On the Fatigue Capacity of Headed Shear Studs in Composite ... · i On the Fatigue Capacity of Headed Shear Studs in Composite Bridge Girders SSRL – 0392-16028-22-0000 SSRL, November

COLLEGE OF ENGINEERING

DEPARTMENT OF CIVIL ENGINEERING (CVEG)

STEEL STRUCTURES RESEARCH LABORATORY (SSRL)

November, 2015

On the Fatigue Capacity of Headed Shear Studs in Composite Bridge Girders

Brianna Ovuoba Gary S. Prinz, Ph.D., P.E.

SSRL Project N° 0392-16028-22-0000

SSRL Report N° 2015-1

Final report submitted to W&W | AFCO Steel

COLLEGE OF ENGINEERING

DEPARTMENT OF CIVIL ENGINEERING (CVEG)

STEEL STRUCTURES RESEARCH LABORATORY (SSRL)

University of Arkansas Department of Civil Engineering 4190 Bell Engineering Center Fayetteville, AR 72701

Telephone : Fax : E-mail : Website :

+ 1 (479) 575-2494 + 1 (479) 575-7168 [email protected] www.ssrl-uark.com

V/ref : Fayetteville, AR, November 2015 N/ref : CVEG Report SSRL No 2015-1

On the Fatigue Capacity of Headed Shear Studs in Composite Bridge Girders

Mandate: W&W | AFCO Steel Mandate Description: Experimental and analytical investigation into the fatigue

capacity of headed shear studs, with a focus on evaluating the location of the CAFL.

Date of Mandate: December, 2015

Specimens: 6 composite push-out specimens were tested.

Reception of the Specimens: December, 2014

Testing Dates: January 2015 – November 2015

Project PI: G.S. Prinz

Collaborators: B. Ovuoba, C. Dang, W.M. Hale

Report Authors: B. Ovuoba and G.S. Prinz

SSRL Director: G.S. Prinz

Signatures : Project PI

Gary S. Prinz, PhD, PE

This report contains 54 pages (13 pages of front matter) This report may not be reproduced in whole or in part without written authorization from the SSRL director

B. Ovuoba and G.S. Prinz

SSRL – 0392-16028-22-0000 SSRL, November 2015

ii

i On the Fatigue Capacity of Headed Shear Studs in Composite Bridge Girders


ACKNOWLEDGEMENTS

This report presents the results of a research project sponsored by W&W|AFCO Steel. We acknowledge the financial and material support provided by W&W|AFCO Steel as well as the assistance and encouragement of the project lead, Mr. Grady Harvell. Expert advice provided throughout the project by Professor W. Micah Hale and Mr. Dennis Noernberg is also recognized. The research was conducted in the Steel Structures Research Laboratory (SSRL) at the University of Arkansas. Laboratory staff and graduate students instrumental in the completion of this work include: David Peachee, Ryan Hagedorn, Richard Deschenes, and Canh Dang. Although many individuals contributed to the research findings presented herein, the authors accept full responsibility for the conclusions presented.



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iii On the Fatigue Capacity of Headed Shear Studs in Composite Bridge Girders


TABLE OF CONTENTS

FRONT MATTER

Acknowledgements ....................................................................................................... i List of Figures .............................................................................................................. v List of Tables ............................................................................................................. vii Notation ....................................................................................................................... ix Report Summary ........................................................................................................ xi

FATIGUE TESTING REPORT

1. Introduction ............................................................................................................. 1 1.1. Background ................................................................................................... 1 1.2. Report Overview ........................................................................................... 2

2. Experimental Program ........................................................................................... 3 2.1. Test Specimen Geometry and Fabrication .................................................... 3 2.2. Test Configuration, Instrumentation, and Loading ....................................... 4

3. Experimental Results .............................................................................................. 5 3.1. Observations and Measured Fatigue Life ..................................................... 5 3.2. Stud Fatigue-Crack Investigations ................................................................ 7

4. Probabilistic Approach to Shear Stud Fatigue Capacity Evaluation ................ 8 4.1. Overview of MLE ......................................................................................... 8 4.2. Influence of Run-Outs on CAFL ................................................................. 10 4.3. Shear Stud Fatigue Dataset and Analysis using MLE................................. 10

5. Proposed Design S-N Curve for Predicting Shear Stud Fatigue Capacity ...... 11 6. Effect of New Shear Stud Fatigue-Life Equation on Composite

Bridge Design ........................................................................................................ 13 6.1. Prototype Bridge Geometries & Considered Traffic Levels ....................... 13 6.2. Design Approach ......................................................................................... 13

6.2.1. Brief Background on Determining the Required Stud Pitch for Fatigue .............................................................................. 13

6.2.2. Background on Determining the Required Stud Pitch for Strength ............................................................................................ 14

6.3. Comparison of Composite Bridge Designs using the AASHTO and Proposed Stud Fatigue Capacities ................................................................ 14

7. Summary and Conclusions .................................................................................. 15 8. References .............................................................................................................. 16 Appendix A. Shear Stud Fatigue Dataset ............................................................... 19 Appendix B. Material Test Data .............................................................................. 23 Appendix C. Verification of Negligible Inertial Effects under High

Frequency Loading ............................................................................. 25 Appendix D. Stud Design Example Calculations for Prototype Bridges ............. 27 Appendix E. Additional Slip and Separation Measurements ............................... 41



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v On the Fatigue Capacity of Headed Shear Studs in Composite Bridge Girders


LIST OF FIGURES

Figure 1. (a) Shear stud mechanism for load transfer across the steel-concrete interface, and (b) shop installed shear studs on a plate girder................................................. 1

Figure 2. Comparison of S-N curves for shear stud fatigue capacity between the AASHTO and Eurocode standards ......................................................................... 2

Figure 3. Push-out specimen geometry and slab rebar locations (all dimensions provided in mm) [7]. ............................................................................................... 3

Figure 4. Casting of concrete slabs on double sided push-out specimens .............................. 4

Figure 5. (a) Experimental setup and (b) specimen instrumentation ...................................... 5

Figure 6. Shear stud failure mode observations for Specimen 1 (failure observed after 12,803,000 cycles at an applied stress range per stud of 60MPa) .................. 6

Figure 7. Average slip versus number of applied cycles for Specimens 1 and 5. ................... 7

Figure 8. Fatigue crack investigation of polished stud sections from (a) Specimen 2 and (b) Specimen 5 .................................................................................................. 8

Figure 9. Fatigue-life curve representation through MLE fitting ............................................ 9

Figure 10. Comparison of AASHTO S-N curve and MLE regression (data in red represent fatigue test results presented in Section 3) ............................................ 11

Figure 11. (a) Comparison of proposed design S-N curve, MLE regression, fatigue data, and current AASHTO curve. (b) Comparison of proposed design S-N curve and existing AASHTO fatigue details. ........................................................ 12

Appendix Figures:

Figure A-1. Common (type A, B, and C) fatigue fractures within shear stud connectors

Figure B-1. Concrete testing machine and cylinder dimensions

Figure C-1. Comparison of slab slip measurements for Specimen 5 during high frequency dynamic loading. Comparisons presented represent (a) 1Hz and 10Hz loading rates, and (b) 1Hz and 20Hz loading rates

Figure D-1. Fatigue Limit State under finite loading for the bridge located in Jackson, Arkansas on US 67 Northbound at the intersection of State Highway 161.

Figure D-2. Fatigue Limit State under infinite loading for bridge located in Jackson, Arkansas on US 67 Northbound at the intersection of State Highway 161.

Figure D-3. Fatigue Limit State under finite loading for bridge located at the intersection of Interstate 540 and the UN PAC Railroad near Van Buren, Arkansas.

Figure D-4. Fatigue Limit State under infinite loading for bridge located at the intersection of Interstate 540 and the UN PAC Railroad near Van Buren, Arkansas.

Figure D-5. Fatigue Limit State under finite loading for bridge located in Sandy Springs, Oklahoma on US 64 at the intersection of S97th W Ave. Two different spans from this bridge are used in these design examples.



vi

Figure D-6. Fatigue Limit State under infinite loading for bridge located in Sandy Springs, Oklahoma on US 64 at the intersection of S97th W Ave. Two different spans from this bridge are used in these design examples.

Figure D-7. Fatigue Limit State under finite loading for bridge located in Sandy Springs, Oklahoma on US 64 at the intersection of S97th W Ave. Two different spans from this bridge are used in these design examples.

Figure D-8. Fatigue Limit State under infinite loading for bridge located in Sandy Springs, Oklahoma on US 64 at the intersection of S97th W Ave. Two different spans from this bridge are used in these design examples.

Figure D-9. Fatigue Limit State under finite loading for bridge located at the intersection of Interstate-540 and Flat Rock Creek near Van Buren, Arkansas.

Figure D-10. Fatigue Limit State under infinite loading for bridge located at the intersection of Interstate-540 and Flat Rock Creek near Van Buren, Arkansas.

Figure D-11. Strength Limit State for the bridge located in Jackson, Arkansas on US 67 Northbound at the intersection of State Highway 161.


Figure D-13. Strength Limit State for the bridge located in Sandy Springs, Oklahoma on US 64 at the intersection of S97th W Ave. Two different spans from this bridge are used in these design examples.


Figure D-15. Strength Limit State for the bridge located at the intersection of Interstate-540 and Flat Rock Creek near Van Buren, Arkansas.

Figure E-1. (a) Slip and (b) separation data from external LVDT measurements

vii On the Fatigue Capacity of Headed Shear Studs in Composite Bridge Girders


LIST OF TABLES

Table 1. Specimen Testing Matrix and Fatigue Results .......................................................... 5

Table 2: Proposed detail category description for shear stud fatigue capacity ...................... 12

Table 3. Considered Bridge Geometries ................................................................................ 13

Table 4 Required number of studs for the AASHTO fatigue capacity, proposed fatigue capacity, and strength limit state. ................................................................. 15

Appendix Tables:

Table A-1: Fatigue dataset for 3/4" diameter shear studs

Table A-2: Fatigue dataset for 7/8" diameter shear studs

Table B-1: Concrete compression test data for push-out specimen slabs



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ix On the Fatigue Capacity of Headed Shear Studs in Composite Bridge Girders


NOTATION

The following terms are used in the text of this report: (ΔF)n = design load-induced fatigue resistance; (ΔF)TH = the constant amplitude fatigue limit; A = constant representing the intercept of the fatigue S-N curve; ADTTSL = single-lane average daily truck traffic (trucks); BM = base metal; CAFL = constant amplitude fatigue limit; CDFNi,Si|γ’ = cumulative density function assuming γ’; d = diameter of shear stud; f’c = concrete compressive strength; fNi = probability of predicting failure at an individual data point; fNi|γ’ = probability of having failure at each given data point; FZ = weld fusion zone; fγ’ = probability that γ’ exists; HAZ = weld heat affected zone; I = moment of inertia of the short-term composite section; L = joint probability or likelihood; LVDT = linear variable differential transducers; m = constant representing the slope of the fatigue S-N curve; MLE = maximum likelihood estimation; N = number of cycles; n = number of shear studs across the flange width; n = required number of studs for the strength limit state; Nf = number of cycles to failure; nf = total number of failure points; nr = total number of run-out points; p = pitch (or spacing) of the row of shear studs along the length of the steel beam; P = total nominal shear force; PDFNi,Si|γ’ = probability density function of failure at each given point; PDFNi,i = probability density function at fatigue test data point (Ni,i); PDFNi = marginal probability density function; Q = first moment of the transformed short-term area of the concrete deck about

the neutral axis of the short-term composite section; Qr = factored shear resistance of one shear connector; RNi = probability of run-out; RNi|γ’ = probability of predicting run-out; S = applied stress range; Vf = vertical shear force range under the applicable fatigue loads; Vsr = applied shear demand at the steel-concrete interface; z* = number of standard deviations shifted from the mean; Zr = fatigue shear resistance of an individual shear stud; maximum likelihood fatigue-life curve parameter (power law constant); = maximum likelihood fatigue-life curve parameter (power law constant); Δσ = applied stress range; γ’ = assumed constant amplitude fatigue limit;



