Research, Development, and Technology

Turner-Fairbank Highway Research Center

6300 Georgetown Pike

McLean, VA 22101-2296

Optimized Sections for High-Strength 

Concrete Bridge Girders — Effect of 

Deck Concrete Strength

Publication No. FHWA-HRT-05-058 OCTOBER 2006
FOREWORD 

For more than 25 years, concretes with compressive strengths in excess of 41 megapascals 

(MPa) (6,000 pounds per square inch (psi)) have been used in the construction of columns of 

highrise buildings. While the availability of high-strength concretes was limited initially to a few 

geographic locations, opportunities to use these concretes at more locations across the United 

States have arisen. Although the technology to produce higher-strength concretes has developed 

primarily within the ready-mix concrete industry for use in buildings, the same technology can 

be applied in the use of concretes for bridge girders and bridge decks. 

The durability of concrete bridge decks has been a concern for many years, and numerous 

strategies to improve the performance of bridge decks have been undertaken. Many of the factors 

that enable a durable concrete to be produced also result in a high-strength concrete. 

Consequently, if a concrete for a bridge deck is designed to be durable, it will probably also have 

a high compressive strength. This report contains an evaluation of the effect of high-performance 

concrete on the cost and structural performance of bridges constructed with high-performance 

concrete bridge decks and high-strength concrete girders. Several areas with the potential for 

improved structural performance through the use of high-performance concretes are investigated. 

This report should also assist designers and owners in recognizing that the use of highperformance concrete in bridges has advantages beyond those of improving durability. 

Gary Henderson 

Director, Office of Infrastructure 

 Research and Development 

Notice 

This document is disseminated under the sponsorship of the U.S. Department of Transportation 

in the interest of information exchange. The U.S. Government assumes no liability for the use of 

the information contained in this document. This report does not constitute a standard, 

specification, or regulation. 

The U.S. Government does not endorse products or manufacturers. Trademarks or 

manufacturers' names appear in this report only because they are considered essential to the 

objective of the document. 

Quality Assurance Statement 

The Federal Highway Administration (FHWA) provides high-quality information to serve 

Government, industry, and the public in a manner that promotes public understanding. Standards 

and policies are used to ensure and maximize the quality, objectivity, utility, and integrity of its 

information. FHWA periodically reviews quality issues and adjusts its programs and processes 

to ensure continuous quality improvement. 
1. Report No 2. Government Accession No. 3. Recipient's Catalog No. 

FHWA-HRT-05-058 N/A N/A 

4. Title and Subtitle 5. Report Date 

October 2006 

 

6. Performing Organization Code 

Optimized Sections for High-Strength Concrete Bridge Girders—Effect of 

Deck Concrete Strength 

N/A 

7. Authors(s) 8. Performing Organization Report No. 

Turner-Fairbank Highway Research Center N/A 

9. Performing Organization Name and Address 10. Work Unit No. (TRAIS) 

N/A 

11. Contract or Grant No. 

DTFH 

13. Type of Report and Period Covered 

Office of Research, Development, and Technology 

Turner-Fairbank Highway Research Center 

Federal Highway Administration 

6300 Georgetown Pike 

McLean, VA 22101 Evaluation, 1995–1997 

12. Sponsoring Agency Name and Address 14. Sponsoring Agency Code 

Office of Research, Development, and Technology 

Federal Highway Administration 

6300 Georgetown Pike 

McLean, VA 22101 

 

15. Supplementary Notes 

Contracting Officer’s Technical Representative: 

 Joseph L. Hartmann, HRDI-06 

16. Abstract 

This report contains an evaluation of the effect of high-performance concrete on the cost and structural performance 

of bridges constructed with high-performance concrete bridge decks and high-strength concrete girders. Bridge 

designers and owners are the main audience.

17. Key Words 18. Distribution Statement 

High-Performance Concrete, Girders, 

Concrete Bridge Decks 

No restrictions. This document is available to the 

Public through the National Technical Information Service; 

Springfield, VA 22161

19. Security Classif. (of this report) 20. Security Classif. (of this page) 21. No. of Pages 22. Price 

 Unclassified Unclassified 93 N/A 

Form DOT F 1700.7 (8-72) Reproduction of completed page authorized (art. 5/94)
ii 

PREFACE 

For over 25 years, concretes with specified compressive strengths in excess of 41 MPa 

(6,000 psi) have been used in the construction of columns of highrise buildings. While the 

availability of the high-strength concretes was limited initially to a few geographic locations, 

opportunities have developed to use these concretes at more locations across the United States. 

As these opportunities have developed, material producers and contractors have accepted the 

challenge to produce concretes with higher compressive strengths. 

In the precast, prestressed concrete bridge field, a specified compressive strength of 41 MPa 

(6,000 psi) for bridge girders has been used for many years. However, strengths at release have 

often controlled the concrete mix design so that actual strengths at 28 days were often in excess 

of 41 MPa (6,000 psi). It is only in recent years that a strong interest in the utilization of concrete 

with higher compressive strengths has emerged. This interest has developed at a few geographic 

locations for specific projects in a manner similar to the development in the building industry. 

In parallel with an increased interest in the use of high-strength concretes in bridge girders, the 

use of high-performance concretes in bridge decks has also been receiving increased attention as 

a means of improving durability. High-performance concretes provide higher resistance to 

chloride penetration, higher resistance to deicer scaling, less damage from freezing and thawing, 

higher wear resistance, and less cracking. Many of the methods used to increase the durability of 

concrete result in a concrete that has a higher compressive strength. However, the higher 

concrete strength is rarely considered because the design of prestressed girders is controlled by 

service load stresses caused by dead load, live load, and impact. 

This report contains an evaluation of the effect of high-performance concrete on the cost and 

structural performance of bridges constructed with high-performance concrete bridge decks and 

high-strength concrete girders. Several areas with the potential for improved structural 

performance through the use of high-performance concretes are investigated. This report should 

assist designers and owners in recognizing that the use of high-performance concrete in bridges 

has advantages beyond those of improving durability. 

The research described in this report was sponsored by the Federal Highway Administration as 

part of their program to encourage the greater use of high-performance concretes in bridges. The 

program includes analytical and experimental research as well as showcase projects. The authors 

believe that high-performance concrete represents a technology with great potential for 

improving the infrastructure of the highway system. 
iii 

SI* (MODERN METRIC) CONVERSION FACTORS 

APPROXIMATE CONVERSIONS TO SI UNITS

Symbol When You Know Multiply By To Find Symbol 

LENGTH 

in inches 25.4 millimeters mm 

ft feet 0.305 meters m 

yd yards 0.914 meters m 

mi miles 1.61 kilometers km 

AREA 

in2 square inches 645.2 square millimeters mm2

ft2 square feet 0.093 square meters m2

yd2 square yard 0.836 square meters m2

ac acres 0.405 hectares ha

mi2 square miles 2.59 square kilometers km2

VOLUME 

fl oz fluid ounces 29.57 milliliters mL 

gal gallons 3.785 liters L 

ft3 cubic feet 0.028 cubic meters m3 

yd3 cubic yards 0.765 cubic meters m3 

NOTE: volumes greater than 1000 L shall be shown in m3

MASS 

oz ounces 28.35 grams g

lb pounds 0.454 kilograms kg

T short tons (2000 lb) 0.907 megagrams (or "metric ton") Mg (or "t") 

TEMPERATURE (exact degrees) o

F Fahrenheit 5 (F-32)/9 Celsius oC 

or (F-32)/1.8 

ILLUMINATION 

fc foot-candles 10.76 lux lx

fl foot-Lamberts 3.426 candela/m2 cd/m2

FORCE and PRESSURE or STRESS 

lbf poundforce 4.45 newtons N 

lbf/in2 poundforce per square inch 6.89 kilopascals kPa 

APPROXIMATE CONVERSIONS FROM SI UNITS 

Symbol When You Know Multiply By To Find Symbol 

LENGTH

mm millimeters 0.039 inches in 

m meters 3.28 feet ft 

m meters 1.09 yards yd 

km kilometers 0.621 miles mi 

AREA mm2

 square millimeters 0.0016 square inches in2 

m2 square meters 10.764 square feet ft2 

m2 square meters 1.195 square yards yd2 

ha hectares 2.47 acres ac

km2 square kilometers 0.386 square miles mi2 

VOLUME 

mL milliliters 0.034 fluid ounces fl oz 

L liters 0.264 gallons gal 

m3 cubic meters 35.314 cubic feet ft3 

m3 cubic meters 1.307 cubic yards yd3 

MASS 

g grams 0.035 ounces oz

kg kilograms 2.202 pounds lb

Mg (or "t") megagrams (or "metric ton") 1.103 short tons (2000 lb) T 

TEMPERATURE (exact degrees) o

C Celsius 1.8C+32 Fahrenheit oF 

ILLUMINATION 

lx lux 0.0929 foot-candles fc 

cd/m2 candela/m2 0.2919 foot-Lamberts fl

FORCE and PRESSURE or STRESS 

N newtons 0.225 poundforce lbf 

kPa kilopascals 0.145 poundforce per square inch lbf/in2

*SI is the symbol for th International System of Units. Approp e riate rounding should be made to comply with Section 4 of ASTM E380. 

(Revised March 2003)
iv 

TABLE OF CONTENTS 

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

BACKGROUND ............................................................................................................. 1 

OPTIMIZED CROSS SECTIONS FOR BRIDGE GIRDERS........................................ 1 

HIGH-PERFORMANCE CONCRETE IN BRIDGE DECKS ....................................... 2 

EFFECT OF HIGH-STRENGTH CONCRETE ON PRESTRESS LOSSES ................. 4 

OBJECTIVES AND SCOPE........................................................................................... 4 

CHAPTER 2. TASK 1: COST ANALYSES OF HIGH-PERFORMANCE 

CONCRETE IN BRIDGE DECKS.............................................................................. 7

RESEARCH APPROACH .............................................................................................. 7 

EFFECTS OF CONCRETE STRENGTH ONLY...........................................................12 

EFFECTS OF CONCRETE COSTS ...............................................................................16 

TASK 1 CONCLUSIONS ...............................................................................................29 

CHAPTER 3. TASK 2: ANALYSES OF FLEXURAL STRENGTH AND 

DUCTILITY...................................................................................................................31

RESEARCH APPROACH ..............................................................................................31 

MATERIAL PROPERTIES ............................................................................................35 

MOMENT-CURVATURE RELATIONSHIPS ..............................................................41 

FLEXURAL STRENGTH...............................................................................................50 

TASK 2 CONCLUSIONS...............................................................................................53 

CHAPTER 4. TASK 3: ANALYSES OF PRESTRESS LOSSES AND LONG-TERM 

DEFLECTIONS.............................................................................................................55

RESEARCH APPROACH ..............................................................................................55 

MATERIAL PROPERTIES ............................................................................................57 

PRESTRESS LOSSES.....................................................................................................67 

LONG-TERM DEFLECTIONS ......................................................................................73 

TASK 3 CONCLUSIONS ...............................................................................................75 

CHAPTER 5. CONCLUSIONS AND RECOMMENDATIONS ..........................................79

CONCLUSIONS..............................................................................................................79 

RECOMMENDATIONS.................................................................................................80 

ACKNOWLEDGMENTS .........................................................................................................81

REFERENCES...........................................................................................................................83
v 

LIST OF FIGURES 

Figure 1. Cross section of girder analyzed—PCI Bulb-Tee (BT-72). All dimensions are in 

millimeters (inches). ..................................................................................................... 5 

Figure 2. Cross section of girder analyzed—Florida Bulb-Tee (FL BT-72). All dimensions 

are in millimeters (inches). ........................................................................................... 5 

Figure 3. Cost chart for a BT-72, 41 MPa.................................................................................. 14 

Figure 4. Optimum cost curves for a BT-72, 41 MPa................................................................ 15 

Figure 5. Optimum cost curves for a BT-72, 83 MPa................................................................ 18 

Figure 6. Optimum cost curves for a BT-72, 55 MPa................................................................ 19 

Figure 7. Optimum cost curves for a BT-72, 69 MPa................................................................ 20 

Figure 8. Comparison of optimum cost curves for a BT-72 with varying concrete strengths. .. 21 

Figure 9. Comparison of optimum cost curves for a FL BT-72 with varying concrete 

strengths. ..................................................................................................................... 22 

Figure 10. Optimum cost curves for a BT-72, 41 MPa with cost premium. ................................ 23 

Figure 11. Optimum cost curves for a BT-72, 55 MPa with cost premium. ................................ 24 

Figure 12. Optimum cost curves for a BT-72, 69 MPa with cost premium. ................................ 25 

Figure 13. Optimum cost curves for a BT-72, 83 MPa with cost premium. ................................ 26 

Figure 14. Optimum cost curves for a FL BT-72, 41 MPa with cost premium............................ 27 

Figure 15. Optimum cost curves for a FL BT-72, 83 MPa with cost premium............................ 28 

Figure 16 (part 1). Cross section of series A girder (BT-72) analyzed in task 2. All 

dimensions are in millimeters (inches). ...................................................................... 34 

Figure 16 (part 2). Cross section of series B girder (BT-72) analyzed in task 2. All 

dimensions are in millimeters (inches). ...................................................................... 34 

Figure 16 (part 3). Cross section of series C girder (BT-72) analyzed in task 2. All 

dimensions are in millimeters (inches). ...................................................................... 34 

Figure 16 (part 4). Cross section of series D girder (BT-72) analyzed in task 2. All 

dimensions are in millimeters (inches). ...................................................................... 34 

Figure 17. Stress–strain curves for concrete used in BEAM BUSTER analysis.......................... 38 

Figure 18. Stress–strain curve for prestressing strand used in BEAM BUSTER analysis........... 40 

Figure 19. Moment-curvature relationships for BT-72, 41 MPa at a span of 24.4 m. ................. 43 

Figure 20. Moment-curvature relationships for BT-72, 83 MPa at a span of 24.4 m. ................. 44 

Figure 21. Moment-curvature relationships for BT-72, 41 MPa at a span of 44.5 m. ................. 45 

Figure 22. Moment-curvature relationships for BT-72, 83 MPa at a span of 53.3 m. ................. 46 

Figure 23 (part 1). Cross section of series A through D girders (BT-72) analyzed in task 3. 

