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AASHTO LRFD Design and Construction Guide Specification for Ultra-High Performance Concrete FHWA-TFHRC Update on Development and Delivery AASHTO CBS T-10 Committee Meeting June 26, 2018 – Burlington, Vermont Ben Graybeal, Ph.D., P.E., Federal Highway Administration, [email protected], (202)493-3122 Rafic G. El Helou, Ph.D., NRC Associate at FHWA-TFHRC, [email protected], (201)493-3482

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AASHTO LRFD Design and

Construction Guide Specification for

Ultra-High Performance Concrete

FHWA-TFHRC Update on Development and Delivery

AASHTO CBS T-10 Committee Meeting

June 26, 2018 – Burlington, Vermont

Ben Graybeal, Ph.D., P.E., Federal Highway Administration,

[email protected], (202)493-3122

Rafic G. El Helou, Ph.D., NRC Associate at FHWA-TFHRC,

[email protected], (201)493-3482

FHWA-TFHRC (Graybeal and El-Helou) AASHTO CBS T-10 Meeting June 26, 2018 2

Objective

Develop a guide specification for the design and construction of structural elements made with UHPC.

Address reinforced concrete and prestressed

concrete, as well as rehabilitation of existing structural

members with UHPC.

AASHTO LRFD Bridge Design

Specifications

Examples of Standalone AASHTO LRFD

Guide Specifications

FHWA-TFHRC (Graybeal and El-Helou) AASHTO CBS T-10 Meeting June 26, 2018 3

Proposed Outline

Section 1: Introduction

Section 2: Material Specifications

Section 3: Design Specifications

Section 4: Construction Specifications

Section 5: Promising Applications

FHWA-TFHRC (Graybeal and El-Helou) AASHTO CBS T-10 Meeting June 26, 2018 4

Proposed Outline

Section 1: Introduction1.1 Scope

2.2 Definitions

2.3 Limitations

2.4 Design Philosophy

Section 2: Material Specifications

Section 3: Design Specifications

Section 4: Construction Specifications

Section 5: Promising Applications

FHWA-TFHRC (Graybeal and El-Helou) AASHTO CBS T-10 Meeting June 26, 2018 5

Definition

• Cement-based composite with optimized gradation of

granular constituents

• Discontinuous pore structure that significantly reduces

permeability compared to conventional concrete

• Discrete steel fiber reinforcement

Portland Cement-Based Supplementary Materials Superplasticizers Fiber Reinforcement

FHWA-TFHRC (Graybeal and El-Helou) AASHTO CBS T-10 Meeting June 26, 2018 6

Definition

What properties constitute a UHPC-class

material for the purpose of this Guide?

FHWA-TFHRC (Graybeal and El-Helou) AASHTO CBS T-10 Meeting June 26, 2018 7

Definition

What properties constitute a UHPC-class

material for the purpose of this Guide?

• Compressive strength ≥ 21.7 ksi (150 MPa)

o ASTM C1856

• Post-cracking sustained tensile strength ≥ 0.70 ksi (5 MPa)

o Direct tension method by Graybeal and Baby, 2013

Direct Tension

Graybeal, B. A., and Baby, F. (2013). “Development of Direct Tension Test Method for Ultra-High-

Performance Fiber-Reinforced Concrete.” ACI Materials Journal, 110(2), 177–186.

FHWA-TFHRC (Graybeal and El-Helou) AASHTO CBS T-10 Meeting June 26, 2018 8

Definition

What properties constitute a UHPC-class

material for the purpose of this Guide?

Chloride Penetration,

ASTM C1856Surface Resistivity,

AASHTO TP95

Freeze-Thaw Resistance,

ASTM C666

• Propose assessment methods to establish durability

performance classes

• Target values for UHPC-class products

Formation Factor Model

Pore Solution Resistivity

Porosity Connectivity

?

