Indirect Determination of Residual Prestressing Force in Post-Tensioned Concrete Beam
Abstract
:1. Introduction
2. Bridge Survey
3. Experimental Program
3.1. Material Properties
3.1.1. Concrete
3.1.2. Prestressing Wires
3.2. Evaluation of Residual Prestressing Force
4. Numerical Analysis
- Concrete (SBeta Material):
- fc,cube = 37.0 MPa; fc,cyl = 31.5 MPa; ft = 2.7 MPa; Ec = 33,980 MPa; ν = 0.20
- Prestressing Wires (Reinforcement–Bilinear):
- fy = 1160 MPa; Ep = 190,000 MPa
- Saw-cuts (Plane Stress Elastic Isotropic):
- ESC = 1.0 kPa; ν = 0.30
5. Discussion
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Nomenclature
SC | saw-cut, |
FE | finite element, |
SG | strain gauge, |
SRA | Slovak Road Administration (in Slovak: Slovenská správa ciest), |
RTC | Rapid Chloride Test, |
σc,0 | stress in concrete before application of saw-cuts (MPa), |
σc,1 | stress in concrete after application of saw-cuts (MPa), |
Δσc | change in stress (MPa), |
Δσc,EXP | experimentally recorded change in stress (MPa), |
Δσc,NUM | numerically determined change in stress (MPa), |
Pmax | maximum prestressing force according to Eurocode 2 (kN), |
Pm0 | prestressing force after transmission according to Eurocode 2 (kN), |
Pm60,theoretical | prestressing force after 60 years of service according to Eurocode 2 (kN), |
Pm60,actual | actual (residual) prestressing force after 60 years of service (kN), |
ΔP | additional prestressing losses caused by external factors (kN), |
Ai | ideal cross-sectional area (m2), |
epi | ideal eccentricity of prestressing force from the neutral axis (m), |
Iyi | ideal second moment of inertia (m4), |
zbi | position of the neutral axis of an ideal cross-section from the bottom edge (m), |
zti | position of the neutral axis of an ideal cross-section from the upper edge (m), |
MG | moment due to dead load (kNm), |
Ec | secant modulus of elasticity of concrete (MPa), |
Ep | modulus of elasticity of prestressing steel (MPa), |
ESC | modulus of elasticity of saw-cuts (MPa), |
σp,max | maximum prestressing steel stress according to Eurocode 2 (MPa), |
fc,cyl | cylindrical compressive strength of concrete (MPa), |
fc,cube | cubic compressive strength of concrete (MPa), |
ft | tensile strength of concrete (MPa), |
ν | Poisson’s ratio (-), |
fy | yield strength of prestressing steel (patented wires) (MPa), |
fpt | tensile strength of prestressing steel (MPa), |
fpk | characteristic tensile strength of prestressing steel (MPa), |
fp,0.1k | characteristic 0.1% proof-stress of prestressing steel (MPa). |
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Span/No. of Beam | Schmidt Hammer Rebound a (-) | aavg. (-) | Rci (MPa) | Rci,avg (MPa) | αt (-) | αw (-) | Rbe,i (MPa) | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
S1/B1 1 | 45 | 46 | 46 | 50 | 46 | 46.6 | 50 | 52 | 52 | 59 | 52 | 53.0 | 0.9 | 1.0 | 47.70 |
S1/B2 | 44 | 49 | 47 | 50 | 50 | 48.0 | 48 | 57 | 53 | 59 | 59 | 55.2 | 0.9 | 1.0 | 49.68 |
S2/B9 | 49 | 49 | 49 | 42 | 42 | 46.2 | 57 | 57 | 57 | 44 | 44 | 51.8 | 0.9 | 1.0 | 46.62 |
