric bearing pads as well as steel reinforced bearing pads. In Method B of the AASHTO Design Specifications[1], the limit for the average compressive stress under service loading for bearings subject to shear is calculated as follows in Equation 2-1 and Equation 2-2. s 1.66 G S 1.6 ksi (2-1) L 0.66 G S (2-2) where s is the service average compressive stress due to the total load (ksi) L is the service average compressive stress due to live load (ksi) G is the shear modulus of elastomer (ksi) S is the shape factor of the thickest layer of the bearing The shear modulus of the neoprene is found in AASHTO with the aid of Table 14.7.5.2-1 reproduced below as Table 2-1. This table allows the designer to specify a hardness value rather than a shear modulus. One of the restrictions of Method B is that an elastomers shear modulus is required to fall in the range of 80 to 175 psi[1]. The use of Method B also requ ires that the summation of the individual elastomer layer heig hts in a bearing pad be a mini mum of twice the maximum shear displacement to which the bearing wi ll ever be subjected. If the mi nimum height is selected, this is the same as having a maximum permitted shear st rain of 50%. The shear strain, along with the shape factor and compressive stress make up the three key factors used to scale the bearing pad samples in this project.

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20 The bearings are additionally specified by their temperature grade. The performance specifications for these grades are defined in Section 18 of the AASHTO LRFD Bridge Construction Specifications[2]. The temperature grade require d is shown in Table 14.7.5.2-2 in Section 14 of the AASHTO LRFD Bridge Design Specifications[1]. This table has been reproduced here in Table 2-2. These grading sp ecifications are used as guidelines for manufactures in supplying neopr ene pads that resist stiffening at to low temperatures. Shear Modulus Test AASHT O Designation: M 251-06 The docum ent cited in AASHTO LRFD Bridge Construction Specifications[2] that covers the material requirements and test procedures for accepting elastomeric bridge bearings has the AASHTO Designation: M 251-06[5]. This document includes the use of an inclined compression test to calculate shear modulus, as shown in Fi gure 2-2. In the inclin ed compression test, the surface slope can vary between 1:10 and 1:20. This style of testing results in the compression varying linearly with shear. M 251-06 also allows for the use of ASTM D 4014 ANNEX-A1[6] with modifications that include shearing the sa mples to 70% strain and calculating the shear modulus with a secant modulus through the stress at 50%. In addition to tests for calculating a typical shear m odulus, AASHTO M 251-06[5] contains a method for calculating the shear modulus as a func tion of time. This shear modulus is found in section A2 A Test Method for Creep and Shear Bond in Elastomeric Bearings and the test setup is shown in Figure 2-3. The testing met hod specifies that the samples measuring 51 mm by 51 mm are to be either hot or cold bonded to the steel plat es shown. Once the bonds have reached sufficient strength the samples are then strained in shear 10 times at a rate of one percent per second to 50% then finally loaded to 50% shear strain in one second. This final 50% strain is held constant for a minimum of 6 hours and the load is recorded after th e first half of an hour

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21 then every five minutes for the remainder of th e testing period. The method for calculating the shear modulus is shown in Equation 2-3. 5.025151 )( )( tload tG (2-3) where load(t) is the load at time t (min) G(t) is the shear modulus (MPa) at time t The (51 x 51) is the area of the sample in mm2, the number 2 is to account for the pair of samples and the 0.5 is the 50% shear strain. Section A2.4.6 of AASHTO M 251-06[5] states that the shear modulus can be predicted for any future time conservatively using a power law equation with coefficients calcula ted using a least-squares method re gression analysis of the data obtained over the six hour period of testing. This power law equation is in the form shown below. battG ) ( (2-4) To estimate the creep deflection at time T of a full size bearin g the shear modulus relationship found using the regression anal ysis is used in the equation below. 1001 )( )60( (%) TG G Creep (2-5) Shear Modulus Test ASTM D 4014 ANNEX-A In the background research, AASHTO[2, 5] references the curren t ASTM specification for finding the shear modulus of an elastomer, ASTM D 4014 ANNEX-A[6]. The ASTM test procedure requires the samples, s hown in Figure 2-4, to be shear strained from 0 to 50% for six cycles while taking from 30 seconds to 60 second s to reach 50% shear strain each cycle. In the ASTM test, the purpose of first five cycles is to stabilize the stress-strain behavior of the elastomer and the additional si xth cycle is used to find the value of the shear modulus. The

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22 first five cycles of the ASTM test used for c onditioning the sample minimi ze a transitory effect know as thixotropic or the Mullins effect which is discussed in more detail later. In this ASTM standard the shear modulus is ca lculated by taking the secant m odulus on the stress-strain graph from the point of 2% of maximum stress to th e point at 25% shear st rain beyond this point (Figure 2-5). It should be noted that no compressive stress is require d in this specification and in order for a reaction to be developed the sample s are bonded to both the ridged outer plates and center shearing plates. If a sample is being checked for a specific sh ear modulus a certain variation is allowed by the ASTM specifications. The ASTM specification states the following: The shear modulus of the elastomer determin ed in accordance with Annex A1 shall not differ by more than 15% from the required shear modulus of the elastomer. This means a sample modulus could be fr om 85 to 115% of the specified value. Florida Department of Transportation The Florida Department of Tran sportation (FDOT) specifications[3, 4] were reviewed to determine the sizes, design requirements and materi al grades that are currently used. Bridge bearing pads based on these standards typically ha ve plan dimensions that range from less than one foot to 4 feet depending on the compression loads and the beam configuration being carried. Some of these combinations are shown in Table 2-3 which comes from the FDOT Standard Drawings[4]. These dimensions are for pads made up of inch thick elastomer layers and are designed to support Type II to VI (AASHTO) beams in prestressed bridges. Table 2-4 contains the standard properties for neoprene that design engineers working in the state of Florida are to us e if they are specifying the bearing pads by durometer hardness instead of shear modulus.

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23 Applications in FDOT Projects A professional bridge engineer was contacted in order to obtain addi tional values of shape factors and typical compressive loads used in th e design of segmental bridges. The information provided included the expected co mpressive stress, shape factor, the number of neoprene layers used, the size of the steel reinforcement and which design methodology was typically used. This information, along with the design guidelines given in the FDOT Standard Specifications,[3] is listed in Table 2-5. Since AASHTO and FDOT currently have no gui delines for dealing with reduced strain rates, current practices involve a certain amount of engineerin g judgment. In particular, another professional bridge engineer provided the following procedure that is used for dealing with long term loading on neoprene bearing pads, such as seasonal temperature change, concrete creep and shrinkage. The shear modulus for neoprene of a given hardness is found by calculating the average of the values listed in the governing specification such as in Table 14.7.5.2-1 of AASHTO (reproduced as Tabl e 2-1) or in the FDOT[3] specification shown in Table 2-4. The corresponding creep deflection at 25 years (taken from the same ta bles) is used to determine the adjusted shear modulus for long term loads by assuming an inversely proportional relationship between shear modulus and deflection. For exampl e, as shown in Table 2-1 and Table 2-4, a 50 durometer pad has a total deflecti on (initial instantaneous plus cr eep) at 25 years equal to 1.25 times the initial instantaneous deflection. This would indicate a shear modulus for long term loads equal to 0.8 or 1/1.25 times the initial shear modulus. Reviewed Literature A literature review was conducted in order to find pertinent information about shear stiffness reductions for long term loads. This review produced information about short-term experiments that were similar to this proposed research. However, only limited information on

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24 long-term experimental testing pertaining to the shear stiffne ss of neoprene bearing pads was found. The majority of long-term experimental testing pertained to compressive behavior, not shear behavior. General Background on Elastomeric Bearings and Elastomers This section covers the research that went into the section of the AASHTO specifications that covers steel reinforced neoprene bearings. It also covers research into the basic viscoelastic properties of neoprene. Lastly, it covers the research that provided the motivation of this current research project. Performance of elastomeric bearings: NCHRP report 298 This report compiled by Roeder, Stanton and Taylor [7] describes Phase II of the National Cooperative Highway Research Program (NCHRP) Pr oject 10-20. Phase I of the Project was a comprehensive state-of-the-art review of neopren e bearing pads. It was initiated in 1981 to update the AASHTO Specifications for Highway bri dges. The report resulte d in the proposal for Method B discussed in AASHTO Design Requirements of elastome ric bridge bearing design. Phase II research findings fell into six categ ories: low temperature behavior, compression loading, rotation, shear and combined loading, st ability and fatigue. These categories are briefly discussed below. The effects of low temperature on the shear modulus of an elastomer are only pronounced near the crystallization temperature which wa s indicated to typically be below 32 degrees Fahrenheit. Below the crystallization temperature elastomers become much stiffer. This effect on shear modulus was studied in detail by Roeder and Stanton(1989) duri ng Phase III. Since Florida experiences only brief periods below the crystallization temperature it was deemed that, at this time, it unnecessary consider the eff ects of low temperature on shear stiffness.

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25 In the NCHRP Report 298 the limiting compressive stress of 1600 psi, now used in the AASHTO specification, was determined based on when debonding occurred in the specimens. The debonding, which actually appeared as cracki ng or tearing in the elastomer near the steel elastomer interface, began at compressions greate r than 2500 psi. It was limited by applying a factor of safety of approximately 1.6 to the compressive stress to this failure stress. The effects of end rotation of the beam were considered an extension of the theories of compression. Rotations were looke d at with respect to moment-ro tation relationships and to the compression and tensions developed in the pads. In the conclusion, it was noted that the moment rotation curves were mainly linear. These results and additional tests were conducted by Stanton, Roeder and MackenzieHelnwein in NCHRP Report 12-68[8]. The test procedure used in Phase II of this re search for shear was similar to that of ASTM D 4014 ANNEX-A. During the test s conducted in shear it was not ed that the co rners of the bearings rolled over if the shear strains exceeded 50%. This rolling of the corners was believed to pose a risk to the reinforcement and could result in tearing of the elastomer. For these reasons the shear deformations are limited to 50% in AASHTO Method B. In Appendix E of the NCHRP report, the rela tionship between shear force and compressive strain was presented for an elastomeric bearing pad as follows: 2 0 0)1(c cr ssh GA V (2-6) where V is shear force is the ratio of total combined thickness to elastomer thickness in a reinforced bearing s is the shear displacement As0 is the shear area of the uncompressed pad hcr0 is the total thickness of all elastomer layers in a reinforced bearing in the unloaded state (not including the reinforcement thickness) c is the compressive strain

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26 This relationship takes into account an increased shear area due to parabolic bulging and the effect of decreased height due to the compression of the elasto mers. The implication is that as compression is increased the required shear for ce for a given displacement also increases, thus increasing the effective shear modulus. In Appendix B of the report the relationship between compressive stress and strain for bonded elastomer pads was given as follows: c = Ecc = Efcc (2-7) where Ec is the effective compressive modulus E is the Youngs modulus fc is a conversion factor fc = Ac + BcS2 (2-8) where Ac is a dimensionless constant re ported as ranging from 0 to 1.33 Bc is a dimensionless constant dependant of the shape of the layer and the ratio of the Youngs modulus to the bulk modulus S is the shape factor of the pad It was reported that research ers have used values of Ac ranging from 0 to 1.33. Additionally it was noted that for practical shape factors Bc is much more important due to the S2 term. This report mentions decreased shear stiffne ss due to a tendency for elastomeric pads to buckle in shear as the shear di splacement increases under a comp ressive load. Though this is mentioned no equation was presented to express th e shear stiffness in terms of this effect. It was also mentioned that during testing co rrections for bulging and buckling stability did not account for all of the test data scatter. Comparing the time and rate dependent mechanical properties of elastomers Meinecke [9] described three important load respon ses that must be accounted for in modeling the behavior of elastomers: instantaneou s response; transient viscoelastic response; and

PAGE 27

27 permanent viscoelastic response. These three factors provide a descri ption of the elastic response, creep and creep recovery in an elastomer. To illustrate these concepts, Meinecke provides expected displacement curves based on the response to various types and durations of loading. Meinecke also provides a basic rheological linear model that accounts for the behavior of elastomers. The elements of a linear model are linear springs and linear viscous dashpots; these elements represent aspects of the material beha vior of a dimensionless elastomeric sample. A linear spring is used to represen t the elastic part of stiffness in an elastomeric sample i.e. the stress versus elastic strain of the sample as s hown in Figure 2-6. Similarly, a linear viscous dashpot is used to represent the viscous respons e of the elastomeric sample response divided by the loaded area of the sample as shown in Figure 2-6. The basic model, illustrated in Figures 2-7, 2-8 and 2-9, shows the expected response to a pulse load, neglecting inertial dynamic effects. At the time the load is applied there is an instantaneous elastic strain. This is followed by both a transient and a permanent viscoelastic response that superimpose on the elastic response. When the load is removed the same elastic response is shown in the opposite direction followed by the relaxing of the transient response. However, there is a permanent set in the material that is not recovered. In the Figures 2-7, 2-8 and 2-9 the dashed lines show what would have happened if the load had not been removed. Meinecke cautions that this is an over-simplified model and the value of 1, the value of the viscous respons e, is not actually a constant. Engineering with rubber Mullins[10] reviews information on the Mullins effect which is a phenomenon where the shear stiffness of a bearing pad seems to reduce with repeated straining. The reduction in

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28 stiffness due to this effect quickly levels off, usually after the first th ree or four cycles of straining. This phenomenon is mainly found in material with large filler content, typically around 30% by volume, the most common filler bei ng carbon black. Carbon black is a substance that comes from the incomplete combustion of petroleum and is similar to soot. The Mullins effect is thought to be a pr oduct of changes occurring in the molecular structure, which consists of long carbon chains which are bonded to sulfur atoms and the molecules of the filler material. The bonds to the filler material are weak, and when the material is first strained part of the force needed achieve a particular level of stra in is due to the breaking of the bonds between the carbon chains and the filler material. Once these bonds are broken and the carbon chains can rearrange, th e force required to strain the pad to any strain level less than the previous maximum strain is not as great. It is important to note that if strains exceed the previous maximum the stress strain relationshi p will pick back up on its original, uncycled, trend. Neoprene elastomer bearings ten year s experience proves their importance Maguire[11] wrote this article in 1967 approximately ten years after the first use of neoprene bridge bearings in the United States. Publis hed in ASCE's Civil E ngineering Journal it championed the use of neoprene bearings with a brief history and recommended changes to the AASHO specifications. The history included the original uses of the bearings stating they were first used shortly after WWII in France and England for railroad bridges. It points out the following failings of the specifications at the time: There was no rule for the length of bearing in relation to the width of the beam except that it needs to fit under the beam. The stress limits were too stringent. There were no reasons given for choo sing one hardness level over another.

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29 No standard sizes had been established increasing the cost of the bearings since manufactures had to retool for each new set of pads. Changes that were recommended: Shape factors should be above 5 to limit the ve rtical deflections to 7% or less with the compressive stress limit. Eliminate the requirement of the use of adhesi ves or mechanical fasteners to secure the bearings in exchange for a minimum compressive stress. Set a total load deflection limit. Require manufactures to place trademarks on the bearings for posit ive identification. Require testing of samples of the bear ing materials during the production run. Eliminate the tear test required then Add 50 durometer physical properties to the list of properties that included only 60 and 70 durometer hardnesses. Pare advocated these changes to increase the usefulness of neoprene bearings and concludes stating that over the te n previous years the neoprene bear ings that had been in service had performed with little or no deterioration. Since then other re ports have continued to tout the virtues of neoprene as a br idge bearing material and push the limits of its use. State-of-the-art elastomeric bridge bearing design Roeder and Staton[12] reported on compression load failures as well as the standards current as of 1991. The modes of compressive failu re included both yielding failures of the reinforcement and delamination of the neoprene layers. The re ported delamination compressive stresses ranged up to 8500 psi but were scattered and no apparent correlation to the shape factor was found. All but one of the delamination failu res were above 2300 psi. It was noted that a failure due to delamination does not result in immediately disastrous consequences for a bridge or building but does reduce the service life of th e bearing by accelerating th e fatigue process.