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xi On the Fatigue Capacity of Headed Shear Studs in Composite Bridge Girders


REPORT SUMMARY

Shear connectors are commonly used in steel bridges to join the concrete deck and steel superstructure, providing a mechanism for shear transfer across the steel-concrete interface. The most common type of shear connector is the headed shear stud. In the current AASHTO LRFD bridge specifications on composite design, shear stud fatigue often governs over static strength, and a large number of shear connectors often result. The stud fatigue capacities presented in the AASHTO standard are largely based on a limited sample of composite fatigue tests performed in the 1960s, with limited fatigue test data at lower stress ranges leading to a somewhat arbitrary constant amplitude fatigue limit (CAFL). The somewhat arbitrary CAFL often governs the composite design for bridges with moderate-to-high traffic demands. This report presents results from an experimental and analytical study into the fatigue behavior of headed shear studs, to address the lack of existing experimental data near the assumed CAFL, and to better characterize the effects of fatigue uncertainty on predicted response. Results from composite push-out specimens tested at stress ranges near the existing AASHTO CAFL suggest an increase of the CAFL to 6.5ksi. Recommendations for modification to the existing AASHTO shear stud S-N fatigue capacity curve are proposed.

xii On the Fatigue Capacity of Headed Shear Studs in Composite Bridge Girders


1 On the Fatigue Capacity of Headed Shear Studs in Composite Bridge Girders


FATIGUE TESTING REPORT

1. Introduction

1.1. Background

Shear connectors are commonly used in steel bridges to join the concrete deck and steel superstructure, providing a mechanism for shear transfer across the steel-concrete interface. Joining the steel and concrete members is advantageous, as the composite steel-concrete section has added strength over the sum of its individual components (the steel girder and concrete deck). This allows for use of lighter steel members and improved economy. The most common type of shear connector is the headed shear stud (see Figure 1(a)).

In the current AASHTO LRFD bridge specifications on composite design, shear studs must satisfy both strength and fatigue requirements [1]. To satisfy strength requirements, the shear connection between the concrete and steel elements must be capable of developing the full plastic capacity of the steel cross-section (create full composite action). To satisfy fatigue requirements, demands at the steel-concrete interface must be lower than the shear stud fatigue capacity as determined from an empirical fatigue capacity curve (called an S-N curve) and anticipated traffic cycles. Fatigue often governs, and a large number of shear connectors often result (see Figure 1(b)). Because traffic cycles are typically fixed from average daily truck traffic extrapolated over a 75-year design life, the S-N curve ultimately determines the required number of shear studs when the design is governed by fatigue.

Figure 1. (a) Shear stud mechanism for load transfer across the steel-concrete interface, and (b) shop installed shear studs on a plate girder (photo courtesy of Bill McElemeny, NSBA)

While many studies have investigated shear stud fatigue [2,3], the stud fatigue requirements in the AASHTO standard are largely based on single-sided push-out tests on 19mm (3/4 in) studs performed by Slutter and Fisher [4]. In the study by Slutter and Fisher, 26 samples containing 19mm (3/4in.) diameter studs were fatigue tested under constant amplitude stress cycles ranging in value from 55MPa (8ksi) to 138MPa (20ksi). To relate the applied stress range to the expected number of cycles for stud fatigue failure (S-N curve equations), a least-squares regression approach was used. Equation 1 presents the stud capacity equation based on the 26 data points from Slutter and Fisher [4], which shows similarity with the current stud fatigue capacity presented in the AASHTO standard [1] (see Equation 2). Note that the least-squares approach for regression analysis fails to account for any uncertainty distribution in the fatigue response, and therefore prevents the creation of characteristic capacity curves having known confidence levels.



2

1753.0072.8)log( N (Eq. 1) Slutter and Fisher [4]

1834.0061.8)log( N (Eq. 2) AASHTO [1]

The current AASHTO fatigue requirements assume a lower shear stud fatigue capacity than comparable specifications throughout the world. Figure 2 shows the current AASHTO shear stud S-N curve along with a comparable curve from the European (Eurocode) standard [5]. Other shear stud S-N curves from the Japanese and British standards are similar in form to the Eurocode curve [6]. The AASHTO specification results in a lower estimation of stud fatigue capacity for all traffic demands, and considers a linear-log regression while the Eurocode, Japanese, and British standards consider log-log fatigue behavior. Note in Figure 2 that the AASHTO S-N curve considers a somewhat arbitrary constant amplitude fatigue limit (CAFL) at 24MPa (3.5ksi). Limited fatigue test data exist at these lower stress ranges to justify this CAFL location, which often governs the stud fatigue design for bridges with moderate-to-high traffic demands (ADTT greater than approximately 960 vehicles). Comparing the required number of studs in a rural short span steel bridge design (having a span of 17.3m (57ft)) at various levels of truck traffic, Lee et al. [6] found that bridges designed to the US requirements needed nearly twice as many shear studs than the corresponding European, British, and Japanese designs. In [6], stud capacities for the US designs were always governed by fatigue requirements.

Figure 2. Comparison of S-N curves for shear stud fatigue capacity between the AASHTO and Eurocode standards

This report presents an experimental and numerical study into the behavior of headed shear studs, to address the lack of existing experimental data near the assumed CAFL, and to better characterize the effects of fatigue uncertainty on predicted response. In this study, composite push-out specimens are fatigue tested at stress ranges near the existing AASHTO CAFL and a probabilistic approach is applied to both new and existing fatigue data to capture uncertainty and variation in the fatigue response.

1.2. Report Overview

The report begins by describing the experimental study, including the specimen geometry, test setup, instrumentation, and loading. Following, the experimental fatigue results are presented and a probabilistic method for fatigue data evaluation is described. Findings from the experimental study are combined with existing data from previous studies to provide a comprehensive data set for re-evaluation of shear stud fatigue capacity. A characteristic S-

1

10

100

100 10000 1000000 100000000

Log

(S)

Log(N)

AASHTO

EuroCode



N curve for estimating shear stud fatigue capacity is proposed and applied to five prototype bridge designs to provide comparison.

2. Experimental Program

The primary objectives of the experimental program are to 1) characterize stud fatigue capacity at low applied stress ranges, 2) re-evaluate the existing CAFL considering both run-out and failure test results, and 3) investigate stud crack formation during low-stress high-cycle fatigue loading.

2.1. Test Specimen Geometry and Fabrication

Figure 3 shows the experimental push-out specimen geometry, consisting of a rolled W10x54 wide-flange section having 4 headed shear studs and a 6 in. cast-in-place concrete slab on each flange. The chosen geometry for the specimens (called herein double-sided push-out specimens) is based on guidelines for shear-stud testing prescribed in the Eurocode [7]. Double-sided push-out specimens are advantageous over single-sided push-out specimens (having a slab on only one side) as they help reduce loading eccentricities and multi-axial stress states within the stud (combined tension and shear). An applied multi-axial stress state in the stud can provide an overly-conservative estimation of fatigue capacity [3,6,8]. In this study, a total of 6 double-sided push-out fatigue tests are performed at four different applied stress levels ranging in value from 30MPa to 60MPa. Due to the significant time associated with high-cycle fatigue testing, only two replicate stress-ranges are considered in the test matrix (replicates at 40MPa and 60MPa).

Figure 3. Push-out specimen geometry and slab rebar locations (all dimensions provided in mm) [7].

W10×

54

150

650

250

250

150

600

100

100 × 19 Østuds (typ.)

150

150

150

150

180 180 180

25

25

600 100

#3 bar (Typ.)



4

Concrete slabs of the test specimen are designed to represent typical composite bridge conditions. All concrete sections consider normal weight concrete from a standard highway bridge deck mix design [9], and each concrete section is cast with the beam in a horizontal position (see Figure 4). To ensure material consistency across the four different stress levels tested, four push-out specimens are simultaneously cast from the same concrete batch. Prior to each fatigue test, adequate concrete compressive strength (at least 80% f’c) is checked from concrete cylinders formed during casting. Concrete strength data for each specimen are presented in Appendix B. To prevent adhesion between the concrete and steel, which can contribute to load transfer across the steel-concrete interface, each steel flange was coated in grease prior to concrete casting [7].

Figure 4. Casting of concrete slabs on double sided push-out specimens

2.2. Test Configuration, Instrumentation, and Loading

The experimental setup, shown in Figure 5(a), is designed to apply rapid shear stress cycles to studs within the push-out specimens. As shown in Figure 5(a), the double-sided push-out specimens are loaded with the beam oriented vertically, and the axial loads applied to the end of the steel wide-flange section. All specimens are subjected to unidirectional loading (specimens are loaded in one direction and then unloaded), resulting in a non-zero mean stress and providing a conservative fatigue loading condition as compared to reversed cycle loading [4]. To prevent separation between the specimen and testing machine at unloading, a pre-load of 1kN is maintained (somewhat shifting the applied mean stress). To ensure uniform contact between the concrete slabs and testing machine base, each specimen was leveled using a gypsum grout mixture.

Linear variable differential transducers (LVDTs) and unidirectional strain gauges are used to provide local measurements during testing. A total of eight LVDTs oriented parallel and perpendicular to the beam axis are included on each test specimen, to measure relative slip and separation between the concrete and steel sections. Unidirectional strain gauges are applied on two specimens to measure shear stresses transferred through the studs. Figure 5(b) shows the specimen instrumentation, including LVDT placement and strain gauge configurations.

Table 1 presents the experimental test matrix, including the specimen concrete strength, applied stress range, loading rate, and the resulting fatigue capacity. In Table 1, the applied stress ranges vary between 30MPa and 60MPa with specimen loading rates applied at between 10Hz and 20Hz. These high frequency loading rates are possible due to the high stiffness of the loading frame and test specimens. Note that measurements from several



pseudo-static loading cycles applied at 1 Hz were used to verify negligible inertial effects at the higher frequency loading (see Appendix C for this verification). Fatigue results provided in Table 1 will be discussed in the following Results section.

Figure 5. (a) Experimental setup and (b) specimen instrumentation

Table 1. Specimen Testing Matrix and Fatigue Results

Specimen Number

Average Concrete Compressive Strength

[MPa]

Applied Stress Range

[MPa] Loading Rate

[Hz] Number of

Cycles Failure (F) or Runout (R)

1 40.87 60 10-20 12,803,000 F

2 48.15 30 10-20 30,053,000 R

3 44.16 40 10-20 12,251,908 R

4 56.37 40 10-20 20,000,000 R

5 44.40 50 10-20 31,401,000 R

6 57.61 60 10-20 30,001,000 R

3. Experimental Results

3.1. Observations and Measured Fatigue Life

All specimens tested demonstrated higher fatigue capacity than the existing AASHTO limit (see again Equation 2), with the only complete fatigue failures occurring in Specimen 1 having an applied stress range of 60MPa. Failure in Specimen 1, evidenced by a complete fracture of the four embedded studs, occurred after 12.8 million cycles. In Specimen 1, fractures originated at the base of the stud weld (see Figure 6(c)) and propagated into the beam flange leaving crater-like indentations in the flange as shown in Figure 6(a). This failure mode is similar those observed in other push-out tests [4,10,11] and resulted in little-to-no damage to the concrete surrounding the stud. Specimen 2 (loaded at a stress range of



6

30 MPa) and Specimen 5 (loaded at a stress range of 50 MPa) survived more than 30 million cycles prior to being declared runouts. Specimens 3 and 4 loaded at 40 MPa were also declared runouts after 12.25 million and 20 million cycles respectively. The resulting fatigue capacities for all eight double-sided push-out specimens are provided in Table 1.

