number: 465 - iapmoes.org · code official approves a fire-resistance-rated assembly, listing the...

Number: 465

Originally Issued: 03/22/2019 Revised: 06/21/2019 Valid Through: 03/31/2020

The product described in this Uniform Evaluation Service (UES) Report has been evaluated as an alternative material, design or method of construction in order to satisfy and comply with the intent of the provision of the code, as noted in this report, and for at least equivalence to that prescribed in the code in quality, strength, effectiveness, fire resistance, durability and safely, as applicable, in accordance with IBC Section 104.11. This document shall only be reproduced in its entirety.

Copyright © 2019 by International Association of Plumbing and Mechanical Officials. All rights reserved. Printed in the United States. Ph: 1-877-4IESRPT • Fax: 909.472.4171 web: www.uniform-es.org • 4755 East Philadelphia Street, Ontario, California 91761-2816 – USA

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BEKAERT CORPORATION

(parent company NV Bekaert SA)

1395 South Marietta Parkway

Building 700, Suite 708

Marietta, Georgia 30067

www.bekaert.com

DRAMIX® Steel Fibers

CSI Section:

03 20 00 – Concrete Reinforcement

03 24 00 – Fibrous Reinforcing

03 30 00 – Cast-in-Place Concrete

03 40 00 – Precast Concrete

03 70 00 – Mass Concrete

05 31 00 – Steel Decking

1.0 RECOGNITION

Dramix® steel fibers described in this report have been

evaluated for use as an alternative, or as a supplement to, the

conventional concrete reinforcement specified by ACI 318,

ACI 360, SDI-C, or for other applications included in this

report. The usage shall be permitted as defined and limited

by the scope of this report. The strength properties were

evaluated for compliance with the following codes:

• 2018, 2015, 2012 International Building Code®

(IBC)

• 2018, 2015, 2012 International Residential Code®

(IRC)

• 2016 California Building Code (CBC) and

California Residential Code (CRC) – Attached

Supplement

• 2017 Florida Building Code, Building (FBC,

Building) and 2017 Florida Building Code,

Residential (FBC, Residential) – Attached

Supplement

• 2014 New York City Building Code (NYCBC) –

Attached Supplement

2.0 LIMITATIONS

Use of the Dramix® steel fibers recognized in this report are

subject to the following limitations:

2.1 The scope of the report is limited to the following specific

Dramix® fiber models: 3D 45/30GG, 3D 45/35BL, 3D

45/50BL, 3D 55/30BG, 3D 55/60BG, 3D 55/60BL, 3D

65/35BG, 3D 65/35GG, 3D 65/40GG, 3D 65/60BG, 3D

65/60GG, 3D 80/50BG, 3D 80/60BG, 3D 80/60GG, 4D

55/60BG, 4D 65/35BG, 4D 65/60BG, 4D 80/60BG, 5D

65/60BG and 5D 65/60GG.

2.2 Dramix® steel fibers shall be blended into the concrete

mix in accordance with Section 3.3 of this report and the

manufacturer’s published installation instructions. If there

are any conflicts between this report and the manufacturer’s

published installation instructions, the more restrictive shall

govern.

2.3 Design and construction of concrete utilizing the Dramix®

steel fibers shall be in accordance with the requirements of

Section 3.0 of this report and the codes and standards

referenced therein.

2.4 The use of the Dramix® steel fibers in Seismic Force

Resisting Systems shall be considered in accordance with

Section A1 of Annex A of this report.

2.5 The use of the Dramix® steel fibers in normal-weight and

lightweight concrete shall be permitted, except as otherwise

restricted by Section 3.0 of this report and the codes and

standards referenced therein.

2.6 When structural plain concrete is used, it shall comply

with Section 1906 of the IBC. When structural plain concrete

is supported directly on the ground, control joints shall be

provided as required by ACI 318-14 Section 14.3.4 (Section

22.3 of ACI 318-11).

2.7 Use of Dramix® steel fibers shall be as approved by a

registered design professional.

2.8 When conventional reinforcement is required for

structural design, such reinforcement shall be provided as

required by the project documents as prepared by the

registered design professional.

2.9 When steel Dramix® steel fibers are added at the ready-

mix plant, a batch ticket, signed by a ready-mix

representative, shall be available to the code official upon

request. The delivery ticket shall include, in addition to the

items noted in ASTM C94, the type and amount of Dramix®

steel fibers added to the concrete mix. Other requirements

relative to fiber inclusion into the concrete matrix and the

related quality assurance provisions shall be as stipulated by

Section 3.0 of this report.

2.10 Fire-resistance rating properties of Dramix® steel fibers

are beyond the scope of this report except as provided by this

section. The steel fibers are permitted to be used as a

component of a fire-resistance rated assembly in accordance

with IBC Section 703.2, based on testing in accordance with

ASTM E119 or UL 263. Alternative methods in IBC Section

703.3 are also permitted. Fire-resistance based on testing in

accordance with ASTM E119 or UL 263 may be established

http://www.bekaert.com/

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when the registered design professional specifies, and then

code official approves a fire-resistance-rated assembly,

listing the specific Dramix® steel fiber models, from the

Underwriters Laboratories Online Certifications Directory.

2.11 Dramix® 3D 55/30BG, 3D 80/50BG, 3D 45/35BL, 3D

65/60BG, 4D 80/60BG, 4D 65/60BG and 4D 55/60BG steel

fibers are manufactured by Bekaert Corporation’s parent

company NV Bekaert SA at its manufacturing facility in

Moen, Belgium. Dramix® 3D 45/30GG, 3D 65/35GG, 3D

65/40GG, 3D 80/60GG, 3D 55/60BG, 3D 65/60GG, 3D

55/60BL, 5D 65/60BG and 5D 65/60GG steel fibers are

manufactured by Bekaert Corporation’s parent company NV

Bekaert SA at its manufacturing facility in Petrovice, Czech

Republic. Dramix® 3D 65/35BG, 3D 80/60BG, 3D 45/50BL

and 4D 65/35BG steel fibers are manufactured by Bekaert

Corporation’s parent company NV Bekaert SA at its facilities

in Moen, Belgium and Petrovice, Czech Republic.

3.0 PRODUCT USE

3.1 General: Dramix® fiber models enumerated in Section

4.0 of this report are used as an alternative to the

conventional reinforcement, either as partial or full

replacement thereof, subject to the stated limitations. The

reinforcement replacement, within the scope of this report,

shall be permitted for structural and non-structural

applications with the structural and non-structural members,

respectively, designed and constructed in accordance with

ACI 318, SDI-C, and ACI 360.

3.2 Design:

3.2.1 Design Scope: Design scope shall be as defined and

limited by Section A1 of Annex A of this report.

3.2.2 Nominal Material Properties: Nominal material

properties used in the design for strength and serviceability

shall be as defined in Section A3 of Annex A of this report.

3.2.3 Determination of Required Strength, Member and

Section Design Strength: Required and design strengths of

members and sections, as applicable, shall be determined in

accordance with Section A4 of Annex A of this report.

3.2.4 Applications Specific Requirements: Structural and

non-structural systems consisting of members, elements and

sections shall be configured in accordance with Section A5

of Annex A of this report.

3.2.5 Serviceability: Structural and non-structural systems

serviceability shall be considered in accordance with

Section A6 of Annex A of this report.

3.2.6 Durability of Members and Systems: Structural and

non-structural system durability shall be considered in

accordance with Section A8 of Annex A of this report.

3.3 Installation: The manufacturer's published installation

instructions for Dramix® steel fibers and this report shall be

strictly adhered to at all times on the jobsite during

installation. Furthermore, Sections A7 and A9 of Annex A

of this report shall apply.

3.4 Quality Assurance: The manufacturer's published

quality assurance specifications for Dramix® and Section A7

of Annex A of this report shall be adhered to.

4.0 PRODUCT DESCRIPTION

Dramix® fibers are cold-drawn, deformed wire fibers with

end anchors complying with the requirements of ASTM

A820, Type I. The fibers are delivered either in loose form or

as glued clips. Dramix® 3D series fibers are manufactured

from non-alloy steel rods complying with ISO 16120-2,

Grade C9D. Dramix® 4D fibers are manufactured from non-

alloy steel rods complying with ISO 16120-2, Grades C15D-

C20D. Dramix® 5D fibers are manufactured from high-

carbon steel rods complying with ISO 16120-2, Grades

C78D-C86D. Dimensions for each fiber model are provided

in Table 1 of this report.

Table 1 – Dramix® steel fiber dimensions

Fiber Model Length (mm) Diameter (mm)

3D 45/30GG 30 0.62

3D 45/35BL 35 0.75

3D 45/50BL 50 1.05

3D 55/30BG 30 0.55

3D 55/60BG, BL 60 1.05

3D 65/35BG, GG 35 0.55

3D 65/40GG 41 0.62

3D 65/60BG, GG 60 0.90

3D 80/50BG 50 0.62

3D 80/60BG, GG 60 0.75

4D 55/60BG 61 1.05

4D 65/35BG 36 0.55

4D 65/60BG 61 0.90

4D 80/60BG 61 0.75

5D 65/60BG, GG 62 0.90 Note: For dimensions in inches, the values from Table 1 shall be divided by

25.4 mm/in.

Galvanized Dramix® steel fibers contain a minimum 0.098

oz/ft2 (30 g/m2) zinc coating. In a Dramix® steel fiber model

designation TD UV/WX YZ, Y= G when the wire is

galvanized, and Y=B when the wire is bright. Z= G when the

fibers are delivered in glued form, and Z= L when the fibers

are loose. The letter T is a designator reflecting the number

of straight wire segments in the end-anchor configuration.

UV designation is indicative of aspect ratio of the product.

based on the length of the product. WX is indicative of the

length of the product.

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Dramix® fibers are packaged in 44.1-pound (20 kg), non-

water-soluble bags; 0.55-pound (250 g); or 2,450-pound

(1100 kg) bags. The glued Dramix® steel fibers are adhered

in clips and separate into individual elements when added to

the concrete mix.

5.0 IDENTIFICATION

Dramix® steel fiber packaging is identified by the Bekaert

Corporation name and trademark, product name, including

Dramix® steel fibers, manufacturing location and evaluation

report number (ER-465). The identification shall also include

the IAPMO Uniform Evaluation Service Mark of

Conformity. Either Mark of Conformity may be used as

shown below:

or IAPMO UES ER-465

6.0 SUBSTANTIATING DATA

6.1 Manufacturer’s descriptive literature and installation

instructions. Test results are from laboratories in compliance

with ISO/IEC 17025.

6.2 Data in accordance with the Evaluation Criteria for

Anchored Steel Fibers in Concrete (IAPMO UES EC 026),

adopted December 2018, editorially revised in January 2019.

6.3 Dimensional and mechanical property test data in

accordance with ASTM A820.

6.4 Flexural performance testing in accordance with ASTM

C1609 and EN14651.

6.5 Data in accordance with the Acceptance Criteria for Steel

Fibers in Concrete (ICC-ES AC208), dated January 2016.

6.6 References listed in Section A2.1 of Annex A of this

report.

7.0 STATEMENT OF RECOGNITION

This evaluation report describes the results of research carried

out by IAPMO Uniform Evaluation Service on Dramix® steel

fibers to assess the conformance to the codes shown in Section

1.0 of this report and documents the product’s certification.

Products are manufactured at locations noted in Section 2.11

of this report under a quality control program with periodic

inspection under the supervision of IAPMO UES.

Brian Gerber, P.E., S.E.

Vice President, Technical Operations

Uniform Evaluation Service

Richard Beck, PE, CBO, MCP

Vice President, Uniform Evaluation Service

GP Russ Chaney

CEO, The IAPMO Group

For additional information about this evaluation report please visit

www.uniform-es.org or email at [email protected]

http://www.uniform-es.org/

mailto:[email protected]

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FLORIDA SUPPLEMENT

BEKAERT CORPORATION (parent company NV Bekaert SA) 1395 South Marietta Parkway Building 700, Suite 708 Marietta, Georgia 30067 www.bekaert.com


CSI Section:







1.0 RECOGNITION

The Dramix® steel fibers evaluated in IAPMO UES ER-465 are satisfactory alternatives to the steel fiber reinforcing prescribed in the following codes and regulations, subject to the additional limitations in Section 2.0 of this supplement:

• 2017 Florida Building Code, Building (FBC,

Building)

• 2017 Florida Building Code, Residential (FBC,

Residential)

2.0 LIMITATIONS

Use of the Bekaert Corporation Dramix® steel fibers recognized in this report is subject to the following limitations.

2.1 Verification shall be provided that a quality assurance

agency audits the manufacturers quality assurance program

and audits the production quality of products, in accordance

with Section (5)(d) of Florida Rule 61G20-3.008. The quality

assurance agency shall be approved by the Commission (or

the building official when the report holder does not possess

an approval by the Commission).

2.2 The requirements for High-velocity Hurricane Zones

(HVHZ) in the 2017 Florida Building Code, Building and the

2017 Florida Building Code, Residential are beyond the

scope of this review.




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CALIFORNIA SUPPLEMENT



CSI Section:







1.0 RECOGNITION

The Dramix® steel fibers evaluated in IAPMO UES ER-465 are satisfactory alternatives to the steel fiber reinforcing prescribed in the following codes, subject to the additional limitations in Section 2.0 of this supplement:

• 2016 California Building Code (CBC)

• 2016 California Residential Code (CRC)

2.0 LIMITATIONS

Use of the Dramix® steel fibers recognized in this report is subject to the following limitations:

2.1 Except as permitted under Section 2.2 of this report, the use of steel fiber reinforcement shall not be permitted in structures regulated by the Division of the State Architect-Structural Safety (DSA-SS), and in applications regulated by the Office of Statewide Health Planning and Development (OSHPD) in accordance with Section 1903A.7 of the CBC.

2.2 The use of steel fiber reinforcement is permitted for use with concrete-filled steel deck in structures regulated by the Division of the State Architect-Structural Safety (DSA-SS), and in applications regulated by the Office of Statewide Health Planning and Development (OSHPD), in accordance with Section 2210A.1.1.3 of the CBC.

2.3 In applications regulated by DSA-SS and OSHPD, inspections shall comply with Chapter 17A of the CBC.




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City of New York Supplement



CSI Section:







1.0 RECOGNITION

The Dramix® steel fibers evaluated in IAPMO UES ER-465 are satisfactory alternatives to the steel fibers prescribed in the following code, subject to the additional requirements in Section 2.0 of this supplement:

• 2014 New York City Building Code (NYCBC)

2.0 LIMITATIONS

Use of the Bekaert Corporation Dramix® steel fibers recognized in this report is subject to the following limitations.

2.1 The performance of the mix design with concrete fibers

added shall be confirmed when using steel fibers in

accordance with Section 1905.3.5.2 of the NYCBC.

2.2 Unless used in application of the provision of ACI 318

Sec. 11.4.6.1(f), steel fibers used in beams need not comply

with the requirements of Section 1905.6.6 of the NYCBC,

except that special inspection requirements shall apply.




Number: 465

Originally Issued: 03/22/2019 Valid Through: 03/31/2020

The product described in this Uniform Evaluation Service (UES) Report has been evaluated as an alternative material, design or method of construction in order to satisfy and comply with the intent of the provision of the code, as noted in this report, and for at least equivalence to that prescribed in the code in quality, strength, effectiveness, fire resistance, durability and safely, as applicable, in accordance with IBC Section 104.11. This document shall only be reproduced in its entirety.

