TECHBRIEF

Research, Development, and 

Technology

Turner-Fairbank Highway 

Research Center

6300 Georgetown Pike

McLean, VA 22101-2296

www.fhwa.dot.gov/research

Development of a Family

of Ultra-High Performance

Concrete Pi-Girders

FHWA Publication No.: FHWA-HRT-14-028 

NTIS Accession No. of the report covered in this TechBrief: 

PB2014-100626 

FHWA Contact: Ben Graybeal, HRDI-40, 

(202) 493-3122, benjamin.graybeal@dot.gov.

Objective

Ultra-high performance concrete (UHPC) is an advanced 

cementitious composite material, which tends to exhibit 

superior properties such as exceptional durability, increased 

strength, and long-term stability. (See references 1–4.) The 

use of existing structural configurations for materials with 

advanced properties results in inefficient designs and less 

cost-effective solutions. Therefore, the purpose of this research 

is to develop a series of optimized sections of UHPC pi-girders to 

effectively utilize the superior mechanical properties of UHPC 

over longer span lengths through finite element analysis (FEA).

Introduction

The Federal Highway Administration (FHWA) at the TurnerFairbank Highway Research Center (TFHRC) has executed a 

research program developing a series of structurally optimized

bridge girders that engage the superior mechanical properties 

of UHPC. Four new, simple span cross-sections were developed

based on the pi-girder concept. The research was performed 

using a calibrated finite element model. The cross-sectional 

parameters that were varied include girder depth, the bulb 

width and height, the web thickness, and the strand layout in 

the bulb. The analysis evaluated the local transverse bending 

capacity of the deck, the global flexural and shear capacity 

of the girder, and the live load deflection of the three-girder 

system. The results indicated that the new cross-sections 

have enough capacity to accommodate span lengths up to 

135 ft (41.1 m). A design chart was developed to facilitate 

preliminary bridge design.
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Calibration of Finite Element 

Model

FEA was used to perform parameter analysis 

and optimize the cross-section because of its 

advantages of being efficient and inexpensive. 

However, the model used in FEA has to be 

verified against experimental results before it 

can be expanded for parametric study. Structural 

tests on a second-generation pi-girder were conducted in the laboratory. A finite element (FE) 

model based on a concrete damage plasticity 

model was built and calibrated based on the 

experimental results.(5,6) The results indicated 

that the FE model can effectively capture the 

behavior of the tested pi-girders with reasonable accuracy. This makes it possible to conduct 

parameter analysis and section optimization 

using the calibrated FE model. 

Deck Thickness

Due to the enhanced mechanical properties of 

UHPC, the deck thickness tends to be reduced 

as compared to conventional concrete bridge 

decks. The thinner deck must be assessed for 

both local and global performance. In particular, 

large wheel loads may induce large stresses 

in the deck, with tensile bending stresses 

perpendicular to the length of the member. 

Different deck thicknesses were investigated, 

along with the influence of diaphragms. A 

single girder model with short span (15 ft (4.6 m)

in this case) was used to suppress global flexure 

and shear failure. Two wheels were placed 

adjacent to each other at the center of the 

deck, creating a 10-inch (0.254-m)-long by

40-inch (1.016-m)-wide area of uniform vertical 

downward pressure. Diaphragms were applied 

at both ends, with three diaphragm types being 

investigated. Table 1 summarizes the maximum 

wheel load when the principal tensile strain 

in the UHPC reached the predefined limiting 

value of 3,000 . The load ratio in the table is 

defined as the ratio between the maximum 

applied load that caused the strain to be reached 

and the wheel load corresponding to Strength I 

limit state in American Association of State 

Highway and Transportation Officials. (AASHTO) 

load and resistance factor design (LRFD).(7)

Global Flexure and Shear Analysis 

at Maximum Possible Span

To facilitate preliminary bridge design, it is 

desirable to develop different cross-sections 

for different span lengths. Across the family of 

new cross-sections, the slope of certain surfaces and fillet radii were unchanged in order 

to facilitate the common use of formwork. The 

increment for girder height was chosen to be 

4 inches (102 mm), and the increment in the bulb 

size (height and width) was 2 inches (51 mm). 

A single girder model was used to investigate 

the relationship between cross-section 

parameters and the span length. The wheel 

load was applied above the web to suppress 

artifacts from transverse bending failure. The 

magnitude of the load corresponds to the 

standard AASHTO LRFD Strength I wheel load. 

In the investigation of flexure capacity, the 

design truck was simulated by applying the 

entire load of the design truck on the wheel 

patch at midspan, which is unrealistic but 

conservative. In the analysis of global shear 

behavior, the load was applied at a distance 

of three times the girder depth away from the 

support point. Through an iterative process, the 

four cross-sections shown in figure 1 through 

figure 4 were developed for different spans. 