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30 Fatigue failure modes were mentioned, but it was reported that limits to the compressive stress and shear strain were sufficient to prev ent this mode. Specifically, shear strains of no more than 50% were said to effectively control failure by fatigue. The article also mentioned that holes in th e reinforcing layers resulted in stress concentrations that reduced the cap acity of the neoprene bearing pads. The intent of the article was to eliminate th e misunderstandings that were restricting the use of neoprene bearings and allow for the use of additional capacity. Elastomeric bearing research NCHRP report 109 The NCHRP Report 109[13] is one of the most similar projects to this one and it presents information on stress relaxation of the shear modul us of neoprene bearings. Stress relaxation is the reduction of stress over time as displacement is held constant. In order to test the stress relaxation of neoprene, samples were create d by gluing together a sandwich of two steel compression plates, two pieces of neoprene with a SF of 2, and a center steel shear plate as shown in Figure 2-10. In order to conduct the test, the sample wa s first compressed approximately 10% of the sample thickness (0.10 in/in) over a period of about 5 minutes. The pads were then loaded in shear four times to approximately 50% shear stra in at a rate of 8% per minute. The multiple cycles were used to condition the neoprene pads After conditioning the pads were loaded to 50% shear strain and held in this position fo r 22 hours while shear load readings were taken every 2 minutes for the first 10 minutes, then at the half hour mark fo llowed by readings at 1 hour, 3 hours, 5 hours, and 22 hours. An example of the data collected is s hown in Figure 2-11. The data in Figure 2-11 and da ta like it was used to genera te Figure 2-12 which displays short-term shear modulus vs. percent relaxation per decade of time in minutes. A decade of time

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31 is defined as the log of time in minutes, i. e. 10 minutes is one decade, 100 minutes is two decades and 1000 minutes is three decades. The calculation for converting Figure 2-11 to a data point in Figure 2-12 is shown in Equation 2-9 and is plotted against the average of shear modulus of the first five conditioning cycles. ))(( )100)(( axation Stress_Rel1 1nr rrn (2-9) where r1 is the shear stress at 1 minute (psi) rn is the shear stress after n decades of time (psi) n is the number of decades of time The trend in Figure 2-12 shows that as the values for shear modulus become greater, the scatter in the percent relaxa tion per decade of time increases For 100 psi shear modulus material the percent relaxation ranges from 1.7% to 7.8% per decade of time. This would translate to a 1.7% to 7.8% reduction in the force required to hold a displacement after 10 minutes. After 100 minutes there would be an additional reduction of 1.7% to 7.8% in the force. An example of this calculation is found in Table 2-6. The longest stress relaxation test reported in NCHRP 109 [13] study was only 22 hours, which is not as long as it takes to apply loads such as those due to seasonal temperature change and prestressed concrete shrinka ge. Table 2-7 shows the values of shear modulus based on the same calculations in Table 2-6 taken to time periods beyond their original te st duration. In the NCHRP 109 research, all shear stra in takes place in six minutes and then held constant for the duration of the test. In this study, the shear strain is applied in a linear fashion over the entire test period. Even though these experiments were co nducted using different approaches, a direct comparison between this current project and the results in NCHRP 109 did provide a starting point for this investigation.

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32 Additional design data based on fullsize bridge bearing pads of neoprene This article[14] presents data generated by E. I. Du Pont De Nemours and Company in 1981. The pad designs tested were fiberglass re inforced, steel reinforced and plain pads. The data reported was for compressive strain vs. stre ss for shape factors ranging from 3 to 20 for hardnesses of both 50 and 60 durometer. Additio nally, tests were conduc ted to evaluate the ultimate load of some of the pads. The steel reinforced pads were reported to have failed in debonding above 5000 psi with two pa ds failing above 10000 psi. Construction and design of prestr essed concrete segmental bridges Podolny and Muller[15] provided a guide for engineers, architects and contractors for the design and construction of prestres sed concrete segmental bridges. This guideline mentions that the shear modulus of neoprene is dependent on th e rate of loading. Podolny and Muller provide a table that contains a list of recommended el astic constants based on hardness, however, they recommend that the values listed be doubled for instantaneous (i.e ., impact) loading (Table 2-8). Design of elastomer bearings This article was published in th e PCI Journal in October of 1964[16], Rejcha describes the considerations that need to be accounted for during the design pro cess of an elastomeric bearing, presents some recommendations and provides a design example. The recommendations made by Rejcha about Elastomer Shear Modulus include the following: For permanent forces, a considerable relaxa tion takes place. Therefore, a reduced modulus, G=0.5G, should be considered. The a bove is related to the effect of shrinkage and creep of a concrete girder, the ve rtical shortening under dead load, etc. This particular interpretation was a major motivation of this research project since no additional justification was given.

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33 Summary of general background There is some misunderstanding as to the behavior of neoprene under long term loading and there needs to be some clarif ication as to what is the shear modulus of neoprene and if there is a lower limit to it. Additio nally, steel reinforced neoprene bearings seem to have a reserve capacity for compression above the limits imposed by AASTHO. Test Methods for Elastomeric Bearings and Complications This section includes research on methods for finding the properties of elastomers as well as some of the complications that arise while conducting tests on elastomers. These complications include interactions between compression and shear as well as problems that might arise due to the manufacturing process. Test method for determining the shea r modulus of elastomeric bearings Topkaya and Yura [17] reviewed the accepted test methods for determining the shear modulus of neoprene pads and in troduced a new method. The new method involved the use of inclined plates to simultaneously comp ress and shear the pads being tested. Quad-shear tests (Figure 2-4) and tests using full size bear ings were run along side the proposed inclined compression te sts (a 1:10 slope and a 1:20 slope) shown in Figure 2-2, to compare the effectiveness of the new test. The compression using the 1:10 slope is 10 times greater than the shear force im parted while the 1:20 slope has compression 20 times greater than the shear force. This paper suggests cycling te sts repeatedly until a repeatable result can be obtained before calculati ng the shear modulus. During testing Topkaya, and Yura[17] found that a change in lo ading rate from 50% shear strain in 2 minutes vs. 14 minut es resulted in a 5% drop in sh ear modulus for neoprene with a specified shear modulus of 200 psi. The change was less pronounced, only 2%, in neoprene with a shear modulus of 100 psi.

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34 In a section of the paper title d Future Research Needs it wa s noted that there existed a need for a Pcorrection factor for the test results. This factor was only recommended to be used for the samples not in bridge designs. Elastomeric bridge bearings: recomme nded test methods: NCHRP report 449 The NCHRP Report 449[18] reviewed several existing testi ng methods with the intention of simplifying and improving the AASHTO specifications. Tests for the following properties were examined. Hardness Shear Modulus Heat Resistance Ozone Resistance Low Temperature Behavior Creep and Compression Set Yura, Kumar, Yakut, Topkaya, Becker, and Collingwood [18] recommended the elimination of some of these tests, in particul ar the tests for hardness, heat resistance, ozone resistance, and compression set. These tests were reported to have limited or no practical value for neoprene bridge bearings. The report al so recommended using the test method for determining the shear modulus of an elastomeric material that involved inclined plates that induced shear into samples placed under compression. It was also noted that shear modulus could be changed in an experiment by changing th e loading rate from 30 % shear in 2-3 minutes to 10 hours. This inclined shear test was not de emed suitable for this current research project due to the need to look at shea r separate from compression. On highly compressible helical springs and rubber rods, and their application for vibration-free mountings Haringx[19-21] developed a theoretical derivation of buckling in rubber rods and springs. This differed from work done on rigid columns due to the low shear resistance of the material.

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35 The derivation accounted for the shear strain contribution to buckli ng by treating it as an additional rotation. Elastic stability of rubber compression springs Gent[22] reviewed research done by Haringx[19-21] and experimented with the buckling of elastomeric columns investigating the shear eff ects. The buckling form of these elastomeric columns is due to the composite nature of th e bearings. Because the compression and tension stiffnesses are so much greater than the sh ear stiffness the buckled shape includes shear deformations (Figure 2-13). Gent also examined the effect of compression on applied shear in these columns. An experimental study of elastomeric brid ge bearings with design recommendations Yura and Muscarella[23] analyzed elastomeric bearing perf ormance of both tapered and flat bearings with the purpose of developing a design pr ocedure for tapered bear ings. This study also indicated that wax infusion to meet AASHTO[1] ozone test requirement is unnecessary and even detrimental for neoprene. In the investigation of inclin ed bearings Yura and Muscarella[23] examined the effect of compression on shear stiffness due to the decrease in buckling stability. Since at the buckling load there would be no shear resistance Yura a nd Muscarella asserted that there was a linear relationship, shown in Equation 2-10, between the shear displacement and the remaining buckling capacity of a bearing under compression. cr initial totalP P 1 (2-10) where initial is the shear deflection due to applied shear force P is the applied compression load Pcr is the buckling load (Equation 2-11)

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36 The buckling equation used by Yura and Mu scarella was based on work done by Gent[22]. This equation is based on the assumption that the top and bottom surfaces of the bearing are parallel to each other and that the applied shear force is app lied to one of these surfaces. 1 4 1 22 0 0 rtS r s crhAG EIf AG P (2-11) where is the total bearing thickness (including steel) divided by total elastomer thickness hrt As is the shear area of bearing fr is the ending stiffness coefficient = 1.0 + 0.575 S2 G0 is the shear modulus of th e elastomer under no compression E is the 3G0 The shear modulus of an elastomer under no compression can be defined as follows. s rtA Vh G 0 (2-12) where V is the force necessary to shear a sample through distance The effect of compression on shear modulus can be seen directly by rewriting Equation 210 in terms of the shear modulus in Equation 2-12 and an effective shear modulus based on the total displacement. cr effP P GG 10 (2-13) where Geff is the shear modulus under compression This is still subject to the assumptions of parallel surfaces and lo ads in the original buckling equation. By replacing Pcr and E with their equations and distributing G0 throughout a linear relationship between Geff and the compression load P is shown in Equation 2-14. 1 2 01 12 1 2 rt s r s effhA If A PGG (2-14)

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37 Slippage of neoprene bridge bearings McDonald, Heymsfield and Avent[24] reviewed existing literature and did field surveys to determine the causes of slippage and conclude with strong reco mmendations to eliminate as much wax as possible from the bearing and th eir surfaces. These recommendations included relaxing the ozone protection requirements and sc raping the surface of the bearings with razor blades. Elastomeric bearings: backgro und information and field study English, Klingner and Yura[25] conducted field surveys to investigate the tendency of bearings to move gradually para llel to the supported beam. In extreme cases the pads would move partially off of their supports and would ha ve eventually let the beam fall to the underlying support if not corrected. This m ovement of the elastomeric bear ings was described as walking out. The behavior of the bearings was found to occur due to thermal movement of bridges. In the field survey the only bearings observed w alking out were made from natural rubber. Neoprene bearing pad slippage at Louisiana bridges Heymsfield, McDonald and Avent[26] report on the investigati on of neoprene bearing pad slippage and conclude that the pads were walking out due to da ily temperature fluctuations and wax being excreted from the pa ds lubricating their surfaces. Summary of test methods and complications There seems to be some relationship be tween compression and shear modulus for elastomeric pads, and even though the relationship is not entirely clear it should be observed over the range of stresses allowed by AASHTO. Ad ditionally, the manufacturing process of neoprene bearings includes the use of wax, which can caus es problematic slippage during the service life of these bearings.

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38 General Background and Models of Viscoelastic Material This section covers research that uses m odels and modeling techniques for elastomeric behavior in an effort to account for the viscoelastic properties of elastomers. The most recently developed of these models tries to take into acco unt the Mullins effect as well as the viscoelastic properties. Basic continuum models References Malvern[27] and Findley, Lai and Onaran[28] review the time dependent properties of viscoelastic materi als. A variety of models are covered including the standard linear model or Kelvin Model shown in Figure 2-14. This standard model is made up of spring elements and a dashpot which are shown in Figure 2-6. The combination of a spring elemen t and dashpot in series is also known as a Maxwell element, shown in Figure 2-15 with its governing differential eq uation. Other models that are examined by References Malvern[27] and Findley, Lai and Onaran[28] include using an infinite number of Maxwell elements in pa rallel with the standard linear model. Molecular theory References Smith[29], Yin and Pariser[30], Ronan, Alshuth and Jerrams[31], Green and Tobolsky[32] and Adkins[33] all look at viscoelastic behavior from the perspective of molecular physics. Using molecular physics to describe th e effect of loading ra te and the effect of temperature on elastomeric materi als requires the use of the random movement of the molecules due to internal heat (Brownian motion) and a temperature scale based on absolute zero. Many of the following papers are based on these concepts. An engineering theory of nonlinear viscoelasticity with applications Schapery[34] discusses relatively simp le stress-strain equations developed for nonlinear isotropic viscoelastic material at constant temp erature. The equations Schapery used are based

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39 on Boits linear thermodynamic theory and they describe the post Mullins behavior. The equations account for all three dimension however they only cover unreinforced behavior and would have to be modified to take into account compatibility when looking at compression of reinforced pads. The shear equation is shown in Equation 2-15. s t s e tseGGtG d d d tGQ )( )(0 (2-15) where Q is the total shear stress is the shear strain is a dummy time variable t is time Ge is the elastic shear modulus (Ge 0) Gs is shear storage modulus series ( Gs 0) s storage exponential coefficient (s > 0) Constitutive modeling of the large strain time-dependent behavior of elastomers Bergstrm and Boyce[35] examined the response of carbon bl ack filled chloroprene rubber. Polychloroprene, more commonly known as neopr ene, is made from chains of chloroprene molecules (C4H5Cl). In the process of vul canization these chains are linked or cross linked to one another with the addition of sulfur atoms. Bergstrm and Boyce use a model proposed by Arruda and Boyce[36] consisting of 8 of these chains form ing a network. Bergstrm and Boyce account for the time dependant behavior by leaving one chain free. Once the network has been deformed due to the application of stress this free chain is allowed to rearrange itself via Brownian motion. While the free chain rearranges its elf the level of strain is held constant in the network and the rest of the network responds to th e strain elastically. Ev entually the free chain will come to oscillate around a configuration that requires the least amount of energy to maintain, resulting in a level of stress in the sample equal to th e elastic stress.

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40 The experiments of Bergstrm and Boyce were conducted on samples that had the Mullins effect removed and their model mimicked th e results of tests of samples placed into compression. One result of the model shown by Bergstrm and Boyce is that no matter how a sample was strained if held in a fixed position th e stress would decay toward the elastic stress. This is shown in test data shown in Figure 2-16 (from Bergstrm and Boyces paper). It is important to note in Figure 2-16 th at after straining is resumed at the previous rate the stress strain relationship recovers to its previous trend. The standard linear model (Figure 2-14) was referenced to aid in the descri ption of the observed behavior. A three-dimensional constitutive model for the large stretch behavior of rubber elastic materials Arruda and Boyce [36] present a model that successfully represents viscoelastic materials in uniaxial extension, biaxial extension, uniaxia l compression, plane stra in compression and pure shear. This is also the basis of Qi and Boyces[37] work. The behavior of rubberlike materials in moderately large deformations Bloch, Chang and Tscgoegl[38] examined crosslinked rubberlik e material with the use of relaxation modulus and strain energy functions. In this paper moderately large deformations referred to in the title refers to strains of up to 150%. Constitutive model for stretch-induced softening of stress-stretch behavior of elastomeric materials Qi and Boyce[37] present a model of visc oelastic material behavior that includes the Mullins effect. This model describes the strain energy density function and how it relates to the strain softening of the viscoelastic material. Th is model bears considerati on due to the fact that almost all bearing pads do not have the Mullins e ffect removed before they are put in service. Additionally, to account for the Mullins effect by testing is both cost prohibitive and technically difficult.

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41 Nonlinear finite element analysis of elastomerstechnical paper MSC Software Corporations paper[39] is on the capabilities of their finite element model software with respect to elastomeric modeli ng. Their paper included which variables their software took into account, and references some of the theory and equations behind the software. Summary of models of viscoelastic material There are theoretical models th at can account for most of the behavior of neoprene. Using these models requires finding the required coefficients and knowing the displa cement history that the bearings are going to go through. None of these models appear to have been validated for the type of long term loading to which bridge bearings are subjected. Possible Temperature Effects This covers research on what possible effect s temperature could have during testing of samples. This predominately is to determine wh at actions can be taken to minimize these effects during the testing of elastomers for this dissertation. Viscoelastic properties of polymers Ferry[40] descries the glass transition temperat ure, which is approximately -58F for neoprene, as the temperature at which the free volu me in an elastomer first starts to increase. Glass transition temperature specifically refers to the fact that elastomers become brittle and can shatter below this temperature. The free volume made up of the voids in the molecular structure is used by the elastomers carbon chains to rearrange in response to an external stress. When the temperature rises above the glass trans ition temperature in a pure elastomer the volume of the voids increases proportiona lly to the change in temperature. This increase of volume makes it easier for the carbon chains to move and this increased mobility has the effect of softening the elastomer.