Slip between the concrete slab and steel beam was observed for all test specimens; however, for specimens loaded at stress ranges at or below 50MPa this slip was minor over then entire cycle history. Figure 7 shows the average slip for each slab of specimens 5 and 1 (loaded at 50MPa and 60MPa respectively). Slip measurements for other specimens having lower applied stress ranges were similar to Specimen 5, and are presented in the Appendix. The slip values presented in Figure 7 are computed by averaging the two LVDTs on each beam flange, providing a single slip value for each slab. In Figure 7 a noticeable slip in slab 1 of Specimen 1 occurs near 3 million cycles, followed by an increase in the slip-per-cycle rate up to failure of the studs at 12.8 million cycles. Slip between the concrete slab and steel beam is an indication of stiffness loss and possible stud damage. Specimen 5, subjected to a lower applied stress range, experienced minimal slip (suggesting little stud damage) over the entire 30 million cycle loading. While slip measurements are helpful in estimating damage within the embedded studs over time, more detailed investigations are required to determine whether fatigue cracks actually exist.

Figure 6. Shear stud failure mode observations for Specimen 1 (failure observed after 12,803,000 cycles at an applied stress range per stud of 60MPa)



Figure 7. Average slip versus number of applied cycles for Specimens 1 and 5.

3.2. Stud Fatigue-Crack Investigations

Metallographic investigation and micro-hardness testing of stud cross-sections cored from completed tests indicate fatigue crack initiations within runout specimens and a critical fracture location near the stud-to-flange weld heat affected zone (HAZ). Stud samples cored from runout Specimens 2 and 5, were sectioned, polished with abrasive paper and diamond powder of increasing fineness (mirror polished to a surface roughness of 1m), and then surface etched with a Nitol solution (5ml HNO3 per 100ml of ethanol). Figure 8 shows the polished stud cross-sections taken from the specimens with the various weld features highlighted, including the weld HAZ, base metals (BM), and fusion zone (FZ). Vickers micro-hardness measurements (shown as contours in Figure 8) highlight material property changes (potential changes in material toughness) within the welded stud-to-flange zone and confirm the location of the HAZ, FZ, and BM. Stud sections taken from Specimen 2 (declared a runout after more than 30 million cycles at 30MPa) show no indication of fatigue crack initiation (see Figure 8(a)); however, samples taken from Specimen 5 (declared a runout after more than 30 million cycles at 50MPa) indicate fatigue cracks initiating near the weld HAZ at the stud-to-flange interface (see Figure 8(b)). The initiated fracture observed in Specimen 5 closely resembles the fracture path shown in Figure 6(c) for failure Specimen 1. These initiated fatigue cracks were present in all studs cored from Specimen 5.

0

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0.4

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Ave

rage

Slip

[m

m]

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Failure at 12.8×106

cycles

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100000 1000000 10000000

Ave

rage

Slip

[m

m]

Cycles

Slab 1 Slab 2

Specimen 5 (= 50MPa)

Specimen 1 (= 60MPa)

1 2



8

Figure 8. Fatigue crack investigation of polished stud sections from (a) Specimen 2 and (b) Specimen 5

4. Probabilistic Approach to Shear Stud Fatigue Capacity Evaluation

Scatter in fatigue test results is inevitable, and can provide uncertainty when predicting fatigue performance. When creating S-N curves for fatigue prediction, quantifying this uncertainty and maximizing the likelihood of predicting an experimental outcome is desired. In the regression analysis by Slutter and Fisher [4] (on which the current AASHTO stud capacity limits are based), S-N curves for shear stud fatigue capacity were created using a simplified least-squares fitting procedure incapable of quantifying the uncertainty in the experimental scatter. In this section, an alternative curve creation approach is proposed, wherein an advanced statistical method called maximum likelihood estimation (MLE) is used to create S-N curves that maximize the joint probability of predicting the observed experimental result. Several studies have successfully used MLE to define curve regressions for large data sets [12,13,14,15]. The following paragraphs describe a random fatigue limit model proposed by Pascual et al. [16] using the MLE method. The newly generated shear stud fatigue data is combined with existing data from the previous studies and analyzed using the random fatigue limit model. A new characteristic shear stud S-N curve considering data uncertainty and having a known confidence level is proposed.

4.1. Overview of MLE

The goal of the MLE approach is to identify a population (probability distribution) at each stress level that is most likely to have generated the experimental data. To achieve this, parameters for the population are chosen that maximize the joint probability of predicting failure at all points (or in other words, to maximize the likelihood of predicting failure at all points). This joint failure probability (or likelihood) is simply the product of every data-point failure probability, written as:

nr

iN

nf

iN ii

RfL11

(Eq. 3)



where, L, fNi, RNi, nf and nr are the likelihood, probability of predicting failure at an individual data point (i), the probability of predicting run-out at an individual data point (i), the total number of failure data-points, and the total number of run-out points respectively.

In this study, a nonlinear generalized reduced gradient optimization algorithm is used to maximize the likelihood given by the variable parameters in the regression model. In determining the individual failure probabilities required in Equation 3, a power-law relationship is assumed to appropriately represent the fatigue data [17,18]. This power-law relationship is given in Equation 4,

)'(loglog SN ee (Eq. 4)

where N is the number of cycles to failure at a given applied stress range, S. Parameters and in Equation 4 are unknown parameters to be determined through MLE and ’ is the assumed CAFL, also to be determined through MLE. Note that for a confidence level of 50%, ’ in Equation 4 will be equal to the mean, , of the CAFL distribution. For other curve confidence levels, ’ is taken as - z* (shifting the CAFL location z* standard deviations from the mean). Equation 5 presents the regression relationship that can be used for confidence levels other than the mean, and Figure 9 depicts the MLE based model assuming the above power-law relationship and considering normally distributed data at each stress-range level.

** ))((loglog zzSN ee (Eq. 5)

Figure 9. Fatigue-life curve representation through MLE fitting

The probability of having failure at each data point (Ni, Si) in Figure 9, given a specific CAFL value (’) and assuming the data at each stress-range level as normally distributed, is given by the conditional probability density function shown in Equation 6.

2

2'|,'| )'log(2

1exp

2

1 iiSNN SNPDFf

iii (Eq. 6)

Because fNi|’ assumes a given ’, the probability that ’ exists (f’) must also be determined (see Equation 7). The resulting probability of predicting failure at Ni is the marginal

Stre

ssL

evel

, S

Fatigue Life, N [Cycles]

Fatigue Limit '

logS'log[N]

Assumed normal distrubution of fatigue data

(Ni, i)



10

probability density function representing the joint probability between fNi|’ and f’ as given in Equation 8.

2

2''

' )'2

1exp

2

1

f (Eq. 7)

i

ii

S

NNNi dffPDFf0

''| ' (Eq. 8)

4.2. Influence of Run-Outs on CAFL

Many S-N curves often only consider failure test results in identifying regression parameters, neglecting run-out test results and their potential influence on curve features such as the CAFL. At certain low stress levels, such as those considered in this study, the possibility exists for run-out test results to occur. MLE allows these run-out test results to influence the S-N curve through the population cumulative distribution function, since run-out simply indicates the absence of failure. In the case of run-outs, the probability of predicting run-out given an assumed CAFL (’) is given by:

'|,'| 1 iii SNN CDFR (Eq. 9)

where CDFNi,Si|’ is the cumulative density function assuming ’. The resulting probability of run-out, RNi, is the marginal probability density function between Equation 9 and Equation 7, given by equation 10.

')1( '0 '|, dfCDFRi

iii

S

SNN (Eq. 10)

4.3. Shear Stud Fatigue Dataset and Analysis using MLE

The complete fatigue data set considered in this study is presented in Table A- 1 of Appendix A, and consists of the six fatigue results described earlier and 100 fatigue results from existing comparable testing found in the literature. The 100 fatigue results taken from the literature were from a total of seven shear stud fatigue studies conducted between 1959 and 1988 [4,10,19,20,21,22,23]. All existing fatigue data presented in Table A- 1 were selected based on four criteria, including: 1) a stud shank diameter of 19mm (3/4 in.); 2) constant amplitude loading; 3) unidirectional loading (no reversed cycles), and 4) failure occurring in the stud shank or weld (i.e. no concrete crushing failures). For conservancy, test results from reversed cycle loading were not included, as they typically result in higher fatigue capacities due to the reduced applied mean stress [4]. Fatigue results from both single-sided and double-sided push-out tests were considered. Additional test data for 7/8” studs from more recent studies (conducted between 2000 and 2014) are used in comparisons (see Table A- 2) [4,8,11,24,25,26].

Analysis of the fatigue dataset presented in Table A- 1 suggests an increase in the CAFL and higher fatigue capacity within the finite-life region for stress-ranges over 117MPa (17ksi). Equation 11 presents the stud fatigue capacity equation resulting from the MLE analysis, with the optimized parameters of , , , , and being 17.26, -2.09, 6.5ksi, 1.45, and 1.21ksi respectively. Note that the stress range parameter in Equation 11 is based on units of ksi. The resulting distribution for the CAFL is characterized by a standard



deviation of 1.21ksi. In Equation 11, the mean CAFL value of 44.8MPa (6.5ksi) suggests an 86% increase in the allowable stress range for infinite life as compared to the current AASHTO standard. Analysis of the data considered uniformly distributed data at each stress-range level, and a mean confidence level (50%) based on the inherent conservancies in fatigue data resulting from push-out specimens [4,6,26].

)5.6(log09.226.17log SN ee (Eq. 11)

Figure 10 shows the resulting regression from the MLE analysis. For comparison, the current AASHTO shear stud S-N curve is also plotted along with the considered fatigue data-set.

Figure 10. Comparison of AASHTO S-N curve and MLE regression (data in red represent fatigue test results presented in Section 3)

5. Proposed Design S-N Curve for Predicting Shear Stud Fatigue Capacity

Given similarities in form between the MLE S-N curve and the S-N curves for various steel bridge fatigue details provided in AASHTO, a simplification of Equation 11 is proposed to provide consistency in design. In AASHTO [1], the design load-induced fatigue resistance for bridge details (excepting fatigue of the stud) takes the form:

TH

m

n FN

AF

1

(Eq. 12)

where m and A are constants representing the slope and intercept of the fatigue S-N curve. In Equation 12, (F)TH is the CAFL, and (F)n is the allowable stress range. To adapt Equation 11 to the form provided in Equation 12, a bi-linear design S-N curve is fit to the power-law relationship determined through MLE using the CAFL asymptote and approximate tangent at 103MPa (15ksi). This simplification provides an avenue for consistency between shear stud fatigue capacities and standard fatigue detail capacity forms. Table 2 presents the proposed detail category description, including the proposed S-N curve constant (A), slope (m), threshold value (CAFL or (F)TH), description of the potential crack initiation point, and an illustrative example of potential damage.

1

10

100

100 10000 1000000 100000000

Str

ess

Ran

ge, S

[ks

i]

Nf

50% Conf.FailuresRun-out

= 6.5 ksi

CAFL distributionfrom failure and runout test data

AASHTO = 3.5 ksi



12

Table 2: Proposed detail category description for shear stud fatigue capacity

Description Category

Constant A

(ksi4)

Threshold (ΔF)TH

ksi Potential Crack Initiation Point Illustrative Examples

9.2 Connection weld or shank of stud-type shear connector attached by fillet or automatic stud welding subjected to shear loading

D' [m = 4]

150 ×108 6.5

Toe of stud-to-flange welds, propagating through the stud shank or into the flange base metal

Figure 11(a) plots the proposed design S-N curve along with the MLE regression and fatigue data, and Figure 11(b) compares the proposed bi-linear design S-N curve with the current AASHTO fatigue detail categories. Note in Figure 11(b), that the proposed stud fatigue design S-N curve indicates a lower fatigue capacity than the curve for fracture in the base metal outside the stud weld, but a higher capacity than the current AASHTO stud fatigue limit. While the proposed design S-N curve is derived from the MLE analysis on ¾” stud fatigue tests, data from other fatigue tests on 7/8” studs fits the general trend of the curve. For comparison, Figure 11(c) is provided to show the proposed design S-N curve with data from both ¾” and 7/8” stud fatigue tests (see Appendix A for the stud fatigue values considered).

