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Publication Number: FHWA-HRT-06-106
Date: September 2009

Design and Evaluation of Jointed Plain Concrete Pavement With Fiber Reinforced Polymer Dowels

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GENERAL CONCLUSIONS FROM THIS RESEARCH

  1. In this research, FRP dowels were found to be good alternatives to traditional steel dowels for transferring joint loads in JPCP pavements. Joints with FRP dowels provided adequate LTE, exceeding the values recommended by AASHTO (75 percent) and ACPA (60 percent) in both laboratory and field tests.
  2. FRP dowel-concrete interfaces in slabs number 1 and 4 were found to be in excellent condition after 5 million HS25 load cycles with no visible damage, microcracks, or separation between FRP dowels and surrounding concrete (refer to figure 36 and figure 44).
  3. The stiffness match between FRP dowels and concrete led to comparable FRP dowel flexing under joint loads, leading to shorter FRP dowel length. The required length of FRP dowels with 3.81-cm (1.5-inch) diameter was 64.7 percent of that for steel dowels with the same diameter. The required length of FRP dowels with a 2.54-cm (1.0-inch) diameter was 69.23 percent of that for steel dowels with the same diameter.
  4. Under the static loading test, slabs with smaller-diameter FRP dowels and smaller spacing provided lower RD than FRP dowels with larger diameter and spacing. During fatigue load cycles up to 5 million, RD from slab number 1 with the smaller diameter and spacing of FRP dowels appeared to increase (0.3256 to 2.0396 cm (0.0128 to 0.0803 inches) from 2 to 5 million cycles with a joint width of 1.016 cm (0.4 inches)), whereas RD from slab number 4 with a larger diameter and spacing of FRP dowels appeared to decrease 32 percent (0.0635 to 0.0432 cm (0.025 to 0.017 inches) from 2 to 5 million cycles with a joint width of 0.0635 cm (0.25 inches).
  5. The LTE from slabs with FRP dowels of smaller diameter and spacing (2.54 cm (1 inch) and 15.24 cm (6 inches)) was found to be sufficient (71.57 percent, when an increased joint width of 1.016 cm (0.4 inch) and higher loading of 1.5 × HS25 were considered) after 5 million load cycles as per AASHTO (70 percent of LTE) and ACPA (75 percent of E or 60 percent of LTE) suggested values. When a good base condition was provided during 5 million loading cycles, slabs with FRP dowels having 3.81-cm (1.5-inch) diameter and 30.48-cm (12-inch) spacing provided good LTE (greater than 80.5 percent). However, with a poor base condition (aggregate movement leading to a concave surface under the slab), the LTE was reduced to 55.26 percent (which is 92.1 percent of 60 percent LTE, corresponding to the ACPA recommended value on joint effectiveness, E = 75 percent). Hence, it is very important to have the proper slab casting procedure and compacted aggregate base.
  6. LTE affected the slab integrity and slab stresses, whereas RD affected ride comfort and impact on the slab at joints. It was important to consider both RD and LTE when the performance of JPCP was evaluated. For example, at 5 million cycles, slab number 4 with 3.81-cm (1.5-inch)-diameter FRP dowels spaced at 30.48 cm (12 inches) c/c had 55.26 percent LTE, but its RD (0.043 cm (0.017 inch)) was less than that of slab number 1 with 2.54-cm (1.0-inch)-diameter FRP dowels and 71.6 percent LTE spaced at 15.24 cm (6 inches) c/c (2.04 cm (0.0803 inch)).
  7. FRP dowels can be used as effective alternatives for construction and rehabilitation of JPCP under highway traffic with advantages of corrosion resistance and decreased maintenance. Long-term performance evaluation of JPCP with FRP dowels is being continued by the Constructed Facilities Center, WVU.

RECOMMENDATIONS

  1. Test more laboratory specimens for establishing possible ranges of LTE and RD values for different diameter, spacing, and length of dowel.
  2. Further investigate crack formation location by using increased FRP dowel length, including deflection shapes.
  3. Evaluate actual dowel bar deflected shapes in the slab under different base removal conditions.
  4. Evaluate the effect of peak bearing stress and average bearing stress on dowel/concrete interface.
  5. Evaluate the effect of fiber volume fraction on dowel behavior, including shear properties that affect joint LTE and RD.
  6. Evaluate the durability of the FRP dowel.
  7. Utilize finite element modeling to envision stress field in the concrete pavement.
  8. Continue long-term field monitoring.

