Simplified prediction of the time dependent deflection of SFRC flexural members

Abstract

It is well known that the inclusion of steel fibres into a concrete matrix has the potential to improve both the serviceability and strength characteristics of reinforced concrete. As a result of decades of academic interest into the material, design provisions for flexural strength, shear strength and short-term serviceability have been incorporated into international codes of practice. However, available design guidelines typically contain little or no guidance for engineers to confidently predict the long-term behaviour of structures manufactured with steel fibre reinforced concrete (SFRC). This limits the full utilization of the material in design practice. This paper presents a simplified model, suitable for design, that can reliably predict the effects of creep and shrinkage in SFRC members containing conventional reinforcement which are subjected to a sustained in-service flexural load. Predictions of the proposed model are compared to available data in the literature and are shown to correlate well.

Appendix 1: Ng et al. [38] model

This Appendix contains additional information that has been provided in the main body of the paper for the sake of brevity.

The model of [38] has been used in Sect. 6 to predict f_0.5 in the absence of experimental data. Over a plane of unit area, the stress carried by steel fibres, f_w, for a given crack width, w, is taken as:

$$f_{{\text{w}}} = K_{{\text{f}}} {\alpha }_{{\text{f}}} {\rho }_{{\text{f}}} {\tau }_{{\text{b}}}$$

(9)

In Eq. 9, α_f is the fibre aspect ratio (l_f/d_f), ρ_f is the volumetric dosage of steel fibres and K_f is a fibre orientation factor. For Mode I fracture in a 3D domain, K_f is taken as:

$$K_{{\text{f}}} = 0.5\sin \left( {\upgamma } \right) \times \left( {1 - {{2w} \mathord{\left/ {\vphantom {{2w} {l_{{\text{f}}} }}} \right. \kern-\nulldelimiterspace} {l_{{\text{f}}} }}} \right)^{2}$$

(10)

In Eq. 10, γ represents the angle between an individual fibre and the loading direction [38] empirically determined γ as:

$${\upgamma } = \min \left( {2\tan^{ - 1} \sqrt {\frac{w}{{1.5d_{{\text{f}}} }}} ,\frac{{\uppi }}{3}} \right)$$

(11)

In Eq. 9, τ_b is the bond stress for the engaged steel fibres and was empirically approximated as:

$${\uptau }_{{\text{b}}} = 2.4f_{{{\text{ct}}}} + 4.5\left( {1 - \frac{2}{{\upgamma }}\sin \left( {\frac{{\upgamma }}{2}} \right)} \right)$$

(12)

f_0.5 for a given fibre type (l_f, d_f) and dosage (ρ_f) may be determined from Eq. 9 by substituting w = 0.5 mm into Eqs. 10 and 11.