Aspects of Vibration-Based Methods for the Prestressing Estimate in Concrete Beams with Internal Bonded or Unbonded Tendons
Abstract
:1. Introduction: The Role of Prestressing in Structural Reliability
2. Efforts in Prestress Estimate
2.1. Dynamic-Based Methods
2.2. Other Methods
2.3. Purpose of the Paper: A Diverse Vibration-Based Approach
3. Problem Formulation
- Compression stresses determine the increase of the natural frequencies, likely affecting the hardening of concrete. Tension stresses determine the lowering of the natural frequencies, likely affecting the softening concrete. The author will refer to the two phenomena as “compression hardening” and “tension softening effect”. This effect is opposite to that caused by external prestressing, which induces the so-called “compression softening” effect;
- The relative variation of the natural frequencies due to prestressing range between −1 and 1% in an interval between −100 and 100 MPa. In ordinary prestressed structures, where concrete may have a −50 MPa compression, the frequency increment is about 0.5%;
- Equation (7) depends on the sole axial deformation, expressed by the ratio . The contour plot in Figure 3 is then invariant to the ratio;
- The functional dependence between the relative frequency variation and is practically linear in the range of interest;
- Natural frequencies can be measured with extreme accuracy, up to the fourth decimal place. The “compression hardening” effect may yield a measurable effect over the natural frequencies.
3.1. Comparison between the “Compression Hardening” and “Compression Softening”
3.2. General Formulation
4. Method
Quantification of the Uncertainty
- Bias of the mechanical model: the model is not entirely representative of the tested structure;
- Bias of the input variables: the estimates of the material property or natural frequencies may be biased;
- Variance of the input variables: the estimates of the material property or the natural frequencies may have variance errors.
5. Testing of the Procedure on a Real Case Problem
Results
6. Discussion
7. Conclusions
Funding
Data Availability Statement
Conflicts of Interest
References
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[kg/m] | 2500 |
A [m] | 6 |
I [m] | 4 |
l [m] | 40 |
Viaduct | Span | Elastic Modulus (MPa) | Estimated Prestressing (kN) | ||||
---|---|---|---|---|---|---|---|
Static T. | Concr. Samp. | Static T. | Concr. Samp. | ||||
Biselli | 12 | 24,900 | / | 18,811,320 | / | 2.655 | 2.00 × 10 |
Cerchiara | 4 | 15,000 | 19,361 | 17,076,890 | 11,105,390 | 2.967 | 2.15 × 10 |
Cerchiara | 7 | 23,700 | 23,299 | 19,959,130 | 20,501,280 | 2.678 | 1.50 × 10 |
Cretara | 9 | 26,000 | 26,416 | 44,637,030 | 44,540,770 | 3.564 | 1.50 × 10 |
Le Grotte | 5 | 36,000 | / | −3,930,700 | / | 2.661 | 2.00 × 10 |
San Nicola | 10 | 26,700 | 29,978 | 17,808,040 | 11,932,910 | 2.683 | 3.50 × 10 |
Temperino | 6 | 35,900 | / | −16,558,670 | / | 2.515 | 5.00 × 10 |
Viaduct | Elastic Moduli Yielding within± 30% (MPa) | |||
---|---|---|---|---|
Biselli | 27,367 | 27,373 | 27,370 | 6 |
Cerchiara | 19,638 | 19,644 | 19,641 | 6 |
Cerchiara | 27,875 | 27,881 | 27,878 | 6 |
Cretara | 45,347 | 45,353 | 45,350 | 6 |
Le Grotte | 27,554 | 27,560 | 27,557 | 6 |
San Nicola | 28,224 | 28,230 | 28,227 | 6 |
Temperino | 23,994 | 24,000 | 23,997 | 6 |
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Aloisio, A. Aspects of Vibration-Based Methods for the Prestressing Estimate in Concrete Beams with Internal Bonded or Unbonded Tendons. Infrastructures 2021, 6, 83. https://doi.org/10.3390/infrastructures6060083
Aloisio A. Aspects of Vibration-Based Methods for the Prestressing Estimate in Concrete Beams with Internal Bonded or Unbonded Tendons. Infrastructures. 2021; 6(6):83. https://doi.org/10.3390/infrastructures6060083
Chicago/Turabian StyleAloisio, Angelo. 2021. "Aspects of Vibration-Based Methods for the Prestressing Estimate in Concrete Beams with Internal Bonded or Unbonded Tendons" Infrastructures 6, no. 6: 83. https://doi.org/10.3390/infrastructures6060083