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On the evaluation of the structural redistribution factor in FRC design: a yield line approach

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Abstract

Fibre-reinforced concrete (FRC) is a material that can be characterized by a high standard deviation in the post-peak tensile region. As consequence, structures made of FRC show a too safe prediction of the maximum bearing capacity when derived from characteristic values identified by means of small standard specimens. The Model Code 2010 has introduced a coefficient, named structural redistribution factor, that is able to take into account a reduced variability of the structural response when compared to that of material. A simplified procedure to provide an upper bound estimation of the structural redistribution factor based on the yield line method and able to take into account the material heterogeneity is presented. As case studies, a FRC full-scale elevated flat slab, a slab on ground and a full-scale beam are considered.

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Abbreviations

CMOD:

Crack mouth opening displacement

COD:

Crack opening displacement

COV:

Coefficient of variation

CTOD:

Crack tip opening displacement

FRC:

Fibre reinforced concrete

d f :

Fibre diameter

E :

Young’s modulus

f c :

Concrete compressive strength

f eq1 :

Average flexural nominal strength in the CTOD range between 0 and 0.6 mm

f eq2 :

Average flexural nominal strength in the CTOD range between 0.6 and 3 mm

f R1 :

Residual flexural nominal strength of FRC corresponding to CMOD = 0.5 mm

f R3 :

Residual flexural nominal strength of FRC corresponding to CMOD = 2.5 mm

f Fts :

FRC serviceability uniaxial tensile residual strength

f Ftu :

FRC ultimate uniaxial tensile residual strength

f If :

Flexural nominal stress corresponding to a CTOD equal to 25 μm

f L :

Limit of proportionality

k :

Subgrade modulus

K :

Fibre orientation factor

K Rd :

Redistribution factor

\(K_{{_{\text{Rd}} }}^{\text{MC}}\) :

Model Code definition of the redistribution factor

K Rdj :

Alternative definitions of the redistribution factor proposed by [1] j = 1, 2, 3, 4

l f :

Fibre length

m :

Moment per unit width

m u :

Ultimate moment per unit width

P :

Load

P cr :

Load at the elastic limit, first cracking load

P max :

Maximum load

P u :

Ultimate load

\(P_{\text{eq}}^{\text{u}}\) :

Ultimate equivalent load

q u :

Distributed load

V :

Fractured volume at failure involved in a structure

V 0 :

Fractured volume at failure involved in a classification test

w u :

Maximum crack opening accepted in structural design

W E :

External work

W I :

Internal work

α :

Percentile level

β:

Factor to account fibre distribution over slab thickness

δ :

Virtual displacement

θ i :

Angle of rotation

υ :

Poisson’s ratio

Hom:

Homogeneous

k :

Characteristic value, 0.05 percentile value

m :

Mean value, 0.5 percentile value

Rand:

Random; heterogeneous

cr:

Cracking

max:

Maximum

u:

Ultimate

α :

Percentile level

^:

Percentile estimate

References

  1. di Prisco M, Martinelli P, Dozio D (2016) The structural redistribution coefficient KRd: a numerical approach to its evaluation. Struct Concr 17:390–407

    Article  Google Scholar 

  2. Cominoli L (2007) Studio sul calcestruzzo fibrorinforzato per applicazioni industriali: dalle proprietà del materiale al comportamento strutturale. PhD thesis. Brescia, University of Brescia, (in Italian)

  3. di Prisco M, Colombo M, Dozio D, Mauri M (2006) Pavimentazione industriale in SFRC: una realizzazione su solai alveolari. In Proceedings of 16 CTE Conference, Parma (in Italian)

  4. di Prisco M, Plizzari G, Vandewalle L (2009) Fibre reinforced concrete: New design perspectives. Mater Struct 42:1261–1281

    Article  Google Scholar 

  5. Fib Model Code for Concrete Structures 2010 (2013) Fédération Internationale du Béton, Ernst & Sohn, Lausanne

  6. Cavalaro SHP, Aguado A (2015) Intrinsic scatter of FRC: an alternative philosophy to estimate characteristic values. Mater Struct 48:3537–3555

    Article  Google Scholar 

  7. Pujadas P, Blanco A, Cavalaro S, Aguado A (2014) Plastic fibres as the only reinforcement for flat suspended slabs: Experimental investigation and numerical simulation. Constr Build Mater 57:92–104

    Article  Google Scholar 

  8. Pujadas P, Blanco A, Cavalaro SHP, Aguado A, Grünewald S, Blom K, Walraven JC (2014) Plastic fibres as the only reinforcement for flat suspended slabs: parametric study and design considerations. Constr Build Mater 70:88–96