FHWA-TFHRC (Graybeal and El-Helou) AASHTO CBS T-10 Meeting June 26, 2018 9

Proposed Outline

Section 1: Introduction

Section 2: Material Specifications2.1 Scope

2.2 Definitions

2.3 Notations

2.4 Testing Fresh Properties

2.5 Testing Mechanical Properties

2.6 Testing Durability Properties

Section 3: Design Specifications

Section 4: Construction Specifications

Section 5: Promising Applications

Testing Mechanical Properties

FHWA-TFHRC (Graybeal and El-Helou) AASHTO CBS T-10 Meeting June 26, 2018 10

Testing Mechanical Properties

Compression Strength• ASTM C39 with modifications in ASTM C1856

Status Modulus of Elasticity and Poisson’s Ratio• ASTM C469 with modifications in ASTM C1856

Creep in Compression• ASTM C512 with modifications in ASTM C1856

Tension Behavior• Graybeal and Baby, 2013

Graybeal, B. A., and Baby, F. (2013). “Development of Direct Tension Test Method for Ultra-High-

Performance Fiber-Reinforced Concrete.” ACI Materials Journal, 110(2), 177–186.

FHWA-TFHRC (Graybeal and El-Helou) AASHTO CBS T-10 Meeting June 26, 2018 11

Direct Tension Testing• Considering including test method in document

• Determines the cracking strength, crack localization strength,

and strain capacity of UHPC materials

• Used to assess tension behavior of five commercially available

UHPCs with typical values published in FHWA-HRT-18-036

• Collaboration ongoing with Iowa DOT pooled fund (1434) to

assess the method through round robin testing

FHWA-HRT-18-036: Properties and Behavior of UHPC-Class Materials

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

0 0.002 0.004 0.006 0.008 0.01

Ax

ial

Str

es

s (

ksi)

Axial Strain (in/in)

First discrete crack

𝒇𝒄𝒓

𝒇𝒄𝒓

𝑬𝒄0.02% strain offset line

Localization

stress/strain

FHWA-TFHRC (Graybeal and El-Helou) AASHTO CBS T-10 Meeting June 26, 2018 13

Proposed Outline

Section 1: Introduction

Section 2: Material Specifications

Section 3: Design Specifications3.1 Scope

3.2 Definitions

3.3 Limitations

3.4 Notation

3.5 Material Models

3.6 Limit States and Design Methodologies

3.7 Design for Flexure and Axial Force Effects

3.8 Design for Shear and Torsion

3.9 Prestressing

3.10 Reinforcement

3.11 Durability

Section 4: Construction Specifications

Section 5: Promising Applications

FHWA-TFHRC (Graybeal and El-Helou) AASHTO CBS T-10 Meeting June 26, 2018 14

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

0 0.002 0.004 0.006 0.008 0.01

Axia

l S

tress

(ksi)

Axial Strain (in/in)

Conventional

Concrete (f 'c = 6 ksi)

Tension Behavior

FHWA-TFHRC (Graybeal and El-Helou) AASHTO CBS T-10 Meeting June 26, 2018 15

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

0 0.002 0.004 0.006 0.008 0.01

Axia

l S

tress

(ksi)

Axial Strain (in/in)

Tension Behavior

First discrete crack

0.02% strain offset line

𝑬𝒄

𝒇𝒄𝒓

𝒇𝒄𝒓

FHWA-TFHRC (Graybeal and El-Helou) AASHTO CBS T-10 Meeting June 26, 2018 16

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

0 0.002 0.004 0.006 0.008 0.01

Axia

l S

tress

(ksi)

Axial Strain (in/in)

Tension Behavior

𝒇𝒄𝒓

𝒇𝒄𝒓

𝒇𝒕𝒖

𝜺𝒕𝒖 𝜺𝒕𝒖

Localization

stress/strain

Ultimate/Localization

stress/strain

𝑬𝒄

First discrete crack

0.02% strain offset line

FHWA-TFHRC (Graybeal and El-Helou) AASHTO CBS T-10 Meeting June 26, 2018 17

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

0 0.002 0.004 0.006 0.008 0.01

Axia

l S

tress

(ksi)

Axial Strain (in/in)

