Annex ADesign of Steel Fibre Reinforced Concrete

NBC 2016 (SP 7:2016) Volume 1

2016 · PDF page 856

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A-1 General

This annex shall apply where steel fibres are used to improve the performance and capacity of reinforced and prestressed concrete structures.

The design of steel fibre reinforced concrete (SFRC) at both the ultimate and serviceability limit states shall be based on the stress $(\sigma) \neq \text{strain} (\varepsilon)$ relationships for SFRC as specified in A-3.3 (see Note 1).

Steel fibres shall not be relied upon in plastic hinge regions for strength requirements (see Note 2).

Steel fibres shall not be relied upon at constructions joints for either serviceability or strength requirements. Design procedure in this clause is for steel-fibre-reinforced concrete with a softening classification only (see Fig. 25). Hardening SFRC and the use of synthetic fibres is beyond the scope of this annex.

1 When using brittle fibres that rely on a fibre pullout failure mechanism to obtain member ductility, care is required for cases where a significant number of fibres fracture or where fibres result in local crushing of the concrete due to the local forces imposed on the matrix by the fibres. Fibre fracture may occur where the bond between the fibre and the matrix is high, and this is more likely in a high strength concrete combined with fibres of high bond capacity and of lower strength steels. 2 The anchorage capacity of steel fibres may be lost in areas where crack widths exceed about $3.5\mathrm{mm}$ . Cracking of this

magnitude can be expected in regions where plastic rotations are expected.

A-2 Definitions

For the purpose of this annex the following definitions shall apply.

A-2.1 Crack Mouth Opening Displacement (CMOD) — The width of a crack shall be measured at its mouth in a flexural tensile test. To measure the CMOD, a displacement transducer/clip gauge shall be mounted along the longitudinal axis at the mid width of the test specimen (beam with nominal size of 150 mm × 150 mm and length L so that 550 mm < L < 700 mm).

A-2.2 Crack Opening Displacement (COD) — The width of a single localized crack, taken as an average on four sides, for a direct tensile test on a strain softening SFRC dog-bone shaped specimen in accordance with A-3.3.7.

A-2.3 Steel Fibre Reinforced Concrete (SFRC) — A mixture of concrete and steel fibres.

A-2.4 Hardening Behaviour — A material that displays an enhanced strength with increasing crack widths beyond that measured at the point of initial cracking of the cementitious matrix.

A-2.5 Softening Behaviour A material that exhibits a loss of strength upon cracking.

PART 6 STRUCTURAL DESIGN — SECTION 5 CONCRETE: 5A PLAIN AND REINFORCED CONCRETE

A-2.6 Target Dosage — The specified quantity of fibres in kilograms per cubic metre of concrete (kg/m³).

A-3 Properties of Sfrc

A-3.1 General

SFRC shall be classified in terms of both its characteristic compressive (cylinder) strength ( $f_{\mathrm{c}}'$ ) (see A-3.2) and its characteristic residual tensile strength ( $f_{1.5}'$ ) (see A-3.3.3).

A-3.2 Compressive Strength

The characteristic compressive strength of SFRC at 28 days ( $f_{c}^{\prime}$ ) shall be determined in accordance with good practice [6-5A(14)].

In the absence of more accurate data, the mean value of the in situ compressive strength ( $f_{cmi}$ ) shall be taken as 90 percent of the mean value of the cylinder strength ( $f_{cm}$ ).

NOTE — The compressive strength of steel fibre reinforced concrete (SFRC) should be determined by means of standard tests on concrete cylinders. The addition of steel fibres to concrete in conventional dosages (less than $100 \, kg/m^{3}$ ) does not change the compressive properties of the concrete.

A-3.3 Tensile Properties

A-3.3.1 Classification

SFRC shall be classified as either softening or hardening as shown in Fig. 25. Hardening SFRC is outside the scope of this annex.

1 A hardening material is defined as one with a tensile strength equal to or greater than 1.1 times the strength of the matrix without fibres and taken at a crack opening displacement (COD) of equal to or greater than $0.3\mathrm{mm}$ .

