AASHTO GFRP-Reinforced Concrete Design Training Course

GoToWebinar by: Professor Antonio Nanni Introducing the Schedule

9:35 am Introduction & Materials (Prof. Antonio Nanni) → Review Questions (Dr. Francisco De Caso) 10:30 am Flexure Response (Prof. Antonio Nanni) → Review Questions (Dr. Francisco De Caso) *** Coffee Break *** → Design Example: Flat Slab (Roberto Rodriguez) 12:00 pm Shear Response (Prof. Antonio Nanni) → Review Questions (Dr. Francisco De Caso) *** Lunch Break (1 hour) *** 1:30 pm → Design Example: Bent Cap (Nafiseh Kiani) 2:00 pm Axial Response (Prof. Antonio Nanni) → Review Questions (Dr. Francisco De Caso) → Design Example: Soldier Pile (Roberto Rodriguez) *** Coffee Break *** 3:00 pm Case Studies & Field Operations (Prof. Nanni & Steve Nolan)

1 Introducing our Presenters & Support

Prof. Antonio Nanni Dr. Francisco DeCaso P.E. PhD. P.E. PhD.

Roberto Rodriguez, Nafiseh Kiani P.E. (PhD. Candidate) (PhD. Candidate)

Alvaro Ruiz, Christian Steputat, (PhD. Candidate) P.E. (PhD. Candidate)

Steve Nolan, P2.E. Support Material - Handouts

3 Support Material - Handouts

4 Support Material - Handouts

5 Support Material - Handouts

6 Support Material - Workbook

7 Support Material - Workbook

8 Other Support Material - FDOT

https://www.fdot.gov/structures/innovation/FRP.shtm

9 Another Training Opportunity

CFRP-Prestressed Concrete Designer Training for Bridges & Structures – Professor Abdeldjelil “DJ” Belarbi, on September 9th, 2020 This 6-hour online training is focused on providing practical designer guidance to FDOT engineers and consultants for structures utilizing Carbon Fiber-Reinforced Polymer (CFRP) Strands for pretensioned bridge beams, bearing piles, and sheet piles. Basic design principles and design examples will be presented for typical FDOT bridge precast elements. Register Now at: https://attendee.gotowebinar.com/register/5898046861643311883

There is no cost to attend this webinar training.

A short preview of this training was provided at the June 30th FDOT Transportation Symposium Webinar Series presentation: FRP Reinforced and Prestressed Concrete Designer Training Introduction

10 AASHTO GFRP-Reinforced Concrete Design Training Course

Let Us Begin !! AASHTO GFRP- Reinforced Concrete Design Training Course Course Content Areas

1. Introduction & Materials

2. Flexure Response

3. Shear Response

4. Axial Response

5. Case Studies & Field Operations Course Overview & Expectations

• Introduction of concepts Concepts • Understanding of methods • Use of available resources

• Review questions AASHTO GFRPQuestions-Reinforced Concrete Design& • Reinforce methods TrainingExamples Course • Apply concepts

• Active participation needed Participation • Ask questions • Opportunity for discussions Learning Objectives

• Know what FRP reinforcement is • Learn the fundamental mechanical properties of FRP bars and bends • Become aware of some major material-based design provisions of concrete members internally reinforced with GFRP bars with particular reference to AASHTO and FDOT documents • Become aware of relevant FRP-RC projects in and out of state

3/77 Course Content Areas

1. Introduction & Materials

2. Flexure Response

3. Shear Response

4. Axial Response

5. Case Studies & Field Operations 1. INTRODUCTION TO FRP-RC & MATERIAL PROPERTIES OF GFRP Table of Contents - Intro & Materials

• Problem Statement

• Where to Use Glass FRP

• FRP Material Properties

• Durability

• Design Guides and Standards

• Concluding Remarks

6/77 Problem Statement

• Failure mechanism for structures exposed to aggressive environments is often corrosion of steel reinforcement

• Traditional corrosion mitigation efforts: ✓ Admixtures ✓ Increase Concrete Cover ✓ Alter Concrete Mix ✓ Membranes & Overlays ✓ Epoxy-Coated, Galvanized SERVICE LIFE OF STRUCTURES or Stainless Steel GREATLY REDUCED BY CORROSION

7/77 FRP Rebars

Fiber reinforced polymer (FRP) bars as alternative reinforcement for concrete

A composite material system made of: Fibers + Resin

8/77 FRP Rebars Key Benefits

• Corrosion resistant • High strength-to-weight ratio • Ease of application & installation • Lightweight ¼ the weight of steel • Transparent to magnetic fields and radar frequencies • Electrically & thermally non-conductive

FIRST COST COMPARABLE WITH EXPOXY-COATED STEEL

9/77 Table of Contents

• Problem Statement

• Where to Use Glass FRP

• FRP Material Properties

• Durability

• Design Guides and Standards

• Concluding Remarks

10/77 Where Should FRP Be Used? • Concrete structures susceptible to corrosion - Steel corrosion by chlorides - Environments that lower concrete pH - Structures with minimum concrete cover • Concrete structures requiring non- ferrous reinforcement due to - Electro-magnetic considerations - Thermal non-conductivity • Where machinery will “consume” the reinforced concrete member (i.e., mining and tunneling)

11/77 Ready for Prime Time

• Structural design defined by ACI & AASHTO (and FDOT) • Bar properties defined by ASTM D7957 (and FDOT) • 600+ installations in US & Canada • Traditional procurement & construction methods

12/77 Table of Contents

• Problem Statement

• Where to Use Glass FRP

• FRP Material Properties

• Durability

• Design Guides and Standards

• Concluding Remarks

13/77 Types of Fiber in FRP Bars

• Carbon Fiber Reinforced Polymer (CFRP)

• Glass Fiber Reinforced Polymer (GFRP)

• Basalt Fiber Reinforced Polymer (BFRP)

• Aramid Fiber Reinforced Polymer (AFRP)

14/77 Types of Resin in FRP Bars

Some Thermoset Resins (Only ones allowed for now): Two-part system composed of resin and hardener resulting in a one-way (irreversible) chemical reaction

• Vinyl Ester

• Epoxy

• Polyester Not allowed in structural applications because of poor durability

15/77 FRP Bar Types

Several commercially available GFRP solid round bars with different external surface (not standardized) deformations:

• (A & F) Sand coated + helical wrap • (B) Helically wrapped • (C) Ribbed • (D) Sand coated • (E) Helically grooved A B C D E F

16/77 FRP Bar Shapes

• Straight bars

• Bent bars

• Spirals

• Twisted strands (PC use)

17/77 Material Specifications FDOT 932-3 and ASTM D7957 specs set minimum QUALIFICATION & QC for Glass (and Basalt)* FRP bars Bar manufacturer not known/selected at the design stage

* FDOT only

18/77 FRP Bar Sizes

Same as steel bars, specified per FDOT 932-3, Table 3-1 and ASTM D7957. Area range (min-max) given for measured values for any surface type

19/77 FRP Mechanical Properties

• Higher tensile strength, but less stiff than steel Tensile Stress-Strain ✓ Provides less confinement to Characteristics concrete and RC members have more deflection than steel-RC • Anisotropic behavior ✓ High strength in the fiber direction ✓ Low shear strength and dowel action (resin dominated) • Elastic up to failure - no ductility ✓ Cannot be used in seismic areas, no plastic hinges formed in RC members

20/77 Typical Tensile Properties

Steel GFRP Yield Stress 40-75 ksi (276-517) (MPa) Guaranteed Tensile Strength, (f* ), f,u 78-160 (Average – 3 sigma) (534-1240) ksi (MPa) Average Elastic Modulus, (E ) f 29,000 6,500 – 8,700 (Average) (200) (45-60) Ksi (GPa)

Yield Strain, (εy) 0.14-0.25% N/A

Guaranteed Tensile Ultimate Strain, (ε*f,u) ~10-12% 1.2-2.4%

21/77 Design Tensile Strength

• Design tensile strength and strain are: ∗ 푓푓푢 = 퐶퐸푓푓푢 AASHTO GFRP 2.4.2.1-1 ∗ 휀푓푢 = 퐶퐸휀푓푢

Where CE is the environmental reduction factor from AASHTO Table 2.4.2.1-1 (red box) (proposed new factors in ACI 440 in green)

Concrete not exposed to Concrete exposed to earth Fiber earth or weather or weather Glass 0.9 0.8 0.85 0.70

22/77 Behavior Function of Temperature

• Thermosets are characterized by

Glass Transition Temperature, Tg

• Resin tensile, compressive, and shear properties diminish when

temperatures approach Tg

o • Tg values of approximately 212 F (100 oC) are required for Vinyl Ester typically used GFRP rebars

• Tg lowers as a result of moisture absorption Elastic Modulus vs Temperature

23/77 Summary: GFRP Differences with Steel

PROs CONs • High longitudinal strength- • No yielding to-weight ratio • Low transverse strength • Corrosion resistance • Relatively low modulus • Electro-magnetic neutrality • High CTE perpendicular to • Good fatigue endurance fibers • Low thermal & electrical • Sensitive to UV, moisture & conductivity alkaline environment • Lightweight • Susceptible to fire & smoke production

24/77 Other Mechanical Properties

Strength of FRP at bend • FRP bars can be fabricated with bends, however the tensile strength at bend is reduced by about 40% Compressive behavior of FRP bars • Reduced strength and stiffness as compared to tensile properties Shear behavior of FRP bars • Unidirectional FRP materials have a lower interlaminar shear modulus and shear strength as compared to steel Behavior under sustained and cyclic loading • FRP bars can undergo creep-rupture under sustained loading and fatigue rupture under cyclic loading

25/77 Material Characterization

Moisture absorption Fiber content Cross-sectional area [ASTM D570] [ASTM D2484] [ASTM D792]

Minimum requirements: FDOT 932, Table 3.2 (straight bars) & 3.3 (bent bars)

26/77 Material Characterization

Tensile test [ASTM D7205]

Minimum requirements: FDOT 932, Table 3.2 & 3.3

AASHTO 2.4.2.1: ffu → Guaranteed tensile strength = average minus three standard deviations

27/77 Material Characterization

Horizontal shear Transverse shear [ASTM D4475] [ASTM D7617]

Minimum requirements: FDOT 932, Table 3.2 (straight bars) & 3.3 (bent bars)

28/77 Material Characterization

Bond-to- concrete [ASTM D7913]

Minimum requirements: FDOT 932, Table 3.2

29/77 Strength of FRP at Bend

• FRP bars can be fabricated with bends; however, the tensile strength of the bend is reduced up to 40% per ASTM D7957 • Bend internal diameter is larger than for steel • FDOT 932-3.3 includes additional specifications for properties of FRP bent bars at bend locations

30/77 Table of Contents

• Problem Statement

• Where to Use Glass FRP

• FRP Material Properties

• Durability

• Design Guides and Standards

• Concluding Remarks

31/77 Durability Assessment

Methods used to assess and validate the durability of FRP bars:

1. Accelerated aging protocols (high temperature; immersion in water w/ or w/o high pH and/or salt) → fast

2. Extraction of samples from real life structures → slow

32/77 GFRP Bars Extracted from Bridges 15-20 Years Old

• Investigation to assess long-term durability of GFRP bars after at least 15 years in service • Cores extracted from eleven bridges located across the United States

33/77 GFRP Bars Extracted from Bridges 15-20 Years Old

left center right

Results indicated reduction in tensile strength of 2.13% over a period of 17 years of service that would correspond to drop in strength of 12.5% over a period of 100 years with degradation rate assumed to be linear

34/77 Durability

Source: Long-term Durability of GFRP Reinforcement in Concrete: A Case Study after 15 Years of Service - O. Gooranorimi, E. Dauer, J. Myers, A. Nanni

NO SIGN OF BOND DEGRADATION NOR LOSS OF CONTACT AND MECHANICAL PROPERTIES AFTER 15 YEARS IN SERVICE

35/77 Table of Contents

• Problem Statement

• Where to Use Glass FRP

• FRP Material Properties

• Durability

• Design Guides and Standards

• Concluding Remarks

36/77 Design Guides and Tools

• Design Guide ‒ Currently available • Uniform Approval Processes ‒ Manufacturer Approval vs. Product Approval • Reliable Design Tools ‒ Commercial vs. Agency based design programs

37/77 Design Guidance & Tools in Florida

Currently available documents: • AASHTO: Only GFRP • FDOT 932-3: GFRP and BFRP

38/77 Design Guidance & Tools in Florida

• Uniform Approval Processes https://mac.fdot.gov/smoreports ‒ Manufacturer Approval vs. Product Approval

39/77 Material Acceptance Criteria

FDOT 932-3 Table 3-4 Property Test Method Requirement Straight Bar ASTM D2584 Fiber Mass or ≥70% Yes Fraction ASTM D3171 Short-Term ASTM D570, Procedure Moisture 7.1; 24 hours immersion at ≤0.25% Yes Absorption 122°F ASTM D7028 (DMA) or ≥230°F Glass Transition ASTM E1356 (DSC; T )/ Yes Temperature m ASTM D3418 (DSC; Tmg) ≥212°F ≥95% of Total Degree of Cure ASTM E2160 Yes polymerization enthalpy Measured Cross- Within range listed in Yes sectional Area Table 3-1 ASTM D7205 Guaranteed ≥ Value listed in Table Yes Tensile Load 3-1

40/77 Design Guidance & Tools In Florida

• Accessible & Reliable Design Tools ‒ Commercial vs. Agency/Institution based design programs

https://www.fdot.gov/structures/proglib.shtm

CFCC-PC/GFRP-RC beta version (to be included in v6.0 with HSSS)

GFRP-RC included

GFRP-RC now included

41/77 Table of Contents

• Problem Statement

• Where to Use Glass FRP

• FRP Material Properties

• Durability

• Design Guides and Standards

• Concluding Remarks

42/77 Concluding Remarks

• There is a strong case for use of FRP in structural concrete exposed to corrosive environment • FRP anisotropic and linear elastic up to failure • Material Specifications and Design Guides exist (ASTM D7957, FDOT-932, AASHTO GFRP,) • Accessible design tools exist

43/77 Questions?

