Mechanical model for the shear strength of steel fiber reinforced concrete (SFRC) beams without stirrups

Abstract

Numerous studies have shown that adding steel fibers to the concrete mixture improves both the shear strength and ductility of reinforced concrete beams. Most current shear design formulations for steel fiber reinforced concrete beams are empirically based and their predictions provide acceptable results when compared with tests results, but only in limited ranges of the parameters involved. On the other hand, many shear theoretical models suggested in the literature are derived by extending previous formulations for conventional reinforced concrete beams, just introducing the stresses transferred across the critical shear crack. Since the effects of steel fibers on the others shear resisting mechanisms are not accounted for, “adjusting” empirical factors must be used to fit the experimental results. There is, therefore, the need for developing mechanical models capable to rationally account for the effects of steel fibers on the global shear strength and on each shear resisting mechanisms. In this paper, the previously derived and validated Multi Action Shear Model for RC elements is extended to steel fiber reinforced concrete beams without stirrups. The effects of steel fibers on each resisting mechanism have been identified and incorporated in the formulation of each shear component and in the Multi-Action Shear Model equilibrium equations. The residual tensile stresses of fibrous concrete, obtained through a simple formulation, has been used to: capture the enhancement of the compression chord contribution; the shear transferred by bridging effect of the fibres along the critical shear crack and by dowel action. The proposed model is shown to properly estimate the shear resistance of a large set of available test data, being able to account for most influencing parameters, like fibers types and amounts, concrete strength, longitudinal reinforcement ratios and beam geometry.

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Abbreviations

As, Asw :

Longitudinal rebar and stirrups area

C :

Resultant of compression force

E c :

Young modulus of plain concrete

F τ :

Fiber factor

G f :

Energy fracture of plain concrete

L f :

Fiber length

M, Mcr :

Bending moment and cracking bending moment

R τ :

Reduction factor

T f :

Horizontal component of fiber resultant force

T l :

Resultant force of longitudinal rebar

VExp, VPre :

Experimental and predicted shear strength

V f :

Volumetric percentage of fibers

Vc, Vcw, Vs, Vl, Vcf :

Shear strength contribution: concrete, concrete web, stirrups, dowel action, and fibers

V u :

Ultimate shear strength

a :

Shear span length

b, d, h :

Width, effective depth and total depth of beam cross-section

d f :

Fiber diameter

d g :

Maximum aggregate size

d 0 :

Effective depth of the cross-section (d), but not less than 100 mm

fck, fcm :

Characteristic and average value of the plain concrete compressive strength

f ct :

Tensile strength under direct tension of plain concrete

fFts, fFtu :

Tensile stress level representative of SLS and ULS

fR1, fR3 :

Residual flexural tensile strength corresponding to CMOD = 0.5 and 2.5 mm

fy, fyw :

Steel rebar and steel stirrups yield strength

k :

Size effect parameter

k dg :

Average crack specimen factor

k v :

Strain-aggregate size parameter

l c :

Critical fiber length

l cr :

Distance from shear critical crack to the support

n :

Homogenization factor

vc, vcw, vs, vl, vcf :

Non-dimensional shear strength contribution: concrete, concrete web, stirrups, dowel action, and fibers

v u :

Non-dimensional ultimate shear strength

x, xf :

Neutral axis depth of plain concrete and SFRC

y :

Vertical abscissa from neutral axis

w u :

Critical crack width

z :

Inner lever arm

β :

Reduction factor

β τ :

Fiber bond factor

εx, εsb :

Average normal strain of concrete and of longitudinal reinforcement

η0, ηl :

Fiber orientation factor and length efficiency factor for fiber

μ cr :

Non-dimensional cracking moment

θ :

Shear crack inclination angle

ρ :

Geometrical percentage of longitudinal reinforcement

σ1, σ2 :

Principal tensile stresses

σ c,crit :

Normal stress at the critical point

σ c,max :

Normal stress at the top fiber of cross-section

σ sy :

Steel fiber yield strength

σ tu :

Average residual tensile stress of SFRC

σx, σy :

Tensile stresses along x and y direction

τ, τu :

Shear stress and ultimate shear stress

τ f :

Mean fiber-matrix shear stress

ξ :

Size and slenderness factor

ζ :

Abscissa along the longitudinal axis beam

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Acknowledgements

The financial support provided by the University of Messina (Italy), through the scholarship granted for a 2-months research and teaching stage of the first author, is acknowledged.

Funding

This work is part of the Research Projects BIA2015-64672-C4-1-R, funded by the Spanish Ministry of Economy and competitiveness, and RTI2018-097314-B-C21, funded by The Spanish Ministry of Science and Innovation.

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Correspondence to Nino Spinella.

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Marì Bernat, A., Spinella, N., Recupero, A. et al. Mechanical model for the shear strength of steel fiber reinforced concrete (SFRC) beams without stirrups. Mater Struct 53, 28 (2020). https://doi.org/10.1617/s11527-020-01461-4

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Keywords

  • Steel fiber reinforced concrete (SFRC)
  • Shear strength
  • Multi Action Shear Model
  • Shear resisting mechanisms
  • Mechanical model