Experimental and Numerical Analysis of an Innovative Combined String–Cable Bridge
Abstract
:1. Introduction
2. Experimental Program
2.1. Design of the Tested Model
2.2. Materials
- 100 kN Electromechanical Universal Testing Machine Mechanical.
- Tensile Grips, tensile power 100 kN.
- This model line combines high-performance, high accuracy, and the highest degree of flexibility.
- Precision strain gauge load cell mounted on crosshead, standardized mounting stud (male) Ø40 mm to mount grips.
- Digital movable crosshead encoder.
2.3. Arrangement of Measuring Points and Loading Scheme
2.4. Loading Test
3. Test Results and Analysis
3.1. Experimental Results
3.1.1. Symmetrical Loading
3.1.2. Asymmetrical Loading
4. Numerical Method and Comparison between Experimental Results
4.1. Modeling and Calculations
4.2. Analysis of Numerical Results
4.3. Comparison of Experimental and Numerical Results
5. Conclusions and Discussion
- The bridge model was deformed symmetrically. It was experimentally established that, under symmetrical loading, the pre-tensioning of the string does not significantly affect the displacements of the nodes of the bridge model.
- In the case of symmetrical loading, increasing the pre-tension of the string causes a greater change in the axial force in the string, while the axial force in the cable does not change. This is because the string has no initial sag and is extremely sensitive to displacements, which immediately induce axial forces in the string.
- The bridge model deformed asymmetrically according to the placement of the live load (when the live asymmetric load was on the left side of the mode). The largest displacements occurred on the side loaded with an asymmetric load (nodes 3L, 5L, and 7L). These displacements increased proportionally to the values of the load ratio γ. This means that in the case of asymmetric loading, kinematic displacements dominate. Since the string has no initial sag, it has no kinematic displacements, so it “stabilizes” the displacements caused by the asymmetric load of the entire bridge model (basically cable displacements). Increasing string pre-tension values also increases this “stabilizing” effect. This is evident from the obtained experimental results.
- Displacements of the part of the model not loaded with live load (nodes 3R, 5R, and 7R) are directed upwards. The higher the values of the load ratio γ, the larger these displacements are in absolute terms. However, in their absolute size, these displacements are significantly smaller than the vertical displacements of the loaded part.
- The tensile forces in the string under asymmetric loading are higher than in the case of symmetrical loading. The cable forces increase with increasing pre-tension values. In this case, the axial forces of the cable change little and are smaller in absolute magnitude (at any value of γ) than the string axial forces.
- In almost all cases, numerically obtained axial forces are higher than the experimentally obtained forces. We can also see that increasing the axial force in the string (if the load does not change) decreases the total displacements of the structure. This is shown by both experimental and numerical analysis data.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
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Bar No. (mm) | Modulus of Elasticity (N/mm2) | Tensile Strength Rm (MPa) | Offset Yield Strength RP0.2 (MPa) |
---|---|---|---|
1 | 200.11 | 857 | 808 |
2 | 203.98 | 859 | 804 |
3 | 201.26 | 859 | 810 |
4 | 205.87 | 853 | 793 |