Thank INTRODUCTION TO FRP-RC & MATERIAL PROPERTIES OF GFRP 1.1 Review Questions: Fundamentals Applied Questions

1.1.1) Where could GFRP reinforcement for concrete be most suitable? ______. a. Any concrete member susceptible to steel corrosion by chlorides b. Any concrete member requiring non-ferrous reinforcement due to electro- magnetic considerations c. As an alternative to epoxy, galvanized, or stainless steel rebars d. Applications requiring thermal non-conductivity e. All the above

46/77 Where Should FRP Be Used?

▪ Concrete structures susceptible to corrosion - Steel corrosion by chlorides - Aggressive agents that lower concrete pH - Structures with minimum cover concrete

▪ Concrete structures requiring non-ferrous reinforcement due to - Electro-magnetic considerations - Thermal non-conductivity

▪ Where machinery will “consume” the reinforced concrete member (i.e., mining and tunneling)

47/77 Applied Questions

1.1.1) Where could GFRP reinforcement for concrete be most suitable? ______. a. Any concrete member susceptible to steel corrosion by chloride ions b. Any concrete member requiring non-ferrous reinforcement due to electro-magnetic considerations c. As an alternative to epoxy, galvanized, or stainless steel rebars d. Applications requiring thermal non-conductivity e. All the above

48/77 Applied Questions

1.1.2) Which of the following is not applicable to GFRP rebars? ______.

a. Corrosion resistant

b. Ductility

c. Low thermal and electrical conductivity

d. Light weight

e. High strength to weight ratio

49/77 FRP Mechanical Properties

50/77 Applied Questions

1.1.2) Which of the following is not applicable to GFRP rebars? ______. a. Corrosion resistant b. Ductility c. Low thermal and electrical conductivity d. Light weight e. High strength to weight ratio

51/77 Applied Questions

1.1.3) The E-modulus of GFRP rebars when compared to steel is approximately ______. a. 3 to 4 times lower b. Comparable c. 2 to 3 times higher d. 3 to 4 times higher

52/77 Applied Questions

53/77 Applied Questions

1.1.3) The E-modulus of GFRP rebars when compared to steel is approximately ______. a. 3 to 4 times lower (6.5-8.7 msi compared to 29 msi) b. Comparable c. 2 to 3 times higher d. 3 to 4 times higher

54/77 Applied Questions

1.1.4) The durability of GFRP rebars ______. a. Has been proven through accelerated aging protocols and by samples extracted from bridges that have been in service for 15 years b. Is unknown c. Is lower than steel d. a) and c) are true

55/77 Durability

Source: Long-term Durability of GFRP Reinforcement in Concrete: A Case Study after 15 Years of Service - O. Gooranorimi, E. Dauer, J. Myers, A. Nanni

NO SIGN OF BOND DEGRADATION NOR LOSS OF CONTACT AND MECHANICAL PROPERTIES AFTER 15 YEARS IN SERVICE

56/77 Applied Questions

57/77 Applied Questions

1.1.5) The density of GFRP is about ______. a. About 4 times lighter than steel b. Similar to that of steel c. About 4 times heavier than steel d. Half that of steel

58/77 FRP Density

Rebar Density Nominal weight (lb./ft) 3 type (lb./ft ) #3 #5 #8 GFRP 125 0.38 1.05 2.68 Steel 505 0.09 0.26 0.66

59/77 Applied Questions

1.1.5) The density of GFRP is about ______. a. About 4 times lighter than steel b. Similar to that of steel c. About 4 times heavier than steel d. Half that of steel

60/77 Applied Questions

1.1.6) FRP has higher strength in the direction ______to the fibers.

a. Transverse

b. Parallel

61/77 Transverse vs. Parallel Strength

Parallel - Tensile Transverse - Shear

• 70 ksi to >150 ksi • > 22ksi • Strength varies per bar size • Almost independent of bar size (shear lag effect)

62/77 Applied Questions

1.1.6) FRP has higher strength in the direction ______to the fibers.

a. Transverse

b. Parallel

63/77 Applied Questions

1.1.7) The tensile strength of GFRP reinforcing bars with bend should be at minimum ______. a. The same as straight GFRP reinforcing bars b. 40% of the straight GFRP reinforcing bars c. 60% of the straight GFRP reinforcing bars d. 140% of the straight GFRP reinforcing bars

64/77 Strength of FRP at Bent

• FRP bars can be fabricated with bends, however the tensile strength of the bend is reduced up to 60% per ASTM D7957

• Bend radius is larger than for steel

• ASTM D7914 includes specifications for strength of FRP bent bars in bend locations

65/77 Applied Questions

66/77 Applied Questions

1.1.8) The guaranteed tensile strength of a GFRP bar as provided by the manufacturer is ______. a. The mean tensile strength of the sample population b. The mean tensile strength of the sample population minus three standard deviations c. The mean tensile strength of the sample population minus two standard deviations d. None of the above

67/77 Material Characterization

Tensile test [ASTM D7205]

Minimum requirements: FDOT 932-3, Table 3.2 & 3.3

AASHTO 2.4.2.1: ffu → Guaranteed tensile strength = mean minus three standard deviations

68/77 Applied Questions

69/77 Applied Questions

1.1.9) At temperatures higher than approximately ______the resin of GFRP bars begins to soften.

a. 60 oF

b. 212 oF

c. 1220 oF

d. 2500 oF

70/77 Behavior at High Temperatures

• Thermosets are characterized by

Glass Transition Temperature, Tg

• Resin tensile, compressive, and shear properties diminish when temperatures

approach Tg

o • Tg values are approximately 212 F (100 oC) for Vinyl Ester typically used GFRP rebars

• Tg lowers as a result of moisture absorption Elastic Modulus vs Temperature

71/77 Applied Questions

1.1.9) At temperatures higher than approximately ______the resin of GFRP bars begins to soften.

a. 60 oF

b. 212 oF

c. 1220 oF

d. 2500 oF

72/77 AASHTO GFRP- Reinforced Concrete Design Training Course AASHTO GFRP- Reinforced Concrete Design Training Course Course Outline

1. Introduction & Materials

2. Flexure Response

3. Shear Response

4. Axial Response

5. Case Studies & Field Operations

1/91 2. FLEXURE RESPONSE OF GFRP REINFORCED CONCRETE Table of Contents

• General Considerations

• Bending Moment Capacity

• Serviceability

• Static & Cyclic Fatigue

• Anchorage and Development

• Special Considerations

• Concluding Remarks

3/91 Flexural Theory

Assumptions: 1. Plane sections remain plane after deformation 2. Ultimate concrete strain is 0.003 3. Tensile strength of concrete and FRP compressive strength are neglected

4. FRP is perfectly bonded to concrete For AASHTO, example 5. Stress-strain of FRP is linear until failure Ultimate Flexural Strength and Demand: 푀 = 1.25푀 + 1.75푀 Mn = nominal capacity 푢 퐷퐶 퐿퐿 For ACI, example Mu = factored demand 휙푀푛 ≥ 푀푢

 = strength reduction factor (depends on the mode of failure) 푀푢 = 1.2푀퐷 + 1.6푀퐿

4/91 Failure Modes

Compression-controlled: concrete crushing Concrete Crushing w

b e  cu f c b  c 1 c 0.85b1 f c bc d N.A Af e ff A f f f f

b1 c = a

5/91 Failure Modes

Concrete Crushing Failure in GFRP- RC Beam

6/91 Failure Modes

Tension-controlled: FRP rupture

FRP Rupture

Concrete stress may be linear b f' or non-linear ec c c c N.A 0.5 f'c bc d Af e fu ffu Af ffu

7/91 Failure Modes

FRP Rupture Failure in GFRP Reinforced Beam

8/91 Failure Modes

Balanced failure: simultaneous concrete crushing & FRP rupture

Concrete Crushing

FRP Rupture

b f’ εcu c

0.85f’cba a=β1c c=cb d N.A

Af f εfu fu Afffu

9/91 General Considerations

• Flexural capacity of an FRP-reinforced flexural member dependent on tension or compression failure modes

• Over or under-reinforced sections are acceptable provided that the strength and serviceability criteria are satisfied

• FRP reinforcement is brittle, but provides warning in terms of large member deflection

• Flexural behavior is not ductile; therefore safety factors are increased (i.e., smaller Φ factors)

10/91 Moment-Curvature Diagrams

120 b b h d Areinf. (in.) (in.) (in.) (in2) (1) (3) 100 8 15 12.5 0.93 (2) 8 15 12.5 1.32 (3) 10 18 15.5 1.2 h d

80 ft) - Areinf.

(2) 60 (1)

Mn

Moment (kip Moment 40

(1) Steel-tension controlled 20 (2) GFRP-concrete crushing (3) GFRP-FRP rupture 0 0 0.0002 0.0004 0.0006 0.0008 0.001 0.0012 0.0014 Curvature (rad/in)

11/91 Balanced Failure

’ εcu = 0.003 0.85 fc

’ C=0.85 fc ab c a=β1c

ε ε f = fu T=Afbffu

b Where it can be shown that: 퐴푓푏 휌 = (AASHTO 2.5.3) 푓 푏푑 ′ 푓푐 퐸푓휀푐푢 휌푓푏 = 0.85훽1 푓푓푢 퐸푓휀푐푢 + 푓푓푢

12/91 Balanced Reinforcement Ratio

IF ρf < ρfb Rupture of FRP will control failure

IF ρf > ρfb Concrete crushing will control failure

TYPICAL VALUES FOR rb , rfb r STEEL GRADE 60 b = 0.0335 r GFRP F80-E6 fb= 0.0078

13/91 Table of Contents

• General Considerations

• Bending Moment Capacity

• Serviceability

• Static & Cyclic Fatigue

• Anchorage and Development

• Special Considerations

• Concluding Remarks

14/91 Nominal Flexural Strength: Compression

Case of concrete crushing controlling failure and stress distribution approximated by rectangular stress block

IF εft < εfu 푎 (AASHTO 2.6.3.2.2-1) 푀 = 퐴 푓 푑 − 푛 푓 푓 2

WHERE

퐴푓푓푓 (AASHTO 2.6.3.2.2-2) 푎 = ′ 0.85푓푐 푏

2 ′ 퐸푓휀푐푢 0.85훽1푓푐 푓푓 = + 퐸푓휀푐푢 − 0.5퐸푓휀푐푢 ≤ 푓푓푢 (AASHTO 2.6.3.1-1) 4 휌푓

15/91 Nominal Flexural Strength: Tension

FRP rupture controlling failure. Whitney’s Stress block not applicable because εc < εcu = 0.003. Simplified and conservative procedure is proposed (i.e., c = cb):

IF εft = εfu 훽1푐푏 푀 = 퐴 푓 푑 − (AASHTO 2.6.3.2.2.-3) 푛 푓 푓푢 2 WHERE

휀푐푢 푐푏 = 푑 (AASHTO 2.6.3.2.2.-4) 휀푐푢 + 휀푓푢

16/91 Strength Reduction Factor (ACI)

 Controlled by FRP Rupture Limit State Controlled by Concrete Crushing Limit State

Φ as a 0.65 function of 0.55 (ACI 440 7.2.3) GFRP Failure by Transition Compression reinforcement FRP Zone Controlled rupture ratio r f r f b 1.4 r f b

0.55 푓표푟 휌푓 ≤ 휌푓푏 휌푓 휙 = 0.3 + 0.25 푓표푟 휌푓푏 < 휌푓 < 1.4휌푓푏 휌 푓푏 (ACI 440 7.2.3) 0.65 푓표푟 휌푓 ≥ 1.4휌푓푏

17/91 Strength Reduction Factors (AASHTO)

Controlled by Concrete  Crushing Limit State

0.75 Φ as a function Compression- 0.55 Tension of strain in Controlled Transition Controlled GFRP (Concrete Crushing) (GFRP Rupture) ε ε 0.8εfd fd ft

0.55 푓표푟 휀푓푡 ≤ 휀푓푑 휀푓푡 휙 = 1.55 − 푓표푟 0.80휀푓푑 < 휀푓푡 < 휀푓푑 휀푓푑 (AASHTO 2.5.5.2) 0.75 푓표푟 휀푓푡 ≥ 0.80휀푓푑

18/91 Minimum Flexural Reinforcement

Minimum longitudinal reinforcement to (AASHTO 2.6.3.3-1) provide adequate level of protection 140 against sudden failure at formation of Mcr2 first flexural crack Mo2 120 Mo1

100 Mcr1 1.33푀푢

80 ϕMn 푀푟 ≥ ൞ 푆푐 1.6푀푐푟 − 푀푑푛푐 − 1 푆푛푐 60

Applied Moment Applied Ductile Response fr = modulus of rupture of concrete 40 Brittle Response Mdnc = total unfactored dead load moment 20 ϕMn Sc = section modulus of the extreme fiber of the composite section 0 1 2 3 4 5

Snc = section modulus for the extreme fiber Displacement of the monolithic or non-composite section Illustrative example on ductile and brittle responses

19/91 Table of Contents

• General Considerations

• Bending Moment Capacity

• Serviceability

• Static & Cyclic Fatigue

• Anchorage and Development

• Special Considerations

• Concluding Remarks

20/91 Serviceability

• Stresses under sustained and cyclic loading must be checked to avoid static (creep-rupture) and cyclic fatigue rupture

• The substitution of FRP for steel on an equal area basis would typically result in larger deflections and wider crack widths

• Deflections under service loads and crack control often govern design • Cracking – Excessive crack width is undesirable for aesthetic and other reasons (e.g., prevent leakage that can damage structural concrete) • Deflection – Deflections should be within acceptable limits imposed by the use of the structure (e.g., supporting attached nonstructural elements without damage)

• Designing FRP-RC beams for concrete crushing typically satisfies serviceability criteria

21/91 Crack Control: Bond Coefficient

Bond coefficient (kb) accounts for the degree of bond between FRP bar and surrounding concrete in ACI 440. Bond reduction factor (Cb) defined as the inverse of kb in AASHTO. Function of surface configuration and materials varies from 70 to 120% of steel bars. 83% assumed in AASHTO 2.6.7.