APPENDIX A. TEST OF TIMBER TIE WITH FRP DOWELS

Before evaluating FRP dowels in concrete slabs joints, pilot tests were carried out using rectangular timber beams. A long timber beam was cut into two halves and drilled with 4.45-cm (1.75-inch)-diameter holes to simulate dowel sockets in a slab. Dowel sockets facilitated placement of instrumented dowels inside the timber beams. Load tests were conducted by turning dowels at 45-degree angles to measure dowel strains from longitudinal and transverse gauges (figure 110 to figure 112).

Four cases were evaluated based on loading position and timber depth (corresponding to positioning of the timber beam surface on the base). Test setup of each case is shown in figure 111.

This photo shows an experimental setup where the fiber reinforced polymer (FRP) dowels were initially tested in timber beams before testing them in concrete pavement slabs. Tests were conducted on the timber beams using dowel bars mounted with longitudinal and transverse gauges. The load was applied through a loading frame, and the strain and deflections were recorded through a strain indicator and a dial gauge.
Figure 110. Photo. Lab test of timber tie with FRP dowel bar as the load transfer device.

 

This diagram shows four different cases of testing named as case I-A, case I-B, case II-A, and case II-B using timber beams with dowel bars embedded in them. Strain gauges were positioned along transverse or longitudinal directions. Beams in cases I-A and I-B had the loads on the left and right timber beams, respectively, and measured 13.97 cm (5.5 inches) in width and 19.05 cm (7.5 inches) in depth. Similarly, beams in cases II-A and case II-B had loads on the left and right timber beams, respectively, and measured 19.05 cm (7.5 inches) in width and 13.97 cm (5.5 inches) in depth.
Figure 111. Diagram. Four timber test cases.

 

This diagram shows orientation of longitudinal and transverse strain gauges mounted on the left side of the dowel bar near its mid-length.
Figure 112. Diagram. Rosette strain gauges.

 

Table 40. Strains during loading and unloading on case I-A.

Loading

 

Unloading

Load (kips)

Transverse Gauge

Longitudinal Gauge

Load (kips)

Transverse Gauge

Longitudinal Gauge

0

0

0

20

1,627

7,836

1

64

576

19

1,610

7,797

2

229

1,707

18

1,580

7,752

3

377

2,585

17

1,554

7,707

4

493

3,182

16

1,527

7,662

5

624

3,848

15

1,498

7,609

6

725

4,389

14

1,467

7,562

7

804

4,770

13

1,432

7,522

8

871

5,118

12

1,391

7,420

9

933

5,415

11

1,346

7,365

10

1,021

5,668

10

1,292

7,167

11

1,105

5,962

9

1,226

7,032

12

1,166

6,188

8

1,135

6,982

13

1,223

6,384

7

1,032

6,670

14

1,285

6,584

6

940

6,495

15

1,347

6,844

5

790

5,957

16

1,393

7,011

4

674

5,610

17

1,451

7,204

3

560

4,971

18

1,515

7,409

2

605

3,987

19

1,564

7,599

1

171

2,370

20

1,627

7,781

0

0

0

1 kip = 4.448 kN

 

Table 41. Strains during loading and unloading on case I-B.

Loading

 

Unloading

Load (kips)

Transverse Gauge

Longitudinal Gauge

Load (kips)

Transverse Gauge

Longitudinal Gauge

0

0

0

20

1,357

5,920

1

59

49

16

1,332

5,976

2

220

592

12

1,302

5,931

3

511

1,787

8

1,265

5,863

4

734

3,238

4

1,081

5,066

5

799

3,419

0

0

136

6

899

3,872

 

7

908

4,040

8

1,012

4,325

9

1,040

4,559

10

1,067

4,740

11

1,106

4,901

12

1,137

5,044

13

1,144

5,091

14

1,152

5,119

15

1,186

5,241

16

1,206

5,339

17

1,251

5,473

18

1,277

5,610

19

1,310

5,746

20

1,357

5,920

1 kip = 4.448 kN

This chart shows longitudinal dowel strain in microstrains on the x-axis and load in kips on the y-axis for case I-A and case I-B. For 88.964 kNs (20 kips) of maximum load, longitudinal strains in dowels for loading in case I-A and unloading in case I-B are
1 kip = 4.448 kN
Figure 113. Chart. Plot for longitudinal strain gauges (case I-A and case I-B).