(a) (b)

(c)

Figure 11. (a) Comparison of proposed design S-N curve, MLE regression, fatigue data, and current AASHTO curve. (b) Comparison of proposed design S-N curve and existing AASHTO fatigue details.

ff

1

10

100

100 10000 1000000 100000000

Str

ess

Ran

ge, S

[ks

i]

Nf

50% Conf.FailuresRun-out

Proposed Design Curve

= 6.5 ksi THn FN

F

4

1810150

1

10

100

100 10000 1000000 100000000

Str

ess

Ran

ge, S

[ks

i]

Nf

Proposed: D'

A

B

C'CD

E

E'

Detail Category

1

1m = 3

ff

m = 4

1.00

10.00

100.00

100 10000 1000000 100000000

Str

ess

Ran

ge, S

[ks

i]

Nf

Failures

Run-out7/8" Stud data



6. Effect of New Shear Stud Fatigue-Life Equation on Composite Bridge Design

To compare the effect of the proposed shear stud fatigue life equation on the existing composite design requirements, design calculations investigating the required number of studs are performed. All design examples in this report use existing bridge geometries of varying span lengths and consider both strength and fatigue limit states.

6.1. Prototype Bridge Geometries & Considered Traffic Levels

Five multi-girder highway bridge span geometries, two levels of single-lane average daily truck traffic (ADTTSL), and two fatigue criteria (the proposed and existing stud fatigue capacities) are considered for a total of 20 composite designs. The two ADTTSL values considered are 500 and 1000, representing low and high traffic demands for both finite and infinite life stud designs under the current AASHTO S-N curve. The five bridge span geometries are taken from existing multi-girder highway bridges located within Arkansas and Oklahoma. Each existing bridge span is simply-supported and originally designed to be composite. Details on span length, concrete deck depth, girder spacing, and girder geometry, for each of the five spans are provided in Table 3. All designs in this study consider ¾ × 4” shear studs.

Table 3. Considered Bridge Geometries

Location Span Length

(ft) Concrete Deck

Depth (in) Girder

Spacing (ft) Girder Section

1a 64 6.5 6.5 W36x150 2 77 6.5 6.5 W36x150 3 65 7.5 8.5 W36x135 4 32 7.5 8.5 W27x84 5 40 6.5 6.25 W21x62

a See calculation examples provided in Appendix D for site-specific bridge location information

6.2. Design Approach

Excepting the designs considering the proposed shear stud fatigue capacity, all shear studs in the prototype bridge geometries are designed in accordance with AASHTO Article 6.10.10. Following typical design practices, shear demands at the steel-concrete interface are calculated at every 10th point along the bridge span (allowing the stud pitch to change along the span). The following sections provide a brief background on Article 6.10.10 in the AASHTO standard.

6.2.1. Brief Background on Determining the Required Stud Pitch for Fatigue

Under fatigue loading, the required pitch (or spacing) of shear studs in a composite bridge girder is dependent on a capacity-to-demand ratio between the individual stud capacity (Zr) and the applied shear demand at the steel-concrete interface (Vsr). Equation 13 presents the capacity-to-demand ratio used by [1], with n being the number of shear studs across the flange width. While the stud fatigue capacity (Zr) is calculated as described earlier (shown again in Equation 14), the demand at the steel-concrete interface is calculated as a shear flow resulting from the girder shear (Vf) caused by the passage of a design-level fatigue truck (see Equation 15).



14

Two fatigue load combinations are considered when calculating shear demands from the design-level truck: Fatigue Load Combination I for higher traffic demands (ADTTSL greater than 960) and Fatigue Load Combination II for lower traffic demands (ADTTSL lower than 960). The loading factors for Fatigue Load Combinations I and II are 0.75 and 1.5 respectively [1].

sr

r

V

Znp

(EQ. 13)

960 ADTT 5.5

960 ADTT log28.45.342

2

ford

fordNZr (U.S. Cust. units) (EQ. 14)

I

QVV f

sr

(EQ. 15)

6.2.2. Background on Determining the Required Stud Pitch for Strength

Similar to the fatigue limit state, the required number of studs for the strength limit state is calculated using a capacity-to-demand ratio, where the nominal shear demand, P, is compared with the factored resistance of an individual shear connector, Qr as shown in Equation 16.

rQ

Pn (EQ. 16)

In Equation 16, the nominal shear demand, P, is determined as the lesser of the longitudinal force in the concrete deck or steel girder. The factored shear capacity, Qr, is calculated as the lesser of the nominal concrete strength (from the area surrounding the stud) and stud steel strength (see Section 6.10.10.4 in [1]).

6.3. Comparison of Composite Bridge Designs using the AASHTO and Proposed Stud Fatigue Capacities

The proposed stud fatigue S-N curve results in fewer required studs than the existing AASHTO S-N curve. Table 4 shows the number of shear studs required to satisfy the fatigue limit state in the five prototype bridge geometries, considering both the AASHTO and proposed stud S-N curves. Note that stud values using the proposed S-N curve remain unchanged between the ADTT 1000 and ADTT 500 levels as the CAFL is shifted relative to the AASHTO curve. For the higher traffic level (ADTT of 1000), the number of required shear studs was reduced by 40-45% using the proposed S-N curve. For the lower traffic level (ADTT of 500) under the lower traffic level, the number of required studs was reduced by between 17-48%.

Note that the required number of studs is somewhat higher than that required by the capacity-to-demand ratio provided in EQ 13, due to the maximum spacing requirement of 24” [1]. Sample calculations for bridge span 1, shown in Figure D-2 of Appendix D, indicate that a significant portion of the composite girder section are limited by the maximum spacing requirement when using the proposed shear stud fatigue S-N curve (the spacing requirement exceedance is highlighted in red). If the maximum stud spacing



requirement were increased, further reductions in the number of required shear studs would be achieved.

Table 4 Required number of studs from the AASHTO and proposed fatigue capacity curves

AASHTO Proposed ADTT 1000 ADTT 500 ADTT 1000 ADTT 500

191 137 114 114 250 176 144 144 236 165 133 133 104 108 56 56 149 153 81 81

Note: Values presented are adjusted to satisfy maximum stud spacing requirements

7. Summary and Conclusions

In this study, six composite push-out specimens were fatigue tested under repeated cyclic loads at stress ranges varying between 30MPa and 60MPa. These composite push-out specimens represent a conservative estimation of stud fatigue damage as the adhesion and friction at the steel-concrete interface were inhibited by greasing of the steel flanges prior to concrete casting. Measured fatigue life from the eight specimens were combined with existing shear stud fatigue data sets in the literature, and analyzed using a probabilistic method called maximum likelihood estimation. Results from the eight fatigue tests and analysis of the new and existing fatigue data provide the following conclusions:

1) The current AASHTO CAFL for headed shear studs provides an overly-conservative estimation of fatigue capacity. Analysis of existing data along with the additional high-cycle fatigue test results suggests an increase in the CAFL from 3.5ksi to 6.5ksi.

2) The current AASHTO S-N curve for finite life of the shear stud underestimates fatigue capacity and is not representative of the larger considered fatigue dataset. An alternative design S-N curve of similar form to the existing AASHTO detail categories (log-log) is proposed. The proposed curve has an m=4 and A= 150x108 and provides a known level of confidence in the estimated fatigue capacity (based on the MLE analysis with a confidence level of 50%) while providing a unification in the fatigue design procedure.

3) For bridge designs subjected to high traffic levels, the number of required shear studs may be reasonably reduced by 40-45% using the proposed design S-N curve. These stud savings vary due to the maximum stud spacing requirement. If the maximum stud spacing requirement were increased, further reductions in the number of required shear studs could be achieved.



16

8. References

[1] AASHTO (2012). "AASHTO LRFD bridge design specifications (6th edition)." American Association of State Highway and Transportation Officials, Washington, DC.

[2] Oehlers, D. J. (1990). "Methods of estimating the fatigue enduraces of stud shear connections." IABSE Proceedings P-145/90, p. 65-84.

[3] Johnson, R. P. (2000). "Resistance of stud shear connectors to fatigue." J. Constructional Steel Research 56(2000), 101-116.

[4] Slutter, R. G., and Fisher, J.W. (1966). "Fatigue strength of shear connectors " Highway Research Record No. 147, Highway Research Board, p. 65-88.

[5] Eurocode_4 (1994). "Design of composite steel and concrete structures - Part 2: General rules and rules for bridges." ENV 1994-2, European Committee for Standardization, Brussels, Belgium.

[6] Lee, K.-C., Abbas, H.H., and Ramey, G.E. (2010). "Review of current AASHTO fatigue design specifications for stud shear connectors." ASCE Structures Congress Proceedings, p. 310-321.

[7] Eurocode_4 (1994). "Design of composite steel and concrete structures - Part 1-1: General rules and rules for buildings." ENV 1994-1-1, European Committee for Standardization, Brussels, Belgium.

[8] Badie, S. S., Tadros, M.K., Kakish, H.F., Splittgerber, D.L., and Baishya, M.C. (2002). "Large shear studs for composite action in steel bridges." J. Bridge Engineering, ASCE 7(3), p.195-203.

[9] AHTD (2014). "Division 800, Section 802: Concrete for structures." The Arkansas Standard Specification for Highway Construction

[10] Hallam, M. W. (1976). "The behaviour of stud shear connectors under repeated loading." Research Report No, R281, University of Sydney, School of Civil Engineering, Sydney, Austrailia.

[11] Feldmann, M., Hechler, O., Hegger, J., and Rauscher, S. (2011). "Fatigue behavior of shear connectors in high performance concrete." Composite Construction in Steel and Concrete VI, pp. 39-51, doi: 10.1061/41142(41396)41144

[12] D'Angelo, L., Rocha, M., Nussbaumer, A., and Bruhwiler, E. (2014). "Creation of S-N-P curves for reinforcing steel bars using a maximum likelihood approach." Proc. Eurosteel, Naples, Italy.

[13] Myers, A. T., Kanvinde, A.M., and Ibarra, L. (2012). "Maximum likelihood based parameter estimation of constitutive models for earthquake engineering." 15th World Conference on Earthquake Engineering, Lisbon, Portugal.

[14] Prinz, G. S., and Nussbaumer, A. (2014). "Effect of radial base-plate welds on ULCF capacity of unanchored tank connections." J. Constructional Steel Research 103(2014), 131-139.

[15] Ling, J., and Pan, J. (1997). "A maximum likelihood method for estimating P-S-N curves." International J. of Fatigue 19(5), 415-419.

[16] Pascual, F. G., and Meeker, W.Q. (1999). "Estimating fatigue curves with the random fatigue-limit model: 1 Introduction." Technometrics 1999

[17] Coffin, L. F. (1954). "A study of the effects of cyclic thermal stresses in ductile metals." ASME, 76, 931-950.



[18] Manson, S. S. (1954). Behavior of materials under conditions of thermal stress. National Advisory Committee for Aeronautics,. Technical note 2933. Tennessee (USA).

[19] Mainstone, R. J., and Menzies, J.B. (1967). "Shear connectors in steel-concrete composte beams for bridges, Part I." Concrete 1(9), pp. 291-302.

[20] Lehman, H. G., Lew, H.S., and Toprac, A.A. (1965). "Fatigue strength of 3/4 inch studs in lightweight concrete." Research Report No. 76-1F, Center for Highway Research, The University of Texas, Austin, Texas.

[21] Naithani, K. C., Gupta, V.K., and Gadh, A.D. (1988). "Behaviour of shear connectors under dynamic loads." Materials and Structures 21

[22] Roderick, J. W., and Ansorian, P. (1976). "Repeated loading of composite beams." Civil Engineering Transactions CE18(2), pp. 109-116.

[23] Thurlimann, B. (1959). "Fatigue and static strength of steel shear connectors, Lehigh University, 1959 Reprint No. 144(59-8)." (1959) Fritz Laboratory Reports. Paper 1253.

[24] Mundie, D. L. (2011). "Fatigue testing and design of large diameter shear studs used in highway bridges." Masters Thesis, Auburn University, Auburn, AL.

