DOT/FRA/ORD-23/26 Final Report | September 2023

High-Strength, Reduced-Modulus, High-Performance 

Concrete for Prestressed Concrete Crosstie 

Applications
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i 

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1. AGENCY USE ONLY (Leave blank) 2. REPORT DATE

May 2021

3. REPORT TYPE AND DATES COVERED

Technical Report

4. TITLE AND SUBTITLE

High-Strength, Reduced-Modulus, High-Performance Concrete for Prestressed Concrete 

Crosstie Applications

5. FUNDING NUMBERS

DTFR5314C00023

6. AUTHOR(S) Dimitris C. Rizos, Ph.D., Adam Zeitouni, Ali Abdulqader

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)

University of South Carolina

Columbia, South Carolina 29208

8. PERFORMING ORGANIZATION 

REPORT NUMBER

9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES)

U.S. Department of Transportation 

Federal Railroad Administration

Office of Railroad Policy and Development

Office of Research, Development, and Technology

Washington, DC 20590

10. SPONSORING/MONITORING

AGENCY REPORT NUMBER

DOT/FRA/ORD-23/26

11. SUPPLEMENTARY NOTES

COR: Cameron Stuart

12a. DISTRIBUTION/AVAILABILITY STATEMENT

This document is available to the public through the FRA eLibrary. 

12b. DISTRIBUTION CODE

13. ABSTRACT (Maximum 200 words)

High-performance concrete (HPC) with early strength development is the material of choice for fabricating prestressed concrete 

railroad ties. However, the higher strength of HPC results in significantly higher elastic modulus values and increases the rigidity 

of the tie, leading to higher amplitude stresses and stress gradients, and eventually to premature cracking and deterioration of the 

railroad ties. This report presents material development and characterization studies of high-strength, reduced-modulus (HSRM) 

concrete and its application for concrete railroad ties. Prototype ties have been fabricated and qualified through testing and 

computer simulations. The fabrication of the HSRM ties did not affect the current fabrication practices and cost. This study shows

that HSRM ties outperformed standard concrete ties by (a) showing smoother stress distribution, (b) delaying the initiation of 

cracks, (c) redistributing the load after first cracking in an effective manner, and (d) failing at higher ultimate loads. Researchers

suggest HSRM concrete is a cost-effective alternative concrete to the industry standard concrete used in ties and has the potential 

to increase its tie service life.

14. SUBJECT TERMS

Concrete, crosstie, weathered aggregate, granite, modulus

15. NUMBER OF PAGES

55 

16. PRICE CODE

17. SECURITY CLASSIFICATION

OF REPORT

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18. SECURITY CLASSIFICATION

OF THIS PAGE

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19. SECURITY CLASSIFICATION

OF ABSTRACT

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20. LIMITATION OF ABSTRACT

NSN 7540-01-280-5500 Standard Form 298 (Rev. 2-89)

Prescribed by ANSI Std. 239-18

298-102
ii

METRIC/ENGLISH CONVERSION FACTORS

ENGLISH TO METRIC METRIC TO ENGLISH

LENGTH (APPROXIMATE) LENGTH (APPROXIMATE)

1 inch (in) = 2.5 centimeters (cm) 1 millimeter (mm) = 0.04 inch (in)

1 foot (ft) = 30 centimeters (cm) 1 centimeter (cm) = 0.4 inch (in)

1 yard (yd) = 0.9 meter (m) 1 meter (m) = 3.3 feet (ft)

1 mile (mi) = 1.6 kilometers (km) 1 meter (m) = 1.1 yards (yd)

1 kilometer (km) = 0.6 mile (mi)

AREA (APPROXIMATE) AREA (APPROXIMATE)

1 square inch (sq in, in2) = 6.5 square centimeters (cm2) 1 square centimeter (cm2) = 0.16 square inch (sq in, in2) 

1 square foot (sq ft, ft2) = 0.09 square meter (m2) 1 square meter (m2) = 1.2 square yards (sq yd, yd2)

1 square yard (sq yd, yd2) = 0.8 square meter (m2) 1 square kilometer (km2) = 0.4 square mile (sq mi, mi2)

1 square mile (sq mi, mi2) = 2.6 square kilometers (km2) 10,000 square meters (m2) = 1 hectare (ha) = 2.5 acres

1 acre = 0.4 hectare (he) = 4,000 square meters (m2) 

MASS - WEIGHT (APPROXIMATE) MASS - WEIGHT (APPROXIMATE)

1 ounce (oz) = 28 grams (gm) 1 gram (gm) = 0.036 ounce (oz)

1 pound (lb) = 0.45 kilogram (kg) 1 kilogram (kg) = 2.2 pounds (lb)

1 short ton = 2,000 pounds 

(lb)

= 0.9 tonne (t) 1 tonne (t) =

=

1,000 kilograms (kg)

1.1 short tons

VOLUME (APPROXIMATE) VOLUME (APPROXIMATE)

1 teaspoon (tsp) = 5 milliliters (ml) 1 milliliter (ml) = 0.03 fluid ounce (fl oz)

1 tablespoon (tbsp) = 15 milliliters (ml) 1 liter (l) = 2.1 pints (pt)

1 fluid ounce (fl oz) = 30 milliliters (ml) 1 liter (l) = 1.06 quarts (qt)

1 cup (c) = 0.24 liter (l) 1 liter (l) = 0.26 gallon (gal)

1 pint (pt) = 0.47 liter (l)

1 quart (qt) = 0.96 liter (l)

1 gallon (gal) = 3.8 liters (l)

1 cubic foot (cu ft, ft3) = 0.03 cubic meter (m3) 1 cubic meter (m3) = 36 cubic feet (cu ft, ft3) 

1 cubic yard (cu yd, yd3) = 0.76 cubic meter (m3) 1 cubic meter (m3) = 1.3 cubic yards (cu yd, yd3)

TEMPERATURE (EXACT) TEMPERATURE (EXACT)

[(x-32)(5/9)] °F = y °C [(9/5) y + 32] °C = x °F

QUICK INCH - CENTIMETER LENGTH CONVERSION

0 1 2 3 4 5

Inches

Centimeters 0 1 2 3 4 5 6 987 1110 1312

QUICK FAHRENHEIT - CELSIUS TEMPERATURE CONVERSIO

 -40° -22° -4° 14° 32° 50° 68° 86° 104° 122° 140° 158° 176° 194° 212°

 

°F

 °C -40° -30° -20° -10° 0° 10° 20° 30° 40° 50° 60° 70° 80° 90° 100°

For more exact and or other conversion factors, see NIST Miscellaneous Publication 286, Units of Weights and 

Measures. Price $2.50 SD Catalog No. C13 10286 Updated 6/17/98
iii

Acknowledgments

The authors acknowledge the support and contributions of CSX Transportation and KSA (now 

ROCLA Concrete Tie). The support and insight provided by Cameron Stuart, John West, Tod 

Echler, Ryan Rolfe, Scott Craig, and Hailing Yu is greatly appreciated. The authors extend their 

appreciation to Professor Michael Sutton at the University of South Carolina for his guidance 

with the StereoDIC system and Sreehari Katil, Russell Inglett, Tim Ross, Josh Breed, Melissa 

Brueckner, and Brigitte Shumpert for their assistance with laboratory and plant activities.
iv

Contents

Executive Summary ........................................................................................................................ 1

1. Introduction ................................................................................................................. 3

1.1 Background ................................................................................................................. 3

1.2 Objectives .................................................................................................................... 5

1.3 Overall Approach ........................................................................................................ 6

1.4 Scope ........................................................................................................................... 6

1.5 Organization of the Report .......................................................................................... 6

2. The Baseline Prestressed Concrete Tie – “Standard” Tie ........................................... 7

2.1 Design Parameters ....................................................................................................... 7

2.2 Concrete Mix Design ................................................................................................... 8

3. HSRM Material Development and Characterization ................................................ 10

3.1 Coarse Aggregates and the HSRM Design Mix ........................................................ 10

3.2 Mechanical Properties ............................................................................................... 10

3.3 Weather Aggregate Selection .................................................................................... 13

4. Prototype Tie Fabrication and Qualification ............................................................. 14

4.1 Material Properties .................................................................................................... 15

4.2 Tie Qualification Tests .............................................................................................. 16

5. Laboratory Setup and Instrumentation ...................................................................... 17

5.1 Reaction Frame .......................................................................................................... 17

5.2 Indoor Track Testing Facility .................................................................................... 17

5.3 Instrumentation .......................................................................................................... 18

5.4 Vision-Based, Full-Field Measurements ................................................................... 18

6. Performance Assessment ........................................................................................... 23

6.1 Rail Seat Flexure Performance .................................................................................. 23

6.2 Mid-Tie Flexure Performance ................................................................................... 24

6.3 Loading under Simulated Track Support Conditions ................................................ 30

7. Conclusion ................................................................................................................. 40

8. References ................................................................................................................. 41

Abbreviations and Acronyms ....................................................................................................... 44
v 

Illustrations

Figure 1. Correlations of modulus of elasticity of HPC with weathered and unweathered 

aggregates with (a) modulus of elasticity of rock material and (b) average compressive 

strength (Petrou, Rizos, Harries, & Hanson, 2004) ................................................................ 5

Figure 2. Geometric design drawings and manufactured ties ......................................................... 7

Figure 3. Weathered granite coarse aggregates: (a) as delivered to USC laboratories, (b) CA2, (c) 

CA3, (d) CA4 ........................................................................................................................ 10

Figure 4. Comparison between HSRM and standard concrete: (a) compressive strength vs. 