More detailed results are summarized in 

table 2. In the table, the strand layout was 

named by the number of strands in each row 

starting from the bottom.
3

Deck

Thickness

(inch)

Load Ratio Wheel Pressure (psi)

Stiff 

Diaphragm

Regular

Diaphragm

Soft

Diaphragm

Stiff

Diaphragm

Regular

Diaphragm

Soft

Diaphragm

4.5 5.228 4.456 2.251 418 356 180

4.0 4.300 3.840 1.748 344 307 140

3.5 3.428 3.204 1.222 274 256 98

Table 1. Maximum load ratio and equivalent wheel pressure when the strength limit state is reached.

1.0 inch = 25.4 mm

1,000 psi = 6.89 MPa

Figure 1. Strand layout of 35-inch (889-mm)-deep section for 80-ft (24.4-m)-span.

Figure 2. Strand layout of 39-inch (991-mm)-deep section for 95-ft (29-m)-span.
4

Figure 4. Strand layout of 47-inch (1,193.8-mm)-deep section for 135-ft (41.1-m)-span.

Figure 3. Strand layout of 43-inch (1,092.2-mm)-deep section for 105-ft (32.0-m)-span.
5

In practice, a bridge span may be shorter than 

the maximum allowable span for a particular cross-section. To facilitate the use of these 

research results, shorter spans were also investigated for each cross-section. To achieve this, 

a parametric analysis was conducted to find 

the maximum span for cross-sections with 

the same depth but different strand layouts. 

The shear capacity was not checked in this 

portion of the analysis, as the shear load was 

basically unchanged. The results of using crosssections with fewer strands on shorter spans 

are summarized in table 3. Combining results 

from previous sections, figure 5 shows a 

graphic representation of the applicable span 

range for each girder depth. Table 4 summarizes 

the properties and applicable span range for 

each proposed cross-section.

Section ID Section I Section II Section III Section IV

Max. Span

(ft (m))

80

(24.4)

95

(29.0)

105

(32.0)

135

(41.1)

Girder depth

(inch (mm))

35

(889)

39

(991)

43

(1,092)

47

(1,194)

Deck Width

(inch (mm))

100

(2,540)

100

(2,540)

104

(2,642)

104

(2,642)

Web Thickness

(inch (mm))

3.37

(85.6)

3.33

(84.5)

5.27

(133.8)

5.23

(132.8)

Bulb Width

(inch (mm))

12.03

(305.6)

11.90

(302.3)

13.77

(349.8)

13.63

(346.2)

Bulb Height

(inch (mm))

7.25

(184.2)

9.25

(235.0)

9.16

(232.7)

11.25

(285.8)

Strand Layout 5-5-5-1 5-5-5-4 6-6-5-3 6-6-6-6-4

Flexure: Max Tensile 

Strain at Midspan () 2,826 2,531 2,520 2,694

Flexure: Max Stress in

Strands (ksi (MPa))

251

(1,730)

247

(1,703)

248

(1,710)

250

(1,724)

Shear: Max Tensile 

Strain in the Web () 457 291 159 189

Table 2. Proposed cross-sections for different span length.

Section ID Section I Section II Section III Section IV

Span

(ft (m))

70

(21.3)

75

(22.9)

80

(24.4)

100

(30.5)

Strand 

Layout 5-5-3 5-5-2 6-6-3 6-6-3

Max Flexural Strain 

at Midspan () 2,301 2,326 2,273 2,285

Max Stress in 

Strands (ksi (MPa))

244.0

(1,862)

244.1

(1,863)

243.8

(1,681)

243.7

(1,680)

Table 3. Modified cross-sections for application on smaller span length.
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Deflection Analysis

In addition to the strength-limit state, AASHTO 

LRFD also contains language regarding the 

flexibility of the structure under live load. 

It recommends that deflection divided by span 

not exceed 0.125. The deflection should be 

taken as the larger of the deflection due to 

design truck alone or due to 25 percent of 

the design truck together with the design 

lane load. Since deflection is primarily driven 

by span length, the deflection check was 

conducted only for the maximum span for each 

cross-section. In this section, a three-girder 

bridge model was used. The deck widths of the 

developed cross-sections are 100 inches (2.54 m) 

or 104 inches (2.64 m). A three-girder system 

is enough to accommodate two traffic lanes. 

This configuration is considered to be conservative compared to other combinations 

of girder numbers and lane numbers. The lane 

load and wheel load were biased toward the 

exterior girder on one side of the bridge. 

This load pattern creates maximum possible 

deflection. Trial simulation indicates that the 

deflection due to truck load is always greater 

than the deflection due to 25-percent truck 

load plus design lane load. Therefore, only 

the deflection under truck load was checked in 

this section. The results are tabulated in table 4, 

which shows that all the cross-sections meet 

the deflection requirements.

Figure 5. Summary of developed cross-sections.