[25] Faust, T., Leffer, A., and Mesinger, M. (2000). "Fatigue of headed studs embedded in LWAC." Second International Symposium on Structural Lightweight Aggregate Concrete 2(2000), pp.212-220.

[26] Provines, J., and Ocel, J.M. (2014). "Strength and fatigue resistance of shear stud connectors." National Accelerated Bridge Construction Conference (ABC), December, 4-5, Miami, Florida.

[27] ASTM (2008). Standard practice for making and curing concrete test specimens in the field. C31/C31M-09. West Conshohicken, Pa.

[28] ASTM (2015). Standard test method for compressive strength of cyllidrical concrete specimens. C39/C39M-15a. West Conshohicken, Pa.



18



Appendix A. Shear Stud Fatigue Dataset

Table A- 1 provides the ¾” stud fatigue data set values used in determining the proposed design S-N curve. Table A- 2 provides the 7/8” stud fatigue values used in comparison. Failure modes described in Tables A-1 and A-2 refer to type A, B, or C fractures as shown in Figure A- 1.

Figure A- 1. Common (type A, B, and C) fatigue fractures within shear stud connectors.

Table A- 1. Fatigue dataset for ¾” diameter shear studs

Reference Test

Number Specimen

Name

No. of Slabs in

Test Studs/Side

Failure Mode

Stress Range (ksi)

Nf (cycles)

Hallam1 1 PS4 2 2 Type A 24.19 52,801 Hallam 2 PS42 2 2 Type A 24.19 52,836 Hallam 3 PS5 2 2 Type A 24.19 58,630 Hallam 4 PS52 2 2 Type A 24.19 67,877 Hallam 5 PS10 2 2 Type A 21.39 61,700 Hallam 6 PS102 2 2 Type A 21.39 75,500Hallam 7 PS11 2 2 Type A 21.39 110,000 Hallam 8 PS112 2 2 Type A 21.39 110,000 Hallam 9 PS12 2 2 Type A 15.99 148,700Hallam 10 PS122 2 2 Type A 15.99 174,800 Hallam 11 PS13 2 2 Type A 15.99 182,600 Hallam 12 PS132 2 2 Type A 15.99 182,600Hallam 13 PS12 2 2 Run-Out 13.89 1,303,669 Hallam 14 PS1 2 2 Type A 13.89 1,303,669 Hallam 15 PS3 2 2 Type A 13.30 652,300Hallam 16 PS32 2 2 Type A 13.30 652,300 Hallam 17 PS2 2 2 Type A 13.30 823,970 Hallam 18 PS22 2 2 Type A 13.30 845,000Hallam 19 PS6 2 2 Type C 13.70 3,170,000 Hallam 20 PS62 2 2 Type C 13.70 3,554,000 Hallam 21 PS7 2 2 Type C 13.70 5,140,000 Hallam 22 PS72 2 2 Type C 13.70 6,096,000 Hallam 23 PS82 2 2 Type C 11.10 20,965,000 Hallam 24 PS8 2 2 Type C 11.10 21,391,000 Hallam 25 PS9 2 2 Type C 11.10 24,305,000

↓ Continued ↓



20

Table A-1: Continued…

Reference Test

Number Specimen

Name

No. of Slabs in

Test Studs/Side

Failure Mode

Stress Range (ksi)

Nf (cycles)

Hallam 26 PS92 2 2 Run-Out 11.10 35,000,000 Lehman/Lew2 1 212 2 4 Run-Out 10.00 6,730,000 Lehman/Lew 2 616 2 4 Run-Out 10.00 5,810,000 Lehman/Lew 3 1020 2 4 Type B/C 10.00 6,711,000 Lehman/Lew 4 214 2 4 Type B/C 12.00 2,960,000 Lehman/Lew 5 618 2 4 Type B/C 12.00 2,223,000 Lehman/Lew 6 216 2 4 Type B/C 14.00 305,000 Lehman/Lew 7 620 2 4 Type B/C 14.00 1,345,000 Lehman/Lew 8 1024 2 4 Type B/C 14.00 390,000 Lehman/Lew 9 620B 2 4 Type B/C 14.00 726,000 Lehman/Lew 10 218 2 4 Type B/C 16.00 292,000 Lehman/Lew 11 622 2 4 Type A 16.00 435,720 Lehman/Lew 12 220 2 4 Type B/C 18.00 100,000 Lehman/Lew 13 624 2 4 Type B/C 18.00 142,680 Lehman/Lew 14 1028 2 4 Type B/C 18.00 340,300 Mainstone3 1 S1 2 2 Type B/C 22.18 76,000 Mainstone 2 S10 2 2 Type B/C 28.07 1,700,000 Mainstone 3 S12 2 2 Type B/C 31.69 679,000 Mainstone 4 S2 2 2 Type B/C 17.66 439,000 Mainstone 5 S20 2 2 Type B/C 35.08 669,000 Mainstone 6 S23 2 2 Stud9 35.08 657,000 Mainstone 7 S24 2 2 Yield 36.22 9,200 Mainstone 8 S25 2 2 Stud 38.48 13,300 Mainstone 9 S27 2 2 Stud 37.35 8,970 Mainstone 10 S28 2 2 Stud 37.35 6,000 Mainstone 11 S30 2 2 Yield 37.35 13,100 Mainstone 12 S31 2 2 Stud 36.22 8,600 Mainstone 13 S32 2 2 Stud 38.48 165,000Mainstone 14 S33 2 2 Stud 37.35 106,000 Mainstone 15 S7 2 2 Stud 17.66 1,940,000 Mainstone 16 S9 2 2 Type B/C 24.45 42,000Nathani4 2 F2 1 1 Stud 22.64 3,200 Nathani 3 F1 1 1 Stud 22.36 1,000 Nathani 4 F3 1 1 Stud 16.77 23,000Nathani 5 F4 1 1 Stud 16.77 21,000 Nathani 6 F5 1 1 Stud 13.98 68,000 Nathani 7 F6 1 1 Stud 13.98 78,000Nathani 8 F7 1 1 Stud 11.18 266,000 Nathani 9 F8* 1 1 Type B/C 11.18 48,000 Nathani 10 F10 1 1 Stud 8.39 685,000Nathani 11 F9+ 1 1 Stud 8.39 1,150,000 Nathani 12 F11 1 1 Run-Out 6.99 2,000,000 Nathani 13 F12 1 1 Run-Out 5.59 2,512,000Roderick5 1 R4 2 2 Yield 21.76 49,300 Roderick 2 R1 2 2 Yield 20.30 616,000 Roderick 3 R2 2 2 Yield 20.30 194,110Roderick 4 R3 2 2 Yield 20.30 190,460 Slutter/Fisher6 1 a3C 1 4 Type B/C 8.00 7,481,100 Slutter/Fisher 2 b3C 1 4 Type B/C 8.00 10,275,900 Slutter/Fisher 3 c3C 1 4 Type B/C 8.00 5,091,200 Slutter/Fisher 4 a6B 1 4 Type B/C 10.00 962,500 Slutter/Fisher 5 b6B 1 4 Type B/C 10.00 919,100

↓ Continued ↓



Table A-1. Continued…

Reference Test

Number Specimen

Name

No. of Slabs in

Test Studs/Side

Failure Mode

Stress Range (ksi)

Nf (cycles)

Slutter/Fisher 6 c6B 1 4 Type B/C 10.00 1,144,600 Slutter/Fisher 7 a6C 1 4 Type B/C 10.00 1,213,600 Slutter/Fisher 8 b6C 1 4 Type B/C 10.00 1,295,300 Slutter/Fisher 9 c6C 1 4 Type B/C 10.00 1,618,900 Slutter/Fisher 10 a2B 1 4 Type B/C 12.00 897,300 Slutter/Fisher 11 b2B 1 4 Type B/C 12.00 565,300 Slutter/Fisher 12 c2B 1 4 Type B/C 12.00 551,100 Slutter/Fisher 13 a4C 1 4 Type B/C 12.00 798,000 Slutter/Fisher 14 b4C 1 4 Type B/C 12.00 1,215,400 Slutter/Fisher 15 c4C 1 4 Type B/C 12.00 1,010,400 Slutter/Fisher 16 P2 1 4 Type B/C 14.00 383,600 Slutter/Fisher 17 a3B 1 4 Type B/C 16.00 139,400 Slutter/Fisher 18 b3B 1 4 Type B/C 16.00 114,700 Slutter/Fisher 19 c3B 1 4 Type B/C 16.00 199,500 Slutter/Fisher 20 a5C 1 4 Type B/C 16.00 335,800 Slutter/Fisher 21 b5C 1 4 Type B/C 16.00 99,200 Slutter/Fisher 22 c5C 1 4 Type B/C 16.00 197,000 Slutter/Fisher 23 P1 1 4 Type B/C 20.00 27,900 Slutter/Fisher 24 a4B 1 4 Type B/C 20.00 41,500 Slutter/Fisher 25 b4B 1 4 Type B/C 20.00 50,700 Slutter/Fisher 26 c4B 1 4 Type B/C 20.00 58,700 Thurlimann7 1 9 2 4 N.S.10 20.00 169,000 Thurlimann 2 10 2 4 N.S. 14 474,000 Ovuoba/Prinz8 1 1 2 4 Type C 8.70 12,803,000 Ovuoba/Prinz 2 2 2 4 Run-Out 4.4 30,053,000 Ovuoba/Prinz 3 3 2 4 Run-Out 5.8 12,251,908 Ovuoba/Prinz 4 4 2 4 Run-Out 5.8 20,000,000 Ovuoba/Prinz 5 5 2 4 Run-Out 7.3 31,401,000Ovuoba/Prinz 6 6 2 4 Run-Out 8.7 30,001,000

1 Hallam, M.W. (1976) [10] 2 Lehman, H.G., Lew, H.S., and Toprac, A.A. (1965) [20] 3 Mainstone, R.J., and Menzies, J.B. (1967) [19] 4 Nathini, K.C., Gupta, V.K., and Gadh, A.D. (1988) [21] 5 Roderick, J.W., and Ansorian, P. (1976) [22] 6 Slutter, R.G., and Fisher, J.W. (1966) [4] 7 Thurlimann, B. (1959) [23] 8 Ovuoba and Prinz (Current test report) 9 Failure occurred near mid height of stud shank 10 Failure mode not specified



22

Table A- 2. Fatigue dataset for 7/8” diameter shear studs

Reference Test

Number Specimen

Name

No. of Slabs in

Test Studs/Side

Failure Mode

Stress Range (ksi)

Nf (cycles)