specimen age and (b) modulus of elasticity vs. specimen age .............................................. 12

Figure 5. Correlation of modulus of elasticity with compressive strength for the HSRM (CA3-

B%) and standard concrete (CA1-B5) .................................................................................. 12

Figure 6. Concrete tie prestressing bed: (a) before placement of concrete; (b) after placement of 

concrete; (c) concrete cylinder preparation and (d) covering bed in preparation of concrete 

curing .................................................................................................................................... 14

Figure 7. Development of compressive strength and elastic modulus of HSRM and standard 

concrete: (a) compressive strength vs. specimen age and (b) modulus of elasticity vs. 

specimen age ......................................................................................................................... 15

Figure 8. Correlation of modulus of elasticity with compressive strength for the HSRM and 

standard concrete .................................................................................................................. 16

Figure 9. The reaction frame used for all load tests ...................................................................... 17

Figure 10. Indoor railway track testing facility ............................................................................ 18

Figure 11. Stereo vision system components ................................................................................ 19

Figure 12. Test setup for the validation study of the DIC data acquisition approach ................... 20

Figure 13. Longitudinal strain profile along a cross-section at the midspan of the prestressed 

concrete tie ............................................................................................................................ 20

Figure 14. Load vs. longitudinal strain at the extreme tension fiber at the midspan as acquired by 

strain gages and the StereoDIC system ................................................................................. 21

Figure 15. Load vs. vertical deflection at the midspan as acquired by LVDTs and the StereoDIC 

system ................................................................................................................................... 21

Figure 16. Color map showing the longitudinal strain field on the surface of the standard tie 

under 46-kip load. Cracks that extend to the first layer of strands are evident. .................... 22

Figure 17. Rail seat positive moment testing ................................................................................ 23

Figure 18. Cracking at 127% and 176% of the design load for the standard and HSRM ties ...... 24

Figure 20. Test setup for the modified 4-point center negative moment test. .............................. 25

Figure 21. Cracking maps as of the standard and HSRM ties during loading .............................. 26

Figure 23. Test setup for cyclic loading test under center binding conditions ............................. 26
vi 

Figure 24. Static tests of the HSRM tie after 13.5 kip load cycles: (a) longitudinal strain εxx field 

color maps; (b) HSRM tie elastic curves between supports; and (c) standard tie elastic 

curves between supports ....................................................................................................... 27

Figure 25. Longitudinal strain field εxx when the crack reaches the first line of strands in the 

standard tie at load 19 kips (left) and HSRM tie at load 20 kips (right). .............................. 28

Figure 26. Static tests of the HSRM tie under 16.5-kips load after predetermined number of 

cycles during Stage 2 of cyclic loading: (a) longitudinal strain εxx field color maps; (b) 

HSRM tie elastic curves between supports; (c) standard tie elastic curves between supports

............................................................................................................................................... 28

Figure 27. Load-deflection for ultimate load test ......................................................................... 29

Figure 28. Longitudinal strain field during testing to failure after 6 million load cycles shown for 

the HSRM ties (left column) and standard ties (right column). ............................................ 29

Figure 29. Loading frame, test setup, and support conditions for loading under simulated track 

support conditions in the laboratory ..................................................................................... 30

Figure 30. Strain gage locations.................................................................................................... 31

Figure 31. Potentiometer locations ............................................................................................... 31

Figure 32. Strain gauge results: (a) rail seat strain gauges; (b) intermediate strain gauges; and (c) 

center strain gauges ............................................................................................................... 32

Figure 33. Average deflection at 20 kips ...................................................................................... 34

Figure 34. Typical cracking pattern after center binding of standard (top) and HSRM (bottom) 

ties ......................................................................................................................................... 34

Figure 35. Three different ballast support condition representing: (a) full support (new track 

condition), (b) loss of center support, and (c) loss of rail seat support ................................. 35

Figure 36. Damage progression for the standard tie (left) and the HSRM tie (right) ................... 36
vii 

Tables

Table 1. Concrete tie design parameters ......................................................................................... 7

Table 2. Nominal capacity of railroad tie ....................................................................................... 8

Table 3. Concrete mix design ......................................................................................................... 9

Table 4. Properties of concrete produced with limestone and weathered granite coarse aggregates 

from 3 sources ....................................................................................................................... 11

Table 5. Modified 4-point bending load at characteristic damage levels ..................................... 25

Table 6. Averaged bending moment results (unit: kip-inches) ..................................................... 33

Table 7. Concrete material properties for the FEA analysis ......................................................... 35

Table 8. Summary of stress reduction for all concrete materials, support conditions and L/V 

ratios. Standard concrete shows nominal stress values in ksi. HSRM ties show the stress 

reduction as a percentage of the stress in the standard tie. ................................................... 38

Table 9. Modified 4-point bending load after 3 and 6 million load cycles ................................... 39
1 

Executive Summary 

Researchers at the University of South Carolina developed a high-strength concrete with a 

modulus of elasticity significantly lower than industry standard designs and tested this new 

material for use in railroad concrete crossties. The research team qualified high-strength, 

reduced-modulus (HSRM) ties according to the AREMA Manual for Railway Engineering 

guidelines and demonstrated their benefits through laboratory testing and computer simulation 

studies. This research was sponsored by Federal Railroad Administration and conducted between 

August 2014 and July 2018. This project utilized university laboratory facilities for modeling and 

testing, produced prototype concrete ties at the KSA (now Rocla Concrete Tie) manufacturing 

plant, and relied upon CSX Transportation technical support throughout the period of 

performance.

This research demonstrates the use of HSRM in prestressed concrete ties to address critical 

issues that affect the service life of standard concrete ties. Specifically, this project shows that 

ties made with HSRM concrete have the same high strength as with standard concrete designs 

but are significantly more flexible, allowing for better load distribution in the tie and the track, 

thus preventing premature cracking. 

The investigations were conducted in three phases: (a) material development and 

characterization, (b) prototype fabrication and product qualification, and (c) performance 

assessment and benefits.

The research team’s findings include:

• The HSRM concrete compressive strength was comparable to the standard mix.

• The HSRM modulus of elasticity was lower than the standard mix, by as much as 50 

percent. 

• HSRM concrete had a much higher abrasion resistance than the standard concrete.

• HSRM ties met the AREMA performance requirements and equaled or exceeded the 

performance of the standard ties. 

• HSRM ties exhibited smoother stress gradients and exhibited stress redistribution after 

initial cracking. 

• HSRM ties have lower stress amplitudes compared to standard ties under the same loads 

• HSRM ties withstood higher ultimate loads. 

• The use of weathered granites to produce the HSRM concrete ties did not impact the 

production process or increase the cost of the ties. 

The use of HSRM represents a technology-based modification in concrete tie manufacturing that 

improves the safety of rail service and maintenance operations without impacting fabrication cost 

and process. This study suggests that the HSRM concrete may become a cost-effective

alternative to the traditional high-performance concrete used in prestressed concrete ties with the 

potential to increase the service life of the tie. 
2 

Testing the in-track performance of HSRM ties under service operating conditions is 

recommended. Future work will also include tie design optimization based on HSRM material, 

investigations on the use of HSRM concrete in other concrete tie designs and systems, as well as 

its use in other railroad infrastructure parts. 
3 

1. Introduction

Researchers at the University of South Carolina developed a high-strength concrete with a 

modulus of elasticity significantly lower than industry standard designs and tested this new 

material for use in railroad concrete crossties. This research was sponsored by Federal Railroad 

Administration and conducted between August 2014 and July 2018. This project utilized 

university laboratory facilities for modeling and testing, produced prototype concrete ties at the 

KSA (now Rocla Concrete Tie) manufacturing plant, and relied upon CSX Transportation 

technical support throughout the period of performance. This introductory section presents the 

background information, motivation, and objectives related to this work. It also discusses the 

scope of work and the approach used to achieve the objectives. 

1.1 Background

Crossties are one of the main structural components of railroad track, supporting the rails and

distributing train axle loads to the ballast. Prestressed concrete ties have become an alternative to 

traditional timber ties for freight, passenger, and transit lines due to their increased strength, 

stability, and durability characteristics (Weart, 2008). Concrete ties must have a longer service 

life and require less maintenance compared to timber ties to offset their higher initial costs. Highstrength (HS) concrete with early strength development is currently the material of choice in the 

fabrication of prestressed concrete railroad ties; they have a design life of over 50 years (Lutch, 

Harris, & Ahlborn, 2009). 

However, concrete ties often do not reach their design life due to several unresolved performance 

issues (Kaewunruen & Remennikov, 2010; Jeong & Yu, 2012). Frequent inspections of many 

railroad tracks have uncovered concrete ties that have prematurely failed or cracked well before 

their designed service life. A 2010 study sponsored by the Railway Tie Association reported that 

of the “29 million ties that were installed since the 1970s, approximately 2.2 to 2.7 million ties 

were reported as failed and replaced” (ZETA-TECH, 2010). That is an approximate failure rate 

of 7.9 to 9.2 percent. These unexpected findings have prompted the need for further field 

investigations to assess the performance and behavior of concrete ties in service. 

In 2014, the Federal Railroad Administration (FRA) studied the performance of concrete ties that 

were installed on the Northeast Corridor (NEC) to determine the factors that lead to early 

cracking (FRA, 2014). The authors sought to study the horizontal cracking phenomenon known 

to appear along the top row of prestressed steel tendons located at one or both ends of a tie. The 

authors sampled different concrete ties of varying age and from five separate locations along 

Amtrak NEC lines. The concrete ties were inspected in both the field and laboratory. The 

concrete ties in the field were examined visually and non-destructively by the impact echo 

method. Laboratory tests were performed for modulus and strength, tensile strength, and flexural 

strength data, among others. Furthermore, the authors simulated various tests on the concrete ties 

by conducting finite element analysis. 