> 1 푊표푟푠푒 푡ℎ푎푛 푠푡푒푒푙 풌 = ቊ 풃 < 1 퐵푒푡푡푒푟 푡ℎ푎푛 푠푡푒푒푙

ퟏ > 1 퐵푒푡푡푒푟 푡ℎ푎푛 푠푡푒푒푙 푪풃 = = ቊ 풌풃 < 1 푊표푟푠푒 푡ℎ푎푛 푠푡푒푒푙 Testing of GFRP-RC beam using four-point setup

22/91 Control of Crack Width

FRP bars are corrosion-resistant; therefore, larger crack widths as compared to steel-RC concrete can be tolerated

The maximum crack width (w) is: GFRP: 0.028 in Steel: 0.017 in Indirect approach controls flexural cracking in terms of maximum bar spacing adopted in AASHTO GFRP 2nd Ed.:

퐶푏퐸푓푤 퐶푏퐸푓푤 푠푚푎푥 ≤ min 1.15 − 2.5푐푐, 0.92 (AASHTO 2.6.7-1) 푓푓푠 푓푓푠

23/91 Control of Crack Width

For calculated stress level and crack width limit, dc (concrete cover) shall satisfy:

퐶푏퐸푓푤 푑푐 ≤ (AASHTO 2.6.7-2) 2푓푓푠휉

24/91 Shrinkage & Temperature Reinforcement

Area of shrinkage and temperature reinforcement may be divided between each face and shall be:

3,132 휌푓,푠푡 = max ; 0.0014 ≤ 0.0036 AASHTO GFRP Shr./Temp. 퐸푓푓푓푑 (2.9.6-1) Reinforcement

Spacing:

• ≤ 3tslab or 12 in.

• Evenly distributed on both surfaces if member is greater than 6 in. Adapted from FDOT Index 400-010

25/91 Shrinkage & Temperature Reinforcement

GFRP-RC retaining wall example: Properties

Width of Wall Average: 13.4 in. Height of Wall: 18 ft. Bar Size of Temp. Reinf. #4 Shr./Temp. Reinforcement

Elastic Modulus of GFRP, Ef 6,500 ksi, 8,700 ksi

Design Tensile Strength, ffd 75.6 ksi, 105 ksi

Minimum Area of S/T Reinf.

2 As = 0.29 in /ft 2 Af,6500 ksi = 0.58 in /ft 2 Af,8700 ksi = 0.55 in /ft

26/91 Deflections

• AASHTO does not allow deflection control by indirect method (e.g., specifying minimum thickness of a member) • Direct method of limiting computed deflections:

✓ Simplified: Effective moment of inertia, Ie ✓ Direct integration of moment curvature relationship Curvature 훿2푦 푀 휙 = = 훿푥2 퐸퐼

Deflection x 푀 푘푤푙3 푦 = ඵ 푑푥 = 퐸퐼 퐸퐼

27/91 Deflections: Effective Inertia

Short-Term Loading

The overall (equivalent) flexural stiffness, EcIe, of a member that has experienced cracking at service varies between EcIg an EcIcr

Ie 퐼푐푟 퐼푒 = ≤ 퐼푔 AASHTO (2.6.3.2-1) Ig 2 푀푐푟 퐼푐푟 1 − 훾푑 1 − 푀푎 퐼푔 퐼 푔 AASHTO (2.6.3.4.2-2 푀푐푟 = 푓푟 푦푡 & 2.6.3.4.2-3)

Ic,t 푀푐푟 훾푑 = 1.72 − 0.72 푀푎 Mcr Ma

Ma = maximum moment in a member at the stage deflection is computed, kip-in

28/91 Long-Term Deflection

The long-term deflection can be calculated from:

Δ(푐푝+푠ℎ) = 휉 Δ𝑖 푠푢푠

= short term deflection due to sustained load (DL + 0.2LL) x = time dependent factor for sustained

load, 2nf Unless a more exact determination is made, long-term deflection may be:

• If instantaneous deflection is based on I : 4.0 g AASHTO GFRP (2.6.3.4.2) • If instantaneous deflection is based on Ie: 3.0

29/91 Table of Contents

• General Considerations

• Bending Moment Capacity

• Serviceability

• Static and Cyclic Fatigue

• Anchorage and Development

• Special Considerations

• Concluding Remarks

30/91 Static Fatigue (Creep Rupture)

FRP reinforcing bars subjected to sustained load can suddenly fail after a time period called endurance time. This phenomenon is known as creep rupture (or static fatigue) Sustained Load

Creep stages in an FRP unidirectional Sustained Load composite

31/91 Creep Rupture Reduction Factor

AASHTO GFRP-1 AASHTO GFRP-2 ∗ 2009 2018 풇풇,풔 = 푪푬푪푪풇풇풖 Design of bridges Design of bridges Creep rupture may govern the CC = 0.20 CC = 0.30 design of bridge

Deck of the Halls River Bridge in Homosassa (FL)

32/91 State-of-the-art in Creep Rupture

Research shows how current limits are conservative and may be raised as technology advances

→ +50% From 0.20 to 0.46 using guaranteed unconditioned line

Sustained load versus logarithmic time-to-failure Sustained Load

33/91 Creep Rupture Provision

Maximum sustained tensile stress in GFRP reinforcement, ffs, calculated using dead loads and live loads included in Service I load combination with live load reduced from 1.0 to 0.2

푓푓푠 ≤ 퐶푐푓푓푑 maximum sustained tensile stress in (AASHTO 2.5.3-1) GFRP reinforcement, ksi where

푛푓푑(1 − 푘) 푓푓푠 = 푀푠,푠 (AASHTO 2.5.3-2) 퐼푐푟

Creep rupture reduction factor, Cc, shall be equal to 0.3 unless manufacturer can provide a research report following ASTM D7337

34/91 Creep Rupture Stress

Based on elastic analysis and the ec fc kd C=1/2 f bkd sustained moment, Ms,s, c d 푛푓푑(1 − 푘) 푓푓,푠 = 푀푠,푠 퐼푐푟 e f T=Af ff b Where:

ff,s = stress level induced in the FRP by sustained loads, psi (AASHTO 2.5.3-1)

Ms,s = the moment due to all sustained loads

퐸푓 푛푓 = modular ratio 퐸푐 3 2 푏푑 푘 = 2휌 푛 + 휌 푛 − 휌 푛 퐼 = 푘3 + 푛 퐴 푑2 1 − 푘 2 푓 푓 푓 푓 푓 푓 푐푟 3 푓 푓

35/91 Cyclic Fatigue

The maximum tensile stress in the GFRP reinforcement, ff,f, shall satisfy: ∗ 푓푓,푓 ≤ 퐶푓퐶퐸푓푓푢=퐶푓푓푓푑 where:

푛푓푑(1 − 푘) (AASHTO 2.5.4) 푓푓,푓 = 푀푠,푓 퐼푐푟

Cf = fatigue rupture reduction factor (set at 0.25 pending future research) ffd = design tensile strength of GFRP reinforcing bars (Eq. 2.4.2.1-1) (ksi) nf = modular ratio (Ef/Ec) d = distance from the extreme compression fiber to centroid of tensile bar (in.) k = ratio of depth of neutral axis to reinforcement depth 4 Icr = moment of inertia of transformed cracked section (in )

Ms,f = moment due to dead loads + fatigue load

36/91 Table of Contents

• General Considerations

• Bending Moment Capacity

• Serviceability

• Static & Cyclic Fatigue

• Anchorage and Development

• Special Considerations

• Concluding Remarks

37/91 Anchorage Introduction

P P

Region with flexural cracks P P ffu at this point

푇 = 퐴푓푓푓푢

Can ffu be developed in the available length?

38/91 Development Length of Straight Bars

GFRP development length is typically longer compared to steel and is a function of the tensile stress in the bar

푓 훼 푓푟 − 340 푓′ 푙 ≥ max 푐 푑 ; 20푑 푑 퐶 푏 푏 AASHTO (2.9.7.4.1-1) 13.6 + where 푑푏

α = 1.5 for top bars and 1.0 for bottom bars

ffr = the required reinforcing stress C = the lesser of the clear cover or ½ the center to center bar spacing

Note: the value of C/db is limited to a max of 3.5

bar-cover bar-bar

39/91 Development Length of Bent Bars

“Standard hook” consists of the hook itself plus a straight length.

Development length for a hooked bar (ldh) is measured as shown:

ldh

dbend 2 Af ffu

Back of hook Point at which ffu is developed The following expression is recommended: 푑 63.2 푏 푓표푟 푓 ≤ 75 푘푠𝑖 ′ 푓푑 푓푐 푓푓푑 푑푏 푙 = 푓표푟 75 푘푠𝑖 < 푓푓푑 ≤ 150 푘푠𝑖 AASHTO (2.9.7.4.3.1) 푑ℎ 1.2 푓′ 푐 푙 ≥ 12푑 푑 푑ℎ 푏 126.4 푏 푓표푟 푓 ≥ 150 푘푠𝑖 ′ 푓푑 푓푐 푙푑ℎ ≥ 9 𝑖푛

40/91 Splices

Types of splices currently possible with GFRP bars ✓ Lap Splice

Mechanical Splice (Coupler)

Splicing GFRP bars by mechanical connections is not permitted unless the full tensile capacity of the GFRP bar is achieved as substantiated by tensile test data per ASTM D7205

41/91 Lap Splices

Lap Splices: Two overlapping bars, possibly tied together; staggered to reduce congestion; must overlap by required lap length

42/91 Tension Lap Splices

AASHTO spec requires staggered splices to provide redundancy

Clear spacing Lapped bar (typ.)

Clear spacing of lap-spliced bars for

determination of lst for staggered splices Minimum splice length: No splice class distinction l calculated to 1.3푙푑 d For GFRP splices: 푙 = ቊ AASHTO (2.9.7.6) 푠푡 12 𝑖푛 provide 25% tensile force

43/91 Table of Contents

• General Considerations

• Bending Moment Capacity

• Serviceability

• Static & Cyclic Fatigue

• Anchorage and Development

• Special Considerations

• Concluding Remarks

44/91 Special Considerations

Multiple layers and/or differing types of bars AASHTO (2.6.3.2.4)

• Due to linear-elastic behavior of FRP, multiple layers cannot be lumped together e C C • Stresses need to be computed at each individual layer e f1 Ff1 F < F f3 fu e F f3 f3

Moment Redistribution AASHTO (1.3)

• Plastic hinges shall not be assumed

• Moment redistribution should not be considered

45/91 Compression Reinforcement

• FRP has a lower compression strength and stiffness than tensile equivalent properties. Difficult to measure, but higher than concrete

• Any FRP bar in compression should be ignored in design calculations and substituted with an equivalent area of

concrete (nf = 1 in compression) AASHTO Article 1.3

46/91 Table of Contents

• General Considerations

• Bending Moment Capacity

• Serviceability

• Static & Cyclic Fatigue

• Anchorage and Development

• Special Considerations

• Concluding Remarks

47/91 Concluding Remarks

• Flexural capacity of FRP-reinforced flexural member dependent on tension or compression failure • FRP reinforcement is brittle, but provides failure warning in terms of member deflection • Serviceability requirements may govern design. Allowable stresses under sustained or cyclic loading must be checked • FRP can be placed in compression zones but not be considered in calculations • Reduced bond properties affect development length and crack control

48/91 Questions?

Thank FLEXURE RESPONSE OF GFRP REINFORCED CONCRETE 2.1 Review Questions: Fundamentals Review Questions

2.1.1) The substitution of GFRP for steel on an equal area basis would typically result in: ______. a. No difference b. Larger deflections and wider crack widths c. Wider crack widths d. Larger deflections

51/91 Moment-Curvature Diagrams

120 b b h d Areinf. (in.) (in.) (in.) (in2) (1) (3) 100 8 15 12.5 0.93 (2) 8 15 12.5 1.32 (3) 10 18 15.5 1.2 h d

80 ft) - Areinf.

(2) 60 (1)

Mn

Moment (kip Moment 40

(1) Steel-tension controlled 20 (2) GFRP-concrete crushing (3) GFRP-FRP rupture 0 0 0.0002 0.0004 0.0006 0.0008 0.001 0.0012 0.0014 Curvature (rad/in)

52/91 Review Questions

53/91 Review Questions

2.1.2) When designing structures with FRP the preferred failure mode in flexure is: ______. a. FRP rupture b. Concrete crushing c. None – it is not safe to design with FRP d. Debonding between reinforcement and concrete

54/91 Failure Modes

Compression-controlled: concrete crushing Concrete Crushing w

b e  cu f c b  c 1 c 0.85b1 f c bc d N.A Af e ff A f f f f

b1 c = a

55/91 Review Questions

2.1.2) When designing structures with GFRP the preferred failure mode in flexure is: ______. a. GFRP rupture b. Concrete crushing c. None – it is not safe to design with GFRP d. Debonding between reinforcement and concrete

56/91 Review Questions

2.1.3) In GFRP-RC flexural design the safety factor is increased (Φ is reduced): ______. a. To account for the design of over-reinforced members b. To consider the long-term behavior c. To consider the lack of ductility d. Because a member governed by GFRP bar rupture will have a brittle failure

57/91 Strength Reduction Factors (AASHTO)

Controlled by Concrete  Crushing Limit State

0.75 Compression- 0.55 Tension Controlled Transition Controlled (Concrete Crushing) (GFRP Rupture)

0.8ε ε ε fd fd ft

0.55 푓표푟 휀푓푡 ≤ 휀푓푑 휀푓푡 휙 = 1.55 − 푓표푟 0.80휀푓푑 < 휀푓푡 < 휀푓푑 휀푓푑 (AASHTO 2.5.5.2) 0.75 푓표푟 휀푓푡 ≥ 0.80휀푓푑

58/91 Review Questions

59/91 Review Questions

2.1.4) A member governed by GFRP bar rupture will have a brittle failure: ______. a. True b. False

60/91 Failure Modes

FRP Rupture Failure in GFRP Reinforced Beam

61/91 Review Questions

2.1.4) A member governed by GFRP bar rupture will have a brittle failure: ______. a. True b. False

62/91 Review Questions

2.1.5) For the flexural design of GFRP-RC members which of the following assumptions is false: a. Plane sections remain plane after deformation b. Tensile strength of concrete is not neglected c. Stress-strain of FRP is linear until failure d. FRP is completely bonded to concrete

63/91 Flexural Theory

Assumptions: 1. Plane sections remains plane after deformation 2. Ultimate concrete strain is 0.003 3. Tensile strength of concrete is neglected

4. FRP is perfectly bonded to concrete For AASHTO example 5. Stress-strain of FRP is linear until failure Ultimate Flexural Strength: 푀푢 = 1.25푀퐷퐶 + 1.75푀퐿퐿 Mn = nominal capacity For ACI example Mu = factored capacity 휙푀푛 ≥ 푀푢

 = strength reduction factor (depends on the mode of failure) 푀푢 = 1.2푀퐷 + 1.6푀퐿

64/91 Review Questions

65/91 Review Questions

2.1.6) Tension lap splice for GFRP bars is: ______. a. The same as the development length of the bar b. 1.25 times the development length of the bar c. 1.30 times the development length of the bar d. 1.60 times the development length of the bar

66/91 Tension Lap Splices

AASHTO specification requires staggered splices to provide redundancy

Clear spacing Lapped bar (typ.)