2 A hardening material is one where multiple cracks can occur prior to crack localization. For material hardening to occur, the fibre dosage is typically such that the strength of the SFRC is at least 10 percent greater than the strength of the same concrete mix without fibres. The value of COD of 0.3 is sufficiently high such that matrix contribution to the strength of the composite is minimal and the tension at this point is substantially taken by the fibres alone. Hardening SFRC is outside of the scope of this annex.

A-3.3.2 Matrix Tensile Strength

The matrix tensile strength of the softening SFRC ( $f_{\mathrm{ct}}$ ) shall be obtained using flexural tensile testing, in accordance with good practice [6-5A(14)].

When only the characteristic compressive (cylinder) strength $(f_{\mathrm{c}}^{\prime})$ has been determined, the mean and characteristic flexural tensile strength of SFRC shall be calculated in accordance with 5.2.2.

NOTE — For strain softening SFRC, the peak strength of the composite may be approximated as the strength of the concrete mix without fibres.

Chart

25A STRAIN SOFTENING SFRC

Chart

25B STRAIN HARDENING SFRC

FIG. 25 CLASSIFICATION OF SFRC

A-3.3.3 Residual Tensile Strength

The standard characteristic residual tensile strength grades $(f_{1,5}^{\prime})$ are $0.4\mathrm{MPa}$ , $0.6\mathrm{MPa}$ , $0.8\mathrm{MPa}$ , $1.2\mathrm{MPa}$ , $1.6\mathrm{MPa}$ and $2.0\mathrm{MPa}$ .

The characteristic residual tensile strengths of concrete at 28 days $(f_{1.5}^{\prime})$ shall be determined statistically from tests carried out in accordance A-3.3.4 or A-3.3.5.

NOTE — The characteristic residual tensile strength depends on the fibre-matrix bond strength, which is usually a function of the compressive strength of the parent concrete, as well as the fibre content. It may be unrealistic to specify a high value of $f_{1.5}^{\prime}$ when using a relatively low value of $f_{c}^{\prime}$ .

A-3.3.4 Determination of Strength by Direct Testing

The characteristic residual tensile strength $(f_{1.5}^{\prime})$ shall be obtained using direct tensile tests as specified in A-3.3.7.

Alternatively, where matched direct and indirect testing has been undertaken in accordance with A-3.3.6 for similar SFRC mixtures, the characteristic residual tensile may be determined as:

f _ {1. 5} ^ {\prime} = k _ {\mathrm{R}, 4} f _ {\mathrm{R}, 4} ^ {\prime}

Where $f_{\mathrm{R},4}'$ is determined in accordance with A-3.3.8 and calculated statistically, and the factor $k_{\mathrm{R},4}$ determined from A-3.3.6.

For the purposes of this clause, similar SFRC mixtures are defined as having the same,

a) fibre type and content,

b) water to cementitious material ratio,

c) maximum aggregate particle size, and

d) compressive strength $(f_{\mathrm{c}}^{\prime})$

1 In calculating the characteristic strength, the population may be treated normally distributed and the strength determined in accordance with accepted standard. A confidence level of 75 percent shall be used such that 95 percent of the population exceeds the characteristic value.

2 The sample standard deviation shall not exceed 25 percent.

A-3.3.5 Determination of Strength by Indirect Testing

The characteristic residual tensile strength $(f_{1.5}^{\prime})$ may be obtained using indirect tests as specified in A-3.3.8 and calculated as:

f _ {1. 5} ^ {\prime} = 0. 4 f _ {\mathrm{R}, 4} ^ {\prime} - 0. 0 7 f _ {\mathrm{R}, 2} ^ {\prime}

A-3.3.6 Residual Tensile Strength-Residual Flexural Strength Relationship

The relationship between residual tensile strength and the residual flexural strength shall be obtained by matched using the same SFRC mixture. Residual tensile strength specimens shall be prepared and tested in accordance with A-3.3.7. Residual flexural tensile tests shall be in accordance with the procedure as mentioned below:

The average width of the specimen and distance between the tip of the notch and the top of the specimen in the mid-span section shall be determined from two measurement to nearest 0.1 mm width and distance in the notch port of the specimen using calipers.

When the CMOD is measured, the displacement transducer shall be mounted along the longitudinal axis at mid width of test specimen such that the distance 'y' between the bottom of specimen and line of measurement is 5 mm or less as mentioned in Fig. 26.

