Predicting the flexural load–deflection response of steel fibre reinforced concrete from strain, crack-width, fibre pull-out and distribution data

Abstract

A semi-analytical model is presented, based on conventional principles of mechanics, to predict the flexure behaviour of steel fibre reinforced concrete. The model uses a stress-block approach to represent the stresses that develop at a cracked section by three discrete stress zones: (a) a compressive zone; (b) an uncracked tensile zone; and (c) a cracked tensile zone. It is further shown that the stress-block, and hence flexural behaviour, is a function of five principal parameters: compressive stress-strain relation; tensile stress-strain relation; fibre pull-out behaviour; the number and distribution of fibres across the cracked section in terms of their positions, orientations and embedment lengths; and the strain/crack-width profile in relation to the deflection of the beam. An experimental investigation was undertaken on both cast and sprayed specimens to obtain relationships for use in the model. The results of the study showed a reasonable agreement between the model predictions and experimental results. However, the accuracy of the model is probably unacceptable for it to be currently used in design. A subsequent analysis highlighted the single fibre pull-out test and the sensitivity of the strain analysis tests as being the main cause of the discrepancies. IntroductionSteel fibre reinforced concrete (SFRC) continues to grow in specialist applications that can utilise its flexibility and enhanced toughness performance, notably sprayed concrete and industrial floors. However, its continued development has been hindered by a general lack of confidence in its design, particularly under flexural load. This is mainly due to a lack of suitable analytical design methods and appropriate material property tests that measure flexural toughness (or strength) parameters. This need is highlighted by the recent RILEM TC162-TDF [1] proposals for test and design methods.Although recent developments in flexural toughness characterisation have attempted to address the latter of these shortcomings, flexural behaviour of SFRC will be better understood, and thereby predicted, if crack formation and the associated fibre reinforcing mechanisms at the critical section can be explicitly considered in terms of the strain distribution, crack-width and deflection of the beam. To this end, the stress-profile concept potentially offers the most acceptable flexural modelling approach because it is simple to understand; uses conventional principles of structural mechanics, and could, therefore, be incorporated into a design rationale similar to that used for conventional reinforced concrete.A variety of stress-profile models have been proposed for predicting the load-deflection behaviour of SFRC by utilising the equilibrium of forces at the cracked section [2][3][4][5]. These models have generally adopted a semi-analytical approach, whereby failure is assumed to occur at a single crack with rigid-body motion of the two broken halves, rotating about a plastic hinge, being the dominant mechanism.The kinematics of failure has bee...

Application of constitutive models in European codes to RC–FRC

“…In order to predict the moment capacity, the load-crack mouth opening relation for a particular FRC is used in the stressstrain profile in the flexural analysis. A similar approach is presented in [30], where a semi-analytical model is proposed to predict the flexural response of SFRC. This model also uses a stress-block approach and relates the flexural capacity of the critical section to the following parameters: the compressive stress-train relation, the tensile stress-strain relation, the fiber pullout, the number and distribution of the fibers across the cracked section (in terms of position, orientation and embedment lengths) as well as the strain/crack width relation at a given mid-span deflection.…”

Prediction of steel fibre reinforced concrete under flexure from an inferred fibre pull-out response

“…A practical example to show the application of the proposed methodology is presented in this section, using data from Jones et al 4 . In order to characterize the pull-out versus crack opening curve, the load/deflection curves from tests undertaken on seven 75mm deep unnotched beams containing 40kg/m 3 of 30mm length and 0.5mm diameter hooked steel fibres were initially analysed ( Figure 5).…”

“…The components of bond can be classified as: the physical and/or chemical adhesion between fibre and matrix; the frictional resistance; the mechanical component (associated with a particular geometry of the fibre be it deformed, crimped, or hooked); and the fibre-to-fibre interlock 2 . To deal with this, several authors 3,4 have determined the average response of the load transmitted by the fibres through the cracked region from pull-out tests of single fibres. Some problems arise with this approach, namely: the number and position of the fibres bridging the crack is not precise, the load supported by each fibre depends on the crack opening displacement (a function of the specimen displacement), the orientation of the fibre and the embedment length.…”

“…To overcome such problems, the authors have examined various permutations of fibre orientation and embedment length and determined the number of fibres using theoretical equations 3 and experimental data 4,5 . This kind of approach, however, has some shortcomings.…”

Flexural Modelling and Finite Element Analysis of FRC Beams Reinforced with PVA and Basalt Fibres and Their Validation

“…erefore, the response of PVA and basalt fibres in concrete is different and cannot be predicted through the available model of steel fibre-reinforced concrete (SFRC) [12]. e reason of unsuitability of available models is that the post-peak stress-strain response of FRC solely depends on the fibre properties including fibre modulus of elasticity, elongation, and bond characteristics [11].…”