Clear spacing of lap-spliced bars for determination of ld for staggered splices No splice class distinction Minimum splice length:

ld calculated to 1.3푙푑 For GFRP splices: 푙푠푡 = ቊ provide 25% AASHTO (2.9.7.6) 12 𝑖푛 tensile force

67/91 Review Questions

68/91 Review Questions

2.1.7) When designing with GFRP the load factors are: ______. a. Higher than the ones used when designing steel RC b. Lower than the ones used when designing steel RC c. The same as the ones used when designing steel RC d. Not defined yet

69/91 Load Factors

AASHTO Table 3.4.1-1

Load factors are applicable with inclusion of new creep rupture limit state and load factors. ퟏ. ퟐ푫푳 + ퟎ. ퟐ푳푳

70/91 Review Questions

2.1.7) When designing with FRP the load factors are: ______. a. Higher than the ones used when designing steel RC b. Lower than the ones used when designing steel RC c. The same as the ones used when designing steel RC d. Not defined yet

71/91 Review Questions

2.1.8) The purpose of shrinkage/temperature reinforcement is: ______. a. Distribute load b. Improve development capacity of GFRP c. Control crack width d. Reduce member thickness

72/91 Shrinkage & Temperature Reinforcement

GFRP reinforced retaining wall example:

Properties

Width of Wall Average: 13.38 inches Height of Wall: 18 feet Bar Size of Temp. Reinf. 4 Shr./Temp. Reinforcement

Elastic Modulus of GFRP, Ef 6500 ksi, 8700 ksi

Design Tensile Strength, ffd 75.6 ksi, 105 ksi

Minimum Area of S/T Reinf.

2 As = 0.29 in /ft 2 Af,6500 ksi = 0.58 in /ft 2 Af,8700 ksi = 0.55 in /ft

73/91 Review Questions

2.1.8) The purpose of shrinkage reinforcement is: ______. a. Distribute load b. Improve development capacity of FRP c. Control crack width d. Reduce member thickness

74/91 FLEXURE RESPONSE OF GFRP REINFORCED CONCRETE 2.2 Design Example: Flat Slab Flat Slab vs. Deck Type

Flat Slab Deck

Girders

Longitudinal Bars Provide Transverse Bars Provide Flexural Resistance Flexural Resistance

76/91 Objectives

• Demonstrate the design of a FLAT SLAB bridge superstructure utilizing method prescribed by AASHTO

89’-1”

44’-61/2” 44’-61/2”

10’-0” 2 Lanes @ 12’-0” 8’-0” 8’-0” 2 Lanes @ 12’-0” 10’-0” Shoulder Shoulder Shoulder Shoulder ℄ Const.

Typical Section

Magnified Cross-Section • Show calculations with emphasis on flexural design for positive moment

77/91 Analysis of Flexural Member with GFRP

Given Af, d, b, ffd No FRP 퐴 푓푓 < 푓푓푑 Determine 휌 = 푓 Rupture 푏푑 Yes 휀푐푢 푐 = 푑 Concrete Crushing Calculate stress in GFRP reinforcement 휀푐푢 + 휀푓푑 at nominal flexural resistance:

2 퐴푓푓푓 퐸 휀 0.85훽 푓′ 푓 푐푢 1 푐 푎 = 훽 푐 푎 = ′ 푓푓 = + 퐸푓휀푐푢 − 0.5퐸푓휀푐푢 ≤ 푓푓푑 1 푏 0.85푓 푏 4 휌푓 푐

푎 푎 푀 = 퐴 푓 푑 − 푀 = 퐴 푓 푑 − Check to see if 푛 푓 푓푑 2 푛 푓 푓 2 GFRP has ruptured

78/91 Analysis of Flexural Member with GFRP

Determine the Resistance Factor

Yes 휀푓푡 ≤ 0.80휀푓푑 휙 = 0.75

휀푓푡 Yes 휙 = 1.55 − 0.80휀푓푑 ≤ 휀푓푡 < 휀푓푑 휀푓푑 No Calculate 휙푀푛 휙 = 0.55

End

79/91 Context

80/91 GFRP Slab Design

Bridge Geometry

Dimension of Bridge in Front View

35’ 35’ 35’

1st Span 2nd Span rd 1’ 6” 3 Span

1’ 6” 1’ 6” 1’ 6” 1’ 6”

Overall bridge length = 105 ft

Bridge design span length = 35 ft Ideal span range: up to 40 ft

81/91 GFRP Reinforcement Properties

Geometric Properties Primary Reinforcement

푡푠푙푎푏 = 18 𝑖푛푐ℎ푒푠 thickness of slab 퐵푎푟푆𝑖푧푒푠푙푎푏.푝푟 = 10

푏 = 12 𝑖푛푐ℎ푒푠 design strip width 퐵푎푟푆푝푎푐푒푠푙푎푏.푝푟 = 4 𝑖푛푐ℎ푒푠

퐶표푣푒푟 = 2 𝑖푛푐ℎ푒푠 cover for GFRP members Secondary Reinforcement Effective Depth of Reinforcement 퐵푎푟푆𝑖푧푒푠푙푎푏.푠푒푐 = 6 1.27𝑖푛 푑푓푙.푠푙푎푏 = 18𝑖푛 − 2𝑖푛 − = 15.9 𝑖푛푐ℎ푒푠 퐵푎푟푆푝푎푐푒 = 8 𝑖푛푐ℎ푒푠 2 푠푙푎푏.푠푒푐

Primary Secondary Reinforcement Reinforcement

Slab Thickness

82/91 Dead & Live Load Analysis

Dead Load Moments Maximum positive moment and corresponding fatigue values

Strength I 푀푠푡푟1.푝표푠 = 100.9 푘𝑖푝 − 푓푡

Service I 푀푠푒푟1.푝표푠 = 64.6 푘𝑖푝 − 푓푡

Live Load 푀푙𝑖푣푒퐿표푎푑.푝표푠 = 39.6 푘𝑖푝 − 푓푡 Only Strength I & Service I Live Load Moments Maximum negative moment and corresponding fatigue values Strength I 푀푠푡푟1.푛푒푔 = 93.2 푘𝑖푝 − 푓푡

Service I 푀푠푒푟1.푛푒푔 = 61.9 푘𝑖푝 − 푓푡

Live Load Only 푀푙𝑖푣푒퐿표푎푑.푛푒푔 = 39.6 푘𝑖푝 − 푓푡

83/91 Check Primary Reinforcement

Positive Moment Region – Flexural Strength at Support

′ 푓푐 = 4,500 푝푠𝑖 concrete compressive strength

′ 훼1 = max 0.75,0.85 − 0.02 푓푐 − 10 = 0.90 [AASHTO BDS 5.6.2.2]

훽1 = 0.85 − 0.05 4.5푘푠𝑖 − 4푘푠𝑖 = 0.83 [AASHTO BDS 5.6.2.2]

Area of primary reinforcement per linear foot

12𝑖푛 퐴 = 1.27𝑖푛2 = 3.8 𝑖푛2 area of GFRP reinforcement per 푓푙.푠푙푎푏 4𝑖푛 foot of negative moment Reinforcement Ratio

2 퐴푓 3.8𝑖푛 휌 = = = 0.02001 푓 푏 ∙ 푑 (1푓푡)(15.9𝑖푛)

84/91 Check Primary Reinforcement

′ 푏 = 12" 훼1푓푐 εft 훽1푐 퐶 훽 푐 2 푐

c 1

9" .

15 n.

= a. 푑

푓푓 푇푓 εfd

Strain Concrete Strain GFRP Stress Force Effective strength in GFRP reinforcements at strength limit state

2 ′ 퐸푓휀푐푢 0.85훽1푓푐 푓푓 = + 퐸푓휀푐푢 − 0.5퐸푓휀푐푢 4 휌푓

(6500푘푠𝑖 ∙ 0.003) 0.85 0.83 4.5 = + (6500 푘푠𝑖)(0.003) − 0.5(6500푘푠𝑖)(0.003) = 46.6푘푠𝑖 4 0.02001 compression 푓푓 = min 푓푓, 푓푓푑 = min 46.6푘푠𝑖, 54.1푘푠𝑖 = 52.3푘푠𝑖 푓푓 < 푓푓푑 controlled

85/91 Calculate Resistance Factor

푏 = 12" GFRP strain check

푓푓 52.3푘푠𝑖 휀 = = = 0.00716 푓푡 9"

퐸푓 6500푘푠𝑖 .

= 푑 푓푓푑 54.1푘푠𝑖 휀푓푑 = = = 0.00833 퐸푓 6500푘푠𝑖

Section Calculate Resistance Factor for Flexural Strength (GFRP)

0.75 𝑖푓 휀푓푡 ≤ 0.80휀푓푑 휀푓푡 ≤ 0.00667 휀 휙 = 푓푡 1.55 − 𝑖푓 0.80휀푓푑 < 휀푓푡 < 휀푓푑 0.00667 ≤ 휀 ≤ 0.00833 휀푓푑 푓푡 0.55 표푡ℎ푒푟푤𝑖푠푒

휙 = 0.69

86/91 Check Primary Reinforcement

푏 = 12"

2 퐴푓푓푓 (3.8𝑖푛 )(52.3푘푠𝑖) 푎 = ′ = = 3.9𝑖푛

0.85푓푐 푏 0.85(4500푝푠𝑖)(12𝑖푛)

15 = Calculate corresponding moment 푑

푎 푀푛 = 퐴푓푓푓푑 푑 − 2 Section 3.9𝑖푛 푀 = 3.8𝑖푛2 46.6푘푠𝑖 15.9𝑖푛 − = 205.9푘 − 푓푡 푛 2

푀푟 = 휙푀푛 = 0.69 224.3푘 − 푓푡 = 142.1푘 − 푓푡

푀푠푡푟1.푝표푠 퐷푒푚푎푛푑/퐶푎푝푎푐𝑖푡푦: 푀표푚푒푛푡2.푠푙푎푏 = = 0.71 푀푟.2.푠푙푎푏

87/91 2.3 Design Example Creep Rupture (Flat Slab) Creep Rupture Limit State

Creep Rupture Limit State

푀1.푐푟푒푒푝.푠푙푎푏 = 50.7푘 − 푓푡 Sustained loads only 퐸 6500푘푠𝑖 2.0 3 ′ 2 푓 퐸푐 = 120,000Φ푙𝑖푚푒푟표푐푘푤푐 푓푐 ∙ 푘푠𝑖 = 4165푘푠𝑖 푛 = = = 1.6 퐸푐 4165푘푠𝑖

푘 = 2푝푛 − 푝푛 2 − 푝푛 = 2 0.02 − 0.02 ∙ 1.6 2 − 0.02 1.6 = 0.2

푏푑3 퐼 = 푘3 + 푛퐴푠푡 푑 − 푘푑 2 = 푐푟 3 12𝑖푛 15.9𝑖푛 3 = 0.2 3 + 1.6 3.8𝑖푛2 15.9𝑖푛 − 0.2 ∙ 15.9𝑖푛2 2 = 1108𝑖푛4 3 푛 ∙ 푑푓1.푠푙푎푏(1 − 푘1.푠푙푎푏) 푓푓1.푐푟푒푒푝 = ∙ 푀1.푐푟푒푒푝.푠푙푎푏 = 11.3푘푠𝑖 퐼푐푟

퐶푐퐶퐸푓푓푢 = 퐶푐푓푓푑 = (0.3)(54.1푘푠𝑖) 퐶푐푓푓푑 = 16.2푘푠𝑖

89/91 2.4 Design Example Minimum Reinforcement (Flat Slab) Minimum Reinforcement

′ 푓푟 = 0.24 푓푐.푠푢푝푒푟 ∙ (푘푠𝑖) = 0.51푘푠𝑖 Concrete Modulus of rupture

푡3 Uncracked concrete 푆 = 푠푙푎푏 푏 = 648𝑖푛3 푟 6 section modulus

푀푐푟.푠푙푎푏 = 1.6푓푟푆푟 = 44.0푘 − 푓푡 Slab cracking moment

푀푚𝑖푛.푠푙푎푏 = min 1.33푀푠푡푟1.푝표푠, 푀푐푟.푠푙푎푏 = 44.0푘 − 푓푡 Minimum required factored flexural resistance

푀푟.푠푙푎푏 = min 푀푟.푝표푠, 푀푟.푛푒푔 = 142.1푘 − 푓푡 Flexural capacity of slab

퐶ℎ푒푐푘푀𝑖푛푅푒𝑖푛푓푠푙푎푏 = 𝑖푓(푀푟.푠푙푎푏 ≥ 푀푚𝑖푛.푠푙푎푏, "OK","No Good")

퐶ℎ푒푐푘푀𝑖푛푅푒𝑖푛푓푠푙푎푏 = "푂퐾"

91/91 AASHTO GFRP- Reinforced Concrete Design Training Course AASHTO GFRP- Reinforced Concrete Design Training Course Course Outline

1. Introduction & Materials

2. Flexure Response

3. Shear Response

4. Axial Response

5. Case Studies & Field Operations

1/60 3. SHEAR RESPONSE OF GFRP REINFORCED CONCRETE Table of Contents

• General Behavior

• Shear Capacity

• Punching Shear

• Special Considerations

• Concluding Remarks

3/60 Uncracked Section

In uncracked sections, shear is carried by the concrete itself

Typically, shear crack starts from a flexural crack once the cracking moment exceeds the cracking strength of concrete (tensile rupture)