Proposed Tension Models

𝑬𝒄

𝒇𝒄𝒓

𝒇𝒄𝒓

𝒇𝒕𝒖

𝜺𝒕𝒖 𝜺𝒕𝒖

Strain Hardening UHPC

UHPC with pseudo-stress plateau

Localization stress/strain

FHWA-TFHRC (Graybeal and El-Helou) AASHTO CBS T-10 Meeting June 26, 2018 18

Proposed Tension Models• Direct tension test method by Graybeal and

Baby, 2013

• First cracking stress, 𝑓𝑐𝑟0.02 % offset method on stress-strain curve

• Cracking strain limit, 𝛾𝜀𝑐𝑟

• Localization stress, 𝑓𝑡𝑢 , and strain 𝜀𝑡𝑢

𝑓𝑐𝑟

𝛾𝑓𝑐𝑟

𝑓𝑐𝑟

𝛾𝑓𝑐𝑟

𝑐 𝑐

𝑐 𝑐

𝜀𝑐𝑟 𝜀𝑡𝑢 𝜀𝑐𝑟 𝜀𝑡𝑢

𝛾𝜀𝑐𝑟 𝜀𝑡𝑢 𝛾𝜀𝑐𝑟 𝜀𝑡𝑢

T2T1

T3 T4

𝑓𝑡𝑢

𝛾𝑓𝑡𝑢

𝜀

𝜀

𝜀

𝜀

𝑓𝑐𝑟

𝛾𝑓𝑐𝑟

𝑓𝑐𝑟

𝛾𝑓𝑐𝑟

𝑐 𝑐

𝑐 𝑐

𝜀𝑐𝑟 𝜀𝑡𝑢 𝜀𝑐𝑟 𝜀𝑡𝑢

𝛾𝜀𝑐𝑟 𝜀𝑡𝑢 𝛾𝜀𝑐𝑟 𝜀𝑡𝑢

T2T1

T3 T4

𝑓𝑡𝑢

𝛾𝑓𝑡𝑢

𝜀

𝜀

𝜀

𝜀

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

0 0.002 0.004 0.006 0.008 0.01

Ax

ial

Str

es

s (

ksi)

Axial Strain (in/in)

First discrete crack

𝒇𝒄𝒓

𝒇𝒄𝒓

𝑬𝒄0.02% strain offset line

Localization

stress/strain

𝛾𝜀𝑐𝑟 = 𝛾𝑓𝑐𝑟 𝑐

FHWA-TFHRC (Graybeal and El-Helou) AASHTO CBS T-10 Meeting June 26, 2018 19

Compression Behavior

0

5

10

15

20

25

0 0.001 0.002 0.003 0.004 0.005 0.006

Axia

l S

tress

(ksi)

Axial Strain (in/in)

FHWA-TFHRC (Graybeal and El-Helou) AASHTO CBS T-10 Meeting June 26, 2018 20

0

5

10

15

20

25

0 0.001 0.002 0.003 0.004 0.005 0.006

Axia

l S

tress

(ksi)

Axial Strain (in/in)

Proposed Compression Model

𝒇𝒄′

𝜺𝒄′ = 𝜺𝒄𝒖

𝜶𝒇𝒄′

𝜺𝒄𝒆

FHWA-TFHRC (Graybeal and El-Helou) AASHTO CBS T-10 Meeting June 26, 2018 21

Proposed Compression Model

21

𝑓𝑐′

𝑐

𝑓𝑐𝑢

𝜀𝑐𝑢

𝑓𝑐′

𝑐

𝑐

𝜀𝑐

𝑓𝑐′

C1 C2

C3

𝜀𝑐𝑢

𝑐

𝑓𝑐′

C4

𝜀𝑐𝑢

𝜀𝑐𝑢

𝜀𝑐 𝜀

𝜀

𝜀

𝜀

0 50 100 150 200

0

10

20

30

40

50

60

70

80

0

2,000

4,000

6,000

8,000

10,000

12,000

0 5 10 15 20 25 30

Compressive Strength (MPa)

Ela

stic

Mo

du

lus

(GP

a)

Ela

stic

Mod

ulu

s (k

si)

Compressive Strength (ksi)

U-AU-BU-CU-DU-EFigure XX (Graybeal 2007)Figure XX

Properties and Behavior

of UHPC-Class Materials

FHWA-HRT-18-036

• Compressive strength, 𝑓𝑐′, with = 0.85

ASTM C39 with modifications listed in ASTM C1856

• Modulus of Elasticity, 𝑐ASTM C469 with modifications listed in ASTM C1856

Or

𝑐 = 1,460 𝑓𝑐′ (ksi)