Copyright © 2019 by International Association of Plumbing and Mechanical Officials. All rights reserved. Printed in the United States. Ph: 1-877-4IESRPT • Fax: 909.472.4171 web: www.uniform-es.org • 4755 East Philadelphia Street, Ontario, California 91761-2816 – USA

Page A1 of A42

IAPMO UES ER-465 Annex A

North American Requirements for the Design of Dramix® Fiber-Reinforced Concrete Members & Systems (US-BD-19)

Number: 465


Page A2 of A42

Table of Contents

A1 SCOPE ......................................................................................................................................................... A4

A2 REFERENCES AND DEFINITIONS ................................................................................................................... A4

A2.1 REFERENCES .................................................................................................................................................. A4

A2.2 DEFINITIONS ................................................................................................................................................. A5

A2.3 NOTATIONS .................................................................................................................................................. A5

A3 DETERMINATION OF FIBER REINFORCED CONCRETE DESIGN PROPERTIES .................................................. A9

A3.1 MATERIAL PROPERTIES ................................................................................................................................... A9

A3.1.1 Concrete and Fiber-Reinforced Concrete .............................................................................................. A9

A3.1.2 Mild Reinforcement and Pre-stressing Steel ....................................................................................... A11

A3.1.3 Other Materials................................................................................................................................... A11

A3.2 MATERIAL CONSTITUTIVE MODELS .................................................................................................................. A11

A3.2.1 Constitutive Models for Analysis ......................................................................................................... A11

A3.2.2 Stress-Strain Relationships for Section Proportioning ........................................................................ A14

A4 DESIGN FOR STRENGTH............................................................................................................................. A14

A4.1 DETERMINATION OF REQUIRED STRENGTH ........................................................................................................ A15

A4.1.1 Applicable Loads and Load Combinations .......................................................................................... A15

A4.1.2 Required Analysis ................................................................................................................................ A15

A4.2 DETERMINATION OF AVAILABLE STRENGTH ....................................................................................................... A16

A4.2.1 Flexural And Axial Strength ................................................................................................................. A17 A4.2.1.1 Flexural Strength ......................................................................................................................................... A17 A4.2.1.2 Axial Strength .............................................................................................................................................. A21 A4.2.1.3 Flexural-Axial Interaction ............................................................................................................................ A21 A4.2.1.4 Stability of Members and Frames ............................................................................................................... A21

A4.2.2 Shear Strength .................................................................................................................................... A21 A4.2.2.1 One-Way Shear ........................................................................................................................................... A22 A4.2.2.2 Two-Way Shear ........................................................................................................................................... A23 A4.2.2.3 Strut-and-Tie Method ................................................................................................................................. A23 A4.2.2.4 Shear Friction .............................................................................................................................................. A24

A4.2.3 Torsion ................................................................................................................................................ A24

A4.2.4 Bearing Strength ................................................................................................................................. A25

A5 SYSTEM AND COMPONENT SPECIFIC REQUIREMENTS .............................................................................. A25

A5.1 STRUCTURAL INTEGRITY ................................................................................................................................. A25

A5.2 SLABS ON GROUND ...................................................................................................................................... A25

A5.3 PILE SUPPORTED SLABS ON GROUND ............................................................................................................... A26

A5.4 STRUCTURAL SLABS ...................................................................................................................................... A27

A5.4.1 One-Way Slabs .................................................................................................................................... A28

A5.4.2 Two-Way Slabs ................................................................................................................................... A28

A5.5 BEAMS ....................................................................................................................................................... A29

A5.6 COLUMNS ................................................................................................................................................... A30

A5.7 WALLS ....................................................................................................................................................... A30

A5.8 ANCHORAGE ............................................................................................................................................... A31

A5.9 FOUNDATION ELEMENTS ............................................................................................................................... A31

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A5.9.1 Pile Caps .............................................................................................................................................. A31

A5.9.2 Piles and Piers ..................................................................................................................................... A31

A5.9.3 Shallow Foundation Elements ............................................................................................................. A32

A5.10 DIAPHRAGMS & SEISMIC FORCE RESISTING SYSTEMS (SFRS) ............................................................................... A33

A5.11 NON-STRUCTURAL COMPONENTS ................................................................................................................... A34

A6 DESIGN FOR SERVICEABILITY ..................................................................................................................... A34

A6.1 DEFLECTIONS .............................................................................................................................................. A34

A6.2 CRACK CONTROL .......................................................................................................................................... A34

A6.2.1 Calculated Crack Width....................................................................................................................... A35

A6.3 MINIMUM REINFORCEMENT .......................................................................................................................... A37

A6.4 STRESS LIMITS IN PRESTRESSED MEMBERS ........................................................................................................ A37

A7 QUALITY ASSURANCE REQUIREMENTS ..................................................................................................... A38

A7.1 GENERAL REQUIREMENTS .............................................................................................................................. A38

A7.2 REQUIREMENTS FOR DRAMIX® FIBERS, TESTING AND COMPOSITION ...................................................................... A38

A7.3 MATERIAL HANDLING OF DRAMIX® FIBERS ....................................................................................................... A38

A7.4 CONSTRUCTION WITH DRAMIX® FIBERS ............................................................................................................ A39

A7.4.1 Distribution of Dramix® Fibers in the FRC Matrix ............................................................................... A39

A8 DURABILITY ............................................................................................................................................... A41

A9 DETAILS OF REINFORCEMENT ................................................................................................................... A42

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A1 Scope

The design requirements stipulated herein are solely valid for the design of steel fiber-reinforced concrete (SFRC) members reinforced with Dramix® steel fiber models listed in Section 2.1 of this report, either solely, in combination with mild reinforcement and/or pre-stressing. When used, pre-stressing reinforcement shall be permitted to be bonded or unbonded.

The provisions are applicable for the design for strength and serviceability. Unless specifically provided otherwise by this Specification or otherwise established through testing or rational analysis acceptable to the building official having jurisdiction, the contribution of steel FRC on strength, serviceability, detailing requirements, ductility, durability or other performance characteristics of a reinforced concrete member or system shall be neglected. Such members and systems shall be designed solely as required by ACI 318, including using exceptions specified thereto by the applicable building code.

Unless otherwise specifically provided herein, all exceptions to ACI 318 stipulated by the applicable building code shall apply. Where a building code does not exist, the exceptions to ACI 318 stipulated by IBC shall apply, unless otherwise specifically provided herein.

These provisions are limited to the design of members not considered a part of the designated Seismic Force Resisting System in Seismic Design Categories C through F, as defined in ASCE 7. No provision of this report shall be considered as indicative of performance of Bekaert Dramix® 3D, 4D and 5D in designated Seismic Force Resisting Systems in Seismic Design Categories C through F.

A2 References and Definitions

A2.1 References

ACI 224R-01 Control of Cracking in Concrete Structures (2001) ACI 318 Building Code Requirements for Reinforced Concrete (2011, 2014) ACI 360 Guide to Design of Slabs-on-Ground (2010) AISI S310 North American Standard for the Design of Profile Steel Diaphragm Panels

(2016) ASCE 7 Minimum Design Loads for Buildings and Other Structures (2010, 2016) ASTM E329 Standard Specification for Agencies Engaged in Construction Inspection, Testing,

or Special Inspection (2018) ASTM A615 Standard Specification for Deformed and Plain Carbon-Steel Bars for Concrete

Reinforcement (2016) ASTM A820 Standard Specification for Steel Fibers for Fiber-Reinforced Concrete (2011) ASTM C1116 Standard Specification for Fiber-Reinforced Concrete (2015) ASTM C1609 Standard Method for Flexural Performance of Fiber-Reinforced Concrete (Using

Beam With Third-Point Loading) (2012) DAfStb Deutscher Ausschuss für Stahlbeton – Richtiline – Stahlfasserbeton (2012) *DIN EN 1992-1-1 Eurocode 2: Design of Concrete Buildings, Part 1-1, German version (2010) EN 14651 Test Method for metallic fibered concrete – Measuring the flexural tensile

strength (limit of proportionality (LOP), residual) (2015) EN 14721 Test method for metallic fibre concrete – Measuring the fibre content in fresh

and hardened concrete (2005) *EN 1990-2002+A1 Eurocode – Basis of Structural Design (2010)*IAPMO UES EC 026 Evaluation Criteria for Anchored Steel Fibers in Concrete (2019)IAPMO UES ER-497 Dramix® Steel Fibers (2019) *fib MC2010 fib Model Code for Concrete Structures (2010) IBC International Building Code (2012, 2015, 2018) ISO/IEC 17025 General requirements for the competence of testing and calibration

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laboratories (2005) ICC-ES AC193 Acceptance Criteria for Mechanical Anchors in Concrete Elements (2018) ANSI/SDI C Standard for Composite Steel Floor Deck – Slabs (2011, 2017) *Note: This standard is not referenced in the report. Reference is provided for background information.

A2.2 Definitions

Defined terms used in conjunction with this report shall be as defined by IBC Sec. 202, ACI 318-14 Sec. 2.3 (or ACI 318-11 Sec. 2.2 when applicable), unless otherwise amended or modified by this section.

Concrete Composition. Each unique concrete mix consisting of a specific aggregate and size, cement type and content, water and admixtures. Fiber Dosage. Weight content of fiber per unit volume of concrete. Fiber Type. Each unique fiber characterized by specific manufacturer, type of material, and geometry. Fiber Reinforced Concrete (FRC) Matrix. Each unique combination of fiber type, fiber dosage, concrete composition and concrete compressive strength. Flexural Strain Hardening (FRC) Matrix. FRC matrix meeting the criteria stipulated by Eq. A3-5. Flexural Strain Softening (FRC) Matrix. FRC matrix not meeting the criteria stipulated by Eq. A3-5. Pile-Supported Slab on Ground. Non-structural slab supported on discrete supports, such as auger-cast piles, drilled piers, controlled-modulus columns, micro-piles or any other similar discrete support. Pile-supported slab on ground is isolated from the structural system and not in the load path of structural forces. Plates. Two-dimensional elements subjected primarily to in-plane bending with or without membrane forces. Shells. Two-dimensional elements subjected to in-plane and out-of-plane bending with or without membrane forces. Slab on Ground. Non-structural slab continuously supported by soil strata of known stiffness modulus. Slab on ground is isolated from the structural system and not in the load path of structural forces. Structural Application. A member or an assembly with influence on stability or strength on the overall structure. Removal of a structural application from the structure would render the structure unstable or invalidate the load path within the structure. Tensile Strain Hardening (FRC) Matrix. FRC matrix meeting the criteria stipulated by Eq. A3-9. Tensile Strain Softening (FRC) Matrix. FRC matrix not meeting the criteria stipulated by Eq. A3-9. Unreinforced Slab. A slab on ground in which neither fibers nor conventional reinforcement is provided for resisting flexural or shear effects.

A2.3 Notations

A0 = gross area enclosed by torsional shear flow path, in.2 (mm2), as defined in ACI 318 Ac = cross-sectional area of member or slab design strip, in.2 (mm2) Ac,eff = effective area of concrete in tension surrounding the mild or prestressing reinforcement at the

depth hc,eff, as illustrated in Figure 6.1, in.2 (mm2) Act = area of concrete in tension right before the formation of the crack under the load effects

corresponding to the applicable service load combinations, in.2 (mm2) Al = total area of longitudinal reinforcement to resist torsion, , in.2 (mm2), as defined in ACI 318 As = area of nonprestressed longitudinal tension reinforcement, in.2 (mm2), as defined in ACI 318 Asc,min = minimum conventional reinforcement for crack control, in.2 (mm2) Ascl,min = For thick members, subjected to axial constraints, minimum reinforcement area

db is as defined by ACI 318-11 Sec. 2.1, in.2 (mm2) A’s = area of compression reinforcement, in.2 (mm2), as defined in ACI 318 At = area of one leg of a closed stirrup, hoop, or tie resisting torsion within spacing s, in.2 (mm2) , as

defined in ACI 318

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Att = area of the FRC tensile strut, excluding the cross-sectional area of any conventional reinforcement occurring within the area Att , in.2 (mm2)

Av,min = minimum shear reinforcement within spacing s, in.2 (mm2), as defined in ACI 318 A’ps = Aps located in Ac,eff , in.2 (mm2) b = width of compression face member, in. (mm), as defined in ACI 318 b0 = perimeter of critical section for two-way shear in slabs and footings, in. (mm), as defined in ACI

318 bslab = effective slab width resisting γfMsc , in. (mm), as defined in ACI 318 bw = web width or diameter of circular section, in. (mm), as defined in ACI 318 CMODn = crack mouth opening distance, as defined by EN14651, corresponding to n of 0, 1,

2, 3 or 4, where n = 0 corresponds to frf d = distance from extreme compression fiber to centroid of longitudinal tension reinforcement, in.

(mm), as defined in ACI 318 d’ = distance from the extreme compression fiber of a member section to the resultant compression

steel reinforcement force as shown in Figures A4.2 through A4.4, in. (mm) d’’ = distance from the extreme compression fiber of a member section to the resultant

FRC resultant force as shown in Figures A4.2 through A4.4, in. (mm) d’’’ = distance from the compression fiber of a member section to the resultant force of the concrete

compression block, as shown in Figures A4.2 through A4.4, in. (mm) db = nominal diameter of bar, wire, or prestressing strand, in. (mm), as defined in ACI 318 dbl = largest db applicable, in. (mm) deq = equivalent diameter of reinforcement, computed based on n number of bars of the diameter

db , in. (mm) dp = distance from the extreme compression fiber of a member section to the centroid of the pre-

stressing reinforcement, as used in Eq. A4-3, in. (mm) dps,eq = equivalent diameter of prestressing steel, in. (mm) dwire = diameter of a single tendon wire, in. (mm) Ec = modulus of elasticity of concrete, psi (MPa), as defined in ACI 318 Ep = modulus of elasticity of prestressing reinforcement, psi (MPa), as defined in

ACI 318 Es = modulus of elasticity of mild reinforcement, psi (MPa), as defined in ACI 318 fc = concrete stress ≤ f’c , psi (MPa) f’c = specified compressive strength of concrete, psi (MPa), as defined in ACI 318 ffct,L = parameter defined by EN14651, psi (MPa)

𝑓𝑐𝑓𝑙𝑚,𝐿1𝑓

= parameter as defined by DAfStb Annex O, psi (MPa)

𝑓𝑐𝑓𝑙𝑚,𝐿2𝑓

= parameter as defined by DAfStb Annex O, psi (MPa)

fns = nominal axial tensile strength corresponding to the strain of 0.0003, psi (MPa) fnu = nominal axial tensile strength corresponding to the strain limit of 0.025, psi (MPa) fpe = compressive stress in concrete due only to effective prestress forces, after allowance for all

prestress losses, at extreme fiber of section if tensile stress is caused by externally applied loads, psi (MPa), as defined in ACI 318

fps = stress in prestressing reinforcement at nominal flexural strength, psi (MPa), as defined in ACI 318

fpu = specified tensile strength of prestressing reinforcement, psi (MPa), as defined in ACI 318

fpy = specified yield strength of prestressing reinforcement, psi (MPa), as defined in ACI 318

fr = modulus of rupture of concrete, psi (MPa), as defined in ACI 318

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fr1 = stress corresponding to CMOD1, psi (MPa), as defined in EN14651 fr2 = stress corresponding to CMOD2, psi (MPa), as defined in EN14651 fr3 = stress corresponding to CMOD3, psi (MPa), as defined in EN14651 fr4 = stress corresponding to CMOD4, psi (MPa), as defined in EN14651 frf = either fr or fct,L, as applicable, psi (MPa) frn = a value of frf, fr1, fr2, fr3 or fr4, as appropriate, psi (MPa) fs = tensile stress in mild reinforcement at service loads, psi (MPa) f’s = compressive stress in mild reinforcement under factored loads, psi (MPa) ft = axial tensile strength of concrete, psi (MPa) ftx = 28-day concrete tensile stress for crack width evaluation, psi (MPa) fx = axial stress acting on the section under consideration, psi (MPa) fy = specified yield strength for nonprestressed reinforcement, psi (MPa), as defined

in ACI 318 fyt = specified yield strength of transverse reinforcement, psi (MPa), as defined

in ACI 318 F4 = parameter as defined by EN14651 FFRC = FRC resisting stress block resultant in a member section, as illustrated in Figures A4.2

through A4.4, lbs (N) Fs = size factor used in Eq. A4-6 h = overall thickness, height, or depth of a member, in. (mm), as defined in ACI 318 hc,eff = the smallest of 2.5(h-d), (h-x)/3, or h/2, as illustrate in Figure A6.1, in. (mm) hsp = test beam depth above the notch, in. (mm), as defined in EN14651 I = moment of inertia of gross cross section about centroidal axis, in.4 (mm4), as

defined in ACI 318 Ie = effective moment of inertia for calculation of deflection, in.4 (mm4), as

defined in ACI 318 k = non-uniform self-equilibration stress coefficient k1 = 1.5 when fx is compressive and 2Rd when fx is tensile kc = stress distribution factor Kc = structural use factor Ko = fiber orientation factor Ks = FRC member size factor ld = development length in tension of deformed bar, deformed wire, plain and deformed welded

wire reinforcement, or pretensioned strand, in. (mm), as defined in ACI 318 L = test beam span, in. (mm), as defined by EN14651 Mn = nominal flexural strength at section, in.-lb (N-mm), as defined in ACI 318 Mn+ = nominal flexural of a Dramix® FRC Section in positive bending, in.-lb (N-mm) Mn- = nominal flexural of a Dramix® FRC Section in negative bending, in.-lb (N-mm) Mpc = nominal flexural strength of plain concrete, in.-lb (N-mm) Msc = factored slab moment that is resisted by the column at a joint, in.-lb (N-mm), as

defined in ACI 318 n = threshold of 0 (at frf), 1, 2, 3 or 4, as applicable, as defined in EN 14651

