Determination of Axial Force in Tie Rods of Historical Buildings Using the Model-Updating Technique
Abstract
:1. Introduction
- The tie rods are generally located at elevated positions;
- High-accuracy displacement sensors should be used due to small vertical displacements. These should be placed on a previously-determined referent location;
- The strain gauge installation can be complicated at elevated positions.
2. Analytical Solution for Lateral Tie Rod Vibration
3. Methodology for Boundary Conditions and Axial Load Identification
4. Case Study Using the Proposed Methodology
4.1. Description of Structure
4.2. Experimental Identification of Dynamic Properties of Tie Rods
4.3. Numerical Simulation
4.3.1. Initial Model
4.3.2. Updated Model
5. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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Boundary Condition | Static System | Coefficient | ||
---|---|---|---|---|
1st Mode | 2nd Mode | nth Mode | ||
Hinge–hinge | 3.142 | 6.283 | ||
Clamp–clamp | 4.730 | 7.853 | ||
Clamp–hinge | 3.927 | 7.069 | ||
Clamp–free | 1.875 | 4.694 |
Tie Rod | L (m) | h (mm) | b (mm) | (Hz) | (Hz) |
---|---|---|---|---|---|
2B‒C | 6.84 | 55 | 55 | 7.25 | 17.94 |
3B‒C | 6.71 | 64 | 64 | 7.56 | 19.00 |
4B‒C | 6.81 | 60 | 60 | 7.31 | 18.69 |
5B‒C | 6.87 | 68 | 68 | 7.31 | 19.56 |
6B‒C | 6.90 | 61 | 61 | 6.94 | 17.50 |
7B‒C | 6.95 | 56 | 56 | 8.25 | 18.88 |
7‒8B | 6.97 | 56 | 56 | 8.13 | 19.38 |
7‒8C | 6.98 | 60 | 60 | 8.63 | 19.38 |
RMSE Values | ||
---|---|---|
Mode Number | Hinge–Hinge | Clamp–Clamp |
1 | 7.06 | 9.15 |
2 | 8.50 | 10.66 |
Mode Number | (Hz) | (Hz) | Relative Error (%) |
---|---|---|---|
1 | 4.83 | 6.94 | 30.20 |
2 | 13.95 | 17.50 | 20.29 |
Mode Number | (Hz) | P (kN) | σ (MPa) | κ |
---|---|---|---|---|
1 | 6.94 | 122.8 | 33.0 | 3.534 |
2 | 17.5 | 137.2 | 36.9 | 6.777 |
2B‒C | 3B‒C | 4B-C | 5B-C | ||||||
---|---|---|---|---|---|---|---|---|---|
Mode Num. | κ | Pn (kN) | σn (MPa) | Pn (kN) | σn (MPa) | Pn (kN) | σn (MPa) | Pn (kN) | σn (MPa) |
1 | 3.534 | 115.8 | 38.3 | 149.6 | 36.5 | 132.1 | 36.7 | 159.4 | 34.5 |
2 | 6.777 | 144.7 | 47.8 | 158.8 | 38.8 | 167.7 | 46.6 | 207.9 | 45.0 |
Mean values | 130.3 | 43.1 | 154.2 | 37.7 | 149.9 | 41.6 | 183.6 | 39.7 | |
6B‒C | 7B‒C | 7‒8B | 7‒8C | ||||||
Mode Num. | κ | Pn (kN) | σn (MPa) | Pn (kN) | σn (MPa) | Pn (kN) | σn (MPa) | Pn (kN) | σn (MPa) |
1 | 3.534 | 122.8 | 33.0 | 170.8 | 54.5 | 166.3 | 53.0 | 215.2 | 59.8 |
2 | 6.777 | 137.2 | 36.9 | 188.7 | 60.2 | 208.1 | 66.4 | 219.6 | 61.0 |
Mean values | 130.0 | 34.9 | 179.8 | 57.3 | 187.2 | 59.7 | 217.4 | 60.4 |
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Duvnjak, I.; Ereiz, S.; Damjanović, D.; Bartolac, M. Determination of Axial Force in Tie Rods of Historical Buildings Using the Model-Updating Technique. Appl. Sci. 2020, 10, 6036. https://doi.org/10.3390/app10176036
Duvnjak I, Ereiz S, Damjanović D, Bartolac M. Determination of Axial Force in Tie Rods of Historical Buildings Using the Model-Updating Technique. Applied Sciences. 2020; 10(17):6036. https://doi.org/10.3390/app10176036
Chicago/Turabian StyleDuvnjak, Ivan, Suzana Ereiz, Domagoj Damjanović, and Marko Bartolac. 2020. "Determination of Axial Force in Tie Rods of Historical Buildings Using the Model-Updating Technique" Applied Sciences 10, no. 17: 6036. https://doi.org/10.3390/app10176036
APA StyleDuvnjak, I., Ereiz, S., Damjanović, D., & Bartolac, M. (2020). Determination of Axial Force in Tie Rods of Historical Buildings Using the Model-Updating Technique. Applied Sciences, 10(17), 6036. https://doi.org/10.3390/app10176036