Based on the results from the FRA study’s extensive examinations, the authors concluded that 

the premature cracking of the concrete ties was caused by a combination of contributing factors. 

The first was a high concentration of tensile stress in the concrete ties, primarily located at the 

location of the prestressing steel, which is caused by the transfer of forces when the prestressed 

strands are released. The second factor was associated with the pressures produced by an alkali-
4 

silica reaction (ASR) that caused excessive internal stresses. Additionally, the authors concluded 

that other factors, such as cyclic freezing and thawing, delayed ettringite formation, and stresses 

due to fastener inserts or unusual tie vibrations were not major contributors to premature 

cracking of these specific ties. 

Longitudinal cracking is not the only concern related to the premature failure of concrete ties.

Zeman (2010), for example, published an extensive study on the rail seat deterioration (RSD) of 

concrete ties. Manda and his co-authors studied the effect of static and dynamic loads on the tie

and fastening system (Manda, Dersch, Edwards, & Lange, 2014). Surveys among the North 

American railroad companies (Zeman, Edwards, Barkan, & Lange, 2009; Van Dyk, Dersch, & 

Edwards, 2016) have shown that the most critical issues in tie performance, in order of 

importance, are: (1) RSD; (2) shoulder/fastener wear or fatigue; (3) derailment damage; (4) 

cracking from center binding; (5) cracking from dynamic loads; and (6) tamping damage, among 

others. The primary causes of RSD appear to be high stresses at the rail seat, a loosened 

fastening system, the presence of moisture, and the presence of abrasive fines. Cracking from 

center binding and dynamic loads is due to the development of high tensile stresses. Therefore, 

the development of high-amplitude stresses and the corresponding stress distribution within the 

tie appears to be a common underlying cause of the most critical issues that affect tie 

performance. In turn, high stresses and stress distribution are directly related to a combination of 

the strength and stiffness of a tie. Typically, a high-strength but relatively flexible load-bearing 

element results in more regularized (smoother) stress field gradients with reduced amplitudes 

that should alleviate the issues associated with high stresses in concrete ties. However, for a 

given tie geometry, strength and stiffness depend on the strength and elastic modulus of the 

materials. The higher strength of high-performance concrete (HPC) is directly related to higher 

values of the elastic modulus, thus increasing the rigidity of the material. Consequently, the 

combination of increased strength, rigidity, and brittleness may lead to premature cracking and 

deterioration of the concrete ties. 

Research conducted in 2000 (Petrou, Rizos, Harries, & Hanson, 2004) revealed that HPC 

mixtures could be classified as U.S. Federal Highway Administration (FHWA) Grade 1 or 2, 

based on their durability and strength properties (Goodspeed, Venikar, & Cook, 1996). In the 

process of the 2000 study, it was incidentally discovered that the values obtained for the modulus 

of elasticity for several the design mixes were well below the range of values specified for Grade 

1 of the FHWA classification. In addition, the elastic modulus of concrete could not be predicted 

using any of the empirical equations (e.g., ACI, 2014; ACI Committee 363, 1992; BSCP, 1972). 

An extensive investigation concluded that the low modulus values are attributable to the degree 

of weathering observed in the granite aggregates. These weathered granite aggregates can be 

found in South Carolina; (Aitkin & Mehta, 1990; Alexander & Milne, 1995; Giaccio, Rocco, 

Violini, Zappitelli, & Zerbino, 1992; Wu, Ke-Ru, Bing, & Dong, 2001). 

The major conclusions of the preceding work have been summarized by Petrou, Rizos, Harries, 

and Hanson (2004): 

(1) The modulus of elasticity of HPC is significantly affected by the extent of weathering 

on crushed granite aggregate and the susceptibility of its source to the weathering 

process, as shown in Figure 1 (a). Weathered aggregates should not be used in HPC 

mixes for bridge construction. 
5 

(2) For unaltered granite aggregate concrete, as the concrete compressive strength 

increases so does the elastic moduli of the associated HPC. For weathered aggregate 

concrete, there is little correlation between the concrete elastic modulus and its 

compressive strength, as shown in Figure 1 (b).

(3) The design code equations may overestimate the elastic modulus of concrete with 

weathered aggregates by as much as 70 percent. 

Figure 1. Correlations of modulus of elasticity of HPC with weathered and unweathered 

aggregates with (a) modulus of elasticity of rock material and (b) average compressive 

strength (Petrou, Rizos, Harries, & Hanson, 2004) 

1.2 Objectives

This work investigates the benefits of using high-strength, reduced-modulus (HSRM) concrete in 

place of the currently used high-strength (standard) concrete mixes in the fabrication of 

prestressed concrete rail ties. The hypothesis is that the use of HSRM in the fabrication of ties

combines the advantages of the high strength of HPC while preserving the structural 

performance advantages of more flexible materials. Specifically, this work demonstrates that 

HSRM ties have the same or higher strength as the standard ties but are significantly more 

flexible, allowing for better load distribution in the tie and the track, smaller stress amplitudes, 

and a smoother stress gradient. This work demonstrates that premature failures can be avoided, 

and damage initiation delayed, thus extending the service life of the ties. 

The objectives of this work are summarized as: 

1. Develop and characterize a HSRM concrete consistent with the specifications for use in 

prestressed concrete ties. 

2. Produce, test, and qualify a prototype prestressed concrete tie made of this HSRM 

concrete material. 

3. Investigate the performance of HSRM and standard ties through physical testing and

computer simulations.

4. Quantify the benefits of using HSRM concrete in place of standard concrete in 

prestressed concrete ties. 
6 

1.3 Overall Approach

To achieve the objectives set in Section 1.2, the research team studied a prestressed concrete tie 

design currently available in the U.S. market. The team adopted the design specifications of this

standard tie in developing the HSRM material and the prototype HSRM tie. A series of physical 

tests and computer simulations compared the performance of the HSRM and standard ties. The

standard tie provided the baseline data for quantifying the performance of the HSRM tie. 

The investigation was conducted in three phases: (a) material development and characterization, 

(b) prototype fabrication and product qualification, and (c) performance assessment and benefits. 

The first phase pertains to material development and characterization of the HSRM concrete

using weathered granite aggregates from different sources. The HSRM concrete mix design was

the same as the standard mix, with the exception that the HSRM used weathered granite as 

coarse aggregate in place of the limestone coarse aggregates used in the standard design. The 

gradation of the weathered granites was the same as the limestone coarse aggregate. The 

mechanical properties of the HSRM and standard concretes and the constituent materials were

determined through ASTM standard testing. In addition to the ASTM standard tests, a lapping 

test was performed on the hardened concrete to measure the abrasion resistance of the concrete. 

This lapping test was developed by University of Illinois Urbana-Champaign (UIUC) (Van Dam, 

2016). 

The second phase focused on the fabrication of prototype HSRM ties and baseline standard ties. 

All ties were fabricated at the KSA concrete tie fabrication facility and shipped to the 

laboratories for testing and qualification. Qualification tests were conducted in accordance with 

AREMA guidelines for prestressed concrete tie testing.

The last phase quantified the benefits of using HSRM concrete in place of standard concrete 

through a comparison of the structural performance of each tie. Researchers conducted these 

studies through lab testing and computer simulations. 

1.4 Scope 

The scope of this work was to develop the HSRM material and establish its mechanical 

properties. This work adopted one commercially available tie design to demonstrate the benefits 

of using HSRM concrete through a direct comparison of the structural performance of HSRM 

and standard ties. The work reported here did not consider the optimization of tie design based 

on the HSRM material. In addition, this study did not consider other commercially available 

designs, including post-tensioning systems or any other concrete mix designs. 

1.5 Organization of the Report

Section 2 introduces the geometry, material, and design parameters of the standard tie considered 

as the baseline in this study. Section 3 describes the development of the HSRM material and the 

determination of its mechanical properties. Section 4 discusses the production of prototype ties 

used in the qualification, testing, and evaluation tasks in this work. Section 5 introduces the 

testing setups and instrumentation used in the experimental tasks of this work, including the 

Stereo DIC data acquisition system and the tie qualification studies. Section 6 presents the 

experimental and analytical investigations conducted to establish the benefits of the HSRM ties 

and discusses the findings. A summary of the findings and recommendations for future work is 

presented in the Conclusion, Section 7. 
7 

2. The Baseline Prestressed Concrete Tie – “Standard” Tie

The tie design used in this study is based on a commercially available tie produced by a major 

U.S. tie manufacturer for a Class I railroad. This section presents the materials, geometry, design 

parameters, and nominal capacities of the standard tie.

2.1 Design Parameters

The length of the tie is 8 feet, 6 inches, and its detailed geometry is shown in Figure 2. 

Prestressing force is applied through eight, 7-wire, ASTM A886 Grade 270 low-relaxation 

strands, each 3/8 inch in diameter, placed in two rows. 

Figure 2. Geometric design drawings and manufactured ties

The baseline tie design parameters are listed in Table 1. 

