Analysis of the Main Aspects Affecting Bonding in Stainless Steel Rebars Embedded in a Hydraulic Medium
<p>Standard stainless-steel rebar.</p> "> Figure 2
<p>Finite element model for the rebar embedded in a prism of mortar whose base measures 12 mm × 12 mm: (<b>a</b>) model of the rebar; (<b>b</b>) model of the prism of mortar that surrounds the rebar.</p> "> Figure 3
<p>Comparison of the stress-strain behavior of samples of hydraulic mortars obtained in the laboratory (M1 and M3) from literature [<a href="#B39-metals-11-00786" class="html-bibr">39</a>] and analyzed by finite elements for this research (MPlane).</p> "> Figure 4
<p>Values of the reaction force transferred from the bar to the surrounding media (100-mm-edge cube) for a displacement equal to 5 × 10<sup>−5</sup> mm.</p> "> Figure 5
<p>Bond shear stress (MPa) measured at the rebar–mortar interface for a displacement equal to 5 × 10<sup>−5</sup> mm from a 100-mm-edge cube, where maximum bond shear stress and bond tensile stress (both in MPa) were set to (<b>a</b>) 0.10/0.10; (<b>b</b>) 0.10/1.00; (<b>c</b>) 1.00/0.10; (<b>d</b>) 1.00/1.00.</p> "> Figure 6
<p>Diagram depicting the parameterization of samples to set the different mechanical and geometrical characteristics of each of the finite element analyses carried out.</p> "> Figure 7
<p>Displacement (mm) vs. force transferred to the mortar joints by rebars embedded in mortar with 5.6 GPa Young’s modulus and 7.5 mm of effective covering up to failure under two different boundary conditions.</p> "> Figure 8
<p>Bonding stresses (MPa) in the interface of a rebar embedded in a prism of mortar with Young’s modulus of 5.6 GPa and 7.5 mm of effective covering when the base face (face number 1) was fixed. Bonding shear stress distribution when the force transferred from the rebar to the mortar was (<b>a</b>) 40% of that transferred under failure; (<b>b</b>) 60% of that transferred under failure; and (<b>c</b>) 100% of that transferred under failure. Bonding normal stress distribution when the force transferred from the rebar to the mortar was (<b>d</b>) 40% of that transferred under failure; (<b>e</b>) 60% of that transferred under failure; and (<b>f</b>) 100% of that transferred under failure.</p> "> Figure 9
<p>Bonding stresses (MPa) in the interface for a rebar embedded in a prism of mortar with Young’s modulus of 5.6 GPa and 7.5 mm of effective covering when three lateral faces (faces number 2, 3, and 4) were fixed. Bonding shear stress distribution when the force transferred from the rebar to the mortar was (<b>a</b>) 40% of that transferred under failure; (<b>b</b>) 60% of that transferred under failure; and (<b>c</b>) 100% of that transferred under failure. Bonding normal stress distribution when the force transferred from the rebar to the mortar was (<b>d</b>) 40% of that transferred under failure; (<b>e</b>) 60% of that transferred under failure; and (<b>f</b>) 100% of that transferred under failure.</p> "> Figure 10
<p>Geometrical parameters of the rebar that ranged in iterative analyses.</p> "> Figure 11