1 inch = 25.4 mm

1 ft = 0.3048 m
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Section ID Section I Section II Section III Section IV

Girder Depth (inch)

Girder Depth (mm)

35

889

39

991

43

1,092

47

1,194

Area (inch2)

Area (x 104 mm2)

877

56.6

935

60.3

1,126

72.7

1,200

77.4

Moment of Inertia (x 109 inch4)

Moment of Inertia (x 1014 mm4)

1.50

6.24

1.84

7.66

1.94

8.07

2.38

9.90

Weight (lb/ft)

Weight (kN/m)

944

13.77

1,006

14.69

1,212

17.69

1,291

18.85

Span Range (ft)

Span Range (m)

70~80

21.3~24.4

75~95

22.9~29.0

80~105

24.4~32.0

100~135

30.5~41.4

Table 4. Section properties and applicable span range for proposed sections.

Section ID Section I Section II Section III Section IV

Span (ft (m)) 80 (24.4) 95 (29.0) 105 (32.0) 135 (41.1)

Midspan Deflection

(inch (mm)) 1.13 (28.7) 1.35 (34.3) 1.51 (38.4) 1.98 (50.3)

Deflection/Span 

(percent) 0.118 0.118 0.120 0.122

Table 5. Deflection under truck loads for refined cross-sections.

Concluding Remarks

This study conducted a parametric analysis to 

develop optimized cross-sections using a finite 

element model calibrated from experimental 

results. The parameters that were considered in 

the optimization include deck thickness, girder 

height, web thickness, bulb size, and strand 

layouts. The proposed sections were designed 

to resist loads in excess of those required by 

the AASHTO LRFD Bridge Design Specifications 

while meeting the live load deflection recommendations. Even though the deck thickness 

analysis demonstrated that 3.5-inch (89-mm) 

deck is sufficient in terms of strength, a deck 

thickness of 4 inches (102 mm) is recommended, 

considering construction tolerances and other 

uncertainties. A family of UHPC pi-girders was 

developed for spans ranging up to 135 ft (41.1 m) 

and loaded under simply supported boundary 

conditions. Girders with depths of 47 inches 

(1,194 mm) can be used on spans of 135 ft (41.1 m) 

or less. Those with 43 inches (1,092 mm), 

39 inches (991 mm), and 35 inches (889 mm) 

can be applied for spans up to 105 ft (32.0 m), 

95 ft (29.0 m), and 80 ft (24.4 m), respectively.
8

Researchers—This study was led by Ben Graybeal at FHWA’s Turner-Fairbank Highway Research Center.

It was conducted by Gang Zhang of PSI, Inc. through laboratory support contract DTFH61-10-D-00017.

For additional information, contact Ben Graybeal at (202) 493-3122 or in the FHWA Office of 

Infrastructure Research and Development located at 6300 Georgetown Pike, McLean, VA 22101-2296.

Distribution—The unpublished report covered in this TechBrief is being distributed through the National 

Technical Information Service at www.ntis.gov.

Availability—This TechBrief may be obtained from the FHWA Product Distribution Center by email to 

report.center@dot.gov, fax to (814) 239-2156, phone to (814) 239-1160, or online at http://www.fhwa.dot.

gov/research.

Key Words—Ultra-high performance concrete, UHPC, finite element analysis, pi-girder, structural 

optimization.

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. The U.S. Government does not endorse 

products or manufacturers. Trademarks or manufacturers’ names appear in this TechBrief only 

because they are considered essential to the objective of the document.

Quality Assurance Statement—The Federal Highway Administration 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 

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ensure continuous quality improvement.

JANUARY 2014 FHWA-HRT-14-028

HRDI-40/1-14(250)E

References

1. Graybeal, B., Ultra-High Performance 

Concrete, Report No. FHWA-HRT-11-038, 

Federal Highway Administration, U.S. 

Department of Transportation, McLean, VA, 

March 2011.

2. Graybeal, B., Material Property Characterization of Ultra-High Performance Concrete, 

Report No. FHWA-HRT-06-103, Federal 

Highway Administration, U.S. Department of 

Transportation, McLean, VA, August 2006.

3. Graybeal, B., Structural Behavior of Ultra-High 

Performance Concrete Prestressed I-Girders, 

Report No. FHWA-HRT-06-115, Federal 

Highway Administration, U.S. Department of 

Transportation, McLean, VA, August 2006.

4. Graybeal, B., Structural Behavior of a 2nd 

Generation UHPC Pi-Girder, Report No. 

FHWA-HRT-09-069, Federal Highway 

Administration, U.S. Department of 

Transportation, McLean, VA, 2009.

5. Chen, L., and Graybeal, B., “Modeling 

Structural Performance of Ultra-High 

Performance Concrete I-Girders,” ASCE 

Journal of Bridge Engineering, 17, No. 5, 

September–October 2012, pp. 754–764.

6. Chen, L., and Graybeal, B., “Modeling 

Structural Performance of 2nd Generation 

Ultra-High Performance Concrete Pi-Girders,” 

ASCE Journal of Bridge Engineering, 17,

No. 4, July–August 2012, pp. 634–643.

7. AASHTO, “AASHTO LRFD Bridge Design 

Specifications, Customary U.S. Units,” 

American Association of State Highway and 

Transportation Officials—6th Edition, 2012.