FHWA-TFHRC (Graybeal and El-Helou) AASHTO CBS T-10 Meeting June 26, 2018 22

𝑓𝑐′

𝑐

𝑓𝑐𝑢

𝜀𝑐𝑢

𝑓𝑐′

𝑐

𝑐

𝜀𝑐

𝑓𝑐′

C1 C2

C3

𝜀𝑐𝑢

𝑐

𝑓𝑐′

C4

𝜀𝑐𝑢

𝜀𝑐𝑢

𝜀𝑐 𝜀

𝜀

𝜀

𝜀

Proposed Compression Model• Compressive strength, 𝑓𝑐

′, with = 0.85ASTM C39 with modifications listed in ASTM C1856

• Modulus of Elasticity, 𝑐ASTM C469 with modifications listed in ASTM C1856

Or

𝑐 = 1,460 𝑓𝑐′ (ksi)

• Elastic strain limit, 𝜀𝑐 = 𝑓𝑐′/ 𝑐

• Ultimate compression strain, 𝜀𝑐𝑢 = 0.0035

22

0.0033

0.0040 0.0042

0.0034

0.0047

0

0.001

0.002

0.003

0.004

0.005

0.006

U-A U-B U-C U-D U-EAx

ial

Str

ain

at

Pea

k C

om

pre

ssiv

eS

tres

s

Properties and Behavior

of UHPC-Class Materials

FHWA-HRT-18-036

FHWA-TFHRC (Graybeal and El-Helou) AASHTO CBS T-10 Meeting June 26, 2018 23

Flexural Analysis

• The simplified proposed models in compression and tension are

adopted.

• The strain conditions are based on strain compatibility and

equilibrium of forces.

