PSI - Issue 64

Pavel Ryjáček et al. / Procedia Structural Integrity 64 (2024) 228 – 237 Pavel Ryjacek/ Structural Integrity Procedia 00 (2019) 000 – 000

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Assuming a combination of individual defects, the principle of superposition on the natural frequencies can be applied. The combination of the simultaneous defects of the main cables, the absence of grouting of the prestressing cables and the significant corrosion loss of the main cables is shown in Tab. 2 in the column "Alpha + Beta".

Table 2. The change of the natural frequencies according to the damage scenarios

Mode shape Mode shape

Undamaged model natural frequency [Hz]

Alfa + Beta

Alfa + Beta + support stiffness increase +400%

Natural frequency [Hz]

Natural frequency change to the undamaged model

Natural frequency [Hz]

Natural frequency change to the undamaged model

1 st mode shape 2 nd mode shape 3 rd mode shape 4 th mode shape 5 th mode shape 6 th mode shape

0,504 0,647 0,943 1,031 1,140 1,532

0,499 0,641 0,946 1,024 1,127 1,516

-0,99% -0,93% +0,32% -0,68% -1,14% -1,04%

0,504 0,655 0,950 1,025 1,151 1,554

0,00%

+1,24% +0.74% -0.58% -0.96% -1.44%

The resulting natural frequencies show that if the bridge would suffer only from a combination of cable defects, this effect would theoretically be detectable. However, the measured natural frequencies also show an increase in the stiffness of the end segments, which has a completely opposite effect. The resulting behaviour is then so complex that it cannot be practically distinguished on the basis of changes in natural frequencies. 12. Discussion of the results Based on the evaluation of the measured deflections of the footbridge by levelling, a slightly increasing deformation of the footbridge for the corresponding temperature condition can be traced. However, this deformation is about 7 times smaller than the normal temperature effects and shows non-negligible variations due to the inaccuracy of the temperature measurement and was therefore difficult to detect. Based on the evaluation of the results of the long-term monitoring, in particular the width of the joint between the precast concrete in span 2 at the pier, it can be stated that the size of the opening increased progressively during the monitoring. For 0°C, the strain at the joint on the vibrating wire sensor increased from 1300 to 1600 and 2100  s, and for minimum temperatures (-8 to -10°C) the increased from 1800 to 2500 and 2700  s. The gaps in the deck joints were however also visible and they are shown in the inspections. Both of the results indicate a reduction in the level of prestressing, probably due to corrosion of the Beta and also to Alfa cables. However, these results are not obvious at first sight, they can be revealed by performing a detailed analysis of the data and in the first case an analysis on a numerical model of the footbridge is necessary. Numerical analysis of the dynamic behaviour of the footbridge has clarified the differences between the natural frequencies and some natural modes measured by dynamic tests of the footbridge in 1997, 2010 and 2013. A large part of the measured differences in natural frequencies can be attributed to the different temperatures of the footbridge during each test. Furthermore, a measurable effect of the influence of the stiffening of the vertical supports of the end segment was demonstrated. It can be concluded that this effect explains the anomalies found in the dynamic test. However, the analysed variants with corrosion damage to the cables did not reveal reliably measurable changes in natural frequencies or natural shapes. From this observation, it can be concluded that the evaluation of the dynamic test results in terms of comparison of natural frequencies and shapes, or MAC coefficient, does not lead to a clear and demonstrable detection of this damage. All of the above-mentioned overlap the very low effects of cable defects on the dynamic properties. Without highly accurate knowledge of the temperature and the elimination of its effects with the help of a numerical model, the influence of corrosion of the cables cannot be detected. Also, the knowledge of the temperature would have to exist from the beginning of the measurements on the undamaged structure. However, such a high accuracy of temperature