All you need to know about the beloved polypropylene macro fibers.
The ADFIL Construction Fibres product DURUS® EasyFinish is a macro synthetic fibre which has endured more than most of us. Initially the fibre underwent tests proving its time dependent durability, cf. EN ISO 13438, and additive impact on the plastic shrinkage. Since then, it has been tested from every angle to get approved in the structural industry. It passed.
The infamous notched threepoint bending test, cf. EN 14651, is the backbone of this whole organization. The standardized beam test is conducted on several beams of the same concrete matrix but with various fiber dosages.
The results from the tests are usually given graphic as the applied load compared to the crack mouth opening displacement (CMOD). In order to maintain workability of the fiber reinforced concrete, the dosage has to be limited, giving a tensionsoftening behavior.
In TR34 ^{1,2} and Model Code 2010 ^{9,10,11} the stress and moment capacities are calculated using the wellknown residual flexural tensile strength values, derived from load values corresponding to four specific crackmouth opening displacements.
Using simplified calculation methods from the Eurocodes or using advanced Finite Element Method, it all comes down to stresses and internal forces. The test result data and intermediate stress and moment capacity calculations are simply compared to the stresses and internal forces induced by the applied loads. Voilà. We can tell you your required dosage of DURUS® EasyFinish fibers in your concrete element.
The calculation program, developed by Daniel Fester Henningsen, Civil Engineer and Technical Specialist at PPCD ApS, is primarily based on Concrete Industrial Ground Floors  A Guide to Design and Construction, Technical Report No. 34, Concrete Society, 4th Edition^{2}, with evidence from the remaining references indicated. This technical document is available for download as a PDF.
The following writ describes the use of fibers as reinforcement in loadbearing concrete structures, in accordance with standards and authorities. The calculations, developed by the undersigned, Daniel Fester Henningsen, Civil Engineer and Technical Specialist at PPCD ApS, are based on constitutive laws, and known engineering methods, and thus lean on Eurocode 2: Design of concrete structures  Part 11: General rules and rules for buildings, EN 199211, European Committee for Standardization (hereinafter referred to as EN2).
One of the primary references used for practical calculations of e.g. the torque capacity and the shearing capacity of a given concrete construction with fibers as reinforcement is Concrete Industrial Ground Floors  A Guide to Design and Construction, Technical Report No. 34, Concrete Society, 4th Edition (Hereinafter referred to as TR34). These calculations are based on recognized, tension strain assumptions ie. constitutive laws of the cross section in question, where the neutral axis is found based on assumptions about the pressure and tensile zone. This method is analogous to the method of EN2 for conventional reinforcement.
The abovementioned stressstrain curves have been found using the standardized threepoint beam test, cf. EN 14651 Test method for metallic fibre concrete. Measuring the flexural tensile strength (hereinafter referred to as EN14651). Although EN14651 concerns metallic fibers, the method for obtaining the socalled flexural tensile strength values is approved as long as the fibers are approved according to EN 148892:2006 Fibres for concrete, Part 2: Polymer fibres. Definitions, specifications and conformity (Hereinafter referred to as EN14889). The fibers used in practice, with dosages based on the calculations, have specifically been tested according to EN14651 and CEmarked according to EN14889.
EN2 does not define reinforcement as only conventional reinforcement, and therefore does not exclude fibers as reinforcement. Thus, reinforcement is just a generic material that imbues concrete structures with tensile and flexural bearing capacity, as well as other additional features such as reduction of shrinkage cracks, shear capacity, etc.
The existing EN2 describes general rules, such as the stress strain relationship from which the stress distribution in a given cross section can be derived, and e.g. the moment capacity found. This must be done on the basis that the material parameters are justified, such as by standardized tests. This procedure is precisely the one used in the calculations for the fiber reinforced concrete.
For inclusion of nonlinear calculation and plasticity theory calculation, see Chapter 5.7: Nonlinear analysis in EN2 (see quotation below), which states that if appropriate nonlinear material models are used, these can be used in calculations in both ULS and SLS (Ultimate Limit State and Serviceabilty Limit State). The nonlinear material models are provided on the basis of previously mentioned EN14651, which is why the calculations further accommodate EN2.
Chapter 5.7 nonlinear analysis: (1) Nonlinear methods of analysis may be used for both ULS and SLS, provided that equilibrium and compatibility are satisfied and an adequate nonlinear behaviour for materials is assumed. The analysis may be first or second order.
It is thus concluded that the calculations used for fiber reinforced concrete are included in EN2, although fiber reinforced concrete is not directly mentioned by name in EN2, since all methods and material parameters obtained are based on standards.
The building regulations 2018 (hereinafter referred to as BR18) mention in § 344(2), that design must be done in accordance with i.a. Eurocode 0: Basic of structural design, EN 1990, European Committee for Standardization (hereinafter referred to as EN0), and Eurocode 1: Actions on structures, EN 1991, European Committee for Standardization (hereinafter referred to as EN1), parts 11 to 17 . § 345 states that, especially for concrete structures, the design planning must take place in accordance with, inter alia, EN2. As is concluded above, the calculations for fiber reinforcement justify these requirements.
In addition to the fact that fiber reinforced concrete is not mentioned directly by name in EN2, BR18 does also mention in § 356 that "§ 344(2) to § 351 and §§ 353355 may be derogated from if it can be ensured and documented by other means that derogation is safe, and if a safety level as described in § 344(2)(1) can be achieved." This documentation is available, with partial coefficients on the loads according to EN0, as well as partial coefficients on the materials according to EN1, and common calculation methods (constitutive laws), which are also evident from EN2.
At a meeting between NCC A/S, COWI A/S, and PPCD ApS regarding potential applications for fiber reinforced concrete  either fiber reinforcement alone, or in composite with conventional reinforcement  a table was drawn up that lists the structural elements where fiber reinforcement is an option. There was absolute consensus on the table, without further debate. The table can be found as the document Application areas with fiber reinforced concrete, or viewed at the end of this document. In construction elements with the possibility of plastic redistribution of the loads, there was in particular no doubt about the possibility of using fibers as reinforcement. These structural elements included foundations, ground slabs, strip foundations and point foundations. There was a more indepth debate on walls, beams, and columns, where the lack of opportunity for plastic redistribution of the loads is a bigger issue. Thus, in these structural elements, conventional reinforcement in composite with fiber reinforcement should be used.
Finally, please note that the responsibility for all calculations lies with the adviser, as it is their documentation that, cf. previously mentioned § 356 in BR18, must be approved by the relevant authorities. This responsibility is described in BR18(1), here especially sections 1619. I.e. the responsibility, if the concrete recipe and the workmanship have been carried out as directed, is incumbent on the person carrying out the documentation.
1.  Concrete industrial ground floors  A guide to design and construction, Technical Report No. 34, Concrete Society, 3rd Edition

