5. Case study

• percentage of vibration critical damping via the 3 dB band with method and curve fitting

• dynamic and static deflections as well as stresses magnitude in certain important parts of

• time history of vibration amplitudes and their classification by classification method (e.g.,

Long-term bridges observation is discussed in literature, e.g., [29–37]. Some dynamic methods used by other authors [33], were applied to correlate relative changes of material, frequencies, and damping with carrying capacity. It was found that used monitoring techniques gave an early indication of incipient deterioration. The main scope of monitoring tests was to evaluate mainly the relative change of well-defined natural frequencies or the corresponding damping and the RMS value of the displacements amplitude of the bridge vibration due to traffic loading. The monitoring technique based on measurement of the bridge vibration time history due to regular traffic is not focused to give detailed bridge information but for making decision if more detailed bridge assessment methods should be used. The sophisticated bridge monitoring was introduced e.g. on the Akhashi Kaikyo bridge in Japan, (Figure 13) completed 1998. At that time, it was the largest and longest suspension bridge in the world. Bridge is a 3-span 2-

Bridge has a impressive 1991-m center span between two main towers that rise 300.0 m above the sea level. The Akashi Kaikyo bridge, being easily affected by natural conditions and traffic means, requires high level of disaster prevention and bridge structure functionality with projected structure parameters. Therefore, to provide centralized control, traffic control and bridge structure and facility monitoring have been integrated into the Traffic Control Center. There, information acquisition and processing are performed continuously 24 h a day, providing vital

Figure 13. Akashi Kaikyo bridge: (a) look-out on the bridge; (b) 24 h a day monitoring center (source: Kobe—Awaji—

Naruto Expressway. Honshu—Shikoku Bridge Authority 1998, advertising material).

hinged bridge with steel-truss-stiffened girders located near Kobe City.

techniques;

130 Bridge Engineering

• DAF and its dependence on vehicle speed;

the bridge structure; and

rain-flow classification method).

traffic and bridge structure information.

4.3. Bridges' dynamic parameters monitoring

The dynamic loading test and the following dynamic monitoring of the Lafranconi bridge over the Danube in Bratislava (Slovakia) are shortly described in this section [38–40]. The dynamic response behavior of a prestressed concrete, seven span highway bridge (761.0 m long) was examined via DLT according to standard [24] in 1990. Excitations of bridge structure were induced by the passage of two fully loaded, multi-axles lorries as well as by the rocket engines. Applied structural measurement technique was developed for in situ testing of the bridges. The DLT results enabled to identify bridge global dynamic characteristics of the bridge, e.g., maximum and RMS of displacements amplitude, natural frequencies f(j), mode shapes, DAF ! δOBS (δOBS = wmax/ws) and the structure amplitude damping parameter (ϑ). The obtained dynamic characteristics were compared with the numerical computed data [29] and standard prescriptions. For maximum and RMS displacements amplitude, and so on, see technical report [2].

#### 5.1. Dynamic loading test of Lafranconi highway bridge over the Danube

The main bridge structure is composed of seven span continuous beams with one bridge frame pier (P3). The total length of the bridge was 761.0 m with spans 83.0 m + 174.0 m + 172.0 m + 4 � 83.0 m. The highway bridge consists of two independent bridges (left and right bridge) with three traffic lanes each (i.e., three in each bridge for one direction only) and sidewalks on both sides. The bridge's longitudinal section is shown in Figure 14. The bridge structure including multispan junctions, the test program, field measurements, and applied instrumentation are fully described in [29]. The vibration amplitudes were measured and recorded in 18 selected points. The measuring station for recording accelerometer signals (DSM-1) was situated on the top of the pier P3, Figure 14. The time history of vertical as well as horizontal vibration amplitudes have been registered by accelerometers in the second and the third span of the bridge. In the other bridge spans were applied inductive displacement transducer with working

Figure 14. Longitudinal section of the Lafranconi highway bridge over the Danube in Bratislava.

range 40 mm. Figure 14 shows the position of the accelerometers marked as A1, A2, A5, and A6 and transducers marked as R1–R10.

the winter time during the years 1991–2001. The theoretical and experimental predictions of

Bridges Subjected to Dynamic Loading http://dx.doi.org/10.5772/intechopen.73193 133