UHPC Cross Section Strain Compatibility Stress Diagram

FHWA-TFHRC (Graybeal and El-Helou) AASHTO CBS T-10 Meeting June 26, 2018 24

𝜀𝑐 ′ 𝜀𝑐𝑢

𝑐

𝑓𝑐′

𝜀

𝛾𝑓𝑐𝑟

𝑐

𝛾𝜀𝑐𝑟 𝜀𝑡𝑢

𝜀

𝜺𝒔 < 𝜺𝒔𝒚

Flexural Behavior

𝒇𝒔′

𝒇𝒔𝜸𝒇𝒄𝒓

𝜺𝒔′𝜺𝒄 𝑬𝒄𝜺𝒄

𝝋𝒄𝒓

𝑴𝒄𝒓

Extreme

tension strain

Compression Model

Tension Model

Extreme

compression strain

𝜸𝜺𝒄𝒓𝑴

𝝋

FHWA-TFHRC (Graybeal and El-Helou) AASHTO CBS T-10 Meeting June 26, 2018 25

𝛾𝑓𝑐𝑟

𝑐

𝛾𝜀𝑐𝑟 𝜀𝑡𝑢

𝜀

𝜺𝒔 = 𝜺𝒔𝒚

Flexural Behavior

𝜸𝒇𝒄𝒓

𝒇𝒔′

𝒇𝒔𝒚𝜸𝒇𝒄𝒓

𝜸𝜺𝒄𝒓

𝜺𝒔′𝜺𝒄 𝑬𝒄𝜺𝒄

𝝋𝒚

𝑴𝒚

Extreme

tension strain

Extreme

compression strain

𝜺𝒕

𝝋𝒄𝒓

𝑴𝒄𝒓

Compression Model

Tension Model

𝑴

𝜀𝑐 ′ 𝜀𝑐𝑢

𝑐

𝑓𝑐′

𝜀

𝝋

FHWA-TFHRC (Graybeal and El-Helou) AASHTO CBS T-10 Meeting June 26, 2018 26

𝛾𝑓𝑐𝑟

𝑐

𝛾𝜀𝑐𝑟 𝜀𝑡𝑢

𝜀

𝜸𝒇𝒄𝒓

Flexural Behavior

𝜺𝒕𝒖

𝜺𝒔 > 𝜺𝒔𝒚

𝜸𝒇𝒄𝒓

𝒇𝒔′

𝒇𝒔𝒚

𝜸𝜺𝒄𝒓

𝜺𝒔′

𝜺𝒄 𝑬𝒄𝜺𝒄

𝑴𝑳

Extreme

tension strain

Extreme

compression strain

𝑴𝒚

𝝋𝒄𝒓

𝑴𝒄𝒓

𝑴

𝝋𝒚 𝝋𝑳

𝜀𝑐 ′ 𝜀𝑐𝑢

𝑐

𝑓𝑐′

𝜀

Compression Model

Tension Model

𝝋

FHWA-TFHRC (Graybeal and El-Helou) AASHTO CBS T-10 Meeting June 26, 2018 27

𝛾𝑓𝑐𝑟

𝑐

𝛾𝜀𝑐𝑟 𝜀𝑡𝑢

𝜀

𝜀𝑐 ′ 𝜀𝑐𝑢

𝑐

𝑓𝑐′

𝜀

Flexural Behavior

𝜺𝒕𝒖

𝜺𝒄𝒖

𝜺𝒔 > 𝜺𝒔𝒚

𝜶𝒇𝒄′

𝜸𝒇𝒄𝒓

𝒇𝒔′

𝒇𝒔𝒚

𝝋𝑼

𝑴𝑼

Extreme

compression

strain

Extreme tension

strain

𝜺𝒕

𝑴𝑳

𝑴𝒚

𝝋𝒄𝒓

𝑴𝒄𝒓

𝑴

𝝋𝒚 𝝋𝑳

Compression Model

Tension Model

𝝋

FHWA-TFHRC (Graybeal and El-Helou) AASHTO CBS T-10 Meeting June 26, 2018 28

Proposed Shear Model Concept

Shear Test of UHPC AASHTO Type II GirderDirect Tension Test

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

0 0.002 0.004 0.006 0.008 0.01

Ax

ial

Str

es

s (

ksi)

Axial Strain (in/in)

First discrete crack

𝒇𝒄𝒓

𝒇𝒄𝒓

𝑬𝒄0.02% strain offset line

Ax

ial

Str

es

s

cotUHPC tcr w vV f b d vd

wb

n UHPC sV V V

Axial Stress

FHWA-TFHRC (Graybeal and El-Helou) AASHTO CBS T-10 Meeting June 26, 2018 29

Prestressing

Stress Limits• Established in terms of compressive strength and cracking

stress

• Ensures section is uncracked at service limit state

• Reduced need for bonded auxiliary reinforcement to control

cracking at transfer

Creep and Shrinkage/Prestress Loss• Creep and Shrinkage models based on commercially

available UHPCs

• Calculate time-dependent losses

FHWA-TFHRC (Graybeal and El-Helou) AASHTO CBS T-10 Meeting June 26, 2018 30

Proposed Outline

Section 1: Introduction

Section 2: Material Specifications

Section 3: Design Specifications

Section 4: Construction Specifications4.1 Scope

4.2 Definitions

4.3 Limitations

4.4 Production Control

4.5 Execution

Section 5: Promising ApplicationsPlacement MethodFlow Test

FHWA-TFHRC (Graybeal and El-Helou) AASHTO CBS T-10 Meeting June 26, 2018 31

Proposed Outline

Section 1: Introduction

Section 2: Material Specifications

Section 3: Design Specifications

Section 4: Construction Specifications

Section 5: Promising Applications

31

Lighter Bridges/Longer Spans Simplified Connections

Cap-to-Column Precast Deck Panels

300’ Girder

FIB 102

0.6" Strands

4'-1"

3'-3"

8"

8'-6"

FIB 102

0.7" Strands

4'-1"

3'-3"

8"

8'-6"

FIB 102 - 6" Web

0.7" Strands

4'-1"

3'-3"

6"

8'-6"

FIB 120 - 6" Web

0.7" Strands

3'-3"

3'-9"

6"

10'

FHWA-TFHRC (Graybeal and El-Helou) AASHTO CBS T-10 Meeting June 26, 2018 32

Ongoing Related Research Activities at

FHWA-TFHRC

• UHPC direct tension testing

• Flexural and shear behavior validation of

proposed models

• Evaluation of existing creep and shrinkage

models for UHPC-class materials

• Assessment of durability methods and

establishing target values for UHPC-class

materials

• Structural design recommendations for 200 to

300 ft span pretensioned girders

FHWA-TFHRC (Graybeal and El-Helou) AASHTO CBS T-10 Meeting June 26, 2018 33

Parallel Activities

PCI Bridge Committee’s UHPC Subcommittee• Info gathering and Girder Design Exercise

Iowa DOT Pooled Fund (1434)• Complimentary effort lending perspective and

insight to the FHWA-TFHRC guide development

• Round Robin test on proposed direct tension

method

NCHRP 18-18: Deck Bulb Tees w/ UHPC• Refining DBT solutions while using UHPC connections

• June 3-5, 2019 in Albany, New York!