2.  Concrete industrial ground floors  A guide to design and construction, Technical Report No. 34, Concrete Society, 4th Edition

3.  Concrete industrial ground floors, ICE design and practice guide, Frank R. Neal, Frank Neal Engineers, Second Edition

4.  Guide to Design of SlabsonGround, ACI 360R10, Reported by ACI Committee 360, American Concrete Institute

5.  Design of floors on ground, Technical Report 550, J. W. E. Chandler, Cement and Concrete Association

6.  Test and design methods for steel fibre reinforced concrete, σεdesign method, RILEM TC 162TDF, Vol. 36, RILEM

7.  Eurocode 2: Design of concrete structures  Part 11: General rules and rules for buildings, EN 199211, European Committee for Standardization

8.  Eurocode 7: Geotechnical design  Part 1: General rules, EN 19971, European Committee for Standardization

9.  Model Code 2010, First complete draft, Volume 1, bulletin 55, International Federation for Structural Concrete (fib)

10.  Model Code 2010, Final draft, Volume 1, bulletin 65, International Federation for Structural Concrete (fib)

11.  Model Code 2010, Final draft, Volume 2, bulletin 66, International Federation for Structural Concrete (fib)

12.  Airport Pavement Design and Evaluation, AC 150/53206E, U.S. Department of Transportation, Federal Aviation Administration

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