Fiber reinforced concrete (FRC) theory

The Reinforcement

Fiber reinforced concrete (FRC)

At PPCD we make calculations of steel and fiber reinforcement, or a combination of the two. When calculating fiber reinforced concrete (FRC) we usually calculate with macro-synthetic polypropylene fiber reinforced concrete (MSFRC) due to the environmentally friendly advantages that can be achieved by using this type of fiber reinforcement. One of the main advantages in terms of sustainability (and costs), is that polypropylene cannot corrode, making it possible to reduce the exposure class of the concrete structure, resulting in less required cement in the concrete mix, and ultimately resulting in much lower CO₂-emission. This can only be accomplished using polypropylene fiber reinforcement.

Therefore, we almost always prescribe the macro-synthetic polypropylene structural fiber DURUS® EasyFinish from ADFIL. Amongst a multiple of different test, most importantly, the DURUS® EasyFinish has undergone the following tests:

EN ISO 13438 to prove its time dependent durability and 100 year longevity
ASTM C1579-13 to prove its additive impact on short-term (plastic) shrinkage
ASTM C1581 to prove its additive impact on long-term (drying and autogenious) shrinkage
EN 14651 to determine the flexural tensile strength and residual flexural strength

Especially the three-point bending test cf. EN 14651 is important, as it provides the stress-strain response curve of the fiber reinforced concrete cross section and corresponding residual flexural strength values. These values are essentiel to calculate the bearing (moment and shear) capacity of the given concrete structures with fiber reinforcement alone, or in combination with steel reinforcement. The theory behind our calculations and software is presented below.

Use our software to make your own calculations with fiber reinforcement and/or steel reinforcement.

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Testing

The structural test

The standardized notched three-point bending test cf. EN 14651 is one of the main tests when working with fiber reinforced concrete (FRC) as it provides the residual flexural strength values used to calculate the bearing (moment and shear) capacity of the given concrete structures with fiber reinforcement alone, or in combination with steel reinforcement. The test is conducted on several beams with various fiber dosages to ensure more precise data and applicable material safety factors cf. EN 1990.

When conducting the notched three-point bending test according to EN 14651, the resuls are initually presented as a graph with the applied load, P, on the vertical Y-axis with the corresponding crack mouth opening displacements, CMOD, on the horizontal X-axis. The following values are especially of interest:

F_R,1 (CMOD₁ = 0,5 mm)
F_R,2 (CMOD₂ = 1,5 mm)
F_R,3 (CMOD₃ = 2,5 mm)
F_R,4 (CMOD₄ = 3,5 mm)

Test to Model

From stress-strain response to model

These load-values are converted to residual flexural tensile strength values from the following equation:

$$ f_{R,i} = \frac{3\,F_{R,i}\,l}{2\,b\,h_{sp}^2} $$

The methods are slightly different when following TR34 ^1,2, Model Code 2010 ^9,10,11, or the coming Annex L to prEN1992-1-1⁷, but the principals are identical. The load-deflection response is converted to a bi-linear stress-strain curve from which the moment capacity can be calculated following the rules of horizontal equilibrium and constitutive laws (moment around the neutral axis).

Since fiber reinforced concrete (FRC) is reinforced in all dimensions, fiber reinforcement also results in an additional shear capacity that can be added to that of either unreinforced concrete, shear/stirrup reinforced concrete, and/or longitudinal steel reinforced concrete.

The principals are analogue to those for steel reinforced concrete. These principals therefore enable the possibility to make calculations with steel reinforcement, fiber reinforcement or a combination.

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 fiber reinforcement and steel reinforcement in your concrete element.

Standards and Codes

European Standards and Model Codes

Not only are the DURUS® EasyFinish fibers from ADFIL produced and tested according to European Standards, but our online programs also follow all parts of the European Standards and Model Code relevant to fiber reinforcement. Below you can see the relevant standards and codes. Further references can be seen below in our Bibliography.

Standard/Code	Name	Description	Comments
EN 14651 + A1:2007	Test method for metallic fibre concrete - Measuring the flexural tensile strength (limit of proportionality (LOP), residual)	This European Standard specifies a method of measuring the flexural tensile strength of metallic fibered concrete on moulded test specimen. The method provides for the determination of the limit of proportionality (LOP) and of a set of residual flexural tensile strength values. This testing method is intended for metallic fibres no longer than 60 mm. The method can also be used for a combination of metallic fibres and, a combination of metallic fibres with other fibres.
EN 14889-2:2006	Fibres for concrete - Part 2: Polymer fibres - Definitions, specifications and conformity	This Part 2 of EN 14889 specifies requirements for polymer fibres for structural or non-structural use in concrete, mortar and grout. NOTE – Structural use of fibres is where the addition of fibres is designed to contribute to the load bearing capacity of a concrete element. This standard covers fibres intended for use in all types of concrete and mortar, including sprayed concrete, flooring, precast, in-situ and repair concretes.	This standard is harmonized and used for CE marking. Only harmonized standards are legislative.
EN 14845-2:2006	Test methods for fibres in concrete - Part 2: Effect on concrete	This European Standard specifies a method for determining the effect of fibres, steel or polymer, on the residual flexural strength of a reference concrete.
fib MC2010	fib Model Code for Concrete Structures 2010	This edition of the Model Code gives an extensive state-of-the-art regarding material properties for structural concrete. This includes constitutive relations for concrete up to strength class C120, and properties of reinforcing and prestressing steel, including prestressing systems. Special attention is given to the application of fibre concrete for structural applications, the application of non-metallic reinforcement, interface characteristics, verification assisted by numerical simulations, verification assisted by testing, and to a number of important construction aspects.

Bibliography

The library behind our knowledge

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 Slabs-on-Ground, ACI 360R-10, 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, σ-ε-design method, RILEM TC 162-TDF, Vol. 36, RILEM
7.	Eurocode 2: Design of concrete structures - Part 1-1: General rules and rules for buildings, EN 1992-1-1, European Committee for Standardization
8.	Eurocode 7: Geotechnical design - Part 1: General rules, EN 1997-1, 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 150/5320-6E, U.S. Department of Transportation, Federal Aviation Administration

Theory

The Reinforcement