= 1 + s, may be conservatively taken as 1.0 in all cases P0 = nominal axial strength at zero eccentricity, lb (N), as defined in ACI 318 Pn = nominal axial compressive strength of member, lb (N), as defined in ACI 318

= when used in Section 3.1.1, total applied load corresponding to the threshold n, here P is given as F in DAfStb, lb (N)

Rd = 1.0 when h < 39 in. (1000 mm) = h/(d39)

Rn = nominal strength of member at section under consideration

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RNL = factor as defined by Eq. A4-15 RT,150

D = equivalent flexural stress, as defined by ASTM C1609

Ru = governing required strength from the analysis using the load and resistance factored design (LRFD) loading combinations

s = degree of static indeterminacy smax = maximum crack spacing, in. (mm)

sr,max = maximum crack width, in. (mm) T150

D = area under the load-deflection diagram resulting from the EN14651 protocol Tn = nominal torsional moment strength or nominal tensile strength, in.-lb (N-mm) Tn,FRC = nominal tensile or torsional strength due to Dramix® FRC, in.-lb (N-mm), Tth = threshold torsional moment, , in.-lb (N-mm), as defined in ACI 318 Us = Mn+/[max(Mn-, pcMpc)] for load effects associated with downward (gravity) forces, 1.0 for

load effects associated with upward (uplift) forces vc = stress corresponding to nominal two-way shear strength provided by concrete, psi (MPa), as defined in ACI 318 vFRC = 0.37KcKoKsfr4, psi (MPa)

vmin = 0.632Fs3/2f’c1/2 for d ≤ 24 in. and US Unit System is used = 0.452Fs3/2f’c1/2 for d > 31 in. and US Unit System is used

= 0.0525Fs3/2f’c1/2 for d ≤ 600 mm and when SI Unit System is used = 0.0375Fs3/2f’c1/2 for d > 800 mm and when SI Unit System is used

For the intermediate range of d between 24 (600 mm) and 31 in. (800 mm), vmin shall be permitted to be determined by interpolation between the above given values.

vn = equivalent concrete stress corresponding to nominal two-way shear strength of slab or footing, psi (MPa), as defined in ACI 318 Vc = nominal shear strength provided by concrete, lb (N), as defined in ACI 318 VC,EC = shear strength contributed by the reinforced section, lbs (N) VFRC = nominal shear strength provided by Dramix® FRC, lbs (N)

Vn = nominal shear strength, lbs (N), as defined in ACI 318 Vs = nominal shear strength provided by shear reinforcement, lbs (N), as defined in ACI 318 wc = effective width of the tie, equal to the width of the adjoining strut, ws, in. (mm) wn = design crack width, in. (mm) ws = width of a strut perpendicular to the axis of the strut, in. (mm), as defined in ACI 318 wt = effective height of concrete concentric with a tie, used to dimension nodal zone, in. (mm), as

defined in ACI 318 X = 0.31 when Ac is in m2 = 1/5000 when Ac is in in.2

c = conversion factor f = fns/ftx ≤ 1.0 k1 = dimensional unit conversion factor k2 = stress unit conversion factor γf = factor used to determine the fraction of Msc transferred by slab flexure at slab-column connections, as defined in ACI 318 δfrf

= deflection corresponding to the stress of frf , in. (mm)

δn = test beam deflection at CMODn, where n = 0, 1, 2, 3 or 4, in. (mm) ’ = quasi-deflection used for the constitutive model shown in Section A4.1.2(c), Figure 4.1 εc = concrete strain ≤ εcu ε’c = concrete strain corresponding to f’c = 0.002

εcm = mean strain in concrete between cracks

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εcu = ultimate concrete strain = 0.003 FRC = strain in FRC s = tensile strain in mild steel εfsm = mean strain in reinforcement under service load combination ’s = compression reinforcement strain Ƞ = coefficient of 1.2 when frf is taken as fr, 1.0 otherwise = angle between axis of strut, compression diagonal, or compression field and the tension chord

of the members, as defined in ACI 318

a = 8.3 when f’c and ftx are in psi, 0.3 when f’c and ftx are in MPab = (1/145) when f’c is in psi, 1 when f’c is in MPac = 145 when ftx is in psi, 1 when ftx is in MPad = 25 when h is in in., 1.0 when h is in mmλ = modification factor to reflect the reduced mechanical properties of lightweight

concrete relative to normalweight concrete of the same compressive strength, asdefined in ACI 318

ξ1 = (ξdbl/dps,eq)1/2 when pre-stressing steel is used in combination with reinforcement in Dramix®

FRC= ξ1/2 when prestressing steel alone is used in combination with Dramix® FRC

ξ = ratio of bond strength between bonded tendons and deformed steel bars in concrete⍴eff = (As + ξ1A’ps)/Ac,eff

pc = strength reduction factor for plain concrete = strength reduction factor, as defined in ACI 318RC = strength reduction factor for mild and pre-stressing steelFRC = strength reduction factor for FRCυ = concrete Poisson’s ratio = 0.17

A3 Determination of Fiber Reinforced Concrete Design Properties

A3.1 Material Properties

A3.1.1 Concrete and Fiber-Reinforced Concrete

Unless noted otherwise, the concrete compressive strength, f’c, modulus of elasticity, Ec shall be defined and determined as stipulated by, and within the limitations of material characteristics of, ACI 318. Poisson’s ratio, 𝝊, of concrete may be taken as 0.17. The contribution of steel fibers to f’c, Ec and 𝝊 is permitted to be neglected in the analysis of SFRC members and systems.

Flexural stresses of fiber reinforced concrete, including fr1, fr2, fr3 and fr4, shall be defined and determined in accordance with EN 14651. The variable frf, as used within this report, shall be taken as ffct,L, where ffct,L is as defined by EN 14651. Alternatively, unless otherwise indicated elsewhere in this report, it shall be permitted to take frf as fr, where fr is computed as provided by Section 19.2.3.1 of ACI 318-14 (Section 9.5.2.3 in ACI 318-11). When frf is taken as fr, the deflection of an EN 14651 test beam corresponding to frf, δfrf

, shall be permitted to be

determined using Eq. A3-1. Therein, the parameters L, b and hsp are as defined by EN 14651.

δfrf=

0.603frfL2

6Echsp (A3-1)

It shall be permitted to relate the deflection δfrf to the corresponding value of CMODfrf

using Eq. A3-2.

Similarly, Eq. A3-2 may be used to relate the tested values of CMODn to the corresponding values of 𝜹n at each specific threshold n.

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𝜹n = 0.85(CMODn)+0.0016 (in.) (A3-2a) 𝜹n = 0.85(CMODn)+0.040 (mm) (A3-2b)

Where: 𝜹n = test beam deflection at threshold n CMODn = crack mouth opening distance at threshold n, as defined by EN 14651 n = threshold of 0 (at frf), 1, 2, 3 or 4, as applicable, as defined by EN 14651 At CMOD0, 𝜹n shall be permitted to be computed by Eq. A3-2, or taken as δfrf

, as computed by Eq. A3-1.

Additionally, it shall be permitted to replace the value of 0.0016 in. in Eq. A3-2a, or the value of 0.04 mm in Eq. A3-2b, as applicable, with δfrf

, as computed by Eq. A3-1.

It shall be permitted, in conjunction with this report and as modified by this Section, to correlate the

results of an EN 14651 testing protocol to the equivalent flexural strength ratio, 𝑅𝑇,150𝐷 , as specified by ASTM

C1609, using Eq. A3-3.

RT,150D =

150T150D

ƞfrfbhsp2 100% (A3-3)

Where: 𝑅𝑇,150

𝐷 = equivalent flexural stress, as defined by ASTM C1609

𝑇150𝐷 = area under the load-deflection diagram resulting from the EN14651 protocol. The

area shall be determined between the points of zero displacement and the displacement corresponding to the load F4, as defined by EN14651. The displacement shall be calculated from the tested values of CMODn using Eq. A3-2. The load-displacement curve may be assumed to be linear between subsequent measurement points.

Ƞ = 1.2 when frf is taken as fr, 1.0 otherwise

It shall be permitted, in conjunction with this report and as modified by this Section, to correlate the

results of residual flexural stresses 𝑓𝑐𝑓𝑙𝑚,𝐿1𝑓

and 𝑓𝑐𝑓𝑙𝑚,𝐿2𝑓

, as defined by DAfStb Annex O, via Eq. A3-2. In such a

conversion, the coefficient of 0.85 in Eq. A3-2 shall be taken as 1.0. For this purpose, it shall be permitted to assume that the residual stress-CMOD curve in EN 14651, or the residual stress-deflection curve from Annex O of DAfStb, is linear between subsequent measurement points.

It shall be permitted to establish fr1, fr2, fr3 and fr4 using the testing protocols defined in ASTM C1609 or Annex O of DAfStb. When ASTM C1609 is used for this purpose, the cross-section size of the specimen shall be 6 in. x 6 in. (150 mm x 150 mm). CMODn corresponding to the value of frn shall be determined using Eq. A3-2, except that the coefficient of 0.85 shall be taken as 1.0 in such a conversion. When a test in accordance with ASTM C1609 or Annex O of DAfStb is performed, frn shall be calculated using Eq. A3-4. When determining CMODn and frn from Eq. A3-2 and A3-4, respectively, linear interpolation of values between subsequent points of test measurements shall be permitted. When testing is performed using ASTM C1609, the test protocol for this purpose shall be extended to allow for the measurement of mid-span deflection of 0.14 in. (3.5 mm). The values corresponding to the beam deflections above 0.14 in. (3.5 mm) shall be disregarded.

𝑓𝑟𝑛 =𝑃𝑛𝐿

𝑏ℎ2 (A3-4)

Where: Pn = total applied load corresponding to the threshold n, where P is given as F in DAfStb L = test beam span, given as L in ASTM C1609 and as l in Annex O of DAfStb b = test beam width h = test beam height, as defined by ASTM C1609 and DAfStb Annex O

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The nominal mechanical properties of a FRC matrix covered in this Section, shall be taken as the mean values obtained on the basis of at least six replicate tests where the maximum permissible coefficient of variation (C.o.V.) shall not exceed 0.25. It shall be permitted to establish the mechanical properties on the basis of five replicate tests provided that C.o.V. does not exceed 0.23.

A FRC matrix meeting the Eq. A3-5 shall be permitted to be considered flexural strain hardening.

0.25(fr1 + fr2 + fr3 + fr4) ≥ 1.1frf (A3-5a) fr4/fr1 ≥ 0.70 (A3-5b)

Test data used to establish numerical values for FRC properties stipulated in this section shall be obtained in a facility compliant with the requirements of ISO/IEC 17025, ASTM E329, or another agency approved as set forth in IBC Section 1703.1.

A3.1.2 Mild Reinforcement and Pre-stressing Steel

Material specifications and properties of mild reinforcing, including the specified yield strength, fy, modulus of elasticity of mild reinforcement, Es, and the material specifications and properties of prestressing steel, including specified yield strength, fpy, specified tensile strength, fpu, and the modulus of elasticity of prestressing steel, Ep, shall be determined according to, and comply with the requirements of, ACI 318.

A3.1.3 Other Materials

When used in conjunction with this report, material properties of other components, such as post-installed anchors, stud rails, mechanical splices, shall be governed by the requirements of ACI 318.

A3.2 Material Constitutive Models

A3.2.1 Constitutive Models for Analysis

When linear-elastic analysis is performed, material properties shall be determined by Section A3.1.1. When material non-linearity is captured by the analysis, stress-strain (σ-ε) constitutive model for concrete shall be permitted to be modeled as given by Eq. A3-6. Concrete compressive strain in a material non-linear analysis shall be limited to the compressive strain of 0.003.

𝑓𝑐 = 𝑓𝑐′ [2

𝜀𝑐

𝜀𝑐′ − (

𝜀𝑐

𝜀𝑐′)

2] (A3-6)

Where: fc = concrete stress

≤f’c 𝜺c = concrete strain

≤ 𝜺cu 𝜺’c = concrete strain corresponding to f’c

= 0.002 𝜺cu = ultimate concrete strain

= 0.003

When material non-linearity is captured by the analysis, steel mild reinforcement shall be permitted to be assumed to be elastic-perfectly plastic. The corresponding constitutive stress strain model is given by Figure A3.1.

When material non-linearity is captured by the analysis, prestressing steel shall be permitted to be assumed to be elastic-perfectly plastic. The corresponding constitutive σ-ε model is given by Figure A3.2.

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When material non-linearity is captured by the analysis, fiber reinforced concrete in tension shall be permitted to be modeled using the constitutive σ-ε model provided in Figure A3.3, where fns and fnu are given by Equations A3.7 and A3.8.

Figure A3.1 Constitutive σ-ε Model for Steel Reinforcement in Tension

Figure A3.2 Constitutive σ-ε Model for Prestressing Steel Reinforcement in Tension

Figure A3.3 Constitutive σ-ε Model for Fiber-Reinforced Concrete in Tension

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When fr4/fr1 0.7, fns = 0.37KoKsKcfr4 (A3-7a)

Otherwise, fns = 0.40KoKsKcfr1 (A3-7b)

Where: fns = nominal axial tensile strength corresponding to the strain of 0.0003 Ko = fiber orientation factor

= 1.0 in slabs, including flat slabs and flat plates, and other horizontally cast members whose section width-to-depth ratio equals or exceeds 5, for the purposes of determining required and available flexural and axial strength = 0.50 for all other purposes, unless another value can be shown as appropriate in a manner acceptable to the building official having jurisdiction

Ks = FRC member size factor = 1.0 for slabs on ground, slabs on piles, mats, and for members with cross-sectional area of 36 in.2 (0.023 m2) or larger where the FRC matrix exhibits a C.O.V. of 0.10 or less resulting from 6 replicate tests in accordance with Section A3.1.1. Otherwise, equal to 0.68 + nXAc ≤ 1.0

X = 0.31 when Ac is in m2 = 1/5000 when Ac is in in.2

n = 1 + s, may be conservatively taken as 1.0 in all cases s = degree of static indeterminacy

= 0 for statically determinate members and when used for purposes of calculating section shear strength, regardless of the degree of static indeterminacy

Ac = cross-sectional area of member or slab design strip, equal to bwh, where bw and h are the section width and height, respectively. For punching shear calculations, bw shall be taken as the punching shear perimeter b0. The parameters b0, bw and h are as defined by ACI 318-11 Sec. 2.1, or ACI 318-14 Sec. 2.2, as applicable. For calculations of one-way shear strength per Section A4.2.2, bw shall be limited to 66 in. (1.7 m). When employing strut-and-tie methodology per Sec. A4.2.2.3, Ac shall be taken as Att/0.9 for the purposes of calculating Ks in determination of fnu per Eq. A3-7. The parameter Att is defined is as defined in Sec. A4.2.2.3. When calculating the slab moment resisted by the column in conjunction with ACI 318-11 Sec. 13.5.3.2 through 13.5.3.4 or ACI 318-14 Sec. 8.4.2.3.2 through 8.4.2.3.5, as applicable, Ac shall be computed on the basis of the section width equal to bslab, as defined by ACI 318 Sec. 2.2. In beams, the area of compression flanges shall be neglected for the purposes of computing Ac. When the cross section is subjected to axial force with ot without bending, Ac shall be replaced by the area of the portion of cross section in axial tension divided by 0.9.

Kc = structural use factor = 0.85 for calculation of section strength in structural members and for strength assessment by non-linear analysis alone per Section 4.0 without application of Eq. A4-1

= 1.0 for non-linear analysis and for strength calculation in non-structural members and systems fnu = cKoKsKcfr4 (A3-8) Where: fnu = nominal axial tensile strength corresponding to the strain limit of 0.025 c = conversion factor = 0.37 for fr4/fr1 0.7 = 0.25 + (fr4/fr1-0.7)/3 for 0.7 ≤ fr4/fr1 ≤ 1.0

= 0.35 + 0.9(fr4/fr1-1)/5 for 1.0 ≤ fr4/fr1 ≤ 1.5 = 0.44 for fr4/fr1 ≥ 1.5

A FRC matrix meeting the Eq. A3-9 shall be permitted to be considered tensile strain hardening.

