Analytical Model for Fictitious Crack Propagation in Concrete Beams

Ulfkjær, J. P.; Krenk, Steen; Brincker, Rune

doi:10.1061/(asce)0733-9399(1995)121:1(7)

Cited by 96 publications

(58 citation statements)

References 5 publications

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“…This indicates that rigid body motion of the two broken halves of the specimen is by far the dominant mechanism. Consequently the failure mode commonly observed, characterised by a main failure crack at mid-span, has clear resemblance with a plastic hinge, a phenomenon suggested by other researchers 10,11 . Nevertheless, the question of how to determine the size and position of the hinge remains.…”

Section: Model Conceptsmentioning

confidence: 65%

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

Prudêncio¹

2005

Mater. Struct.

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Section: Model Conceptsmentioning

confidence: 65%

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

Prudêncio¹

2005

Mater. Struct.

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“…Obviously, the determination of the length of the hinge is critical in the calculation of strain. Ulfkjaer et al [17] applied the hinge model to a three-point bending beam and obtained a value of s equal to h sp /2. This was based on simulated elasto-plastic analysis and comparison with experiments.…”

Section: + =mentioning

confidence: 99%

“…Using the cracked hinge model proposed by Ulfkjaer et al [17] and adopted for fibre reinforced concrete by Olesen [18], the tensile strain can be obtained by equation 5. Obviously, the determination of the length of the hinge is critical in the calculation of strain.…”

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confidence: 99%

Stress-strain characteristic of SFRC using recycled fibres

Tlemat¹

2005

Mater. Struct.

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Abstract:This paper presents work from a comprehensive study on the development of a flexural design framework for concrete reinforced with steel fibres that are recovered from used tyres. The experimental flexural behaviour of notched concrete prisms reinforced with these fibres is initially presented. For comparison purposes, prisms reinforced with industrially produced fibres are also considered. An attempt to adopt an existing RILEM design framework to derive appropriate tensile stress-strain blocks is made, but problems are identified with key parameters of the framework. The influence of crack propagation and location of neutral axis depth on the tensile stress distribution is examined. Following an analytical study, it is concluded that the uniaxial stress-strain model, proposed by RILEM overestimates the load-carrying capacity and should be modified by utilising more advanced analytical techniques. RésuméCet article présente une étude sur le développement d'un cadre flexural de conception pour le béton armé à base de fibres d'acier récupérées des pneus utilisés. Le comportement flexural expérimental des prismes en béton entaillés renforcés avec de fibres est initiallement presenté. Aux fins de comparison, des prismes renforcés à base de fibres industriellement produites sont également considérés. Pour déduire les blocs de tension appropriés de contraintedeformation, une tentative d'adopter un cadre existant de conception de RILEM est effectuée, cependant des problèmes sont identifiés avec les paramètres clé du cadre. L'influence de la propagation de fissure et ainsi que la location de la profondeur d'axe neutre sur la distribution de tension d'effort est examinée. A la suite d'une analyse analytique, on peut conclure que le modèle de contraintedeformation uniaxial, proposé par RILEM surestime la charge de portance et devrait être modifié en utilisant des techniques analytiques plus élaborées.

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“…Tensile strain-softening, according to a stress/crack-width relationship (σ-w), then occurs until the critical crack width is reached (at around 0.05 mm) at which point the real crack develops (i.e. σ=0) [5][6][7].Under compression, the concrete is assumed to behave according to a parabolic stress-strain relationship, similar to those defined in most design codes [2-3]. However, because there is no single relationship between stress and strain in the cracked region, a variety of approaches have been used to model tensile stress.…”

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

2007

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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...

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Analytical Model for Fictitious Crack Propagation in Concrete Beams

Cited by 96 publications

References 5 publications

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

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

Stress-strain characteristic of SFRC using recycled fibres

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

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