 

Table 42. Strains during loading and unloading on case II-A.

Loading  

Unloading

Load
(kips)

Transverse Gauge

Longitudinal Gauge

Load (kips)

Transverse Gauge

Longitudinal Gauge

0

0

0

20

1

7

2

1

8

16

1

6

4

1

7

12

1

6

6

1

7

8

1

6

8

1

7

4

1

6

10

1

7

0

0

0

12

1

7

 

14

1

7

16

1

6

18

1

7

20

1

7

1 kip = 4.448 kN

 

Table 43. Deflections of timber tie on case I-A.


Load (kips)

Dial Gauge Reading at Loaded End
(inch)

Deflection at x1 (inch)

Dial Gauge Reading at Unloaded End (inch)

Deflection at x2 (inch)

0

0.469

0.000

0.515

0.000

1

0.402

0.067

0.490

0.025

2

0.335

0.134

0.465

0.050

3

0.238

0.231

0.468

0.047

4

0.170

0.299

0.467

0.048

5

0.130

0.339

0.466

0.049

6

0.080

0.389

0.465

0.050

7

0.048

0.421

0.465

0.050

8

0.020

0.449

0.465

0.050

9

-0.190

0.659

0.465

0.050

10

-0.170

0.639

0.465

0.050

11

-0.160

0.629

0.465

0.050

12

-0.150

0.619

0.465

0.050

13

-0.162

0.631

0.465

0.050

14

-0.176

0.645

0.466

0.049

15

-0.197

0.666

0.466

0.049

16

-0.215

0.684

0.467

0.048

17

-0.229

0.698

0.467

0.048

18

-0.247

0.716

0.468

0.047

19

-0.262

0.731

0.468

0.047

20

-0.275

0.744

0.469

0.046

1 kip = 4.448 kN
1 inch = 2.54 cm

 

Table 44. Deflections of timber tie on case I-B.


Load (kips)

Dial Gauge
Reading at
Loaded End
(inch)

Deflection at
y1 (inch)

Dial Gauge Reading at Unloaded End (inch)

Deflection at
y2 (inch)

0

0.915

0.000

0.525

0.000

1

0.870

0.045

0.501

0.024

2

0.825

0.090

3

0.660

0.255

4

0.575

0.340

0.406

0.119

5

0.515

0.400

6

0.462

0.453

7

0.430

0.485

8

0.390

0.525

0.397

0.128

9

0.365

0.550

10

0.331

0.584

11

0.300

0.615

12

0.272

0.643

0.388

0.137

13

0.250

0.665

14

0.228

0.687

15

0.202

0.713

16

0.185

0.730

0.383

0.142

17

0.165

0.750

18

0.140

0.775

19

0.123

0.792

20

0.090

0.825

0.382

0.143

— No data at corresponding loads.
1 kip = 4.448 kN
1 inch = 2.54 cm

This chart shows timber tie deflection in inches on the x-axis and load in kips on the
1 kip = 4.448 kN
Figure 114. Chart. Load versus deflection (inches) of timber tie for case I-A.

 

This chart shows timber tie deflection in inches on the x-axis and load in kips on the y-axis for case I-B. For 88.964 kNs (20 kips ) of maximum load, deflection in inches for case I-A is 2.0955 and 0.363 cm (0.825 and 0.143 inch ) for loading and unloading, respectively.
1 kip = 4.448 kN
Figure 115. Chart. Load deflection (arm with regular gauge) for case I-B.

Joint Effectiveness from Case I-A and Case I-B Under 20 kips Loading

Case I-A

Equation 68. Quotient of 2 times deflection at unloaded side. The quotient of 2 times deflection at unloaded side divided by deflection total of both sides equals the quotient of 2 times 0.046 divided by the sum of 0.744 plus 0.046, end of quotient, times 100 as a percent, which in turn equals 12.15 as a percent.