Feldman1 1 HSIt1 2 4 Type B/C 26.3 2113520 Feldman 2 HSIt2 2 4 Type B/C 26.3 2265273 Feldman 3 HSIt3 2 4 Type B/C 26.3 2505680 Slutter/Fisher 1 e3I 1 4 8 4885100 Slutter/Fisher 2 e2H 1 4 12 2133000 Slutter/Fisher 3 e4I 1 4 12 587700 Slutter/Fisher 4 e3H 1 4 16 112500 Slutter/Fisher 5 e5I 1 4 16 134300 Slutter/Fisher 6 e4H 1 4 20 33000 Badie/Tadros2 1 SS-5-25 1 8 Stud 20 27000 Badie/Tadros 2 SS-5-23 1 8 Stud 18 60000 Badie/Tadros 3 SS-5-21 1 8 Stud 16 285000 Badie/Tadros 4 SS-5-20 1 8 Stud 15 189000 Badie/Tadros 5 SS-5-19 1 8 Stud 14 157000 Badie/Tadros 6 SS-5-18 1 8 Stud 13 935000 Badie/Tadros 7 SS-5-17 1 8 Concrete 12 400000 Badie/Tadros 8 SS-5-16 1 8 Stud 11 2452000 Badie/Tadros 9 SS-5-15 1 8 Stud 10 600000 Badie/Tadros 10 SS-5-14 1 8 Run-Out 9 2000000 Badie/Tadros 11 SS-5-10 1 8 Run-Out 5 2500000 Mundie3 1 S-0.875-22-A 2 4 Type B/C 22 325557 Mundie 2 S-0.875-22-B 2 4 Type B/C 22 80346 Mundie 3 S-0.875-22-C 2 4 Type B/C 22 245121 Mundie 4 S-0.875-22-D 2 4 Type B/C 22 91598 Mundie 5 S-0.875-18-A 2 4 Type B/C 18 1586515 Mundie 6 S-0.875-18-B 2 4 Type B/C 18 2654243 Mundie 7 S-0.875-18-C 2 4 Type B/C 18 986718 Mundie 8 S-0.875-18-D 2 4 Type B/C 18 235326Mundie 9 S-0.875-26-A 2 4 Type B/C 26 38295 Mundie 10 S-0.875-26-B 2 4 Type B/C 26 56507 Mundie 11 S-0.875-26-C 2 4 Type B/C 26 36094Mundie 12 S-0.875-26-D 2 4 Type B/C 26 38101 Faust4 1 1 2 2 N.S. 16.1 566000 Faust 2 2 2 2 N.S. 16.1 522600Faust 3 3 2 2 N.S. 16.8 720000 Faust 4 4 2 2 N.S. 20.57 83700 Faust 5 5 2 2 N.S. 20.94 103600 Faust 6 6 2 2 N.S. 21.32 96500 Faust 7 7 2 2 N.S. 24.31 60400 Faust 8 8 2 2 N.S. 15.71 550000 Faust 9 9 2 2 N.S. 14.97 907000 Faust 10 10 2 2 N.S. 14.97 913000 Faust 11 11 2 2 N.S. 23.57 39140 Provines/Ocel5 1 1F1 F.S.6 N.A. 20 175000 Provines/Ocel 2 2F1 F.S. N.A. 20 174000 Provines/Ocel 3 3F2 F.S. N.A. 20 51000 Provines/Ocel 4 4F1 F.S. N.A. 20 91000 Provines/Ocel 5 2F2 F.S. N.A. 16 260000 Provines/Ocel 6 3F1 F.S. N.A. 16 747000 Provines/Ocel 7 4F2 F.S. N.A. 16 680000

1 Feldman, et al. (2011) [11]

2 Badie, et al. (2002) [8]

3 Mundie, D.L. (2011) [24]

4 Faust, et al.(2000) [25] 5 Provines, J., and Ocel, J.M. (2014) [26] 6 Full-scale beam test



Appendix B. Material Test Data

B1. Concrete Cylinder Fabrication and Testing

Concrete compressive strength was determined for the slab of each push-out specimen using cylinder compression tests. Approximately 12 concrete cylinders were created and tested from each concrete batch (four specimen slabs) following procedures outlined in the ASTM specifications [27,28]. Because concrete strength can change over time, compressive testing of the concrete cylinders coincided with beginning of each fatigue test. Figure B- 1 shows the test setup used to determine concrete compressive strength, consisting of a Forney concrete compression machine capable of applying 400 kips of axial force. Also shown in Figure B- 1 is the sample concrete cylinder geometry. Note that while the push-out specimens contain two concrete slabs, created from two separate concrete batches, the material strengths provided in Table 1 of Section 2 represent the average concrete strength from both slabs.

Figure B- 1. Concrete testing machine and cylinder dimensions

Table B-1 shows the age and strength of each individual concrete sample. In Table B-1 the number of cylinders available for material testing slightly varies between push-out specimens due to the amount of remaining concrete following casting.

Table B- 1. Concrete compression test data for push-out specimen slabs

Concrete Compressive Strength, f’c, MPa

1 2 3 4 5 6

Slab 1

42.0 47.3 40.2 54.2 46.8 58.4

38.4 46.8 40.7 56.6 40.7 55.4

-- 47.2 -- 61.4 -- 51.9

-- 43.8 -- -- -- --

-- 47.7 -- -- -- --

-- 43.3 -- -- -- --

Slab 2

45.4 50.2 46.9 58.4 45.7 57.3

37.6 49.7 48.9 56.8 -- 58.2

-- 48.2 -- 58.3 -- 57.0

-- 48.2 -- -- -- --

-- 54.3 -- -- -- --

-- 50.9 -- -- -- --

Average f’c, MPa 40.9 48.1 44.2 57.6 44.4 56.4

1

f'c

2

f'c



24



Appendix C. Verification of Negligible Inertial Effects under High Frequency Loading

To ensure appropriate applied stress ranges, all specimen loads applied in this study are determined by a controlled loop process driven by local load cell measurements (i.e. load controlled testing). Given that the load cell measurements are taken by a device mounted to the moving loading ram, at higher loading frequencies the possibility exists for inertial forces to influence load measurements and therefore the applied specimen loads.

To verify negligible inertial effects at higher frequency loadings and ensure consistency in the applied load across loading rates, the local slab slip response of the push-out specimens are compared under pseudo-static loading frequencies (1Hz) and high frequency loadings (20Hz). All slip measurements are taken from LVDTs locally mounted to the specimens. Figure C-1 shows the resulting slip versus time at 1Hz, 10Hz, and 20Hz loading frequencies for Specimen 5. From Figure C-1, peak displacement measurements remain similar across all loading rates. Assuming that the specimen stiffness remained relatively constant within 1,000 loading cycles, these similar slip readings indicate that the loads applied to the specimens are not influenced by inertial effects from the load cell movement at high frequencies.

Figure C-1. Comparison of slab slip measurements for Specimen 5 during high frequency dynamic loading. Comparisons presented represent (a) 1Hz and 10Hz loading rates, and (b) 1Hz and 20Hz loading rates

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0 0.2 0.4 0.6 0.8 1

Dis

plac

emen

t [m

m]

Time [sec]

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0 0.2 0.4 0.6 0.8 1

Dis

plac

emen

t [m

m]

Time [sec]

1Hz Loading

Similar displamementamplitude

Similar displamementamplitude

10Hz Loading

1Hz Loading

20Hz Loading

a)

b)



26



Appendix D. Stud Design Example Calculations for Prototype Bridges

The following figures provide calculation details for the number of required studs in the 5 prototype bridges. Note the values highlighted in red indicate a required pitch that exceeds the maximum stud spacing requirement as specified by [1] (in this case the maximum spacing limit is used).

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0.4

17.6

20.1

15.7

13.7

17.6

20.1

1614

61.3

15.3

45.3

59.3

14.0

18.0

536

2096

60.

514

.516

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.116

.714

.516

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1769

.07.

737

.751

.710

.821

.253

620

966

0.5

12.3

14.0

22.5

19.7

12.3

14.0

2220

76.7

0.0

30.0

44.0

7.6

24.5

536

2096

60.

610

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.212

.911

.310

.712

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11T

otal

174

152

176

157

Tra

nsve

rse

Spa

cing

No.

Stu

ds in

R

ow

Tru

ck D

etai

ls Unf

acto

red

Loa

dF

acto

red

Loa

d

3in

3st

uds

Mod

ular

R

atio

8

Equ

iv.

Wid

thL

oad

Fac

tors

9.8

in

Fig

ure

D-3

. Fat

igue

Lim

it S

tate

und

er f

init

e lo

adin

g fo

r br

idge

loca

ted

at th

e in

ters

ecti

on

of I

nter

stat

e 54

0 an

d th

e U

N P

AC

Rai

lroa

d ne

ar V

an B

uren

, Ark

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s.



30

FA

TIG

UE

LIM

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TA

TE

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dge

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nL

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To

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m

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thA

rea

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lang

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Fla

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eb

Thi

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ssI

Ste

elD

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n f'

cy b

ar

ftin

ftft

inin

2in

inin

in4

psi

in2

76.6

66.

56.

51

W36

x150

35.9

44.2

120.

940.

625

9040

4000

30.4

Tra

nsfo

rmed

Sec

tion

Pro

pert

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ar S

tud

Spe

cifi

cati

ons

She

ar R

esis

tanc

e

Axl

eE

s29

000

ksi

Dia

met

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75in

AD

TT

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00

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nt A

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1ki

psE

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t4

inn

1cy

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dle

Axl

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kips

28.5

kips

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cy

cles

Bac

k A

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32ki

ps28

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AS

HT

O α

2.67

Pro

pose

d α

3.80

Fat

igue

Loa

d C

ombi

natio

nI

AA

SH

TO

CA

FL

3.50

ksi

Fat

igue

Fac

tor

1.5

Pro

pose

d C

AF

L6.

50ks

i

Impa

ct F

acto

r1.

15A

AS

HT

O Z

r3.

09ki

ps

Inte

rior

Gird

er D

istr

ibut

ion

Fac

tor

0.52

Pro

pose

d Z

r5.

74ki

ps

Ext

erio

r G

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Dis

trib

utio

n F

acto

r0.

85

Loc

atio

nR

ear

Axl

e L

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ion

Mid

dle

Axl

e L

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ion

Fro

nt

Axl

e L

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ion

Rea

ctio

n A

Vf

Q

IV

srp

AA

SH

TO

p

Pro

pose

dN

o. S

tuds

A

AS

HT

ON

o. S

tuds

P

ropo

sed

Adj

uste

d S

paci

ng

AA

SH

TO

Adj

uste

d S

paci

ng

Pro

pose

d

Adj

uste

d N

o. S

tuds

A

AS

HT

O

Adj

uste

d N

o.

Stu

ds

Pro

pose

d

ftft

ftft

kips

kips

in3

in4

kips

/inin

inin

inin

inin

0.0

76.7

46.7

32.7

48.9

48.9

536

2096

61.

37.

413

.818

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413

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107.

769

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620

966

1.1

8.5

15.9

32.3

17.4

8.5

15.9

3217

15.3

61.3

31.3

17.3

36.1

36.1

536

2096

60.

910

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1523

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729

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620

966

0.8

12.2

22.7

22.6

12.2

12.2

22.7

2312

30.7

46.0

16.0

2.0

23.2

23.2

536

2096

60.

615

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.79.

515

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1138

.338

.38.

30.

017

.417

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620

966

0.4

20.9

38.8

13.2

7.1

20.9

24.0

1311

46.0

30.7

60.7

74.7

40.9

23.2

536

2096

60.

615

.629

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.79.

515

.624

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1153

.723

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620

966

0.8

12.2

22.7

22.6

12.2

12.2

22.7

2312

61.3

15.3

45.3

59.3

28.1

36.1

536

2096

60.

910

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.727

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1569

.07.

737

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.721

.742

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620

966

1.1

8.5

15.9

32.3

17.4

8.5

15.9

3217

76.7

0.0

30.0

44.0

15.3

48.9

536

2096

61.

37.

413

.818

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.07.

413

.819

10T

otal

250

135

250

143

Tra

nsve

rse

Spa

cing

No.

Stu

ds in

R

ow

Tru

ck D

etai

ls Unf

acto

red

Loa

dF

acto

red

Loa

d

3in

3st

uds

Mod

ular

R

atio

8

Equ

iv.

Wid

thL

oad

Fac

tors

9.8

in

Fig

ure

D-4

. Fa

tigu

e L

imit

Sta

te

unde

r in

fini

te

load

ing

for

brid

ge

loca

ted

at

the

inte

rsec

tion

of

Inte

rsta

te 5

40 a

nd th

e U

N P

AC

Rai

lroa

d ne

ar V

an B

uren

, Ark

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s.



FA

TIG

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rea

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eb

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ssI

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elD

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n f'

cy b

ar

ftin

ftft

inin

2in

inin

in4

psi

in3

657.

58.

51.

5W

36x1

3535

.639

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0.79

0.6

7800

4000

33.0

Tra

nsfo

rmed

Sec

tion

Pro

pert

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ar S

tud

Spe

cifi

cati

ons

She

ar R

esis

tanc

e

Axl

eE

s29

000

ksi

Dia

met

er0.

75in

AD

TT

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0

Fro

nt A

xle

8ki

ps4.

0ki

psE

c36

05ks

iH

eigh

t4

inn

1cy

cles

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dle

Axl

e32

kips

16.1

kips

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cy

cles

Bac

k A

xle

32ki

ps16

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psA

AS

HT

O α

3.96

Pro

pose

d α

4.52

Fat

igue

Loa

d C

ombi

natio

nII

AA

SH

TO

CA

FL

3.50

ksi

Fat

igue

Fac

tor

0.75

Pro

pose

d C

AF

L6.