Average: | 202.81 | 857 | 803.75 |
Loading Type | , kN/m | Prestressing Force, kN | |
---|---|---|---|
Dead load | - | 0.320 | T1 = 0.472 T2 = 1.084 T3 = 1.506 |
Symmetrical | - | 0.255 | T1 = 0.472 T2 = 1.084 T3 = 1.506 |
Asymmetrical | 1 | 0.255 | T1 = 0.472 T2 = 1.084 T3 = 1.506 |
2 | 0.510 | T1 = 0.472 T2 = 1.084 T3 = 1.506 | |
3 | 0.765 | T1 = 0.472 T2 = 1.084 T3 = 1.506 |
Loading Type | Vertical Displacements, mm | |||||||
---|---|---|---|---|---|---|---|---|
Measurement points of structure | 1L | 3L/9L | 5L/10L | 7L/11L | 7R/11R | 5R/10R | 3R/9R | 1R |
Dead load | 0 | −1.87 | −2.54 | −2.76 | −2.65 | −2.41 | −1.66 | 0 |
Live load, symmetrical | 0 | −3.06 | −4.64 | −5.66 | −5.95 | −4.98 | −3.22 | 0 |
Loading Type | Vertical Displacements, mm | |||||||
---|---|---|---|---|---|---|---|---|
Measurement points of structure | 1L | 3L/9L | 5L/10L | 7L/11L | 7R/11R | 5R/10R | 3R/9R | 1R |
Dead load | 0 | −1.82 | −2.45 | −2.84 | −2.9 | −2.57 | −2.08 | 0 |
Live load, symmetrical | 0 | −3.32 | −4.72 | −5.9 | −5.91 | −4.57 | −2.95 | 0 |
Loading Type | Vertical Displacements, mm | |||||||
---|---|---|---|---|---|---|---|---|
Measurement points of structure | 1L | 3L/9L | 5L/10L | 7L/11L | 7R/11R | 5R/10R | 3R/9R | 1R |
Dead load | 0 | −1.97 | −3.07 | −3.3 | −3.4 | −3.07 | −2.19 | 0 |
Live load, symmetrical | 0 | −3.64 | −5.02 | −5.96 | −5.95 | −5.35 | −3.57 | 0 |
Element | Shear Forces, kN | ||
---|---|---|---|
T1 = 0.472 kN | T2 = 1.084 kN | T3 = 1.506 kN | |
String | 2.95 | 3.31 | 4.02 |
Cable | 3.30 | 3.49 | 3.31 |
Loading Type | Vertical Displacements, mm | |||||||
---|---|---|---|---|---|---|---|---|
Measurement points of structure | 1L | 3L/9L | 5L/10L | 7L/11L | 7R/11R | 5R/10R | 3R/9R | 1R |
Live load, asymmetrical γ = 1 | 0 | −10.09 | −18.55 | −18.4 | 6.55 | 12.01 | 6.88 | 0 |
Live load, asymmetrical γ = 2 | 0 | −14.85 | −27.51 | −25.52 | 13.72 | 20.6 | 10.96 | 0 |
Live load, asymmetrical γ = 3 | 0 | −18.28 | −33.3 | −30.15 | 17.2 | 25.78 | 12.94 | 0 |
Loading Type | Vertical Displacements, mm | |||||||
---|---|---|---|---|---|---|---|---|
Measurement points of structure | 1L | 3L/9L | 5L/10L | 7L/11L | 7R/11R | 5R/10R | 3R/9R | 1R |
Live load, asymmetrical γ = 1 | 0 | −10.78 | −17.11 | −15.69 | 6.63 | 10.11 | 3.23 | 0 |
Live load, asymmetrical γ = 2 | 0 | −15.39 | −26.02 | −23.07 | 13.62 | 18.41 | 7.04 | 0 |
Live load, asymmetrical γ = 3 | 0 | −18.74 | −32.05 | −28.21 | 18.09 | 23.79 | 9.16 | 0 |
Loading Type | Vertical Displacements, mm | |||||||
---|---|---|---|---|---|---|---|---|
Measurement points of structure | 1L | 3L/9L | 5L/10L | 7L/11L | 7R/11R | 5R/10R | 3R/9R | 1R |
Live load, asymmetrical γ = 1 | 0 | −10.31 | −16.22 | −14.65 | 5.18 | 8.09 | 2.53 | 0 |
Live load, asymmetrical γ = 2 | 0 | −15.39 | −24.88 | −21.43 | 11.75 | 15.88 | 5.61 | 0 |
Live load, asymmetrical γ = 3 | 0 | −18.88 | −31.13 | −26.65 | 16.3 | 21.29 | 7.76 | 0 |
Load Type | kN | ||
---|---|---|---|
T1 = 0.472 kN | T2 = 1.084 kN | T2 = 1.506 kN | |
Asymmetrical γ = 1 | 3.20 | 3.79 | 4.26 |
Asymmetrical γ = 2 | 3.86 | 4.44 | 4.92 |
Asymmetrical γ = 3 | 4.88 | 5.45 | 5.93 |
Load type | kN | ||
Asymmetrical γ = 1 | 3.03 | 3.03 | 2.97 |
Asymmetrical γ = 2 | 3.42 | 3.40 | 4.10 |
Asymmetrical γ = 3 | 3.77 | 3.76 | 4.50 |
Loading Type | Vertical Displacements, mm | |||||||
---|---|---|---|---|---|---|---|---|
Measurement points of structure | 1L | 3L | 5L | 7L | 7R | 5R | 3R | 1R |
Dead load | 0 | −2.19 | −2.92 | −3.27 | −3.27 | −2.92 | −2.19 | 0 |
Live load, symmetrical | 0 | −3.59 | −5.16 | −5.94 | −5.94 | −5.16 | −3.59 | 0 |