(68)

Case I-B


Equation 69. Quotient of 2 times deflection at unloaded side divided by deflection. The quotient of 2 times deflection at unloaded side divided by deflection total of both sides equals the quotient of 2 times 0.143 divided by the sum of 0.825 plus 0.143, end of quotient, times 100 as a percent, which in turn equals 29.55 as a percent

(69)

In this preliminary test, joint effectiveness obtained in timber with 3.81-cm (1.5-inch) FRP dowels was low. This was due to several factors, such as the low stiffness of timber material and the larger hole diameter (4.45 cm (1.75 inches)) for accommodating 3.81-cm (1.5-inch)-diameter FRP dowels.

APPENDIX B. ANALYTICAL EVALUATION OF EFFECT OF FRP DOWEL SHEAR MODULUS ON PAVEMENT RD

Analytical evaluation was conducted to find the effect of a dowel shear modulus on pavement RD. Parameters used for calculation are listed below. Detailed data are shown in tables 44 and 45, and figure 16 and figure 17:

FRP dowel.

  • Diameter, d = 3.81 and 2.54 cm (1.5 and 1.0 inches).
  • Length, L = 45.72 cm (18 inches).
  • Spacing between each dowel, b = 15.24, 30.32, 25.4, and 30.48 cm (6, 8, 10, and 12 inches).
  • Modulus of elasticity, Ed = 3.79 × 104 MPa (5.5 × 106 psi) for 3.81-cm (1.5-inch)- diameter dowel and Ed = 4.14 × 104 MPa (6.0 × 106 psi) for 2.54-cm (1.0-inch) diameter.
  • Shear modulus of dowel, low Gd = 0.28 × 104 MPa (0.4 × 106 psi), and high Gd = 5.17 × 104 MPa (0.75x106 psi).
  • Moment of inertia of the dowel,

(70)

Equation 70. Uppercase I subscript d equals the quotient. Uppercase I subscript d equals the quotient of the following: pi times d to the power 4 divided by 64, which in turn equals 10.34 cm (0.248505 inches) to the power 4.

  • Cross-sectional area of dowel, A = 4.496 cm2 (1.77 inches2).

Concrete pavement.

  • Compressive strength, fc′ = 31.026 MPa (4,500 psi).
  • Modulus of elasticity,

Equation 71. Uppercase E subscript c. Uppercase E subscript c equals 57,000 times f subscript c prime to the power 0.5, which in turn equals 2.64 times 10 to the power

(71)

  • Pavement thickness, h = 27.94 cm (11 inches).
  • Joint width, z = 0.635 cm (0.25 inch).
  • Poisson’s ratio of concrete, n = 0.2.
  • Modulus of dowel support, K0 = 4.15 × 104 kg/cm3 (1.5 million pci).

Base.

  • Modulus of subgrade reaction, k = 11.072 kg/cm3 (400 pci).

Load.

  • Design Traffic Load HS25, applied wheel load Pw = 9.071 metric tons (20,000 lb).
  • Design load transfer by joint = 45 percent.
  • Pt = load transferred across the joint
           

Equation 72. Uppercase P subscript t equals load transferred across the joint. Uppercase P subscript t equals load transferred across the joint, which in turn equals uppercase P subscript w times 0.45, which in turn equals 4.082 metric tons or (9,000 lbs).

(72)           

Table 45. RD with low dowel shear modulus (Gd = 2.758 × 103 MPa (0.4 × 106 psi)).


Diameter of Dowel
(inches)

Bending Deflection (inch)

Bending Deflection
(inch)

Shear
Deflection
(inch)

Total Relative
Deflection
(inch)

1.0

0.0045

0.0045

0.0025

0.0114

1.5

0.0022

0.0022

0.0011

0.0055

1.0

0.0057

0.0057

0.0031

0.0145

1.5

0.0028

0.0028

0.0014

0.0070

1.0

0.0067

0.0067

0.0037

0.0171

1.5

0.0033

0.0033

0.0016

0.0082

1.0

0.0076

0.0076

0.0042

0.0195

1.5

0.0037

0.0037

0.0019

0.0093

1 inch = 2.57 cm

 

Table 46. RD with high dowel shear modulus (Gd = 5.17 × 103 MPa (0.75 × 106 psi)).