4/60 Cracked Section

In cracked sections, shear is carried by complex transfer mechanisms ≈ d cot θ

Stirrup Vcc Vcc : Compression Zone Contribution

d Vd : Dowel Action

Vca : Aggregate V Long. Reinf. ca Interlock Vcr Vcr : Residual Tensile Strength of Concrete V = A f Vd f f fv Vf : GFRP Stirrup Contribution

Vsupport Components of Shear Resistance in Structural Concrete Beams

5/60 Shear Failure

Shear failure modes of members with FRP stirrups

• Shear-tension failure mode (controlled by the rupture of FRP shear reinforcement)

• Shear-compression failure mode (controlled by the crushing of the concrete web)

6/60 RC with FRP Shear Reinforcement

• Low modulus of elasticity • High tensile strength and no yield point • Tensile strength of the bent portion lower than the straight portion • Low transverse shear resistance (i.e., low dowel action of flexural bars) • Larger crack widths compared to steel (i.e., lower N.A. depth)

Substitution of FRP for steel on an equal area basis would typically result in lower shear strength in both shear reinforced and non- shear reinforced members

7/60 Table of Contents

• General Behavior

• Shear Capacity

• Punching Shear

• Special Considerations

• Concluding Remarks

8/60 Shear Capacity

Ultimate Limit State 푉푢 ≤ 휙 푉푛 휙 = 0.75

Nominal Shear Resistance 푉푛 = 푉푐 + 푉푓

′ Shear Resistance of Concrete 푉푐 = 0.0316훽 푓푐 푏푣푑푣 (AASHTO 2.7.3.4-1)

퐴푓푣 푓푓푣 푑푣 co푡(휃) Shear Resistance of GFRP 푉 = 푓 푠 Stirrups (AASHTO 2.7.3.5-1)

β and θ are function of the level of strain in the reinforcement (MCFT*), but align to θ ACI values if the simplified method is used. *Modified Compression Field Theory

9/60 Factor β and θ

β: Factor indicating ability of diagonally cracked concrete to transmit tension and shear θ: Angle of inclination of diagonal compressive stresses

• Simplified Method 훽 = 5푘 휃 = 45° (AASHTO 2.7.3.6.1)

2 : ratio of depth of neutral axis to depth of flexural 푘 = 2휌푓푛푓 + (휌푓푛푓) − 휌푓푛푓 k reinforcement (AASHTO 2.5.3-4)

• General Method 휃 = 29 + 3500휀푓 (AASHTO 2.7.3.6.2-3) 4.8 -Sections with minimum transverse reinforcement 훽 = (AASHTO 2.7.3.6.2-1) 1 + 750휀푓 4.8 51 -Sections without minimum transverse reinforcement 훽 = (AASHTO 2.7.3.6.2-2) 1 + 750휀푓 39 + 푠푥푒

휀푓: longitudinal tensile strain of the GFRP 푠푥푒: crack spacing as influenced by aggregate size (AASHTO 2.7.3.6.2-7)

10/60 Transverse Reinforcement

Types of Transverse Reinforcement

• Stirrups or ties

• Spirals or hoops

Shear resistance of FRP reinforcement when using spirals

퐴푓푣 푓푓푣 푑푣 푐표푡휃 + 푐표푡훼 푠푖푛훼 푉 = (AASHTO 2.7.3.5) 푓 푠 S: Pitch of spiral 훼: Angle of inclination of transverse reinforcement to longitudinal axis 휃: Angle between a strut and the longitudinal axis of a member

11/60 Design Tensile Strength

Design Tensile Strength for Shear 풇풇,풔풅

푓푓,푠푑 = 푚푖푛(푓푓푣, 푓푓푏, 푓푓푑) (AASHTO 2.7.3.5)

Tensile Strength of GFRP for Shear Design

푓푓푣 = 0.004퐸푓 ≤ 푓푓푏  Typically governs for GFRP Tensile Strength of GFRP at Bends

푟푏 푓푓푏 = 0.05 + 0.3 푓푓푢 ≤ 푓푓푢 푑푏

rb = internal radius of bend of reinforcing bar Tensile Strength of GFRP db = diameter of reinforcing bar ∗ 푓푓푑 = 퐶퐸푓푓푢  FDOT 932-3 requires this to > 60% of straight bars for qualification

12/60 Transverse Reinforcement 휙푉 ➢ For any member required when: 푉 > 푐 푢 2

➢ Except for the slabs and footings: 푉푢 > 휙푉푐 Minimum GFRP Transverse Reinforcement 푏푣푠 (AASHTO 2.7.2.4-1) 퐴푓푣,푚푖푛 ≥ 0.05 푓푓푣 Maximum GFRP Transverse Reinforcement

′ (AASHTO 2.7.2.5) 푉푓 ≤ 0.25 푓푐 푏푣푑푣

Maximum Spacing of Transverse Reinforcement

푆 ≤ 푀푖푛 {0.5푑 , 24 푖푛. } (AASHTO 2.7.2.6)

13/60 FRP Stirrups

• GFRP stirrups should be provided with 90-degree hooks

• Required tail length for GFRP stirrups: Lthf ≥ 12db (AASHTO C2.10.2.3.2)

• Maximum tensile strain in FRP shear reinforcement: 0.004 (AASHTO 2.7.3.5-2) 풓 r = bend radius • A minimum 풃 = 3 is recommended b 풅풃 db=bar diameter

(ASTM D7957)

14/60 Table of Contents

• General Behavior

• Shear Capacity

• Punching Shear

• Special Considerations

• Concluding Remarks

15/60 Punching Shear

Shear Resistance of the Concrete

′ Two-way shear 푉푐 = 0.316푘 푓푐 푏0 푑푣 (AASHTO 2.10.5.1.3)

k: ratio of depth of neutral axis to depth of flexural reinforcement 푑 b : computed away from the column face 0 2

For Members with Transverse Reinforcement

퐴푓푣 푓푓푣 푑푣 푉 = (AASHTO 2.10.5.1.3) 푓 푠

16/60 Table of Contents

• General Behavior

• Shear Capacity

• Punching Shear

• Special Considerations

• Concluding Remarks

17/60 Special Considerations

• 90-degree bends instead of 135-degree

• Typically two overlapping “C or U” stirrups are used instead of a closed loop stirrup

Set of overlapping closed ties to enclose all bars

Crosstie

18/60 Special Considerations

• Field bending or straightening of GFRP bars not possible

• All stirrups are pre-bent

19/60 Table of Contents

• General Behavior

• Shear Capacity

• Punching Shear

• Special Considerations

• Concluding Remarks

20/60 Concluding Remarks

• Shear equations and structural theory remain mostly the same as for conventional steel-RC • The contribution of both concrete and stirrups to shear capacity is reduced in FRP-RC • Closer stirrup spacing because of lower strength and stiffness • Strength of FRP stirrups is reduced at bends • A limit on FRP stirrup strain is imposed because of crack width concerns • Complex bent shapes are currently not available, but technology is advancing

21/60 Questions?

Thank SHEAR RESPONSE OF GFRP REINFORCED CONCRETE 3.1 Review Questions: Fundamentals Review Questions

3.1.1) For GFRP stirrups, does the maximum amount of transverse reinforcement requirement similar to steel-RC still apply: ______. a. True b. False

24/60 Transverse Reinforcement 휙푉 ➢ Required when: 푉 > 푐 푢 2 ➢ For the slabs and footings: 푉푢 > 휙푉푐

Minimum GFRP Transverse Reinforcement 푏푣푠 퐴푓푣,푚푖푛 ≥ 0.05 푓푓푣 Maximum GFRP Transverse Reinforcement

′ (AASHTO 2.7.2.5) 푉푓 ≤ 0.25 푓푐 푏푣푑푣

Maximum Spacing of Transverse Reinforcement

푆 ≤ 푀푖푛 {0.5푑 , 24푖푛. } (AASHTO 2.7.2.6)

25/60 Review Questions

3.1.1) For GFRP stirrups, does the maximum amount of transverse reinforcement requirement similar to steel-RC still apply: ______. a. True b. False

26/60 Review Questions

3.1.2) The shear strength of GFRP-RC members: ______. a. Is comparable to the shear strength of steel-RC members b. Is lower than the shear strength of steel-RC members c. Is higher than to the shear strength of steel-RC members d. Cannot be compared to the shear strength of steel-RC members

27/60 Shear Capacity

Ultimate Limit State 푉푢 ≤ 휙 푉푛 휙 = 0.75

Nominal Shear Resistance 푉푛 = 푉푐 + 푉푓

′ Shear Resistance of Concrete 푉푐 = 0.0316훽 푓푐 푏푣푑푣 (AASHTO 2.7.3.4)

퐴푓푣 푓푓푣 푑푣 co푡(휃) Shear Resistance of GFRP 푉 = (AASHTO 2.7.3.5) 푓 푠 Stirrups

β and θ are a function of the level of strain in the reinforcement θ (MCFT) but aligns to ACI values if the simplified method is used

28/60 Review Questions

29/60 Review Questions

3.1.3) The required tail length of GFRP stirrups is at least equal to or more than: ______. a. 4 times the bar diameter b. 8 times the bar diameter c. 12 times the bar diameter d. 16 times the bar diameter

30/60 FRP Stirrups

• GFRP stirrups should be provided with 90-degree hooks

• Required tail length for GFRP stirrups: Lthf ≥ 12db (AASHTO C2.10.2.3.2)

• Maximum tensile strain in FRP shear reinforcement: 0.004 (AASHTO 2.7.3.5-2)

풓풃 rb= bend radius • A minimum = 3 is recommended d =bar diameter 풅풃 b

(ASTM D7957)

31/60 Review Questions

32/60 Review Questions

3.1.4) GFRP stirrups can be bent on site with EOR approval? a. True b. False

33/60 Special Considerations

• Field bending or straightening of GFRP bars not possible

• All stirrups are pre-bent

34/60 Review Questions

3.1.4) GFRP stirrups can be bent on site with EOR approval? a. True b. False

35/60 Review Questions

3.1.5) The minimum bent radius allowed for a GFRP stirrup is generally ______. (Select all that apply) a. Larger than required for steel, with a minimum of rb/db = 3 b. Can be equivalent to steel, if verified by manufacturer c. Smaller than required for steel reinforcement due to lower elastic modulus d. Dependent on field bending and cannot be prescribed

36/60 FRP Stirrups

• GFRP stirrups should be provided with 90-degree hooks

• Required tail length for GFRP stirrups: Lthf ≥ 12db (AASHTO C2.10.2.3.2)

• Maximum tensile strain in FRP shear reinforcement: 0.004 (ACI 440.1R8.3)

풓풃 rb= bend radius • A minimum = 3 is recommended d =bar diameter 풅풃 b

(ASTM D7957)

37/60 Review Questions

3.1.5) The minimum bent radius allowed for a GFRP stirrup is generally ______. (Select all that apply) a. Larger than required for steel, with a min. of rb/db = 3 b. Can be equivalent to steel, if verified by manufacturer c. Smaller than required for steel reinforcement due to lower elastic modulus d. Dependent on field bending and cannot be prescribed

38/60 Review Questions

3.1.6) When designing GFRP shear reinforcement, the following shapes are possible to manufacturer: ______. (Select all that apply) a. Two C’s b. Two U’s c. Closed stirrup, providing the tails overlap d. L shapes for end hooks e. Special bends for complex shapes

39/60 Special Considerations

• 90-degree bends instead of 135-degree

• Typically two overlapping “C or U” stirrups are used instead of a closed loop stirrup.

Set of overlapping closed ties to enclose all bars

Crosstie

40/60 Applied Questions

3.1.6. When designing GFRP shear reinforcement, the following shapes are possible to manufacturer: ______. (Select all that apply) a. Two C’s b. Two U’s c. Closed stirrup, providing the tails overlap d. L shapes for end hooks e. Special bends for complex shapes

41/60 Review Questions

3.1.7) The maximum spacing of transverse GFRP reinforcement is generally ______. a. 12 in. b. 24 in. c. 0.5d d. Minimum value of 0.5d* or 24in.

* Flexural reinforcement depth

42/60 Transverse Reinforcement 휙푉 ➢ Required when: 푉 > 푐 푢 2

➢ For the slabs and footings: 푉푢 > 휙푉푐 Minimum GFRP Transverse Reinforcement 푏푣푠 퐴푓푣,푚푖푛 ≥ 0.05 푓푓푣 Maximum GFRP Transverse Reinforcement

′ (AASHTO 2.7.2.5) 푉푓 ≤ 0.25 푓푐 푏푣푑푣

Maximum Spacing of Transverse Reinforcement

푆 ≤ 푀푖푛 {0.5푑 , 24푖푛. } (AASHTO 2.7.2.6)

43/60 Review Questions

3.1.7) The maximum spacing of GFRP transverse reinforcement is generally ______. a. 12 in. b. 24 in. c. 0.5 d d. Minimum value of 0.5d* or 24in.

*Flexural reinforcement depth

44/60 SHEAR RESPONSE OF GFRP REINFORCED CONCRETE 3.2 Design Example: Bent Cap (Halls River Bridge) Shear Design Flowchart

Shear Design

Find nominal shear resistance of the concrete (Vc)

Find shear strength of transverse reinforcement (ff,sd)

46/60 Shear Design Flowchart

Find design tensile strength of GFRP (ffd)

Find design tensile strength of bent (ffb)

Find tensile strength of GFRP for shear design (ffv)

47/60 Shear Design Flowchart

Select 퐴푓푣 ≥ 퐴푓푣.푚푖푛

Find shear resistance of GFRP (Vf)

Find nominal shear strength

48/60 Shear Design Flowchart

Check shear design

Check spacing of GFRP stirrups

Finish

49/60 Bent Cap- Halls River Bridge

Part 1: Load Generator

Part 2: Frame Analysis

Part 3: Design & AASHTO Checks

50/60 Bent Cap- Halls River Bridge

Part 1: Load Generator Input Data Number of beams 9 Number of columns 6 Beam spacing 6.63 ft. Column spacing 10.38 ft. Beam width 24 in. Column width 18 in. Beam height 21 in. Beam self weight 181 plf.