50ks

i

Impa

ct F

acto

r1.

15A

AS

HT

O Z

r2.

23ki

ps

Inte

rior

Gird

er D

istr

ibut

ion

Fac

tor

0.58

Pro

pose

d Z

r2.

54ki

ps

Ext

erio

r G

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Dis

trib

utio

n F

acto

r0.

59

Loc

atio

nR

ear

Axl

e L

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ion

Mid

dle

Axl

e L

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ion

Fro

nt

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e L

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ion

Rea

ctio

n A

Vf

Q

IV

srp

AA

SH

TO

p

Pro

pose

dN

o. S

tuds

A

AS

HT

ON

o. S

tuds

P

ropo

sed

Adj

uste

d S

paci

ng

AA

SH

TO

Adj

uste

d S

paci

ng

Pro

pose

d

Adj

uste

d N

o. S

tuds

A

AS

HT

O

Adj

uste

d N

o.

Stu

ds

Pro

pose

d

ftft

ftft

kips

kips

in3

in4

kips

/inin

inin

inin

inin

0.0

65.0

35.0

21.0

26.1

26.1

581

2127

60.

79.

410

.712

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.99.

410

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116.

558

.528

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121

276

0.6

10.9

12.4

21.5

18.8

10.9

12.4

2119

13.0

52.0

22.0

8.0

18.8

18.8

581

2127

60.

513

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1619

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515

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121

276

0.4

16.1

18.4

14.5

12.7

16.1

18.4

1513

26.0

39.0

9.0

0.0

11.9

11.9

581

2127

60.

320

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1032

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50.

08.

78.

758

121

276

0.2

28.2

32.2

8.3

7.3

24.0

24.0

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39.0

26.0

56.0

0.0

20.3

11.9

581

2127

60.

320

.623

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1045

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121

276

0.4

16.1

18.4

14.5

12.7

16.1

18.4

1513

52.0

13.0

43.0

57.0

17.4

18.8

581

2127

60.

513

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1658

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536

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121

276

0.6

10.9

12.4

21.5

18.8

10.9

12.4

2119

65.0

0.0

30.0

44.0

10.2

26.1

581

2127

60.

79.

410

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410

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11T

otal

164

144

165

146

Tra

nsve

rse

Spa

cing

No.

Stu

ds in

R

ow

Tru

ck D

etai

ls Unf

acto

red

Loa

dF

acto

red

Loa

d

3in

3st

uds

Mod

ular

R

atio

8

Equ

iv.

Wid

thL

oad

Fac

tors

12.8

in

Figu

re D

-5. F

atig

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imit

Sta

te u

nder

fin

ite

load

ing

for

brid

ge lo

cate

d in

San

dy S

prin

gs,

Okl

ahom

a on

US

64

at t

he i

nter

sect

ion

of S

97th

W A

ve.

Tw

o di

ffer

ent

span

s fr

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his

brid

ge a

re u

sed

in th

ese

desi

gn e

xam

ples

.



32

FA

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UE

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IT S

TA

TE

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Spe

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m

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rea

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ssW

eb

Thi

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ssI

Ste

elD

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n f'

cy b

ar

ftin

ftft

inin

2in

inin

in4

psi

in3

657.

58.

51.

5W

36x1

3535

.639

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0.79

0.6

7800

4000

33.0

Tra

nsfo

rmed

Sec

tion

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pert

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ar S

tud

Spe

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cati

ons

She

ar R

esis

tanc

e

Axl

eE

s29

000

ksi

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met

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AD

TT

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00

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nt A

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ps8.

1ki

psE

c36

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iH

eigh

t4

inn

1cy

cles

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dle

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kips

32.2

kips

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cy

cles

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k A

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ps32

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psA

AS

HT

O α

2.67

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pose

d α

3.80

Fat

igue

Loa

d C

ombi

natio

nI

AA

SH

TO

CA

FL

3.50

ksi

Fat

igue

Fac

tor

1.5

Pro

pose

d C

AF

L6.

50ks

i

Impa

ct F

acto

r1.

15A

AS

HT

O Z

r3.

09ki

ps

Inte

rior

Gird

er D

istr

ibut

ion

Fac

tor

0.58

Pro

pose

d Z

r5.

74ki

ps

Ext

erio

r G

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Dis

trib

utio

n F

acto

r0.

59

Loc

atio

nR

ear

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e L

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Mid

dle

Axl

e L

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ion

Fro

nt

Axl

e L

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ion

Rea

ctio

n A

Vf

Q

IV

srp

AA

SH

TO

p

Pro

pose

dN

o. S

tuds

A

AS

HT

ON

o. S

tuds

P

ropo

sed

Adj

uste

d S

paci

ng

AA

SH

TO

Adj

uste

d S

paci

ng

Pro

pose

d

Adj

uste

d N

o. S

tuds

A

AS

HT

O

Adj

uste

d N

o.

Stu

ds

Pro

pose

d

ftft

ftft

kips

kips

in3

in4

kips

/inin

inin

inin

inin

0.0

65.0

35.0

21.0

52.1

52.1

581

2127

61.

46.

512

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76.

512

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106.

558

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121

276

1.2

7.6

14.1

30.9

16.6

7.6

14.1

3117

13.0

52.0

22.0

8.0

37.6

37.6

581

2127

61.

09.

016

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530

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121

276

0.8

11.2

20.8

20.9

11.3

11.2

20.8

2111

26.0

39.0

9.0

0.0

23.8

23.8

581

2127

60.

614

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814

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50.

017

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121

276

0.5

19.6

36.4

11.9

6.4

19.6

24.0

1210

39.0

26.0

56.0

0.0

40.6

23.8

581

2127

60.

614

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814

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121

276

0.8

11.2

20.8

20.9

11.3

11.2

20.8

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52.0

13.0

43.0

57.0

34.8

37.6

581

2127

61.

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016

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1458

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536

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121

276

1.2

7.6

14.1

30.9

16.6

7.6

14.1

3117

65.0

0.0

30.0

44.0

20.3

52.1

581

2127

61.

46.

512

.117

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76.

512

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10T

otal

236

127

236

132

Tra

nsve

rse

Spa

cing

No.

Stu

ds in

R

ow

Tru

ck D

etai

ls Unf

acto

red

Loa

dF

acto

red

Loa

d

3in

3st

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Mod

ular

R

atio

8

Equ

iv.

Wid

thL

oad

Fac

tors

12.8

in

Fig

ure

D-6

. F

atig

ue L

imit

Sta

te u

nder

inf

init

e lo

adin

g fo

r br

idge

loc

ated

in

Sand

y Sp

ring

s,

Okl

ahom

a on

US

64

at t

he i

nter

sect

ion

of S

97th

W A

ve.

Tw

o di

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ent

span

s fr

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brid

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re u

sed

in th

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desi

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xam

ples

.



FA

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UE

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IT S

TA

TE

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dge

Spe

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To

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B

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m

Dep

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rea

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lang

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idth

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ssW

eb

Thi

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ssI

Ste

elD

esig

n f'

cy b

ar

ftin

ftft

inin

2in

inin

in4

psi

in4

327.

58.

51.

5W

27x8

426

.724

.810

0.64

0.46

2850

4000

26.9

Tra

nsfo

rmed

Sec

tion

Pro

pert

ieShe

ar S

tud

Spe

cifi

cati

ons

She

ar R

esis

tanc

e

Axl

eE

s29

000

ksi

Dia

met

er0.

75in

AD

TT

SL50

0

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nt A

xle

8ki

ps4.

0ki

psE

c36

05ks

iH

eigh

t4

inn

2cy

cles

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dle

Axl

e32

kips

16.1

kips

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,000

cy

cles

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k A

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ps16

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psA

AS

HT

O α

2.67

Pro

pose

d α

3.80

Fat

igue

Loa

d C

ombi

natio

nII

AA

SH

TO

CA

FL

3.50

ksi

Fat

igue

Fac

tor

0.75

Pro

pose

d C

AF

L6.

50ks

i

Impa

ct F

acto

r1.

15A

AS

HT

O Z

r1.

50ki

ps

Inte

rior

Gird

er D

istr

ibut

ion

Fac

tor

0.58

Pro

pose

d Z

r2.

14ki

ps

Ext

erio

r G

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Dis

trib

utio

n F

acto

r0.

59

Loc

atio

nR

ear

Axl

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ion

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dle

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e L

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e L

ocat

ion

Rea

ctio

n A

Vf

Q

IV

srp

AA

SH

TO

p

Pro

pose

dN

o. S

tuds

A

AS

HT

ON

o. S

tuds

P

ropo

sed

Adj

uste

d S

paci

ng

AA

SH

TO

Adj

uste

d S

paci

ng

Pro

pose

d

Adj

uste

d N

o. S

tuds

A

AS

HT

O

Adj

uste

d N

o.

Stu

ds

Pro

pose

d

ftft

ftft

kips

kips

in3

in4

kips

/inin

inin

inin

inin

0.0

32.0

2.0

0.0

17.1

17.1

313

9057

0.6

5.1

7.2

7.6

5.3

5.1

7.2

85

3.2

28.8

0.0

0.0

14.5

14.5

313

9057

0.5

6.0

8.5

12.8

9.0

6.0

8.5

139

6.4

25.6

0.0

0.0

12.9

12.9

313

9057

0.4

6.7

9.6

11.4

8.0

6.7

9.6

118

9.6

22.4

0.0

0.0

11.3

11.3

313

9057

0.4

7.7

11.0

10.0

7.0

7.7

11.0

107

12.8

19.2

0.0

0.0

9.7

9.7

313

9057

0.3

9.0

12.8

8.5

6.0

9.0

12.8

96

16.0

16.0

0.0

0.0

8.0

8.0

313

9057

0.3

10.8

15.4

7.1

5.0

10.8

15.4

75

19.2

12.8

0.0

0.0

6.4

9.7

313

9057

0.3

9.0

12.8

8.5

6.0

9.0

12.8

96

22.4

9.6

0.0

0.0

4.8

11.3

313

9057

0.4

7.7

11.0

10.0

7.0

7.7

11.0

107

25.6

6.4

0.0

0.0

3.2

12.9

313

9057

0.4

6.7

9.6

11.4

8.0

6.7

9.6

118

28.8

3.2

0.0

0.0

1.6

14.5

313

9057

0.5

6.0

8.5

12.8

9.0

6.0

8.5

139

32.0

0.0

30.0

0.0

15.1

17.1

313

9057

0.6

5.1

7.2

7.6

5.3

5.1

7.2

85

Tot

al10

876

108

76

Tra

nsve

rse

Spa

cing

No.

Stu

ds in

R

ow

Tru

ck D

etai

ls Unf

acto

red

Loa

dF

acto

red

Loa

d

3in

2st

uds

Mod

ular

R

atio

8

Equ

iv.

Wid

thL

oad

Fac

tors

12.8

in

Fig

ure

D-7

. F

atig

ue L

imit

Sta

te u

nder

fin

ite

load

ing

for

brid

ge l

ocat

ed i

n S

andy

Spr

ings

, O

klah

oma

on U

S 6

4 at

the

int

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ctio

n of

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th W

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wo

diff

eren

t sp

ans

from

thi

s br

idge

are

use

d in

thes

e de

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mpl

es.



34

FA

TIG

UE

LIM

IT S

TA

TE

Bri

dge

Spe

cifi

cati

ons

Spa

nL

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elD

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n f'

cy b

ar

ftin

ftft

inin

2in

inin

in4

psi

in4

327.

58.

51.