Table 1. Concrete tie design parameters

Description Symbol Value

Area of tie at rail seat Atr 81.00 in2

Area of tie at center Atc 71.5 in2

Strand eccentricity at rail seat e 0.45 in

Section modulus wrt to bottom of tie SB 108.5 in4

Strand diameter ds 3/8 in
8 

Description Symbol Value

Strand area As 0.11 in2

Prestressing force per strand Pi 17.25 kip

Effective force per strand Pe 15.36 kip

Strand initial stress σi 156.2 ksi

Effective strand stress σie 139 ksi

Number of strands Ns 8

Total prestressing force Psi 138 kip

Total effective force Pse 123 kip

Modulus of elasticity for steel Es 29,000 ksi

Assuming a standard sign convention for internal forces in a beam, and defining the “top” and 

“bottom” of the tie to be as shown in Figure 2, the nominal moment, associated stress, and 

corresponding force required to produce the design moment in qualification tests set forth in 

AREMA Manual for Railway Engineering Chapter 30, Section 4.9.1, at the top and bottom of 

the strand, is summarized in Table 2. 

Table 2. Nominal capacity of railroad tie

2.2 Concrete Mix Design

The tie manufacturer provided the concrete mix design for the standard tie. The manufacturer’s 

mix design yields a concrete with a minimum 7 ksi compressive strength at 28 days. The 

standard concrete reaches a compressive strength of 4 ksi within 24 hours after pour to meet the 

strength demands for de-tensioning of the strands. Type III cement, conforming to ASTM C150, 

provides high early strength. Admixtures are used in the mix to increase the workability of the 

wet concrete and control the air entrainment during production. The concrete mix design is 

shown in Table 3. 
9 

Table 3. Concrete mix design

Material Amount Comments

Cement 600 lb/yd3 ASTM C-150 Type III, low alkali (Speed, Indiana )

Water 234 lb/yd3 City water

Coarse Aggregate 1,842 lb/yd3 Plum Run Stone (size #67, ASTM C-33)

Sand 1,333 lb/yd3 Plum Run Stone (ASTM C-33)

Micro Air 0.7 oz/cwt Master Builders (ASTM C-260 Air Entraining Admixture)

Glenium 10 oz/cwt Master Builders (ASTM C-494 Super)
10 

3. HSRM Material Development and Characterization

This section presents the steps for developing the HSRM concrete material and summarizes the 

test results for identifying its mechanical properties. 

3.1 Coarse Aggregates and the HSRM Design Mix

The reduction of the elastic modulus in concrete is achieved using weathered granites as the 

coarse aggregate. The researchers obtained crushed weathered granite from three quarries, 

hereafter identified as CA2, CA3, and CA4. Figure 3 shows the aggregate as delivered and 

samples of the CA2, CA3, and CA4 weathered granite aggregates. The HSRM concrete mix 

design was the same as the standard concrete mix design introduced in Section 2.2, with the 

exception that the coarse aggregates were replaced with the crushed weathered granite material 

by weight. The tie manufacturer delivered the plum run stone coarse aggregate that they use in 

the production of standard ties. The plum run stone is a limestone coarse aggregate and is 

hereafter identified as CA1. In addition, the tie manufacturer shipped the plum run stone sand for 

use in the standard and HSRM prototype tie fabrication. 

Figure 3. Weathered granite coarse aggregates: (a) as delivered to USC laboratories, (b) 

CA2, (c) CA3, (d) CA4 

3.2 Mechanical Properties

A series of tests were conducted on each of the aggregates and fresh and hardened concrete 

samples to determine commonly reported properties (Table 4). A second batch was produced and 

tested to verify the consistency. These results were within 3 percent of the first batch. In addition 

to the ASTM standard tests, UIUC developed lapping test was performed on the hardened 

concrete to measure the abrasion resistance of the concrete. The test is designed to simulate the 

abrasion mechanism causing RSD. The abrasion was measured as the rate of loss of material in 

mm/sec during testing; lower values indicate better performance. All specimen fabrication and 

testing activities were performed in the materials and structures laboratory at USC, except for the 

lapping test. This test was conducted at the Rail Transportation and Engineering Center 

(RailTEC) laboratory at UIUC. 
11 

Table 4. Properties of concrete produced with limestone and weathered granite coarse 

aggregates from 3 sources

Researchers observed that: 

1. The voids and density of limestone and weathered granite aggregates were very similar; 

however, the LA abrasion test showed that weathered granite aggregate exhibited higher loss. 

2. The fresh concrete properties were very similar for all concrete mixes. 

3. The aggregate type did not affect the compressive and flexural strength of concrete. 

4. The modulus of elasticity of concrete containing weathered granite coarse aggregate was

significantly lower (up to 50 percent) than the standard concrete. 

5. The lapping test showed superior performance of the HSRM concrete compared to standard 

concrete. This seemed contradictory to the LA abrasion test results on the aggregates. This 

was attributed to the different abrasion mechanisms between the two tests. The impact by the 

steel spheres in the LA abrasion test broke the structure of the partially weathered granite 

aggregate, causing the measured loss. However, once aggregate was confined in the cement 

matrix, the higher hardness of granites contributed to the better performance of the HSRM 

under grinding. 

The graphs in Figure 4 (a) and (b) show the development of the compressive strength and 

modulus of elasticity for each batch with respect to time.
12 

Figure 4. Comparison between HSRM and standard concrete: (a) compressive strength vs. 

specimen age and (b) modulus of elasticity vs. specimen age 

Figure 5. Correlation of modulus of elasticity with compressive strength for the HSRM 

(CA3-B%) and standard concrete (CA1-B5) 

Researchers observed that the compressive strength developed as expected for both the HSRM 

and standard concrete, with the HSRM concrete exhibiting a compressive strength equal or 

greater than the standard concrete. However, the modulus of elasticity for the HSRM concrete 

appeared to plateau after its early strength was achieved, while the modulus of elasticity for the 

standard concrete continued to increase as its strength increased over time. The modulus 

reduction achieved by both plant batches was 20 to 30 percent at 14 days and 43 to 56 percent at 

56 days. It was evident that there was a very weak correlation between the modulus of elasticity 

and compressive strength for the HSRM material, as shown in Figure 5. 
13 

3.3 Weather Aggregate Selection

In summary, the weathered granite aggregates from all three sources produced HSRM concretes 

that met or exceeded the material property requirements of the standard concrete specified in the 

tie design adopted in this study. In addition, all three aggregates produced HSRM concretes that 

exhibited the lower elastic modulus sought after in this research, and all three exhibited higher 

resistance to surface abrasion than the standard concrete. Therefore, all three materials were 

deemed appropriate to produce the prestressed concrete ties. However, due to limitations in the 

scope of work, just one aggregate was selected to produce the prototype tie for the product 

qualification and performance assessment tasks. CA2 produced the least reduction in the elastic 

modulus of concrete and may not demonstrate the full benefits of the technology. CA4 produced 

the greatest reduction of the elastic modulus of concrete, but with a slightly lower compressive 

strength. Aggregate CA3 produced the highest strength concrete with a reduction in elastic 

modulus that was comparable, though slightly higher, to CA4. In addition, the CA3 concrete 

showed a higher resistance to surface abrasion than CA4 and had fresh concrete properties that 

compared better to the standard concrete. Therefore, CA3 was chosen to produce the prototype 

ties.
14 

4. Prototype Tie Fabrication and Qualification

Standard and prototype (HSRM) concrete ties were produced at the same time and in the same 

prestressing bed at a major tie manufacturer plant on two different dates, approximately 12 

months apart. In this plant, the freshly mixed concrete was poured into a pre-stressing bed, which 

consisted of 37 steel cavities arranged in series. Each cavity contained eight steel tie forms and

was enclosed on both ends by removable steel plates. The steel strands ran continuously 

throughout the length of the bed, eight strands per steel form. Before the placing the concrete, the 

strands were pre-tensioned, with an initial force of 17.25 kips, by a hydraulic system at one end 

of the bed. On the other end of the bed, the steel stands were anchored on a bulkhead. For 

simplicity, the bed end containing the hydraulic system was designated the “live end,” and the 

bed end anchoring the strands is the “dead end.” 

Figure 6. Concrete tie prestressing bed: (a) before placement of concrete; (b) after 

placement of concrete; (c) concrete cylinder preparation and (d) covering bed in 

preparation of concrete curing
15 

The plant produced 32 prototype HSRM ties with aggregate CA3, and 32 standard ties with

aggregate CA1 over 2 days of production. The first five cavities from the live end were used for 

HSRM tie production. The manufacturer shipped the 64 ties to the Structural Testing Laboratory 

at USC approximately 3 months after fabrication. 

4.1 Material Properties

The HSRM concrete batches were identified as CA3-B5 and CA3-B7 and the standard concrete 

batches as CA1-B5 and CA1-B7, with batches B5 and B7 corresponding to the first and second 

production dates, respectively. The graphs in Figure 7 (a) and (b) show the development of the 

compressive strength and modulus of elasticity for each batch with respect to time. The concrete 

batches produced in the laboratory, CA1-B1 and CA3-B1, are also plotted for reference.

Figure 7. Development of compressive strength and elastic modulus of HSRM and 

standard concrete: (a) compressive strength vs. specimen age and (b) modulus of elasticity 

vs. specimen age 

Researchers observed that the plant-produced concrete batches had properties consistent with the 

concrete batches developed in the laboratory during the material development and qualification 

phase. The compressive strength developed as expected for both the HSRM and standard

concrete, with the HSRM concrete exhibiting a compressive strength comparable to the standard

concrete. However, the modulus of elasticity for the HSRM concrete appeared to plateau after its 

early strength was achieved, while the modulus of elasticity for the standard concrete continued 

to increase over time. The modulus reduction achieved by both plant batches was approximately 

35 percent at 58 days and 40 percent at 168 days. Figure 8 shows the correlation between the 

modulus of elasticity and compressive strength of the HSRM and standard concrete materials for 

the plant-produced batches. 
16 

Figure 8. Correlation of modulus of elasticity with compressive strength for the HSRM and 

standard concrete

4.2 Tie Qualification Tests

Qualification testing of the standard and HSRM ties followed the test procedures set forth in the 

AREMA Manual for Railway Engineering, Chapter 30 – Ties, Part 4.9.1.1 a-f, and 4.9.1.2 a, b.. 