51/60 Bent Cap- Halls River Bridge

Part 1: Load Generator

Input Data Backwall Cap height 36 in. Cap width 48 in. Cap length 59.9 ft.

Dead load of wearing surfaces and utilities 165 lb./ft.

Additional dead load of structural and nonstructural attachments 20 lb./ft.

52/60 Part 1: Load Generator

Bridge cross section with live load locations generated by MathCad program

Beam Live Loads

53/60 Part 1: Load Generator

Summary of factored loads on cap generated by Mathcad Mathcad worksheet computes all loads on the bent cap from the beam reactions. Live loads are generated for each beam using the lever rule and tributary area methods

Factored total load Factored total load Load cases per LRFD parallel to cap (x) perpendicular to cap (z)

54/60 Part 2: Frame Analysis

Connection of columns to bent cap (Fixed or Pinned) Fixed Beam load Distributed

55/60 Part 2: Frame Analysis

Shear and Moment Diagrams for Limit State Strength I (max vertical load)

56/60 Part 3: GFRP Design & AASHTO Checks

Environmental reduction factor (CE) 0.7 Tensile modulus of elasticity (Ef) 6,500 ksi Shear Reinforcement Zone V1 Zone V2 Size of stirrup bar 4 Size of stirrup bar 4 No. of bar legs 4 No. of bar legs 4 Spacing 4 in. Spacing 8 in. Length of Zone V2 (Lv2) 36 in. Length of Zone V1 (Lv1) 36 in.

57/60 Part 3: GFRP Design & AASHTO Checks

Zone V3 Size of stirrup bar 4 No. of bar legs 4 Spacing 12 in.

Zone V4 (Cap overhang) Size of stirrup bar 4 No. of bar legs 4 Spacing 12 in.

Length of Zone V4 (Lv4) 36 in.

Zone V5 (Cap overhang) Size of stirrup bar 4 No. of bar legs 4 Spacing 12 in.

58/60 Shear Design Example

Nominal Shear Resistance of the Concrete

′ 푉푐 = 0.0316훽 푓푐 푏푣푑푣 = 64.75 kip

Simplified method for concrete sections not subjected to axial tension 훽 = 5푘 (AASHTO 2.7.3.6.1)

Shear Resistance of GFRP Reinforcement

퐴푓푣 푓푓푣 푑푣 co푡(휃) 푉 = = 137 푘푖푝 푓 푠 The Maximum Demand to Capacity Ratio

푽풖 푉푢 = 162 푘푖푝 풎풂풙 = ퟏ. ퟎퟕ 푽풓 푉푟 = 0.75 (64.75 + 137) = 151푘푖푝

59/60 Shear Design Example

Problem areas

Maximum demand to capacity ratio = 1.07

60/60 AASHTO GFRP- Reinforced Concrete Design Training Course AASHTO GFRP- Reinforced Concrete Design Training Course Course Outline

1. Introduction & Materials

2. Flexure Response

3. Shear Response

4. Axial Response

5. Case Studies & Field Operations

1/75 4. AXIAL RESPONSE OF GFRP REINFORCED CONCRETE Table of Contents – Axial & More

• Strength of GFRP-RC Columns • Design Considerations

• P-M Diagram Example

• Slenderness Effect

• Concluding Remarks

3/75 Design Codes

Only US guide/code including compression members

AASHTO GFRP 1st Ed. AASHTO GFRP 2nd Ed. (No provisions included) (Provisions included)

4/75 Introduction – Pure Compression

P Review of Steel-RC Columns

′ 푃표 = 푃푐 + 푃푠 = 0.85푓푐 퐴푔 − 퐴푠 + 푓푦퐴푠

Basic Concept for GFRP-RC Columns

′ 푃표 = 푃푐 + 푃푓 = 0.85푓푐 퐴푔 − 퐴푓 + 푓푓퐴푓

(AASHTO GFRP 2.6.4.2)

As reported in Afifi et al. (2014) and Mohamed et al., (2014), mechanical properties of GFRP in compression exceed those of concrete and GFRP bar loaded in compression therefore, equivalency could be assumed (Deitz, Harik, and Gesund, 2003)

5/75 Axial Loading Failure Modes

Column test at NIST 12-in Tie Spacing 3-in Tie Spacing

Behavior of Full-Scale Concrete Columns Internally Reinforced with Glass FRP Bars under Pure Axial Load (De Luca, et al., 2009)

6/75 Axial Loading Failure Modes

GFRP-RC Columns After Failure Circular Concrete Columns with GFRP Longitudinal Bars, Hoops, or Spirals under Axial Loads (University of Sherbrooke; courtesy of Prof. Brahim Benmokrane)

7/75 Factored Compressive Resistance - AASHTO

Factored Pure Compressive Resistance - AASHTO

푃푟 = 휙푃푛 (AASHTO GFRP 2.6.4.2-1)

• For members with spiral or hoop reinforcements

′ 푃푛 = 0.85 0.85푓푐 퐴푔 − 퐴푓 (AASHTO GFRP 2.6.4.2-2) • For members with tie reinforcement

′ 푃푛 = 0.80 0.85푓푐 퐴푔 − 퐴푓 (AASHTO GFRP 2.6.4.2-3)

2 Af = area of GFRP reinforcement (in ) 2 Ag = gross area of section (in ) f’c = specified compressive (ksi) Pn = nominal axial resistance, without flexure (kips) Pr = factored axial resistance, without flexure (kips)

8/75 Factored Tensile Resistance - AASHTO

Factored Pure Tensile Resistance - AASHTO

(AASHTO GFRP 2.6.6.2-1) 푃푟 = 휙푃푛 in which:

푃푛 = 푓푓푑퐴푓 (AASHTO GFRP 2.6.6.2-2)

푓푓푑 = 퐶퐸푓푓푢 (AASHTO GFRP 2.4.2.1-1) where: 2 Af = area of GFRP reinforcement (in ) ffd = design tensile strength of GFRP reinforcing bars considering reductions for service environment (ksi)

Pn = nominal axial resistance (kip)

9/75 Table of Contents

• Strength of GFRP-RC Columns

• Design Considerations

• P-M Diagram Example

• Slenderness Effect

• Concluding Remarks

10/75 Design Considerations

Minimum & Maximum Longitudinal Reinforcement Minimum and maximum area of the longitudinal GFRP reinforcing shall be:

0.01 ≤ 퐴푓/퐴푔 ≤ 0.08 AASHTO GFRP 4.5.6

Provision adopted for GFRP-RC are analogous to Steel-RC design provisions in AASHTO & ACI Limit on Maximum Tensile Strain in GFRP To avoid strains that lead to unacceptable deformation and loss of stiffness of the column (Jawaheri & Nanni, 2013):

휀푓푑 = min(휀푓푢, 0.010) and 푓푓푑 = min(푓푓푢, 0.010퐸푓)

11/75 Design Considerations

Limits on maximum spacing of Transverse Reinforcement: confinement, buckling of longitudinal reinforcement L L

Lower elastic modulus than steel

AASHTO GFRP 4.7.5.4 – Tied Members Theoretical: 푙푒푎푠푡 푑𝑖푚푒푛푠𝑖표푛 표푓 푐표푙푢푚푛 푠푚푎푥 ≈ 14푑푏 푠푚푎푥 = 푚𝑖푛 ቐ푑/4 12 𝑖푛푐ℎ푒푠

12/75 Table of Contents

• Strength of GFRP-RC Columns

• Design Considerations

• P-M Diagram Example

• Slenderness Effect

• Concluding Remarks

13/75 Context

GFRP Cage Assembly, Casting and Installation of RC Piles

14/75 Combined P-M Failure Modes

Rectangular Concrete Column Failure with GFRP Bars and Ties (Guérin et al., 2018) GFRP-Columns After Failure

Compression Side Side View Tension Side

15/75 Developing P-M Interaction Diagram

Schematic P-M diagram for two identical columns having the same amounts of GFRP and steel reinforcement. Include the following five points. Note location of balance point for GFRP-RC

16/75 Developing P-M Interaction Diagram

Create a P-M interaction diagram for the following tied column section: f’ = 5,000 psi 18” c Ef = 6,500 ksi Ec= 4,291 ksi ffd = 59.2 ksi εfd = 0.00911 12 - #8 GFRP bars evenly spaced

18” Include the following points: • Pure compression • Zero tension • Pure flexure Equivalent FDOT standard index non-prestressed • Balance point • Pure tension 18”x18”, 12 GFRP bars

17/75 Developing P-M Interaction Diagram

Pure Compression Strain in GFRP reinforcement cannot exceed the strain maximum strain in concrete (0.003). Contribution of GFRP in compression is difficult assess, show zero and non-zero contribution

Strain Stress Force b 0.003 0.85f’c

εf1 ff1 Cs1 = Af1 ff1 d1 Cs2 = Af2 ff2 εf2 ff2 d2 C.L. Cc

εf3 ff3 Cs3 = Af3 ff3 d3 Cs4 = Af4 ff4 εf4 ff4 d4

18/75 Developing P-M Interaction Diagram

Pure Compression b 0.003 Cf1 = Af1 ff1

εf1 3” Cf2 = Af2 ff2 ε 7” C.L. f2 Cc εf3 11” Cf3 = Af3 ff3

εf4 15” Cf4 = Af4 ff4

Moment at this point: 푀 = 0 푘 − 𝑖푛 Should we add this term?

′ Capacity in pure compression: 푃 = ퟎ. ퟖퟓ풇풄 푨품 − 푨풇 + 퐴푓,푡표푡(휀푐푢퐸푐)

2 2 푪풄 = 0.85 5푘푠𝑖 324𝑖푛 − 9.48𝑖푛 = ퟏퟑퟑퟕ 풌 (AASHTO GFRP 2.6.4.2)

19/75 Developing P-M Interaction Diagram

Discussion on contribution of GFRP in Compression

• Current AASHTO provisions do not account for GFRP compression contribution • Force up to 0.003 compressive strain times a stiffness conservatively equal to that of concrete is appropriate • For pure compression: 퐴푓,푡표푡(휀푐푢퐸푐)

20/75 Developing P-M Interaction Diagram

Adding the compressive component of GFRP reinforcement (휀푓 = 0.003) 18" − 0" 퐶 = 4 0.79𝑖푛2 ퟒퟐퟗퟏ풌풔풊 0.003 = 40.7푘 푓1 18" 18" − 0" 퐶 = 2 0.79𝑖푛2 ퟒퟐퟗퟏ풌풔풊 0.003 = 20.3푘 푓2 18" 18" − 0" 퐶 = 2 0.79𝑖푛2 ퟒퟐퟗퟏ풌풔풊 0.003 = 20.3푘 푓3 18" 18" − 0" 퐶 = 4 0.79𝑖푛2 ퟒퟐퟗퟏ풌풔풊 0.003 = 40.7푘 푓4 18" Adding all forces: 푃 = 1337푘 + 40.7푘 + 20.3푘 + 20.3푘 + 40.7푘 = ퟏퟒퟓퟗ 풌

9% increase over current AASHTO equation

21/75 Developing P-M Interaction Diagram

Next point: Zero tension on the extreme GFRP bar layer

Pure Compression Zero Tension

Compression

(Mn, Pn) GFRP reinforced

Pure Flexure Tension Balance Point M

Pure Tension

22/75 Developing P-M Interaction Diagram

Zero Tension Point where there is zero tension in the bottom reinforcement layer

Strain Stress / Force b 퐶 = 훼 훽 푓′푐푏 εcu = 0.003 푐 1 1 푐

εf1 d1 a C.L. εf2 c d2

εf3

d3 N.A. εf4 =0

23/75 Developing P-M Interaction Diagram

Zero Tension 푐 = 푑 neutral axis Strain at bottom GFRP reinforcement layer is zero GFRP bars in compression are treated as concrete

푇푓4 = 0 푘𝑖푝 Zero tension

Calculate the force in concrete

′ ′ 퐶푐 = 푏 ∙ 푎 훼1푓푐 = 푏 ∙ 훽1푐 훼1푓푐 = (18𝑖푛 ∙ 0.80 ∙ 15𝑖푛)(0.85)(5푘푠𝑖) = 918푘𝑖푝

Calculate the axial force

푃 = ෍ 퐹 = 퐶푐 = 918푘

24/75 Developing P-M Interaction Diagram

Zero Tension (Continued) Calculate distance of forces from center line and then solve using for moment

훽 푐 푦 = 푦 − 1 Concrete level: 퐶푐 푁.퐴. 2 0.8 15𝑖푛 = 9𝑖푛 − = 3𝑖푛 Cc 2 푦퐶푐 th 4 Level: 푦푓4 = 푑4 − 푦푁.퐴. = 15𝑖푛 − 9𝑖푛 = 6𝑖푛

푦푓4

Taking moments Tf4=0

푀 = 푦퐶푐퐹퐶푐 + 푦푓4푇푓4 = 918푘 3𝑖푛 + 0푘 6𝑖푛 = 229 푘 − 푓푡

25/75 Developing P-M Interaction Diagram

Next point: Pure flexure (P= zero)

Pure Compression Zero Tension

Compression

(Mn, Pn) GFRP reinforced

Pure Flexure Tension M Balance Point

Pure Tension

26/75 Developing P-M Interaction Diagram Pure Flexure Pure flexure occurs when axial load is zero and the failure mode is governed by concrete crushing (potentially also by GFRP failure depending on cross-section) Strain Stress Force ′ b 퐶푐 = 훼훽1푓푐 푐푏 εcu = 0.003 f’c

N.A. c d1

휀푓2 ff2 Tf2 d2 C.L. 휀 f 푓3 f3 Tf3 d3 휀 푓4 ff4 Tf4 d4

푇푓 = 퐴푓휀푓퐸푓

27/75 Developing P-M Interaction Diagram

Pure Flexure

푃 = ෍ 퐹 = 퐶푐 + 푇푓2 + 푇푓3 + 푇푓4 = 0푘

Calculate forces in terms of c, and then solve by imposing horizontal equilibrium 푐 − 7𝑖푛 푇 = 2 ∙ 0.79𝑖푛2 6500푘푠𝑖 0.003 푓2 푐

푐 − 11𝑖푛 푇 = 2 ∙ 0.79𝑖푛2 6500푘푠𝑖 0.003 푓3 푐

푐 − 15𝑖푛 푇 = 4 ∙ 0.79𝑖푛2 6500푘푠𝑖 0.003 푓4 푐

28/75 Developing P-M Interaction Diagram

퐶푐 = 0.85 0.8 5푘푠𝑖 18𝑖푛 푐 = 61.2푐 Solving for c: 푐 − 7 푇 = 30.8 푓2 푐 푐 − 11 푇 = 30.8 푓3 푐 푐 − 15 푇 = 61.6 푓4 푐 Substituting into equilibrium equation: 푐 − 7 푐 − 11 푐 − 15 30.8 + 30.8 + 61.6 + 61.2푐 = 0 푐 푐 푐 c = 4.01𝑖푛.

