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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
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′′