Diameter of Dowel
(inches)

Bending Deflection
(inch)

Bending Deflection
(inch)

Shear Deflection
(inch)

Total Relative Deflection
(inch)

1.0

0.0045

0.0045

0.0013

0.0103

1.5

0.0022

0.0022

0.0006

0.0050

1.0

0.0057

0.0057

0.0017

0.0131

1.5

0.0028

0.0028

0.0007

0.0063

1.0

0.0067

0.0067

0.0020

0.0154

1.5

0.0033

0.0033

0.0009

0.0074

1.0

0.0076

0.0076

0.0022

0.0175

1.5

0.0037

0.0037

0.0010

0.0085

1 inch = 2.57 cm

 

This graph depicts relative deflection of concrete slab with 2.54-cm (1.0-inch)-diameter FRP dowel type A and 3.81-cm (1.5-inch)-diameter dowel type B. The concrete slab with f prime subscript c equals 31.026 MPa  (4,500 psi) has a joint width of 0.635 cm 
(0.25 inch), and the dowel shear modulus G subscript d equals 2.8 multiplied by 10 superscript 3 MPa  (0.4 multiplied by 10 superscript 6 psi). The slab is resting on a grade with K equals 2.758 MPa  (400 psi). Values of shear deflection, bending deflection on one side of the center line and bending deflection on the other side of the center line, are shown by stacking their magnitude in each bar. The respective values for dowel type A at 15.24 cm (6 inches) center-to-center (c/c) are 0.00635, 0.01143, and 0.01143 cm (0.0025, 0.0045, and 0.0045 inch). The values for dowel type B at 15.24 cm (6 inches) c/c are 0.0028, 0.056, and 0.056 cm (0.0011, 0.0022, and 0.0022 inch). The values for dowel type A at 20.32 cm (8 inches) c/c are 0.0079, 0.014, and 0.014 cm (0.0031, 0.0057, and 0.0057 inch). The values for dowel type B at 20.32 cm (8 inches) c/c are 0.0036, 0.0071, and 0.0071 cm (0.0014, 0.0028, and 0.0028 inch). The values for dowel type A at 
25.4 cm (10 inches) c/c are 0.0094, 0.017, and 0.017 cm (0.0037, 0.0067, and 
0.0067 inch). The values for dowel type B at 25.4 cm (10 inches) c/c are 0.0041, 0.0083, and 0.0083 cm (0.0016, 0.0033, and 0.0033 inch). The values for dowel type A at 
30.48 cm (12 inches) c/c are 0.010<sup>6</sup>, 0.0193, and 0.0193 cm (0.0042, 0.0076, and 
0.0076 inch). The values for dowel type B at 30.48 cm (12 inches) c/c are 0.0048, 0.0094, and 0.0094 cm (0.0019, 0.0037, and 0.0037 inch).
1 inch = 2.54 cm
Figure 116. Graph. Components of RD for dowel types A (2.54-cm (1.0-inch) diameter) and
B (3.81-cm (1.5-inch) diameter), with k = 11.072 kg/cm3 (400 pci), fc' = 31.026 MPa
(4,500 psi), joint width = 0.635 cm (0.25 inch), and Gd = 2.8 × 103 MPa (0.4 × 106 psi).


This graph depicts relative deflection of concrete slab with 2.54-cm (1.0-inch)-diameter FRP dowel type A and 3.81-cm (1.5-inch)-diameter dowel type B. The concrete slab with f prime subscript c equals 31.026 MPa  (4,500 psi) has a joint width of 0.635 cm 
(0.25 inch), and the dowel shear modulus G subscript d equals 5.17 multiplied by 10 superscript 4 MPa  (0.75 multiplied by 10 superscript 6 psi). The slab is resting on a grade with K equals 2.758 MPa  (400 psi). Values of shear deflection, bending deflection on one side of the center line and bending deflection on other side of the center line, are shown by stacking their magnitude in each bar. The values for dowel type A at 15.24 cm 
(6 inches) center-to-center (c/c) are 0.0033, 0.01143, and 0.01143 cm (0.0013, 0.0045, and 0.0045 inch). The values for dowel type B at 15.24 cm (6 inches) c/c are 0.00152, 0.00559, and 0.00559 cm (0.0006, 0.0022, and 0.0022 inch). The values for dowel type A at 20.32 cm (8 inches) c/c are 0.00431, 0.0145, and 0.0145 cm (0.0017, 0.0057, and 0.0057 inch). The values for dowel type B at 20.32 cm (8 inches) c/c are 0.00178, 0.00711, and 0.00711 cm (0.0007, 0.0028, and 0.0028 inch). The values for dowel type A at 25.4 cm (10 inches) c/c are 0.00508, 0.0170, and 0.0170 cm (0.0020, 0.0067, and 0.0067 inch ). The values for dowel type B at 25.4 cm (10 inches) c/c are 0.0022, 0.0084, and 0.0084 cm (0.0009, 0.0033, and 0.0033 inch). The values for dowel type A at 
30.48 cm (12 inches) c/c are 0.0066, 0.019, and 0.019 cm (0.0026, 0.0076, and 
0.0076 inch). The values for dowel type B at 30.48 cm (12 inches) c/c are 0.00254, 0.0094, and 0.0094 cm (0.0010, 0.0037, and 0.0037 inch).
1 inch = 2.54 cm
Figure 117. Graph. Components of RD for dowel types A (2.54-cm (1.0-inch) diameter)
and B (3.81-cm (1.5-inch) diameter), with k = 11.072 kg/cm3 (400 pci), fc' = 31.026 MPa
(4,500 psi), joint width = 0.635 cm (0.25 inches), and Gd = 5.17 × 103 MPa (0.75 × 106 psi).