All dimensions are in millimeters (inches). ................................................................ 59 

Figure 23 (part 2). Cross section of series E girder (BT-72), 24.4 m (80-ft) span, analyzed 

in task 3. All dimensions are in millimeters (inches). ................................................ 59 

Figure 23 (part 3). Cross section of series E girder (BT-72), 44.5 m (146-ft) span, analyzed 

in task 3. All dimensions are in millimeters (inches). ................................................ 59 

Figure 23 (part 4). Cross section of series E girder (BT-72), 53.3 m (175-ft) span, analyzed 

in task 3. All dimensions are in millimeters (inches). ................................................ 59 

Figure 24. Variation of specific creep with compressive strength as published. ......................... 62 

Figure 25. Variation of ultimate specific creep with compressive strength. ................................ 63 

Figure 26. Variation of specific creep with age............................................................................ 66 

Figure 27. Prestressing strand stress versus time for varying girder concrete strength, 

28-MPa deck strength, and 44.5-m span..................................................................... 68 
vi 

Figure 28. Prestressing strand stress versus time for 83-MPa girder concrete strength, 

55-MPa deck strength, and varying spans. ................................................................. 69 

Figure 29. Midspan deflection versus time for varying girder concrete strengths, 28-MPa 

deck strength, and 44.5-m span. ................................................................................. 74 

Figure 30. Midspan deflection versus time for 41-MPa girder concrete strength, varying 

deck concrete strengths, and 44.5-m span. ................................................................. 76 

Figure 31. Midspan deflection versus time for 83-MPa girder concrete strength, 55-MPa 

deck strength, and varying spans. ............................................................................... 77 
vii 

LIST OF TABLES 

Table 1. Task 1 variables (SI units). ............................................................................................... 8 

Table 2. Task 1 variables (English units). ...................................................................................... 8 

Table 3. Deck design (English units)............................................................................................ 10 

Table 4. Deck design (SI units). ................................................................................................... 10 

Table 5. Ratios for high-strength concrete.................................................................................... 11 

Table 6. In-place costs as per ACI Committee 363. ..................................................................... 11 

Table 7. Selected ratios for cost index per unit area to premium costs. ....................................... 12 

Table 8. Relative premium costs of high-strength concretes........................................................ 17 

Table 9. Task 2 variables (SI units). ............................................................................................. 32 

Table 10. Task 2 variables (English units). .................................................................................. 33 

Table 11. Calculated values of modulus of elasticity. .................................................................. 36 

Table 12. Calculated stresses and strains at maximum moment (SI units)................................... 48 

Table 13. Calculated stresses and strains at maximum moment (English units).......................... 49 

Table 14. Calculated flexural strengths (SI units). ....................................................................... 51 

Table 15. Calculated flexural strengths (English units)................................................................ 52 

Table 16. Task 3 variables (SI units). ........................................................................................... 56 

Table 17. Task 3 variables (English units). .................................................................................. 57 

Table 18. Values of creep used in PBEAM. ................................................................................. 64 

Table 19. Comparison of prestress losses (SI units)..................................................................... 71 

Table 20. Comparison of prestress losses (English units). ........................................................... 72 

1 

CHAPTER 1. INTRODUCTION 

BACKGROUND 

For more than 25 years, concretes with compressive strengths in excess of 41 megapascals 

(MPa) (6,000 pounds per square inch (psi)) have been used in the construction of columns of 

highrise buildings.(1) While the availability of high-strength concretes was limited initially to a 

few geographic locations, opportunities to use these concretes at more locations across the 

United States have arisen. With the increase of such opportunities, material producers have 

accepted the challenge to manufacture concretes with higher compressive strengths. Although 

the technology to produce higher-strength concretes has developed primarily within the readymix concrete industry for use in buildings, the same technology can be applied in the use of 

concretes for bridge girders and bridge decks. 

For precast, prestressed concrete bridge girders, compressive strengths in excess of 41 MPa 

(6,000 psi) have rarely been specified. However, strengths at release have frequently controlled 

the concrete mix design so that actual strengths at 28 days are often in excess of 41 MPa 

(6,000 psi). In recent years, a strong interest in using concrete with higher compressive strengths 

for bridge applications has emerged at a few geographic locations in a manner similar to the 

developments in the building industry. Several research studies have addressed the application of 

high-strength concrete in bridge girders and have identified the potential benefits of this 

approach (e.g., the use of fewer girders per cross section, longer span lengths, and more 

economical structures). (See references 2–6.) 

The durability of concrete bridge decks has been a concern for many years, and numerous 

strategies to improve the performance of bridge decks have been undertaken. These include the 

use of greater cover to the reinforcing steel, the use of epoxy-coated reinforcing steel, the use of 

special admixtures in concrete to reduce permeability, and the use of sealers to reduce the 

penetration of chlorides into the concrete. Most codes and specifications now recognize that a 

more durable concrete can be achieved through the use of a low water-to-cementitious-material 

ratio, appropriate air entrainment, and appropriate cementitious materials to produce a low 

permeability concrete. These concretes are now becoming known as high-performance concretes 

where high-performance includes durability and ease of placement as well as strength. Many of 

the factors that enable a durable concrete to be produced also result in a high-strength concrete. 

Consequently, if a concrete for a bridge deck is designed to be durable, it will probably also have 

a high compressive strength. This research program was initiated, therefore, to investigate the 

cost and structural advantages of using high-performance concretes in bridge decks. 

OPTIMIZED CROSS SECTIONS FOR BRIDGE GIRDERS 

In the early applications of prestressed concrete, designers developed their own ideas of the 

"best" girder cross section to use. As a result, each bridge used a different girder shape, making it 

impossible to reuse girder formwork on subsequent contracts. Girder shapes were subsequently 

standardized in the interest of improving economy of construction which, in turn, led to the 

development of the standard American Association of State Highway and Transportation 

Officials–Prestressed Concrete Institute (AASHTO–PCI) sections for bridge girders. Girder 

types I through IV were developed in the late 1950s, and types V and VI in the 1960s. 
2 

Adoption of the AASHTO standard bridge girders simplified design practice and led to the wider 

use of prestressed concrete for bridges. Standardization resulted in considerable cost savings in 

the construction of bridges. However, following the original adoption of the standard AASHTO–

PCI shapes, individual States again developed their own standard sections for improved 

efficiency and economy. In l980, the Federal Highway Administration (FHWA) initiated an 

investigation to identify new optimized sections for major prestressed concrete girders. 

In an FHWA study published in 1982, Construction Technology Laboratories, Inc. identified the 

Bulb-Tee, Washington, and Colorado girders as the most structurally efficient sections.(7,8) A 

cost effectiveness analysis recommended the use of the Bulb-Tee girder (with a 152-millimeter 

(mm) (6-inch) web) as a national standard for precast, prestressed concrete bridge girders in the 

United States for span lengths ranging from 24 to 43 meters (m) (80 to 140 feet (ft)). 

Subsequently, the PCI Committee on Concrete Bridges developed a modified section for use as a 

national standard.(9) The modifications resulted in a slightly heavier section that was easier to 

produce and handle. This cross section was later adopted by several States and is identified as 

the Bulb-Tee (BT-72) in this report. Several other versions of the Bulb-Tee have also been 

developed in different geographic locations.(10,11)

A recently completed report for the FHWA entitled Optimized Sections for High-Strength 

Concrete Bridge Girders concluded that the use of existing girder cross sections with concrete 

compressive strengths up to 69 MPa (10,000 psi) will allow longer span lengths and more 

economical structures.(6) In order for concrete with compressive strengths in excess of 69 MPa 

(10,000 psi) to be used effectively, additional prestressing forces must be applied to the cross 

section. Report conclusions were based on analyses performed using the computer program 

BRIDGE which determines relative unit costs and maximum span lengths for different 

prestressed concrete bridge designs. All analyses were based on the assumption that concrete in 

the deck had a compressive strength of 28 MPa (4,000 psi) and that the prestress losses have a 

constant value of 310 MPa (45,000 psi). However, these assumptions may not reflect true 

behavior and current trends in the usage of high-performance concretes. 

HIGH-PERFORMANCE CONCRETE IN BRIDGE DECKS 

The American Concrete Institute (ACI) has defined high-performance concrete as concrete 

meeting special performance and uniformity requirements that cannot always be achieved 

routinely using only conventional constituents and normal mixing, placing, and curing 

practices.(12) These requirements may involve enhancements of the following: 

• Ease of placement and compaction without segregation. 

• Long-term mechanical properties. 

• Early age strength. 

• Toughness. 

• Volume stability. 

• Long life in severe environments. 

For bridge decks, high-performance concrete needs to have enhanced long-term mechanical 

properties, enhanced toughness, and long life in severe environments. Volume stability is also 

desirable. From a construction standpoint, ease of placement and compaction without 
3 

segregation is also essential. Therefore, a concrete to be used for a durable and long-lasting 

bridge deck needs to meet all the requirements of a high-performance concrete as defined by 

ACI. 

In the Strategic Highway Research Program (SHRP) C-205, high-performance concrete for 

pavements and bridges was defined as concrete with the following characteristics: 

• A maximum water–cementitious material ratio of 0.35. 

• A minimum durability factor of 80 percent as determined by ASTM C666 Method A. 

• A minimum strength criteria of: 

1. 21 MPa (3,000 psi) within 4 hours of placement. 

2. 34 MPa (5,000 psi) within 24 hours. 

3. 69 MPa (10,000 psi) within 28 days.(13)

For bridge decks, items 1 and 2, as defined by SHRP, are clearly essential and desirable for longterm durability performance. However, the use of a water-to-cementitious-material ratio of 0.35 

will result in a concrete compressive strength at 28 days well in excess of the 28 MPa (4,000 psi) 

that is often specified for today's bridge decks and could well be in the range of 41 to 55 MPa 

(6,000 to 8,000 psi). 

The use of high-performance concretes in bridge decks is receiving an increased amount of 

attention as a means of improving durability. High-performance concretes provide higher 

resistance to chloride penetration, higher resistance to deicer scaling, less damage from freezing 

and thawing, higher wear resistance, and less cracking. Many of the methods used to increase the 

durability of concrete result in a concrete that has a higher compressive strength. However, the 

higher concrete strength is rarely considered because the design of long-span prestressed girders 

is controlled by service load stresses caused by dead load, live load, and impact. 

In a recent project for the Louisiana Transportation Research Center, four full-size, prestressed 

concrete girders were tested to destruction in flexure.(14) While the specified strength of concrete 

in the girders was 69 MPa (10,000 psi), the bridge design for these girders required concrete with 

a compressive strength of only 29 MPa (4,200 psi) in the deck. However, analyses of the cross 

section indicated that failure in flexure would occur by crushing of the deck concrete. 

Consequently, a concrete compressive strength of 41 MPa (6,000 psi) was specified for the deck 

to ensure flexural failure by fracture of the strands. Although the flexural strength of the section 

was reached when the strands fractured, evaluation of the test results indicated that the section 

was close to failure by crushing the concrete deck even when 41 MPa (6,000 psi) concrete was 

used in the deck. 

It was noted in a previous report that as girder concrete strength increased, a point of diminishing 

benefits was reached.(6) The primary cause of these diminishing returns is decreasing strand 

eccentricity. Once strands have to be placed within the web, the efficiency of additional strands 

decreases rapidly. Finally, a point is reached where no more space is available for additional 

strands. The only benefit, therefore, is an increase in the concrete tensile strength. Another factor 

contributing to the reduced benefits was the deck concrete strength. In calculating the composite 

section properties, transformed girder–deck section was used. As girder strength increased and 

deck strength remained constant, the composite section properties decreased with a 

corresponding increase in service load stresses in the girder for the same span length and girder 
4 

spacing. The use of a high-performance concrete in the deck with a higher modulus of elasticity 

will result in an increase in the composite section properties. 

EFFECT OF HIGH-STRENGTH CONCRETE ON PRESTRESS LOSSES 

When compared with the properties of conventional strength concretes, high-strength concrete 

has a higher modulus of elasticity, a higher tensile strength, and reduced creep. The higher 

modulus of elasticity results in less elastic shortening in prestressed concrete girders at time of 

release for the same stress level. This reduction in shortening may be offset by the use of higher 

prestress levels with high-strength concrete. The higher tensile strength does not have a direct 

effect on prestress losses but allows high-strength girders to be designed for a higher permissible 

tensile stress. This, in turn, results in higher service load design moments. 

Creep per unit stress of high-strength concrete is lower than the creep for conventional strength 

concretes.(13) Thus, the direct substitution of a high-strength concrete in place of a lower strength 

concrete will result in less prestress losses. However, the utilization of a higher level of prestress 

will offset the reduction in creep per unit stress. The magnitude of the net result will depend on 

the reduction in creep per unit stress and the increase in stress level. 

Prior to casting the deck, prestress losses depend on the properties of the girder concrete alone. 

After the deck is cast, prestress losses depend on the properties of the deck concrete as well as 

the girder concrete. When the deck concrete has a strength significantly lower than the strength 

of the girder concrete, the deck concrete may have a major influence on the magnitude of 

prestress losses in the bridge. Consequently, the utilization of a higher-strength concrete in the 

bridge deck can be beneficial in reducing prestress losses. A reduction in prestress losses means 

that for the same amount of initial prestress, a greater force is available for design at service 

load. Since the amount of force available at service load controls the design of long-span girders, 

reduced prestress losses will be beneficial in the more effective utilization of high-strength 

concrete. 

Another factor related to elastic shortening, creep, and prestress losses is the change in camber. 

Girders produced with high-strength concrete are likely to have less initial camber at release and 

less change in camber. Bridges produced with high-performance concretes in the decks and 

girders may undergo less deflection changes after the deck is cast. 

OBJECTIVES AND SCOPE 

Based on the above background, the objectives of the research were to evaluate the following: 

• Effect of using high-performance concretes in the deck on the cost per unit area. 

• Effect of using high-performance concretes in the deck and girders on flexural strength 

and ductility. 

• Effect of high-performance concretes in the deck and girders on prestress losses and 

long-term deflections. 

The objectives were accomplished in three separate tasks. Each task used a different research 

approach as described in the following chapters. 
5 

For each task, the analyses were based on a PCI Bulb-Tee (BT-72) cross section with a depth of 

1.83 m (72 inches). In the previous investigation, the PCI Bulb-Tee was identified as the most 

cost-effective cross section for span lengths up to 45.7 m (150 ft) at all concrete compressive 

strength levels.(6) For span lengths greater than 45.7 m (150 ft) and for all concrete compressive 

strength levels, the Florida BT-72 and Nebraska NU-1800 were the most cost effective. In the 

present investigation, some analyses were also performed using the FL BT-72. The cross 

sectional dimensions of the BT-72 and FL BT-72 are shown in figures 1 and 2, respectively. 

Figure 1. Cross section of girder analyzed—PCI Bulb-Tee (BT-72). 

All dimensions are in millimeters (inches). 

Figure 2. Cross section of girder analyzed—Florida Bulb-Tee (FL BT-72). 

All dimensions are in millimeters (inches). 

7 

CHAPTER 2. TASK 1: COST ANALYSES OF HIGH-PERFORMANCE 

CONCRETE IN BRIDGE DECKS 

RESEARCH APPROACH 

Analyses to evaluate the effect of using high performance concrete in bridge decks on the cost 

per unit area were performed using a computer program called BRIDGE. 