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42 Low temperature behavior and acceptance criteria for elastomeric bridge bearings: NCHRP report 325 Roeder, Stanton, and Feller[41] write about ways low temper atures stiffen elastomeric bearings. One reported way is cr ystallization; this refers to the increase of shear modulus over time due to the cooling of the molecular struct ure down to a point where the carbon chains begin to stick to each other between the sulfur bonds. Th ey indicate that this only begins to occur below 50F in neoprene. Instan taneous stiffening is another phenomena that is due to the reduction in internal energy in an elastomer. It is characterized as an immediately measureable stiffing when a sample has reached thermal equi librium. They also mention that the glass transition temperature is the temperature at which samples of elastomers may fracture in a brittle manor. Roeder, Stanton, and Feller[41] also developed design requirements and acceptance test procedures for low temperature elastomeric bridge bearings. Performance of elastomeric bridge bearings at low temperatures Yakuts[42] dissertation formed the basis of Yakut and Yuras[43] work. The dissertation shows more clearly exponential trends in shear modulus due to instantaneous stiffening for neoprene and natural rubber. When additional filler was used to increase the shear modulus of an elastomer the instantaneous stiffening became more pronounced with decreasing temperature. The neoprene samples had been specified to ha ve shear moduli of 100 psi and 150 psi however, the actual shear moduli values were closer to 110 psi and 230 psi respectiv ely. The trends in Yakuts data are shown in Figure 2-17. Summary of temperature Neoprene behaves in a nonlinear fashion and temp erature can play a roll in the stiffness of neoprene bearings. However, AASHTO requires the designer to select of a grade of neoprene

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43 that has been formulated to minimize this temperat ure effect and this sele ction criteria is shown in Table 2-2. Summary of Literature Review It should be noted that not all of the literature reviewed was di rectly related to the research objective and some was redundant. A summary of the references are in Appendix B. During the course of researching neoprene bearing pads, no models were found for steel reinforced neoprene bearings which were based on the strain rate in highway applications. However, as shown in the literature, reduced strain rate do es result in a reduction in eff ective shear modulus. Because of this observation, it is necessary to investigate to what extent this occurs. The literature reviewed revealed that the critical parameters to monitor in the investigation were; shape factor, the effect of compression on shear modulus and cyclings effect on shear modulus Additionally the literature reviewed provided insi ght into a potential te sting problem related to pad slippage due to the addition of wax to the neoprene.

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44 Figure 2-1. Shape factor calculation example Figure 2-2. Inclined shear test setup Figure 2-3. Shear creep test setup.[5] (Source: Figure A2-1 pp. M 251-11) Figure 2-4. Test set up ASTM D 4014 ANNEX-A.[6] (Source: Figure A1.1 pp. 5)

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45 Figure 2-5. Example of ASTM D 4014 shear modulus determin ation from the sixth cycle A B Figure 2-6. Examples of model elements. A) Spring element. B) Dashpot element. Figure 2-7. Four parameter visc oelastic model and pulse load.[9] (Source: Figure 1 pp. 1146)

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46 A B C Figure 2-8. Piecewise strain vs. time response.[9] A) Elastic response. B) Viscoelastic response. C) Permanent set. (Source: Figure 1 pp. 1146) Figure 2-9. Superposition of strain vs. time response.[9] (Source: Figure 1 pp. 1146)

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47 Figure 2-10. Sample for re laxation testing NCHRP 109 [13] Figure 2-11. Typical shear st ress time graph constant 50% shear strain NCHRP 109[13] (Source: Figure A-10 pp. 21) Figure 2-12. Shear modulus (Gave) vs. stress relaxation pe r decade of time NCHRP 109[13] (Source: Figure A-13 pp. 23) Shear Stress Relaxation over Time Data Envelope

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48 A B C D Figure 2-13. Shear buckling. A) Axially Loaded Bearing B) Euler Buck ling C) Euler Buckling with Shear Contribution D) Pure Shear Buckling Figure 2-14. Standard linear model Figure 2-15. Maxwell element

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49 Figure 2-16. Test data from constitutive modeling of the large strain time-dependent behavior of elastomers.[35] (Source: Figure 8 pp. 8) Figure 2-17. Elastomer shear moduli variation with temperature.[42] (Source: Figure 5.28 pp. 106)

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50 Table 2-1. Shear modulus AASHTO table 14.7.5.2-1[1] Hardness (shore A) 50 60 70 Shear modulus @ 73F (ksi) 0.095-0.130 0.130-0.200 0.200-0.300 Creep deflection @ 25 years divided by instantaneous deflection 0.25 0.35 0.45 Note: (Source: pp. 14-53) Table 2-2. Elastomer grade AASHTO table 14.7.5.2-2[1] Low-temperature zone A B C D E 50-Year low temperature (F) 0 -20 -30 -45 <-45 Maximum number of consecutive days when the temperature does not rise above 32F 3 7 14 N/A N/A Minimum low-temperature elastomer grade 0 2 3 4 5 Minimum low-temperature elastomer grade when special force provisions ar e incorporated 0 0 2 3 5 Note: (Source: pp. 14-54) Table 2-3. Steel reinforced elastomer FDOT bearing pad dimensions for AASHTO beams[4] Bearing pad dimension Number of layers Pad type Beam type L W Shape factor A II (AASHTO) 1-0 1-2 6.46 3 III (AASHTO) 10 1-6 6.43 3 IV (AASHTO) 10 1-10 6.88 3 V & VI (AASHTO) and Florida bulb-Ts 11 2-0 7.54 3 B II (AASHTO) 1-4 1-2 7.47 4 III (AASHTO) 1-2 1-6 7.88 4 IV (AASHTO) 1-0 1-10 7.76 4 V & VI (AASHTO) and Florida bulb-Ts 1-2 2-0 8.84 4 Table 2-4. Neoprene properties FDOT[3] Durometer Hardness 50 60 70 Shear modulus at 73F [23C] 85-110 psi [0.59 to 0.76 MPa] 120-155 psi [0.83 to 1.07 MPa] 160-270 psi [1.10 to 1.86 MPa] Creep deflection at 25 years instantaneous deflection 25% 35% 45% Note: (Source: pp. 8)

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51 Table 2-5. Typical b earing pad properties Property Value, range or method Maximum compressive stress From 1.0 to 1.6 ksi with 1.0 ks i FDOT standard (unless stated otherwise)[3] Durometer hardness 50 to 70 with 50 being FDOT standard (unless stated otherwise)[3] Shear modulus 85 to 110 psi shear modulus being FDOT standard[3] for a hardness of 50 or % of the shear modulus specified[6] Shape factor range From 6 to 9 for standard AASHTO beam sizes From 12 to 28 in segmental bridges examples Number of layers From 2 to 15 la yers in segmental bridge examples Steel thickness 1/16 inch with 14 gauge specified by FDOT[3] Method used AASHTO LRFD Section 14.7.5 Steel Reinforced Bearing Method B (also used in FDOT Design Examples) [1] Table 2-6. Relaxation examples Number of decades (n) Time in minutes Time in days Shear modulus G (psi) based on reductions 1.7% loss / decade 7.8% loss / decade 0 1 6.94 E-4 100 100 1 10 6.94 E-3 98.3 92.2 2 100 6.94 E-2 96.6 85.0 3 1000 0.694 95.0 78.4 4 10000 6.94 93.4 72.3 Table 2-7. Extended relaxation example Number of decades (n) Time in minutes Time in days Shear modulus G (psi) based on reductions 1.7% loss / decade 7.8% loss / decade 4.64 43200 30 92.1 63.8 5.11 129600 90 91.3 60.1 5.72 525600 365 90.3 55.4

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52 Table 2-8. Elastic constants[15] Hardness Youngs modulus E Shear modulus G (IRHD ) (N/mm2) / ((psi)) (N/mm2) / ((psi)) 45 1.80 / (261) 0.54 / (78.3) 50 2.20 / (319) 0.64 / (92.8) 55 3.25 / (471) 0.81 / (117) 60 4.45 / (645) 1.06 / (154) 65 5.85 / (848) 1.37 / (199) Note: (Source: Table 5.1 pp. 246)

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53 CHAPTER 3 METHODOLOGY Developing the Samples In order to develop a test program, a sample size needed to be chosen with consideration of both the design of pads for the field and pads used in previous research. The majority of the full size of steel reinforced pads used in bridges are too unwieldy for la boratory testing. It is also exceptionally difficult to reproduce loads due to the dead weight of a bridge superstructure for the larger pads in the lab. Ther efore, the only viable alternative was to scale the bearing pads to a more manageable size. Since a variety of shape factors are used in the field it was decided to have samples with a similar range of shape factors. The range of 8 to 24 was chosen as representative for larger bridges based on the values in Tables 2-3 and 2-4. It was also decided to use samples with grade 0 material which is what is t ypically used in Florida. The standard design shear modulus of neoprene specified in the FD OT Standard Specifications[3] has a durometer hardness of 50 and approximately a 100 psi shear modulus. This is what was specified in the samples design. A base line compression stress of 1.0 ksi was chosen for the majority of the tests in this study. However, FDOT[3] and AASHTO[1] provide an upper limit for a compressive stress of 1.6 ksi with additional testing, theref ore the test apparatus was develope d to be able to reproduce this stress. A pad with eight steel reinforced layers was selected as a median representative based on the information provided. Once the number of layers was chosen the typical maximum compressive stress was used to calculate a bearing area. The sample size was chosen to be no larger than 12 inch x 12 inch due to concerns over high compressive loads. These concerns were primarily related to laboratory safety around high pressure hydraul ic lines and concerns about

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54 being able to produce those loads.. The layer th icknesses were varied to create the range of shape factors. Pads having uniform layer thickness fr om 1/8 inch to 3/8 inch were used to create shape factors ranging from 24 to 8, respectively. The thickness of the steel reinforcement was varied proportionately within the limits of the manufacturing process (Table 3). The manufacturer could not provide sa mples that contain steel thinner than 16 gauge sheet metal due to problems caused by the process of vulcanization. Table 3-1 lists the final properties and dimensions for the neoprene bearing pad sample s and as an example drawing Figure 3-1 shows the design of the SF 24 sample. All of the othe r samples were similar in design with only the dimensions varying as noted in Table 3-1. In the ordering of the samples, 100 psi shea r modulus material was specified however, upon receipt of the specimens it was found that, 50 durometer hardness material was supplied instead. This information on the material status was supplied with the shipment of the samples. The manufacture chosen to make these samples is a regular supplier for FDOT projects and used the same process in their fabrication as typically used for FDOT. Because of the substitution of material, the samples were in compliance with FD OT and could have been placed into service in a Florida bridge. Test Program In order to determine the most relevant information for use of this research, the method typically used in the design of bridge bearings was referred to in the development of this test program. AASHTO[1] specifies that the minimum elastomer thickness is twice the maximum shear displacement. This is equivalent to making the maximum shear strain allowed by AASHTO[1] 50%. Since this value was also cited[7] as a limiting factor in the serviceability of these bearings it was determined that this maximum shear strain would be the limit of these tests. Strain rates were chosen to determine the time dependent properties of the material and to

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55 provide a basis for establishing trends. In addition to variations in strain rates for different shape factors, the effects of initial new pad stiffness compared to pad stiffness after the removal of the Mullins effect, and the effects of different le vels of compressive stre ss were also considered in the test program. The determination of the change in stiffness due to the Mullins effect removal is particularly important owing to the fact that bearings in the field are not cycled prior to being placed into service. Strain Rates The strain rates for this study range from 50% shear strain in 45 seconds to 50% shear strain in 90 days. The rates were chosen to conform with those found in ASTM D 4014[6], as well as conforming with strain ra tes that would reach 50% shear strain in 12 hours, a week and three months. These rates were chosen to co rrespond to daily, weekly, and seasonal temperature changes. All tests were conducted from zero to a maximum positive shear strain of 50% with the exception of the 18-minute cyclical test. The 18minute cyclical test was conducted with strains that range from positive to negative 50%. In this report, tests are referred to by the time taken to go from 0 to 50% strain as shown in Table 3-2. For visualization purpos es, Figure 3-2 depicts a scale representation of a 12 inch by 12 inch pad with 3 inches of neoprene in both the initial prestrained configuration and how it ap pears at 50% shear strain. In the end a total of 45 tests were conducted; three of these tests were thrown out due to sensor malfunctions during testing. Mullins Effect Since some literature indicated the possibility that both transitory and permanent deformations could occur in the samples, the order of the tests and time between tests were chosen to minimize the impact of potential pe rmanent deformations on the results. Although permanent deformations were not observed during the course of testi ng, another type of permanent change was observed, the Mullins effect (stress softening). In order to quantify the

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56 Mullins effect, it was necessary to eliminate this effect in at least some of the samples. The Mullins effect was eliminated by using a short te rm 18 minute cyclic loading test; straining the samples to 50% shear strain multiple times prio r to conducting other tests. To account for the fact that new bearing pads in the field will exhibit initial pad stiffness (i.e. Mullins effect is not removed) tests were run at various strain rate s with and without elimination, of the Mullins effect. Transitory deformations were found to dissi pate upon the removal of the compression at the end of each test. As a result, tests were run in a sequence that let the pads rest after each test and recover from this transitory deformation. The 18 minute test was chosen to match the loading rate in ASTM D 4014[6] which was 0 to 50% shear strain over 30 to 60 seconds. Based on the ASTM rate a complete cycle is from 0 to +50% then to -50% and back to 0% shear st rain should range from 2 to 4 minutes. Using six cycles at the average rate of 3 minutes per cy cle the total duration of the test is 18 minutes. The last 3 minute period of the 6 cycle test is the relevant test[6] for certifying the shear modulus of an elastomeric sample with the Mullins effect removed. Since the first cycle of the 6 cycle test did not have the Mullins effect removed it was used to determine the initial shear modulus at this strain rate. For the purpose of this report an individual cycle will be referred to as a sec. test. Table 3-4 shows the number of tests that were c onducted with and without the removal of the Mullins effect. Multiple Compressive Stresses For the purpose of looking at the interacti on between compressive stress and effective shear modulus some tests were conducted at multiple compressive stresses. To examine this relationship a series of 12 hour l ong tests were run at the compressi ve stresses of 0.5 ksi, 1 ksi 1.2 ksi, and 1.5 ksi. The tests not included in Table 3-5 were all conducted at 1 ksi compression.

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57 Design of Test Apparatus The testing process was accomplished with the aid of compression and friction. This was started by sandwiching a thin steel plate between two sample pads similar to what is shown in Figure 2-10 then compressing the samples betwee n two thick steel plates. Once the samples reached the desired compressive load, the shear plat e was displaced. In the initial testing, these steel plates were cleaned then roughened with a hammer. The smoothness of this surface was not considered a problem since the coefficient of friction of neoprene on steel was assumed to be greater than 0.05. This assumption proved to be incorrect due in part to wax that was infused into the neoprene samples during the ma nufacturing process as previously noted[23, 24, 26]. Once the samples were in compression this wax bloomed to the surface and resulted in pad slippage when the shear plate was loaded. The slippage was found to occur in the range of 15-25 psi shear stress for 12 hour tests and 35-40 psi for 45 second tests. In order to prevent slipping the surfaces of the plates were roughened to about th e equivalent of Coated Abrasive Manufacturers Institute (CAMI) 30-50 grit sand paper with a pneumatic weld chipping hammer. The compression loading was accomplishe d with a 400-ton double acting cylinder (Enerpac model number CLRG-4006). Once the samp les reached the desired compressive stress the steel plate between the two samples was th en either pushed or pulled at a controlled displacement rate, and the load required to hold this displacement was measured. With data on displacement, load, and given the geometry of the pads, the shear modulus of the material could be calculated. In order to provide a correlation between th e short-term stiffness, which was typically known, and the long-term stiffness both shortterm and long-term tests were conducted on the same samples. To accommodate the range in load ing rates, it was determined that two separate loading systems would be the most practical.

