Relation between Shear Stresses and Flexural Tensile Stresses from Standardized Tests of Extracted Prismatic Specimens of an SFRC Bridge Girder
Abstract
:1. Introduction
2. Materials and Methods
2.1. The R/SFRC Box Girder Prototype
2.2. Materials and Mix Proportions
2.3. Mechanical Tests
2.4. Edge Effects
2.5. Computed Tomography Scanning and Fiber Counting
3. Results and Discussion
3.1. Mechanical Behavior and Effect of the Distribution and Density of Fibers
3.1.1. 6W Specimens
3.1.2. 8W Specimens
3.1.3. 6R-8R Reference Specimens
3.1.4. Top-Flange Specimens of the Transverse or X-Axis Direction
3.1.5. Top Flange Specimens of the Longitudinal or Y-Axis Direction
3.1.6. 9R-12R Reference Specimens
3.1.7. Summary of the Analysis of the Shear Behavior
3.1.8. Correlation between Fiber Density and Mechanical Parameters
3.2. Shear/Flexural Tensile Stress Ratio versus Crack Opening and Normalized Crack Dilatancy Law
4. Conclusions
- A normalized crack dilatancy law, vs. CMOD, was proposed, which allowed for the determination of a relation with flexural tests carried out under the EN14651 setup, while acknowledging the significant dispersion of the experimental results. In addition, a crack width–slip relation was proposed, which can complete the estimation of the shear behavior from the flexural results. This is advantageous considering that the flexure test is less instrumented and easier to execute than a shear test setup and is also available for non-wealthy laboratories. Given that the batching method influences the mechanical response of SFRC, this bridge between standardized tests is additionally relevant by being based on the experimental results of the extracted prisms of a prototype.
- The dispersion of the shear mechanical properties in a structural element can only be known by performing tests on specimens extracted from a prototype. The scatter of results occurred not only between points of extraction but also between two halves of the same specimen extracted. This study acquires value given that it quantitatively presents the variability of mechanical performance in a structural element. It strengthens the ideas that SFRC is a heterogenous material; thus, prototype construction is highly recommended to determine the actual mechanical response.
- The alignment of fibers perpendicular to the flow direction of fresh concrete was confirmed by the results of top-flange prisms. In addition, when fiber density increases, the point of the change in behavior from a controlled slip to a significant increase in it can be delayed.
- The batching method highly influenced the fiber density and the fiber orientation in the cross-sections. A proportional relation between the fiber density and the shear strength was found for the specimens extracted from the prototype model, but not for the reference specimens. Mode II fracture energy absorbed up to failure vs. fiber density did not display a clear trend. In a future work, the fiber orientation will be obtained, and inverse analysis will be carried out for the tests performed. The obtention of the fiber orientation will allow for the classification of the prisms in clusters according to the efficiency of the mechanical response of the fiber; thus, it is expected that the dispersion of results can be reduced.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Materials | Proportions (kg/m3) |
---|---|
Coarse aggregate (d < 9.5 mm) | 454.0 |
River sand | 830.6 |
Sieved river sand (d < 0.85 mm) | 100.0 |
Crushed Silica (Mesh No. 325) | 70.0 |
Cement CP III 40 | 360.0 |
Fly ash | 168.0 |
Silica fume | 45.0 |
Water | 180.0 |
Dramix 65/35 BG Steel fibers | 117.0 |
Superplasticizer (% cement weight) | 8.0 |
Viscosity modifying agent (% cement weight) | 0.1 |
Cross-Sections (cm2) | Spans, D (cm) | Labels of Specimens | |||
---|---|---|---|---|---|