Computer Program BRIDGE 

The computer program BRIDGE was written as part of a previous investigation for the 

Optimized Sections for Precast, Prestressed Bridge Girders and was later revised.(6,7) The 

required input of BRIDGE consists of girder span, spacing, and cross section; concrete and 

strand characteristics; and relative costs of materials. The program determines deck thickness 

and deck reinforcement, the required number of prestressing strands, and the cost index per unit 

surface area of bridge deck. It also provides section properties, moments, stress levels, and 

deflections. Comparisons are made based on relative costs for simply supported spans. A 

complete description of BRIDGE is given in reference 6. 

The following variables were used in the analyses using BRIDGE: 

• Girder concrete strength: Concrete strength of the girders at 28 days was varied from 41 

MPa (6,000 psi) upward in increments of 14 MPa (2,000 psi) to 83 MPa (12,000 psi); 

release strength was taken as 75 percent of the 28-day strength. 

• Deck concrete strength: Strength of the deck concrete was varied from 28 MPa (4,000 

psi) upwards in increments of 14 MPa (2,000 psi) to 69 MPa (10,000 psi). 

• Unit weights of concrete were taken as 2.32, 2.37, 2.42, 2.48, and 2.5 megagrams per 

cubic meter (Mg/m3

) (145, 148, 151, 155 and 156 lb/ft3, respectively) for concrete 

compressive strengths of 28, 41, 55, 69 and 83 MPa (4,000, 6,000, 8,000, 10,000, and 

12,000 psi, respectively). 

• Girder cross section: Analyses were made for the BT-72 and the FL BT-72. 

• Span length: Spans in excess of 24.4 m (80 ft) up to a maximum possible span length 

were considered. 

• Girder spacing: No maximum spacing was placed on the girders; effective deck span was 

not allowed to exceed 4.9 m (16 ft); minimum spacing corresponded to the flanges of the 

two girders touching each other. 

• Deck thickness: Deck thickness varied with girder spacing according to a predetermined 

design; minimum deck thickness was 190 mm (7.5 inches). 

• Relative unit costs of materials: Two sets of relative unit costs as discussed later were 

used. 

The complete combination of variables is defined in tables 1 and 2. It is recognized that the use 

of a deck concrete strength of 69 MPa (10,000 psi) in combination with a girder concrete 

strength of 41 MPa (6,000 psi) is unlikely to occur. However, the complete combination of 

variables has been included for comparison purposes. 
8 

Table 1. Task 1 variables (SI units). 

Girder 

Section 

Girder 

Strength 

(MPa) 

Deck Strength 

(MPa) 

Girder 

Concrete 

Premium 

Deck Concrete

Premium 

BT-72 

BT-72 

BT-72 

BT-72 

41 

55 

69 

83 

28, 41, 55, 69 

28, 41, 55, 69 

28, 41, 55, 69 

28, 41, 55, 69 

No 

No 

No 

No 

No 

No 

No 

No 

BT-72 

BT-72 

BT-72 

BT-72 

41 

55 

69 

83 

28, 41, 55, 69 

28, 41, 55, 69 

28, 41, 55, 69 

28, 41, 55, 69 

No 

 Yes 

 Yes 

 Yes 

 Yes 

 Yes 

 Yes 

 Yes 

FL BT-72 

FL BT-72 

41 

83 

28, 41, 55, 69 

28, 41, 55, 69 

No 

 No 

No 

No 

FL BT-72 

FL BT-72 

41 

83 

28, 41, 55, 69 

28, 41, 55, 69 

No 

 Yes 

 Yes 

 Yes 

Table 2. Task 1 variables (English units). 

Girder 

Section 

Girder 

Strength 

(psi) 

Deck Strength 

(ksi) 

Girder 

Concrete 

Premium 

Deck Concrete

Premium 

BT-72 

BT-72 

BT-72 

BT-72 

6,000 

8,000 

10,000 

12,000 

4, 6, 8, 10 

4, 6, 8, 10 

4, 6, 8, 10 

4, 6, 8, 10 

No 

No 

No 

No 

No 

No 

No 

No 

BT-72 

BT-72 

BT-72 

BT-72 

6,000 

8,000 

10,000 

12,000 

4, 6, 8, 10 

4, 6, 8, 10 

4, 6, 8, 10 

4, 6, 8, 10 

No 

 Yes 

 Yes 

 Yes 

 Yes 

 Yes 

 Yes 

 Yes 

FL BT-72 

FL BT-72 

6,000 

12,000 

4, 6, 8, 10 

4, 6, 8, 10 

No 

No 

No 

No 

FL BT-72 

FL BT-72 

6,000 

12,000 

4, 6, 8, 10 

4, 6, 8, 10 

No 

 Yes 

 Yes 

 Yes 
9 

The following default assumptions in BRIDGE were used: 

• Design conforms to AASHTO specifications. 

• Live load consists of HS 20-44 loading. 

• Girders are simply supported. 

• Design is based on a typical interior girder. 

• Concrete deck is cast in place and acts compositely with the girder. Deck formwork is 

supported on the girder. The transformed area of strands was neglected. 

• Strands are Grade 270 with a 12.7 mm (0.5 inch) diameter and have an idealized, trilinear 

stress–strain curve. 

• Strands are spaced at 51-mm (2-inch) centers (minimum spacing of 51-mm (2-inches) 

from concrete surface to center of the strand). 

• Total prestress losses are constant and equal 310 MPa (45,000 psi). Separate analyses for 

prestress losses are discussed in chapter 4 of this report. 

• Relative unit costs of materials and labor are constant for each cost analysis. 

• Cost analysis comparisons are for the precast girder and a cast-in-place deck only. Costs 

of substructure and approach fills are not considered. 

• Design is based on flexural strength at midspan. It is assumed that the compressive and 

tensile stressed that would develop at the ends of the girders if all strands were straight 

can be handled by the draping of strands, by additional top strands at the ends of the 

girders, or by debonding some strands at the ends of the girders. 

It is recognized that shipping lengths, girder weights, lateral stability of girders, prestressing bed 

capacities that exist today, and plant capabilities to produce high-strength concretes could limit 

the type of girders that can be produced. However, these limitations were not used as a means to 

restrict potential applications. The intent of the project was to look beyond current production 

capabilities. 

The computer program BRIDGE determines cast-in-place deck thickness and reinforcement 

from design aids prepared by the Washington State Department of Transportation.(15) Designs 

aids were based on AASHTO and ACI guidelines.(16,17) For effective slab spans less than 2.1 m 

(7 ft), the design aids use a slab thickness of 175 mm (7 inches). However, for this project the 

FHWA requested that the minimum slab thickness be increased to 190 mm (71⁄2 inches). Slab 

reinforcement was then determined based on the new minimum slab thickness. Results of the 

design are shown in table 3 with the SI equivalents provided in table 4. These data as English 

units were stored within BRIDGE. 
10 

Table 3. Deck design(15) (English units). 

Slab Reinforcement* Effective Slab Span (ft) Slab Thickness (inches) Bar Size Spacing (inches)

1 to 3 inclusive 7 1⁄2 No. 5 11.0 

3 to 4 inclusive 7 1⁄2 No. 5 9.5 

4 to 5 inclusive 7 1⁄2 No. 5 8.5 

5 to 6 inclusive 7 1⁄2 No. 5 7.0 

6 to 7 inclusive 7 1⁄2 No. 6 9.0 

7 to 8 inclusive 7 1⁄2 No. 6 8.0 

8 to 9 inclusive 8 No. 6 8.0 

9 to 10 inclusive 8 1⁄2 No. 6 8.0 

10 to 11 inclusive 8 3⁄4 No. 6 7.5 

11 to 12 inclusive 9 No. 7 10.0 

12 to 13 inclusive 9 1⁄2 No. 7 10.0 

13 to 14 inclusive 9 3⁄4 No. 7 9.5 

14 to 15 inclusive 10 No. 7 9.5 

15 to 16 inclusive 10 1⁄2 No. 7 9.5 

 * Reinforcement shown is for each of top and bottom layers. 

Table 4. Deck design(15) (SI units). 

Effective Slab Span Slab Reinforcement* 

(m) 

Slab Thickness 

(mm) Bar Size Spacing (mm) 

0.3 to 0.9 inclusive 190 15 M 280 

0.9 to 1.2 inclusive 190 15 M 240 

1.2 to 1.5 inclusive 190 15 M 215 

1.5 to 1.8 inclusive 190 15 M 180 

1.8 to 2.1 inclusive 190 20 M 230 

2.1 to 2.4 inclusive 190 20 M 205 

2.4 to 2.7 inclusive 200 20 M 215 

2.7 to 3.0 inclusive 215 20 M 215 

3.0 to 3.4 inclusive 225 20 M 200 

3.4 to 3.7 inclusive 230 20 M 195 

3.7 to 4.0 inclusive 240 20 M 195 

4.0 to 4.3 inclusive 250 20 M 190 

4.3 to 4.6 inclusive 255 20 M 190 

4.6 to 4.9 inclusive 265 20 M 190 

 * Reinforcement shown is for each of top and bottom layers. 

Relative Costs 

The material weight for girder concrete, deck concrete, strands, reinforcing steel, and epoxycoated reinforcing steel is also calculated by BRIDGE. The relative cost of materials is then 

determined as the product of material weight and relative unit cost. The summation of the 

relative cost of materials is then divided by deck area to give the cost index per unit area. In the 

previous investigation, analyses were made to determine the effect of the premium cost for 

higher-strength girder concretes on the cost per unit area.(6) Based on a limited survey of 

industry, the ratios in table 5 were assumed for the premium cost for higher-strength concrete 

used in the girders. 
11 

Table 5. Ratios for high-strength concrete. 

For the current investigation, the premium costs for higher-strength concrete in the girders were 

assumed to be those shown as intermediate ratio. 

In the previous investigation, the deck concrete strength was assumed to be 28 MPa (4,000 psi) 

and the relative cost of the deck concrete was the same as that of the 41-MPa (6,000-psi) girder 

concrete.(6)

To investigate the costs of using high-strength concrete in bridge decks, it was necessary to 

determine the relative in-place costs for different strength concretes. Analyses of the data in the 

previous report indicated that the cost based on materials alone for a 69-MPa (10,000-psi) 

concrete would be about 72 percent higher than that of a 28-MPa (4,000-psi) concrete.(6) On the 

assumption that the labor to deliver and place the concretes will be only slightly dependent on 

concrete strength, the relative premium costs of higher-strength concrete in place will be lower 

than these numbers. In-place costs for high-strength concrete have been published by ACI 

Committee 363 and these data are shown in table 6.(1) 

Table 6. In-place costs as per ACI Committee 363. 

Strength $/yd3 $/m3 Relative Cost 

48 MPa (7,000 psi) 80 105 1.00 

62 MPa (9,000 psi) 85 111 1.06 

76 MPa (11,000 psi) 104 136 1.30 

Based on these data, it was decided to use two sets of ratios for premium costs of high-strength 

concrete in the decks to determine the sensitivity of the cost index per unit area to the premium 

costs. The selected ratios are in table 7. 

Concrete Strength Minimum 

Ratio 

Intermediate 

Ratio 

Maximum 

Ratio 

41 MPa (6,000 psi) 1.00 1.00 1.00 

55 MPa (8,000 psi) 1.00 1.05 1.10 

69 MPa (10,000 psi) 1.00 1.13 1.25 

83 MPa (12,000 psi) 1.00 1.25 1.50 
12 

Table 7. Selected ratios for cost index per unit area to premium costs. 

Deck Concrete Strength No Premium Ratio* Premium Ratio* 

 28 MPa (4,000 psi) 1.00 1.00 

 41 MPa (6,000 psi) 1.00 1.05 

 55 MPa (8,000 psi) 1.00 1.13 

 69 MPa (10,000 psi) 1.00 1.25 

 * Costs are relative to 41-MPa (6,000-psi) girder concrete. 

Analyses were performed for both the no premium ratio and the premium ratio. 

EFFECTS OF CONCRETE STRENGTH ONLY 

The computer program BRIDGE determines the deck thickness and reinforcement based on a 

design aid prepared by the Washington State Department of Transportation.(15) The design aid is 

based on AASHTO and ACI guidelines and uses a concrete compressive strength at 28 days of 

28 MPa (4,000 psi).(16,17) The design aid is based on the distribution of loads and design of 

concrete slabs given in the AASHTO Standard Specifications for main reinforcement 

perpendicular to traffic.(16) Discussions with several bridge engineers indicated that many States 

use design aids similar to the one incorporated into BRIDGE. 

In the AASHTO design of concrete slabs, deck thickness and reinforcement are calculated to 

resist the bending moments caused by the dead load of the slab and the live load moment for the 

selected concentrated wheel load. In flexural design for under-reinforced sections, the concrete 

compressive strength has little effect on the flexural strength of the section. Consequently, the 

use of high-strength concrete in the deck will not impact the flexural strength of the deck. Based 

on this design approach, the deck thickness and the amount of reinforcement required to resist a 

given bending moment will not decrease as higher-strength concretes are used. Therefore, no 

revision was made to the design aid for use with higher-strength concretes in the decks. In 

addition, a minimum slab thickness of 190 mm (7.5 inches) was requested by FHWA. This 

controlled the deck thickness for effective span lengths up to 2.4 m (8 ft). Thus the use of higherstrength concrete in bridge decks will not reduce the thickness of the deck or the weight of the 

superstructure. In fact, the higher-strength concretes in the deck will slightly increase the dead 

load of the superstructure because of the higher density of the higher-strength concretes. 

The computer program BRIDGE was used to perform cost efficiency analyses for various 

strengths of concrete in the girders and bridge decks. A sample cost chart for a BT-72 is shown 

in figure 3. The figure shows the cost index per unit surface area of the bridge deck versus span 

length for various girder spacings. The "optimum cost curve" is obtained where the end points of 

each individual cost curve are joined as shown by the dashed line in figure 3. This optimum cost 

curve indicates the least cost index for a particular span and varies as a function of girder spacing 

(see figure 3). As reported in previous investigations, for a given span, the cost index per unit 

area of a bridge deck decreases as girder spacing increases.(6,7) In all optimum cost curves used 

in this report, the girder spacing is allowed to vary to obtain the optimum cost. 
13 

Optimum cost curves are generated for a constant girder and deck concrete strength. The cost 

chart in figure 3 is for girder concrete strength at 28 days of 41 MPa (6,000 psi) and a 28-day 

concrete strength for the deck of 28 MPa (4,000 psi). Additional optimum cost curves can be 

generated for other deck concrete strengths for the same girder cross section and the same girder 

concrete strength. Figure 4 is a plot of the optimum cost curves for a BT-72 with a girder 

concrete strength of 41 MPa (6,000 psi) and deck concrete strengths of 28, 41, 55, and 69 MPa 

(4,000, 6,000, 8,000, and 10,000 psi, respectively). The data in figure 4 are based on the 

assumption that there is no cost premium for the higher-strength concrete. This figure illustrates 

that, at the shorter span lengths, there are no cost advantages or disadvantages in using the 

higher-strength concrete in the bridge deck. However, at the longer span lengths a slight 

advantage is achieved in a reduction in cost for the same span length. Alternatively, the ability to 

achieve a slightly longer span length is obtained. For the same girder cross section, these 

advantages occur because of the higher moment of inertia of the composite cross section that is 

achieved with the higher-strength concretes in the deck. In addition, the increase in the moment 

of inertia of the composite section will result in less live load deflection. 
14 

2000

2200

2400

2600

2800

3000

3200

3400

3600

3800

4000

4200

4400

4600

4800

5000

5200

20 25 30 35 40 45 50 55 60

Span, m

Cost Index per square meter

1.4 m girder spacing

1.8 m girder spacing

2.4 m girder spacing

optimum cost curve

1 m = 3.281 ft

Figure 3. Cost chart for a BT-72, 41 MPa. 