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58 The short-term loading rate of 3 minutes per cycle was based on tests cited in the literature review. This relatively quick application of loading was accom plished with a 60-ton hydraulic double acting cylinder using an elect ronically controlled servo va lve connected to a constant hydraulic pressure source. An electric hydraulic pump was used for this pressure source. The slow rate of displacement needed in the long-term test was simulated by moving a ball-screw jack with a stepper mo tor controlled by a computer at th e rate of 0.001 inch per cycle. This resolution translates to a strain rate of 0.002 in/in per cycle in the thinnest sample pad. Figure 3-6 shows the testing apparatus with the short-term loading mechanism connected and the long-term loading mech anism disconnected. During norma l operating conditions either the short-term or long-term loading system was connected, but not both. The loading jacks were connected to the central shearing plat e through load cel ls with a 30 kip capacity. The shear displacement data was m onitored with two potentiometers (POTs) which were read continually for the short-term tests and after every movement for the long-term tests. The control program used a calculated number of steps of the stepper motor to control the displacement rate of the samples during the long-ter m tests. Operating the system in this manner allowed for accurate movement without relying on fluctuating readings from the POTs. A photo of the test apparatus is shown in Figure 3-4. Major Components of the Test Apparatus The test mechanism can be broken down into five major parts: Compression mechanism Long-term shear loading mechanism Short-term shear loading mechanism Reaction frame Instrumentation

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59 Compression Mechanism The compressive load in the sample bear ings was applied with a 400-ton double acting cylinder Enerpac model CLRG-4006 pressurized by a 2/4-ton double ac ting cylinder Enerpac model number RD-46 (4 ton advancing, 2 ton retr acting). The compressive load was measured by a 300 kip load cell. The hydraulic fluid in the 4-ton double acting cy linder was pressurized by suspending a weight from it. The pressurized side of the 4-ton cylinde r was connected to the extension side of the 400-ton cylinder to compress the samples. In theory the two-jack system shown in Figure 3-5 allows a constant pressure to be maintained as the sample pads creep under compression. An example of this method of c onstant pressure was found in the research by Muscarella and Yura[23] done for the Texas Department of Tr ansportation. Ov er typical shortterm testing creep is not a factor, but with durations up to 90 days creep becomes a consideration. The combinations of cylinders available to produce the load required in testing are compared in Table 3-6. The two criteria for de termining the combination of the two jacks was first, keeping the line pressu re below 3000 psi, and second, minimizing the number of times the hydraulic system would need to be refilled ba sed on the assumed maximum of 0.04 inch of compression creep in the thickest samples. A schematic of the hydraulic system is shown in Figure 3-6. Some components rated at 10 ksi were chosen due to concerns over the high pressures in the hydraulic system. The hydraulic system was designed so that the fluid reservoir in the 2/4 ton cylinder could be refilled since it was expected to drain dow n due to the compressive creep of the samples during long-term testing. The same pump used in the short-term testing hydraulic system was used to refill the compression mechanism.

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60 Long-Term Shear Loading Mechanism The long-term shearing mechanism was controlle d by a computer due to the duration of the test. A hydraulic jack was ruled out for th e long-term loading mechanism due to concerns over leaks. After investigating the operating capacity of a ball screw jack from Joyce/Dayton Corporation, a 10 ton jack with the addition of a 100:1 reducer was chosen. A ball screw model was picked due to its reduced internal friction; internal friction could cause the jack to only be able to move in jumps instead of a continuous mo tion. In combination w ith the reducer, the jack can be operated at a fine resolu tion of motion with a small motor. A stepper motor was chosen over a conventional motor to operate the jack because of its ability to be operated by a computer with precision control and then hold its position during possible power outages. Figure 3-7 shows the ball screw jack in position during operating. Short-Term Shear Loading Mechanism The short-term shearing mechanism was capable of moving the shear plate in a cyclic fashion with periods of approximately 3 minutes each. The load required to shear a pair of 144 in2 bearing pads made from an elastomer with 100 psi shear modulus to 50% strain is 12 kips. A safety factor of 1.3 was used in the design ca lculations of the system. For the short-term shearing mechanism the controlling factor was the hydraulic pressure rating of 3 ksi for the servo valve used to control the hydraulic cylinder rather than any other load requirements. In order to create the 12 kip shear load and operate at or below the 3 ksi pressure limit a 60 ton cylinder was incorporated into the design. Since the short-term loading system is idle for long periods of time, the section of the support frame housing the short-term loading system was made to be removable. The ability to remove the short-term loading system allows it to be used with multiple testing apparatuses if it

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61 became necessary. Figure 3-8 shows the 60 ton cylinder mounted and connected to the shear plate through a 30 ki p load cell. Instrumentation The test data was collected from two linear variable differential transformers (LVDTs), two potentiometers (POTs), three load cells, and a temperature sensor. Two POTs were used to measure the horizontal displacement of the shear plate and two LVDTs were used to monitor the vertical creep of the samples and the vertical rotation of the shear plate. Two load cells with a 30 kip capacity and were used to monitor shear fo rces during the short-te rm and long-term loading tests. Additionally the disconnect ed load cell signal was used as a baseline value to eliminate noise in the other two lo ad cell signals. The final load cell with a 300 kip capacity and was used to monitor the compressive load applied by the 400 ton cylinder. The temperature sensor was used for monitoring fluctuations in ambient temperature. Procedure The procedure used to run these tests started with placing the pa ds in the test apparatus. The pads were centered over the 400 ton cylinder w ith the shear plate between them and then the 400 ton cylinder was raised so that the top pad was within 0.1 inches of the top reaction plate. The LVDT sensors were then lowered to a point where they are partially compressed to establish the starting position of the shear pl ate vertically. The Labview progr am was then started to begin collecting data as soon as th e pads begin compressing. Compression It was initially thought that the counter weight system would be able to maintain a constant compressive stress during the stre ss relaxation of the pa ds but it was found that the 2/4 ton slave cylinder used for the compression system had a re latively high internal fr iction which prevented it from moving smoothly. Because of this high in ternal friction the compressive stress did not

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62 remain constant as stress relaxation occurred in the pads. This was accounted for by first over pressurizing the pads and then allowing them to rest prior to testing. The compressive stress reached the target pressure by the time the sample reached maximum shear strain. The increase in compressive stress was around 20% of the target value for each test with this being reduced to about 10% by the time the shear load was applie d. An example of the compressive stress load history is shown in Figure 3-9. A slight additional loss in compression was obs erved during the shearing of the samples. This additional loss is thought to be due to the samples not undergoing pure shear but instead undergoing mostly shear with some bending. Once the pads were brought up to the starti ng compressive load (20% higher than the target), the compressive hydrauli c system was closed and allowed to set for around 2.5 hours. Using a targeted compressive stress rather than strain was used since both AASHTO and FDOT place limits on stress rather than strain. Shearing The shear loading was displacement controlled a nd as such there were certain parts of the computer program that monitors the readings of the POTs to control how fast the shearing jacks reached 50% shear strain. Additionally, this feed back determined when the shearing jacks direction was to reverse. Thr oughout the testing, readings from the various sensors are recorded to a text file which can then be analyzed in a spreadsheet program. Temperature Factors Since all but one of the tests average temperat ures were within the allowable limits of the ASTM test[6] and based on the trend exhibited by Yakuts[42] data in conjunction with the reduced filler used in the samples the effect of temperature were expected to be negligible.

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63 Figure 3-1. Pad design for shape factor of 24 (1 inch pad or SF-24 pad) A B Figure 3-2. Bearing deformation. A) Ini tial pad. B) Shear strained to 50%.

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64 Figure 3-3. Test apparatus cross section Figure 3-4. Test apparatus photo

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65 Figure 3-5. Compression mechanism

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66 Figure 3-6. Hydraulic system diagram Figure 3-7. Long-term shear loading mechanism

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67 Figure 3-8. Short-term shear loading mechanism Figure 3-9. Compressive stress losses during SF 12, 1.5 ksi, 12 hour test

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68 Table 3-1. Sample physical dimensions Shape factor Layer thickness (in) Elastomer thickness (in) Steel gage & thickness (in) Number of neoprene layers Overall dimensions (in) 8 0.375 3.0 12 0.1050 8 12 x 12 x 3.735 12 0.250 2.0 15 0.0670 8 12 x 12 x 2.469 16 0.1875 1.5 16 0.0598 8 12 x 12 x 1.919 24 0.125 1.0 16 0.0598 8 12 x 12 x 1.419 Note The side cover for the steel in all of the pads is equal to 1/16th of an inch. Table 3-2. Testing matrix Duration / type Shear strain vs. time 50% strain max. Time from 0 to 50% shear strain 18 min / 2 way linear (6 cycle at 3 min each) (removing the Mullins effect) 45 seconds 24 hr / 2 way linear 12 hours 14 day / 2 way linear 7 days 90 day / linear 90 days Table 3-3. Testing matrix: duration variation Elastomer thickness (in) Shape factor Number of tests 45 seconds 12 hours 7 days 90 days 1 24 2 6 1.5 16 2 10* 2 2 2 12 2 5 3 8 2 7 1 1 A single test was conducted for 9.5 hrs and a single test was conducted at 7.2 hrs

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69 Table 3-4. Testing matrix: with a nd without Mullins effect removed Elastomer thickness (in) Shape factor Number of tests 45 seconds 12 hours 7 days 90 days w/ w/o w/ w/o w/ w/o w/ w/o 1 24 1 1 6 1.5 16 1 1 7* 3** 1 1 1 1 2 12 1 1 5 3 8 2 6 1 1 1 A single test was conducted for 9.5 hrs ** A single test was conducted for 7.2 hrs Table 3-5. Testing matrix: 12 hour compression variation Elastomer thickness (in) Shape factor Number of tests 0.5 ksi 1 ksi 1.2 ksi 1.5 ksi 1 24 3 2 1 1.5 16 3 6 1 2 12 1 1 2 3 8 1 4 2 Table 3-6. Cylinder combinations (b ased on 1.6 ksi compressive stress) Adv.Ret.Adv.Ret. Adv.Ret.Adv.Ret. 25010456.823.711.814056420.790.346.1313792.417.101 30010070.723.511.813258420.790.346.1311083.008.831 40013886.7929.9911.812655420.790.346.139033.6910.841 500169113.338.3711.812034420.790.346.136924.8114.152 600207132.645.7911.811738420.790.346.135915.6316.562 800263182.359.9911.811264420.790.346.134307.7422.783 1000370227.283.9711.811014420.790.346.133459.6528.384 Fluid needed for creep (in3) Travel for small cylinder (in) Number of strokes for refills Max cylinder cap. (tons) Cylinder eff. area (in2) Max cylinder cap. (tons) Cylinder eff. area (in2) High load cylinderLow load cylinder Line pressure (psi) Required weight (lbs) Stroke (in) Stroke (in)

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70 CHAPTER 4 TEST RESULTS This chapter provides sample data from th e test program, the methodology used to determine the shear modulus, and general results. A complete summary of all data is in Appendix A. Sample Data The displacement history from the 90 day test of the sample having a SF equal to 16 is shown in Figure 4-1. This test used a pair of bearing pads where each pads total elastomer thickness was 1.5 inches and as such a 50% shear strain was equivalent to 0.75 inch of shear displacement. This test was conducted using ap proximately a 1 ksi compressive stress. The corresponding recorded shear force history is shown in Figure 4-2. This history consists of the total force applied to the top and bottom pads. The force history for an individual pad would show half of the load in Figure 4-2. The histories shown in Figures 4-1 and 4-2 we re used to generate the strain and stress histories shown in Figure 4-3 a nd 4-4 respectively. The shear strain shown in Figure 4-3 is calculated by dividing the horizontal displacement by the original height of an individual pads total elastomer thickness, in this case 1.5 inches. The shear stress is calculated by dividing the total load by two and then dividing the result by the loaded area. Determination of Shear Modulus Figures 4-3 and 4-4 are combined to form Figure 4-5 which shows a shear stress-strain graph. In order to calculate a shear modulus si milar to the ASTM modulus as shown in Figure 2-3 a second order curve was fit to the ascending portion of the stress-strain graph. This curve overlaid onto the graph and the corresponding points used to calculate the shear modulus are

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71 shown in Figure 4-6. Using a second order cu rve eliminates the fluctuation observed in the stress-strain graphs. Calculating a shear modulus in the same ma nner as ASTM, i.e. the shear modulus is calculated by taking the secant modulus on the st ress-strain graph from the point of 2% of maximum stress to the point at 25% shear strain beyond this point, will be called the ASTM Method in this dissertation. The ASTM method shear modulus for the 90 day SF 16 test is 79.3 psi. An alternative method for calculating a shear modulus used by Yura et al[18, 23] is found using a secant modulus drawn through the origin (0 psi stress and 0% stra in) and the value of stress at 50% strain. For this study a similar method was examined with th e difference from previous studies is that instead of the origin used as a starting point, th e first point will be the same one used in the ASTM method shear modulus calculation; this is shown in Figure 4-6. The value for the shear modulus calculated this way is 75.1 psi. The average ratio of the shear modulus from the 50% method to the shear modulus from the ASTM me thod for the tests shown in Table 4-1 is 92% and there is only a 3.7% coefficien t of variation (COV) in this ratio. Since this is such a small COV this report will only be referring to the shear modulus from the ASTM method from this point on. The shear modulus using th e 50% method is 8% less than this. General Results A summary of the shear moduli from all of the tests is provided in Table 4-1. The values that are indicated as New Pad refer to pads that have not had the Mu llins effect removed. Additionally, the New Pad values for sec test s refer to the first cycle of the six cycle test.

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72 Figure 4-1. Displacement time history from 90 day test (SF = 16) Figure 4-2. Load time history from 90 day test (SF = 16)

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73 Figure 4-3. Strain history from 90 day test (SF = 16) Figure 4-4. Stress history fr om 90 day test (SF = 16)

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74 Figure 4-5. Stress-str ain history from 90 day test (SF = 16) Figure 4-6. ASTM method shear modul us from 90 day test (SF = 16)

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75 Table 4-1. Shear moduli result table Sample thickness (in) S F Duration Compression (ksi) New pad GASTM (psi) G50% (psi) G50% / GASTM (%) 1 24 45 sec 1 YES 102.7 90.1 87.8 1 24 45 sec 1 NO 95.5 85.4 89.3 1 24 12 hr 0.45 NO 87.2 75.5 86.6 1 24 12 hr 0.5 NO 85.8 75.2 87.6 1 24 12 hr 0.5 NO 85.1 74.7 87.8 1 24 12 hr 1 NO 83.3 77.3 92.8 1 24 12 hr 1 NO 85.2 74.9 88.0 1 24 12 hr 1.44 NO 82.0 74.8 91.2 1.5 16 45 sec 1 YES 101.0 87.6 86.7 1.5 16 45 sec 1 NO 91.5 84.3 92.1 1.5 16 7.2 hr 1.06 YES 95.4 88.0 92.2 1.5 16 9.5 hr 0.52 NO 93.8 83.2 88.7 1.5 16 12 hr 0.47 NO 93.0 81.9 88.1 1.5 16 12 hr 0.5 NO 93.8 82.6 88.1 1.5 16 12 hr 1 YES 98.0 90.1 91.9 1.5 16 12 hr 1 NO 79.9 75.6 94.6 1.5 16 12 hr 1 NO 84.1 80.6 95.8 1.5 16 12 hr 1 NO 82.8 74.8 90.4 1.5 16 12 hr 1.01 YES 96.2 89.2 92.8 1.5 16 12 hr 1.53 NO 86.3 80.3 93.0 1.5 16 7 day 1 YES 89.4 82.6 92.4 1.5 16 7 day 1 NO 81.3 77.1 94.9 1.5 16 90 day 1 YES 89.8 82.3 91.6 1.5 16 90 day 1.1 NO 79.3 75.1 94.8 2 12 45 sec 1 YES 97.3 85.1 87.5 2 12 45 sec 1 NO 85.7 79.5 92.7 2 12 12 hr 0.5 NO 84.7 74.5 88.0 2 12 12 hr 1 NO 78.1 73.7 94.4 2 12 12 hr 1 NO 76.9 69.2 90.0 2 12 12 hr 1.5 NO 68.0 62.1 91.3 2 12 12 hr 1.53 NO 70.2 65.4 93.0 3 8 45 sec 1 NO 69.5 68.9 99.1 3 8 45 sec 1 NO 66.9 65.6 98.0 3 8 12 hr 0.5 NO 77.2 68.1 88.2 3 8 12 hr 0.92 NO 65.7 62.6 95.3 3 8 12 hr 0.98 NO 74.8 71.6 95.7 3 8 12 hr 1 NO 73.4 71.2 97.0 3 8 12 hr 1.08 YES 77.0 71.1 92.4 3 8 12 hr 1.2 NO 61.6 58.6 95.1 3 8 12 hr 1.23 NO 57.5 53.0 92.1 3 8 7 day 1.08 YES 75.6 71.1 94.0 3 8 90 day 1 YES 77.8 73.0 93.9

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76 CHAPTER 5 DISCUSSION OF RESULTS This chapter covers variations in shear m odulus with respect to short term product qualification loading and short term field loadi ng (i.e. 50% strain in 45 seconds vs. 12 hours); short term field loading and long term field load ing (i.e. 50% strain in 12 hours up to 90 days); the number of loading cycles (i.e. pre and post Mu llins effect removal); and finally, the variation of shear modulus with compressive stress. Variations in Shear Modulus Initial Change due to Strain Rate The ASTM 4014 ANNEX-A[6] product qualification test fo r shear modulus requires the use of a strain rate in the range of 50% strain within 30 to 60 s econds and with the shear modulus determined using data gathered after the Mullins effect has been removed. Figure 5-1 shows the shear moduli for all of the shape factors tested at 1 ksi compressive stress (with the Mullins effect removed) having strain rates of 50% shear strain in 45 seconds and in 12 hours. The strain rate of 50% strain in 12 hours is representative of the quickest rate that pads would experience in the field. Table 5-1 shows that a shear modulus found us ing the rapid strain rates in ASTM 4014 ANNEX-A [6] should be reduced by about 7% to account for the lower in strain rate seen in the field. Changes due to Short Term Field Loading vs. Long Term Field Loading Figure 5-2 shows the change in shear modulus over longer durations (i.e. slower) strain rates. This figure also includes shear moduli calculated using samples that have not had the Mullins effect removed prior to testing. The trends in this figure indicate that at strain rates at or below 50% in 0.5 days (12 hours) there is no si gnificant change in th e shear modulus. The

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77 change recorded was a maximum of 7.5% from 0.5 days to 90 days and a maximum of 3.7% from 7 days to 90 days. Changes due to the Number of Loading Cycles The change due to of the Mullins effect is summarized in Table 5-2. This table indicates that for shear moduli calculated using the ASTM method (defined in Chapter 4) are on average 12% higher prior to the removal of the Mullins effect for 50 durometer harness material. This indicates that new pads in the field would be st iffer than expected since they would not have experienced cycling prior to installation. Some samples were tested repeatedly under the identical conditions after being allowed to rest. Table 5-3 shows that the stiffness eliminated by cycling does not appear to recover with time. Changes due to the Compressive Stress The effect of compression on shear modulus is shown in Figure 5-3. All of the shear moduli in Figure 5-3 are only for tests that had a strain rate of 50% over 12 hours. Figure 5-3 also shows trend lines based on to a least-er ror-squared fit to the moduli using a linear relationship between shear modulus and compressi ve stress. A linear re lationship was chosen because Muscarella and Yuras model (Equation 2-14) indicated that the relationship between compressive stress and effective shear modulus was linear. ASTM 4014 ANNEX-A [6] does not specify a compression stress and it requires that the samples are bonded to the reaction pl ates as well as the shear plat es. This, in conjunction with the lack of a compression component in Figure 2-4, seems to indicate that no compression stress should be used during this type of testing. Due to this implication the trend lines in Figure 5-3 were extended through a point on the graph of 0 ksi compression in order to predict what the average moduli of each shape factor would have been if the test was conducted without the use of compression.