APPENDIX C. FIBER BURNOUT TESTS FOR DETERMINING FIBER WEIGHT FRACTION AND FIBER VOLUME FRACTION FOR FRP DOWELS

Burnout tests were conducted to determine the FWF and FVF for both 2.54-cm (1.0-inch)- diameter FRP dowels and 3.81-cm (1.5-inch)-diameter FRP dowel. Details are listed in table 46 and table 47.

Table 47. FWF and FVF for FRP dowel with 2.54-cm (1.0-inch) diameter.

Sample

FRP Sample
Total

Resin Weight (g)

E-glass Fiber

Fiber Weight Fraction (FWF, percent)

Fiber Volume Fraction (FVF, percent)

Weight (g)

Volume (inches3)

Weight (g)

Volume (inches3)

A1

23.00

0.7399

6.38

16.62

0.3977

72.26

53.75

A2

23.12

0.7383

6.40

16.72

0.4001

72.31

54.20

Average

 

72.29

53.98

Note: E-glass fiber volume was calculated by using E-glass fiber weight pided by its density (2.55 g/cm3),
a converter factor 1 cm3 = 0.06102374 in3 was used for the calculations.
1 inch = 2.54 cm

Table 48. FWF and FVF for FRP dowel with 3.81-cm (1.5-inch) diameter.

Sample

FRP Sample Total

Resin Weight
(g)

E-glass Fiber

Fiber Weight Fraction (FWF, percent)

Fiber Volume Fraction (FVF, percent)

Weight (g)

Volume (in3)

Weight (g)

Volume (in3)

B1

54.81

1.7737

16.736

38.074

0.9111

69.47

51.37

B2

54.19

1.7576

16.546

37.644

0.9009

69.47

51.25

Average

 

69.47

51.31

Note: E-glass fiber volume was calculated by using E-glass fiber weight pided by its density (2.55 g/cm3
(0.092 lb/in3)); a conversion factor of 1 cm3 = 0.06102374 in3 was used for the calculations.
1 inch = 2.54 cm

REFERENCES

  1. American Association of State Highway and Transportation Officials (AASHTO), AASHTO Guide for Design of Pavement Structures. AASHTO. Washington, DC, 1993.
  2. Friberg, B.F., "Design of Dowels in Transverse Joints of Concrete Pavements," Transactions, American Society of Civil Engineers, Vol. 105, No. 2081, 1940.
  3. Vijay, P.V. and Ganga Rao, H.V.S., Development of Fiber Reinforced Plastics for Highway Application: Aging Behavior of Concrete Beams Reinforced with GFRP Bars.
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  18. Tabatabaie, A.M., Barenburg, E.J., and Smith, R.E. "Longitudinal Joint Systems in Slipformed Rigid Pavements." Vol. II-Analysis of Load Transfer Systems for Concrete Pavements, Report No. DOT/FAA.RD-79/4, Federal Aviation Administration, 1979.
  19. Porter, M.L., Guinn, Jr., R.J. Assessment of Dowel Bar Research. Iowa DOT Project HR1080, Center for Transportation Research and Education, Iowa State University, 2002.
  20. ACI Committee 325. "Structural Design Considerations for Pavement Joints." ACI Journal, Vol. 53, July, pp. 1–29, 1956.

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