Five HSRM ties and five standard ties were tested in the Structures Laboratory at USC. Testing 

per AREMA 4.9.1.2 was conducted by RailTEC at UIUC on two HSRM and two standard ties. 

The average compressive strength at the time of testing of the CA1-B5 and CA3-B5 concrete 

was 9.9 ksi and 9.8 ksi, respectively. The average modulus of elasticity of the standard concrete 

CA1-B5 was 5,300 ksi, and of the CA3-B5 HSRM 3,400 ksi, representing an average reduction 

of 36 percent. 

All HSRM and standard ties passed the AREMA qualification tests. However, one of the 

standard ties marginally passed the “Rail Seat A” positive loading test. A crack was detected in 

this tie when loads reached the design load level.
17 

5. Laboratory Setup and Instrumentation

This section presents the test setup and the instrumentation for tests conducted at USC 

laboratories. In addition, it introduces the 3-dimensional, vision-based data acquisition system 

for digital image correlation (DIC) used for the full-field deformation, surface strain 

measurements, and crack detection.

5.1 Reaction Frame

All load testing was conducted in a reaction frame. The actuator was a 110-kips MTS with a 6-

inch stroke. The actuator was also equipped with a load cell and LVDT. All tests were carried 

out in load control mode. The reaction frame is shown in Figure 9. 

Figure 9. The reaction frame used for all load tests 

5.2 Indoor Track Testing Facility

In addition to the reaction frame tests, the ties were tested under simulated track conditions in the 

full-scale indoor track load testing facility. Figure 10 shows the track panel configuration. 
18 

Figure 10. Indoor railway track testing facility

5.3 Instrumentation

Conventional measurement devices were employed for all tests. Specifically, linear voltage 

differential transformers (LVDTs) were used to measure the deflections at discrete locations on 

the specimen and to measure strand slippage. For deflection measurements, the LVDTs were

secured to a single 2- by 4-foot wood board at predetermined spacing with their tips in contact 

with the surface of the tie. For strand slippage measurements, the LVDT was clamped to the 

specimen and the tip was in contact with the exposed strand face Strain gages, specifically 

designed for use on concrete elements, were also attached to the surface of the tie. 

5.4 Vision-Based, Full-Field Measurements

Digital image correlation (DIC) is a unique suite of non-contacting, vision-based, full-field 

measurement methods developed over the past 3 decades (Luo, Chao, Sutton, & Peters, 1993; 

Luo, Chao, & Sutton, 1994) (Sutton, Orteu, & Schreier, 2009; Sutton, 2013). The DIC methods 

can be used for large and extremely small specimens. Measurements using both 2-dimensional 

and 3-dimensional DIC have been successfully made for a wide range of materials, loading, and 

temperature conditions. In addition to deformation measurements, the method can detect crack 

development and propagation and damage evolution. The following sections present the DIC 

system and one validation study used in this work. Details on the data acquisition and image 

processing procedures and additional verification and application studies of the DIC system used 

in this work have been published in the literature (Rajan et al., 2017; Sutton, et al., 2017). 

5.4.1 Imaging System and Components

. The stereo DIC system used in this research consisted of a pair of cameras and lenses, low-heatemission lighting, a computer for image acquisition, cables, calibration tablets, speckle 

application kits, and VIC-3D® software, as shown in Figure 11. 
19 

Figure 11. Stereo vision system components

5.4.2 DIC Validation Study

To verify the consistency among the measurements taken by the different instrumentation, a 

validation study was conducted. To this end, a four-point bending test of the standard concrete 

tie for center binding loading was completed. The specimen was loaded to 20 kips, and the load 

was applied in 2-kip increments. The load rate was set to 5 kips per minute, and the load was

held for 1 minute at each increment. The test setup is shown in Figure 12. The instrumentation 

consisted of: 

(a) One strain gage installed at the midspan and two strain gages installed at 15 inches on 

each side of the midspan and at the tension side of the tie, as shown in Figure 12. 

(b) One LVDT installed at the midspan and two LVDTs installed at 15 inches on each 

side of the midspan at the tension side of the tie. 

(c) StereoDIC imaging of the side of the tie to compute the deformation and strain fields 

during testing. At each load hold, images were acquired and correlated to the images of 

the unloaded specimen. 
20 

Figure 12. Test setup for the validation study of the DIC data acquisition approach 

Figure 13 shows the longitudinal strain profile at the midspan cross-section of the prestressed 

concrete tie as computed from DIC measurements for load levels of 14, 18, and 20 kips. The 

horizontal axis shows the longitudinal strain, and the vertical axis shows the location along the 

depth of the tie. Strain gage measurements were acquired at a single point on the tension surface 

of the tie. Figure 13 also shows the strain gage measurements as dots at about -85 mm on the yaxis. Note that the DIC computed strain field extended from +70 mm to -70 mm along the crosssection and did not capture the strain values at the location of the strain gages. It was evident, 

however, that when the strain profile lines computed by the DIC were extrapolated to the 

location of the strain gages, the DIC measurements and strain gage measurements were in 

excellent agreement. 

Figure 13. Longitudinal strain profile along a cross-section at the midspan of the 

prestressed concrete tie 
21 

Figure 14 shows the longitudinal strain at the location of the strain gages as acquired by the 

strain gage at different loads. There is excellent agreement between the longitudinal strain value 

as computed by the DIC system and extrapolated to the location of the strain gage. 

Figure 14. Load vs. longitudinal strain at the extreme tension fiber at the midspan as 

acquired by strain gages and the StereoDIC system 

The last comparison study in this report pertains to the load-deflection response at the midspan 

of the tie as measured by the LVDT and the DIC system when the tie was loaded beyond the first 

cracking to approximately 70 kips. Figure 15 shows the load deflection response where the 

excellent agreement between the two data acquisition systems was evident. The DIC data 

acquisition system was superior to the conventional LVDT and strain gage systems by far, since 

it captured the full strain fields and identified crack size and location on the surface of the 

specimen monitored, as demonstrated in Figure 16. 

Figure 15. Load vs. vertical deflection at the midspan as acquired by LVDTs and the 

StereoDIC system
22 

Figure 16. Color map showing the longitudinal strain field on the surface of the standard 

tie under 46-kip load. Cracks that extend to the first layer of strands are evident.
23 

6. Performance Assessment

This section presents a comparative study on the performance of the HSRM and standard ties 

under service and ultimate loads and various support conditions and demonstrates the benefits of 

HSRM concrete in prestressed ties. These studies were based on both experimental 

investigations and parametric investigations through computer simulations. The experimental 

investigations were largely based on the testing program at the University of South Carolina and 

details on the test setups are available in Abdulqader (2017). The computer simulations were

based on finite element analysis (FEA). The development, calibration, verification, and 

validation of the associated FEA models, as well as the parametric studies, are available in 

Zeitouni (2017). The following sections discuss three areas that demonstrate the benefits of using 

HSRM in concrete ties, i.e., load to first cracking, amplitude and gradient of the stress and strain 

fields, and ultimate load capacity as observed in rail seat loading tests and loading under center 

binding conditions. 

6.1 Rail Seat Flexure Performance

The experimental setup was as indicated in AREMA qualification tests Chapter 30, section 

4.9.1.4 (AREMA, 2013) and is shown in Figure 17. Three HSRM ties and three standard ties 

were tested in positive moment configuration and loaded to failure. The average load to first 

cracking of the HSRM ties was 10 percent higher than the design load, while the average load to 

first cracking of the standard tie was 1 percent higher than the design load. At the design load, 

the longitudinal strain fields were captured by the StereoDIC system and typical fields are also 

shown in Figure 17 in the form of color maps superimposed on the side of the ties. 

Figure 17. Rail seat positive moment testing

The damage evolution in each tie is particularly interesting. Researchers observed that the 

HSRM concrete yielded a smoother strain gradient than the standard concrete. Loading 

continued until failure of the ties. The average value of the ultimate load of the standard tie was 

92 kips (180 percent of the design load). The ultimate load to failure in two of the three HSRM 
24 

ties exceeded the 105-kip capacity of the actuator, while the third tie failed at 97 kips, 

representing failure at least at 200 percent of the design load. 

Similar observations were made at load levels of 127 percent and 175 percent of the design load. 

Figure 18 shows the longitudinal strain field as a color map superimposed on the side of the ties 

at the two loading levels for a representative standard and HSRM tie. At 127 percent of the 

loading, a very distinct crack formed on the standard tie that extended to the first line of strands, 

while there was evidence that a second crack had started to form. At 175 percent of the loading, 

the standard tie exhibited two very distinct and deep cracks that approached the second line of 

strands, indicating imminent failure. However, HSRM ties at 175 percent of the design load 

exhibited a third crack that never appeared in the standard tie. Note that this third crack appeared 

at approximately 160 percent of the design load. All three cracks were shallower compared to the 

standard tie and did not reach the second line of strands at this loading level. Note that similar 

behavior was observed for rail seat loading for negative moments. 