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78 ASTM 4014 ANNEX-A[6] specifies a rate of strain such that straining from 0 to 50% is over 30 to 60 seconds. In order to compare the average of the intercepts in Figure 5-3 to the range of values found in the FDOT specifications[3] the intercepts average needed to be adjusted for the increased strain rate. This was accomp lished by multiplying the average intercept value by the inverse of the average ratio of 12 hour test results to 45 second test results (the Mean found in Table 5-1, i.e. 1/93.3%). This strain rate corrected value is shown in Equation 5-1. Recalling that the range of shear modulus for 50 durometer hardness neoprene in the FDOT Specifications[3] is 85 psi to 110 psi, it se ems that if these samples had been tested under no compression as in ASTM 4014[6] they would have been certified acceptable. Mean G G0 sec45 (5-1) psi psi G 7.98 933.0 6.91sec45 Table 5-4 shows the predicted values of effective shear modulus based on compressive stress using Equation 2-14 shown ag ain below. These calculated values are based on the average shear modulus under no compression (Figure 5-3). Only tests longer th an 45sec and with the Mullins effect removed were included in Table 54 to remove those contributions to the shear moduli. 1 2 01 12 1 2 rt s r s effhA If A PGG (2-14) where is the total bearing thickness (including steel) divided by total elastomer thickness hrt As is the shear area of bearing fr is the ending stiffness coefficient = 1.0 + 0.575 S2 G0 is the shear modulus of th e elastomer under no compression Geff is the shear modulus under compression I is the moment of inertia hrt is the total elastomer thickness

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79 Figure 5-4 shows the trends from the value pr edicted by Muscarella and Yuras model and the measured values from Table 5-4. The trends in Figure 5-4 are very similar to those found in Figure 5-3 showing this is a good model. Temperature The temperatures fluctuated during some tests, however, all but one test had the average temperature within the ASTM test accepted range. Equation 2-14 was use to calculate the values of the shear moduli at no compressive stress in or der to verify that temp erature had no effect on the shear modulus results of all of the shear m oduli. After correcting th em further for duration and the Mullins effect, the results were plotted in Figure 5-5. Figure 5-5 s hows that the values of the shear moduli had no noticeable trend with respect with temperature. Final Analysis of Strain Rate Based on Muscarella and Yuras[23] model and the analysis of the Mullins effect, a prediction can be made for the re sults of all of the tests if they had been conducted under no compression and had been cycled sufficiently to remove the Mullins effect. This calculation is performed by dividing the value of the shear moduli that did not have the Mullins effect removed by the average of the ratio of pre-removal to post-removal shear moduli, i.e. 1.12 for 50 durometer hardness material. Adjusting the shear modulus values with Mullins removed to a zero compression test state is accomplished with the use of Muscarella and Yuras model. This is accomplished by adding the reduction in shear moduli the model predicts for the compression under which each test was conducted to the resu lting shear moduli. An example of these calculations is shown in Equations 5-2 and 5-3 for the test of a new pad with a shape factor of 16 under a compressive load of 144 kips with a measured shear modulus of 89.8 psi. 12.16 mea thG G (Mullins effect adjustment) (5-2)

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80 12.1 8.896psi Gth psi Gth2.806 cr adjP P G Gth16 (Compression loading adjustment) (5-3) kip Pcr009,2 (From Equation 2-11) kip kip psi Gadj009,2 144 1 2.80 psi Gadj4.86 (Predicted post-cycled 0 ksi compression test result) With all of the data collected adjusted in this manner, a clear trend can be seen in the relationship between shear modulus and strain rate. The data resu lting from these calculations is shown in Figure 5-6. It is important to note that these pr edictions conform to the ASTM standard testing method in compression a nd the removal of the Mullins effect. From Figure 5-6 it can be seen more clearly th at for stain rates that conform to highway bridge applications there is no substantial cha nge in the shear modulus with strain rate. Additionally the only substa ntial change is approximately 7% change in shear modulus from the ASTM strain rate to the typical highway applicati on stain rates. The form of the fitted trend line reflects an elastic structure w ithin the neoprene samples combined with a viscous component which decays exponentially with decreasing strain rate. The trend eventually stabilizes around the elastic modulus value of th e internal elastic structure. Because of the negligible change in the shear modulus over the strain rates seen in the field is was not necessary to use one of the more comp licated models encountered in the course of the literature review into this subjec t. However during the research program attempts were made to make use of these models. This was ultimately un able to be accomplished because of the lack of

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81 change in the shear modulus for di fferent strain rates which led to the inability to accurately fit all of the coefficients necessary in these models. Summary The theory that neoprene softens as strain ra te is reduced is gene rally supported by the trends shown in Figure 5-1 and Figure 5-6. Ho wever, research found in the literature review[2940] and the trend shown in Figure 5-6 indicate that there is a lower limit to this reduction in stiffness. The shear modulus found using ASTM 4014 ANNEX-A[6] uses a strain rate of 50% strain over 30 to 60 seconds, which makes the reported modulus approximately 7% higher compared to the modulus resulting fro m field strain rate conditions. This increase in reported shear modulus is offs et by the fact that new pads in the field do not typically have the Mullins effect removed as is required in ASTM testing. This results in a 12% decrease in the reported results in the AS TM testing for shear modulus for 50 durometer hardness material. The net effect is that for the sa me material new pads in the field are 5% stiffer than what would be expected based on ASTM tests. Table 5-4 shows a correlation between observed shear modu li and the value predicted using Muscarella and Yuras model (Equation 2-14). These values fall within the % range of error allowed by ASTM[6] making the model a valid predicto r of bearing shear behavior under compression. The range of values for shear modulus found in the FDOT Specifications[3] and AASHTO[2] for 50 durometer hardness neoprene cover a spread of .5 psi and .5 psi respectively from the average values In addition to this, the ASTM[6] standard and FDOT Specifications[3] allow a variation of % of the targ et shear modulus in verifying the shear modulus of a sample. All of this adds to the un certainty of the actual sh ear modulus of a pad in

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82 the field. This uncertainty along with the addi tion of the effect of co mpression encompasses all the variations observed in this study. Because the shear modulus seems to stabilize at durations above 12 hours it is recommended that tests for beari ng pads be conducted using a cons tant strain rate of 50 percent over a 12 hour duration. It is also recommended that these tests be conducted without the Mullins effect being removed first to find the stiffness that is initially present in the field, as well as conducting a 12 hour test after the Mullins effect is removed to find the final stiffness seen after repeated cycling of long term use. A dditionally, it is recommended that the tests be conducted at the expected service dead load and using the appropriate sh ape factor and number of layers because of the influence of compressive stress on the shear modulus. The original contribution of this research is the conclusion that the shear stiffness or effective shear modulus of steel reinforced neopre ne bearing pads is esse ntially a constant value for the strain rates occurring in highway applications. The only observed change in shear modulus due to strain rate, was the approximately 7% drop as the strain rate changed from that used in ASTM standard testing to the strain rate s in typical highway appl ications. Additionally it was observed that the shear modulus reported us ing ASTM test procedures under estimates the shear modulus that would be present in a new pad by approximately 12% for 50 durometer hardness material due to the rem oval of a component of the origin al stiffness by repeated cycling of the material samples. Finally, the Yura and Muscarella[23] model to account for the compression contribution to the reduction in effective shear modulus provided an excellent description for the behavior observed in fl at steel reinforced neoprene bearings.

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83 0.0 10.0 20.0 30.0 40.0 50.0 60.0 70.0 80.0 90.0 100.0 0.001 0.01 0.1 1 10 100 Time (hr)Shear Modulus (psi) Figure 5-1. Mullins removed shear moduli (45 sec and 12 hr) of 1 ksi compression tests 0 10 20 30 40 50 60 70 80 90 100 0.1110100 Time (day)Shear Modulus (psi) 1.5 in (SF 16) New Pad 1.5 in (SF 16) New Pad 3 in (SF 8) Figure 5-2. Long-term modulus change with duration

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84 0.0 10.0 20.0 30.0 40.0 50.0 60.0 70.0 80.0 90.0 100.0 00.250.50.7511.251.51.75 Compressive Stress (ksi)Shear Modulus (psi) Intercepts 1 in (SF 24) 88.1 psi 1.5 in (SF 16) 95.1 psi 2 in (SF 12) 92.6 psi 3 in (SF 8) 90.5 psi Average 91.6 psi Figure 5-3. ASTM method 12 hr shear moduli vs. compression 0 10 20 30 40 50 60 70 80 90 100 00.250.50.7511.251.51.75 Compressive Stress (ksi)Effective Shear Modulus (psi) Figure 5-4. Shear moduli vs. compression with predicted by Yura and Muscarella[23]

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85 0.0 20.0 40.0 60.0 80.0 100.0 120.0 60657075808590 Temperature (oF)Shear modulus (psi) Figure 5-5. Shear modulus vs. temperature 0 20 40 60 80 100 120 0.00010.0010.010.1110100 Time to 50% Strain (day)Shear Modulus (psi) G=90.5+6.94e(-4.10t) Figure 5-6. Strain rate data summary

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86 Table 5-1. Initial shear modulus change due to reduced strain rate SF GASTM (psi) Average GASTM (psi) 12 hr / 45 sec G (%) 45 sec 12 hr 45 sec 12 hr 24 95.5 85.2 95.5 84.2 88.2 83.3 16 91.5 79.9 91.5 82.3 90.0 84.1 82.8 12 85.7 78.1 85.7 77.5 90.4 76.9 8 66.9 65.7 68.2 71.3 104.6 69.5 73.4 74.8 Mean 93.3 Change 6.7 Standard deviation 7.59 COV 8.14 Table 5-2. Mullins effect change Duration SF G (psi) G (psi) Average change (%) Mullins removed Average Mullins removed w/o w/ w/o w/ 45 sec 24 102.7 95.5 102.7 95.5 107 16 101.0 91.5 101.0 91.5 110 12 97.3 85.7 97.3 85.7 113 12 hr 8 77.0 74.8 77.0 71.3 108 8 73.4 8 65.7 16 98.0 79.9 97.1 82.3 118 16 96.2 84.1 16 82.8 7 day 16 89.4 81.3 89.4 81.3 110 90 day 16 89.8 79.3 89.8 79.3 113 Mean 112 Standard deviation 3.69 COV 3.31

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87 Table 5-3. Recovery of Mullins effect with time Date Sample thickness (in) G (psi) Days from previous test Change (%) 1/9/2007 1 83.3 11/18/2007 1 85.2 313 2.2 1/16/2007 1.5 79.9 2/1/2007 1.5 84.1 16 5.2 11/20/2007 1.5 82.8 292 -1.6 1/6/2007 2 78.1 11/14/2007 2 76.9 312 -1.5 12/29/2006 3 74.8 1/4/2007 3 73.4 6 -1.9 Mean 0.5 Standard deviation 3.1 COV 624 Table 5-4. Predicted compression adju sted shear modulus vs. measures SF (ksi) Geff (psi) G measured (psi) Geff / Gmeas 24 0.45 90 87.2 1.04 24 0.5 90 85.8 1.05 24 0.5 90 85.1 1.06 24 1 89 85.2 1.04 24 1 89 83.3 1.06 24 1.44 87 82.0 1.07 16 0.52 88 93.8 0.94 16 0.47 89 93 0.95 16 0.5 88 93.8 0.94 16 1 85 79.9 1.06 16 1 85 84.1 1.01 16 1 85 82.8 1.03 16 1.53 82 86.3 0.94 16 1 85 81.3 1.05 16 1.1 84 79.3 1.06 12 0.5 86 84.7 1.01 12 1 80 78.1 1.02 12 1 80 76.9 1.04 12 1.5 74 68.0 1.09 12 1.53 74 70.2 1.05 8 0.5 78 77.2 1.02 8 0.92 67 65.7 1.03 8 0.98 66 74.8 0.88 8 1 65 73.4 0.89 8 1.2 60 61.6 0.97 8 1.23 59 57.5 1.03 Mean 1.01 Standard Deviation 0.06 COV 6%

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88 CHAPTER 6 CONCLUSION The objective of this project was to evaluate the interaction between the shear m odulus of steel reinforced neoprene beari ng pads and shear strain rates of highway applications. The following interactions related to variations in th e shear modulus were investigated for pads with various shape factors: Short term product qualification load ing vs. short term field loading Short term field loading vs long term field loading Number of loading cycles Effects of compressive stress Forty-two tests were performed using test equipment designed to apply a shear strain at a variety of rates while applying a sustained co mpressive load. Test results indicated: There was an average 7% reduction in the shear modulus when it was observed at the strain rates typically seen in highway applications as opposed to shear moduli found using strain rates in the range required by ASTM D4014. There was a maximum of 7.5% reduction in sh ear modulus when comparing the higher shear modulus found using short term field loading (50% strain in 12 hours) to the shear modulus found using long term field loadi ng (50% strain in 90 days). However, on average for typical highway application strain rates there is no significant change in the shear modulus. The shear modulus for new pads in the field that have not been subjected to repeated load cycles (i.e., removal of the Mu llins effect) are approximately 12% for 50 durometer hardness material higher than the same pads after load cycling. In elastomeric bearings as compression increases, within the limit of AASHTO specifications, the shear modulus reduces, par ticularly for bearing pads with low shape factors. The trends seen seem to confor m to previous work by Muscarella and Yura[23] with flat bearings within the % range allowed by ASTM[6]. Based on the results of the forty-two tests conducted in this study, it is recommended that upper and lower tolerance values for the shear modulus be used for calculations instead of a single value. The limits in ASTM D 4014 are % of the specified shear modulus. However,

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89 the upper value of this range should be increased by 5% to account for the net effect of the lack of cycling (+12%) and the reduced strain rates (-7%) in the field. Since the cycling effect will eventually dissipate, the lower va lue of this range should be reduced by 7%. This results in values that are +20% and -22% of a specified shear modulus. To simplify calculations, the recommendation is to use % of a specified shear modulus. For example, neoprene with a specified shear modulus of 100 psi, with tolerance values defined by ASTM of 85 to 115 psi, should actually be considered to be both 80 a nd 120 psi in calculations with no compression. Adjustments for compression should be in accordance with Equation 2-14 from Muscarella and Yura[23]. The implication of these recommendations for a design engineer would mean that instead of one calculation based on the shea r stiffness of the bearings th ere would be a minimum of two separate calculations, one for both the high and the low value of the range of shear moduli. Additionally, if a designer chooses multiple pads with smaller shape factors instead of one pad with a large shape factor, us ing the effect of shear modulus reduction due to compression (Equation 2-14) may result in smaller calculated fo rces than previously considered. The end result of these lower forces could be construction cost savings.