1 MPa = 145 psi 
15 

2000

2200

2400

2600

2800

3000

3200

3400

3600

3800

4000

4200

4400

4600

4800

5000

5200

20 25 30 35 40 45 50 55 60

Span, m

Cost Index per square meter

28 MPa

41 MPa

55 MPa

69 MPa

1 m = 3.281 ft

Figure 4. Optimum cost curves for a BT-72, 41 MPa. 

1 MPa = 145 psi 
16 

A comparison of optimum cost curves for a BT-72 girder with a girder concrete strength of 

83 MPa (12,000 psi) and deck concrete strengths of 28, 41, 55, and 69 MPa (4,000, 6,000, 8,000, 

and 10,000 psi, respectively) and no cost premium is shown in figure 5. In this combination, 

there are no real cost advantages or disadvantages with the use of the higher-strength concrete in 

the deck. Similar data for a BT-72 girder with concrete strengths of 55 MPa (8,000 psi) and 69 

MPa (10,000 psi) and no cost premium are shown in figures 6 and 7, respectively. 

Figure 8 shows a cost comparison for the BT-72 with girder compressive strengths of 41, 55, 69, 

and 83 MPa (6,000, 8,000, 10,000, and 12,000 psi, respectively) and deck concrete strengths of 

28 and 69 MPa (4,000 and 10,000 psi, respectively). This figure illustrates the benefits and 

limitations of using higher-strength concrete with no cost premiums in precast, prestressed 

bridge girders. At shorter span lengths there are no benefits realized by using the higher-strength 

concretes. However, at longer span lengths, it is more economical to use the higher-strength 

concrete in the girders. The higher-strength concrete in the girders results in larger prestressing 

forces and, consequently, greater girder spacings for a given span length, thus reducing unit 

costs. These data have been confirmed in previous investigations.(6,7) For the very long span 

lengths, it is possible only to design for these lengths using the higher-strength concretes. Figure 

8 also indicates another important point: the diminishing returns associated with the use of highstrength concrete, the primary cause of which is decreasing strand eccentricity. Once strands are 

placed within the web, the efficiency of the cross section begins to decrease rapidly. The 

incremental benefit of each succeeding strand decreases when sufficient room within the flange 

does not exist. Once additional prestressing force cannot be induced in the girder, the beneficial 

effects are limited to the increase in concrete tensile strength (which increases only as the square 

root of the compressive strength).(1)

Optimum cost curves for a FL BT-72 with girder concrete strengths of 41 and 83 MPa (6,000 

and 12,000 psi, respectively) and varying deck concrete strengths are shown in figure 9. The data 

represent the cost index per unit area when there is no cost premium for the higher-strength 

concrete. This figure shows a pattern of results similar to that shown in figure 8 for the BT-72. In 

a previous investigation, the FL BT-72 was found to be more cost effective than the BT-72 for 

span lengths greater than 46 m (150 ft). These data show the same results. 

EFFECTS OF CONCRETE COSTS 

It is reasonable to expect the payment of a premium for the use of high-strength concrete in 

bridge decks. This premium results from the increased cost of materials to be used in the 

concrete, the inexperience of bridge contractors in placing and finishing these concretes, and the 

necessity of proper curing procedures. Analyses were therefore made using the cost premiums 

indicated in table 8. 
17 

Table 8. Relative premium costs of high-strength concretes. 

Girder Deck Strength (MPa (psi)) 

Strength 

(MPa (psi)) Cost 28 (4,000) 

41 

(6,000) 

55 

(8,000) 

69 

(10,000) 

41 (6,000) 1.00 1.00 1.05 1.13 1.25 

55 (8,000) 1.05 1.00 1.05 1.13 1.25 

69 (10,000) 1.13 1.00 1.05 1.13 1.25 

83 (12,000) 1.25 1.00 1.05 1.13 1.25 

Optimum cost curves for a BT-72 with girder concrete strengths of 41, 55, 69, and 83 MPa 

(6,000, 8,000, 10,000, and 12,000 psi, respectively) and varying deck concrete strengths are 

shown in figures 10, 11, 12, and 13, respectively. Optimum cost curves for a FL BT-72 with 

girder concrete strength of 41 and 83 MPa (6,000 and 12,000 psi, respectively) are shown in 

figures 14 and 15, respectively. These figures indicate that at span lengths of 24 m (80 ft), 

increasing the deck concrete strength from 28 MPa to 69 MPa (4,000 to 10,000 psi) results in an 

increase in the cost per unit area of approximately 10 percent for both the Bulb-Tee and the 

Florida Bulb-Tee. At span lengths of 44.5 m (146 ft) the percentage of increase is approximately 

8 percent for both strengths of girder concrete. At the maximum span lengths achievable with the 

BT-72 and the FL BT-72 with a girder concrete strength of 83 MPa (12,000 psi), the increase is 

approximately 5 percent. 
18 

2000

2200

2400

2600

2800

3000

3200

3400

3600

3800

4000

4200

4400

4600

4800

5000

5200

20 25 30 35 40 45 50 55 60

Span, m

Cost Index per square meter

28 MPa

41 MPa

55 MPa

69 MPa

1 m = 3.281 ft

Figure 5. Optimum cost curves for a BT-72, 83 MPa. 

1 MPa = 145 psi 
19 

2000

2200

2400

2600

2800

3000

3200

3400

3600

3800

4000

4200

4400

4600

4800

5000

5200

20 25 30 35 40 45 50 55 60

Span, m

Cost Index per square meter

28 MPa

41 MPa

55 MPa

69 MPa

1 m = 3.281 ft

Figure 6. Optimum cost curves for a BT-72, 55 MPa. 

1 MPa = 145 psi 
20 

2000

2200

2400

2600

2800

3000

3200

3400

3600

3800

4000

4200

4400

4600

4800

5000

5200

20 25 30 35 40 45 50 55 60

Span, m

Cost Index per square meter

28 MPa

41 MPa

55 MPa

69 MPa

1 m = 3.281 ft

Figure 7. Optimum cost curves for a BT-72, 69 MPa. 

1 MPa = 145 psi 
21 

2000

2200

2400

2600

2800

3000

3200

3400

3600

3800

4000

4200

4400

4600

4800

5000

5200

20 25 30 35 40 45 50 55 60

Span, m

Cost Index per square meter

41 MPa/28 Mpa

41 MPa/69 MPa

55 MPa/28 MPa

55 MPa/69 MPa

69 MPa/28 MPa

69 MPa/69 MPa

83 MPa/28 MPa

83 MPa/69 MPa

Concrete Strengths: Girder/Deck

1 m = 3.281 ft

Figure 8. Comparison of optimum cost curves for a BT-72 with varying concrete strengths. 

1 MPa = 145 psi 
22 

2000

2200

2400

2600

2800

3000

3200

3400

3600

3800

4000

4200

4400

4600

4800

5000

5200

20 25 30 35 40 45 50 55 60

Span, m

Cost Index per square meter

41 MPa/28 MPa

41 MPa/41 MPa

41 MPa/55 MPa

41 MPa/69 MPa

83 MPa/28 MPa

83 MPa/41 MPa

83 MPa/55 MPa

83 MPa/69 MPa

Concrete Strengths: Girder/Deck

1 m = 3.281 ft

Figure 9. Comparison of optimum cost curves for a FL BT-72 

with varying concrete strengths. 

1 MPa = 145 psi 
23 

2000

2200

2400

2600

2800

3000

3200

3400

3600

3800

4000

4200

4400

4600

4800

5000

5200

20 25 30 35 40 45 50 55 60

Span, m

Cost Index per square meter

28 MPa

41 MPa

55 MPa

69 MPa

Deck Strengths

1 m = 3.281 ft

Figure 10. Optimum cost curves for a BT-72, 41 MPa with cost premium. 

1 MPa = 145 psi 
24 

2000

2200

2400

2600

2800

3000

3200

3400

3600

3800

4000

4200

4400

4600

4800

5000

5200

20 25 30 35 40 45 50 55 60

Span, m

Cost Index per square meter

28 MPa

41 MPa

55 MPa

69 MPa

Deck Strengths

1 m = 3.281 ft

Figure 11. Optimum cost curves for a BT-72, 55 MPa with cost premium. 

1 MPa = 145 psi 
25 

2000

2200

2400

2600

2800

3000

3200

3400

3600

3800

4000

4200

4400

4600

4800

5000

5200

20 25 30 35 40 45 50 55 60

Span, m

Cost Index per square meter

28 MPa

41 MPa

55 MPa

69 MPa

Deck Strengths

1 m = 3.281 ft

Figure 12. Optimum cost curves for a BT-72, 69 MPa with cost premium. 

1 MPa = 145 psi 
26 

2000

2200

2400

2600

2800

3000

3200

3400

3600

3800

4000

4200

4400

4600

4800

5000

5200

20 25 30 35 40 45 50 55 60

Span, m

Cost Index per square meter

28 MPa

41 MPa

55 MPa

69 MPa

Deck Strengths

1 m = 3.281 ft

Figure 13. Optimum cost curves for a BT-72, 83 MPa with cost premium. 

1 MPa = 145 psi 
27 

2000

2200

2400

2600

2800

3000

3200

3400

3600

3800

4000

4200

4400

4600

4800

5000

5200

20 25 30 35 40 45 50 55 60

Span, m

Cost Index per square meter

28 MPa

41 MPa

55 MPa

69 MPa

Deck Strengths

1 m = 3.281 ft

Figure 14. Optimum cost curves for a FL BT-72, 41 MPa with cost premium. 

1 MPa = 145 psi 
28 

2000

2200

2400

2600

2800

3000

3200

3400

3600

3800

4000

4200

4400

4600

4800

5000

5200

5400

20 25 30 35 40 45 50 55 60

Span, m

Cost Index per square meter

28 MPa

41 MPa

55 MPa

69 MPa

Deck Strengths

1 m = 3.281 ft

Figure 15. Optimum cost curves for a FL BT-72, 83 MPa with cost premium. 

1 MPa = 145 psi 
29 

Consequently, it may be concluded that even if a 69-MPa (10,000-psi) concrete has an in-place 

cost that is 25 percent greater than a 28-MPa (4,000-psi) concrete, the overall unit cost of the 

superstructure will only increase in the range of 5–10 percent. 

TASK 1 CONCLUSIONS 

The analyses performed in task 1 considered only the initial costs. They did not take into account 

that high-strength concrete in the deck is also high-performance concrete and will have improved 

durability compared to a deck produced with a lower strength concrete. This should result in less 

maintenance costs and reduced life cycle costs. A life cycle cost study is beyond the scope of 

work of this report. 

Based on analyses made in task 1, the following conclusions are made: 

• The use of high-strength concrete in bridge decks will not result in a reduction of deck 

thickness or in the amount of transverse reinforcement in the deck. Therefore, no cost 

savings can be expected from a reduction in materials. 

• The use of high-strength concrete in bridge decks allows for a slight increase in the 

maximum span length of the BT-72 and FL BT-72. 

• With no premium costs for high-strength concrete in the deck and girders, there is a slight 

reduction in the cost per unit area for the longer span lengths. 

• With a 25 percent increase in the in-place cost of the deck concrete, the overall unit cost 

of the superstructure will only increase in the range of 5–10 percent. 

• The use of high-strength concrete in bridge decks will result in less live load deflection. 

31 

CHAPTER 3. TASK 2: ANALYSES OF FLEXURAL 

STRENGTH AND DUCTILITY 

The general philosophy in prestressed concrete design is that concrete members shall be 

designed so that the steel is yielding as ultimate capacity is approached. This is generally 

achieved by specifying a maximum amount of reinforcement for a given cross section. When the 

reinforcement exceeds the specified amount, the design-moment strength is based on the 

compression portion of the moment couple. In an over-reinforced section, an increase in the 

compressive strength of the deck concrete results in an increase in the moment capacity. It 

should be noted that current design requirements have been developed based on lower strength 

concretes. It was, therefore, deemed appropriate to investigate the flexural strength and ductility 

that would result when higher-strength concretes are used in bridge decks. 

RESEARCH APPROACH 

Analyses for the effect of higher concrete strengths on the flexural strength and momentcurvature relationships were investigated using a computer program known as BEAM BUSTER. 

The program BEAM BUSTER performs a moment-curvature analysis of a reinforced or 

prestressed element using actual material properties. The program takes into account uncracked, 

cracked, and post-yield behavior of flexural members for a specified cross section and curvature. 

The program BEAM BUSTER calculates the strains and stresses that satisfy equilibrium of 

forces on the cross section and compatibility of strains. A cross section may be divided into 

many elements. A different stress–strain curve may be utilized for each element of the cross 

section. The stress–strain data are input as discrete data points along the complete stress–strain 

curve for each element specified in the cross section. 

Analyses were performed for the following variables: 

• Girder concrete compressive strength: 41 and 83 MPa (6,000 and 12,000 psi, 

respectively). 

• Deck concrete compressive strength: 28, 41, 55, and 69 MPa (4,000, 6,000, 8,000 and 

10,000 psi, respectively). 

• Girder cross section: PCI Bulb-Tee with a depth of 1.83 m (72 inches). 

• Span lengths: 24.3, 44.5, and 53.3 m (80, 146, and 175 ft, respectively). 

The combination of variables selected for analysis is defined in tables 9 and 10. The 

combinations were selected to represent a range of girder strengths and spans. 
32 

Table 9. Task 2 variables (SI units). 