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0.5(fns + fnu) ≥ 1.1ft (A3-9) Where:

ft = axial tensile strength of concrete

= 4√𝑓𝑐′ when f’c is in psi

= 0.33√𝑓𝑐′ when f’c is in MPa

It shall be permitted to determine the values of fns/(K0KsKc) and fnu/(K0KsKc) at corresponding strains of 0.0003 and 0.025, respectively, directly through tensile specimen tests acceptable to the building official having jurisdiction. When a maximum strain larger than 0.025 is used in proportioning of cross-sections in accordance with Sec. A4.2.1.1, the values of fns/(K0KsKc) and fnu/(K0KsKc) shall be determined through direct tensile specimen tests acceptable to the building official having jurisdiction. The minimum cross-sectional area of a horizontally cast specimen used for this purpose shall be at least 36 in.2 (23,000 mm2).

A3.2.2 Stress-Strain Relationships for Section Proportioning

Stress-strain (σ-ε) relationships for steel mild reinforcement, pre-stressing reinforcement and concrete in compression shall be as stipulated in Section A3.2.1. Alternatively, σ-ε relationship for concrete in compression may be considered using the equivalent rectangular stress-strain relationship as provided by ACI 318-11 Sec. 10.2.7 or Sec. ACI 318-14 Sections 22.2.2.4.1 through 22.2.2.4.3, as applicable. The σ-ε relationshipsfor fiber-reinforced concrete in tension shall be as provided by Figure A3.4.

Figure A3.4 σ-ε Relationship for Fiber-Reinforced Concrete in Tension

A4 Design for Strength

The design for strength shall assure that the required strength does not exceed design strength, as stipulated by Eq. A4-1.

Ru ≤ 𝜙Rn (A4-1) Where:

Ru = governing required strength from the analysis using the load and resistance factored design (LRFD) loading combinations, determined as stipulated by Section A4.1

𝜙Rn = design strength, calculated as the product of nominal strength and strength reduction factor, as stipulated in Section A4.2

𝜙 = strength reduction factor, as provided by Section A4.2 of this report

When non-linear analysis under factored loads is performed in accordance with Section A4.1.2(c) and A4.1.2(d) for the purposes of evaluating flexural performance, and such an analysis is executed directly

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through the application of constitutive σ-ε models presented in Section A3.2.1, Equation A4-1 shall be considered satisfied by analysis under factored loads alone, if a stable equilibrium can be found using factored constitutive models for FRC, prestressing and mild reinforcing steel. In such an analysis, the stress components of the σ-ε models shall be factored by the following stress-reduction factors: 𝜙RC = strength reduction factor for mild and prestressing steel = 0.90 𝜙FRC = strength reduction factor for FRC = 0.80 A4.1 Determination of Required Strength

Required strength calculated per the requirements of this report shall meet the provisions of Sections A4.1.1 and A4.1.2.

A4.1.1 Applicable Loads and Load Combinations

Load shall be applied as stipulated by IBC or IRC, as applicable. For loads not prescribed by IBC or IRC, as applicable, the provisions of ASCE 7 shall be observed.

Load combinations shall be consistent with strength design or the LRFD methodology and shall be as prescribed by IBC or IRC Sec. R301.1.3, as applicable.

A4.1.2 Required Analysis

The analysis requirements of Chapter 6 of ACI 318-14, or Chapters 8, 9 and 10 of ACI 318-11, as applicable, shall be observed, except as amended by the additional system requirements of this Section and by Section A5 of this report.

The applicable types of analysis, subject to the limitations stipulated by this report, are as noted in Sections A4.1.2(a) through A4.1.2(d).

(a) Linear elastic analysis (first order analysis), whereby the equilibrium is imposed upon the undeformed

state of the structure and each constitutive material is assumed as perfectly elastic under analysis loads.

(b) Geometric-nonlinear (or second-order elastic) analysis, whereby the equilibrium is imposed upon the

deformed state of a stable material-elastic structure. The requirements for the exact and the

approximate methods of second-order analysis shall be as outlined in Ch. 10 of ACI 318-11, or Ch. 6 of

ACI 318-14, as applicable.

(c) Material-nonlinear (or inelastic) analysis, whereby the equilibrium is imposed on the undefermoed state

of the system, but where the material ductility allows for redistribution of load among sub-components

of the system through inelastic deformations of the material. Redistribution of loads shall be permitted

up to any point of stable equilibrium before achieving the state of collapse. It shall be permitted to

capture non-linear effects of material directly through the constitutive relationships of Section A3.1.2.

Alternatively, it shall be permitted to model the non-linear response of a fiber-reinforced concrete matrix

using the fr-’ relationship as provided by Figure A4.1. The values of EI and frf and fr1 through fr4 are as

defined in Section A3.1.1. Therein, where a particular section of the continuum contains mild

reinforcement and/or prestressing steel in addition to FRC, the contribution to and the effect of FRC on

the non-linear response shall be permitted to be neglected. Alternatively, the combined response may

be established by test, or modeled using rational approach, in a manner acceptable to the building official

having jurisdiction.

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Figure A4.1 Modeling of Non-linearity through fr-’ Relationship

(d) Second-order inelastic analysis is the inelastic analysis in which the equilibrium is imposed on a stable

equilibrium of a deformed structure.

It shall not be permitted to use the analyses defined by Section A4.1.2(d) of this report in members and systems reinforced with fibers only. Such an analysis shall only be permitted in FRC systems in which the minimum flexural reinforcement in each member, as stipulated by ACI 318, is provided in the form of mild reinforcement and/or post-tensioning.

Finite element analysis, when employed as a part of executing Section A4.1.2(a) through A4.1.2(d), shall be required to satisfy the requirements of ACI 318-11 Chapter 10, or ACI 318-14 Chapter 6, as applicable.

A4.2 Determination of Design Strength

Available strength of members and systems, as applicable, shall be determined in accordance with Sections A4.2.1 through A4.2.3.

It shall be permitted to determine strength of members, systems and components through full-scale testing in accordance with IBC Sec. 1709.

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A4.2.1 Flexural And Axial Strength

Flexural and axial-flexural strength envelope shall be established from stress-strain compatibility of individual elements contributing to the strength of the section, including FRC, concrete in compression, mild steel in tension and compression, and prestressing. Flexural, axial, and flexural-axial strength determination shall meet the requirements of Sections A4.2.1.1 through A4.2.1.3, as applicable. A4.2.1.1 Flexural Strength

Flexural strength of a cross-section shall be established using Sec. A4.2.1.1(a). If section equilibrium of forces for a particular cross-section cannot be established within the strain constraints of Sec. A4.2.1.1(a), it shall be permitted to determine flexural strength of the section using A4.2.1.1(b) or A4.2.1.1(c) for cross-sections with combined fiber and mild reinforcement, or Section A4.2.1.1(c) for cross-sections with Dramix® fibers as the sole form of reinforcement.

(a) Flexural Model I

Flexural Model I shall be as defined by Figure A4.2 and given by Eq. A4-2. The - relationships

for the individual constituents of the cross-section shall be as stipulated by Section A3.2.2.

Mn =

RCAsfs(d − d′′′) +

RCAs

′ fs′(d′ − d′′′) +

FRCFFRC(d′′ − d′′′) (A4-2)

Where: Mn = factored moment strength RC = strength reduction factor for bending strength due to conventional reinforcement,

ACI 318-11 Sec. 9.3.2, or ACI 318-14 Sec. 21.2, as applicable As = cross-sectional area of tensile mild reinforcement fs = stress in tensile mild reinforcement A’s = cross-sectional area of compression mild reinforcement f’s = stress in compression mild reinforcement FRC = strength reduction factor for bending strength due to FRC = 0.80

The dimensional parameters d, d’’ and d’’’ appearing in Eq. A4-2 are as depicted in Figure

A4.2. The depth d’’’ shall represent the length from the top of the cross-section to the centroid of the compressive stress block. For representation of concrete compressive stress block per ACI 318-11 Sec. 10.2.7 or Sec. ACI 318-14 Sections 22.2.2.4.1 through 22.2.2.4.3, d’’’ = a/2. The following are the conditions of applicability of Flexural Model I:

(1) The maximum tensile strain in FRC, FRC, shall not exceed 0.025, unless a larger value can be

established through rational analysis or testing acceptable to the building official having

jurisdiction.

(2) For cross-sections with combined mild reinforcement and FRC, the tensile strain in mild steel,

s, shall meet the requirements of ACI 318-11 Sec. 10.3.5 or ACI 318-14 Sections 7.3.3.1,

8.3.3.1 and 9.3.3.1, as applicable.

(3) For cross-sections with combined reinforcement meeting the requirements of Sec.

A4.2.1.1(a)(2), but not meeting the tension-controlled cross-section requirement of ACI 318-

11 Sec. 10.3.4 or ACI 318-14 Table 21.2.2, the value of RC shall be modified as given by ACI

318-11 Sec. 9.3.2.2 or ACI 318-14 Table 21.2.2, as applicable. The modified value of FRC in

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such a cross-section shall be calculated as that given by ACI 318-11 Sec. 10.3.4 or ACI 318-14

Table 21.2.2, as applicable, multiplied by the factor of (8/9).

(4) For cross-sections without mild reinforcement, the requirements of Section A4.2.1.1(a)(2)

shall be imposed on FRC.

(5) For cross-sections reinforced with Dramix® fibers alone and meeting the requirements of

Section A4.2.1.1(a)(4), but not meeting the tension-controlled cross-section requirement of

ACI 318-11 Sec. 10.3.4 or ACI 318-14 Table 21.2.2, the value of FRC in such a cross-section

shall be calculated as that given by ACI 318-11 Section 10.3.4 or ACI 318-14 Table 21.2.2, as

applicable, multiplied by the factor of (8/9).

(6) Concrete compressive strain, c, shall be set to the maximum usable value stipulated by ACI

318-11 Section 10.2.3 or ACI 318-14 Section 22.2.2.1.

(7) Compression reinforcement strain, ’s, and the corresponding stress, f’s, shall be established

from strain compatibility of the cross-section.

Figure A4.2 Flexural Model I

(b) Flexural Model II

Flexural Model I shall be as defined by Figure A4.3 and given by Equation A4-2. The -

relationships for the individual constituents of the cross-section shall be as stipulated by Section

A3.2.2. The dimensional parameters d, d’’ and d’’’ appearing in Eq. A4-2 are as depicted in Figure

A4.3. The depth d’’’ shall represent the length from the top of the cross-section to the centroid of the

compressive stress block.

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For representation of concrete compressive stress block per ACI 318-11 Section 10.2.7 or Section ACI 318-14 Sections 22.2.2.4.1 through 22.2.2.4.3, d’’’ = a/2. The following are the conditions of applicability of Flexural Model II:

(1) The maximum tensile strain in FRC, FRC, shall be set equal to 0.025, unless a larger value can

be established through rational analysis or testing acceptable to the building official having

jurisdiction.

(2) The tensile strain in mild steel, s, shall meet the requirements of ACI 318-11 Sec. 10.3.5 or

ACI 318-14 Sections 7.3.3.1, 8.3.3.1 and 9.3.3.1, as applicable.

(3) For cross-sections meeting the requirements of Sec. A4.2.1.1(b)(2), but not meeting the

tension-controlled cross-section requirement of ACI 318-11 Sec. 10.3.4 or ACI 318-14 Table

21.2.2, the value of RC shall be modified as given by ACI 318-11 Sec. 9.3.2.2 or ACI 318-14

Table 21.2.2, as applicable.

(4) Concrete compressive strain, c, shall be set to the maximum usable value stipulated by ACI

318-11 Section 10.2.3 or ACI 318-14 Section 22.2.2.1.



Figure A4.3 Flexural Model II

(c) Model III

Flexural Model III shall be as defined by Figure A4.4 and given by Equation A4-2. The -

relationships for the individual constituents of the cross-section shall be as stipulated by Section

A3.2.2, except that ACI 318-11 Section 10.2.7 or ACI 318-14 Sections 22.2.2.4.1 through 22.2.2.4.3, as

applicable, shall not apply.

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The dimensional parameters d, d’’ and d’’’ appearing in AEq. 4-2 are as depicted in Figure A4.4. The depth d’’’ shall represent the length from the top of the cross-section to the centroid of the compressive stress block. The following are the conditions of applicability of Flexural Model III:

(1) The maximum tensile strain in FRC, FRC, shall be equal to 0.025, unless a larger value can be

established through rational analysis or testing acceptable to the building official having

jurisdiction.

(2) For cross-sections with combined mild reinforcement and FRC, the tensile strain in mild steel,

s, shall meet the requirements of ACI 318-11 Sec. 10.3.5 or ACI 318-14 Sections 7.3.3.1,

8.3.3.1 and 9.3.3.1, as applicable.

(3) For cross-sections with combined reinforcement meeting the requirements of Sec.

A4.2.1.1(c)(2), but not meeting the tension-controlled cross-section requirement of ACI 318-

11 Sec. 10.3.4 or ACI 318-14 Table 21.2.2, the value of RC shall be modified as given by ACI

318-11 Sec. 9.3.2.2 or ACI 318-14 Table 21.2.2, as applicable.

(4) Concrete compressive strain, c, shall be as required for the strain compatibility of the cross-

section, but not larger than 0.003.



Figure A4.4 Flexural Model III

When applicable, the contribution of pre-stressing on the moment strength shall be permitted to be calculated using Equation A4-3 and considered using the flexural strength models Section A4.2.1.1(a) through A4.2.1.1(c), as applicable. Stress in prestressed reinforcement, fps, shall be determined per ACI 318-14 Section 22.2.4, or ACI 318-11 Section 18.7, as applicable.

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Mn = RC

[Asfs(d − d′′′) + Apsfps(𝑑𝑝 − d′′′)] + RC

As′ fs

′(d′ − d′′′) + FRC

FFRC(d′′ − d′′′) (A4-3)

In Equation A4-3, the parameter dp represents the distance from the extreme compression fiber to the centroid of the pre-stressing reinforcement in the cross-section, as defined by ACI 318-11 Sec. 2.1, or ACI 318-14 Sec. 2.2, as applicable. A4.2.1.2 Axial Strength

The effect of Dramix® fibers on the compressive strengths Pn and P0, as computed by ACI 318-11 Section 10.3.6, or ACI 318-14 Sections 22.4.2.2 and 22.4.2.3, as applicable, shall be neglected.

Except for the FRC matrices exhibiting axial strain hardening, it shall not be permitted to use Dramix® fibers as the sole form of reinforcement in resisting axial tension. Axial tensile strength provided by Dramix® FRC, except for resisting shrinkage and temperature effects, shall be computed using Eq. A4.4. It shall be permitted to resist axial tension with Dramix® FRC in combination with conventional reinforcement, provided the member is proportioned to resist at least 70 percent of the factored tensile forces through conventional reinforcement. When tension strength is provided by Dramix® FRC in combination with mild and prestressing reinforcement, the tensile strength calculated using Eq. A4-4, shall be added to the tensile strength computed using ACI 318-14 Sec. 22.4.3, whether ACI 318-11 or ACI 318-14 applies.

Tn =

FRCAcfnu (A4-4)

Where: Tn = factored tensile strength Ac = area of fiber-reinforced concrete cross-section The provisions of this Section shall not be construed as applicable to the use of FRC for the purposes of resisting shrinkage and temperature effects. Internal tensile forces due to shrinkage and temperature effects shall be considered in accordance with Section A5. A4.2.1.3 Flexural-Axial Interaction

It shall be permitted to consider the contribution of Dramix® FRC to flexural forces in combined axial-flexural interaction. The requirements of Sec. A4.2.1.1 and A4.2.1.2 shall apply. A4.2.1.4 Stability of Members and Frames

Contribution of FRC to the system and member stability shall be established through testing in accordance with IBC Sec. 1709. Alternatively, contribution of FRC to the system and member geometric properties shall be permitted to be neglected in the analysis when determining the required member and system strength, and member and frame stability considered as required by the provisions of ACI 318. The contribution of Dramix® fibers to the calculated design strength shall be considered per Sections A4.2.1.1 through A4.2.1.3.

A4.2.2 Shear Strength

One-way shear of a FRC section shall be established as provided by Section A4.2.2.1. Punching shear strength shall be as established by Section A4.2.2.2.

When minimum shear reinforcement requirements for beams are satisfied using fiber reinforced concrete per the provisions of ACI Section 11.4.6.1(f), or per ACI 318-14 Section 9.6.3.1, as applicable, all requirements of those provisions shall be satisfied, irrespective of Section A4.2.2.1 of this report. It shall, however, be permitted to use the resulting mechanical properties of the FRC matrix per Section A3.1.1 to compute the shear strength of the member using Section A4.2.2.1 of this report.

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A4.2.2.1 One-Way Shear

One-way shear available strength of a Dramix® FRC section shall be computed using Equation A4-5.