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90 APPENDIX A RESEARCH DATA 048121620 10 0 10 Load vs. TimeTime (min)Load (kip)P t 048121620 0.6 0.2 0.2 0.6 Displacement vs. TimeTime (min)Displacement (in) t 0.6 0.4 0.200.20.40.6 10 0 10 Load vs. DisplacementDisplacement (in)Load (kip)P 60 40 200204060 40 20 0 20 40 Stress vs. StrainStrain (percent)Stress (psi) Figure A-1. Shape factor 24, 1.0 ksi compre ssion, 45 second test new pad (start) data

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91 048121620 10 0 10 Load vs. TimeTime (min)Load (kip)P t 048121620 0.6 0.2 0.2 0.6 Displacement vs. TimeTime (min)Displacement (in) t 0.6 0.4 0.200.20.40.6 10 0 10 Load vs. DisplacementDisplacement (in)Load (kip)P 60 40 200204060 40 20 0 20 40 Stress vs. StrainStrain (percent)Stress (psi) Figure A-2 Shape factor 24, 1.0 ksi co mpression, 45 second test (end) data

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92 0510152025 0 5 10 15 Load vs. TimeTime (hr)Load (kip)P t 0510152025 0 0.2 0.4 0.6 Displacement vs. TimeTime (hr)Displacement (in) t 00.10.20.30.40.50.6 0 5 10 15 Load vs. DisplacementDisplacement (in)Load (kip)P 0102030405060 0 10 20 30 40 50 Stress vs. StrainStrain (percent)Stress (psi) Figure A-3. Shape factor 24, 0.5 ks i compression, 12 hour test 1 data

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93 0510152025 0 5 10 15 Load vs. TimeTime (hr)Load (kip)P t 0510152025 0 0.2 0.4 0.6 Displacement vs. TimeTime (hr)Displacement (in) t 00.10.20.30.40.50.6 0 5 10 15 Load vs. DisplacementDisplacement (in)Load (kip)P 0102030405060 0 10 20 30 40 50 Stress vs. StrainStrain (percent)Stress (psi) Figure A-4. Shape factor 24, 0.5 ksi compression, 12 hour test 2 data. The st ress at 50% shear strain was calculated from a 2nd order curve fit on the asce nding portion of the graph.

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94 0510152025 0 5 10 15 Load vs. TimeTime (hr)Load (kip)P t 0510152025 0 0.2 0.4 0.6 Displacement vs. TimeTime (hr)Displacement (in) t 00.10.20.30.40.50.6 0 5 10 15 Load vs. DisplacementDisplacement (in)Load (kip)P 0102030405060 0 10 20 30 40 50 Stress vs. StrainStrain (percent)Stress (psi) Figure A-5. Shape factor 24, 0.5 ks i compression, 12 hour test 3 data

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95 0510152025 0 5 10 15 Load vs. TimeTime (hr)Load (kip)P t 0510152025 0 0.2 0.4 0.6 Displacement vs. TimeTime (hr)Displacement (in) t 00.10.20.30.40.50.6 0 5 10 15 Load vs. DisplacementDisplacement (in)Load (kip)P 0102030405060 0 10 20 30 40 50 Stress vs. StrainStrain (percent)Stress (psi) Figure A-6. Shape factor 24, 1.0 ks i compression, 12 hour test 1 data

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96 0510152025 0 5 10 15 Load vs. TimeTime (hr)Load (kip)P t 0510152025 0 0.2 0.4 0.6 Displacement vs. TimeTime (hr)Displacement (in) t 00.10.20.30.40.50.6 0 5 10 15 Load vs. DisplacementDisplacement (in)Load (kip)P 0102030405060 0 10 20 30 40 50 Stress vs. StrainStrain (percent)Stress (psi) Figure A-7. Shape factor 24, 1.0 ksi compression, 12 hour test 2 data. : The stress at 50% shear strain was calculated from a 2nd order curve fit on the asce nding portion of the graph.

PAGE 97

97 0510152025 0 5 10 15 Load vs. TimeTime (hr)Load (kip)P t 0510152025 0 0.2 0.4 0.6 Displacement vs. TimeTime (hr)Displacement (in) t 00.10.20.30.40.50.6 0 5 10 15 Load vs. DisplacementDisplacement (in)Load (kip)P 0102030405060 0 10 20 30 40 50 Stress vs. StrainStrain (percent)Stress (psi) Figure A-8. Shape factor 24, 1.4 ksi compression, 12 hour test data

PAGE 98

98 048121620 10 0 10 Load vs. TimeTime (min)Load (kip)P t 048121620 0.9 0.3 0.3 0.9 Displacement vs. TimeTime (min)Displacement (in) t 0.9 0.6 0.300.30.60.9 10 0 10 Load vs. DisplacementDisplacement (in)Load (kip)P 60 40 200204060 40 20 0 20 40 Stress vs. StrainStrain (percent)Stress (psi) Figure A-9. Shape factor 16, 1.0 ksi compre ssion, 45 second test new pad (start) data

PAGE 99

99 048121620 10 0 10 Load vs. TimeTime (min)Load (kip)P t 048121620 0.9 0.3 0.3 0.9 Displacement vs. TimeTime (min)Displacement (in) t 0.9 0.6 0.300.30.60.9 10 0 10 Load vs. DisplacementDisplacement (in)Load (kip)P 60 40 200204060 40 20 0 20 40 Stress vs. StrainStrain (percent)Stress (psi) Figure A-10. Shape factor 16, 1.0 ksi co mpression, 45 second test (end) data

PAGE 100

100 0510152025 0 5 10 15 Load vs. TimeTime (day)Load (kip)P t 0510152025 0 0.3 0.6 0.9 Displacement vs. TimeTime (day)Displacement (in) t 00.150.30.450.60.750.9 0 5 10 15 Load vs. DisplacementDisplacement (in)Load (kip)P 0102030405060 0 10 20 30 40 50 Stress vs. StrainStrain (percent)Stress (psi) Figure A-11. Shape factor 16, 1.1 ksi co mpression, 7.2 hour test new pad data

PAGE 101

101 0510152025 0 5 10 15 Load vs. TimeTime (hr)Load (kip)P t 0510152025 0 0.3 0.6 0.9 Displacement vs. TimeTime (hr)Displacement (in) t 00.10.20.30.40.50.6 0 5 10 15 Load vs. DisplacementDisplacement (in)Load (kip)P 0102030405060 0 10 20 30 40 50 Stress vs. StrainStrain (percent)Stress (psi) Figure A-12. Shape factor 16, 0.5 ks i compression, 9.5 hour test data

PAGE 102

102 0510152025 0 5 10 15 Load vs. TimeTime (hr)Load (kip)P t 0510152025 0 0.3 0.6 0.9 Displacement vs. TimeTime (hr)Displacement (in) t 00.150.30.450.60.750.9 0 5 10 15 Load vs. DisplacementDisplacement (in)Load (kip)P 0102030405060 0 10 20 30 40 50 Stress vs. StrainStrain (percent)Stress (psi) Figure A-13. Shape factor 16, 0.5 ks i compression, 12 hour test 1 data

PAGE 103

103 0510152025 0 5 10 15 Load vs. TimeTime (hr)Load (kip)P t 0510152025 0 0.3 0.6 0.9 Displacement vs. TimeTime (hr)Displacement (in) t 00.150.30.450.60.750.9 0 5 10 15 Load vs. DisplacementDisplacement (in)Load (kip)P 0102030405060 0 10 20 30 40 50 Stress vs. StrainStrain (percent)Stress (psi) Figure A-14. Shape factor 16, 0.5 ks i compression, 12 hour test 2 data

PAGE 104

104 0510152025 0 5 10 15 Load vs. TimeTime (day)Load (kip)P t 0510152025 0 0.3 0.6 0.9 Displacement vs. TimeTime (day)Displacement (in) t 00.150.30.450.60.750.9 0 5 10 15 Load vs. DisplacementDisplacement (in)Load (kip)P 0102030405060 0 10 20 30 40 50 Stress vs. StrainStrain (percent)Stress (psi) Figure A-15. Shape factor 16, 1.0 ksi co mpression, 12 hour test 1 new pad data

PAGE 105

105 0510152025 0 5 10 15 Load vs. TimeTime (hr)Load (kip)P t 0510152025 0 0.3 0.6 0.9 Displacement vs. TimeTime (hr)Displacement (in) t 00.150.30.450.60.750.9 0 5 10 15 Load vs. DisplacementDisplacement (in)Load (kip)P 0102030405060 0 10 20 30 40 50 Stress vs. StrainStrain (percent)Stress (psi) Figure A-16. Shape factor 16, 1.0 ks i compression, 12 hour test 1 data

PAGE 106

106 0510152025 0 5 10 15 Load vs. TimeTime (hr)Load (kip)P t 0510152025 0 0.3 0.6 0.9 Displacement vs. TimeTime (hr)Displacement (in) t 00.150.30.450.60.750.9 0 5 10 15 Load vs. DisplacementDisplacement (in)Load (kip)P 0102030405060 0 10 20 30 40 50 Stress vs. StrainStrain (percent)Stress (psi) Figure A-17. Shape factor 16, 1.0 ks i compression, 12 hour test 2 data

PAGE 107

107 0510152025 0 5 10 15 Load vs. TimeTime (hr)Load (kip)P t 0510152025 0 0.3 0.6 0.9 Displacement vs. TimeTime (hr)Displacement (in) t 00.150.30.450.60.750.9 0 5 10 15 Load vs. DisplacementDisplacement (in)Load (kip)P 0102030405060 0 10 20 30 40 50 Stress vs. StrainStrain (percent)Stress (psi) Figure A-18. Shape factor 16, 1.0 ks i compression, 12 hour test 3 data

PAGE 108

108 0510152025 0 5 10 15 Load vs. TimeTime (day)Load (kip)P t 0510152025 0 0.3 0.6 0.9 Displacement vs. TimeTime (day)Displacement (in) t 00.150.30.450.60.750.9 0 5 10 15 Load vs. DisplacementDisplacement (in)Load (kip)P 0102030405060 0 10 20 30 40 50 Stress vs. StrainStrain (percent)Stress (psi) Figure A-19. Shape factor 16, 1.0 ksi co mpression, 12 hour test 2 new pad data

PAGE 109

109 0510152025 0 5 10 15 Load vs. TimeTime (hr)Load (kip)P t 0510152025 0 0.3 0.6 0.9 Displacement vs. TimeTime (hr)Displacement (in) t 00.150.30.450.60.750.9 0 5 10 15 Load vs. DisplacementDisplacement (in)Load (kip)P 0102030405060 0 10 20 30 40 50 Stress vs. StrainStrain (percent)Stress (psi) Figure A-20. Shape factor 16, 1.5 ksi compression, 12 hour test data

PAGE 110

110 02.85.68.411.214 0 5 10 15 Load vs. TimeTime (day)Load (kip)P t 02.85.68.411.214 0 0.3 0.6 0.9 Displacement vs. TimeTime (day)Displacement (in) t 00.150.30.450.60.750.9 0 5 10 15 Load vs. DisplacementDisplacement (in)Load (kip)P 0102030405060 0 10 20 30 40 50 Stress vs. StrainStrain (percent)Stress (psi) Figure A-21. Shape factor 16, 1.0 ksi compression, 7 day test new pad data

PAGE 111

111 02.85.68.411.214 0 5 10 15 Load vs. TimeTime (day)Load (kip)P t 02.85.68.411.214 0 0.3 0.6 0.9 Displacement vs. TimeTime (day)Displacement (in) t 00.150.30.450.60.750.9 0 5 10 15 Load vs. DisplacementDisplacement (in)Load (kip)P 0102030405060 0 10 20 30 40 50 Stress vs. StrainStrain (percent)Stress (psi) Figure A-22. Shape factor 16, 1.0 ksi compression, 7 day test data

PAGE 112

112 01836547290 0 5 10 15 Load vs. TimeTime (day)Load (kip)P t 01836547290 0 0.3 0.6 0.9 Displacement vs. TimeTime (day)Displacement (in) t 00.150.30.450.60.750.9 0 5 10 15 Load vs. DisplacementDisplacement (in)Load (kip)P 0102030405060 0 10 20 30 40 50 Stress vs. StrainStrain (percent)Stress (psi) Figure A-23. Shape factor 16, 1.0 ksi compression, 90 day test new pad data

PAGE 113

113 01938577695 0 5 10 15 Load vs. TimeTime (day)Load (kip)P t 01938577695 0 0.3 0.6 0.9 Displacement vs. TimeTime (day)Displacement (in) t 00.150.30.450.60.750.9 0 5 10 15 Load vs. DisplacementDisplacement (in)Load (kip)P 0102030405060 0 10 20 30 40 50 Stress vs. StrainStrain (percent)Stress (psi) Figure A-24. Shape factor 16, 1.1 ksi compression, 90 day test data

PAGE 114

114 048121620 10 0 10 Load vs. TimeTime (min)Load (kip)P t 048121620 1.2 0.4 0.4 1.2 Displacement vs. TimeTime (min)Displacement (in) t 1.2 0.8 0.400.40.81.2 10 0 10 Load vs. DisplacementDisplacement (in)Load (kip)P 60 40 200204060 40 20 0 20 40 Stress vs. StrainStrain (percent)Stress (psi) Figure A-25. Shape factor 12, 1.0 ksi compre ssion, 45 second test new pad (start) data

PAGE 115

115 048121620 10 0 10 Load vs. TimeTime (min)Load (kip)P t 048121620 1.2 0.4 0.4 1.2 Displacement vs. TimeTime (min)Displacement (in) t 1.2 0.8 0.400.40.81.2 10 0 10 Load vs. DisplacementDisplacement (in)Load (kip)P 60 40 200204060 40 20 0 20 40 Stress vs. StrainStrain (percent)Stress (psi) Figure A-26. Shape factor 12, 1.0 ksi co mpression, 45 second test (end) data

PAGE 116

116 0510152025 0 5 10 15 Load vs. TimeTime (hr)Load (kip)P t 0510152025 0 0.4 0.8 1.2 Displacement vs. TimeTime (hr)Displacement (in) t 00.20.40.60.811.2 0 5 10 15 Load vs. DisplacementDisplacement (in)Load (kip)P 0102030405060 0 10 20 30 40 50 Stress vs. StrainStrain (percent)Stress (psi) Figure A-27. Shape factor 12, 0.5 ks i compression, 12 hour test 1 data

PAGE 117

117 0510152025 0 5 10 15 Load vs. TimeTime (hr)Load (kip)P t 0510152025 0 0.4 0.8 1.2 Displacement vs. TimeTime (hr)Displacement (in) t 00.20.40.60.811.2 0 5 10 15 Load vs. DisplacementDisplacement (in)Load (kip)P 0102030405060 0 10 20 30 40 50 Stress vs. StrainStrain (percent)Stress (psi) Figure A-28. Shape factor 12, 1.0 ks i compression, 12 hour test 1 data

PAGE 118

118 0510152025 0 5 10 15 Load vs. TimeTime (hr)Load (kip)P t 0510152025 0 0.4 0.8 1.2 Displacement vs. TimeTime (hr)Displacement (in) t 00.20.40.60.811.2 0 5 10 15 Load vs. DisplacementDisplacement (in)Load (kip)P 0102030405060 0 10 20 30 40 50 Stress vs. StrainStrain (percent)Stress (psi) Figure A-29. Shape factor 12, 1.0 ks i compression, 12 hour test 2 data

PAGE 119

119 0510152025 0 5 10 15 Load vs. TimeTime (hr)Load (kip)P t 0510152025 0 0.4 0.8 1.2 Displacement vs. TimeTime (hr)Displacement (in) t 00.20.40.60.811.2 0 5 10 15 Load vs. DisplacementDisplacement (in)Load (kip)P 0102030405060 0 10 20 30 40 50 Stress vs. StrainStrain (percent)Stress (psi) Figure A-30. Shape factor 12, 1.5 ks i compression, 12 hour test 1 data

PAGE 120

120 0510152025 0 5 10 15 Load vs. TimeTime (hr)Load (kip)P t 0510152025 0 0.4 0.8 1.2 Displacement vs. TimeTime (hr)Displacement (in) t 00.20.40.60.811.2 0 5 10 15 Load vs. DisplacementDisplacement (in)Load (kip)P 0102030405060 0 10 20 30 40 50 Stress vs. StrainStrain (percent)Stress (psi) Figure A-31. Shape factor 12, 1.5 ks i compression, 12 hour test 2 data