PART 6 STRUCTURAL DESIGN — SECTION 5 CONCRETE: 5A PLAIN AND REINFORCED CONCRETE

a) The concrete mix shall be batched to ensure a uniform distribution of fibres, the SFRC shall be placed in the moulds in a manner that does not interfere with the distribution of the fibres and, the SFRC shall be compacted using lightly applied external vibration; and

b) A minimum of 12 specimens shall be tested. The reference factor $k _ { \mathrm { R } , 4 }$ shall be determined as:

k _ {\mathrm{R}, 4} = f _ {1. 5 \mathrm{m}} / f _ {\mathrm{R}, 4 \mathrm{m}}

where

f1.5 = mean residual tensile strengths corresponding to a COD of 1.5 mm,

determined in accordance with A-3.3.7.

$f _ { \mathrm { R } , 4 \mathrm { m } }$ = mean residual flexural tensile strengths corresponding to a CMOD of 3.5 mm, determined in accordance with A-3.3.8.

NOTE — The residual tensile strength (as obtained from a direct tensile test) is a fundamental material property of SFRC. This clause allows the concrete producer and steel fibre manufacturer to correlate the direct tensile strength of their particular SFRC mix design with the flexural tensile strength.

A-3.3.7 Residual Tensile Strength Test

The residual tensile strength shall be obtained using the testing arrangement shown in Fig. 27 and with the following criteria:

All dimensions in millimetres.

NOTE — There is considerable discussion in the literature on whether the ends of the specimens should be fixed at each end, pinned at each end or fixed at one end and pinned at the other. The adoption of one pinned and one fixed end is a pragmatic decision between the ideal condition (fixed at each end) and limitations in manufacturing of specimens that are perfectly square at their ends for alignment within the testing machine. With both ends fixed any misalignment induces a moment in the specimen during gripping. This moment can induce a tensile stress on one side of the specimen, weakening the specimen. In some situations, the moment induced may be sufficient to crack the concrete. The inclusion of the universal joint at one end eliminates residual tensions that may result from the gripping procedure.

FIG. 27 Testing Arrangement for Direct Tension

a) The critical section shall be where the cross-sectional area is a minimum.

b) The SFRC mix shall be batched to ensure a uniform distribution of fibres, and shall be placed in the moulds in a manner that does not interfere with the distribution of the fibres. The SFRC shall be compacted using lightly applied external vibration.

c) The specimen shall be connected to the testing machine in such a manner that the machine does not apply a load to the specimen during the process of tightening of the grips and prior to testing.

d) One end of the specimen shall be connected to the testing machine through a universal joint such that no moment is applied to the end of the specimen.

e) Displacement measurements shall be taken on each of the four sides with the COD taken as the average of these measurements.

f) A minimum of twelve specimens shall be tested.

Tests where the failure of the specimen is outside of the testing region, or where the results are influenced by the test specimen boundaries, shall be retested.

h) The characteristic values of the tensile strength $f _ { 0 , \ast }$ and $f _ { 1 , 5 ^ { \circ } }$ corresponding to CODs of 0.5 mm and 1.5 mm, respective $\mathrm{]y,}$ shall be determined statistically as the 95 percentile confidence value assuming the population is normally distributed.

j) The mean values of $f _ { \mathrm { 0 , 5 m } }$ and $f _ { 1 . 5 \mathrm { m } , }$ corresponding to CODs of 0.5 mm and 1.5 mm, respectively, shall be determined

statistically as the $5 0 ^ { \mathrm { t h } }$ percentile confidence value assuming the population is normally distributed.

The stress results obtained from the test shall be multiplied by the three-dimensional orientation factor $k _ { 1 }$ , where,

k _ {1} = \frac {1}{0 . 9 4 + 0 . 6 \ell_ {\mathrm{f}} / b} \leq 1

And $\ell _ { \mathrm { f } }$ is the length and b is taken as the average of the width and depth of the specimen taken at the critical section.

NOTE — The factor k removes the influence of the boundaries on the fibre distribution and converts the results of the test to a state where the fibres can be considered to be randomly orientated in three-dimensional space.