<p>Chart depicting the reaction force <span class="html-italic">F</span> (N) produced by a 5 × 10<sup>−5</sup> mm displacement of a rebar embedded in mortar prisms with different edges, different Young’s modulus and different boundary conditions: (<b>a</b>) Mortar with Young’s modulus of 5.6 GPa; (<b>b</b>) mortar with Young’s modulus of 10 GPa; (<b>c</b>) mortar with Young’s modulus of 20 GPa; (<b>d</b>) mortar with Young’s modulus of 50 GPa.</p> "> Figure 12
<p>Equivalent strain energy distribution in the mortar joints (E = 5.6 GPa) when face 1 of the prism is fixed and 5 × 10<sup>−5</sup> mm displacement is applied to the base of the rebar: (<b>left</b>) base section of 50 x 50 mm<sup>2</sup>; (<b>right</b>) base section of 12 × 12 mm<sup>2</sup>.</p> "> Figure 13
<p>Distribution of bond shear stress (MPa) in the interface in a prism of mortar (E = 5.6 MPa) for a displacement equal to 5 × 10<sup>−5</sup> mm when Faces 2, 3, and 4 are fixed, for a prism with dimensions: (<b>a</b>) 12 × 12 mm<sup>2</sup>; (<b>b</b>) 50 × 50 mm<sup>2</sup>.</p> ">
Abstract
:1. Introduction
2. Materials and Methods
2.1. Modelling Rebars by Finite Elements
2.2. Modelling Mortar Joints by Finite Elements
2.3. Modelling Contacts
3. Results
3.1. Thickness of Covering, Boundary Conditions, and Material
3.2. Rib Shape
4. Discussion
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Acknowledgments
Conflicts of Interest
Appendix A
Maximum Bond Shear Stress (MPa) | Maximum Bond Tensile Stress (MPa) | Reaction Force F (N) |
0.10 | 0.10 | 14.333 |
0.25 | 14.346 | |
0.50 | 14.348 | |
1.00 | 14.349 | |
0.25 | 0.10 | 17.825 |
0.25 | 17.859 | |
0.50 | 17.864 | |
1.00 | 17.866 | |
0.50 | 0.10 | 21.362 |
0.25 | 21.432 | |
0.50 | 21.444 | |
1.00 | 21.446 | |
1.00 | 0.10 | 26.654 |
0.25 | 27.003 | |
0.50 | 27.074 | |
1.00 | 27.092 |
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Boundary Conditions | Effective Covering (mm) | F (N) | |||
---|---|---|---|---|---|
* E1 | * E2 | * E3 | * E4 | ||
Fixed base (1) | 6 | 4.846 | 8.07 | 13.769 | 26.074 |
7.5 | 6.479 | 10.779 | 18.287 | 34.375 | |
10 | 8.636 | 14.384 | 24.432 | 44.732 | |
12.5 | 10.251 | 17.075 | 28.89 | 49.997 | |
15 | 10.539 | 17.648 | 30.021 | 50.605 | |
25 | 12.633 | 20.941 | 34.734 | 49.328 | |
Two fixed lateral faces (2, 3) | 6 | 12.91 | 22.275 | 35.564 | 50.379 |
7.5 | 12.67 | 21.987 | 37.243 | 50.698 | |
10 | 10.33 | 18.066 | 33.671 | 50.172 | |
12.5 | 8.91 | 15.637 | 29.947 | 50.406 | |
15 | 6.82 | 12.021 | 23.319 | 47.906 | |
25 | 5.512 | 9.741 | 19.029 | 42.943 | |
Three fixed lateral faces (2, 3, 4) | 6 | 17.899 | 30.457 | 43.622 | 49.251 |
7.5 | 17.358 | 29.775 | 44.931 | 50.366 | |
10 | 13.916 | 24.158 | 42.513 | 50.126 | |
12.5 | 11.894 | 20.745 | 38.599 | 50.094 | |
15 | 9.024 | 15.834 | 30.348 | 48.786 | |
25 | 7.446 | 13.112 | 25.371 | 49.535 | |
Four fixed lateral faces (2, 3, 4, 5) | 6 | 20.502 | 34.492 | 43.613 | 50.869 |
7.5 | 19.552 | 33.238 | 44.414 | 51.268 | |
10 | 15.441 | 26.706 | 44.889 | 50.568 | |
12.5 | 13.089 | 22.768 | 41.415 | 50.317 | |
15 | 9.858 | 17.262 | 32.917 | 48.821 | |
25 | 8.124 | 14.287 | 27.546 | 48.663 |
Wc (mm) | We (mm) | B (°) | Bf (°) | hr (mm) | s (mm) | * F3LF | ** F4LF | * F3LF | ** F4LF |
---|---|---|---|---|---|---|---|---|---|