Vn = [VC,EC + 1.1VFRC + Vs] ≥(Vc + Vs) (A4-5) Where:

= strength reduction factor for shear per ACI 318-11 Sec. 9.3.2, or ACI 318-14 Sec. 21.2, as applicable

Vn = available shear strength, lbs (N) VC,EC = shear strength contributed by the reinforced section, lbs (N) = 0 for members with Vs > 0, otherwise

=[0.15𝐹𝑠𝑘2 (100𝐴𝑠

𝑏𝑤𝑑𝑓𝑐

′/𝑘2)1/3

+ 0.12𝑓𝑝𝑒] 𝑏𝑤𝑑 ≥ (𝑣𝑚𝑖𝑛 + 0.12𝑓𝑝𝑒)𝑏𝑤𝑑 (A4-6)

Fs = size factor

= 1 + √200

𝑘1𝑑≤ 2.0

As = cross-sectional area of longitudinal reinforcement at the section at which the shear is calculated, in.2 (mm2)

bw = member width, as defined by ACI 318-11 Sec. 2.1, or ACI 318-14 Sec. 2.2, as applicable, in. (mm) d = distance from extreme compression fiber to centroid of longitudinal tension reinforcement per

ACI 318-11 Sec. 2.1 or ACI 318-14 Sec 2.2, in. (mm) k1 = dimensional unit conversion factor

= 25.4 when d is in in. = 1.00 when d is in mm

k2 = stress unit conversion factor = 145 when f’c is in psi = 1 when f’c is in MPa

fpe = effective prestress stress, as defined by ACI 318-11 Sec. 2.1 or ACI 318-14 Sec. 2.2, as applicable, psi (MPa)

Vc = shear strength provided by concrete, computed per ACI 318-11 (Sec. 11.2, 11.3 or 11.11), or per ACI 318-14 (Sec. 22.5.1.3 through 22.5.1.5) as applicable, lbs (N)

VFRC = shear strength provided by Dramix® FRC, lbs (N) = vFRCbwh (A4-7) = 0 when the member is in uniaxial tension vFRC = 0.37KcKoKsfr4, psi (MPa) (A4-8) vmin = 0.632Fs

3/2f’c1/2 for d ≤ 24 in. and US Unit System is used = 0.452Fs3/2f’c1/2 for d > 31 in. and US Unit System is used

= 0.0525Fs3/2f’c1/2 for d ≤ 600 mm and when SI Unit System is used = 0.0375Fs3/2f’c1/2 for d > 800 mm and when SI Unit System is used

For the intermediate range of d between 24 (600 mm) and 31 in. (800 mm), vmin shall be permitted to be determined by interpolation between the above given values.

Vs = shear strength provided by conventional reinforcement, computed per ACI 318-11 (Sec. 11.4, 11.9.9 or 11.1) or ACI 318-14 Sec. 22.5.1.6, as applicable, lbs (N)

h = member thickness or height, as applicable, as defined by ACI 318-14 Sec. 2.2, in. (mm) The reinforcement corresponding to the cross-sectional area As in Eq. A4-6 shall be extended for the

distance equal to at least (d + ld) beyond the section at which shear is being considered. The length ld is as defined by ACI 318-11 Section 2.1, or Sec. ACI 318-14 Section 2.2, as applicable.

Limitations and requirements of ACI 318-11 (Sec. 11.1 through 11.4) or ACI 318-14 (Sec. 22.5.1 through 22.5.10, except 22.5.1.1), as applicable, shall apply unless otherwise can be shown through testing acceptable to

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the building official having jurisdiction, except that the minimum shear reinforcement requirement of ACI 318-11 Section 11.4.6.1 or ACI 318-14 Section 9.6.3.1, as applicable, shall be considered per Sec. A5.5 of this report.

Except when established otherwise through testing acceptable to the building official having jurisdiction, VFRC = 0 when Vc is required to be computed using ACI 318-11 11.2.2.3 or ACI 318-14 Sec. 22.5.7, as applicable. 4.2.2.2 Two-Way Shear

(a) Design using ACI 318-14 When designing per ACI 318-14, two-way shear strength shall be considered per ACI 318-14 Sec. 22.6, except that ACI 318-14 Eq. 22.6.1.2 and 22.6.1.3 shall be taken modified as Eq. A4-9 and A4-10, respectively.

vn = vc + 1.1vFRC (A4-9) vn = vc + max(vs, 1.1vFRC) (A4-10) In Equations A4-9 and A4-10, the value of vFRC shall not be taken as larger than 0.4vc. This requirement shall apply in addition to the limits of ACI 318-14 Section 22.6.6. In application of Equations A4-9 and A4-10, it shall be permitted the resisting stress vFRC acts over the full depth of the section h, as defined by ACI 318-14 Sec. 2-2. Instead of Eq. A4-10, it shall be permitted to determine the punching shear strength provided by combined contribution of FRC, concrete and shear reinforcement through testing per IBC Section 1709. (b) Design using ACI 318-11 When designing per ACI 318-11, two-way shear shall be considered per ACI 318-11 Section 11.11, except as modified by this Section.

Equation 11-2 of ACI 318-11 shall be modified as provided by Eq. A4-11 of this report. In the Eq. A4-11, the parameters Vn, Vc, Vs and bo are as defined by ACI 318-11 Sec. 2.1.

Vn = Vc + max(Vs, 1.1VFRC) (A4-11) Where: VFRC = nominal punching shear strength provided by Dramix® FRC =vFRChb0

In Eq. A4-11, the value of VFRC shall be limited to 0.4Vc. This requirement shall be applied in addition to the stress limit requirements of ACI 318-11 Sections 11.11.3.1, 11.11.3.2, 11.11.4.8, 11.11.5.1, 11.11.5.2, 11.11.5.4, 11.11.7.2, and 11.11.7.3. In ACI 318-11 Equations 11-38, the term Vc shall be replaced with (Vc + 1.1VFRC), and the term (Vc + Vs) in ACI 318-11 Eq. 11-39 shall be replaced with [Vc + max(1.1VFRC, Vs)]. A4.2.2.3 Strut-and-Tie Method

It shall be permitted to neglect the effect of Dramix® FRC in application of strut-and-tie methodology of ACI 318-11 Appendix A or ACI 318-14 Chapter 23, as applicable. Alternatively, it shall be permitted to consider the capacity of Dramix® FRC in calculation of tie strength per ACI 318-11 Sec. A.4, or ACI 318-14 Sec. 23.7, as applicable, provided that one of the following conditions is satisfied:

(a) The member is reinforced with a tensile strain hardening Dramix® FRC matrix,

(b) The member is reinforced with a flexural strain hardening Dramix® FRC matrix and the tie is

configured to resist tensile forces in combination with the conventional reinforcement, in which the

conventional reinforcement is proportioned to resist at least 70 percent of the factored tie forces,

(c) The tensile stresses in the tie do not exceed the value of fnu, as defined by Section A3.2.1, and

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(d) For the purposes of design of general zones per ACI 318-11 Section 18.13.5.1(a) or ACI 318-14 Sec.

25.9.4.3.1(a), as applicable, it shall be permitted to calculate the resistance on the basis of fnu in

combination with conventional reinforcement. When used for this purposes, requirements of Sec.

A4.2.2.3(b) do not apply.

When the contribution of Dramix® FRC to the tensile strength of a tie is considered, subject to the conditions of this Section, the nominal tensile strength of a tie due to contribution of FRC shall be computed using Eq. A4-12 and added to the nominal tie strength, Fnt, computed by ACI 318-11 Eq. A-6, or ACI 318-14 Eq. 23.7.2, as applicable.

Tn,FRC = 1.1Attfnu (A4-12) Where:

Tn,FRC = nominal tensile strength of FRC tie Att = area of the FRC tensile strut, excluding the cross-sectional area of any conventional

reinforcement occurring within the area Att = wtwc

wt = effective height of concrete concentric with a tie, as defined by ACI 318-11 Section 2.1, or ACI 318-14 Sec. 2.2, as applicable

wc = effective width of the tie, equal to the width of the adjoining strut, ws, as defined by ACI 318-11 Section 2.1, or ACI 318-14 Section 2.2, as applicable

A4.2.2.4 Shear Friction

Where shear strength of a member is established using shear friction approach of ACI 318-11 Section 11.6, or ACI 318-14 Section 22.6, as applicable, the effect of Dramix® fibers on shear strength shall be neglected. A4.2.3 Torsion

Unless established through full-scale independent testing of structural members or systems, as appropriate, contribution of fibers to the member torsional strength may conservatively be neglected and the strength of a section in torsion shall be determined per ACI 318-11 Section 11.5, or ACI 318-14 Section 22.7, as applicable.

Alternatively, when ACI 318-14 is used for the design or members with FRC matrices exhibiting tensile strain hardening, it shall be permitted to be to consider the torsional resistance provided by Dramix® fibers using ACI 318-14 Sec. 22.7.6, except that the ACI 318-14 Eq. 22.7.6.1 for the calculation of nominal torsional strength, Tn, shall be modified as provided by Eq. A4-13. The variables Tn, A0, At, fyt, , Al, fy and s shall be as given by Section 22.7.6 and as defined by ACI 318-14 Section 2.2.

Tn =2A0Atfyt

scotθ + 1.1Tn,FRC (A4-13a)

Tn =2A0Alfy

scotθ + 1.1Tn,FRC (A4-13b)

Where: Tn,FRC = torsional strength due to Dramix® FRC, calculated as the product of the axial tensile strength,

vFRC, and the area corresponding to the principal plane of failure. Tn,FRC shall be permitted to be taken as 1.1Tth, where Tth is given by ACI 318-14 Section 22.7.5.1, as applicable, except that the

term √𝑓𝑐′ therein shall be replaced with vFRC.

When ACI 318-11 is used for the design of members with FRC matrices exhibiting tensile strain

hardening, it shall be permitted to be to consider the torsional resistance provided by Dramix® fibers using ACI 318-14 Sec. 11.5, except that the ACI 318-11 Eq. 11-21 for the calculation of nominal torsional strength, Tn, shall

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be modified as provided by Eq. A4-14. The variables Tn, A0, At, fyt, and s shall be as given by Section 22.7.6 and as defined by ACI 318-14 Section 2.1.

Tn =2A0Atfyt

scotθ + 1.1Tn,FRC (A4-14)

Where: Tn,FRC = torsional strength due to Dramix® FRC, calculated as the product of the axial tensile strength,

vFRC, and the area corresponding to the principal plane of failure. Tn,FRC shall be permitted to be taken as 1.1Tth, where Tth is given by 318-11 Section 11.5.2.2, as applicable, except that the term

√𝑓𝑐′ therein shall be replaced with vFRC.

When a tensile strain hardening Dramix® FRC matrix is used to provide torsional resistance, all requirements of ACI 318-11 Sec. 11.5, or ACI 318-14 Sec. 22.7, except as modified herein, shall apply. Tensile strain hardening Dramix® FRC matrix shall be permitted to be provided as the sole source of torsional resistance only in statically indeterminate structures where moment redistribution is possible. A4.2.4 Bearing Strength

It shall be permitted to neglect the contribution of FRC to the bearing strength, and consider bearing strength of a Dramix® FRC member or system using the provisions of ACI 318-11 Section 10.14, or ACI 318-14 Section 22.8, as applicable. A5 System and Component Specific Requirements

System and member specific requirements stipulated by this section shall be satisfied for each specific component and system for which the required and design strengths are determined using the provisions of Section A4. Except for the systems and components covered in Sections A5.2 and A5.3, elements and systems stipulated in Section A5 of this report shall be configured as capable of deformations of at least five times those calculated using linear elastic analysis and uncracked section properties under service load combinations. Alternatively, such elements and systems shall be capable of undergoing maximum deformations of at least 20 times those calculated using linear elastic analysis and uncracked section properties under service load combinations. This requirement shall be permitted to be shown as satisfied through analysis or testing in accordance with IBC Section 1709. It shall be permitted to consider this requirement satisfied for each system and component in which conventional integrity and the prescribed minimum flexural reinforcement is provided in the form of mild or pre-stressing reinforcement per the requirements of ACI 318-11 or ACI 318-14, as applicable. A5.1 Structural Integrity

Structural members and systems incorporating Dramix® SFRC shall be required to meet the structural integrity requirements of 2012/2015 IBC Sec. 1615 or 2018 IBC Sec. 1616, as applicable. It shall not be permitted to employ Dramix® SFRC to in part or fully supplant the reinforcement or framing requirements necessary to satisfy the structural integrity requirements.

A5.2 Non-Structural Slabs on Ground When reinforced with Dramix® fibers for flexural effects, slabs on ground shall be constructed with FRC

matrices exhibiting the minimum value of RT,150D , as defined by Sec. A3.1.1, of 30 percent.

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Except as required otherwise by this Section, it shall be permitted to reinforce slabs on ground with Dramix® fibers for the resistance of flexural, shear, and shrinkage and temperature effects, with or without supplemental mild and pre-stressing reinforcement.

In-plane forces resulting from abrupt changes in slab geometry, such as those at re-entrant corners or at column isolation joints, shall be resisted with conventional reinforcement solely or in combination with FRC.

It shall be permitted to determine the required strength under factored forces using the analyses per Section A4.1.2(a) or A4.1.2(c) of this report. When the analysis of slabs on ground is performed using Section A4.1.2(c), it shall be permitted to approximate the effect of non-linear deformations on redistribution of flexural effects through the system by performing an analysis under factored forces using Section A4.1.2(a) and reducing the required strength from such an analysis by the factor RNL given by Eq. A4-15, provided that the effect of any geometric discontinuities has been considered. For load effects associated with upward (uplift) forces, affected systems shall be reinforced with a flexural strain hardening FRC matrix, or be otherwise reinforced such that Mn+ and Mn- both exceed pcMpc. The parameters Mn+, Mn- and pcMpc are as defined in Eq. A4-15.

RNL = 1 + Us (A4-15) Where:

Us = Mn+/[max(Mn-, pcMpc)] for load effects associated with downward (gravity) forces = 1.0 for load effects associated with upward (uplift) forces

Mn+ = available flexural of a Dramix® FRC Section in positive bending, determined per Sec. A4.2.1.1

Mn- = available flexural of a Dramix® FRC Section in negative bending, determined per Sec. A4.2.1.1, corresponding to the region of the slab under consideration in negative bending

pcMpc = available flexural strength of plain concrete, to be taken as Mn, where Mn is as given by ACI 318-11 Sec. 22.5.1 or ACI 318-14 Sec. 11.5.1.1 and 14.5.2.1, except that shall be

permitted to be taken as pc and 𝑓𝑟 = 7.5√𝑓𝑐′ shall be used in lieu of 𝑓𝑟 = 5√𝑓𝑐

′

pc = strength reduction factor for plain concrete, taken as 0.75

For the purposes of this section, in lieu of the requirements of Section Section A4.1.1, loads shall be permitted to be factored by a factor of 1.2 for static loads and an additional load factor of 1.25 for dynamic loads, unless other load factors are required by the registered design professional.

When finite element analysis is used either in conjunction of with Section A4.1.2(a) or Section A4.1.2(c) for the purposes of flexural design under strength level factored forces, it shall be permitted to integrate the results of the analysis for the purposes of section proportioning over the strip not exceeding five times the slab thickness.

Design for one-way and two-way shear shall be performed on the basis of a linear-elastic analysis per Section A4.1.2(a).

For unreinforced slabs designed per ACI 360, the minimum reinforcement using Dramix® fibers shall be provided for shrinkage and temperature effects as required by Section A6.

Structural integrity reinforcement shall not be required for the systems meeting the requirements of this Section.

When distributed mild reinforcement is used in combination with Dramix® FRC for the purposes of this Section, maximum reinforcement spacing of ACI 318 for one-way or two-way slabs, as applicable, shall be applied. When prestressing steel is used in combination with Dramix® FRC for the purposes of this Section, maximum tendon spacing and minimum prestress requirements of ACI 318 for one-way or two-way slabs, as applicable, shall be applied.

A5.3 Pile Supported Non-Structural Slabs on Ground

When reinforced with Dramix® fibers for flexural effects, pile supported slabs on ground shall be supported by the discrete supports, such as piles, meeting the requirements of IBC Section 1810.

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Except as required otherwise by this Section, it shall be permitted to reinforce slabs on ground with Dramix® fibers for the resistance of flexural, shear, and shrinkage and temperature effects, with or without supplemental mild and pre-stressing reinforcement. However, only Dramix® FRC matrices exhibiting flexural strain hardening shall be permitted when the steel fibers are the sole form of flexural reinforcement used in the slab. Available strength shall be determined using Section A4.