29/75 Developing P-M Interaction Diagram

Pure Flexure (Continued)

Calculate the Moment: Sum moments around center line Concrete lever arms: Summing Moments Around Center 훽 푐 0.8 4.01𝑖푛 푦 = 푦 − 1 = 9𝑖푛 − = 7.4𝑖푛 퐶푐 푁.퐴. 2 2 C 푦 c 푦푓2 = 푦푁.퐴. − 푑2 = 9𝑖푛 − 7𝑖푛 = 2𝑖푛 퐶푐 푦푓2 Tf2 푦 푦푓3 = 푑3 − 푦푁.퐴. = 11𝑖푛 − 9𝑖푛 = 2𝑖푛 푓3 푦푓4 Tf3

푦푓4 = 푑4 − 푦푁.퐴. = 15𝑖푛 − 9𝑖푛 = 6𝑖푛 Tf4

푀 = 푦퐶푐퐶푐 + 푦푓2푇푓2 + 푦푓3푇푓3 + 푦푓4푇푓4 = 231 푘 − 푓푡

30/75 Developing P-M Interaction Diagram Next point: Balance failure, simultaneous GFRP rupture and concrete crushing. Design failure strain in GFRP about 5 times larger than yield strain for Grade 60 steel

31/75 Developing P-M Interaction Diagram

Balance Point: strain, stress and force distribution (equivalent stress block)

Strain Stress Force

′ b 퐶푐 = 훼1훽1푓푐 푐푏 εcu = 0.003 f’c c N.A. d1 f f2 Tf2 d2 C.L. ff3 Tf3

ff4 Tf4 d4 푓푓푑 휀f푑 = = 0.00911 푇푓 = 퐴푓휀푓퐸푓 퐸푓

32/75 Developing P-M Interaction Diagram

Balance Point

Strain Stress Force b ′ εcu = 0.003 f’c 퐶푐 = 훼1훽1푓푐 푐푏 c d N.A. d1=3”; d2=7”; 1 d 2 C.L. d3=11”; d4=15” d3 f f4 Tf4 d4 푓푓푑 휀f푑 = = 0.00911 푇푓 = 퐴푓휀푓퐸푓 퐸푓

휀푐푢 Find the neutral axis: 푐 = 푑 휀푓푑 + 휀푐푢 0.003 푐 = 15𝑖푛 = 3.72𝑖푛 0.00911 + 0.003

33/75 Developing P-M Interaction Diagram

Calculate GFRP strain and stresses: Second layer GFRP strain 푐 − 푑 3.72𝑖푛 − 7𝑖푛 휀 = 휀 2 = 0.003 = −0.00265 푓2 푐푢 푐 3.72𝑖푛

푓푓2 = 퐸푓휀푓2 = 6500푘푠𝑖 −0.00265 = −17.2 푘푠𝑖 Third layer GFRP strain 푐 − 푑 3.72𝑖푛 − 11𝑖푛 휀 = 휀 3 = 0.003 = −0.00588 푓3 푐푢 푐 3.72𝑖푛

푓푓3 = 퐸푓휀푓3 = 6500푘푠𝑖 −0.00588 = −38.2 푘푠𝑖 Fourth layer GFRP strain 푐 − 푑 3.72𝑖푛 − 15𝑖푛 휀 = 휀 4 = 0.003 = −0.00911 푓4 푐푢 푐 3.72𝑖푛

푓푓4 = 퐸푓휀푓4 = 6500푘푠𝑖 −0.00911 = −59.2 푘푠𝑖 = 퐟퐟퐝

34/75 Developing P-M Interaction Diagram

Balance Point (Continued) Calculate the Forces:

′ 퐶푐 = 푏 ∙ 푎 훼1훽1푓푐

퐶푐 = 18𝑖푛 ∙ 0.85 ∙ 3.72𝑖푛 0.8 5푘푠𝑖 = 277.5푘

푃 = ෍ 퐹 = 퐶푐 + 푇푓2 + 푇푓3 + 푇푓4

Sum forces by multiplying GFRP stress by areas

푃 = 277.5푘 − 17.2푘푠𝑖 1.58𝑖푛2 −(38.2푘푠𝑖)(1.58𝑖푛2) − 59.2푘푠𝑖 3.16𝑖푛2

P= −47.1푘 Balance point occurs when axial load is tension

35/75 Developing P-M Interaction Diagram

Calculate the Moment: Sum moments around section centerline Concrete and GFRP bars lever arms: 훽 푐 0.8 3.72𝑖푛 푦 = 푦 − 1 = 9𝑖푛 − = 7.5𝑖푛 퐶푐 푁.퐴. 2 2

Cc 푦푓2 = 푦푁.퐴. − 푑2 = 9𝑖푛 − 7𝑖푛 = 2𝑖푛 푦 퐶푐 푦푓2

푦푓3 = 푑3 − 푦푁.퐴. = 11𝑖푛 − 9𝑖푛 = 2𝑖푛 푦푓3 푦푓4 Tf3 푦푓4 = 푑4 − 푦푁.퐴. = 15𝑖푛 − 9𝑖푛 = 6𝑖푛 Tf4

Summing Moments Around Center Line

푀 = 퐶푐푦퐶푐 − 푦푓2푇푓2 + 푦푓2푇푓3 + 푦푓4푇푓4 = 241 푘 − 푓푡

36/75 Developing P-M Interaction Diagram

Next point: Pure axial tension. There is no concrete contribution

Pure Compression Zero Tension

Compression

(Mn, Pn) GFRP reinforced

Pure Flexure Tension Balance Point M

Pure Tension

37/75 Developing P-M Interaction Diagram

Zero Moment (Tension) The first point is tension only, so the concrete is assumed to not contribute

Strain Stress Force b Cc = 0 T = A f ε s1 f1 fd1 f1 ffd1 d1 T = A f ε s2 f2 fd2 C.L. f2 ffd2 d2 Ts3 = Af3 ffd3 ε f3 ffd3 d3 Ts4 = Af4 ffd4 εf4 ffd4 d4

휀푓 = 휀푓푑

38/75 Developing P-M Interaction Diagram

Zero Moment (Tension) b Cc = 0 ε Ts1 = Af1 ffd1 f1 ffd1 d1 T = A f ε s2 f2 fd2 C.L. f2 ffd2 d2 Ts3 = Af3 ffd3 ε f3 ffd3 d3 Ts4 = Af4 ffd4 εf4 ffd4 d4 휀푓 = 휀푓푑 Calculate force components assuming all GFRP bars rupture

푃 = ෍ 퐹 = 퐹푓1 + 퐹푓2 + 퐹푓3 + 퐹푓4

푃 = 12 0.79𝑖푛2 59.2푘푠𝑖 = 561.1푘𝑖푝 M= 0푘𝑖푝 − 푓푡

39/75 AASHTO Resistance Factor for GFRP

Controlled by Concrete Controlled by FRP f Crushing Limit State Rupture Limit State

0.75 0.55 Compression- Tension Controlled Transition Controlled (Concrete Crushing) (GFRP Rupture)

0.8ε ε ε fd fd ft

The safety factor Φ needs to be calculated for each moment-axial load combination (as each P-M point has a different stress in tension reinforcement)

40/75 Developing P-M Interaction Diagram

Limiting the factored compressive load: 0.85 = spiral or hoop reinforcement 0.80 = tie reinforcement 2 2 푃푛,.푚푎푥 = 0.80 0.85(5푘푠𝑖) 324𝑖푛 − 9.48𝑖푛

푃푛,.푚푎푥 = 1070.6푘𝑖푝

Point Mn Pn φ φMn φPn Pure 0 k-ft 1070 k 0.75 0 k-ft 802 k Compression Zero Tension 229 k-ft 918 k 0.75 172 k-ft 689 k Pure 231 k-ft 0 k 0.64 148 k-ft 0 k Moment Balance Point 241 k-ft -47 k 0.55 133 k-ft -26 k Pure Tension 0 k-ft -561 k 0.55 0 k-ft -309 k

41/75 Developing P-M Interaction Diagram

P-M Diagram for factored Unfactored P-M diagram for and unfactored values different assumptions on GFRP compression contribution

42/75 Table of Contents

• Strength of GFRP-RC Columns

• Design Considerations

• P-M Diagram Example

• Slenderness Effect

• Concluding Remarks

43/75 Slenderness Effect

Slender Columns As column bends, there is an out-of-plane deflection P (Δ). Δ will cause second-order moment

푀2푛푑 표푟푑푒푟 = 푃∆

Δ This second-order moment is in addition to any other moment applied to the column and decreases the strength of the overall column

By definition, a column is considered slender when this second order moment decreases the capacity by more than 5%

푃푙표푛푔 P Criterion ≤ 0.95 푃푠ℎ표푟푡

44/75 Determination of EI

Flexural stiffness, EI, ad effective length, kL, are the parameters determining the slenderness effect

GFRP-RC columns are affected more by slenderness due to smaller EI

Jawaheri & Nanni, 2017 offer both simplified and detailed expressions for EI analogous to ACI 318-14:

0.2퐸푐퐼푔 Simplified 퐸퐼 = + 0.03퐸푐퐼푔 1 + 훽푑푛푠

0.2퐸 퐼 푃푢,푠푢푠푡푎𝑖푛푒푑 Detailed 푐 푔 where 훽푑푛푠 = 퐸퐼 = + 0.75퐸푓퐼푓 푃푢 1 + 훽푑푛푠

45/75 Design Considerations

Slenderness Ratio P Mirmiran et al., 2001 showed that, for GFRP-RC columns not braced against side-way, the limit should be reduced to 17

(a) Sway permitted L

푘퐿 푘퐿 H ≤ 22 (ACI 318-14) ≤ ퟏퟕ 푟 푟

(b) Braced L

푘퐿 푀 푘퐿 푀1 1 (ACI 318-14) ≤ ퟐퟗ + 12 ≤ ퟑퟎ ≤ 34 + 12 ≤ 40 푟 푀 푟 푀2 2

M1/M2 is negative if column is bent in single curvature, and positive P for double curvature

46/75 Alignment Charts

The coefficient k can be determined through the use of alignment charts based on relative stiffness of framing members

ψA and ψB are found based upon members framing into joint

휑퐴

퐸퐼 σ 퐿 휑 = 푐표푙푢푚푛 𝑖 퐸퐼 σ 퐿 푏푒푎푚

휑퐵

(a) Nonsway Frames (b) Sway Frames

47/75 Determination of EI

For GFRP reinforced concrete members, stiffness of restraining members needs approximation. Values are provided below in the table

휑퐴

퐸퐼 σ 퐿 휑 = 푐표푙푢푚푛 𝑖 퐸퐼 σ 푚 퐿 푏푒푎푚

휑퐵 Approved by ACI 440 committee adapting Bischoff (2017) for expected range of reinforcing ratios and elastic modulus. Jawaheri, H. & Nanni, A., (2017) provide further information.

48/75 Table of Contents

• Strength of GFRP-RC Columns

• Design Considerations

• P-M Diagram Example

• Slenderness Effect

• Concluding Remarks

49/75 Concluding Remarks

• Elastic modulus of GFRP in compression matches that of concrete (conservative assumption) • Transverse reinforcement spacing affected by smaller elastic modulus of GFRP • Minimum longitudinal GFRP reinforcement ratio for columns same as for steel • P-M diagram can be constructed using similar procedure as for steel-RC columns • GFRP-RC not appropriate for seismic application

50/75 Questions?

Thank AXIAL RESPONSE OF GFRP REINFORCED CONCRETE 4.1 Review Questions: Fundamentals Applied Question

4.1.1) The compressive capacity of GFRP reinforcement ______. a. Is used to improve ductility b. Is used to satisfy maximum strain requirements of AASHTO c. Is not considered for low loads d. Can be used in design up until a concrete strain of 0.003

53/75 Introduction

P Review of Steel RC Columns

′ 푃표 = 푃푐 + 푃푠 = 0.85푓푐 퐴푔 − 퐴푠 + 푓푦퐴푠

Basic Concept for GFRP RC Columns

′ 푃표 = 푃푐 + 푃푠 = 0.85푓푐 퐴푔 − 퐴푠 + 푓푦퐴푠

As reported in reference, the mechanical properties of GFRP exceed those of concrete and therefore, equivalency can be

assumed. GFRP bar loaded in compression (Deitz, Harik, and Gesund, 2003)

54/75 Applied Question

55/75 Applied Question

4.1.2) Compared to steel reinforced columns, the transverse spacing requirements for GFRP reinforced columns are the same.

a. True

a. False

56/75 Design Considerations

Limits on Maximum Spacing of Transverse Reinforcement: confinement, buckling of longitudinal reinforcement L L

Lower elastic modulus than steel

Theoretical: AASHTO 4.7.5.4 – Tied Members 푙푒푎푠푡 푑𝑖푚푒푛푠𝑖표푛 표푓 푐표푙푢푚푛 푠푚푎푥 ≈ 14푑푏 푠푚푎푥 = 푚𝑖푛 ቐ푑/4 12 𝑖푛푐ℎ푒푠

57/75 Applied Question

4.1.2) Compared to steel reinforced columns, the transverse spacing requirements for GFRP reinforced columns are the same.

a. True

b. False

58/75 Applied Question

4.1.3) Compared to steel reinforced columns, the ultimate tensile capacity is reduced.

a. True

b. False

59/75 Developing P-M Interaction Diagram

Schematic P-M diagram for two identical columns having the same amounts of GFRP and steel reinforcement

P Pure Compression FRP strain on one side = 0

Pure Compression Zero Tension Zero Tension

Compression (Mn, Pn) steel reinforced (Mn, Pn) GFRP reinforced Balance Point

Pure Moment

Tension Pure Moment Balance Point M Pure Tension

Pure Tension

60/75 Applied Question

4.1.3) Compared to steel reinforced columns, the ultimate tensile capacity is reduced.

a. True

b. False

61/75 Applied Question

4.1.4) When constructing a moment-interaction diagram for a GFRP reinforced column, the balance points refers to: ______. a. The point at which the GFRP reinforcement yields and concrete crushes b. The point at which the GFRP reinforcement ruptures and concrete crushes c. The point at which the GFRP reinforcement yields before concrete crushes d. The point at which the concrete crushes, but the GFRP reinforcement has not ruptured.