eff.cov. = 6 mm | eff.cov. = 25 mm | ||||||||
1 | 2.5 | 55 | 67.5 | 0.45 | 4 | 17.685 | 20.23 | 6.494 | 7.046 |
1.5 | 17.77 | 20.339 | 6.506 | 7.059 | |||||
2 | 17.861 | 20.454 | 6.518 | 7.074 | |||||
2.5 | 17.949 | 20.567 | 6.517 | 7.073 | |||||
3 | 18.029 | 20.66 | 6.527 | 7.084 | |||||
3.5 | 18.085 | 20.737 | 6.536 | 7.094 | |||||
2.5 | 1 | 55 | 67.5 | 0.45 | 4 | 17.9 | 21.122 | 6.573 | 7.136 |
1.5 | 17.911 | 20.72 | 6.53 | 7.088 | |||||
2 | 17.935 | 20.724 | 6.534 | 7.092 | |||||
2.5 | 17.949 | 20.723 | 6.53 | 7.088 | |||||
3 | 17.948 | 20.726 | 6.532 | 7.092 | |||||
3.5 | 17.972 | 20.742 | 6.532 | 7.09 | |||||
2.5 | 2.5 | 15 | 67.5 | 0.45 | 4 | 18.393 | 20.756 | 6.528 | 7.086 |
20 | 18.071 | 20.546 | 6.518 | 7.073 | |||||
25 | 18.075 | 20.567 | 6.517 | 7.073 | |||||
30 | 18.074 | 19.958 | 6.457 | 7.002 | |||||
35 | 18.078 | 20.13 | 6.474 | 7.022 | |||||
40 | 18.093 | 20.327 | 6.494 | 7.045 | |||||
45 | 18.1 | 20.567 | 6.517 | 7.072 | |||||
50 | 17.934 | 20.817 | 6.545 | 7.105 | |||||
55 | 17.949 | 21.085 | 6.574 | 7.14 | |||||
2.5 | 2.5 | 55 | 45 | 0.45 | 4 | 17.981 | 21.363 | 6.606 | 7.177 |
50 | 17.907 | 20.604 | 6.569 | 7.132 | |||||
55 | 17.931 | 20.513 | 6.519 | 7.074 | |||||
60 | 17.935 | 20.544 | 6.52 | 7.075 | |||||
65 | 17.95 | 20.546 | 6.518 | 7.074 | |||||
70 | 17.951 | 20.568 | 6.519 | 7.074 | |||||
75 | 17.95 | 20.567 | 6.516 | 7.071 | |||||
80 | 17.943 | 20.564 | 6.522 | 7.078 | |||||
85 | 17.952 | 20.557 | 6.526 | 7.083 | |||||
90 | 17.954 | 20.567 | 6.525 | 7.063 | |||||
2.5 | 2.5 | 55 | 67.5 | 0.15 | 4 | 17.464 | 20.571 | 6.525 | 7.082 |
0.25 | 17.604 | 20.503 | 6.514 | 7.069 | |||||
0.35 | 17.761 | 20.517 | 6.514 | 7.069 | |||||
0.45 | 17.949 | 20.548 | 6.517 | 7.072 | |||||
0.55 | 18.15 | 20.567 | 6.517 | 7.073 | |||||
0.65 | 18.358 | 20.563 | 6.525 | 7.082 | |||||
0.75 | 18.58 | 20.597 | 6.52 | 7.076 | |||||
2.5 | 2.5 | 55 | 67.5 | 0.45 | 3 | 18.203 | 20.888 | 6.551 | 7.112 |
4 | 17.949 | 20.567 | 6.517 | 7.073 | |||||
5 | 17.793 | 20.367 | 6.503 | 7.056 | |||||
6 | 17.632 | 20.166 | 6.489 | 7.039 |
Effective Covering | Wc | We | B | Bf | hr | s |
---|---|---|---|---|---|---|
6 mm | 0.30 | 0.06 | 0.38 | 0.01 | 0.78 | −0.35 |
25 mm | 0.22 | 0.07 | 0.28 | −0.11 | 0.80 | −0.29 |
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Ancio, F.; Rodriguez-Mayorga, E.; Hortigon, B. Analysis of the Main Aspects Affecting Bonding in Stainless Steel Rebars Embedded in a Hydraulic Medium. Metals 2021, 11, 786. https://doi.org/10.3390/met11050786
Ancio F, Rodriguez-Mayorga E, Hortigon B. Analysis of the Main Aspects Affecting Bonding in Stainless Steel Rebars Embedded in a Hydraulic Medium. Metals. 2021; 11(5):786. https://doi.org/10.3390/met11050786
Chicago/Turabian StyleAncio, Fernando, Esperanza Rodriguez-Mayorga, and Beatriz Hortigon. 2021. "Analysis of the Main Aspects Affecting Bonding in Stainless Steel Rebars Embedded in a Hydraulic Medium" Metals 11, no. 5: 786. https://doi.org/10.3390/met11050786
APA StyleAncio, F., Rodriguez-Mayorga, E., & Hortigon, B. (2021). Analysis of the Main Aspects Affecting Bonding in Stainless Steel Rebars Embedded in a Hydraulic Medium. Metals, 11(5), 786. https://doi.org/10.3390/met11050786