In-plane forces resulting from abrupt changes in slab geometry, such as those at re-entrant corners or at column isolation joints, shall be resisted with conventional reinforcement solely or in combination with FRC. It shall be permitted to determine the required strength under factored forces using the analyses per Section A4.1.2(a) or A4.1.2(c) of this Specification. Circular or regular polygon-shaped discrete slab supports shall meet the requirements of ACI 318-11 Section 13.6.3.1, or ACI 318-14 Section 8.10.1.3, as applicable, for the purposes of considering flexural and one-way shear effects.

When finite element analysis is used either in conjunction of with Section A4.1.2(a) or Section A4.1.2(c), the results of such an analysis shall be permitted to be integrated into discrete values of factored shear, moment and axial force as follows:

(a) For slabs on piles reinforced solely with fibers, or with a combination of fibers and mild reinforcement,

it shall be permitted to integrate the results of a finite element analysis into discrete values of factored

shear, moment and axial force over the section widths configured as column and middle strips, as defined

by ACI 318-11 Section 13.2.1 and 13.2.2, or ACI 318-14 Section 8.4.1.5 and 8.4.1.6, as applicable.

Integration of forces over the smaller widths shall be permitted.

(b) For pre-stressed Dramix® FRC slabs on piles with or without mild reinforcement, integration of forces

per Section A5.3(a) shall be permitted. Alternatively, the section forces may be integrated at each pile as

the width representing the sum of half-way distances to the centerlines of adjacent pile supports.

Design for one-way and two-way shear shall be performed on the basis of a linear-elastic analysis per Section A4.1.2(a). Structural integrity reinforcement shall not be required for the systems meeting the requirements of this Section. Reinforcement for shrinkage and temperature effects shall be provided by Section A6.

When distributed mild reinforcement is used in combination with Dramix® FRC for the purposes of this Section, maximum reinforcement spacing of ACI 318 for one-way or two-way slabs, as applicable, shall be applied. When prestressing steel is used in combination with Dramix® FRC for the purposes of this Section, maximum tendon spacing and minimum prestress requirements of ACI 318 for one-way or two-way slabs, as applicable, shall be applied.

A5.4 Structural Slabs

Only flexural strain hardening FRC matrices meeting the criteria stipulated by Eq. A3-5 shall be permitted in elevated slabs for the purposes of calculating the available flexural, one-way shear, or two-way shear strength as provided by this Section and Section A4. Reinforcement of elevated slabs for shrinkage and temperature effects shall be as provided by Section A6. The required forces shall be determined using first-order linear elastic analysis per Section A4.1.2(a). Provisions of Sections A5.4.1 and A5.4.2 apply to elevated structural slabs. For slabs on ground subjected to vertical structural loads, applicable provisions of Section A5.9.3 shall apply. Additionally, for structural slabs on ground subjected to in-plane forces, applicable provisions of Sec. A5.10 shall apply.

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A5.4.1 One-Way Slabs

Except where specifically provided otherwise by this Section, the requirements of ACI 318-14 Chapter 7, or the corresponding sections of ACI 318-11, as applicable, shall be met, and the effects of Dramix® fibers shall be neglected, unless otherwise demonstrated through testing per IBC Sec. 1709 or other evidence acceptable to the building official having jurisdiction. Minimum flexural reinforcement in non-prestressed one-way slabs shall be required in the form of mild reinforcement per ACI 318-11 Section 7.12.2.1 or ACI 318-14 Section 7.6.1.1, as applicable. However, it shall be permitted to use Dramix® fibers to provide the difference between the required flexural strength and the flexural strength provided by the minimum reinforcement per ACI 318-11 Sec. 318-11 Section 7.12.2.1, or ACI 318-14 Section 7.6.1.1, as applicable.

It shall be permitted to meet the requirements of ACI 318-11 Section 18.8.2, and 18.9.2, or ACI 318-14 Section 7.6.2.1 and 7.6.2.2, as applicable, using Dramix® fibers alone, or in combination with mild reinforcement.

The contribution of Dramix® FRC towards meeting the requirements of ACI 318-11 Sec. 7.6.2.3 or ACI 318-14 Sec. 18.9.2, as applicable, shall be neglected unless testing or analysis can be produced indicating equivalent performance and deemed acceptable by the building official having jurisdiction. It shall be permitted to provide one-way shear strength in one-way slabs using Dramix® fibers as provided by Section A4.2.2.1. Where punching shear occurs in one-way slabs due to concentrated forces or supports, it shall be permitted to consider such effects using Section A4.2.2.2. The minimum shear reinforcement requirements of ACI 318-11 Section 11.4.6.1, or ACI 318-14 Sec. 7.6.3.1, as applicable, shall be permitted to be satisfied with Dramix® FRC, provided that the resulting shear strength of the FRC matrix equals or exceeds that corresponding to Av,min. The minimum reinforcement, Av,min, is as defined by ACI 318-11 Sec. 2.1, or ACI 318-14 Section 2.2, as applicable.

When conventional reinforcement is provided for minimum flexural requirements, serviceability, or structural integrity, Dramix® FRC shall be permitted to be used to generate the difference between the required and the design flexural strength provided by such reinforcement.

A5.4.2 Two-Way Slabs

Except where specifically provided otherwise by this Section, the requirements of ACI 318-14 Chapter 8, or the corresponding Sections of ACI 318-11, as applicable, shall be met, and the effects of Dramix® fibers shall be neglected, unless otherwise demonstrated through testing per IBC Sec. 1709 or other evidence acceptable to the building official having jurisdiction.

The stress limit of ACI 318-11 Sec. 18.3.3 or ACI 318-14 Sec. 8.3.4.1, as applicable, shall be satisfied unless testing per IBC Section 1709 or other evidence can satisfactorily demonstrate to the building official having jurisdiction a commensurate behavior and serviceability performance with a higher stress limit for a corresponding fiber reinforced concrete matrix.

It shall be permitted to consider the contribution of Dramix® to the calculation of the factored moment 𝜸FMsc per ACI 318-11 Section 13.5.3.2 through 13.5.3.4 or ACI 318-14 Section 8.4.2.3.2 through 8.4.2.3.5, as applicable, with the appropriate modification in Ks, as noted in Section A3.2.1 of this Specification. The parameter 𝜸FMsc shall be as defined by ACI 318-11 Section 2.1 or ACI 318-14 Section 2.2, as appropriate.

Except for the bottom reinforcement in column strips, minimum flexural reinforcement in non-prestressed two-way slabs shall per ACI 318-11 Section 7.12.2.1 or ACI 318-14 Section 8.6.1.1, as applicable, shall be permitted to be satisfied using Dramix® FRC solely or in combination with conventional reinforcement. Where Dramix® FRC is provided as the sole form of reinforcement towards the minimum reinforcement requirements, the provisions of ACI 318-11 Section 13.3.8.1 or ACI 318-14 Section 8.7.4.1.3, as applicable, shall not apply. The contribution of Dramix® towards meeting the requirement of ACI 318-11 Section 7.12.2.1 or ACI 318-14 Section 8.6.2.3, as applicable, shall be defined as the FRC matrix that provides factored flexural strength equivalent to that of ASTM A615 Grade 60 reinforcement calculated per ACI 318-11 Section 7.12.2.1, or ACI 318-

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14 Section 8.6.2.3, as applicable, and placed in the tensile zone of the section, assuming the least clear cover permitted by ACI 318 for the application considered.

When conventional reinforcement is provided for minimum flexural requirements, serviceability, or structural integrity, Dramix® FRC shall be permitted to be used to generate the difference between the required and the design flexural strength provided by such reinforcement.

It shall be permitted to provide one-way and two-way shear strength in two-way slabs using Dramix® fibers as provided by Section A4.2.2.1 and Sec. A4.2.2.2, respectively, except that the adjustment to Vc, as provided by ACI 318-11 Section 8.13.8, or ACI 318-14 Sec. 8.8.1.5, as applicable may be applied.

In Seismic Design Category (SDC) D through F, the provisions of ACI 318-11 Section 21.3.6.1, or ACI 318-14 Section 18.4.5, as applicable, shall be met in addition to those of this Section. The strength resulting from the provided shear reinforcement, when required by these ACI 318 provisions, shall be permitted to be calculated using Section A4.2.2.2. A5.5 Beams

In members reinforced with Dramix® fibers, the required forces shall be determined using first-order linear elastic analysis per Section A4.1.2(a).

Only flexural strain hardening Dramix® FRC matrices meeting the criteria stipulated by Eq. A3-5 shall be permitted in beams, including structural grade beams, for the purposes of calculating the design flexural and one-way shear strength as provided by this Section and Section A4.

When a tensile strain hardening Dramix® FRC matrix is used in conjunction with Section A4.2.3 to provide torsional resistance, the minimum reinforcement requirements of ACI 318-11 Section 11.5.3.7 through 11.5.3.11, 11.5.4, 11.5.5 and 11.5.6, or the requirements ACI 318-14 Sec. 9.7.5 and 9.7.6, as applicable, notwithstanding the other member- and system-specific requirements of Section A5, shall be satisfied.

It shall be permitted to use Dramix® fibers in combination with conventional reinforcement to satisfy the requirements of ACI 318-11 Section 10.5.1 or ACI 318-14 Section 9.6.1, as applicable. The conventional reinforcement provided shall at the minimum be that required by the applicable detailing and integrity reinforcement provisions of ACI 318, except that integrity and detailing requirements shall not apply in structural grade beams reinforced with Dramix® fibers as the sole form of flexural and shear reinforcement. The contribution of Dramix® towards meeting the requirement of ACI 318-11 Section 10.5.1 or ACI 318-14 Section 9.6.1, as applicable, shall be defined as the FRC matrix that provides factored flexural strength equivalent to that of ASTM A615 Grade 60 reinforcement calculated per ACI 318-11 Section 10.5.1 or ACI 318-14 Section 9.6.1, as applicable, and placed in the tensile zone of the section, assuming the least clear cover permitted by ACI 318 for the application considered.

It shall not be permitted to use Dramix® fibers alone to satisfy the requirement ACI 318-11 Section 18.8.2 or ACI 318-14 Section 9.6.2, as applicable. However, Dramix® fibers may be used to contribute towards the required flexural strength in addition to that provided through conventional reinforcement used to satisfy these minimum requirements.

One-way shear capacity shall be permitted to be calculated using Dramix® fibers using Section A4.2.2.1. In so doing, it shall be permitted to disregard the provisions of ACI 318-11 Section. 11.4.6, or ACI 318-14 Section 9.6.3, as applicable, unless the limit (Vc+Vs) in Eq. A4-5 governs. Alternatively, when the minimum shear reinforcement requirements are satisfied through the provisions of ACI 318-11 Sec. 11.4.6, or ACI 318-14 Section 9.6.3, as applicable, it shall be permitted to use the resulting configuration of Dramix® FRC matrix and stirrups to compute the available strength per Section A4.2.2.1 of this report. Contribution of Dramix® fibers to the flexural and shear strength of deep beams, as defined by ACI 318-11 Section 11.7.1 or ACI 318-14 Section 9.9.1.1, is permitted to be neglected. Alternatively, it is permitted to capture the effects of nonlinear strain distribution in a deep beam section using Sec. A4.2.2.3 of this report. Reinforcement requirements of ACI 318-11 Section 11.7.4 or ACI 318-14 Section 9.9.3.1, as applicable, shall apply, unless test data per IBC 1709 or experimental evidence acceptable to the building official having

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jurisdiction can be produced to justify its reduction or omission. Unless demonstrated otherwise through such evidence, the requirement of ACI 318-11 Section 11.7.3 or ACI 318-14 Section 9.9.2.1, as applicable, shall apply.

Additionally, full-scale testing per IBC Sec. 1709 or analysis acceptable to the building official having jurisdiction can be used to demonstrate the effect of Dramix® fibers on flexural and shear strength of deep beams.

In SDC D through F, the provisions of ACI 318-11 Sec. 21.13, or ACI 318-14 Sec. 18.14.3 and 18.14.4, as applicable, shall be met in addition to those of this Section.

A5.6 Columns

All design and detailing requirements of ACI 318-11 or ACI 318-14, as applicable, shall be met and the contribution of Dramix® fibers on such requirements shall be neglected unless otherwise permitted by this Section.

It shall be permitted to provide resistance to flexural forces, including those resulting from second-order effects, with Dramix® in combination with conventional reinforcement. Conventional reinforcement shall at the minimum be configured to meet the detailing, integrity and minimum reinforcement requirements of ACI 318-11 or ACI 318-14, as applicable. When reinforcement for flexural effects is provided through Dramix® fibers as a form of reinforcement, the required forces shall not have been determined using a material-nonlinear analysis.

Dramix® fibers shall not be permitted to serve as the sole form of reinforcement in columns. Longitudinal mild reinforcement per ACI 318-11 Sec. 10.9.1 and 10.9.2, or ACI 318-14 Sec. 10.6.1.1 and 10.7.3.1, as applicable, shall be provided.

One-way shear strength is permitted to be considered using Section A4.2.2.1 of this report. The minimum shear reinforcement requirements of ACI 318-11 Section 11.4.6.1, or ACI 318-14 Section 10.6.2.1, as applicable, shall be permitted to be satisfied with Dramix® FRC, provided that the resulting shear strength of the FRC matrix equals or exceeds that corresponding to Av,min. The minimum reinforcement, Av,min, is as defined by ACI 318-11 Sec. 2.1, or ACI 318-14 Sec. 2.2, as applicable.

In SDC D through F, the provisions of ACI 318-11 Sec. 21.13, or ACI 318-14 Sec. 18.14.3 and 18.14.4, as applicable, shall be met in addition to those of this Section.

A5.7 Walls

Only flexural strain hardening Dramix® FRC matrices meeting the criteria stipulated by Eq. A3-5 shall be permitted in walls.

ACI 318-11 Section 14.5 or ACI 318-14 Section 11.5.3, as appropriate, shall not be used in conjunction with walls reinforced using Dramix® fibers for flexure. Also, the effect of Dramix® fibers shall be neglected in computation of required flexural strength per ACI 318-11 Section 14.8.3 or ACI 318-14 Section 11.8.3.1, as applicable. However, it shall be permitted to use FRC in resisting the flexural effects resulting from the analysis performed per ACI 318-11 Section 14.8.3 or ACI 318-14 Section 11.8.3.1, as applicable.

Minimum vertical and horizontal reinforcement shall be provided in accordance with 318-14 Section 11.6.1 or corresponding provisions of ACI 318-11, as applicable, for walls subjected to gravity loads in addition to their own weight. However, it shall be permitted to provide the in-plane and out-of-plane flexural capacity for such walls using Dramix® fibers, in addition to that generated by the minimum reinforcement. For walls not subject to in-plane bending and to gravity loads in addition to their own weight, minimum flexural and shear reinforcement requirements of ACI 318-14 Section 11.6.1 or corresponding sections of ACI 318-11, as applicable, shall be permitted to be provided in the form of Dramix® fiber reinforcement. The contribution of Dramix® towards meeting the requirement of ACI 318-14 Section 11.6.1 or corresponding sections of ACI 318-11, as applicable, shall be defined as the FRC matrix that provides factored flexural and shear strength equivalent to that of ASTM A615 Gr. 60 vertical and longitudinal reinforcement calculated and provided per ACI 318-11 Section ACI 318-14 Sec. 11.6.1 or corresponding sections of ACI 318-11, as applicable, where the reinforcement providing flexural strength is placed assuming the least clear cover permitted by ACI 318 for the application considered.

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The requirements of the ACI 318-14 Section 11.6.2 or the corresponding sections of ACI 318-11, as applicable, may be met using Dramix® fibers, provided that the resulting shear strength of the FRC matrix calculated using Section A4.2.2.1 equals or exceeds that corresponding to the conventional reinforcement stipulated by ACI 318-14 Sec. 11.6.2 or the corresponding Sections of ACI 318-11, as applicable.

In SDC D through F, the provisions of ACI 318-11 Sec. 21.13.7, or ACI 318-14 Sec. 18.14.6, as applicable, shall be met in addition to those of this Section.