Figure 18. Cracking at 127% and 176% of the design load for the standard and HSRM ties

6.2 Mid-Tie Flexure Performance 

Among the most critical issues affecting the performance of concrete ties is cracking of the tie 

from center binding (Zeman, Edwards, Barkan, & Lange, 2009). Tensile stresses on the top 

surface of the tie are not effectively redistributed in the tie due its high rigidity. In this section, 

the performance of the HSRM ties is evaluated through laboratory testing under monotonic and 

cyclic loading. 

6.2.1 Monotonic Loading and Pure Moment Conditions

A 4-point bending test, demonstrated the benefits of using the lower rigidity HSRM concrete

(Abdulqader, 2017). The test was a modification of the AREMA standard test, Section 4.9.1.6, 

Center Negative Bending Moment Test (AREMA, 2013). To create a wider shear-free region on 

the tie, loading was applied through a spreader beam with the loading points spaced 34 inches 

apart. The testing configuration is shown in Figure 20. 
25 

Figure 19. Test setup for the modified 4-point center negative moment test. 

The total load required to create the center negative design moment in the modified 4-point 

bending was computed as Pdesign = 32 kips. The tie was loaded to failure, and the load was 

recorded when: (a) the first crack appeared, (b) the crack reached the first line of strands, and (c) 

the tie failed. Table 5 shows the recorded values as a percentage of the design load, %Pdesign. The 

nominal value of the load in kips is also shown in parentheses. The cracking maps, as captured 

by the DIC system, are shown in Figure 21 for three load levels. Note that the HSRM tie 

exhibited a higher number of cracks that were not equally spaced compared to the standard tie. 

This was a strong indication of stress redistribution after first cracking. 

Table 5. Modified 4-point bending load at characteristic damage levels 

First Crack

%Pdesign (kips)

Crack to 1st Strand

%Pdesign (kips)

Ultimate

%Pdesign (kips)

Standard Tie 131 (42) 143 (46) 250 (80)

HSRM Tie 137 (44) 156 (50) 263 (84)

Difference 6 (2) 13 (4) 13 (4)
26 

Figure 20. Cracking maps as of the standard and HSRM ties during loading

6.2.2 Cyclic Loading

The fatigue behavior of prestressed concrete ties under center binding support condition has long 

been a subject of interest, yet only limited research has been reported in the literature. The load 

carrying capacity and fatigue behavior of prestressed concrete ties under cyclic loads were

experimentally investigated by means of a 4-point, midspan negative bending test. The ties were

supported to prevented lateral and longitudinal movement during the loading cycles. Figure 23

shows the test setup. 

Figure 21. Test setup for cyclic loading test under center binding conditions

The AREMA manual does not provide any guidelines for such a test. USC developed the 

following test procedure: 

Fatigue Testing Procedure

Stage 1: Three million load cycles were applied. The load range was 2 kips to 13.5 kips and 

corresponded to 90 percent of the load that would develop the design moment at midspan. The 

load was applied at a frequency of 2 cycles per second. The load cycling was paused every 48 

hours (approximately 350,000 cycles), and a monotonic static test was performed from 2 kips to 

13.5 kips. During the static test, the side surface of the ties was imaged at loads 2, 6, 8, 10, 12, 

and 13.3 kips for full-field DIC deformation measurements. After the image acquisition, the 
27 

cyclic testing resumed. Once the 3 million load cycles were reached, the tie was loaded until a 

crack reached the first level of strands. At this point the load was recorded. 

Stage 2: Cyclic loading was then restarted as in Stage 1 but the load was applied in the range of 2 

kips to 16.5 kips. The upper limit corresponded to 110 percent of the load associated to the 

design moment. As in Stage 1, the cyclic loading was paused every 48 hours, the tie was loaded 

monotonically to 16.5 kips, and images were acquired at load levels 2, 4, 6, 8, 10, 12, 13.5, 15, 

and 16.5 kips for DIC full-field deformation measurements. The cyclic loading continued until 

an additional 3 million cycles were applied, for a total of 6 million cycles. 

Stage 3: The tie was loaded monotonically until failure, and the full-field deformation 

measurements were captured at load levels 0, 2, 6, 8, 10, 12, 13.5, 15, 16.5, 18, 20, 22.5, 27, 29, 

31, and 33 kips. If failure did not occur, the load was increased manually by 1 kip until failure. 

Results

Stage 1 

The strain field did not show any significant changes during the first 3 million load. All strain in 

the HSRM tie remained in the range -400 με to 440 με when the tie was loaded to 90 percent of 

the design load (13.5 kips). The maximum deflection at the midspan was 0.046 ± 8x10-4 inches. 

No cracking was detected through visual inspection or the DIC measurements. Figure 24 (a) 

shows the strain field color map superimposed on the side of the tie between the rail seats when 

the tie was loaded statically with 13.5 kips force after 1.177x106, 2.027 x106, 2.745 x106, and 

3x106 load cycles. The standard tie showed similar behavior, as expected. The maximum 

deflection at the midspan was 0.031 ± 5x10-4 inches. It is evident that the HSRM tie is about 48 

percent more flexible than the standard tie which is consistent with the reduction of modulus of 

elasticity of the HSRM concrete. Figure 24 (b) and (c) show the corresponding elastic curve 

between the supports for the HSRM and standard tie. 

Figure 22. Static tests of the HSRM tie after 13.5 kip load cycles: (a) longitudinal strain εxx

field color maps; (b) HSRM tie elastic curves between supports; and (c) standard tie elastic 

curves between supports
28 

After 3 million load cycles, the ties were loaded until a crack reached the first line of strands. 

The corresponding loads were 19 kips for the standard tie and 20 kips for the HSRM tie, and the 

associated strain fields are shown in Figure 25. 

Figure 23. Longitudinal strain field εxx when the crack reaches the first line of strands in 

the standard tie at load 19 kips (left) and HSRM tie at load 20 kips (right).

Stage 2 

Both ties were subjected to an additional 3 million cycles. The strain field did not change 

significantly. All strain in the HSRM tie remains in the range -420 με to 460 με when the tie was

loaded to 90 percent of the design load (13.5kips) and in the range -510 με to 715 με when the tie 

was loaded to 110 percent of the design load (16.5 kips). The maximum deflection at the 

midspan was 0.0676 ± 1x10-4 at 110 percent of the design load. No additional cracking was

detected. Furthermore, the pre-existing cracks did not propagate. Figure 26 (a) shows the strain 

field color map superimposed on the side of the tie between the rail seats when the tie was loaded 

statically with 16.5 kips force after 0.848x106, 1.348 x106, 2.174 x106, and 3x106 load cycles in 

the range 0–16.5 kips. The standard tie showed similar behavior, as expected. The maximum 

deflection at the midspan was 0.043 ± 6x10-4 inches. In this case the HSRM tie is approximately 

57 percent more flexible than the standard tie. Figure 26 (b) and (c) show the corresponding 

elastic curve between the supports for the HSRM and standard tie. 

Figure 24. Static tests of the HSRM tie under 16.5-kips load after predetermined number of 

cycles during Stage 2 of cyclic loading: (a) longitudinal strain εxx field color maps; (b) 

HSRM tie elastic curves between supports; (c) standard tie elastic curves between supports
29 

Stage 3 

At the end of the 6 million cycles, both ties were loaded to failure. The ultimate load that caused 

the HSRM tie to fail (collapse) was 35 kips, while the standard tie collapsed at 33 kips. Figure 27

shows the load-deflection curve at a point, P, between the loading points, as indicated in the inset 

of Figure 27. The linear elastic stiffnesses for the HSRM and standard ties were estimated at 338 

kips/in and 441 kips/in, respectively, representing a 30 percent difference. 

Figure 28 shows the formation and progression of cracks as the load increased. The HSRM ties 

better distributed the load, as evidenced by the more regularized strain field around and between 

the cracks, in contrast to the standard ties, where the cracks were very distinct and were longer at 

the same load level. 

Figure 25. Load-deflection for ultimate load test

Figure 26. Longitudinal strain field during testing to failure after 6 million load cycles 

shown for the HSRM ties (left column) and standard ties (right column). 
30 

6.3 Loading under Simulated Track Support Conditions 

The performance of the HSRM and standard ties under simulated track support conditions was

compared using laboratory tests and computer simulations. 

6.3.1 Laboratory Testing

Laboratory testing under simulated track support conditions was carried out by RailTEC at the

Research and Innovation Laboratory (RAIL) at the Harry Schnabel, Jr. Geotechnical Laboratory

in Champaign, Illinois. This section presents a summary of the tests and findings as reported by 

RailTEC (2016). Ties were tested using a loading frame, shown in Figure 29, where both rail 

seats were loaded simultaneously in the vertical direction. Ties were tested under two support 

conditions: full support and center-binding. To simulate these different support conditions, 

rubber pads were used. The pads chosen were 1 inch (25.4 mm) thick and 1 foot (305 mm) long 

and wide. The pads had a hardness of 50 Shore A durometer. To simulate full support, they were

placed under the entire length of the tie, and to simulate severe center-binding, they were placed 

under the center 4 feet of the tie. The tests were executed according to the static-load testing 

procedure developed by RailTEC at UIUC (Bastos, Dersch, & Edwards, 2015). The test plan was

designed to produce strains, bending moments, vertical deflection, and center-cracking under a 

given rail seat load. To accomplish this, strain gauges and potentiometers were used. 