Series 

Girder 

Strength 

(MPa) 

Deck 

Strength 

(MPa) 

Span 

(m) 

No. of 

Strands*

Flange 

Width 

(m) 

A 

41 

41 

41 

41 

28 

41 

55 

69 

24.4 

24.4 

24.4 

24.4 

19 

19 

19 

19 

2.44 

2.44 

2.44 

2.44 

B 

83 

83 

83 

83 

28 

41 

55 

69 

24.4 

24.4 

24.4 

24.4 

19 

19 

19 

19 

2.44 

2.44 

2.44 

2.44 

C 

41 

41 

41 

41 

28 

41 

55 

69 

44.5 

44.5 

44.5 

44.5 

41 

41 

41 

41 

1.37 

1.37 

1.37 

1.37 

D 

83 

83 

83 

83 

28 

41 

55 

69 

53.3 

53.3 

53.3 

53.3 

76 

76 

76 

76 

1.37 

1.37 

1.37 

1.37 

* For consistency between tasks, the odd number of strands calculated by 

program BRIDGE in task 1 was retained in task 2. 
33 

Table 10. Task 2 variables (English units). 

Series 

Girder 

Strength 

(psi) 

Deck 

Strength 

(psi) 

Span 

(ft) 

No. of 

Strands*

Flange 

Width 

(inches) 

A 

6,000 

6,000 

6,000 

6,000 

4,000 

6,000 

8,000 

10,000 

80 

80 

80 

80 

19 

19 

19 

19 

96 

96 

96 

96 

B 

12,000 

12,000 

12,000 

12,000 

4,000 

6,000 

8,000 

10,000 

80 

80 

80 

80 

19 

19 

19 

19 

96 

96 

96 

96 

C 

6,000 

6,000 

6,000 

6,000 

4,000 

6,000 

8,000 

10,000 

146 

146 

146 

146 

41 

41 

41 

41 

54 

54 

54 

54 

D 

12,000 

12,000 

12,000 

12,000 

4,000 

6,000 

8,000 

10,000 

175 

175 

175 

175 

76 

76 

76 

76 

54 

54 

54 

54 

* For consistency between tasks, the odd number of strands calculated by 

program BRIDGE in task 1 were retained in task 2. 

The cross sections used in the analyses are shown in figure 16. For purposes of simplicity, the 

non-prestressed reinforcement in the deck was not included in the analyses. The flange width of 

the composite section and number of strands were based on the calculations performed by the 

program BRIDGE in task 1. 

Prior to performing the analyses, it was necessary to define the stress–strain curves for the 

individual constituent materials consisting of deck concrete, girder concrete, and prestressing 

strand. 
34 

Figure 16 (part 1). Cross section of series A 

girder (BT-72) analyzed in task 2. All 

dimensions are in millimeters (inches). 

Figure 16 (part 2). Cross section of series B 

girder (BT-72) analyzed in task 2. All 

dimensions are in millimeters (inches). 

Figure 16 (part 3). Cross section of series C 

girder (BT-72) analyzed in task 2. All 

dimensions are in millimeters (inches). 

Figure 16 (part 4). Cross section of series D 

girder (BT-72) analyzed in task 2. All 

dimensions are in millimeters (inches). 
35 

MATERIAL PROPERTIES 

Required input for the program BEAM BUSTER consists of stress–strain curves for each 

element analyzed in the cross section. Therefore, it was necessary to define a family of stress–

strain curves for different strength concretes and to select an appropriate curve for the 

prestressing strand. 

Stress–Strain Curves for Concrete 

Since the calculations for ductility are very sensitive to the assumed shape of the stress–strain 

curves, it was necessary to establish a family of curves that realistically represent the properties 

of high-strength concrete. Several researchers have experimentally determined the complete 

stress-strain curves of concrete for strengths up to about 100 MPa (14,500 psi).(18,19) The 

measurements have indicated that the following occur with increasing strength: 

• The initial slope of the stress–strain curve increases. 

• The ascending portion of the stress–strain curve is more linear. 

• The strain at peak stress increases. 

• The slope of the descending portion of the curve increases. 

The slope of the ascending portion of the stress–strain curve is the modulus of elasticity of the 

concrete. Several equations have been proposed that relate the modulus of elasticity, Ec, to the 

concrete compressive strength, f'c, and the unit weight of the concrete, wc, including: 

ACI 318:(20) (1) 

Martinez:(21) (2) 

Canadian Code:(22) (3) 

Ahmad:(19) (4) 

Values of modulus of elasticity calculated according to the above equations are tabulated in 

table 11. 

1.5 ' 33 c c c E = w f

( ) 1.5

'

145

40,000 1,000,000 ⎟

⎠

⎞ ⎜

⎝

⎛ = + c

c c

w E f

( ) 1.5

'

143.5

39,740 1,000,000 ⎟

⎠

⎞ ⎜

⎝

⎛ = + c

c c

w E f

( ) ( )

0.325 5 ' 2.

c c c E = w f
36 

Table 11. Calculated values of modulus of elasticity. 

Equation 

ACI(19) Martinez(20) Canadian 

Code(21) Ahmad(18)

Compressive

Strength 

(MPa) 

Unit 

Weight 

(kg/m3

) 

(GPa) (GPa) (GPa) (GPa) 

28 2320 25.1 24.3 24.5 25.8 

41 2370 31.7 29.2 29.0 31.0 

55 2420 37.8 33.5 33.9 35.9 

69 2480 43.9 38.1 38.5 39.1 

83 2500 48.5 41.4 41.8 44.3 

(psi) (lb/ft3) (106 psi) (106 psi) (106 psi) (106 psi) 

4,000 145 3.64 3.53 3.55 3.75 

6,000 148 4.60 4.23 4.21 4.50 

8,000 151 5.48 4.86 4.92 5.20 

10,000 155 6.37 5.53 5.59 5.97 

12,000 156 7.04 6.01 6.07 6.43 

The ACI equation was based on an analysis for concrete strengths up to about 41 MPa (6,000 

psi).(20,23) Several investigators have indicated that the ACI equation tends to overestimate the 

modulus of elasticity for the higher-strength concretes.(1,13,19) The Martinez equation was 

developed as an alternative for the ACI equation and gives lower values of modulus of elasticity 

at the higher strength levels.(21) Some publications have indicated that the Martinez equation may 

underestimate the modulus of elasticity at the very high strength levels.(19) The Canadian Code 

equation was based on the Martinez equation with some rounding off for use in SI units and then 

converted back into English units. The rounding off results in slightly different calculated values. 

The Ahmad equation was based on a statistical analysis of data. Modulus values from the Ahmad 

equation lie between those of the ACI and the Martinez equations. For the present investigation, 

it was decided to use the ACI values for concrete strengths of 28 and 41 MPa (4,000 and 6,000 

psi, respectively) and to use the values by the Ahmad equation for concrete strengths of 55, 69, 

and 83 MPa (8,000, 10,000, and 12,000 psi, respectively). 

Collins et al. have indicated that the strain at peak stress, ε'

c , can be calculated from the 

following equation:(24) 

 (5) 1

'

'

− = ×n

n

E

f

c

c

c ε
37 

where 

 in MPa units (6) 

 in psi units (7) 

These equations were used in the present analyses to calculate the strain at peak stress from the 

modulus of elasticity and concrete compressive strength. 

Several investigators have published algebraic expressions to accurately describe the shape of 

the rising and descending branch of the stress-strain curve. The following expression was 

proposed by Popovics:(25) 

 (8) 

where fc = stress at a strain of εc. 

Thorenfeldt proposed a modification to Popovic's equation to increase the slope of the 

descending portion of the stress-strain curve.(26) He introduced a factor, k, to modify the equation 

as follows: 

 (9) 

where k = 1 on the ascending portion of the curve, and k is greater than 1 for the descending 

portion of the curve. Collins has suggested the following for the descending portion of the 

curve.( 24) 

 in MPa units (10) 

 in psi units (11) 

Stress–strain curves generated using the above approach are shown in figure 17. 

17

0.8

'

c f n = +

2500

0.8

'

c f n = +

( )

n

c

c c

c

c

c

n

n

f

f

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ − +

= ×

'

' '

1

ε

ε ε

ε

( )

nk

c

c c

c

c

c

n

n

f

f

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ − +

= ×

'

' '

1

ε

ε ε

ε

62

0.67

'

c f k = +

9000

0.67

'

c f k = +
38 

-20

-10

0

10

20

30

40

50

60

70

80

90

-500 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000

Strain, millionths

Stress, MPa

28 MPa

41 MPa

55 MPa

69 MPa

83 MPa

1 MPa = 145 psi

Figure 17. Stress–strain curves for concrete used in BEAM BUSTER analysis.
39 

To provide some tensile capacity to the concrete prior to cracking, the stress–strain curves 

developed in compression were extrapolated backwards using the following assumptions: 

• The slope of the curve in tension is the same as that in compression near the origin. 

• A maximum tensile stress, ft, calculated by the following equation, was used:(19)

 (12) 

The stress–strain curve in compression was calculated out to a strain of 0.005. The calculated 

stress–strain curves were then compared with the measured curves obtained by Kaar.(18) These 

comparisons were made to ensure that the calculated curves showed reasonable agreement with 

measured data. It should also be noted that in these curves, the peak stress corresponds to the 

designated concrete compressive strength. In concrete column testing, it has been observed that 

the maximum stress obtained in the column concrete can be less than the strength measured on a 

standard concrete cylinder. This difference is attributed to the difference in size and shape 

between the reinforced concrete column and the concrete cylinder; the differences in concrete 

casting, vibration, and curing; and to differences in the rate of loading. In his original column 

research, Hognestad chose a value of 0.85 for the ratio between maximum stress in the column 

and concrete cylinder strength.(27) He indicated that this factor may be systematically too high or 

too low and may not be a constant. In tests of plain concrete columns subjected to linearly 

varying strain, Hognestad and Kaar deduced (separately) that the factor was close to 1.0, varying 

from 0.96 to 1.12.(18,28) In design, a value of 0.85 is normally used. However, for purposes of the 

present analyses, a value of 1.0 was selected. 

Stress–Strain Properties of Strand 

An assumed stress–strain curve for strand was used in computer program BRIDGE in task 1. 

This curve is shown in figure 18. A slight modification to the curve was made for use in the 

program BEAM BUSTER. This modification is shown in figure 18. 

( )

2 / 3 '

t 2.30 c f = f
40 

0

200

400

600

800

1000

1200

1400

1600

1800

2000

0 10000 20000 30000 40000 50000 60000

Strain, millionths

Stress, MP

a

BRIDGE

BEAM BUSTER

1 MPa = 145 psi

Figure 18. Stress–strain curve for prestressing strand used in BEAM BUSTER analysis. 
41 

MOMENT-CURVATURE RELATIONSHIPS 

The moment-curvature relationships were calculated in two parts. In the first part, the moment 

was applied to the noncomposite section consisting of the prestressed concrete girder only. This 

part of the calculation represents the moments caused by girder dead load and deck dead load, 

and assumes that the dead load of the deck is carried entirely by the girder prior to development 

of composite action. 

In the second part of the calculation, the moment-curvature relationship was calculated for the 

composite section. This calculation represents any moment applied after the deck and girder act 

as a composite member. To ensure compatibility between the two parts of the analyses, it was 

necessary to match the moment-curvature relationships at the transition point between the two 

parts of the calculation. This was accomplished by making an artificial adjustment in the stressstrain curves for the concrete deck. The deck was assumed to consist of three layers of concrete 

and a separate adjustment was made for each layer. The girder concrete was assumed to consist 

of one layer. For a specified input curvature, the program BEAM BUSTER calculates the 

corresponding moment that results in equilibrium of forces and compatibility of strains. The 

output consists of curvature, moment, and selected strains and stresses. If compatibility of strains 

or equilibrium of forces cannot be calculated for a given curvature, the calculation for that 

curvature is terminated after a specified number of iterations. This generally occurs after the 

stress-strain curve for a concrete element or prestressing strand has returned to zero strain. 

Moment-curvature relationships for the four series of analyses described in tables 9 and 10 are 

shown in figures 19 through 22. Figures 19 and 20 show the relationships for 41-MPa (6,000 psi) 

and 83-MPa (12,000-psi) girder strength concrete, respectively, at a span of 24.4 m (80 ft)—the 

minimum span length considered in this investigation. Figure 21 shows the relationship for a 

girder compressive strength of 41 MPa (6,000 psi) at a span of 44.5 m (146 ft)—the longest span 

for which a 41 MPa (6,000 psi) compressive girder can be designed. Figure 22 shows the 

relationship for a girder with concrete compressive strength of 83 MPa (12,000 psi) at a span of 

53.3 m (175 ft)—the longest span length for which an 83 MPa (12,000 psi) girder can be 

designed. 

All of the moment-curvature relationships show a similar shape that can be divided into four 

parts. The first part consists of the moment-curvature relationship for the noncomposite section. 

This begins at a negative curvature because of the prestressing force and continues until a 

moment equivalent to the dead load of the deck and girder have been applied. The second part of 

the moment-curvature relationship consists of the moment applied to the composite section prior 

to cracking of the concrete. This part has a slightly steeper slope than that for the noncomposite 

section because of the higher stiffness of the composite section. The third part of the curve 

consists of the moment-curvature relationship following cracking and prior to yielding of the 

prestressing strand. The slope of this portion of the curve is considerably less than the curve for 

the uncracked section. The slope is greatest for the sections that contain the largest number of 

strands. The final part of the curve consists of the moment-curvature relationship following 

yielding of the strand. This portion of the curve is largely horizontal and generally continues 

until the end point of one of the stress-strain curves is reached. The moments corresponding to 

girder and deck dead load, girder and deck dead load and live load plus impact, and required 

strength are also shown on the figures. 
42 

As shown in figures 19 and 20, the moment-curvature relationships for the girders containing 

19 strands at a span of 24.4 m (80 ft) are not influenced by the deck concrete strength. Minor 

differences do occur, but at the scale shown in these figures, the differences are not discernible. 

The maximum moment for these sections is achieved when the prestressing strand reaches its 

maximum stress (which was assumed to be at a strain of 6 percent). This indicates that these 

cross sections will have a flexural capacity determined by fracture of the prestressing strand. 

These sections had a final curvature that was about 10 times the curvature when the first strands 

yielded. 

The impact of utilizing higher-strength concrete in the deck is more evident in figures 21 and 22. 

In the cross sections with a larger number of strands, the breaking strength of the strand is not 

reached prior to the flexural strength of the section being achieved. 
43 

0

2000

4000

6000

8000

10000

12000

14000

16000

18000

20000

22000

0 5 10 15 20 25 30 35

Curvature, microradians/mm

Moment, kN-m

28 MPa

41 MPa

55 MPa

69 MPa

Deck Strengths

1 mm = 0.0394 in

1 kN-m = 0.7376 k-ft

Figure 19. Moment-curvature relationships for BT-72, 41 MPa at a span of 24.4 m. 

1 MPa = 145 psi 
44 

0

2000

4000

6000

8000

10000

12000

14000

16000

18000

20000

22000

0 5 10 15 20 25 30 35

Curvature, microradians/mm

Moment, kN-m

28 MPa

41 MPa

55 MPa

69 MPa

Deck Strengths

1 mm = 0.0394 in

1 kN-m = 0.7376 k-ft

Figure 20. Moment-curvature relationships for BT-72, 83 MPa at a span of 24.4 m. 