• Goal:

o Share knowledge

o Facilitate collaboration

o Advance the use of UHPC

• Interactive Expert Discussions

• Paper Presentations

• Student Competition

• Design Awards

• Hands-On Site Visits and Peer Exchange

2nd International Interactive Symposium on UHPC

34

AASHTO LRFD Design and

Construction Guide Specification for

Ultra-High Performance Concrete

FHWA-TFHRC Update on Development and Delivery

AASHTO CBS T-10 Committee Meeting

June 26, 2018 – Burlington, Vermont

Ben Graybeal, Ph.D., P.E., Federal Highway Administration,

[email protected], (202)493-3122

Rafic G. El Helou, Ph.D., NRC Associate at FHWA-TFHRC,

[email protected], (201)493-3482

Additional Slides

FHWA-TFHRC (Graybeal and El-Helou) AASHTO CBS T-10 Meeting June 26, 2018 37

• Direct tension test method by Graybeal and

Baby, 2013

• First cracking stress, 𝑓𝑐𝑟0.02 % offset method on stress-strain curve

• Cracking strain limit, 𝛾𝜀𝑐𝑟

• Localization stress, 𝑓𝑡𝑢 , and strain 𝜀𝑡𝑢Obtain maximum attained stress during the test, 𝑓𝑡𝑚𝑎𝑥 and its corresponding strain.

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

0 0.002 0.004 0.006 0.008 0.01

Ax

ial

Str

es

s (

ksi)

Axial Strain (in/in)