A5.8 Anchorage

The effect of Dramix® fibers on the strength of anchorage to concrete shall be neglected and the strength of anchorage in concrete shall be evaluated in accordance with Appendix D of ACI 318-11 or Chapter 17 of ACI 318-14, as applicable. Alternatively, it shall be permitted to evaluate the strength and performance of concrete anchorage for any particular Dramix® FRC matrix using ICC-ES AC 193 and other applicable criteria acceptable to the building official having jurisdiction. All applicable provisions of ACI 318-11 Appendix D or ACI 318-14 Chapter 17, as applicable, shall be met. A5.9 Foundation Elements

Requirements of this section shall apply to structural elements charged with transmitting load effects from the superstructure to the supporting sub-base. Applicable requirements of Section A5.5 shall apply to the design of grade beams, including those meeting the ACI 318 definition of a deep beam. The requirements of Section A5.7 shall apply to the design of foundation walls.

For foundations and foundation elements in SDC D through F, all requirements of ACI 318-11 Section 21.12, or ACI 318-14 Section 18.13, as applicable, shall be applied in addition to those of this Section.

A5.9.1 Pile Caps

In the design of deep foundation elements, including piles, piers and pile caps, ACI 318-11 Sec. 15.2.2 or ACI 318-14 Sec. 13.4.1.1, as applicable, shall apply. Design of pile caps shall be performed only using flexural strain hardening of Dramix® FRC and meet the applicable requirements of Sec. A4, in addition to the following:

(a) ACI 318-11 Section 8.5.4.2(a) and Section 8.5.4.2(b), or ACI 318-14 Section 13.4.2.1, 13.4.2.2 and

13.4.2.5 shall apply.

(b) ACI 318-14 Section 13.4.2.3(a) and (b) shall apply and be implemented using the requirements of

Sections A4.2.2.1 and A4.2.2.2, respectively, of this report.

(c) ACI 318-11 Section 8.5.4.2(d) or ACI 318-14 Section 13.4.2.4, as applicable, shall apply, except that

the requirements of Section A4.2.2.3 of this report shall be satisfied.

(d) ACI 318-14 Section 13.4.2.5 shall apply in conjunction with designs performed using either ACI 318-

11 or ACI 318-14 in conjunction with this report.

A5.9.2 Piles and Piers

It shall be permitted to use flexural strain hardening Dramix® FRC matrices to provide flexural strength under strength level factored load effects either solely or in combination with mild reinforcement or restressing. For tensile resistance, it shall be permitted to use such FRC matrices only in combination with conventional and mild reinforcement proportioned to resist at least 70 percent of the factored tensile effects. Stress limits per IBC Section 1810.3.2.6 shall apply and the contribution of fibers to the allowable stresses stipulated therein shall be neglected. All other requirements of IBC shall apply.

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The effect of fibers on pile or pier stiffness under service loads shall be neglected, unless test data per IBC Sec. 1709, or other commensurate evidence, can demonstrate such effect to the satisfaction of the building official having jurisdiction. In conjunction with the design with either ACI 318-11 or ACI 318-14, provisions of ACI 318-14 Section 13.4.3.1 and Section A5.6 of this Specification shall apply for piers and piles subject to flexural buckling. A5.9.3 Shallow Foundation Elements

ACI 318-11 Sections 15.2.2, 15.7 and 15.9.1 or ACI 318-14 Sections 13.3.1.1 through 13.3.1.3, as applicable shall apply.

It shall be permitted to design two-way combined footings and matt foundations reinforced for flexural, one-way shear and two-way shear effects using flexural strain hardening Dramix® matrices with or without supplemental reinforcement or pre-stressing reinforcement. It shall be permitted to determine the required flexural and shear strength using linear elastic analysis or material non-linear analysis. The design strength shall be determined using applicable provisions of Section A4 while satisfying the requirements of Section A5.4.2 of this Specification, except as follows:

(a) ACI 318-11 Sections 15.10.2 through 15.10.4 or ACI 318-14 Sections 13.3.4.2 through 13.3.4.4, as

applicable, shall apply,

(b) It shall be permitted to satisfy the minimum reinforcement requirements of ACI 318-11 Section 15.10.4 or ACI 318-14 Section 13.3.4.4, as applicable, using conventional reinforcement, or fiber reinforcement alone or in combination with conventional reinforcement. The contribution of Dramix® towards meeting the requirement of ACI 318-11 Section 15.10.4 or 318-14 Section 13.3.4.4, as applicable, shall be defined as the FRC matrix that provides factored flexural strength equivalent to that of longitudinal reinforcement calculated and provided per these ACI 318 provisions, where the reinforcement providing flexural strength is placed assuming the least clear cover permitted by ACI 318 for the application considered.

It shall be permitted to design one-way shallow footings, including strip footings and combined footings, reinforced for flexural, one-way shear and two-way shear effects using flexural strain hardening Dramix® matrices with or without supplemental reinforcement or pre-stressing reinforcement. It shall be permitted to determine the required flexural and shear strength using linear elastic analysis or material non-linear analysis. The available strength shall be determined using applicable provisions of Section A4, while satisfying the requirements of Section A5.4.1 and A5.5 of this Specification, except as follows:

(a) ACI 318-11 Section 15.4.3 or ACI 318-14 Section 13.3.2.2, as applicable, shall apply,

(b) Either flexural strain softening or flexural stain hardening Dramix® FRC matrices shall be permitted as a form of flexural and shear reinforcement in elements Seismic Design Categories (SDC) A, B or C, or for elements in SDC D, E or F meeting the requirements of ACI 318-11 Section 22.10.1 or ACI 318-14 Section 14.1.4(a) and (b), as applicable.

It shall be permitted to design two-way isolated shallow footings using flexural strain hardening Dramix® matrices with or without supplemental reinforcement or pre-stressing reinforcement. It shall be permitted to determine the required flexural and shear strength using linear elastic analysis or material non-linear analysis. The design strength shall be determined using applicable provisions of Section A4, while satisfying the requirements of Section A5.4.2 and A5.5 of this report, except as follows:

(a) ACI 318-11 Sections 15.2.1, 15.4.3 and 15.4.4, or ACI 318-14 Sections 13.3.3.1 through 13.3.3.3, as applicable, shall apply,

(b) Either flexural strain softening or flexural stain hardening Dramix® FRC matrices shall be permitted as a form of flexural and shear reinforcement in elements in Seismic Design Categories (SDC) A, B or C, or for elements in SDC D, E or F meeting the requirements of ACI 318-11 Section 22.10.1 or ACI 318-14 Sec. 14.1.4(a) and (b), as applicable.

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Walls used as grade beams shall be designed using applicable provisions of Section A5.6 and A5.7. A5.10 Diaphragms & Seismic Force Resisting Systems (SFRS)

The effect of Dramix® on strength and performance of Seismic Force Resisting Systems is outside the scope of this report. The performance of a Dramix® FRC matrix in a concrete-filled steel deck diaphragm shall for each particular configuration be evaluated and considered in accordance AISI S310.

When the diaphragm design is performed in accordance with Chapter 12 of ACI 318-14, it shall be permitted to disregard the contribution of Dramix® fibers on diaphragm strength in shear and flexure, as well as its contribution to the strength of diaphragm elements, including chords and collectors. Alternatively, for diaphragms comprising flexural strain hardening Dramix® matrices the following shall be permitted in conjunction with ACI 318-14 Chapter 12 for cast-in-place diaphragms, including topping slabs on precast elements, provided the following conditions have been met:

(a) When used, strut-and-tie design per ACI 318-14 Section 12.4.2.4 and Section 12.5.1.3(b) shall satisfy

the requirements of Section A4.2.2.3 of this specification.

(b) It shall be permitted to use tensile strain hardening Dramix® fibers to reinforce the tensile boundary

elements per ACI 318-14 Section 12.5.1.3(a). Alternatively, it shall be permitted to use the flexural

strain hardening Dramix® matrices for this purpose in combination with conventional reinforcement,

provided the conventional reinforcement is configured to resist at least 70 percent of the factored

tensile chord demand. Cross-sectional area of a Dramix® reinforced FRC tensile chord shall be

determined from ACI 318-14 Section 12.5.2.3 and the available strength calculated using Section

A4.2.1.4.

(c) Shear strength shall be permitted to be determined using Section A4.2.2.1 of this report instead of

ACI 318-14 Section 12.5.3.3, except that the shear strength so determined shall be limited by that

obtained by ACI 318-14 Eq. 12.5.3.3 and Eq. 12.5.3.4 in which the term √𝑓𝑐′ does not exceed 100 psi

(0.69 MPa), unless otherwise can be established as adequate through testing per IBC Section 1709.

(d) ACI 318-14 Sec. 12.5.3.5(a) shall also apply to the value of f’c used in Sec. A4.2.2.1 of this Specification.

Contribution of fibers towards the requirement of ACI 318-14 Sec. 12.5.3.5(b) shall be neglected.

(e) It shall be permitted to use tensile strain hardening Dramix® fibers to reinforce the tensile boundary

elements per ACI 318-14 of Sec. 12.5.4.2. Alternatively, it shall be permitted to use the flexural strain

hardening Dramix® matrices for this purpose in combination with conventional reinforcement,

provided the conventional reinforcement is configured to resist at least 70 percent of the factored

tensile chord demand. Cross-sectional area of a Dramix® reinforced FRC tensile chord shall be

determined from ACI 318-14 Section 12.5.2.3 and the design strength calculated using Section

A4.2.1.4. Anchorage and dowelling of the collector member into other members in the load path of

the collector force shall not be permitted to be performed using Dramix® fibers and shall meet the

requirements of ACI 318-14 Section 12.5.4.3.

(f) Slabs meetings the requirements of Section A5.4.1 or A5.4.2, as appropriate, shall be permitted to be

considered as meeting ACI 318-14 Section 12.6.2.

For diaphragms in SDC D through F, ACI 318-11 Section 21.11, or ACI 318-14 Section 18.12, as applicable, shall apply. It shall be permitted to consider the contribution of Dramix® FRC to the flexural, shear and tensile strength of diaphragms and diaphragm components, as applicable, using the provisions (a) through (f) of this section.

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A5.11 Non-structural Components

It shall be permitted to design other non-structural components and systems not explicitly covered by Section 5 of this Specification, such as non-impact fence walls, architectural precast components, or non-cantilever site walls, using either flexural strain softening or flexural strain hardening Dramix® matrices as the form of shear and flexural reinforcement with or without supplemental conventional reinforcement. However, when the FRC matrices are used for flexural resistance, they shall exhibit the minimum value of RT,150

D , as defined

by Section A3.1.1, of 30 percent. Available strength of the components so considered shall be determined using applicable provisions of

Section A4 of this specification. When distributed mild reinforcement is used in combination with Dramix® FRC for the purposes of this

Section, maximum reinforcement spacing of ACI 318 for one-way slabs, two-way slabs, walls or beams, as applicable, shall be applied. When prestressing steel is used in combination with Dramix® FRC for the purposes of this Section, maximum tendon spacing and minimum prestress requirements of ACI 318 for one-way or two-way slabs, as applicable, shall be applied.

A6 Design for Serviceability

Provisions of ACI 318-14 Chapter 24 shall apply and be satisfied and the contribution of Dramix® fibers towards satisfying serviceability requirements shall be neglected unless specifically indicated otherwise by the provisions of this section.

A6.1 Deflections

For the purposes of implementation of the provisions of ACI 318-14 Section 24.2.3.4 through 24.2.3.9, or the corresponding sections of ACI 318-11, as applicable, members incorporating combined Dramix® fibers and conventional reinforcement shall be treated considering in calculations the conventional reinforcement alone and neglecting the effect of Dramix® fibers, unless the contribution of fibers to the effective moment of inertia can be accounted for by testing in accordance with IBC Section 1709. For the purposes of implementation of the provisions of ACI 318-14 Sections 24.2.3.4 through 24.2.3.9, or the corresponding provisions of ACI 318-11, as applicable, members incorporating Dramix® fibers and no conventional reinforcement, the contribution of fibers to the effective member stiffness EcIe, can be accounted for by testing per IBC Section 1709. Alternatively, it shall be permitted to establish such a relationship through an iterative process by achieving system equilibrium under service loads on the basis of fr-’ relationship per Section 4.1.2(c). Effects of Dramix® shall be disregarded when satisfying deflection requirements using ACI 318-11 Section 9.5.2.1 and 9.5.3.1, or ACI 318-14 Section 7.3.1.1, 8.3.1.1 and 9.3.1.1, as applicable. A6.2 Crack Control

When specific crack width of less than 0.02 in. (0.5 mm) is determined and limited by calculation, it shall be permitted to neglect the contribution of Dramix® fibers to crack control in member, whereby the crack control shall be accomplished through the provisions of ACI 318-14 Section 24.3, or the corresponding provisions of ACI 318-11, as applicable, unless experimental evidence in accordance with IBC Section 1709 can be produced demonstrating the effect of Dramix® fibers on crack control of one-way and two-way slabs and beams. Alternatively, when cracks are to be limited for aesthetic reasons to a specific width, it shall be permitted to control cracks by applications of the provisions of Section A6.2.1. For general crack control under shrinkage and temperature effects through the provision of minimum reinforcement, Section A6.3 shall apply.

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A6.2.1 Calculated Crack Width

When the design crack width, wn, is limited by the specifier to a specific value in slabs and other similar plates or shells of essentially uniform thickness, constructed with flexural strain hardening matrices of Dramix® FRC, it shall be permitted to compute wn using Eq. A6-1. When crack width calculated using Eq. A6-1 is calculated in presence of distributed conventional reinforcement, the maximum spacing requirements for walls, one-way or two-way slabs of ACI 318 shall be applied, as applicable. Crack widths computed shall not exceed the values permitted by the project specifications, or those indicated by Section 8 of this report, whichever are more stringent.

( )cmsmf

maxn εεsw −= (A6-1)

where: wn = design crack width smax = maximum crack spacing

εfsm = mean strain in reinforcement under service load combination εcm = mean strain in concrete between cracks Maximum crack spacing, sr,max, may be calculated using Eq. A6-2. The quantity (εsm – εcm) in Eq. A6-1 is permitted to be determined using Eq. A6-3.

( ) ( )tx

eqs

f

eff

eq

fmax3.6f

dfα1

3.6ρ

dα1s −−= (A6-2)

Where: deq = equivalent diameter of reinforcement, computed based on n number of bars of the diameter db, where db is as defined by ACI 318-11 Sec. 2.1, or ACI 318-14 Section 2.2, as applicable. When defomred steel bars of the same diameter is used, deq = db.

= (n1db12+n2db22+…+nxdbx2)/(n1db1+n2db2+…+nxdbx) fs = stress in tension reinforcement assuming a cracked section and without consideration of the

effects of fibers. For prestressed members, fs may be taken as the difference in stress in the pre-stressing steel at the cracking moment and that at the state of zero strain in concrete at the depth of the pre-stressing steel. The reinforcement and the member shall be configured such that fs does not exceed fy.

⍴eff = (As + ξ1A’ps)/Ac,eff

A’ps = Aps located in Ac,eff ξ1 = (ξdbl/dps,eq)1/2 when pre-stressing steel is used in combination with reinforcement in Dramix®

FRC = ξ1/2 when prestressing steel alone is used in combination with Dramix® FRC ξ = ratio of bond strength between bonded tendons and deformed steel bars in concrete, evaluated

through testing or other evidence acceptable to the building official having jurisdiction. In absence of such values, the values from Table A6-1 may be used. Linear interpolation between the values shown is permitted as a function of f’c.

Table A6-1 Bond Ratio, ξ

Pre-tensioning Strands

Bonded Post-tensioning Strands f’c ≤ 7 ksi (50 MPa) f’c ≥ 10 ksi (70 MPa)

0.6 0.5 0.25

dbl = largest db applicable

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dps,eq = equivalent diameter of prestressing steel = 1.75dwire for a single 7-wire strand = 1.20dwire for a single 3-wire strand = 1.6(Aps)1/2 for tendon bands

dwire = diameter of a single tendon wire Ac,eff = effective area of concrete in tension surrounding the mild or prestressing reinforcement at the

depth hc,eff, as illustrated in Figure A6.1 hc,eff = the smallest of 2.5(h-d), (h-x)/3, or h/2, as illustrated in Figure A6.1 ftx = 28-day concrete tensile stress for crack width evaluation, psi (MPa)

= a(f’c)2/3 for f’c ≤ 7,000 psi (50 MPa) = c2.12[ln(1+ (bf’c+8)/10)] for f’c > 7,000 psi (50 MPa)

a = 8.3 when f’c and ftx are in psi, 0.3 when f’c and ftx are in MPa b = (1/145) when f’c is in psi, 1 when f’c is in MPa c = 145 when ftx is in psi, 1 when ftx is in MPa f = fns/ftx ≤ 1.0

( )( )

( )s

sf

s

efftxsfcmsm

f

E

fα10.6

E

ρ/0.4ffα1εε −

−−=− (A6-3)

Figure A6.1 Illustration of Ac,eff and hc,eff

For slabs subject to internal restraints due to discrete anchor points provided by columns, piles, discontinuities in slab depth or geometry, or any other effects except for friction against soil at the slab surface, the resulting tensile forces shall be resisted either with a tensile strain hardening Dramix® FRC matrix, conventional reinforcement, or a combination of conventional reinforcement and Dramix® FRC. When used in combination with conventional reinforcement for the purposes of controlling cracking to a specific width in conjunction with this Section, the minimum conventional reinforcement for crack control, Asc,min, shall be provided per Eq. A6-4. When the member is pre-stressed, the Asc,min is permitted to be taken as zero, provided the minimum prestress requirements of Section A5 of this report are met. When crack control is not established

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per Section A6.2.1, Asc,min shall be permitted to be neglected and the minimum reinforcement established by Section A6.3.