62/75 Developing P-M Interaction Diagram

Balance Point Balance point is when concrete crushes and tension reinforcement ruptures simultaneously. (Since there is no yielding of GFRP) Strain Stress Force

′ b 퐶푐 = 훼1훽1푓푐 푐푏 εcu = 0.003 f’c

d1 d - c N.A. d2 C.L.

ff3 Tf3 d3 c

ff4 Tf4 d4 푓푓푑 휀f푑 = 푇푓 = 퐴푓휀푓퐸푓 퐸푓

63/75 Applied Question

64/75 Applied Question

4.1.5) When designing a slender GFRP reinforced column, special considerations should be made to determining slenderness ratio and EI?

a. True

b. False

65/75 Determination of EI

Effect of Creep Jawaheri & Nanni, 2017 offer both simplified and detailed expressions analogous to ACI 318-14:

0.2퐸푐퐼푔 Simplified 퐸퐼 = + 0.03퐸푐퐼푔 1 + 훽푑푛푠

0.2퐸 퐼 푃푢,푠푢푠푡푎𝑖푛푒푑 Detailed 푐 푔 where 훽푑푛푠 = 퐸퐼 = + 0.75퐸푓퐼푓 푃푢 1 + 훽푑푛푠

66/75 Applied Question

4.1.5) When designing a slender GFRP reinforced column, special considerations should be made to determining slenderness ratio and EI?

a. True

b. False

67/75 AXIAL RESPONSE OF GFRP REINFORCED CONCRETE 4.2 Design Example: Solider Pile in Wing Wall Pile Example

Consider the following example:

GFRP-RC Piles

69/75 Pile Example

EL = 7.77 ft

Soil Properties 훾 = 110 푝푐푓 MHW = 0.31 ft 휙 = 30 푑푒푔푟푒푒푠

EL = -3.5 ft 푐 = 0 푘푠푓

Cross Section

70/75 Pile Example

푃푐푎푝 = 푃𝑖푙푒 푆푝푎푐𝑖푛푔 × 퐶푎푝퐻푒𝑖푔ℎ푡 × 퐶푎푝푊𝑖푑푡ℎ × 훾푐

퐷𝑖푠푡푟𝑖푏푢푡푒푑 퐹표푟푐푒 = 푅푒푠푢푙푡푎푛푡 퐸푎푟푡ℎ 푃푟푒푠푠푢푟푒 × 푃𝑖푙푒 푆푝푎푐𝑖푛푔

71/75 Pile Example

P Laterally Loaded Pile Model cap

p-z spring Ground Surface

t-z spring

Q-z spring

72/75 Pile Example

Laterally Loaded Pile Results

Shear Moment Axial Lateral Deflection 10 10 10 10

5 5 5 5

0 0 0 0

-5 -5 -5 -5

-10 -10 -10 -10

Elevation(ft) Elevation(ft) Elevation(ft) Elevation(ft)

-15 -15 -15 -15

-20 -20 -20 -20

-25 -25 -25 -25 -30 -20 -10 0 10 20 30 -150 -75 0 75 150 -100 -75 -50 -25 0 -0.4 -0.2 0.0 0.2 0.4 Shear (kips) Moment (kip-ft) Axial (kips) Deflection (in)

Max: 15.3 kip 97.4 kip-ft 87.7 kip 0.301 in Min: -22.9 kip -33.4 kip-ft -63.0 kip -0.037 in

73/75 Pile Example

Plotting Demand Point in P-M Diagram

74/75 Questions? AASHTO GFRP- Reinforced Concrete Design Training Course Course Outline

1. Introduction & Materials

2. Flexure Response

3. Shear Response

4. Axial Response

5. Case Studies & Field Operations

1/57 5. CASE STUDIES & FIELD OPERATIONS Table of Contents – Case Studies

• iDock (Marine Dock) • NE 23rd Avenue Bridge over Ibis Waterway (FPN 434359-1-52-01) • Halls River Bridge (HRB) (FPN 430021-1-52- 01) • SR-A1A Flagler Beach (Segment 3), (FPN 440557-7-52-01) • FDOT Fast Facts

3/57 iDock Construction Intent - Miami, Florida

• Replacement of hurricane Irma- damaged dock with GFRP-RC precast concrete components, CIP BFRP- RC continuity pour and GFRP gratings • Provide a demo prototype for precast-concrete dock modular-system, that exhibits extended durability and resilience to extreme events

4/57 Traditional vs. Innovative Approach

• Traditional: precast steel- PC piles and cast in-place RC caps with timber decking • Innovative: precast modular-units with rapid assembly time with GFRP & BFRP reinforcement to eliminate corrosion-related maintenance and provide higher resistance

5/57 iDock Design

Four-span bridge-type dock with precast GFRP-RC driven piles, GFRP-RC pile- bent caps and slab- beams. Continuity CIP pour with BFRP bars and mesh

6/57 Precast Construction

7/57 Precast Construction

Slab

Pile Cap

Pile

8/57 Precast Construction

9/57 Pile-Driving and Slab Installation

Piles installed in original steel-PC pile locations

Precast Slab-Beam Pile-Driving at iDock installed in sections after cap placement

10/57 iDock Precast Element Installation

11/57 iDock Connections (Cap-Slab)

• GFRP dowel bars (greenish) connecting horizontal to vertical components • BFRP (darker color) bars for flexural continuity • Connection cast in place to interlock precast components and create continuity over the four spans

12/57 Dowels, Placement and Testing

GFRP Dowels Slab-Beam with Grating Cylinder Testing

Placement of Components and Material Testing for Q/A

13/57 Conclusions and Remarks

Components employed for the iDock project: 8 precast GFRP-RC Driven Piles [12x12 in. x 24 ft.] 4 precast GFRP-RC Pile-Bent Caps [12x30 in. x 8 ft.] 8 precast GFRP-RC Slab-Beams [8x33 in. x 10 to 12 ft.]

14/57 Conclusions and Remarks

Primary Benefits Realized/Expected: • FRP reinforcement eliminates the need for deep concrete cover, concrete mixture additives, and waterproofing sealants needed for reinforcement corrosion protection • Lightweight reinforcement allows for significantly lower labor and equipment costs due to ease of handling and transportation savings • Additional owner benefits include an extended service life and significantly reduced maintenance costs

15/57 Table of Contents – Case Studies

• iDock (Marine Dock) • NE 23rd Avenue Bridge over Ibis Waterway (FPN 434359-1-52-01) Under construction • Halls River Bridge (HRB) (FPN 430021-1-52- 01) • SR-A1A Flagler Beach (Segment 3), (FPN 440557-7-52-01) • FDOT Fast Facts

16/57 Ibis Waterway – A No-steel Bridge

• IBIS-Waterway located at Lighthouse Point, Broward County, Florida • Project consists of replacing existing bridge sub- and superstructure, while adding intermediate-bents • Total CFRP-PC and GFRP-RC construction. • First GFRP-RC 3-span continuous flat-slab bridge in Florida • First time use of two experimental partially-prestressed GFRP piles

17/57 IBIS Waterway Bridge Layout

Three-span IBIS-Waterway bridge with CIP flat-slab, CIP caps, precast PC panels and piles

18/57 Production of Experimental GFRP Piles

Partially-prestressed Cutting of GFRP GFRP piles tendons

• 18x18 in. cross- section • 53 ft. long • 12 prestressed #4 GFRP bars • 12 unstressed #8 GFRP bars

Casting of piles at Gate Precast Company in Jacksonville, FL

19/57 Production of Experimental GFRP Piles

#4 GFRP bars (220 ft. long) uncoiled & coupled to 7-wire steel strands to reach length of the prestressing bed (about 430 ft.)

20/57 Pile-Driving in “very dense” Soil Conditions

Initiation of pile driving with needed soil predrilling

Pile alignment via Pile installation template construction challenging due to to allow for FDOT power lines and tight specified tolerances site conditions

21/57 GFRP-RC Intermediate Bent Cap Beams

GFRP cage assemblies with spliced-bars at intermediate pile locations. GFRP bars inspected and lab-tested for Q/A

22/57 GFRP-RC Intermediate Bent Cap Beams

Completing assembly Casting and forming completed and forms stripped

23/57 Learning Outcomes from IBIS Waterway

• Geotechnical challenges at site

• Experimental GFRP partially- prestressed piles successfully fabricated and driven

• Construction progressing as planned

24/57 Table of Contents – Case Studies

• iDock (Marine Dock) • NE 23rd Avenue Bridge over Ibis Waterway (FPN 434359-1-52-01) • Halls River Bridge (HRB) (FPN 430021-1-52- 01) • SR-A1A Flagler Beach (Segment 3) (FPN 440557-7-52-01) • FDOT Fast Facts

25/57 First of a Kind 5-span Bridge

FRP PC/RC Structure • FDOT replacement project / County Owner • Five 37-ft. spans • CFRP-PC piles and sheet piles • GFRP-RC bulkheads, deck and railings • Proprietary girders

26/57 Halls River Bridge

Prototype for Future FRP Bridge-Projects

27/57 Sheet Piles: CFRP-PC/GFRP-RC (FDOT Index D22440)

• CFRP Strands (8 ∅ 0.6 in.) • GFRP Ties (#4 @ 4 in. • C40/45 (12 x 30 in.) • 13 to 26 ft. depth • Cantilever or tied-back

28/57 Bent Caps: GFRP-RC (FDOT Software Bent Cap v1.0)

• GFRP Bars (12 #8 T&B) • GFRP Ties (#5 @ 5 in.) • C38 (48 x 36 in.) • 10 ft. long • Cast-in-place

29/57 Deck: GFRP-RC (AASHTO GFRP 2nd Edition)

• GFRP Bars (Top & Bottom) • Primary: #6 @ 4.5 in. • Secondary: #6 @ 6 in. • C30/37 (8.5 in. depth) • 6.5 ft. girder spacing • Cast-in-place

30/57 Learning Outcomes from Halls River Bridge

- FRP Sub/Superstructure (1st Project) - HSCS/GFRP Hybrid (1st Project) - 100+ Year Service Life - Performance monitoring - Prototype for future FDOT Bridges

31/57 Table of Contents – Case Studies

• iDock (Marine Dock) • NE 23rd Avenue Bridge over Ibis Waterway (FPN 434359-1-52-01) • Halls River Bridge (FPN 430021-1-52-01) • SR-A1A Flagler Beach (Segment 3) (FPN 440557-7-52-01) • FDOT Fast Facts

32/57 Flagler Beach, FL (SR-A1A) Damage & Recovery

33/57 GFRP Design for Secant-Pile Seawall

• 4920-ft. long secant pile seawall

• First FDOT project with about 1.5 million linear feet of GFRP bars

• Secant piles in high chloride content sand, high water table and periodically exposed to salt spray

34/57 GFRP bar site delivery and storage

• Straight bars, bent bars, hoops and toe bent bars

• Site storage and protective measures from elements

35/57 GFRP Bars - Cage Assembly

36/57 GFRP Bars - Cage Assembly

• Cages constructed with 25 #8 GFRP bars, spiral ties and “toe-end”

• GFRP cages were 38-ft. in length

37/57 Guide Wall for GFRP Secant-Piles

Secant-piles installed via guide wall form

Guide wall trench boxes Removal of steel installed to assure pile formwork prior to drilling alignment secant-piles

38/57 Concrete Grouting of GFRP Secant-Piles

Concrete grouting of Secant-piles

1,847 Secant-piles installed. 5,000 linear feet Secant-pile cages delivered to pile-drilling of pile-cap area and ready for installation

39/57 Flagler Beach - GFRP pile cage installation

GFRP cage installation

Auger-cast primary piles 36 in. in diameter and 36 ft. long Secondary piles18 ft. long

40/57 Continuous pile-cap and dune restoration

Pile-cap placement and dune restoration/re- establishment

Project completed in 4½ months

41/57 Aspects of GFRP Use

PROs CONs • Quick installation • Bent-shapes need to be • Light weight pre-fabricated by pultruder • Assembly time savings • No on-site bending of GFRP • “Toe” or “No-Toe” option • “Skin-itching” (protective • GFRP cages remain in- clothes should be worn) place, i.e., “no flotation” • More GFRP than black steel bars are needed

42/57 Learning Outcomes from SR-A1A

• No Secant-Pile cage alterations needed. Installed all 1,847 piles as per design-phase • Quick and reliable installation in soft to medium dense sands • GFRP cage assemblies resulted, in up to 52% time savings over “black steel” • Toe assemblies may be removed in future projects • Less noise pollution through Secant- Pile installation vs. Sheet-Pile installation

43/57 Table of Contents – Case Studies

• iDock (Marine Dock) • NE 23rd Avenue Bridge over Ibis Waterway (FPN 434359-1-52-01) • Halls River Bridge (FPN 430021-1-52-01) • SR-A1A Flagler Beach (Segment 3), (FPN 440557-7-52-01) • FDOT Fast Facts

44/57 www.fdot.gov/structures/innovation

45/57 www.fdot.gov/structures/innovation

Multiple online resources available

46/57 www.fdot.gov/structures/innovation

Fast-Fact sheets for selected FDOT and affiliated projects in Florida (completed and under construction)

47/57

Questions?

Thank AASHTO GFRP- Reinforced Concrete Design Training Course