1 MPa = 145 psi 
45 

0

2000

4000

6000

8000

10000

12000

14000

16000

18000

20000

22000

0 5 10 15 20 25 30

Curvature, microradians/mm

Moment, kN-m

28 MPa

41 MPa

55 MPa

69 MPa

Deck Strengths

1 kN-m = 0.7376 k-ft

1 mm = 0.0394 in

Figure 21. Moment-curvature relationships for BT-72, 41 MPa at a span of 44.5 m. 

1 MPa = 145 psi 
46 

0

2000

4000

6000

8000

10000

12000

14000

16000

18000

20000

22000

0 5 10 15 20 25 30

Curvature, microradians/mm

Moment, kN-m

28 MPa

41 MPa

55 MPa

69 MPa

Deck Strengths

1 kN-m = 0.7376 k-ft

1 mm = 0.0394 in

Figure 22. Moment-curvature relationships for BT-72, 83 MPa at a span of 53.3 m. 

1 MPa = 145 psi 
47 

For the 44.5-m (146-ft) and 53.3-m (175-ft) spans, the use of higher-strength concrete in the 

deck resulted in a slightly higher flexural capacity and a small increase in the final curvature. For 

the 44.5-m (146-ft) span girders, the final curvature was six to eight times the curvature at yield 

of the lower layer of strands. This indicated that the sections achieve adequate ductility even 

though fracture of the strand was not achieved at maximum moment. For the 53.3-m (175-ft) 

spans, the final curvature was about four times the curvature at yield of the lower layer of 

strands. This ductility is less than was obtained with the shorter span lengths but one that still 

corresponds to a very large deflection which would give adequate visual warning of impending 

failure. 

The strand stresses, deck strains, and girder strains at maximum moment are tabulated in tables 

12 and 13. The strand stress is the stress in the lower layer of strands. The deck strain is the 

strain at the top surface of the deck. The girder strain is the strain at the top surface of the girder. 

This table shows that for series A and B, the strand stress reached the breaking strength of the 

strand while the maximum deck strain was 2,160 millionths, which is only slightly greater than 

the assumed strain at peak stress for the 28 MPa (4,000 psi) concrete. For the other strength 

concretes, the deck strains are less than the strains at peak stress. Also for series A and B 

sections, the depth of the neutral axis was less than the deck thickness so that the strain at the top 

of the girder was tensile and sufficient to cause cracking. This is denoted by the letter "T" in the 

last column of the table. Series A and B sections had a flange width of 2.44 m (96 inches), so 

there was sufficient concrete area to allow development of the compression force for the flexural 

resistance. 
48 

Table 12. Calculated stresses and strains at maximum moment (SI units). 

Series 

Girder 

Strength 

(MPa) 

Deck 

Strength

(MPa) 

Span

(m) 

Strand 

Stress 

(GPa) 

Deck 

Strain 

(millionths)

Girder 

Strain* 

(millionths) 

A 

41 

41 

41 

41 

28 

41 

55 

69 

24.4 

24.4 

24.4 

24.4 

1.90 

1.90 

1.90 

1.90 

2,160 

1,720 

1,540 

1,430 

 T 

 T 

 T 

 T 

B 

83 

83 

83 

83 

28 

41 

55 

69 

24.4 

24.4 

24.4 

24.4 

1.90 

1.90 

1.90 

1.90 

2,160 

1,720 

1,550 

1,430 

 T 

 T 

 T 

 T 

C 

41 

41 

41 

41 

28 

41 

55 

69 

44.5 

44.5 

44.5 

44.5 

1.84 

1.83 

1.86 

1.87 

4,250 

2,900 

3,020 

2,740 

1,340 

360 

 T 

 T 

D 

83 

83 

83 

83 

28 

41 

55 

69 

53.3 

53.3 

53.3 

53.3 

1.80 

1.79 

1.81 

1.80 

3,640 

2,560 

2,710 

2,410 

2,025 

1,320 

1,090 

800 

 * T denotes tensile strain sufficient to cause cracking. 
49 

Table 13. Calculated stresses and strains at maximum moment (English units). 

Series 

Girder 

Strength 

(psi) 

Deck 

Strength

(psi) 

Span

(ft) 

Strand 

Stress 

(ksi) 

Deck 

Strain 

(millionths)

Girder 

Strain* 

(millionths) 

A 

6,000 

6,000 

6,000 

6,000 

4,000 

6,000 

8,000 

10,000 

80 

80 

80 

80 

275 

275 

275 

275 

2,160 

1,720 

1,540 

1,430 

 T 

 T 

 T 

 T 

B 

12,000 

12,000 

12,000 

12,000 

4,000 

6,000 

8,000 

10,000 

80 

80 

80 

80 

275 

275 

275 

275 

2,160 

1,720 

1,550 

1,430 

 T 

 T 

 T 

 T 

C 

6,000 

6,000 

6,000 

6,000 

4,000 

6,000 

8,000 

10,000 

146 

146 

146 

146 

267 

266 

270 

271 

4,250 

2,900 

3,020 

2,740 

1,340 

360 

 T 

 T 

D 

12,000 

12,000 

12,000 

12,000 

4,000 

6,000 

8,000 

10,000 

175 

175 

175 

175 

261 

260 

262 

262 

3,640 

2,560 

2,710 

2,410 

2,025 

1,320 

1,090 

800 

 * T denotes tensile strain sufficient to cause cracking. 

Series C and D cross sections contained 41 and 76 strands, respectively, and had a flange width 

of 1.38 m (54 inches). Consequently, the demands on the deck for the development of the 

compressive force were much higher than in series A and B. Flexural strength of the section was 

limited by the strain capacity of the deck concrete for all deck concrete strength levels. For all 

strengths of deck concrete, the deck concrete strains at maximum moment exceeded the strains at 

peak stress as shown in figure 17. For the sections with 28-MPa (4,000-psi) deck concrete, the 

strains exceeded the normally assumed limit of 3,000 millionths (0.003 strain). To maintain the 

deck strains below 3,000 millionths, a concrete deck strength of at least 41 MPa (6,000 psi) is 

needed. It should also be noted that with one exception, all of the cross sections in series C and 

D have reinforcement indices that permit the flexural design to be based on yielding of the steel. 

The exception is the 83/28-MPa (12,000/4,000-psi) combination of girder and deck strengths. 

For this section, the strain in the girder is close to the strain at peak stress for the 83-MPa 

(12,000-psi) girder concrete. This is a combination that should be avoided. Based on the 

analyses, it appears that there should be a limit on the difference between the girder concrete 

strengths and the deck concrete strength. However, the limited scope of this investigation does 

not permit the development of a rationale analysis. As an interim measure, it is proposed that the 

specified deck concrete strength should be at least 60 percent of the specified girder concrete 

strength at 28 days when the specified girder concrete strength exceeds 41 MPa (6,000 psi). 
50 

FLEXURAL STRENGTH 

The flexural strengths for each of the sections analyzed in task 2 are tabulated in tables 14 and 

15. The required strength and design strength were calculated using the computer program 

BRIDGE in task 1. The required strength was based on the following equation: 

(13) 

The design strength was calculated through an iteration process.(17) The number in the first 

column of nominal strengths was based on the design strength divided by a strength reduction 

factor of 0.9. The second column of nominal strengths were calculated using the AASHTO 

provisions.(16) The calculated strengths represent the maximum moments determined by the 

program BEAM BUSTER and are assumed to represent the real strengths of the sections. For all 

sections analyzed, the design strength exceeded the required strength and the calculated strength 

was greater than the nominal strength calculated by two different methods. It should also be 

noted that the nominal strengths provided an excellent prediction of the calculated strengths. 

Comparisons of required strengths with calculated strengths are shown in figures 19 through 22. 

M = 1.3 (Dead Load Moment + 1.67 (Live Load + Impact Moment)) 
Table 14. Calculated flexural strengths (SI units). 

Moments (kN·m) 

Series 

Girder 

Strength 

(MPa) 

Deck 

Strength 

(MPa) 

Span 

(m) Required 

Strength 

Design 

Strength* 

Nominal 

Strength* 

Nom

Streng

A 

41 41 41 41 

28 41 55 69 

24.4 24.4 24.4 24.4 

6,060 6,060 6,060 6,060 

6,100 6,100 6,100 6,100 

6,780 6,780 6,780 6,780 

6,646,706,726,74

B 

83 83 83 83 

28 41 55 69 

24.4 24.4 24.4 24.4 

6,060 6,060 6,060 6,060 

6,100 6,100 6,100 6,100 

6,780 6,780 6,780 6,780 

6,646,706,726,74

C 

41 41 41 41 

28 41 55 69 

44.5 44.5 44.5 44.5 

9,720 9,720 9,720 9,720 

11,730 12,120 12,370 12,550 

13,030 13,463 13,734 13,951 

12,9513,3313,5213,67

D 

83 83 83 83 

28 41 55 69 

53.3 53.3 53.3 53.3 

13,600 13,600 13,600 13,600 

16,970 17,490 17,960 18,330 

18,660 19,430 19,950 20,360 

18,2419,1619,7720,24

 * Calculated by the program BRIDGE.  ** Calculated per AASHTO. *** Calculated by the program BEAM BUSTER. 

51 
Table 15. Calculated flexural strengths (English units). 

Moments (ft-kip) 

Series 

Girder 

Strength 

(psi) 

Deck 

Strength 

(psi) 

Span 

(ft) Required 

Strength 

Design 

Strength* 

Nominal 

Strength* 

Nom

Streng

A 6,000 6,000 

6,000 6,000 

4,000 6,000 8,000 

10,000 

80 80 80 80 

4,470 4,470 4,470 4,470 

4,500 4,500 4,500 4,500 

5,000 5,000 5,000 5,000 

4,904,944,964,97

B 12,000 12,000 

12,000 12,000 

4,000 6,000 8,000 

10,000 

80 80 80 80 

4,470 4,470 4,470 4,470 

4,500 4,500 4,500 4,500 

5,000 5,000 5,000 5,000 

4,904,944,964,97

C 6,000 6,000 

6,000 6,000 

4,000 6,000 8,000 

10,000 

175 175 175 175 

7,170 7,170 7,170 7,170 

8,650 8,940 9,120 9,260 

9,610 9,930 

10,130 10,290 

9,559,839,97

10,08

D 12,000 12,000 

12,000 12,000 

4,000 6,000 8,000 

10,000 

175 175 175 175 

10,030 10,030 10,030 10,030 

12,520 12,900 13,250 13,520 

13,910 14,330 14,720 15,020 

13,4514,1314,5814,93

 * Calculated by the program BRIDGE.  ** Calculated per AASHTO. *** Calculated by the program BEAM BUSTER. 

52 
53 

TASK 2 CONCLUSIONS 

Based on the task 2 analyses, the following conclusions are made: 

• For span lengths of 24.4 m (80 ft) with lower amounts of prestressing strands, the use of 

high-strength concrete did not affect the flexural strengths. 

• At the maximum span lengths for each girder concrete strength, the use of high-strength 

concrete in the decks had a slight effect in increasing the design and nominal strengths. 

The use of high-strength concrete also increased the flexural ductility of the cross 

sections. 

• To ensure that the flexural strength is based on yielding of the reinforcement and to limit 

the strains in the deck, a minimum deck concrete strength of 41 MPa (6,000 psi) is 

recommended for span lengths in excess of 24.4 m (80 ft) when concrete girder strength 

exceeds 41 MPa (6,000 psi). Until further analyses can be performed, the specified deck 

concrete strength should be at least 60 percent of the specified girder concrete strength at 

28 days when the specified girder concrete strength exceeds 41 MPa (6,000 psi). 

• The applicability of the AASHTO specification for flexural design should be examined 

with respect to the use of higher-strength concretes and larger differential strengths 

between the deck and girder concretes.(16)

55 

CHAPTER 4. TASK 3: ANALYSES OF PRESTRESS LOSSES AND 

LONG-TERM DEFLECTIONS 

RESEARCH APPROACH 

Analyses to determine the effect of high-performance concrete on prestress losses and long-term 

deflections were performed using a computer program known as PBEAM.(29) The program 

PBEAM is capable of analyzing composite prestressed concrete structures of any cross sectional 

shape having one axis of symmetry. The program accounts for the effects of nonlinearity of 

stress-strain response of materials and their variations of strength, stiffness, creep, and shrinkage 

of concrete, and relaxation of steel with time. A step-by-step method is used in the timedependent analysis, and a tangent stiffness method is implemented for solving nonlinear 

response. 

Precast, prestressed bridge girders with composite cast-in-place decks are modeled using a 

discrete element method. Element deformations and forces are estimated by analyzing stressstrain relationships of a series of rectangular fibers distributed over the depth of a cross section. 

Strain in each fiber is assumed to be constant at the centroidal axis of the fiber, and strain 

distribution varies linearly through the depth of a section. For each time step, the equilibrium at 

each element is maintained by determining the time-dependent stress corresponding to the level 

of strain in each fiber. The stress multiplied by area is summed over all fibers and force 

equilibrium is checked. If necessary, the strain distribution is adjusted and the process is 

repeated until all forces balance. A more detailed description of the program PBEAM and its 

verification against experimental data are given in references 29 and 30. 

The following assumptions were utilized in the program PBEAM: 

• Girders are simply supported. 

• Calculations are based on a typical interior girder. 

• Release of the prestressing strands occurs at an age of one day in several increments. 

Dead load is added at each increment. 

• Concrete deck is cast in place and is cast when the girder is 83 days old. At age 90 days, 

the concrete deck acts compositely with the girder. Deck formwork is considered to be 

supported on the girder. 

• Strands are low relaxation Grade 270 with a 12.7 m (0.5 inches) diameter spaced at 

51-mm (2-inch) centers. Minimum cover to center of strands is 51 mm (2 inches). 

• Girder cross section is a BT-72. Material properties are varied according to the 

discussion in section 4.2. 

Analyses were performed for the following variables: 

• Girder concrete compressive strength: 41, 55, 69, and 83 MPa (6,000, 8,000, 10,000, and 

12,000 psi, respectively). 

• Deck concrete compressive strength: 28, 41, 55, and 69 MPa (4,000, 6,000, 8,000 and 

10,000 psi, respectively). 

• Span lengths: 24.4, 44.5, and 53.3 m (80, 146, and 175 ft, respectively). 
56 

The combination of variables are defined in tables 16 and 17. Cross sections of the girders are 

shown in figure 23. Series A through D represent a complete parametric study of girder concrete 

strength and deck concrete strength for constant cross section and span length. Series E is an 

investigation of span lengths for a constant concrete strength. Design of the cross sections for 

series A and E were based on the analyses performed in task 1. 