Figure 27. Loading frame, test setup, and support conditions for loading under simulated 

track support conditions in the laboratory

Six strain gauges were used on each tie: one at each rail seat, one at each intermediate location 

between the rail seats and center, and two at the center. Tie sides were marked as side A and side 

B, with the strain gauge numbering running from side A to side B. Fifteen potentiometers were

used for measuring vertical displacements and quantifying tie shape under loading. Supported by 

a separate frame, the potentiometers were placed along the top of the tie at even spacing. They 

were similarly numbered 1 to 15, running from side A to side B. The strain gage and 

potentiometer location are depicted in Figure 30 and Figure 31, respectively. 
31 

Figure 28. Strain gage locations 

Figure 29. Potentiometer locations 

For each tie, the full-support case was tested first, with data recorded from 0- to 20-kip loads at 

each rail seat. The center-bound case was then tested in the same manner. During center-binding 

tests, marks of all crack locations were made on the tie while it was subjected to a 20-kip rail seat 

load. 

Strain

Strain gauge data were collected and compared across tie types and support conditions using box 

and whisker plots (Figure 32). In all cases, the rail seat load was 20 kips on both rail seats. The 
32 

diamonds in the box plots represent the mean strain for each case, and horizontal lines inside 

each box represent the median strain. In the full support condition, the rail seats experienced 

strains roughly in the range of -100 με to -200 με. The negative sign indicates a compressive 

strain, consistent with the positive bending expected at the rail seats. In the severe center-binding 

condition, however, they experienced virtually no strain, as one would expect based on EulerBernoulli beam theory. This trend applied to both standard and HSRM ties. The effect on the 

center strain gauges was the opposite of that on the rail seats, as expected. The center of the tie

experienced very little strain under the full support condition, and typical strains of -400 με to -

600 με under center-binding. 

Figure 30. Strain gauge results: (a) rail seat strain gauges; (b) intermediate strain gauges; 

and (c) center strain gauges

By looking at the box plots, the difference between the strains of standard and HSRM ties was

not clear. A statistical model was developed to aid in the analysis. This model was adapted from 

prior work and incorporated the concept of completely randomized design with two factors (Ott 

& Longnecker, 2008). 

The effects of support condition and crosstie type (Standard or HSRM) were determined to be 

either significant or insignificant based on a two-way analysis of variance (ANOVA). The 

ANOVA results show that support condition is significant at any reasonable confidence level. 

Although the effects of the crosstie type showed significant difference between the standard and 
33 

HSRM crossties at an 85 percent confidence level, there is not enough evidence to assess the 

effects of the crosstie type at 90 percent confidence level. Increasing the number of tested 

crossties would help to increase the confidence level. 

Bending Moments

Bending moments were calculated for each of the 6 gauges in each of the 12 tests. Data points 

taken from identical tie types and locations were then averaged (that is, six data points per 

average, excepting the standard tie rail seat data, which had five data points due to the existence 

of a bad strain gauge on rail seat A of tie 1) to give the results shown in Table 6. 

Table 6. Averaged bending moment results (unit: kip-inches)

Tie Type Support Type Railseat

kip-in

Intermediate

kip-in

Center

kip-in

Standard 

Tie

Full Support 168 62 27

Center-Bound -14 -255 -309

HSRM 

Tie

Full Support 136 17 -26

Center-Bound -9 -307 -306

The results showed that the standard and HSRM ties behaved similarly under loading. In the 

center-bound case, the standard ties had an average center bending moment of -309 kip-in and 

the HSRM ties had a center bending moment of -306 kip-in. HSRM ties tended to have greater 

intermediate negative bending moments than their standard counterparts for the center-binding 

support condition. This observation indicated a smoother load distribution in the HSRM ties and 

led to the introduction of the modified 4-point bending test designed at USC and discussed in 

Section 6.2.1. In the full support condition, the standard ties exhibited a positive bending 

moment at the bottom of the tie, indicating positive center bending. 

Vertical Displacements

The vertical displacement data taken from the potentiometers were averaged for each tie type for 

each support case, as well as for each side of the tie (that is, six test data points went into each 

average value, except for the center). The graphs of these data are in Figure 33. Average 

deflection at 20 kips represent the shape of the tie under loading. In the full support case, there 

was very little overall displacement in any part of the tie. The HSRM ties deflected the most at 

the ends of the tie, with the average displacement there being 0.0833 inch. Unexpectedly, the 

standard ties actually underwent positive center-bending, and thus their maximum average 

displacement in the full support condition was at the center. The deflection here was on average 

0.061 inch, while at the ends of the tie it was only 0.054 inch. This agreed with the bending 

moment results presented in the preceding section. In the center-bound support condition, 

deflections were much greater, particularly at the ends of the ties. Standard ties deflected on 

average 0.314 inch at the ends, and HSRM ties 0.334 inch at the ends. Note that the deflections 

of the HSRM and standard ties were very similar for the center-bound conditions when the 

material remained in the linear elastic range, i.e. no damage had taken place. This observation 
34 

was consistent with the deflections obtained from the modified 4-point bending tests, as 

discussed in Section 6.2.1 and shown in Figure 22. 

Figure 31. Average deflection at 20 kips 

Cracking

A qualitative analysis of the crack patterns produced after loading under the center-bound 

support condition showed that the standard ties had fewer cracks that formed across the entire 

width, while the HSRM ties exhibited more, shorter cracks that did not extend through the width 

of the tie. Typical cracked HSRM and standard ties are shown in Figure 34. These observations 

were consistent with the findings of the modified 4-point bending tests discussed in Section 

6.2.1. 

Figure 32. Typical cracking pattern after center binding of standard (top) and HSRM 

(bottom) ties 
35 

6.3.2 Parametric Studies through Computer Simulations

The parametric studies for the simulated track support condition were conducted based on FEA. 

Detailed non-linear material models of the ties and the development, validation, and verification 

of the tie models have been presented in Zeitouni (2017) and Zeitouni, Rizos, and Qian (2018). 

The FEA model was developed in ABAQUS and considered the prestressing strand action 

explicitly in a separate analysis step. The damaged plasticity model was adopted for modeling 

the concrete, and cohesion elements were used for modeling the concrete-strand bond. 

Additional information about these constitutive models is available in Zeitouni (2017). Three 

concrete materials were considered – the standard concrete and two HSRM concretes with 

modulus reductions of 23 percent and 40 percent. These values represented a typical reduction 

range observed in the course of this work. The concrete material properties are listed in Table 7. 

Table 7. Concrete material properties for the FEA analysis 

Three distinct support conditions were considered in this study. The three supports were selected 

to simulate a concrete tie that was fully supported beneath, at its two ends, and at its middle 

region by the ballast. Each rail seat was loaded with a vertical (V) load up to 40 kips, yielding a 

total vertical load of 80 kips. To account for trains moving on a curved track, a second load case 

was considered where a lateral (L) load equal to 12 kips was applied on one rail seat toward the 

field side. Thus, ratios of L/V=0.0 and L/V=0.6 were considered. The three models are shown in 

Figure 35. For each combination of boundary conditions, concrete material, and L/V ratio, the 

longitudinal stress (S33), von Mises stress, and tensile damage were measured throughout the tie

and recorded for each simulation. 

Figure 33. Three different ballast support condition representing: (a) full support (new 

track condition), (b) loss of center support, and (c) loss of rail seat support 

In all support and load cases, the HSRM exhibited stress amplitude reduction and a smoother 

distribution of the stress field.
36 

The support conditions shown in Figure 35 (a) and (b) did not produce any damage in the tie for 

all materials and all L/V ratios, and the tie response remained linear elastic. However, the centerbinding condition shown in Figure 35 (c), caused the response of the tie to become nonlinear 

before the axle load was reached, and cracking started to form on the top surface of the ties. 

Figure 36 shows the damage progression, where it was verified that crack initiation occurred at 

higher loads (39 kips on the standard and 43.8 kips for the HSRM tie) when HSRM concrete was

used. The crack pattern was consistent with what had been observed in the laboratory, i.e., very 

distinct, width-wide cracks appeared in the standard tie as opposed to multiple shorter cracks on 

the HSRM tie.

Figure 34. Damage progression for the standard tie (left) and the HSRM tie (right)

In all cases, however, the stresses were reduced when the 23 percent and the 40 percent HSRM 

concrete material was used. To quantify this reduction, the concrete tie was divided into three 

distinct regions to further compare the performance of each concrete tie. The three regions were

defined as “End A,” “End B,” and the “Center” region. Within each region, locations of concern, 

such as sites where large stress amplitudes were observed or sites that were most prone to 

develop cracks under increasing loads, were recorded along the top and bottom surfaces of the 

concrete tie. The center region represented the midsection of the tie with a constant cross-section

(middle 36 inches [914.4 mm]). End A depicted the region facing the field side, which contained

the rail seat with the combination of vertical and lateral loads (if applicable). This region was 33 

inches (838.2 mm) long and began at the tie end and terminated where the center region began. 

In contrast, End B represented the remaining 33 inches (838.2 mm) of the tie on the opposite side 

of the tie where only vertical loads were applied. 

The two HSRM concrete ties considered in this study outperformed the standard concrete tie in 

all the load and support scenarios by better distributing the stresses throughout the tie. This effect 

was most pronounced in the center-binding support case, when the initiation of cracks appeared

on the HSRM ties at higher loads as compared to the standard concrete ties. The HSRM-22.6 

percent tie experienced its first crack approximately 2.84 kips and 1.36 kips after the standard 

concrete tie has already cracked for the L/V=0 and L/V=0.6 load cases. The HSRM-40 percent

delayed the initiation of cracks by undergoing an additional 4.7 kips and 2.77 kips for the L/V=0 

and L/V=0.6 load cases, when compared to the standard tie. Finite element simulations showed
37 

that reducing the elastic modulus of the standard concrete by 40 percent could allow as high as 

4.7 kips of additional load before the first crack was initiated. The positive behavior of the 

concrete ties was not just noticed in the nonlinear regions of the tie but also in the linear regions. 