A-3.3.8 Residual Flexural Tensile Strength

The residual flexural tensile strength $f _ { \mathrm { R , j } }$ shall be determined from 3 point notched bending tests on 150 mm square section prisms. The notch depth shall be 25 mm and the test conducted in accordance with A-3.3.6. The force F shall be plotted against the crack mouth opening displacement (CMOD), as shown in Fig. 28, and the residual flexural stress calculated as:

\frac {3 F _ {\mathrm{j}} L}{2 b h _ {\mathrm{sp}} ^ {2}}

where

$b$ = width of the specimen, in mm;

$h _ { \mathrm { s p } }$ = distance between tip of the notch and top of cross-section, in mm;

Chart

FIG. 28 LOAD VERSUS CMOD FOR RESIDUAL FLEXURAL TENSION

PART 6 STRUCTURAL DESIGN — SECTION 5 CONCRETE: 5A PLAIN AND REINFORCED CONCRETE

$L = \text{span, in mm; and}$

$F_{\mathrm{Rj}} =$ load recorded at $\mathrm{CMOD_j}$ (see Fig. 28).

A-3.4 Modulus of Elasticity

The mean modulus of elasticity at the appropriate age $(E_{\mathrm{cj}})$ shall be determined in accordance with good practice [6-5A(14)].

NOTE — The addition of steel fibres to concrete in conventional dosages (100 kg/m $^{3}$ and less) does not change the elastic modulus of the concrete.

A-4 Design of Reinforced Sfrc Members

A-4.1 General

This clause applied to reinforced and prestressed beams subjected to any combination of shear force, bending moment and axial force. This clause does not apply when torsion acts in conjunction with shear or to non-flexural members.

A-4.2 Strength of Beams in Bending and Combined Bending and Axial Force

Calculations for strength of cross-sections in bending shall incorporate equilibrium and strain-compatibility considerations and be consistent with the following assumptions:

a) Plane sections normal to the axis shall remain plane after bending.

b) Stress in the fibre reinforced concrete in that part of the cross-section in tension shall be taken to be $f'_{1.5}$ , where $f'_{1.5}$ is the characteristic residual tensile stress determined in accordance with A-3.3.3.

c) Distribution of compressive stress shall be determined from a stress-strain relationship for the concrete.

The strength of a section in bending, or in combined bending and axial force, shall be determined using rectangular stress blocks for the concrete in compression and concrete in tension, as shown in Fig. 29.

A-4.3 Minimum Reinforcement Requirements for Bending

The minimum tensile reinforcement shall be not less than that determined using the principles given in this annex, excluding fibres.

A-4.4 Strength of Beams in Shear

A-4.4.1 Design Shear Strength of a Beam

The design shear strength of a beam shall be taken as $\phi V_{\mathrm{u}}$

where

V _ {\mathrm{u}} = V _ {\mathrm{ue}} + V _ {\mathrm{uf}} + V _ {\mathrm{us}}

Where $V_{\mathrm{uc}}$ is determined from 39, $V_{\mathrm{us}}$ is determined from 39 and $V_{\mathrm{ufc}}$ is determined from A-4.4.2.

Notwithstanding the above equations, the fibres component to the shear strength of a beam, $V_{uf}$ , shall not exceed the greater of $0.3V_{u}$ and that determined by A-4.4.3 with $V_{us}$ taken as zero.

A-4.4.2 Contribution to Shear Strength by Steel Fibres

The contribution of the fibres to the ultimate shear strength $V_{\mathrm{uf}}$ of an SFRC beam shall be calculated from the following equation:

V _ {\mathrm{uf}} = 0. 7 k _ {\theta} b _ {\mathrm{v}} d _ {0} f _ {1. 5} ^ {\prime}

where

k _ {\theta} = \cos \theta_ {\mathrm{v}} \leq 1. 2 8

$\theta_{v}$ = angle between the axis of the concrete compression strut and the longitudinal axis of the member and shall be taken as not less than $38^{\circ}$

A-4.4.3 Minimum Shear Reinforcement

The minimum contribution from the total of the transverse steel reinforcement and fibres shall satisfy the following:

\left(V _{\mathrm{us}} + V_{\mathrm{uf}}\right)_{\min}\geq 0.1b_{\mathrm{v}}d_{0}\sqrt{f_{\mathrm{c}}^{\prime}} \text{and}\geq 0.6b_{\mathrm{v}}d_{0}

A-4.5 Design for Serviceability Limit States