Table 16. Task 3 variables (SI units). 

Series 

Girder 

Strength 

(MPa) 

Deck 

Strength 

(MPa) 

Span 

(m) 

No. of 

Strands* 

A 

41 

41 

41 

41 

28 

41 

55 

69 

44.5 

44.5 

44.5 

44.5 

41 

41 

41 

41 

B 

55 

55 

55 

55 

28 

41 

55 

69 

44.5 

44.5 

44.5 

44.5 

41 

41 

41 

41 

C 

69 

69 

69 

69 

28 

41 

55 

69 

44.5 

44.5 

44.5 

44.5 

41 

41 

41 

41 

D 

83 

83 

83 

83 

28 

41 

55 

69 

44.5 

44.5 

44.5 

44.5 

41 

41 

41 

41 

E 

83 

83 

83 

55 

55 

55 

24.4 

44.5 

53.3 

20 

77 

77 

* For consistency between tasks, the odd number of strands calculated 

by the program BRIDGE in task 1 were retained in task 3. 
57 

Table 17. Task 3 variables (English units). 

Series 

Girder 

Strength 

(psi) 

Deck 

Strength 

(psi) 

Span 

(ft) 

No. of 

Strands* 

A 

6,000 

6,000 

6,000 

6,000 

4,000 

6,000 

8,000 

10,000 

146 

146 

146 

146 

41 

41 

41 

41 

B 

8,000 

8,000 

8,000 

8,000 

4,000 

6,000 

8,000 

10,000 

146 

146 

146 

146 

41 

41 

41 

41 

C 

10,000 

10,000 

10,000 

10,000 

4,000 

6,000 

8,000 

10,000 

146 

146 

146 

146 

41 

41 

41 

41 

D 

12,000 

12,000 

12,000 

12,000 

4,000 

6,000 

8,000 

10,000 

146 

146 

146 

146 

41 

41 

41 

41 

E 

12,000 

12,000 

12,000 

8,000 

8,000 

8,000 

80 

146 

175 

20 

77 

77 

 * For consistency between tasks, the odd number of strands calculated by 

the program BRIDGE in task 1 were retained in task 3. 

To satisfy design stress conditions at the ends of the girders, every strand within the width of the 

web was draped upwards at the ends. The drape started at a distance of 30 percent of the span 

from the end of the girders. The center 40 percent of the span length had the strands at maximum 

and constant eccentricity. 

MATERIAL PROPERTIES 

The computer program PBEAM allows for a variety of inputs for material properties and also 

contains default values. Because the properties of high-performance concrete may be different 

from those used as the basis for the default properties, a study was made to select the most 

appropriate material properties for analysis. This study involved selecting appropriate properties 

for modulus of elasticity, shrinkage, and creep, and their variation with time. 

Modulus of Elasticity 

In task 2, complete stress-strain curves for various strengths of concrete were established. The 

slope of the ascending portion of the stress-strain curve is the modulus of elasticity. The 

following equations were utilized for calculation of the modulus: 

For f'c of 28 and 41 MPa (4,000 and 6,000 psi, respectively): 
58 

 in SI units (14) 

 in English units(20) (1) 

For f'c of 55, 69, and 83 MPa (8,000, 10,000, and 12,000 psi): 

 in SI units (15) 

 in English units(19) (4) 

For the girder concrete, the variation of compressive strength with time was determined from the 

following equation: 

 (16) 

where 

(f'c)t = compressive strength at a concrete age of t days 

(f'c)28 = compressive strength at a concrete age of 28 days 

The above relationship was based on the recommendations of ACI 209 and corresponds to a 

compressive strength at 1 day equal to 75 percent of the compressive strength at 28 days.(31)

( ) 5 ' 1.

c 0.043 c c E = w f

( ) 5 ' 1.

c 33 c c E = w f

( ) ( )

0.325 2.5 '

c 0.0000339 c c E = w f

( ) ( )

0.325 2.5 '

c c c E = w f

( ) ( ) t

t

f

f

c

c t

0.346 0.988 28

'

'

+ =
59 

Figure 23 (part 1). Cross section of series A 

through D girders (BT-72) analyzed in 

task 3. All dimensions are in 

millimeters (inches). 

Figure 23 (part 2). Cross section of series E 

girder (BT-72), 24.4 m (80-ft) span, analyzed in 

task 3. All dimensions are in 

millimeters (inches). 

Figure 23 (part 3). Cross section of series E 

girder (BT-72), 44.5 m (146-ft) span, 

analyzed in task 3. All dimensions are in 

millimeters (inches). 

Figure 23 (part 4). Cross section of series E 

girder (BT-72), 53.3 m (175-ft) span, analyzed 

in task 3. All dimensions are in 

millimeters (inches). 
60 

For the deck concrete, the variation of compressive strength was assumed to be in accordance 

with ACI 209 as follows:(31)

 (17) 

Equation 17 reflects a slower strength gain for moist, cured concrete compared with equation 16 

which applies to rapid strength development. 

Consequently, for a specified 28-day compressive strength, the compressive strength at any other 

age may be calculated. Using this value of compressive strength, the corresponding modulus of 

elasticity for the concrete can be determined. In this manner, the variation of modulus of 

elasticity with time can be calculated. 

Shrinkage 

Most research has indicated that the final shrinkage of high-strength concretes is of the same 

order of magnitude as that for lower strength concretes.(1) Consequently, the values proposed by 

ACI 209 were utilized in the program PBEAM analysis. ACI 209 recommends that, in the 

absence of specific creep and shrinkage data for local aggregates and conditions, an average 

value of 780 millionths be utilized for the shrinkage of a 153- by 305-mm (6- by 12-inch) 

cylinder exposed to drying at 40 percent relative humidity.(31) This value was then corrected for 

the effects of girder size and relative humidity in accordance with the procedures of ACI 209. An 

average mean annual relative humidity of 70 percent was taken as representing a large portion of 

the United States. Consequently, a relative humidity correction factor of 0.7 was applied. A size 

correction factor of 0.837 was also applied as representing a volume-to-surface-area ratio of 3.0 

for a BT-72. These two correction factors resulted in a final shrinkage strain for the girder of 457 

millionths. The shrinkage strain of the girder concrete was assumed to vary with time according 

to the following equation:(31)

 (18) 

where 

(εsh)t = shrinkage at time t

(εsh)u = final shrinkage strain 

For the concrete in the deck, a relative humidity correction factor of 0.7 was applied along with a 

size correction for a 190-mm (7.5-inch) thick deck of 0.77, resulting in a final shrinkage of 420 

millionths. The deck shrinkage was assumed to vary with time according to the following 

equation:(31)

 (19) 

It is possible that, with the higher-strength concretes and the use of fly ash or silica fume to 

obtain the strengths, the concrete may take longer to dry out than the lower strength concretes. 

Consequently, the assumed variation of shrinkage with time may not truly reflect actual 

behavior. However, a lack of data for steam-cured, high-strength concretes precluded the 

determination of an alternative equation. 

( ) ( ) t

t

f

f

c

c t

4.00 0.85 28

'

'

+ =

( )

( ) t

t

sh u

sh t

+ = ε 55

ε

( )

( ) t

t

sh u

sh t

+ = ε 35

ε
61 

Creep of Girder Concrete 

Creep of concrete can be expressed in terms of creep coefficients or specific creep. The creep 

coefficient is the ratio of creep strain to the initial strain at loading. For most concretes, the 

values vary between 1.30 and 4.15. Specific creep is defined as creep strain per unit stress and 

varies between 15 and 220 millionths/MPa (0.1 and 1.5 millionths per psi). The relationship 

between creep coefficient and specific creep is as follows: 

Creep coefficient = specific creep × modulus of elasticity at age of loading 

The computer program PBEAM allows the input of creep as a creep coefficient. However, for 

purposes of selecting appropriate creep values for use in the analyses, the following discussion is 

based on specific creep. 

Specific creep data for 153- by 305-mm (6- by 12-inch) cylinders published by several authors 

are shown in figure 24. These data have been obtained for a variety of concrete constituent 

materials, cured under different conditions, loaded at different ages, and maintained under 

constant load for different lengths of time. To partially eliminate the variable associated with the 

length of time under load, the published data were corrected to final values based on variations 

of creep with time following the equations listed above. A plot of the same data including this 

correction factor is shown in figure 25. All of the data are for cylinders maintained at 50 percent 

relative humidity while under load. A comparison with the predicted values according to ACI 

209 for 50 percent relative humidity is also included in figure 25. This curve is very close to the 

best fit for all data. 

The solid symbols shown in figure 25 are for concrete specimens obtained by steam 

curing.(14,30,32) Since it is anticipated that high-strength concrete prestressed girders will either be 

produced by steam curing or will achieve relative high temperatures from heat of hydration, the 

effects of curing temperatures on the properties of concrete are important. Hanson indicated that 

the effect of atmospheric steam curing was to reduce the creep of concrete cylinders containing 

type I cement by 20–30 percent and that of concretes containing type III cements by 30–40 

percent below that of the same concretes moist cured for 6 days(32) It is also apparent from figure 

25 that the reduction in specific creep as compressive strength increases is more rapid with the 

steam-cured concretes than with the moist-cured concretes. Figure 25 shows a best-fit curve to 

the data for steam-cured concretes alone. This curve indicates a very rapid change in the specific 

creep as the concrete compressive strength increases. However, no data are available for 

concrete compressive strengths above 69 MPa (10,000 psi), so the validity of the extrapolation 

beyond 69 MPa (10,000 psi) is questionable. Consequently, in the PBEAM analyses, a variation 

of specific creep with concrete compressive strength was selected that lay between the ACI 209 

values and that for steam cured concrete alone. This line is labeled in figure 25 as PBEAM. 

Since most of the data in figure 25 represent concrete loaded at 28 days, this age was selected as 

the age for which the specific creep values would be selected. Values of specific creep and creep 

coefficient for 28-day age of loading at 50 percent relative humidity and a volume-to-surface 

ratio of 1.5 are listed in table 21. These data were then corrected using the procedures of ACI 

209 for a relative humidity of 70 percent, a volume-to-surface ratio of 3.0 corresponding to a 

BT-72, and a loading age of 1 day. The corrected calculated creep coefficients for each concrete 

strength are tabulated in table 18. These values were used in the PBEAM analyses. 
62 

0

20

40

60

80

100

120

140

160

0 20 40 60 80 100 120 140

Compressive Strength, MPa

Specific Creep, mill/MPa

Oesterle (30)

Hanson (32)

Bruce (14)

Burg (33)

Perenchio (34)

Wolsiefer (35)

Smadi (36)

Ghosh (37)

Luther (38)

1 MPa = 145 psi

Figure 24. Variation of specific creep with compressive strength as published. 
63 

0

20

40

60

80

100

120

140

160

0 20 40 60 80 100 120 140

Compressive Strength, MPa

Specific Creep, mill/MP

a

Oesterle (30)

Hanson (32)

Bruce (14)

Burg (33)

Perenchio (34)

Wolsiefer (35)

Smadi (36)

Ghosh (37)

Luther (38)

ACI 209 (30)

Steam Cured

PBEAM

1 MPa = 145 psi

Figure 25. Variation of ultimate specific creep with compressive strength. 
Table 18. Values of creep used in PBEAM. 

 Specific Creep Creep Coeffi

28-Day Loading Age = 28 Days 

Compressive 

Strength 

Unit 

Weight 

28-Day 

Modulus of

Elasticity RH = 50% V/S = 1.5 RH = 50% V/S = 1.5 R

V

MPa kg/m3 GPa millionths/MPa 

 41  55  69  83 

2,370 2,420 2,480 2,500 

31.7 35.9 39.1 44.3 

72.5 56.9 47.0 40.3 

2.30 2.04 1.93 1.79 

 psi lb/ft3 106 psi millionths/psi 

6,000 8,000 

10,000 12,000 

 148  151  155  156 

 4.60  5.20  5.97  6.43 

0.500 0.392 0.324 0.278 

2.30 2.04 1.93 1.79 

64
65 

The variation of creep with time was assumed to be in accordance with the following equation 

by ACI 209:

 (20)

where 

υt = creep at time t 

υu = final value of creep 

t = number of days under load 

The effect of age of loading was also assumed to be in accordance with ACI 209 as follows: 

 (21)

where 

γla = correction factor for age of loading 

t

la = age of concrete at loading 

The resulting relationship between specific creep and age for different strength concretes and 

two ages of loading are shown in figure 26. 

Creep of Deck Concrete 

Since the equations utilized by ACI for creep coefficient represented a good fit for the data 

shown in figure 25, it was decided to use the ACI 209 values for the creep properties of the 

concrete used in the deck. The calculated creep coefficient for a deck with a thickness of 190 m 

(7.5 inches) was 1.44. 

Steel Relaxation 

Since steel relaxation was not a primary parameter in the evaluation, the default values contained 

within PBEAM were utilized. These are based on the PCI recommendations.(39) 

t u t

t

υ υ 0.60

0.60

10 + =

( ) 0.094 1.3 −

la = la γ t
66 

0

10

20

30

40

50

60

70

80

0 30 60 90 120 150 180 210 240 270 300 330 360

Age, days

Specific Creep, mill/MPa

41 MPa, load day 1

55 MPa, load day 1

69 MPa, load day 1

83 MPa, load day 1

41 MPa, load day 90

55 MPa, load day 90

69 MPa, load day 90

83 MPa, load day 90

1 MPa = 145 psi

Figure 26. Variation of specific creep with age. 
67 

PRESTRESS LOSSES 

The variation of prestressing strand stress with time for the bottom layer of strands for two 

BT-72 girders with concrete compressive strengths of 41 and 83 MPa (6,000 and 12,000 psi, 

respectively) and a span of 44.5 m (146 ft) is shown in figure 27. Each curve consists of four 

stages. The first stage comprises the initial elastic shortening caused by release of the 

prestressing. In PBEAM, this is accomplished by applying the prestressing force in a series of 

stages corresponding to the addition of the girder dead load. The force is applied in increments to 

prevent cracking of the concrete. The second stage of the curves consists of prestress losses 

between the time of release and the time when the deck is cast on the girder. The third stage is 

the elastic change in stress caused by application of the dead load of the deck concrete to the 

girder cross section. The fourth and final stage of the curve consists of losses in strand stresses as 

the composite girder is loaded by the dead load of the deck and girder. For this analysis, no 

additional dead load was assumed after the deck was added. The general shape of the curve was 

the same for all span lengths and concrete strengths analyzed. 

At each level of girder concrete compressive strength, the variation of deck concrete 

compressive strength did not have any effect on prestress losses. This occurs because the deck 

does not become an effective part of the composite section until the fourth stage of each curve. 