PAGE 121

121 048121620 10 0 10 Load vs. TimeTime (min)Load (kip)P t 048121620 1.8 0.6 0.6 1.8 Displacement vs. TimeTime (min)Displacement (in) t 1.8 1.2 0.600.61.21.8 10 0 10 Load vs. DisplacementDisplacement (in)Load (kip)P 60 40 200204060 40 20 0 20 40 Stress vs. StrainStrain (percent)Stress (psi) Figure A-32. Shape factor 8, 1.0 ksi co mpression, 45 second test 1 (end) data

PAGE 122

122 048121620 10 0 10 Load vs. TimeTime (min)Load (kip)P t 048121620 1.8 0.6 0.6 1.8 Displacement vs. TimeTime (min)Displacement (in) t 1.8 1.2 0.600.61.21.8 10 0 10 Load vs. DisplacementDisplacement (in)Load (kip)P 60 40 200204060 40 20 0 20 40 Stress vs. StrainStrain (percent)Stress (psi) Figure A-33. Shape factor 8, 1.0 ksi co mpression, 45 second test 2 (end) data

PAGE 123

123 0510152025 0 5 10 15 Load vs. TimeTime (hr)Load (kip)P t 0510152025 0 0.6 1.2 1.8 Displacement vs. TimeTime (hr)Displacement (in) t 00.30.60.91.21.51.8 0 5 10 15 Load vs. DisplacementDisplacement (in)Load (kip)P 0102030405060 0 10 20 30 40 50 Stress vs. StrainStrain (percent)Stress (psi) Figure A-34. Shape factor 8, 0.5 ksi compression, 12 hour test data

PAGE 124

124 0510152025 0 5 10 15 Load vs. TimeTime (hr)Load (kip)P t 0510152025 0 0.6 1.2 1.8 Displacement vs. TimeTime (hr)Displacement (in) t 00.30.60.91.21.51.8 0 5 10 15 Load vs. DisplacementDisplacement (in)Load (kip)P 0102030405060 0 10 20 30 40 50 Stress vs. StrainStrain (percent)Stress (psi) Figure A-35. Shape factor 8, 0.9 ks i compression, 12 hour test 1 data

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125 0510152025 0 5 10 15 Load vs. TimeTime (hr)Load (kip)P t 0510152025 0 0.6 1.2 1.8 Displacement vs. TimeTime (hr)Displacement (in) t 00.30.60.91.21.51.8 0 5 10 15 Load vs. DisplacementDisplacement (in)Load (kip)P 0102030405060 0 10 20 30 40 50 Stress vs. StrainStrain (percent)Stress (psi) Figure A-36. Shape factor 8, 1.0 ks i compression, 12 hour test 2 data

PAGE 126

126 0510152025 0 5 10 15 Load vs. TimeTime (hr)Load (kip)P t 0510152025 0 0.6 1.2 1.8 Displacement vs. TimeTime (hr)Displacement (in) t 00.30.60.91.21.51.8 0 5 10 15 Load vs. DisplacementDisplacement (in)Load (kip)P 0102030405060 0 10 20 30 40 50 Stress vs. StrainStrain (percent)Stress (psi) Figure A-37. Shape factor 8, 1.0 ksi ksi compre ssion, 12 hour test 3 data The stress at 50% shear strain was calculated from a 2nd order curve fit on the ascending portion of the graph.

PAGE 127

127 0510152025 0 5 10 15 Load vs. TimeTime (hr)Load (kip)P t 0510152025 0 0.6 1.2 1.8 Displacement vs. TimeTime (hr)Displacement (in) t 00.30.60.91.21.51.8 0 5 10 15 Load vs. DisplacementDisplacement (in)Load (kip)P 0102030405060 0 10 20 30 40 50 Stress vs. StrainStrain (percent)Stress (psi) Figure A-38. Shape factor 8, 1.1 ksi compression, 12 hour test new pad data

PAGE 128

128 0510152025 0 5 10 15 Load vs. TimeTime (hr)Load (kip)P t 0510152025 0 0.6 1.2 1.8 Displacement vs. TimeTime (hr)Displacement (in) t 00.30.60.91.21.51.8 0 5 10 15 Load vs. DisplacementDisplacement (in)Load (kip)P 0102030405060 0 10 20 30 40 50 Stress vs. StrainStrain (percent)Stress (psi) Figure A-39. Shape factor 8, 1.2 ks i compression, 12 hour test 1 data

PAGE 129

129 0510152025 0 5 10 15 Load vs. TimeTime (hr)Load (kip)P t 0510152025 0 0.6 1.2 1.8 Displacement vs. TimeTime (hr)Displacement (in) t 00.30.60.91.21.51.8 0 5 10 15 Load vs. DisplacementDisplacement (in)Load (kip)P 0102030405060 0 10 20 30 40 50 Stress vs. StrainStrain (percent)Stress (psi) Figure A-40. Shape factor 8, 1.2 ks i compression, 12 hour test 2 data

PAGE 130

130 02.85.68.411.214 0 5 10 15 Load vs. TimeTime (day)Load (kip)P t 02.85.68.411.214 0 0.6 1.2 1.8 Displacement vs. TimeTime (day)Displacement (in) t 00.30.60.91.21.51.8 0 5 10 15 Load vs. DisplacementDisplacement (in)Load (kip)P 0102030405060 0 10 20 30 40 50 Stress vs. StrainStrain (percent)Stress (psi) Figure A-41. Shape factor 8, 1.1 ksi compression, 7 day test new pad data

PAGE 131

131 01938577695 0 5 10 15 Load vs. TimeTime (day)Load (kip)P t 01938577695 0 0.6 1.2 1.8 Displacement vs. TimeTime (day)Displacement (in) t 00.30.60.91.21.51.8 0 5 10 15 Load vs. DisplacementDisplacement (in)Load (kip)P 0102030405060 0 10 20 30 40 50 Stress vs. StrainStrain (percent)Stress (psi) Figure A-42. Shape factor 8, 1.0 ksi compression, 90 day test new pad data

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132 APPENDIX B ADDITIONAL LITERATURE REVIEW Additional Literature Summary It should be noted that not all of the literature reviewed was di rectly related to the research objective and some was redundant. Th e literature that fell within th ese categories is found here. Elastomeric bearings : state-of-the-art Roeder and Stanton[44] reviewed the uses of elastome ric bearings and provide a brief description of the state of the practice with regards to this type of bearing. This includes a discussion of both theoretical and experimental research on elastomeri c bearings, this was updated in 1991[12]. Effect of bearing pads on prestressed concrete bridges Yazdani, Eddy, and Cai [45] wrote about the potential benefits of restraining forces coming from elastomeric bearing pads in the design of bridge beams. For the source of these restraint effects Yazdani, Eddy, and Cai noted when pr operly designed these bearing pads transmit only 5% of the shear due to live loads to the substructure, (cited from AASHTO 1996a). This transmission of live load, however, has a corresp onding restraining effect on the beams. In the article they report the results of modeling AASHTO Type III and V beams in two simply supported Florida bridges using a finite element program using modeled after bearing pads vs. rollers. The article provides reports on actual fiel d test results of the shear stiffness of existing bridges vs. the predicted stiffness of those bridges. It reviews pr evious papers citing stiffening of neoprene pads due to low temperat ures and aging of pads. Yazdan i, Eddy, and Cai conclude that bridge beams could in some cases have lower midspan moments due to these end restraints. These end restraints provide resistance to the rotation of the beams wh en they are loaded by

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133 creating a resisting moment. However, using these reductions in design would require a high level of knowledge about the amount these pads restrain the bridge girders. Restraint effect of bearings Sen and Spillett[46] reported on the effects of bearing rest raint at temperatures ranging from -2F to 109F. For a bridge constructed at 80 F they found that the restraint effect of the bearings reduced the maximum midspan mome nt of the bridge by 15% at the lowest temperature. Figure B-1 illustrates these rest raining effects. Their conclusion included verification of AASHTO predicti ons of the load distribution. Load-deformation characteristics of elastomeric bridge bearing pads Clark and Moultrop [47] reported on a comparison study of three different elastomers: neoprene, butyl rubber and chlo rinated butyl rubber (chlorobutyl). This comparison included low temperature effects, acceler ated aging and room temperature as control for both shear loading and compression loading. Shear loadings were conducted at a variety of compressive loads and appeared to be a precursor to NCHRP Report 109[13]. This paper contained data on these various tests, however, in that data it appeared that all samples exhibited creep in both shear and compression. The appa rent creep showed up as an increase of deflection over time once the addition of loading had ceased. The re ported data appeared to display creep that increased at a logarithmically decreasing rate over time. Rotational effects on elastomeric bearings Both Elastomeric Bearing Pads Under Combined Loading[48] and NCHRP 12-68[8] report on the effect of rotation on shear capacity of bridge bearing pads. Both papers tested and modeled a variety of types of elastomeric bear ings to develop design procedures with new rotational and compressive limits for AASHTO.

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134 Influence of compression upon the shear properties of bonded rubber blocks Porter and Meinecke[49] looked at the contribut ion of the compressive load to shearing with a sample having a shape factor of 0.625. By taking into account the compressive strain, which increases the effective shear st rain and the internal moment induced by eccentric compressive load Porter and Meinecke were able to correct the shear stress-strain to match an uncompressed condition. The article provides an example based on a circular pad put into compression then sheared. The circular pads were chosen due to the uniform bulge of th e pad under compression. Porter and Meinecke provided a description of how the co mpression of the pads increases the effective shear area. This increased area increases the required force necessary to shear the compressed pad. Additionally it was noted that as the pads decreased height due to their compression a fixed shear displacement would equate to an increase shear strain. The effect of compression, however, was noted as also reducing the shear for ce needed due to the vector contribution of the compressive force. These effects are described in the following equations: As = (1.2 + 2/3u)2 (B-1) This effective shear area (As) is based on an assumed parabolic bulge with Porter and Meinecke citing Handbook of Chemistry and P hysics the Chemical Rubber Company, 45th edition 1963. where u = 3rx/(4t) (B-2) Where u is the peak distance that the pad bulges out (Figure B-2). x is the compressive deflection r is the radius of the pad t is the original thickness of the pad Unfortunately, the bulge equation does not apply to all shapes of bearing pads.

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135 Porter and Meinecke define the compression contri bution to the shear for ce due to the internal moment induced by the offset compression load shown in Figure B-3 as the following: Fs2 = Fc sin a (B-3) where Fs2 is added to the externally applied shear force to come up with th e total shear loading Fc is the compressive force a = s/(t x) (B-4) s is the shear displacement Compression, bending, and shear of bonded rubber blocks Gent and Meinecke[50] also make the assumption that th e shape of the bulge of a pad under compression is parabolic and provided a refere nce to the Proceedings of the Cambridge Philosophical Society (1954). Although Gent and Meinecke do not deal with the combination of compression and shear they do explore the effects of pads bulging on the compressive stiffness of the pad. The following equations are presented: F = fc AEe (B-5) where e is the compressive strain A is the uncompressed cross-sectional area E is the Young's modulus fc = fc1 + fc2 (B-6) where 2 222 1)2 /()( 3 2 3 4 hbahab fc (B-7) a and b are the lengths of the sides h is the original height of the pad fc2 = F2/AEe (B-8) Where F2 is derived based on the relationship be tween compressive strain and maximum bulge displacement kx. This relationship is a function of the excess hydrostatic pressure due to

PAGE 136

136 the restraining effects of the bonded surfaces (Figure B-4). Equation B-9 is the maximum outward displacement of the plane at x. Equa tion B-11 is generalized for a finite length. exkx2 3 (B-9) dxhEk dPx x)/( 3 82 (B-10) Pdxdy F2 (B-11) where Px is the excess hydrostatic pressure Behavior of elastomeric bridge bearings: computational results Hamezeh, Tassoulas and Becker[51] use finite element models to investigate the shear stiffness of both flat and tapered bearings. These results from finite element modeling including the redistribution of the compressive stress under shear loading. The mode ls revealed that under a shear load the compressive stress redistributes to shift the centroid of the compressive load to mitigate the internal moment in the pad. After this redistribution there is negligible internal moment. The compression of bonded rubber blocks Gent and Lindley[52] review existing theory and conduc t experiments to determine the relationship between the shape factor, the addi tion of carbon black and the Youngs modulus of rubber. Based on test using cy lindrical disks they concluded that as more carbon black was added the effect of the shape factor on the Y oungs modulus diminished ultimately reaching half of the theoretical value. This relationship was strictly empirical and based on compressive strains of less than 5%. No add itional explanation was provided.

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137 Engineering with rubber In Engineering with Rubber[53] (a text by the same name as the Mullins[10] article) it was noted that the thixotropic or s tress softening effect is suspected to recover over time. Additionally, stress softening was said to increas e with the amount of carbon black used and the amount of carbon black is increas ed in order to increase an elastomers shear modulus. This results in a more pronounced Mullin s effect in neoprene with highe r shear moduli. The increase of shear modulus in neoprene compared to the am ount of the filler carbon black used is shown in Table B-1. The section of the text about Design of Components not ed that there are other relationships that affect the shear stiffness, in particular a correlation between appa rent shear modulus, shape factor, and compressive strain. The relationship was presented in the form of the graph in Figure B-5. In the figure, an oval surrounds the part of the graph that most of th is study will be dealing with. The author of this portion of the text was contacted to determine the methodology used to develop this graph; the authors response was that the information is propitiatory. Figure B-5 is to be used in conjunction with Table B-2 and Equati on B-12. The Equation B-12 is the effective Youngs modulus[53]. Ec = E0(1 + 2S2) (B-12) S is the shape factor of the sample is a coefficient provided by Gent to fit data Stress analysis of rubber blocks und er vertical loading and shear loading Suh[54] looked at both theoretica l and FEA calculations for both bonded rubber and rubber held in place with frictional forces alone. The samples used in testing were chosen to have a small hysteresis and the calculations were based on the assumption of elastic material properties. The conclusions for large shear strains include th at the internal normal stresses are in tension

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138 throughout the material based on the elastic and uncompressible assumption. Suh goes on to state that these stresses are markedly affected by the shape of the free surfaces in the undeformed state. Hydrostatic tensile fracture of a polyurethane elastomer Lindsey[55] investigated the fracture of polymeric materials in hydros tatic tensile fields. In this investigation Lindsey used energy methods of fracture anal ysis, but there were problems duplicating the ideal boundary conditions imposed by the mathematical treatment. Steel bridge bearings Both Roeder and Stanton[56] as well as Bradberry, Cotham, and Medlock[57] provide guidelines for designing bearings, including elastomeric bearings, for steel bridges including steel box girders. However, for the shear modul us of neoprene bearing these design guidelines duplicate those found in AASHTO specifications. Earthquake isolation References Imbimbo and Kelly[58], Dicleli[59], Makris and Zhang, [60], Tsai and Kelly[61], Kelly[62] and Maleki [63] all report on the use of elastomeric bearings for seismic isolation of structures. All but one of thes e ignore details of the shear modulus of the elastomer and that one[58] treats the elastomer as nonlin ear but this is over a shear st rain range of up to 500%. The reported nonlinearity was shown using experimental results where the secant shear modulus was seen to drop to approximately half at around 200% shear strain, fr om 111 psi to 60.5 psi, then rise to approximately double, 215 psi, at 500% shear strain. Effects of axial load on elastomeric isolation bearings Koh, and Kelly[64] investigate the dynamic properties of elastomeric isolation bearings. These include effects of compressi on on the behavior on the bearings.

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139 Stability of elastomeric isolators: critical load tests and computations Nagarajaiah and Buckle[65] looked at the effect of shear displacement had on the critical buckling load in isolation bearings. Evaluation of low-temperature test meth ods for elastomeric bridge bearings Yakut and Yura[66] review existing test procedures for elastomeric bearings and make recommendations about eliminating and modifyi ng of various tests. These modifications included changing both the AASHTO M251 and ASTM D1043 low temperature tests to more closely reflect the actual c onditions that bearings woul d experience in service. Parameters influencing performance of elastomeric bearings at low temperatures Yakut and Yura[43] investigated the effect of cyclic compression, cyclic shear, rate of loading, type of elastomer compound, temperature history, creep and the slip coefficient. In neoprene, tests run with cyclic compression resulted in a lowe r compressive modulus if there was a variable temperature history, however, at a constant temperature cyclic compression increased the effective compression modulus. These effects were much less pronounced in natural rubber. In both elastomeric types a slower shear loading rate resulted in a lower shear modulus. The coefficient of friction varied but did not seem to have a significant trend with temperature. This value had a coefficient of vari ation of 0.07 with the lowest reported value of 0.29. Compressive creep in all samples, as repo rted as a percentage of initial displacement, increased with decreasing temperature. It was noted that only some of the results of their research were presented in this article while others were presented in other collaborative papers. Elastomeric bearing design, construction, and materials Stanton and Roeder[67] review research on the materials, mechanics, experimental work and design pertaining to elastomeri c bearings and elastomers.

