A Simplified Inverse Analysis Procedure for the Stress-Crack Opening Relationship of Fiber-Reinforced Concrete
Abstract
:1. Introduction
- The need to use specific computational programs for structural analysis;
- The high computational cost;
- The significant time spent performing the inverse analysis.
2. Three-Point Bending Test (3PBT)
3. Analytical Model for Determination of (F–CMOD)anal Diagrams
4. The Inverse Analysis Procedure
4.1. The Concept of Inverse Analysis
- -
- Parameters of the tested sample: span (L), height (H), width (b), and notch depth (), according to Figure 4;
- -
- Concrete parameters: compressive strength () and tensile strength () of FRC; is the average tensile strength obtained according to [40];
- -
- Fiber parameters: length () and diameter ();
- -
- In order to determine the error, the experimental results of the F–CMOD curve, (F–CMOD)exp curve, were obtained through experimental results of the 3PBT must be input data, as well as the maximum deflection ().
4.2. Parameters of SFRC Direct Tensile Behavior
4.2.1. Initial Parameters Determination
4.2.2. Determination of
4.2.3. Determination of
4.2.4. Determination of
4.2.5. Determination of
4.2.6. Choice of the Best Fit Curve
4.2.7. Validation of the Inverse Analysis Procedure
5. Results and Discussions
5.1. Generalities
5.2. Determination of
5.3. Determination of
5.4. Determination of
5.5. Determination of
5.6. Full Diagram
5.7. Inverse Analysis
6. Conclusions
- -
- The inverse analysis can be performed with the procedure proposed, obtaining results compatible with the experimental response, considering a margin of error of less than 10%;
- -
- The methodology developed reduces the number of iterations of the developed algorithm, providing faster processing;
- -
- This procedure does not require FEM software.
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Author | Denomination | [MPa] | [MPa] | [mm/mm] | Fiber Kind | Concrete Kind |
---|---|---|---|---|---|---|
[27] | SFRSCC B | 55 | 2.23 | 35/0.55 | Steel, HE | SFRSCC |
[31] | C45-f90 | 45 | 2.4 | 35/0.55 | Steel, HE | SFRSCC |
[24] | RSFRC1%_2 | 45 | 3.34 | 23/0.22 | recycled | SFRSCC |
[29] | FRC60-1 | 60 | 3.26 | 60/0.75 | Steel, HE | SFRC |
Concrete | Reference | [MPa] | [mm] | [-] | [mm] | [-] | [mm] | [-] | [mm] |
---|---|---|---|---|---|---|---|---|---|
SFRSCC B | This study | 2.45 | 0.20 | 2.94 | 1.39 | 1.96 | 2.78 | 1.71 | 4.38 |
[27] | 2.23 | 0.20 | 2.90 | 1.40 | 1.71 | 2.80 | 0.95 | 4.38 | |
C45-f90 | This study | 3.79 | 0.20 | 4.17 | 1.39 | 3.41 | 2.78 | 2.65 | 8.75 |
[31] | 3.60 | 0.20 | 3.92 | 1.50 | 3.25 | 2.50 | 2.36 | 2.50 | |
RSFRC1%_2 | This study | 3.60 | 0.13 | 3.24 | 0.91 | 2.16 | 1.83 | 1.80 | 8.75 |
[24] | 3.34 | 0.10 | 3.20 | 0.95 | 2.07 | 1.80 | 1.67 | 2.50 | |
FRC60-1 | This study | 3.30 | 0.34 | 3.30 | 2.39 | 1.65 | 4.77 | 0.99 | 8.75 |
[29] | 3.26 | 0.30 | 3.16 | 2.40 | 1.49 | 4.80 | 0.82 | 2.50 |
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Carvalho, P.P.M.d.; Lameiras, R.d.M. A Simplified Inverse Analysis Procedure for the Stress-Crack Opening Relationship of Fiber-Reinforced Concrete. Buildings 2023, 13, 1166. https://doi.org/10.3390/buildings13051166
Carvalho PPMd, Lameiras RdM. A Simplified Inverse Analysis Procedure for the Stress-Crack Opening Relationship of Fiber-Reinforced Concrete. Buildings. 2023; 13(5):1166. https://doi.org/10.3390/buildings13051166
Chicago/Turabian StyleCarvalho, Pedro Paulo Martins de, and Rodrigo de Melo Lameiras. 2023. "A Simplified Inverse Analysis Procedure for the Stress-Crack Opening Relationship of Fiber-Reinforced Concrete" Buildings 13, no. 5: 1166. https://doi.org/10.3390/buildings13051166