Upper and Lower Bounds to Pull-Out Loading of Inclined Hooked End Steel Fibres Embedded in Concrete
Abstract
:1. Introduction
2. Analytical Pull-Out Model for Inclined Hooked-End Fibre
2.1. Fibre Failure Criteria
2.1.1. Transverse Isotropy
2.1.2. Upper and Lower Bounds
2.1.3. Experimental Data
2.2. Fibre Strength Tests
2.3. Matrix Composition and Materials
3. Pull-Out Tests of Inclined Fibres
4. Bounding Model Refinements
5. Conclusions
- In this paper, a new bounding approach and associated novel testing methods have been developed to predict the pull-out response of misaligned hooked-end steel fibres embedded in a concrete matrix.
- An upper bound estimate of the pull-out strength is based upon a transversely isotropic failure condition that arises in the straight length of the inclined fibre shank. Therein, the bound accounts for the orientation and anisotropic strength properties of the deep-drawn fibre and the off-axis plane stress state that exists within its straight shank.
- The transversely isotropic failure criterion applies to deep-drawn wire, where grains are elongated through multiple reductions to achieve their final diameter. Metallography revealed that elongated grains, with an aspect ratio exceeding five, were aligned with the fibre’s length direction.
- Novel fibre strength tests have been proposed to measure the transverse and shear strengths required for positioning an upper bound limit curve in a plot of failure load versus fibre orientation.
- The lower bound limit is based on the complete pull-out of an aligned, hooked-end fibre embedded in a cementitious matrix. The peak force is that required to straighten the hook end. The experimental data are used to set the initial peak nominal stress (force/area) limit for an aligned fibre. For slightly inclined fibres, this stress increases, with it being inversely proportional to the cosine of the inclination angle. Normally, in a strong matrix, where spalling is absent, the lower bound mode is restricted to a range of 0–30°. Beyond this range, fibre failure occurs in the upper bound mode, where the shank undergoes necking.
- Where spalling occurs during pull-out, a lower bound range may be extended to allow the fibre to bend in closer to alignment with the pulling force. This applies, provided that such bending does not result in fibre breakage where then the bending has contributed to an upper bound failure, albeit with reduced orientation. To determine which failure mode spalling contributes to, it is suggested here that an additional intermediate bound be placed on the strength of the concrete mix in the interface region where spalling occurs.
- A comparison between the u. b. and l. b. modes of failure proposed here, and the division arising between them, has provided an explanation of all available experimental data thus far. Finally, the motivation for the present study was to account for the two failure modes observed in pull-out testing of misaligned hooked-end steel fibre. Such behaviour is relevant to concrete reinforcement with short fibres having random orientations, as seen in pre-cast concrete sections, such as tunnels and viaducts. Where loading is complex, a random fibre orientation ensures some alignment with varying principal stress directions. In contrast, the rebar method of reinforcement is restricted to alignment with the unvarying direction of maximum tension in beams and columns.
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Hook (θ°) | σ1f | WE, N | σ2f = 0.99WE | σ1f/σ2f | WS/N | σ12f = 1.05WS | σ1f/σ12f |
---|---|---|---|---|---|---|---|
3D (60°) | 1160 | 1000 | 990 | 1.17 | 650 | 682.5 | 1.70 |
4D (45°) | 1500 | 1300 | 1240 | 1.21 | 850 | 892.5 | 1.68 |
5D (45°) | 2300 | 2150 | 2129 | 1.08 | 1300 | 1365 | 1.80 |
Mix Proportion (kg/m3) | W/B | Compressive Strength (28d) (MPa) | Modulus of Elasticity (28d) (MPa) | |||
---|---|---|---|---|---|---|
Cement | (0–4) mm Fine aggregates | (6–10) mm Coarse aggregates | Water | |||
363 | 812 | 979 | 200 | 0.55 | 32 | 26,700 |
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Rees, D.W.A.; Abdallah, S. Upper and Lower Bounds to Pull-Out Loading of Inclined Hooked End Steel Fibres Embedded in Concrete. Fibers 2024, 12, 65. https://doi.org/10.3390/fib12080065
Rees DWA, Abdallah S. Upper and Lower Bounds to Pull-Out Loading of Inclined Hooked End Steel Fibres Embedded in Concrete. Fibers. 2024; 12(8):65. https://doi.org/10.3390/fib12080065
Chicago/Turabian StyleRees, David W. A., and Sadoon Abdallah. 2024. "Upper and Lower Bounds to Pull-Out Loading of Inclined Hooked End Steel Fibres Embedded in Concrete" Fibers 12, no. 8: 65. https://doi.org/10.3390/fib12080065