Simplified Method of Determination of Natural-Vibration ... · At the present moment, a suspension bridge is the most suitable type of structure for very long-span bridges. Suspension
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Table 6. Horizontal Support Reaction Depending on Prestressing Level
Prestressing Level P,
kN Prestressing Level, MPa
Support reaction from
main cable H, kg m/s2
Support reaction from
stabilization cable Hs, kg m/s2
2 69.7 200 112.5
4 139.4 400 205.4
6 209.1 600 295.6
8 278.7 800 383.5
10 348.4 1000 464.9
Table 7. Analytically Determined Natural-Vibration Frequencies of the
Physical Model of the Prestressed Suspension Structure
Prestressing
level P, kN
Number of natural-vibration frequency
1 2 3
Natural frequency ωi, Hz
2 10.7 23.8 32.4
4 13.2 26.5 35.9
6 15.3 28.9 39.1
8 17.2 31.2 42.1
10 18.8 33.2 44.8
Table 8. Comparison of Experimentally and Analytically Determined
Natural-Vibration Frequencies
Prestressing
level P, kN
Number of natural-vibration frequency
1 2 3
Difference between experimentally ant analytically
determined natural-vibrations frequencies, %
2 -15.9 11.5 16.2
4 -16.0 6.8 14.1
6 -18.2 3.2 11.6
8 -16.5 2.1 10.7
10 -15.4 1.8 9.4
The maximum difference between experimentally and analytically determined natural-vibration frequencies does not
exceed 20%, which is enough for design process of structures alternatives.
5. Conclusions
The first vertical natural-vibration frequency of the physical model of the prestressed suspension structure with span
2100 mm changed from 7.24 to 21.69 Hz, the second frequency changed from 14.55 to 32.61 Hz and the third frequency
changed from 21.78 to 40.53 Hz, while prestressing level changed from 0 to 10 kN, respectively.
Mode shape of the first natural-vibration frequency of the model consists of two half-waves, mode shapes of the second
and third natural vibration frequencies consist of three and four half-waves, respectively. Mode shape with one half- wave
does not appear.
Changing of the prestressing level allow to adjust dynamic characteristics of prestressed suspension bridge. Increasing of
prestressing level increases natural-vibration frequency and contra wise. This advantage of prestressed suspension structure
allows improving dynamic characteristics of the bridge and excluding possibility of resonance appearance.
The difference between results, which were calculated by the developed simplified determination method of natural-
vibration frequencies of the prestressed suspension structure and experimentally achieved by the model testing, does not
exceed 20%. Therefore the method is applicable for preliminary dynamic analyses of structures.
Acknowledgements
This work has been supported by the European Social Fund within the project “Support for the implementation of
doctoral studies at Riga Technical University”.
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