    Article  Google Scholar 

  9. Salehian H, Barros JAO, Taheri M (2014) Evaluation of the influence of post-cracking response of steel fibre reinforced concrete (SFRC) on load carrying capacity of SFRC panels. Constr Build Mater 73:289–304

    Article  Google Scholar 

  10. Johansen KW (1962) Yield-line theory. Cement and Concrete Association, London

    Google Scholar 

  11. CNR-DT 204 (2006) Guidelines for design, construction and production control of fiber reinforced concrete structures, National Research Council of Italy

  12. DafStb Guideline (2014) Steel fibre reinforced concrete, German Committee for reinforced concrete

  13. Kasper T, Stang H, Mjoernell P, Slot H, Vitt G, Thrane LN, Reimer L (2014) Design guideline for structural applications of steel fibre reinforced concrete, SFRC Consortium

  14. Drucker DC (1961) On structural concrete and the theorems of limit analysis. Int Assoc Bridge Struct Eng Pub 21:49–59

    Google Scholar 

  15. Meyerhof GG (1962) Load carrying capacity of concrete pavements. ASCE J Soil Mech Found Div 88(3):89–115

    Google Scholar 

  16. di Prisco M, Ferrara L, Caverzan A (2012) Self-compacting fibre reinforced concrete: is the material really isotropic? In: 3rd Iberian Congress on self-compacting concrete, Madrid

  17. EN 14651 (2004) Test method for metallic fiber concrete—Measuring the flexural tensile strength (limit of proportionality, residual)

  18. UNI 11039 (2003) Steel fibre reinforced concrete—Part I: Definitions, classification specification and conformity. Part II: test method for measuring first crack strength and ductility indexes. Italian Board for Standardization

  19. EN 1990 (2006) Eurocode—basis of structural design. European Committee for Standardization, Brussels

  20. Lee TH, Mosalam KM (2004) Probabilistic fiber element modeling of reinforced concrete structures. Comput Struct 82:2285–2299

    Article  Google Scholar 

  21. Hordijk D (1991) Local approach to fatigue of concrete. PhD Thesis. Delft, delft University of technology

  22. Parmentier B, Van Itterbeeck, P, Skowron A (2014) The behaviour of SFRC flat slabs: the Limelette full-scale experiments for supporting design model codes. In: Charron JP, Massicotte B, Mobasher B, Plizzari G (eds) FRC 2014 Joint ACI-fib International Workshop—fibre reinforced concrete: from design to structural applications, Montreal

  23. di Prisco M, Martinelli P, Parmentier B (2016) On the reliability of design approach for FRC structures according to Model Code 2010: the case of elevated slabs. Struct Concr. doi:10.1002/suco.201500151

    Google Scholar 

  24. di Prisco M, Ferrara L, Lamperti MGL (2013) Double edge wedge splitting (DEWS): An indirect tension test to identify post-cracking behaviour of fibre reinforced cementitious composites. Mater Struct 46:1893–1918

    Article  Google Scholar 

  25. Sorelli L, Meda A, Plizzari GA (2006) Steel fiber concrete slabs on ground: a structural matter. ACI Struct J 103:551–558

    Google Scholar 

  26. Dozio D (2008) SFRC structures: identification of the uniaxial tension characteristic constitutive law. PhD Thesis. Milano, Politecnico di Milano

  27. di Prisco M, Colombo M, Dozio D (2013) Fibre-reinforced concrete in fib Model Code 2010: principles, models and test validation. Struct Concr 14:342–361

    Article  Google Scholar 

  28. Baumann RA, Weisgerber FE (1983) Yield-line analysis of slabs-on-grade. J Struct Eng ASCE 109:1553–1568

    Article  Google Scholar 

  29. Meda A (2003) On the extension of the yield-line method to the design of SFRC slabs on grade. Stud Res 24:223–240

    Google Scholar 

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Authors and Affiliations

  1. Department of Civil and Environmental Engineering, Politecnico di Milano, P.za L. da Vinci 32, 20133, Milan, Italy

    Matteo Colombo, Paolo Martinelli & Marco di Prisco

Authors
  1. Matteo Colombo
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  2. Paolo Martinelli
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  3. Marco di Prisco
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Correspondence to Paolo Martinelli.

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Colombo, M., Martinelli, P. & di Prisco, M. On the evaluation of the structural redistribution factor in FRC design: a yield line approach. Mater Struct 50, 100 (2017). https://doi.org/10.1617/s11527-016-0969-3

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