Live load, asymmetrical γ = 1 | 0 | −16.11 | −19.55 | −11.43 | 5.04 | 13.2 | 11 | 0 |
Live load, asymmetrical γ = 2 | 0 | −23.27 | −28.25 | −15.64 | 9.56 | 21.86 | 18.17 | 0 |
Live load, asymmetrical γ = 3 | 0 | −28.02 | −34.04 | −18.52 | 12.38 | 27.39 | 22.77 | 0 |
Loading Type | Vertical Displacements, mm | |||||||
---|---|---|---|---|---|---|---|---|
Measurement points of structure | 1L | 3L | 5L | 7L | 7R | 5R | 3R | 1R |
Dead load | 0 | −2.25 | −2.9 | −3.23 | −3.23 | −2.9 | −2.25 | 0 |
Live load, symmetrical | 0 | −3.62 | −5.14 | −5.91 | −5.91 | −5.14 | −3.62 | 0 |
Live load, asymmetrical γ = 1 | 0 | −15.01 | −18.36 | −10.99 | 4.13 | 11.74 | 9.92 | 0 |
Live load, asymmetrical γ = 2 | 0 | −22.14 | −27 | −15.23 | 8.48 | 20.17 | 16.89 | 0 |
Live load, asymmetrical γ = 3 | 0 | −26.97 | −32.89 | −18.18 | 11.28 | 25.7 | 21.49 | 0 |
Loading Type | Vertical Displacements, mm | |||||||
---|---|---|---|---|---|---|---|---|
Measurement points of structure | 1L | 3L | 5L | 7L | 7R | 5R | 3R | 1R |
Dead load | 0 | −2.36 | −2.86 | −3.13 | −3.13 | −2.86 | −2.36 | 0 |
Live load, symmetrical | 0 | −3.68 | −5.11 | −5.85 | −5.85 | −5.11 | −3.68 | 0 |
Live load, asymmetrical γ = 1 | 0 | −14.36 | −17.66 | −10.73 | 3.6 | 10.89 | 9.29 | 0 |
Live load, asymmetrical γ = 2 | 0 | −21.46 | −26.25 | −14.97 | 7.84 | 19.16 | 16.13 | 0 |
Live load, asymmetrical γ = 3 | 0 | −26.33 | −32.18 | −17.96 | 10.62 | 24.69 | 20.72 | 0 |
Loading Type | Vertical Displacements, mm | |||||||
---|---|---|---|---|---|---|---|---|
Local points of structure | 1L | 3L | 5L | 7L | 7R | 5R | 3R | 1R |
T1 = 0.472 kN | ||||||||
Live load, symmetrical | 0 | 20% | 10% | 3% | −2% | 1% | 11% | 0 |
Live load, asymmetrical γ = 1 | 0 | 60% | 5% | −38% | −23% | 10% | 60% | 0 |
Live load, asymmetrical γ = 2 | 0 | 57% | 3% | −39% | −30% | 6% | 66% | 0 |
Live load, asymmetrical γ = 3 | 0 | 53% | 2% | −39% | −28% | 6% | 76% | 0 |
T2 = 1.084 kN | ||||||||
Live load, symmetrical | 0 | 9% | 9% | 0% | −1% | 9% | 17% | 0 |
Live load, asymmetrical γ = 1 | 0 | 39% | 7% | −30% | −38% | 16% | 207% | 0 |
Live load, asymmetrical γ = 2 | 0 | 44% | 4% | −34% | −38% | 10% | 140% | 0 |
Live load, asymmetrical γ = 3 | 0 | 44% | 3% | −36% | −38% | 8% | 135% | 0 |
T3 = 1.506 kN | ||||||||
Live load, symmetrical | 0 | −1% | 3% | 0% | −1% | −7% | −5% | 0 |
Live load, asymmetrical γ = 1 | 0 | 39% | 9% | −27% | −31% | 35% | 267% | 0 |
Live load, asymmetrical γ = 2 | 0 | 39% | 6% | −30% | −33% | 21% | 188% | 0 |
Live load, asymmetrical γ = 3 | 0 | 39% | 3% | −33% | −35% | 16% | 167% | 0 |
Parameter | Results | ||
---|---|---|---|
T1 = 0.472 kN | T2 = 1.084 kN | T3 = 1.506 kN | |
, kN, sym | 7.80% | 11.48% | 0.75% |
, kN, γ = 1 | −0.31% | −1.85% | −4.23% |
, kN, γ = 2 | 10.10% | 6.98% | 3.25% |
, kN, γ = 3 | 7.17% | 4.77% | 1.52% |
, kN, sym | 7.93% | 1.15% | 6.65% |
, kN, γ = 1 | −8.58% | −8.91% | −7.41% |
, kN, γ = 2 | 3.51% | 3.53% | −14.15% |
, kN, γ = 3 | 14.06% | 13.83% | −4.89% |
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Beivydas, E.; Juozapaitis, A. Experimental and Numerical Analysis of an Innovative Combined String–Cable Bridge. Appl. Sci. 2024, 14, 7542. https://doi.org/10.3390/app14177542
Beivydas E, Juozapaitis A. Experimental and Numerical Analysis of an Innovative Combined String–Cable Bridge. Applied Sciences. 2024; 14(17):7542. https://doi.org/10.3390/app14177542
Chicago/Turabian StyleBeivydas, Edmundas, and Algirdas Juozapaitis. 2024. "Experimental and Numerical Analysis of an Innovative Combined String–Cable Bridge" Applied Sciences 14, no. 17: 7542. https://doi.org/10.3390/app14177542