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140 Natural rubber structural bearings Lindley[68] provides a brief overview of a verity of properties of natural rubber bearings including aspects of their manufacture, variations of stiffness with filler such as carbon black and the effects of dynamic stiffening.

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141 Figure B-1. Expansion restra int reduction in moment. Figure B-2. Pad bul ging under compression.[49] (Source: Figure 1 pp. 1134) Figure B-3. Pad in original pos ition and in sheared position w ith shear strain equal to a. [49] (Source: Figure 4 pp. 1136)

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142 Figure B-4. Cross section of an infinite st rip of an elastomer bulging under compression. [50] (Source: Figure 1 pp. 49) Figure B-5. Relationship between compressive strain, shape factor and apparent shear modulus.[53] (Source: Figure 8.3 pp. 228)

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143 Table B-1. Effect of carbon black on shear modulus of neoprene[53] Carbon black (*phr) 25 50 75 Shore A hardness 53 64 78 Shear modulus (psi) 145 180225 Tensile strength (psi) 325 340385 Breaking elongation (%) 400 350300 *phr Parts by weight pe r 100 parts by weight of neoprene (Source: pp. 32) Table B-2. Coefficient table[53] Shear modulus G (kPa) Youngs modulus E0 (kPa) Bulk modulus Eb (MPa) Material compressibility coefficient 296 896 979 0.93 365 1158 979 0.89 441 1469 979 0.85 524 1765 979 0.80 621 2137 1007 0.73 793 3172 1062 0.64 1034 4344 1124 0.57 1344 5723 1179 0.54 1689 7170 1241 0.53 2186 9239 1303 0.52 Note: (Source: Table 8.1 pp. 229)

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144 LIST OF REFERENCES 1. AASHTO Bridge Design Speci fications Customary U.S. Units Third Edition 2004, American Association of State Highway and Transportation Official s, Sections 14.7.5, 14.7.6, 3.4.1. 2. AASHTO Bridge Construction Specifications Customary U. S. Units Third Edition 2004, American Association of State Highway and Tr ansportation Officials, Sections 18.1, 18.2. 3. Structure Specifications for R oad and Bridge Construction, 2004, Florida Department of Transportation, Section 932, Tallahassee, FL. http://www2.dot.state.fl.us/SpecificationsEstim ates/Implemented/2004Bk/2004Bk.aspx Accessed Jan 17, 2006. 4. Structures Design Office Eng lish Standard Drawings, 2005.2, Florida Department of Transportation, Last revised Ma rch 17, 2005, Tallahassee, FL. http://www.dot.state.fl.us/structures/CADD/standards/standards.shtm Accessed Jan 17, 2006. 5. Plain and Laminated Elastomeric Bridge Bearings, AASHTO Designation: M 251-06, American Association of State Highway and Transportation Official s, Washington, DC. 6. Standard Specification for Plain and Steel-Laminated Elastomeric Bearings for Bridges, ASTM Standard D 4014, American Society for Testing and Materials, 1995 Annual Book of ASTM Standards, Vol. 04.03, p. 409, Philadelphia, PA. 7. Roeder, C. W., Stanton, J. F., Taylor, A. W., Performance of Elastomeric Bearings, National Cooperative Highway Research Progr am Report 298, University of Washington, Seattle, Washington, 1987. 8. Stanton, J. F., Roeder, C. W., Mackenzie-Heln wein, P., White, C., Kuester, C., Craig, B., Rotational Limits for Elastomeric Bearings, NCHRP 12-68, Seattle, WA. December 2006. 9. Meinecke, E. A., Comparing the Time and Rate Dependent Mechanical Properties of Elastomers, The University of Akron, Institute of Polymer Science, Akron, Ohio 44325, Presented at a meeting of th e Rubber Division, American Ch emical Society, Las Vegas, Nevada, May 20-23, 1980. 10. Mullins, L., Engineering with Rubber, Chemtech, December 1987, pp. 720-727. 11. Maguire, C. A. et al, Neoprene Elastomeric BearingsTen Years Experience Proves their Importance, Civil Engineer-ASCE, November 1967. pp. 37-39 12. Roeder, C. W., Stanton, J. F., Elastomeric Bearings: State-of-the-Art Journal of Structural Engineering, Vol. 109 No. 12, December 1983, pp. 2853-2871.

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145 13. Minor, J. C., and Egen, R. A., Elastomeric Bearing Research, National Cooperative Highway Research Program Report 109, Batte lle Memorial Institute, Columbus, Ohio, 1970. 14. Bell, L. W., Shloss, A. L., Subramanian, N. S., Additional Design Data Based on Full-Size Bridge Bearing Pads of Neoprene, Presented to the World C ongress on Joint Sealing and Bearing Systems for Concrete Structures. September 28, 1981. 15. Podolny, W. Jr., Muller, J. M., Construction and Design of Prestressed Concrete Segmental Bridges, John Wiley & Sons, New York, 1982. 16. Rejcha, C., Design of Elastomeric Bearings PCI Journal, October 1964, pp. 62-78. 17. Topkaya, C., Yura, J. A., Test Method for De termining the Shear Modulus of Elastomeric Bearings, Journal of Structural Engineering, June 2002, pp. 797-805. 18. Yura, J., Kumar, A., Yakut, A., Topkaya, C., Becker, E., Collingwood, J., Elastomeric Bridge Bearings: Recommended Test Methods, National Cooperative Highway Research Program Report 449, University of Texas, Austin, Texas, 2001. 19. Haringx J. A., On Highly Compressible Helical Springs and Rubber Rods, and Their Application for Vibratio n-free Mountings, I. Philips Research Reports, 3, 1948 pp. 401449. 20. Haringx J. A., On Highly Compressible Helical Springs and Rubber Rods, and Their Application for Vibratio n-free Mountings, II. Philips Research Reports, 4, 1949 pp. 4980. 21. Haringx J. A., On Highly Compressibl e Helical Springs and Rubber Rods, and Their Application for Vibratio n-free Mountings, III. Philips Research Reports, 4, 1949 pp. 206220. 22. Gent, A. N., 1964, Elastic Stability of Rubber Compression Springs, Journal Mechanical Engineering Science, Vol. 6 No. 4, pp. 318-326. 23. Muscarella, J. V., Yura, J. A., An Experimental Study of Elastomeric Brid ge Bearings with Design Recommendations. Publication FHWA/TX-98/13043, Texas Department of Transportation, October 1995. 24. McDonald, J., Heymsfield, E., Avent, R. R ., Slippage of Neoprene Bridge Bearings, Journal of Bridge Engineering, August 2000, pp. 216-233. 25. English, B. A., Klingner, R. E., Yura, J. A., Elastomeric Bearings: Background Information and Field Study. Publication FHWA/TX-95/1304-1, Texas Department of Transportation, June 1994. 26. Heymsfield, E., McDonald, J., Avent, R. R., Neoprene Bearing Pad Slippage at Louisiana Bridges, Journal of Bridge Engineering, January/February 2001, pp. 30-36.

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146 27. Malvern, L. E., Introduction to the Mechanics of a Continuous Medium, Prentice-Hall, Inc., Upper Saddle River, NJ, 1969. 28. Findley, W. N., Lai, J. S., Onaran, K., Creep and Relaxation of Nonlinear Viscoelastic Materials with an Introduction to Linear Viscoelasticity, North-Holland Publishing Company, Amsterdam, New York, 1976. 29. Smith, T. L., Viscoelastic Behavior of Polyisobutylene under Constant Rates of Elongation, Journal of Polymer Science, Vol. XX, 1956, pp. 89-100. 30. Yin, T. P., Pariser, R., Dynamic Mech anical Properties of Neoprene Type W Journal of Applied Polymer Science Vol. 7, 1963 pp. 667-673. 31. Ronan, S., Alshuth, T., Jerrams, S., An Approach to the Estimation of Long-Term Stress Relaxation in Elastomers, KCK, October 2007, pp. 559-563. 32. Green, M. S., Tobolsky, A. V., A New Appro ach to the Theory of Relaxing Polymeric Media The Journal of Chemical Physics, Vol. 14 No 2, February 1946, pp. 80-92. 33. Adkins, J. E., Some General Results in the Theory of Large Elastic Deformations Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, Vol. 231, No. 1184, Jul. 19, 1955, pp. 75-90. 34. Schapery, R. A., An Engineering Theory of Nonlinear Viscoelasticity with Applications International Journal of Solids and Structures, Vol. 2, 1966, pp. 407. 35. Bergstrm, B., Constitutive Modeling of the Large Strain Time-Dependent Behavior of Elastomers, Journal of Mechanical and Physics of Solids, Vol. 46, 1998 pp. 931-954. 36. Arruda, E. M. and Boyce, M. C., A threedimensional constitutiv e model for the large stretch behavior of rubb er elastic materials, Journal of the Mechanics and Physics of Solids, Vol. 41, Issue 2, February 1993, pp. 217-412. 37. Bloch, R., Chang, W. V., Ts cgoegl, N. W., The Behavior of Rubberlike Materials in Moderately Large Deformations, Journal of Rheology Vol. 22 No. 1, 1978 pp. 1-32. 38. Qi, H. J., Boyce, M. C., Constitutive model fo r stretch-induced softening of stress-stretch behavior of elastomeric materials, Journal of the Mechanics and Physics of Solids, Vol. 52, Issue 10, October 2004, pp. 2187-2205. 39. Nonlinear Finite Element Analysis of Elastomers Technical Paper, MSC Software Corporation, 2000, pp. 1-62. 40. Ferry, J. D., Viscoelastic Properties of Polymers, John Wiley & Sons, Inc., London, New York, 1980.

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147 41. Roeder, C. W., Stanton, J. F., Feller, T., Low Temperature Behavior and Acceptance Criteria for Elastomeric Bridge Bearings, National Cooperative Highway Research Program Report 325, University of Wash ington, Seattle, Washington, 1989. 42. Yakut, A., Performance of Elastomeric Bridge Bearings at Low Temperatures, Ph.D. Dissertation, University of Texas at Austin, May 2000. 43. Yakut, A., Yura, J. A., Parameters Influenci ng Performance of Elastomeric Bearings at Low Temperatures Journal of Bridge Engineering, August 2002, pp. 986-994. 44. Roeder, C. W., Stanton, J. F., State of the Art Elastomeric Bridge Bearing Design, ACI Structural Journal, January-February 1991, pp. 31-41. 45. Yazdani, N., Eddy, S., Cai, S. C., Effect of Bearing Pads on Precast Prestressed Concrete Bridges, Journal of Bridge Engineering, August 2000, pp. 224-232. 46. Sen, R. and Spillett, K., Restraint Effect of Bearings (Phase I), A Report on a Research Project Sponsored by the Florida Department of Transportation in cooperation with the U.S. Department of Tran sportation, January 1994. 47. Clark, E. V., Moultrop, K., Load Deforma tion Characteristics of Elastomeric Bridge Bearing Pads, Highway Research Record #34, Highway Research Bo ard Washington D.C., 1966, pp. 91-116. 48. Mtenga, P. V., Project Title: Elastomeric Bearing Pads Under Combined Loading, FDOTFHWA Sponsored Research Project, Florida Department of Transportation, March 2007 49. Porter, L. S., Meinecke, E. A., Influence of Compression upon the Shear properties of Bonded Rubber Blocks, Presented at a m eeting of the Rubber Division, American Chemical Society, Las Vega s, Nevada, May 20-23. 1980. 50. Gent, A. N., Meinecke, E. A., Compression, Bending, and Shear of Bonded Rubber Blocks, Polymer Engineering and Science January 1970, Vol. 10 No 1, pp. 48-53. 51. Hamzeh, O. N., Tassoulas, J. L., Becker, E. B ., Behavior of Elastomeric Bridge Bearings: Computational Results, Journal of Bridge Engineering, August, 1998. 52. Gent, A. N., Lindley, P. B., The Compression of Bonde d Rubber Blocks, Proceedings / Institution of Mechanical Engineers, Vol. 173 No 3 1959. 53. Campion, R. P., Ellul, M. D., Finney, R. H., Ge nt, A. N., Hamed, G. R., Hertz, Jr., D. L., James, F. O., Lake, G. J., Miller, T. S., Scott, K. W., Sheridan, P. M., Sommer, J. G., Stevenson, A., Sueyasu, T., Thomas A. G., Wang, C., Yeoh, O. H., Engineering with Rubber ed. 2, Hanser Publishers, Munich, 2001. 54. Suh, J. B., Stress Analysis of Rubber Blocks under Vertical Loading and Shear Loading, Ph.D. Dissertation, Dept. of Mechanical Engineering, University of Akron, August, 2007.

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148 55. Lindsey, G. H., Hydrostatic Tensile Fracture of a Polyurethane Elastomer, Ph.D. Dissertation, California Institute of Technology, December 1966. 56. Roeder, C. W., Stanton, J. F., Steel Bridge Bearing Se lection and Design Guide American Iron and Steel Institute, Highway Structures Design Handbook, Vol. 2, Chapter 4, 1997. 57. Bradberry, T. E., Cotham, J. C., Medlock, R. D. Elastomeric Bearings for Steel Trapezoidal Box Girders Bridges, In Transportation Research Record: Journal of the Transportation Research Board, No. 1928, Transportation Research Board of the National Academies, Washington D.C., 2005, pp. 27-38. 58. Imbimbo, M., Kelly, J. M., Influence of Mate rial Stiffening on Stab ility of Elastomeric Bearings at Large Displacements, Journal of Engineering Mechanics, September 1998, 1045-1049. 59. Dicleli, M., Seismic Design of Lifeline Bridge using Hybrid Seismic Isolation Journal of Bridge Engineering, March/April 2002, pp. 94-103. 60. Makris, N., Zhang, J., Seismic Response An alysis of Highway Overcrossing Equipped with Elastomeric Bearings and Fluid Dampers, Journal of Structural Engineering, June 2004, pp. 830-845. 61. Tsai, H.-C., Kelly, J. M., Stiffness Analysis of Fiber-Reinforced Rectangular Seismic Isolators, Journal of Engineering Mechanics, April 2002, pp. 462-470. 62. Kelly, J. M., Tension Buckling in Multilayer Elastomeric Bearings, Journal of Engineering Mechanics, December 2003, pp. 1363-1368. 63. Maleki, S., Effect of Side Retainers on Se ismic Response of Bridges with Elastomeric Bearings, Journal of Bridge Engineering, January/February 2004, pp. 95-100. 64. Koh, C. G., Kelly, J. M., Effects of Axial Load on Elastomeric Isolation Bearings, Earthquake Engineering Research Ce nter, UBC/EER-86/12, November 1987. 65. Nagarajaiah, S., Buckle, I., Stability of Elastomeric Isol ators: Critical Load Tests and Computations, MCEER Bulletin, Vol. 16, No.1, Spring/Summer 2002. 66. Yakut, A., Yura, J. A., Evaluation of LowTemperature Test Met hods for Elastomeric Bridge Bearings, Journal of Bridge Engineering January/February 2002, pp. 50-56. 67. Stanton, J. F., Roeder, C. W., Elastomeric Bearing Design, Construction, and Materials, NCHRP Report 248, Seattle, WA., August 1982. 68. Lindley, P. B., Natural Rubber Structural Bearings, ACI, SP70-20 Vol. 70, January 1981.

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149 BIOGRAPHICAL SKETCH Da mon Allen was born in late 1970, in southern Indiana. When he was six years old his family moved to Florida where he entered public school. He was able to attend classes at Santa Fe Community College in his se nior year of high school, which began his college education. After taking 44 credit hours of courses, he beca me unsure of his educational goals and how he was going to pay for them, so he dropped out and jo ined the local carpenter s union. He worked his way through a four-year apprenticeship program and received his journeymans card. Within months of topping out (completi ng his apprenticeship) in 1996, he became engaged to Melanie Barr and returned to Santa Fe Community College with the hope of pursuing a PhD in structural engineering at the University of Florida. He was married in 1997 and after going to school part-time for a few years, he finished his AA in summer 2000. He then transferred to the University of Florida where he received a bachelo rs degree in 2003 and a masters degree in 2007.