Proposed Tension Model

𝛾𝜀𝑐𝑟 = 𝛾𝑓𝑐𝑟 𝑐

Maximum tension

stress𝒇𝒕𝒎𝒂𝒙

𝒇𝒕𝒎𝒂𝒙

𝑓𝑐𝑟

𝛾𝑓𝑐𝑟

𝑓𝑐𝑟

𝛾𝑓𝑐𝑟

𝑐 𝑐

𝑐 𝑐

𝜀𝑐𝑟 𝜀𝑡𝑢 𝜀𝑐𝑟 𝜀𝑡𝑢

𝛾𝜀𝑐𝑟 𝜀𝑡𝑢 𝛾𝜀𝑐𝑟 𝜀𝑡𝑢

T2T1

T3 T4

𝑓𝑡𝑢

𝛾𝑓𝑡𝑢

𝜀

𝜀

𝜀

𝜀

𝑓𝑐𝑟

𝛾𝑓𝑐𝑟

𝑓𝑐𝑟

𝛾𝑓𝑐𝑟

𝑐 𝑐

𝑐 𝑐

𝜀𝑐𝑟 𝜀𝑡𝑢 𝜀𝑐𝑟 𝜀𝑡𝑢

𝛾𝜀𝑐𝑟 𝜀𝑡𝑢 𝛾𝜀𝑐𝑟 𝜀𝑡𝑢

T2T1

T3 T4

𝑓𝑡𝑢

𝛾𝑓𝑡𝑢

𝜀

𝜀

𝜀

𝜀

FHWA-TFHRC (Graybeal and El-Helou) AASHTO CBS T-10 Meeting June 26, 2018 38

Proposed Tension Model

𝑓𝑐𝑟

𝛾𝑓𝑐𝑟

𝑓𝑐𝑟

𝛾𝑓𝑐𝑟

𝑐 𝑐

𝑐 𝑐

𝜀𝑐𝑟 𝜀𝑡𝑢 𝜀𝑐𝑟 𝜀𝑡𝑢

𝛾𝜀𝑐𝑟 𝜀𝑡𝑢 𝛾𝜀𝑐𝑟 𝜀𝑡𝑢

T2T1

T3 T4

𝑓𝑡𝑢

𝛾𝑓𝑡𝑢

𝜀

𝜀

𝜀

𝜀

𝑓𝑐𝑟

𝛾𝑓𝑐𝑟

𝑓𝑐𝑟

𝛾𝑓𝑐𝑟

𝑐 𝑐

𝑐 𝑐

𝜀𝑐𝑟 𝜀𝑡𝑢 𝜀𝑐𝑟 𝜀𝑡𝑢

𝛾𝜀𝑐𝑟 𝜀𝑡𝑢 𝛾𝜀𝑐𝑟 𝜀𝑡𝑢

T2T1

T3 T4

𝑓𝑡𝑢

𝛾𝑓𝑡𝑢

𝜀

𝜀

𝜀

𝜀

• Direct tension test method by Graybeal and

Baby, 2013

• First cracking stress, 𝑓𝑐𝑟0.02 % offset method on stress-strain curve

• Cracking strain limit, 𝛾𝜀𝑐𝑟

• Localization stress, 𝑓𝑡𝑢 , and strain 𝜀𝑡𝑢Obtain maximum attained stress during the test, 𝑓𝑡𝑚𝑎𝑥 and its corresponding strain.

If 𝑓𝑐𝑟 ≤ 𝑓𝑡𝑚𝑎𝑥 ≤ 1.2𝑓𝑐𝑟 ,

UHPC with pseudo stress plateau

Obtain localization strain, 𝜀𝑡𝑢 , right before softening when the stress falls below 𝑓𝑐𝑟without recovery.

If 𝑓𝑡𝑚𝑎𝑥≥ 1.2𝑓𝑐𝑟 ,

Strain Hardening UHPC,

set 𝑓𝑡𝑢 = 𝑓𝑡𝑚𝑎𝑥

Obtain localization strain, 𝜀𝑡𝑢 , at 𝑓𝑡𝑚𝑎𝑥.

𝛾𝜀𝑐𝑟 = 𝛾𝑓𝑐𝑟 𝑐

FHWA-TFHRC (Graybeal and El-Helou) AASHTO CBS T-10 Meeting June 26, 2018 39

FIB 102

0.6" Strands

4'-1"

3'-3"

8"

8'-6"

FIB 102

0.7" Strands

4'-1"

3'-3"

8"

8'-6"

FIB 102 - 6" Web

0.7" Strands

4'-1"

3'-3"

6"

8'-6"

FIB 120 - 6" Web

0.7" Strands

3'-3"

3'-9"

6"

10'

UHPC Girder with Cast-in-Place O.C. Deck

F.I.B.-102, O.C. Girder F.I.B.-102, UHPC Girder

(66) 0.6 in. diameter

strands at bottom flange

(66) 0.6 in. diameter

strands at bottom flange

FIB 102

0.6" Strands

4'-1"

3'-3"

8"

8'-6"

FIB 102

0.7" Strands

4'-1"

3'-3"

8"

8'-6"

FIB 102 - 6" Web

0.7" Strands

4'-1"

3'-3"

6"

8'-6"

FIB 120 - 6" Web

0.7" Strands

3'-3"

3'-9"

6"

10'

UHPC

Convention

al concrete

FHWA-TFHRC (Graybeal and El-Helou) AASHTO CBS T-10 Meeting June 26, 2018 40

FIB 102

0.6" Strands

4'-1"

3'-3"

8"

8'-6"

FIB 102

0.7" Strands

4'-1"

3'-3"

8"

8'-6"

FIB 102 - 6" Web

0.7" Strands

4'-1"

3'-3"

6"

8'-6"

FIB 120 - 6" Web

0.7" Strands

3'-3"

3'-9"

6"

10'

Maximum Possible Bridge Span

F.I.B.-102, Ordinary Concrete Girder

200 ft

205 ft

(66) 0.6 in. diameter strands at bottom flange

F.I.B.-102, UHPC Girder with O.C. Deck(66) 0.6 in. diameter strands at bottom flange

UHPC

Convention

al concrete

0 ft

FHWA-TFHRC (Graybeal and El-Helou) AASHTO CBS T-10 Meeting June 26, 2018 41

UHPC Girder with Cast-in-Place O.C. Deck

Modified F.I.B.-102, UHPC

(74) 0.7 in. diameter

strands at bottom flange

FIB 102

0.6" Strands

4'-1"

3'-3"

8"

8'-6"

FIB 102

0.7" Strands

4'-1"

3'-3"

8"

8'-6"

FIB 102 - 6" Web

0.7" Strands

4'-1"

3'-3"

6"

8'-6"

FIB 120 - 6" Web

0.7" Strands

3'-3"

3'-9"

6"

10'