At the beginning of the fourth stage, the compressive stress in the deck is zero. The only increase 

in compressive stress occurs as the concrete girder shortens and tries to shorten the deck with a 

corresponding force transferred into the deck. However, at the same time, the deck is also 

shrinking and this shrinkage is of the same order of magnitude as the shortening of the top flange 

of the girder. Consequently, there is very little transfer of force between the girder and the deck, 

and the deck does not have a significant impact on the prestress losses. It should be noted that all 

the analyses in this investigation were based on a composite section becoming effective at 90 

days. It is possible that the effect of the deck concrete compressive strength may be greater for 

earlier ages of loading. 

The variation of strand stress with time for the three girders containing 83-MPa (12,000-psi) 

concrete compressive strength and varying span lengths is shown in figure 28. It can be seen that 

the prestress losses varied with span length, the 44.5-m (146-ft) length having the largest total 

loss. This is consistent with the magnitude of stress at the level of the bottom layer of strands 

following release. For the girder with the span length of 44.5 m (146 ft), the concrete 

compressive stress at release was the highest of the three girders. Consequently, the elastic 

shortening and the creep shortening were also higher. 
68 

1000

1050

1100

1150

1200

1250

1300

1350

0 90 180 270 360 450 540 630 720 810 900 990 1080

Time, days

Strand Stress, MPa

41 MPa

83 MPa

1 MPa = 145 psi

Figure 27. Prestressing strand stress versus time for varying girder concrete strength, 

28-MPa deck strength, and 44.5-m span. 
69 

1000

1050

1100

1150

1200

1250

1300

1350

0 90 180 270 360 450 540 630 720 810 900 990 1080

Time, days

Strand Stress, MPa

24.4 m span

44.5 m span

53.3 m span

1 m = 3.281 ft

1 MPa = 145 psi

Figure 28. Prestressing strand stress versus time for 83-MPa girder concrete strength, 

55-MPa deck strength, and varying spans. 
70 

The prestress losses determined for each level of girder concrete compressive strength are 

tabulated in tables 19 and 20. The tabulated losses are the calculated losses for the lower layer of 

prestressing strand in the girder cross section. The total losses are those determined from the 

program PBEAM at an age of 25 years starting with an initial stress of 1.30 GPa (189,000 psi) in 

the prestressing strand. The shrinkage stresses were calculated from the assumed shrinkage strain 

based on a modulus of elasticity of the prestressing strand of 193 GPa (28,000,000 psi). The 

elastic shortening at release corresponds to the prestress loss determined from the program 

PBEAM during application of the prestressing force. Because of the manner in which the 

analyses are performed, a small amount of relaxation is included in these stresses. The creep and 

relaxation losses represent the net difference between the total losses and the shrinkage and 

elastic losses. Because of the manner in which the program PBEAM calculates the interactive 

stresses from creep and relaxation, it is not possible to separate the two effects in the analysis. 

Consequently, they are listed together in tables 19 and 20. From the analyses, it can be seen that 

the direct substitution of a higher-strength concrete for one of lower strength reduces the 

prestress losses, part of the reduction being caused by the lower elastic losses and part by the 

lower creep losses. It may also be concluded from tables 19 and 20 that the magnitude of the 

total prestress losses will not be greater through the use of high-strength concrete in the girders 

and are likely to be less. 

Prestress losses calculated according to AASHTO standard specifications are also shown in 

tables 19 and 20 for comparison with the losses calculated according to PBEAM.(16) In the 

current specifications, the creep losses are calculated based on the concrete stresses at the center 

of gravity of the prestressing steel. For purposes of comparison, the AASHTO losses shown in 

tables 19 and 20 were calculated using the procedure detailed in AASHTO specifications, but the 

stresses were calculated at the level of the bottom layer of prestressing steel. For the shorter span 

lengths, the AASHTO calculations show reasonable agreement with the PBEAM calculations. 

However, for the higher-strength concretes at the longer span lengths considerable deviation 

exists. For all calculations, the elastic losses compare favorably. However, AASHTO 

underestimates the losses caused by shrinkage and overestimates considerably the losses caused 

by creep. These data indicate that a revision of the AASHTO specification to take into account 

the different creep properties of the high-strength concretes is needed. 
71 

Table 19. Comparison of prestress losses (SI units). 

Losses (MPa) Girder 

Strength 

(MPa) 

Span 

(m) Elastic Shrinkage Creep Relaxation Total 

 PBEAM 

41 44.5 104 88 119 311 

55 44.5 92 88 99 279 

69 44.5 81 88 85 254 

83 44.5 75 88 76 239 

83 24.4 54 88 60 202 

83 44.5 130 88 116 334 

83 53.3 106 88 93 287 

 AASHTO 

41 44.5 98 45 126 16 285 

55 44.5 83 45 128 17 173 

69 44.5 72 45 130 19 266 

83 44.5 66 45 131 19 261 

83 24.4 45 45 91 23 204 

83 44.5 112 45 212 10 379 

83 33.3 92 45 181 14 332 
72 

Table 20. Comparison of prestress losses (English units). 

Girder Losses (ksi) 

Strength 

(psi) 

Span 

(ft) Elastic Shrinkage Creep Relaxation Total 

 PBEAM 

6,000 146 15.1 12.8 17.2 45.1 

8,000 146 13.4 12.8 14.4 40.6 

10,000 146 11.8 12.8 12.4 37.0 

12,000 146 10.9 12.8 11.0 34.7 

12,000 80 7.8 12.8 8.7 29.3 

12,000 146 18.8 12.8 16.8 48.4 

12,000 175 15.4 12.8 13.5 41.7 

 AASHTO 

 6,000 146 14.2 6.5 18.2 2.3 41.2 

 8,000 146 12.1 6.5 18.6 2.5 39.7 

10,000 146 10.5 6.5 18.8 2.7 38.5 

12,000 146 9.6 6.5 19.0 2.8 37.9 

12,000 80 6.5 6.5 13.2 3.4 29.6 

12,000 146 16.2 6.5 30.7 1.5 54.9 

12,000 175 13.4 6.5 26.2 2.0 48.1 
73 

LONG-TERM DEFLECTIONS 

The variation of midspan deflection with time for four girders of varying girder concrete 

compressive strength and at a constant deck concrete strength of 28 MPa (4,000 psi) is shown in 

figure 29. These curves consist of four stages. The initial stage corresponds to an upward 

deflection at release of prestressing and includes the effects of prestressing and dead load of the 

girder. The second stage consists of continued upward deflection as a result of creep in the 

concrete. The third stage consists of a downward deflection caused by the dead load of the deck 

at the time the concrete deck is placed at 83 days. The fourth stage consists of further downward 

deflection as a result of creep and shrinkage followed by a period in which the deflections 

essentially level off. By age 1,000 days, the maximum net deflection was +6 mm (0.25 inch). 

These analyses indicate that very little change occurs after 180 days, consistent with results 

obtained by Bruce.(14)

The effect of deck concrete compressive strength on midspan deflection is shown in figure 30. 

This figure shows the concrete compressive strength of the deck had very little effect on the 

midspan deflections (which was true for all girder strength levels). 

The variation of midspan deflection with time for the 83-MPa (12,000 psi) concrete girders with 

varying span lengths is shown in figure 31. The deflections of the 24.4-m (80-ft) girder are 

relatively small compared with the deflections of the girder for other span lengths. This results 

partly from the shorter span length but also from the relatively low number of strands (only 20). 

The initial camber of the 44.5-m (146-ft) girder is similar to the camber of the girders shown in 

figure 29 for the same span length. A slight difference in camber occurs because of the different 

number of strands: 77 for the girder in figure 31 compared with 41 for the girders in figure 29. 

The downward deflection caused by casting the deck and the subsequent creep and shrinkage are 

larger for the girder shown in figure 31 compared with that in figure 29 because of the larger 

girder spacing. The net result for the girder shown in figure 31 is a downward deflection of 

approximately 20 mm (0.8 inch).
74 

-10

0

10

20

30

40

50

60

70

80

90

100

0 90 180 270 360 450 540 630 720 810 900 990 1080

Time, days

Midspan Deflection, mm

41 MPa

55 MPa

69 MPa

83 MPa

1 MPa = 145 psi

1 mm = 0.0394 in

Figure 29. Midspan deflection versus time for varying girder concrete strengths, 

28-MPa deck strength, and 44.5-m span. 
75 

The 53.3-m (175-ft) span girder shows a deflection pattern after release that is different from the 

other girders. For a short time, the girder creeps upwards but it then reverses direction. 

Following release of the prestress, the stress distribution across the depth of the girder is nearly 

constant. This is different from the other girders where the compressive stress in the bottom 

flange is always greater than the stress in the top flange. Following a small amount of prestress 

loss, the compressive stress in the top flange exceeds the stress in the bottom flange and the 

girder begins to creep downwards. A large deflection occurs when the deck is cast because of the 

long span. The final result is a downward deflection of approximately 90 mm (3.5 inches). This 

deflection is small compared with the span length (1 in 600) and could be compensated for by 

cambering the deck formwork. However, it indicates that there may be deflection considerations 

that could limit the span length for which high-strength concrete girders can be used. 

TASK 3 CONCLUSIONS 

Based on the task 3 analyses, the following conclusions are made: 

• The use of high-strength concrete in the decks did not change the magnitude of the 

prestress losses. 

• Prestress losses in high-strength concrete girders will generally be less than the losses in 

lower strength concrete girders. 

• The current AASHTO procedure for calculations of prestress losses needs to be modified 

to account for the properties of high-strength concrete. 

• The use of high-strength concrete in the decks did not affect the magnitude of the longterm deflections. 

• The use of high-strength concrete in girders in place of lower strength concrete will result 

in less initial camber and similar long-term deflections for the same span lengths. 

• There may be deflection requirements that limit the span lengths for which high-strength 

concrete girders can be used.
76 

-10

0

10

20

30

40

50

60

70

80

90

100

0 90 180 270 360 450 540 630 720 810 900 990 1080

Time, days

Midspan Deflection, mm

28 MPa

69 MPa

1 MPa = 145 psi

1 mm = 0.0394 in

Figure 30. Midspan deflection versus time for 41-MPa girder concrete strength, 

varying deck concrete strengths, and 44.5-m span. 
77 

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 90 180 270 360 450 540 630 720 810 900 990 1080

Time, days

Midspan Deflection, mm

24.4 m span

44.5 m span

53.3 m span

1 m = 3.281 ft

1 mm = 0.0394 in

Figure 31. Midspan deflection versus time for 83-MPa girder concrete strength, 

55-MPa deck strength, and varying spans. 

79 

CHAPTER 5. CONCLUSIONS AND RECOMMENDATIONS 

CONCLUSIONS 

Based on the analyses described in this report, the following conclusions are made. 

Cost Analyses 

• The use of high-strength concrete in bridge decks will not result in a reduction of deck 

thickness or in the amount of transverse reinforcement. Therefore, no corresponding 

savings will occur. 

• The use of high-strength concrete in bridge decks allows for a slight increase in 

maximum span lengths of bulb-tee girders. 

• An increase of 25 percent in the in-place cost of high-strength deck concrete will only 

increase the overall superstructure cost by 5 to 10 percent. 

• The use of high-strength concrete in bridge decks will result in less live-load deflection. 

Flexural Strength and Ductility 

• The use of high-strength concrete in bridge decks did not affect flexural strengths of the 

shorter span girders. At the maximum span lengths for each girder concrete strength, the 

high-strength concrete in the decks had a slight effect in increasing the flexural strength 

and ductility of the section. 

• A minimum specified deck concrete strength of 41 MPa (6,000 psi) should be used for 

span lengths in excess of 24.4 m (80 ft) when girder concrete compressive strength 

exceeds 41 MPa (6,000 psi). Until further analyses can be performed, the specified deck 

concrete strength should be at least 60 percent of the specified girder concrete strength at 

28 days when the specified girder concrete strength exceeds 41 MPa (6,000 psi). 

• The applicability of the AASHTO specifications for flexural strength design with highstrength concrete needs to be evaluated. 

Prestress Losses and Long-Term Deflections 

 

• The use of high-strength concrete in the decks did not affect the magnitude of the 

prestress losses or long-term deflections. 

• Prestress losses in high-strength concrete girders will generally be less than the losses in 

lower strength concrete girders. 

• The current AASHTO procedure for calculation of prestress losses needs to be modified 

to account for the properties of high-strength concrete. 

• The use of high-strength concrete in girders in place of lower strength concrete will result 

in less initial camber and similar long-term deflections for the same span lengths. 

• Deflection requirements may limit the span lengths for which high-strength concrete 

girders with high-strength concrete decks can be used. 
80 

RECOMMENDATIONS 

The Federal Highway Administration should continue to pursue the use of high-performance 

concrete in bridge decks. The impact of the increased initial costs is likely to be small compared 

to the long-term benefits. In addition to specifying durability requirements for the deck concrete, 

a minimum compressive strength of 41 MPa (6,000 psi) should be specified when the girder 

concrete compressive strength at 28 days is specified to be in excess of 41 MPa (6,000 psi) and 

span length exceeds 24.4 m (80 ft). 

The industry should continue to pursue the usage of concrete with compressive strengths up to 

69 MPa (10,000 psi) for prestressed concrete girders. The present research has not identified any 

limitations that would prevent existing design procedures from being utilized for concrete 

compressive strengths up to 69 MPa (10,000 psi). Special attention should be given to the 

deflections of long-span girders. 

Additional work should be undertaken to evaluate the applicability of current design procedures 

for bridges constructed with high-performance concrete. This is particularly important for the 

longer span lengths where the amount of prestressing will be large and the girders will be spaced 

close together so that the effective width of the top flange is limited. A rationale should be 

developed that addresses the effects of the difference in compressive strength between the deck 

and girder concretes. Additional work is needed to address long-term deflections of long-span 

girders. 

In a previous report, it was concluded that the application of high-strength concrete in bridge 

girders is limited by the amount of prestressing force that can be applied to the cross section.(6) A 

reduction in the assumed prestress losses will allow a higher force to be used in design for the 

same amount of prestressing steel. There is, however, a lack of data about the creep and 

shrinkage of high-strength concrete as used in prestressed girders. As part of the ongoing 

showcase projects, FHWA should encourage the monitoring of prestress losses and measurement 

of creep and shrinkage properties of the concretes. 
81 

ACKNOWLEDGMENTS 

The authors would like to express their appreciation to the following individuals and 

organizations who provided information relative to this project: 

W. Vincent Campbell, Bayshore Concrete Products Corporation 

Reid W. Castrodale, Portland Cement Association 

Z. T. George, Texas Concrete Company 

Howard W. Knapp, Rocky Mountain Prestress, Inc. 

David Pellizzari, Alfred Benesch & Company 

Habib Tabatabai, Construction Technology Laboratories, Inc. 

Max J. Williams, Gulf Coast Pre-Stress, Inc. 

83 

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Recycled

Recyclable HRDI-06/10-06(750)E