5W

27x8

426

.724

.810

0.64

0.46

2850

4000

26.9

Tra

nsfo

rmed

Sec

tion

Pro

pert

ieShe

ar S

tud

Spe

cifi

cati

ons

She

ar R

esis

tanc

e

Axl

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s29

000

ksi

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met

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75in

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00

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nt A

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1ki

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inn

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cles

Mid

dle

Axl

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kips

32.2

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cy

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Bac

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32ki

ps32

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AS

HT

O α

1.38

Pro

pose

d α

3.20

Fat

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Loa

d C

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natio

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AA

SH

TO

CA

FL

3.50

ksi

Fat

igue

Fac

tor

1.5

Pro

pose

d C

AF

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50ks

i

Impa

ct F

acto

r1.

15A

AS

HT

O Z

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09ki

ps

Inte

rior

Gird

er D

istr

ibut

ion

Fac

tor

0.58

Pro

pose

d Z

r5.

74ki

ps

Ext

erio

r G

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Dis

trib

utio

n F

acto

r0.

59

Loc

atio

nR

ear

Axl

e L

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ion

Mid

dle

Axl

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ion

Fro

nt

Axl

e L

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ion

Rea

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n A

Vf

Q

IV

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AA

SH

TO

p

Pro

pose

dN

o. S

tuds

A

AS

HT

ON

o. S

tuds

P

ropo

sed

Adj

uste

d S

paci

ng

AA

SH

TO

Adj

uste

d S

paci

ng

Pro

pose

d

Adj

uste

d N

o. S

tuds

A

AS

HT

O

Adj

uste

d N

o.

Stu

ds

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pose

d

ftft

ftft

kips

kips

in3

in4

kips

/inin

inin

inin

inin

0.0

32.0

2.0

0.0

34.2

34.2

313

9057

1.2

5.2

9.7

7.3

4.0

5.2

9.7

74

3.2

28.8

0.0

0.0

29.0

29.0

313

9057

1.0

6.2

11.5

12.4

6.7

6.2

11.5

127

6.4

25.6

0.0

0.0

25.8

25.8

313

9057

0.9

7.0

12.9

11.0

5.9

7.0

12.9

116

9.6

22.4

0.0

0.0

22.5

22.5

313

9057

0.8

7.9

14.8

9.7

5.2

7.9

14.8

105

12.8

19.2

0.0

0.0

19.3

19.3

313

9057

0.7

9.3

17.2

8.3

4.5

9.3

17.2

84

16.0

16.0

0.0

0.0

16.1

16.1

313

9057

0.6

11.1

20.7

6.9

3.7

11.1

20.7

74

19.2

12.8

0.0

0.0

12.9

19.3

313

9057

0.7

9.3

17.2

8.3

4.5

9.3

17.2

84

22.4

9.6

0.0

0.0

9.7

22.5

313

9057

0.8

7.9

14.8

9.7

5.2

7.9

14.8

105

25.6

6.4

0.0

0.0

6.4

25.8

313

9057

0.9

7.0

12.9

11.0

5.9

7.0

12.9

116

28.8

3.2

0.0

0.0

3.2

29.0

313

9057

1.0

6.2

11.5

12.4

6.7

6.2

11.5

127

32.0

0.0

30.0

0.0

30.2

34.2

313

9057

1.2

5.2

9.7

7.3

4.0

5.2

9.7

74

Tot

al10

456

104

56

Tra

nsve

rse

Spa

cing

No.

Stu

ds in

R

ow

Tru

ck D

etai

ls Unf

acto

red

Loa

dF

acto

red

Loa

d

3in

2st

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Mod

ular

R

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8

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iv.

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thL

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Fac

tors

12.8

in

Figu

re D

-8.

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Lim

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load

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for

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ge l

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4 at

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are

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FA

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inin

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psi

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406.

56.

250.

75W

21x6

221

18.3

8.24

0.61

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413

3040

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form

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d S

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0

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SH

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3.50

ksi

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tor

0.75

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50ks

i

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Inte

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tor

0.51

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80

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ear

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TO

p

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dN

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A

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HT

ON

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tuds

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uste

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paci

ng

AA

SH

TO

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uste

d S

paci

ng

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pose

d

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d N

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tuds

A

AS

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d N

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Stu

ds

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pose

d

ftft

ftft

kips

kips

in3

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kips

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inin

inin

inin

0.0

40.0

10.0

0.0

17.5

17.5

178

4205

0.7

4.0

5.7

11.9

8.3

4.5

5.7

118

4.0

36.0

6.0

0.0

14.7

14.7

178

4205

0.6

4.8

6.8

20.0

14.0

4.8

6.8

2014

8.0

32.0

2.0

0.0

11.9

11.9

178

4205

0.5

5.9

8.5

16.2

11.4

5.9

8.5

1611

12.0

28.0

0.0

0.0

9.8

9.8

178

4205

0.4

7.2

10.3

13.3

9.3

7.2

10.3

139

16.0

24.0

0.0

0.0

8.4

8.4

178

4205

0.4

8.4

12.0

11.4

8.0

8.4

12.0

118

20.0

20.0

0.0

0.0

7.0

7.0

178

4205

0.3

10.1

14.4

9.5

6.7

10.1

14.4

107

24.0

16.0

0.0

0.0

5.6

8.4

178

4205

0.4

8.4

12.0

11.4

8.0

8.4

12.0

118

28.0

12.0

0.0

0.0

4.2

9.8

178

4205

0.4

7.2

10.3

13.3

9.3

7.2

10.3

139

32.0

8.0

38.0

0.0

16.1

11.9

178

4205

0.5

5.9

8.5

16.2

11.4

5.9

8.5

1611

36.0

4.0

34.0

0.0

13.3

14.7

178

4205

0.6

4.8

6.8

20.0

14.0

4.8

6.8

2014

40.0

0.0

30.0

0.0

10.5

17.5

178

4205

0.7

4.0

5.7

11.9

8.3

4.5

5.7

118

Tot

al15

510

915

310

9

Tra

nsve

rse

Spa

cing

No.

Stu

ds in

R

ow

Tru

ck D

etai

ls Unf

acto

red

Loa

dF

acto

red

Loa

d

3in

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Mod

ular

R

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8

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thL

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tors

9.4

in

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D-9

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Lim

it S

tate

und

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init

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adin

g fo

r br

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loc

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at

the

inte

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of

Inte

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40 a

nd F

lat R

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Cre

ek n

ear

Van

Bur

en, A

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36

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inin

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psi

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406.

56.

250.

75W

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221

18.3

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0.61

50.

413

3040

0021

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form

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i

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ion

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tor

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80

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ear

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ng

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d S

paci

ng

Pro

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d

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tuds

A

AS

HT

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d N

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Stu

ds

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pose

d

ftft

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kips

kips

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kips

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inin

inin

inin

0.0

40.0

10.0

0.0

35.1

35.1

178

4205

1.5

4.2

7.7

11.5

6.2

4.5

7.7

116

4.0

36.0

6.0

0.0

29.5

29.5

178

4205

1.2

5.0

9.2

19.4

10.4

5.0

9.2

1910

8.0

32.0

2.0

0.0

23.9

23.9

178

4205

1.0

6.1

11.4

15.7

8.5

6.1

11.4

168

12.0

28.0

0.0

0.0

19.6

19.6

178

4205

0.8

7.4

13.8

12.9

7.0

7.4

13.8

137

16.0

24.0

0.0

0.0

16.8

16.8

178

4205

0.7

8.7

16.1

11.1

6.0

8.7

16.1

116

20.0

20.0

0.0

0.0

14.0

14.0

178

4205

0.6

10.4

19.3

9.2

5.0

10.4

19.3

95

24.0

16.0

0.0

0.0

11.2

16.8

178

4205

0.7

8.7

16.1

11.1

6.0

8.7

16.1

116

28.0

12.0

0.0

0.0

8.4

19.6

178

4205

0.8

7.4

13.8

12.9

7.0

7.4

13.8

137

32.0

8.0

38.0

0.0

32.3

23.9

178

4205

1.0

6.1

11.4

15.7

8.5

6.1

11.4

168

36.0

4.0

34.0

0.0

26.7

29.5

178

4205

1.2

5.0

9.2

19.4

10.4

5.0

9.2

1910

40.0

0.0

30.0

0.0

21.0

35.1

178

4205

1.5

4.2

7.7

11.5

6.2

4.5

7.7

116

Tot

al15

081

149

81

Tra

nsve

rse

Spa

cing

No.

Stu

ds in

R

ow

Tru

ck D

etai

ls Unf

acto

red

Loa

dF

acto

red

Loa

d

3in

2st

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Mod

ular

R

atio

8

Equ

iv.

Wid

thL

oad

Fac

tors

9.4

in

Figu

re D

-10.

Fat

igue

Lim

it S

tate

und

er i

nfin

ite

load

ing

for

brid

ge l

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STRENGTH LIMIT STATEProperties Bridge Span 1 φsc 0.85 Strength Limit State Stud Req. Asc 0.44 in2 Qn 26.5 kip f'c 4000 psi Qn check 26.5 kip Ec 3605 ksi Qn check NOT OK Fu 60 ksi Qr 22.5 kip bs 78 P1p 1724 kip ts 6.5 P2p 2191 kip Fyw 50 ksi P 1724 kip D 34.02 in2 Total (n) 76 studs tw 0.625 Fyt 50 ksi bft 12 tft 0.94 Fyc 50 ksi bfc 12 tfc 0.94

Figure D-11. Strength Limit State for the bridge located in Jackson, Arkansas on US 67 Northbound at the intersection of State Highway 161.


STRENGTH LIMIT STATEProperties 2

φsc 0.85 Strength Limit State Stud Req.

Asc 0.44 in2 Qn 26.5 kip

f'c 4000 psi Qn check 26.5 kip

Ec 3605 ksi Qn check NOT OK

Fu 60 ksi Qr 22.5 kip

bs 78 P1p 1724 kip

ts 6.5 P2p 2191 kip

Fyw 50 ksi P 1724 kip

D 34.02 in2 Total (n) 76 studs

tw 0.625

Fyt 50 ksi

bft 12

tft 0.94

Fyc 50 ksi

bfc 12

tfc 0.94

Bridge Span



38









bs 102 P1p 2601 kip

ts 7.5 P2p 1969 kip



tw 0.6

Fyt 50 ksi

bft 12

tft 0.79

Fyc 50 ksi

bfc 12

tfc 0.79

Bridge Span







bs 102 P1p 2601 kip

ts 7.5 P2p 1225 kip



tw 0.46

Fyt 50 ksi

bft 10

tft 0.64

Fyc 50 ksi

bfc 10

tfc 0.64

Bridge Span



Figure D-15. Strength Limit State for the bridge located at te intersection of Interstate-540 and Flat Rock Creek near Van Buren, Arkansas.







bs 75 P1p 1658 kip

ts 6.5 P2p 902 kip



tw 0.4

Fyt 50 ksi

bft 8.24

tft 0.615

Fyc 50 ksi

bfc 8.24

tfc 0.615

Bridge Span



40



Appendix E. Additional Slip and Separation Measurements

Slip and separation provide an indication of stud fatigue damage during testing. Figure E-1 provides the slip and separation data for Specimens 1, 3, 4, 5, and 6. Note that LVDT data for Specimen 2 is not provided as it was lost from the acquisition device during a power outage prior to test completion.

(a) (b)

Figure E-1. (a) Slip and (b) separation data from external LVDT measurements

0

0.1

0.2

0.3

0.4

0.5

0.6

Ave

rage

Slip

[m

m]

Specimen 1Δσ= 60MPa

Failure at12.8x106

cycles

0

0.1

0.2

0.3

0.4

0.5

0.6

Ave

rage

Slip

[m

m]


0

0.1

0.2

0.3

0.4

0.5

0.6

Ave

rage

Sli

p [m

m]


0

0.1

0.2

0.3

0.4

0.5

0.6

Ave

rage

Slip

[m

m]


0

0.1

0.2

0.3

0.4

0.5

0.6

100000 1000000 10000000

Ave

rage

Slip

[m

m]

Cycles


Documents

On the Fatigue Capacity of Headed Shear Studs in Composite ... · i On the Fatigue Capacity of Headed Shear Studs in Composite Bridge Girders SSRL – 0392-16028-22-0000 SSRL, November