Asc.min = ftxkck(1 - f)Act/fs (A6-4)

Where: k = non-uniform self-equilibration stress coefficient = 1.0 for h ≤ 12 in. (300 mm) =0.65 for h ≥ 31 in. (800 mm) = 1.0 – 0.35[(dh – 300)/500] for 12 in. < h < 31 in. (300 mm < h < 800 mm) d = 25 when h is in in., 1.0 when h is in mm kc = stress distribution factor

= 1.0 for sections in direct tension

= 0.4 [1 −𝑓𝑥

𝑘1𝑅𝑑𝑓𝑡𝑥] for sections in eccentric tension, tension in combination with moment, or

sections subject to moment Act = area of concrete in tension right before the formation of the crack under the load effects

corresponding to the applicable service load combinations fx = axial stress acting on the section under consideration Rd = 1.0 when h < 39 in. (1000 mm) = h/(d39) k1 = 1.5 when fx is compressive and 2Rd when fx is tensile

For thick members, subjected to axial constraints, minimum reinforcement area, Ascl,min, shall be imposed within the portion of the section subjected to the restraint stresses. The quantity of steel calculated by Eq. A6-3 and provided in the region under consideration may also be used to satisfy the requirement for Ascl,min. The quantity of steel Ascl,min shall be as provided by Eq. A6-4.

Ascl.min = ftx(1 - f)Ac,eff/fs ≥ ftx(k - f)Act/fy (A6-4)

A6.3 Minimum Reinforcement

The minimum reinforcement for shrinkage and temperature required by ACI 318-11 Section 7.12 and 16.4.1, or ACI 318-14 Section 24.4, as applicable, may be reduced or eliminated by the use of Dramix® FRC reinforcement in accordance with IAPMO UES ER-497, except that the use of Dramix® fiber models listed in Table 1 of this report shall be permitted for this purpose.

When the member considered is a composite slab otherwise compliant with the requirements of SDI-C-2011 or SDI-C-2017, as applicable, it shall be permitted to satisfy the reinforcement requirements of SDI-C-2011 Sec. 2.4.B.13.a.1 or or SDI-C-2017 Sec. 2.4.B.15.a.1, using IAPMO UES ER-497, except that the use of Dramix® models listed in Table 1 of this report shall be permitted for this purpose. In conjunction with this provision, the requirements of SDI-C-2011 2.4.B.13.a.2 and 2.4.B.13.a.3, or SDI-C-2017 2.4.B.15.a.2 and 2.4.B.15.a.3, as applicable, may be neglected. A6.4 Stress Limits in Prestressed Members

The effect of Dramix® fibers on the requirements of ACI 318-14 Sec. 24.5 or the corresponding provisions of ACI 318-11, as applicable, shall be neglected, unless experimental evidence per IBC Section 1709 or other evidence acceptable to the official having jurisdiction can be submitted, demonstrating the equivalence in performance of a specific Dramix® FRC matrix with respect to the requirements of ACI 318-14 Sec. 24.5, or the corresponding provisions of ACI 318-11, as applicable.

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A7 Quality Assurance Requirements

A7.1 General Requirements

Unless noted otherwise, the provisions of ACI 318-14 Chapter 26 or the corresponding provisions of ACI 318-11, as applicable, shall apply in addition to and as further modified and in addition to the other specificprovisions of this Section.A7.2 Requirements for Dramix® Fibers, Testing and Composition

The provisions of ACI 318-14 Section 26.4.2.2(d) and 26.12.5.1(a), or the corresponding provisions of ACI 318-11, as applicable, shall not apply unless Dramix® fibers are used in conjunction with the provisions of ACI 318-11 Section 11.4.6.1, or ACI 318-14 Sec. 9.6.3.1, as applicable, are used in design. When these ACI 318 provisions are used in combination with any other portion of this report in the design of a member of a system, both ACI 318-14 Section 26.4.2.2(d) and 26.12.5.1(a), or the corresponding provisions of ACI 318-11, as applicable, and all the provisions of this Section shall apply. Where a conflict exists, the more stringent provision shall apply.

ACI 318-14 Section 26.4.2.1(a)(11) or the corresponding provision of ACI 318-11, as applicable, shall be deleted and replaced with the following: “If used in conjunction with IAPMO UES ER-465 or ACI 318 Sec. 9.6.3.1, Dramix® fiber type and fiber dosage specified to the nearest whole lb/yd3 or the nearest 0.5 kg/m3 increment.”

The Dramix® FRC properties shall be established per Section A3.1.1. For the establishing the mechanical properties per Section A3.1.1, it shall be permitted to perform a linear interpolation between the series of tests corresponding to concretes of the same compressive strength and composition but with varying Dramix® fiber dosages, provided that the dosage ranges do not exceed 33 lbs/yd3 (20 kg/m3).

Test reports containing the values per Section A3.1.1 shall comply with the requirements of that Section and EN14651, except that it shall be permitted to record, measure and/or report all the reported values in inches, pounds per square inch, pounds, and pounds per cubic foot, as applicable. Furthermore, the reporting requirements of EN14651 Section 10 shall be modified and amended by the following:

(i) Concrete compressive strength,

(ii) Slump,

(iii) The name “Bekaert Dramix®” along with the commercial designation of the specific fiber per

Table 1 of this report,

(iv) The entry EN14651 Section 10(p) shall be modified to read: “reference to EN14651 and IAPMO

UES ER-465,”

(v) Serial number of the container with the test fibers,

(vi) Photograph or a sample fiber corresponding to each unique series of test.

The licensed design professional in responsible charge of the project shall perform a review to assure that the concrete composition specified is consistent with the Dramix® FRC matrix stipulated in the construction documents.

A7.3 Material Handling of Dramix® Fibers

Dramix® fibers containers shall be kept out of weather and be stored prior to mixing such that no individual palletized unit consisting of sixty 44-pound (20-kg) bags, or a single 2440-pound (1200-kg) bag, is stacked height-wise. Dramix® fibers shall be kept clean and free of soil, bonding chemicals or any other form of contamination.

Dramix® containers shall be verified for the presence of Bekaert container designator, accuracy of the Dramix® fiber indicated with respect to that specified by the project documentation, and for the presence of the mark per Section A5 of this report.

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A7.4 Construction with Dramix® Fibers

Dramix® steel fibers shall be added to the concrete mix at the batching plant to the other constituents of the FRC matrix per Section 2.9 of this report. In-field addition of fibers to the concrete mix shall be permitted, provided the appropriate quality control measures assuring accuracy in dosing and distribution can be maintained.

Concrete shall be sufficiently mixed to assure uniform distribution of Dramix® fibers throughout the FRC matrix, but at the minimum 70 revolutions of a drum, or four minutes of the mixing speed thereof shall be achieved. The distribution shall be verified in accordance with Section A7.4.1.

No construction technique shall take place so as to forcibly disturb the composition of a FRC matrix during mixing or casting of concrete, such as:

(i) Removal or addition of fibers during casting,

(ii) Addition of concrete constituents during casting, such as water, cement or additives not approved

by the licensed design professional,

(iii) Attempt to affect fiber orientation in member by pulling, magnetically collecting or distributing

fibers in a mixed or wet cast concrete,

(iv) Substitution or combination of fibers of the Dramix® series, other than that specified in the

project documentation, without an approval of the licensed design professional,

(v) Substitution or combination with fibers of a type other than from the Bekaert Dramix® series

described in this report,

(vi) Concrete with Dramix® steel fibers shall comply with applicable provisions of ASTM C1116.

A7.4.1 Distribution of Dramix® Fibers in the FRC Matrix

Field verification of Dramix® fibers in wet concrete shall be performed in the form of either (a) discrete sampling or (b) continuous monitoring as follows:

(a) Discrete sampling is permitted to be executed in the form of a washout test in accordance with EN 14721,

or another comensurate standard, except that the minimum sample size for conducting the test shall

consist of a fresh concrete specimen of minimum 0.35 cubic foot (10 l) in volume, but not exceeding 0.50

cubic foot (15 l). The compliance shall be be assured through three individual test samples taken from

the first, second and the third 1/3 of the discharged concrete volume. The samples shall be taken directly

from the truck, at the point of discharge, and collected from the free flow of concrete without the aid of

shovels or other disturbances. The testing frequency shall at the minimum consist of the first mixer truck

as described herein, and the same frequency based on placement time and volume thereafter as

stipulated for f’c by ACI 318-11 Section 5.6.2.2 or ACI 318-14 Section 26.12.2.1(b), as applicable. The

reporting requirements of such a test shall be those stipulated by Section 8 of EN14721, except for the

following modifications:

(i) Identification of the testing/inspection agency,

(ii) Time of and dates of the specimen collection and the completion of the test,

(iii) Identification “Bekaert Dramix®” along with the specific commercial fiber designator per Tabe 1 of this report,

(iv) Density of fresh concrete in pounds per cubic foot (kg/m3) reported to the nearest 1

pound per cubic foot (0.5 kg/m3),

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(v) Item EN 14721 Section 8(c) shall also be permitted to be reported in cubic feet , to theprecision of three significant figures.

(vi) Item EN 14721 Section 8(d) shall also be permitted to be reported in pounds, to theprecision of three significant figures.

(vii) Item EN 14721 Sec. 8(e) shall be modified to read: “the calculated fiber content per unitvolume of each sample in pounds per cubic yard (kg/m3) to the nearest 1 pound per cubicyard (0.5 kg/m3),”

(viii) Item EN 14721 Section 8(e) shall be modified to read: “the calculated average fibercontent per unit volume for the test series in pounds per cubic yard (kg/m3) to thenearest 1 pound per cubic foot (0.5 kg/m3),”

(ix) Item EN14721 Sec. 8(g) shall be deleted.

(x) Item EN14721 Sec. 8(i) shall be modified to read: “a statement from the owner’sinspection entity indicating that the test was performed in accordance with IAPMO UESER-465, with any deviations thereto and the reasons therefore documented.”

No individual acceptable sample shall indicate the measured dosage of more than 20 percent below the specified dosage. An acceptable average of the three tests shall not indicate a measured dosage of more than 10 percent below the specified dosage. Members and systems cast with measured dosages below such limits shall be evaluated by the licensed design professional. Such an evaluation shall take place with the corresponding tested values of f’c.

(b) In lieu of determination of fiber content through discrete sampling, removal from the concrete matrixand the subsequent weight measurement per Section A7.1.4(a), the content of steel fibers in wetconcrete may be determined through continuous electromagnetic detection of steel fibers duringconcrete placement.

Concrete flow during placement may be measured using fluid speed sensors and unltrasound-basedsensor of flow height. Continuous monitoring device so constructed may provide real-timemonitoring or retrievable record of data. Data may be reported in the form of a moving average, ordosage measured over a specified range, as required by the project specification and therequirements of this Section.

The equipment used for the purposes of continuous electromagnetic detection shall be verified asyielding the average dosage within ±1 pound per cubic yard (±0.5 kg/m3) of the test performed byEN14721 and modified by this Section. The verification shall be performed by an independenttesting/inspection agency and repeated bianualy, or as stipulated by the licensed design professionalfor the project for which the equipment is used.

The content of Dramix® fibers per unit volume shall be determined from the continuously recordeddata and discretized over randomly selected unit volumes of 0.35-0.50 cubic feet (10-15 l) from thefirst, second and the third one-third of the volume discharged from the truck mixer.

The data so recorded shall conform to the same precision, acceptability and remediationrequirements stipulated by Section A7.4.1(a). As an alternative, it shall be permitted to evaluate thefiber dosage on the basis of three individual moving average measurements capturing the entire ofthe concrete volume of a mixer truck and subsequently reporting the results as three continuousmoving average measurements, each discretized over one third of the truck volume. The movingaverage shall be discretized over the increments of 3.5 cubic feet (100 l) by volume of passingconcrete. The reporting requirements shall be the same as per Section A7.4.1(a) except as modifiedand amended by the following:

(i) Identification of the testing/inspection agency,

(ii) Time of and dates of the specimen collection and the completion of the test,

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(iii) Identification of the electromagnetic detection device type, manufacturer and a specificdevice identifier in the form of a serial number or another unique designation,

(iv) Identification “Bekaert Dramix®” along with the specific commercial fiber designator perTabe 1 of this report,

(v) Density of fresh concrete in lb/ft3 (kg/m3) reported to the nearest 1 cubic feet (0.5kg/m3), reported as a discrete value, or a moving average plot, as applicable,

(vi) Item EN 14721 Section 8(c) shall also be permitted to be reported in cubic feet, to theprecision of three significant figures, reported as a discrete value, or a moving averageplot, as applicable,

(vii) Item EN 14721 Section 8(d) shall also be permitted to be reported in lbs, to the precisionof three significant figures, reported as a discrete value, or a moving average plot, asapplicable,

(viii) Item EN 14721 Section 8(e) shall be modified to read: “the calculated fiber content perunit volume of each sample in lb/yd3 (kg/m3) to the nearest 1 pound per cubic yard (0.5kg/m3), reported as a discrete value, or a moving average plot, as applicable,”

(ix) Item EN 14721 Section 8(e) shall be modified to read: “the calculated average fibercontent per unit volume for the test series in lb/yd3 (kg/m3) to the nearest 1 pound percubic yard (0.5 kg/m3), except that this reporting item shall not be required when theevaluation on the basis of a moving avarege is used,”

(x) Item EN14721 Section 8(g) shall be deleted.

(xi) Item EN14721 Section 8(i) shall be modified to read: “a statement from the owner’sinspection entity indicating that the test was performed in accordance with IAPMO UESER-465, with any deviations thereto and the reasons therefore documented.”

For the measurements discretized over the volumes of 0.35-0.50 cubic feet (10–15 l) and reported as discrete values, individual acceptable sample shall indicate the measured dosage of more than 20 percent below the specified dosage. An acceptable average of the three tests shall not indicate a measured dosage of more than 10 percent below the specified dosage. For an acceptable FRC matrix assessed on the basis of moving average, no portion of the the moving average trendline shall drop more than 15 percent below the specified dosage.

For the purposes assessing the acceptability of the FRC matrix homogenity by the moving average method, the first and the last 3 percent of the concrete by volume shall be permitted to be disregarded. However, the entire volume shall be recorded and its influence on the moving average curve included in calculations.

Members and systems cast with measured dosages below such limits shall be evaluated by the licensed design professional. Such an evaluation shall take place with the corresponding tested values of f’c.

A8 Durability

The durability requirements of ACI 318-11 Chapter 5, or ACI 318-14 Chapters 19 and 20, as applicable, shall apply.

Additionally, when Dramix® reinforcement is used in combination with reinforcement or otherwise for crack width control for the purposes of meeting specific durability requirements, design shall be performed using service load combinations and the provisions of Section A6.2.1 of this report. The crack width requirements based on a particular exposure shall be as stipulated by ACI 224R-01 Table 4-1, or as stipulated by

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the project specifications, whichever is more stringent. When cracks are also controlled for serviceability reasons, the cracks shall also not exceed the limits stipulated for serviceability reasons.

When the maximum crack larger than .016 inch (0.40 mm) is specified for a particular exposure, the member or system under consideration meeting other requirements of this report shall be permitted to be considered as satisfying the crack width requirement without further analysis.

A9 Details of Reinforcement

When reinforcement is used in conjunction with this Specification, all details of reinforcement, including aspects pertaining to spacing, confinement, development, lap splices and terminations shall be in accordance with the applicable general and member specific sections of ACI 318-14 Chapter 25, or the corresponding sections of AC 318-11, as applicable, with the effect of Dramix® fibers thereon neglected.

It shall be permitted to consider the effect of Dramix® fibers on confinement of reinforcement and development length is such effect can be demonstrated by testing per IBC Section 1709.

The end of Annex A

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