F.I.B.-102, O.C. Girder

(66) 0.6 in. diameter

strands at bottom flange

FIB 102

0.6" Strands

4'-1"

3'-3"

8"

8'-6"

FIB 102

0.7" Strands

4'-1"

3'-3"

8"

8'-6"

FIB 102 - 6" Web

0.7" Strands

4'-1"

3'-3"

6"

8'-6"

FIB 120 - 6" Web

0.7" Strands

3'-3"

3'-9"

6"

10'

Convention

al concrete

FHWA-TFHRC (Graybeal and El-Helou) AASHTO CBS T-10 Meeting June 26, 2018 42

Maximum Possible Bridge Span

F.I.B.-102, Ordinary Concrete Girder

200 ft

205 ft

257 ft

F.I.B.-102 with 6” web, UHPC Girder with O.C. Deck

(66) 0.6 in. diameter strands at bottom flange

F.I.B.-102, UHPC Girder with O.C. Deck(66) 0.6 in. diameter strands at bottom flange

(74) 0.7 in. diameter strands at bottom flange

UHPC

Convention

al concrete

FIB 102

0.6" Strands

4'-1"

3'-3"

8"

8'-6"

FIB 102

0.7" Strands

4'-1"

3'-3"

8"

8'-6"

FIB 102 - 6" Web

0.7" Strands

4'-1"

3'-3"

6"

8'-6"

FIB 120 - 6" Web

0.7" Strands

3'-3"

3'-9"

6"

10'

0 ft

FHWA-TFHRC (Graybeal and El-Helou) AASHTO CBS T-10 Meeting June 26, 2018 43

Maximum Possible Bridge Span

F.I.B.-102, Ordinary Concrete Girder

200 ft

205 ft

257 ft

F.I.B.-102 with 6” web, UHPC Girder with O.C. Deck

(66) 0.6 in. diameter strands at bottom flange

F.I.B.-102, UHPC Girder with O.C. Deck(66) 0.6 in. diameter strands at bottom flange

(74) 0.7 in. diameter strands at bottom flange

300 ft

UHPC Girder with O.C. Deck?

UHPC

Convention

al concrete

0 ft

FIB 102

0.6" Strands

4'-1"

3'-3"

8"

8'-6"

FIB 102

0.7" Strands

4'-1"

3'-3"

8"

8'-6"

FIB 102 - 6" Web

0.7" Strands

4'-1"

3'-3"

6"

8'-6"

FIB 120 - 6" Web

0.7" Strands

3'-3"

3'-9"

6"

10'

FHWA-TFHRC (Graybeal and El-Helou) AASHTO CBS T-10 Meeting June 26, 2018 44

300 ft Girder Composite UHPC Girder with

regular Concrete Deck

FIB 102

0.6" Strands

4'-1"

3'-3"

8"

8'-6"

FIB 102

0.7" Strands

4'-1"

3'-3"

8"

8'-6"

FIB 102 - 6" Web

0.7" Strands

4'-1"

3'-3"

6"

8'-6"

FIB 120 - 6" Web

0.7" Strands

3'-3"

3'-9"

6"

10'

UHPC

Convention

al concrete

(92) 0.7 in. diameter strands at

bottom flange

Extreme

tension

strain

FHWA-TFHRC (Graybeal and El-Helou) AASHTO CBS T-10 Meeting June 26, 2018 45

300 ft Girder Composite UHPC Girder with

regular Concrete Deck

Crack Localization of UHPC at extreme tension fiber

FIB 102

0.6" Strands

4'-1"

3'-3"

8"

8'-6"

FIB 102

0.7" Strands

4'-1"

3'-3"

8"

8'-6"

FIB 102 - 6" Web

0.7" Strands

4'-1"

3'-3"

6"

8'-6"

FIB 120 - 6" Web

0.7" Strands

3'-3"

3'-9"

6"

10'

UHPC

Convention

al concrete

(92) 0.7 in. diameter strands at

bottom flange

Extreme

tension

strain

−0.004

0.00230.0013

0.0016

−1.00 𝑘𝑠𝑖

−1.00 𝑘𝑠𝑖

16.5 𝑘𝑠𝑖

Strain Diagram Concrete Stress Diagram

3.97 𝑘𝑠𝑖

3.70 𝑘𝑠𝑖

4′4′′