S2/B10 | 46 | 43 | 45 | 42 | 45 | 44.2 | 52 | 46 | 50 | 44 | 50 | 48.4 | 0.9 | 1.0 | 43.56 |
S3/B9 | 43 | 43 | 48 | 42 | 47 | 44.6 | 46 | 46 | 55 | 44 | 53 | 48.8 | 0.9 | 1.0 | 43.92 |
S3/B10 | 48 | 45 | 44 | 44 | 42 | 44.6 | 55 | 50 | 48 | 48 | 44 | 49.0 | 0.9 | 1.0 | 44.10 |
i | Rbe,i (MPa) | Rbe,i,avg (MPa) | Rbe,i—Rbe,i,avg (MPa) | [Rbe,i—Rbe,i,avg]2 (MPa2) |
---|---|---|---|---|
1 | 47.70 | 45.93 | 1.77 | 3.13 |
2 | 49.68 | 45.93 | 3.75 | 14.06 |
3 | 46.62 | 45.93 | 0.69 | 0.48 |
4 | 43.56 | 45.93 | −2.37 | 5.62 |
5 | 43.92 | 45.93 | −2.01 | 4.04 |
6 | 44.10 | 45.93 | −1.83 | 3.35 |
Sample | fc,cyl (MPa) | Ec (MPa) |
---|---|---|
CC1 | 32.6 | 34,130 |
CC2 | 30.9 | 33,150 |
CC3 | 31.1 | 34,660 |
Average | 31.5 | 33,980 |
Sample | Millivolt Reading (mV) | Chloride Ion Content (% Cl−/ms) | Chloride Ion Content (% Cl−/mc) |
---|---|---|---|
CH1 | 18.4 | 0.1980 | 1.3860 |
CH2 | 22.3 | 0.1862 | 1.3030 |
CH3 | 7.2 | 0.3010 | 2.1070 |
CH4 | 8.6 | 0.2950 | 2.0650 |
Saw-Cuts SC1–23/120 | Saw-Cuts SC2–31/120 | ||||||||
---|---|---|---|---|---|---|---|---|---|
i | σc,0 (MPa) | σc,1 (MPa) | Δσc (MPa) | Δσc (%) | i | σc,0 (MPa) | σc,1 (MPa) | Δσc (MPa) | Δσc (%) |
1 | −5.04 | −1.44 | 3.60 | 71.41 | 12 | −5.04 | −0.33 | 4.71 | 93.45 |
2 | −5.04 | −1.44 | 3.60 | 71.35 | 13 | −5.04 | −0.33 | 4.71 | 93.48 |
3 | −5.04 | −1.99 | 3.05 | 60.58 | 14 | −5.04 | −0.78 | 4.26 | 84.58 |
4 | −5.04 | −1.99 | 3.05 | 60.58 | 15 | −5.04 | −0.78 | 4.26 | 84.60 |
5 | −5.04 | −2.24 | 2.80 | 55.58 | 16 | −5.04 | −1.01 | 4.03 | 79.96 |
6 | −5.04 | −2.24 | 2.80 | 55.57 | 17 | −5.04 | −1.00 | 4.05 | 80.23 |
7 | −5.04 | −2.24 | 2.80 | 55.51 | 18 | −5.04 | −1.00 | 4.05 | 80.23 |
8 | −5.04 | −2.24 | 2.80 | 55.52 | 19 | −5.04 | −0.74 | 4.30 | 85.35 |
9 | −5.04 | −2.00 | 3.04 | 60.33 | 20 | −5.04 | −0.74 | 4.30 | 85.35 |
10 | −5.04 | −1.48 | 3.56 | 70.62 | 21 | −5.04 | −0.27 | 4.77 | 94.55 |
11 | −5.04 | −1.48 | 3.56 | 70.68 | 22 | −5.04 | −0.28 | 4.77 | 94.52 |
Avg. | −5.04 | −1.89 | 3.15 | 62.52 | Avg. | −5.04 | −0.66 | 4.38 | 86.94 |
Comparison | Comparison | ||||||||
Δσc,EXP–Δσc,NUM (MPa) | −0.02 | Δσc,EXP–Δσc,NUM (MPa) | −0.18 | ||||||
Δσc,EXP/Δσc,NUM (-) | 0.99 | Δσc,EXP/Δσc,NUM (-) | 0.96 |
Ai (mm2) | Iyi (mm4) | zbi (mm) | zti (mm) | epi (mm) |
---|---|---|---|---|
318532.396 | 4.4532 × 1010 | 614.662 | 435.338 | 505.432 |
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Kraľovanec, J.; Moravčík, M.; Bujňáková, P.; Jošt, J. Indirect Determination of Residual Prestressing Force in Post-Tensioned Concrete Beam. Materials 2021, 14, 1338. https://doi.org/10.3390/ma14061338
Kraľovanec J, Moravčík M, Bujňáková P, Jošt J. Indirect Determination of Residual Prestressing Force in Post-Tensioned Concrete Beam. Materials. 2021; 14(6):1338. https://doi.org/10.3390/ma14061338
Chicago/Turabian StyleKraľovanec, Jakub, Martin Moravčík, Petra Bujňáková, and Jozef Jošt. 2021. "Indirect Determination of Residual Prestressing Force in Post-Tensioned Concrete Beam" Materials 14, no. 6: 1338. https://doi.org/10.3390/ma14061338