In the continuously supported and end supported simulations, the concrete ties remained in the 

linear region and no plastic strains were developed. Even in the linear region, it was obvious that 

the two HSRM material models showed favorable responses when compared to the standard tie. 

For the continuously supported tie, it was preferred for the concrete tie to have lower tensile and 

compressive stress in its middle, top, and bottom fibers. Both HSRM concrete ties exhibited this 

desired behavior. As compared to the standard tie, the HSRM-22.6 percent showed as high as an 

11 percent increase in the compressive stress at the top fibers of the tie which were susceptible to 

tension cracking with increasing loads and as high as a 4.83 percent reduction in the compressive 

stresses in the bottom fibers of the tie which would reach crushing with increasing loads. The 

HSRM-40 percent showed as high as a 20.37 percent increase in the compressive stress at the top 

fibers of the tie (moving further from a tensile state) and as high as a 9.48 percent reduction in 

the compressive stresses in the bottom fibers of the tie, when compared to the standard tie. 

For the end supported ties, it was preferred for the concrete tie to have lower tensile stresses in 

the bottom fibers of the tie and lower compressive stresses in the top fibers of the tie. Again, both 

HSRM ties exhibited this desired behavior. The HSRM-22.6 percent tie showed as high as a 6.67 

percent reduction in the compressive stresses at the top fibers and as high as a 77.8 percent

increase in the compressive stresses at the bottom fibers (moving further from a tensile state), 

when compared to the standard tie. The HSRM-40 percent tie showed as high as a 12.95 percent

reduction in the compressive stresses at the top fibers while delaying the development of pure 

tensile stresses at the bottom fibers of the concrete, thus preventing cracking when compared to 

the standard tie. 

The percent reduction is summarized in Table 8. Researchers observed that the stress reduction 

was higher for the more resilient concrete, HSRM-40 percent. Note that the values shown for the 

standard tie were the nominal recorded stress values. Researchers also noted that stress reduction 

was achieved in all support and load combinations and that the maximum benefits of over 50 

percent stress reduction were realized for the case of center-binding conditions on a tangent 

track. The detailed FEM analysis is presented in Zeitouni (2017). 
38 

Table 8. Summary of stress reduction for all concrete materials, support conditions and 

L/V ratios. Standard concrete shows nominal stress values in ksi. HSRM ties show the 

stress reduction as a percentage of the stress in the standard tie.

6.3.3 In-Track Testing

The objective of this series of tests was to assess the performance of the HSRM ties under 

simulated in-track conditions. Testing was performed in the Indoor Track Testing Facility 

discussed in Section 4.2, and the track was symmetrically loaded by a 110-kip MTS actuator 

through a spreader beam. Two different track configurations were tested. Both track panels were

16 feet long and contained nine ties spaced 20 inches on-center. RE132 rail was installed with eclip fasteners. The first case considered a standard track, consisting of the standard ties. The 

second track was an HSRM track consisting of HSRM. The testing procedure for both tracks 

consisted of cyclic loading of the track and monotonic loading of the loaded tie. 

The first series of tests involved cyclic load testing of the tracks to investigate the in-track 

performance of each tie type and was similar to the procedure discussed in Section 6.2.2, where

cyclic load-testing was performed in three stages: 

Stage 1: Three million load cycles were applied. The load ranged from 2 kips to 36 kips. This 

load corresponded to 90 percent of the load that would cause initial damage under center-binding 

conditions. The load was applied at a frequency of up to 3.5 cycles per second. Once the 3 

L/V = 0 (V = 80k

) L/V = 0.6 (V = 80k

) L/V = 0 (V = 80k) L/V = 0.6 (V = 80k

) L/V = 0 (V = 36k

) L/V = 0.6 (V = 28k

)

End A 2% 1% 7% 1% 1% 1%

Center 5% 11% 7% 6% 26% 15%

End B 2% 2% 7% 4% 1% 1%

End A 4% 2% 11% 2% Center Governs Center Governs

Center 4% 5% 10% 24% 7% 4%

End B 4% 13% 11% 78% Center Governs Center Governs

End A 4% 2% 13% 2% 2% 1%

Center 9% 20% 13% 12% 52% 30%

End B 4% 4% 13% 8% 2% 2%

End A 10% 4% 19% 2% Center Governs Center Governs

Center 8% 9% 18% 45% 14% 9%

End B 10% 26% 19% 149% Center Governs Center Governs

End A -18.7 -20.2 -20.0 -18.6 -6.55 -6.85

Center -5.79 -4.10 -17.1 -22.9 5.13 4.92

End B -18.7 -19.1 -20.0 -20.3 -6.55 -6.38

End A -4.81 -3.10 -3.92 -13.2 Center Governs Center Governs

Center -16.5 -15.9 -7.02 -3.04 -26.2 -25.9

End B -4.81 -1.72 -3.92 -0.763 Center Governs Center Governs

Longitudinal Stress, S33 (Mpa)

Continuous Support End Supports Center Support

HSRM-22.6%

Top Bottom

HSRM-40%

Top Bottom

Standard

Top Bottom
39 

million load cycles were reached, the loaded tie was removed from the track and loaded in a 

modified 4-point bending configuration (Section 6.2.1) until a crack reached the first level of 

strands. DIC was used to map a full 3-dimensional strain field of the tie during this loading. At 

this point the load was recorded. 

Stage 2: Cyclic loading was then restarted as in Stage 1 and to the same load range of 10 kips to 

36 kips. The cyclic loading continued until an additional 3 million cycles were applied, for a total 

of 6 million cycles. 

Stage 3: The loaded tie was removed from the track and was loaded in a modified 4-point 

bending configuration (Section 6.2.1) until failure. The full field deformation measurements and 

failure load were captured. 

Table 9 shows the load required to induce first crack, and for the crack to reach the first line of 

strands during the 4-point bending test at the end of Stage 1, and the load required to fail the tie, 

at the end of Stage 3. Researchers noted that the capacities of the ties after cyclic loading in the 

testing track was consistent with the tests in Section 6.2.1. 

Table 9. Modified 4-point bending load after 3 and 6 million load cycles

First Crack (stage

2)

%Pdesign (kips)

Crack to 1st Strand

(stage 2)

%Pdesign (kips)

Ultimate (stage 3 )

%Pdesign (kips) 

Standard Tie 131 (42) 159 (51) 280 (90)

HSRM Tie 144 (46) 172 (55) 312 (100)

Difference 13 (4) 13 (4) 32 (10)
40 

7. Conclusion

This report presents the development of a HSRM concrete and its benefits in prestressed concrete 

railroad ties. The use of weathered granites as aggregates in higher strength concretes has 

consistently produced a resilient concrete material that has a modulus of elasticity significantly 

lower (up to 50 percent) than standard concretes that contain limestone coarse aggregates. In this 

work the weathered granite was used as a direct substitute of the limestone aggregate used in a 

current design without any further modifications to the concrete mix or the tie design. The 

experimental investigations and the computer simulations presented in this report quantify the 

benefits of using the HSRM-resilient concrete in prestressed concrete railroad ties. The following 

conclusions are noted: 

• The HSRM concrete compressive strength was comparable to the standard mix.

• The HSRM modulus of elasticity was lower than the standard mix, by as much as 50 

percent.

• HSRM concrete had a much higher abrasion resistance than the standard concrete.

• HSRM ties met the AREMA performance requirements and equaled or exceeded the 

performance of the standard ties.

• HSRM ties exhibited smoother stress gradients and exhibited stress redistribution after 

initial cracking. 

• HSRM ties have lower stress amplitudes compared to standard ties under the same loads 

• HSRM ties withstood higher ultimate loads. 

• The use of weathered granites to produce the HSRM concrete ties did not impact the 

production process or increase the cost of the ties.

The use of HSRM represents a technology-based modification in concrete tie technology that 

improves the safety of rail service and maintenance operations without impacting fabrication cost 

and processes. Note that additional benefits may be gained if the tie were redesigned to take 

advantage of the HSRM material properties. This is a topic for future investigations. This study 

suggests that the HSRM concrete may be a cost-effective alternative concrete to the traditional 

high-performance concrete used in prestressed concrete ties with the potential to increase the 

service life of the tie. 
41 

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44 

Abbreviations and Acronyms

HSRM High Strength Reduced Modulus concrete

USC University of South Carolina

SCDOT South Carolina Department of Transportation

HPC High Performance Concrete 

L/V Lateral to Vertical Load Ratio

DIC Digital Image Correlation

StereoDIC Stereoscopic Digital Image Correlation

DAQ Data Acquisition

LVDT Linear Variable Differential Transformer

FEA Finite Element Analysis

HS High Strength

Atr Area of tie at rail seat

Atc Area of tie at center

e Strand eccentricity at rail seat

SB Section modulus wrt to bottom of tie

ds Strand diameter

As Strand area

Pi Prestressing force per strand

Pe Effective force per strand

σi Strand initial stress

σie Effective strand stress

Ns Number of strands

Psi Total prestressing force

Pse Total effective force

Es Modulus of elasticity for steel

Ec Modulus of elasticity of concrete

fc

’ Concrete compressive strength

ft Concrete tensile strength

ν Poisson’s ratio