Top | Bottom | Mock-Up | Reference | ||
6 × 6 | 4 × 6 | 6 | 6 | 6W-XY | 6R-XY |
8 × 8 | 5 × 8 | 6.5 | 6.5 | 8W-XY | 8R-XY |
9 × 9 | 6 × 9 | 7 | 7 | 9TF-XY | 9R-XY |
12 × 12 | 8 × 12 | 6.5 | 9 | 12TF-XY | 12R-XY |
At Peak | ||||||
---|---|---|---|---|---|---|
Group | Prism | Details * | ||||
1 | 6W-6A | NRR | 2.84 | 18.66 | 0.69 | 26.33 |
6W-6B | NRR | 2.84 | 12.82 | 1.59 | 27.60 | |
6W-7A | NRR | 1.86 | 7.23 | 0.61 | 12.39 | |
6W-7B | RRE | 1.75 | 4.91 | 1.01 | 11.18 | |
6W-9A | RRE | 2.81 | 20.70 | 0.26 | 44.81 | |
6W-9B | NRR | 3.07 | 14.65 | 0.05 | 27.57 | |
6W-11B | RRE | 2.07 | 8.72 | 0.71 | 19.77 | |
2 | 8W-6A | NRR | 4.02 | 15.66 | 0.29 | 26.08 |
8W-11A | NRR, PF | 1.81 | 13.45 | 0.54 | 19.07 | |
8W-12A | NRR | 3.04 | 8.28 | 1.15 | 9.23 | |
8W-12B | NRR, PF | 3.25 | 14.16 | 0.51 | 1.72 | |
3 | 6R-1A | NRR | 3.08 | 13.46 | 0.40 | 16.63 |
6R-2A | SRR, PF | 4.58 | 13.13 | 0.55 | 20.02 | |
6R-2B | NRR, PF | 2.13 | 7.30 | - | 10.50 | |
6R-3A | NRR | 4.05 | 14.10 | 0.35 | 17.53 | |
6R-3B | NRR, PF | 5.36 | 12.83 | 0.67 | 13.77 | |
8R-1B | NRR, PF | 2.89 | 12.40 | 0.49 | 14.51 | |
8R-2A | NRR | 3.63 | 16.99 | 0.52 | 27.40 | |
8R-2B | NRR | 3.16 | 15.61 | 0.24 | 32.54 | |
8R-3A | NRR, PF | 2.79 | 13.33 | 0.52 | 16.77 | |
8R-3B | NRR, PF | 4.27 | 11.72 | 0.45 | 24.82 | |
4 | 9TF-3A | NRR, PF | 2.96 | 12.74 | 0.17 | 0.76 |
9TF-3B | NRR, AF | 4.23 | 23.07 | 0.25 | 3.16 | |
9TF-4A | NRR, AF | 2.65 | 21.42 | 0.20 | 2.69 | |
12TF-3A | NRR, AF | 2.68 | 17.47 | 0.26 | 50.89 | |
12TF-3B | NRR, AF | 4.01 | 18.74 | 0.12 | 41.70 | |
12TF-4B | NRR, AF | 4.18 | 23.27 | - | 57.40 | |
5 | 9TF-2A | NRR, AF | 1.73 | 11.20 | 0.31 | 18.61 |
9TF-2B | RRE, PF | 1.10 | 7.44 | 0.19 | 2.10 | |
12TF-1B | NRR | 1.76 | 9.90 | 0.22 | 4.58 | |
12TF-7A | NRR | 1.23 | 10.33 | 0.17 | 3.18 | |
12TF-7B | NRR, AF | 1.26 | 7.40 | 0.12 | 21.76 | |
6 | 9R-1A | NRR | 3.53 | 9.72 | 0.08 | 0.83 |
9R-2A | RRE, PF | 4.25 | 8.84 | 0.21 | 1.13 | |
9R-2B | RRE, PF | 3.33 | 9.85 | 0.42 | 1.21 | |
9R-3A | RRE, SCL | 3.74 | 14.08 | - | 21.39 | |
9R-3B | RRE, PF | 3.14 | 14.08 | 0.18 | 7.97 | |
12R-1A | NRR, AF | 3.26 | 9.41 | 0.20 | 2.21 | |
12R-2A | NRR, AF | 4.21 | 14.63 | 0.03 | 16.72 | |
12R-2B | NRR | 3.37 | 14.93 | 0.44 | 32.83 |
Group | N° Prisms | Avg. | CV | Avg. | CV | Avg. | CV | Avg. | CV | Avg. | CV |
W | 11 | 47.61 | 0.22 | 14.39 | 0.37 | 0.67 | 0.62 | 82.42 | 0.37 | 23.53 | 12.87 |
R | 18 | 35.22 | 0.28 | 15.01 | 0.18 | 0.36 | 0.49 | 95.95 | 0.48 | 18.19 | 11.42 |
TF-T | 6 | 39.60 | 0.33 | 23.65 | 0.20 | 0.20 | 0.26 | 107.35 | 0.50 | 32.80 | 30.94 |
TF-L | 5 | 63.69 | 0.08 | 11.23 | 0.17 | 0.20 | 0.32 | 111.56 | 0.57 | 12.19 | 10.17 |
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Quiroga Flores, A.; Mendes de Andrade, R.G.; Pfeil, M.S.; Barros, J.A.O.; Battista, R.C.; Oliveira de Araújo, O.M.; Tadeu Lopes, R.; Toledo Filho, R.D. Relation between Shear Stresses and Flexural Tensile Stresses from Standardized Tests of Extracted Prismatic Specimens of an SFRC Bridge Girder. Materials 2022, 15, 8286. https://doi.org/10.3390/ma15238286
Quiroga Flores A, Mendes de Andrade RG, Pfeil MS, Barros JAO, Battista RC, Oliveira de Araújo OM, Tadeu Lopes R, Toledo Filho RD. Relation between Shear Stresses and Flexural Tensile Stresses from Standardized Tests of Extracted Prismatic Specimens of an SFRC Bridge Girder. Materials. 2022; 15(23):8286. https://doi.org/10.3390/ma15238286
Chicago/Turabian StyleQuiroga Flores, Alfredo, Rodolfo Giacomim Mendes de Andrade, Michèle Schubert Pfeil, Joaquim A. O. Barros, Ronaldo Carvalho Battista, Olga Maria Oliveira de Araújo, Ricardo Tadeu Lopes, and Romildo Dias Toledo Filho. 2022. "Relation between Shear Stresses and Flexural Tensile Stresses from Standardized Tests of Extracted Prismatic Specimens of an SFRC Bridge Girder" Materials 15, no. 23: 8286. https://doi.org/10.3390/ma15238286