Bridge testing and experimental procedures: the bridge vibration amplitudes were measured and recorded in selected points of the second (174.0 m) and the third span (172.0 m) of the bridge. The time history of bending vertical amplitude vibration has been recorded by accelerometers at points marked as Al, A2, A5, and A6 (see also Figure 14) that were situated in the same position as during DLT [29]. Output signals from accelerometers were preamplified and recorded by portable computer (PC) with relevant software and hardware facilities for 24 h continuing test. The analysis of the experimental measured data has been carried out in the laboratory conditions. The records obtained in the bridge monitoring tests were investigated by using frequency analyzer BK-2034 and mentioned PC facilities. Figure 16 shows power spectral density example of the monitoring test performed in August, 1994. The damping parameters were found by means of the 3 dB bandwidth method and curve fitting techniques. The amplitude analysis has been used to obtain RMS amplitude value of the bridge vibrations during the monitoring tests. As an example, Figure 17 shows results in the form of dominant frequency, damping for lowest natural frequency in bending vibrations and RMS amplitude value from the monitoring period of years 1990–1997. A 2.7% change in frequency was observed during an year (summer-winter) but it is systematic from 1 year to the next year and is maybe due to changes in ambient temperature. The frequencies measured at the same of the annular monitoring period have changes from year to year small and non–systematic (coefficient of

In comparison with the determined changes in structures natural frequency of about 30% corresponding to advanced failure observed in [31], it may be considered negligible. There are not systematic changes of structure damping but scattering of results are big [29]. These changes are maybe caused by changes in temperatures during the day; also, there are influences of changes in length of bridge which can modify support conditions and structural

From monitoring results follow difference values of the displacement RMS amplitude measured in May 1991 in comparison with other measurements results. It was caused by both side motor traffic flows only on the left bridge. All the following monitoring measurements were performed in conditions of the one-side traffic flow on each of the both Lafranconi bridge. The changes of the amplitude RMS value are caused mainly by changes of the intensity of the

Figure 16. Power spectral density G33(f) of the bridge vibration displacement amplitude at point A3.

the bridge behavior and former DLT results are reported in [29, 38].

variation of about 0.01).

regular motor traffic on the bridge.

damping.

Output signals from the accelerometers were preamplified and recorded on two PC and fourchannel portable tape FM recorders (BK-7005) and the signals from the inductive displacement transducers were recorded simultaneously by 12-channel portable tape recorder and FM recorder (BK-7005). The DAF have been determined by analyses of bridge amplitude vibration records from computer or tape recorders via relevant PC software pocket (Disys, 1990). The frequency response spectra (power spectrum Dxx(f), power spectral densities Gxx(f), cross power spectral densities Gxy(f), etc.) have been obtained by PC spectral analysis programs and by coupled two-channel analyzer BK-2032 in the frequency range 0–10 Hz. Output signal in the form of power spectrums were recorded by digital recorder (BK-7400) and plotted by x–y plotter BK-2308. The bridge vibrations ambient-ability have been investigated by means of the correlation and spectral analysis by cross-correlation functions Rxy(t) and coherence function γ<sup>2</sup> xy(f). Examples of amplitude (a), and spectral (b) analyses results, DAF dependence on lorry velocities (c) and calculated and measured natural frequencies comparison (d) are depictured in Figure 15.

#### 5.2. Bridge dynamic parameters monitoring

In this section, bridge monitoring process and results are shortly described. Lafranconi bridge over the Danube has been investigated by 24 h of bridge monitoring tests in the summer and

Figure 15. Examples of amplitude (a), and spectral (b) analyses results; DAF dependence on lorry velocities (c) and calculated and measured natural frequencies comparison (d).

the winter time during the years 1991–2001. The theoretical and experimental predictions of the bridge behavior and former DLT results are reported in [29, 38].

range 40 mm. Figure 14 shows the position of the accelerometers marked as A1, A2, A5, and

Output signals from the accelerometers were preamplified and recorded on two PC and fourchannel portable tape FM recorders (BK-7005) and the signals from the inductive displacement transducers were recorded simultaneously by 12-channel portable tape recorder and FM recorder (BK-7005). The DAF have been determined by analyses of bridge amplitude vibration records from computer or tape recorders via relevant PC software pocket (Disys, 1990). The frequency response spectra (power spectrum Dxx(f), power spectral densities Gxx(f), cross power spectral densities Gxy(f), etc.) have been obtained by PC spectral analysis programs and by coupled two-channel analyzer BK-2032 in the frequency range 0–10 Hz. Output signal in the form of power spectrums were recorded by digital recorder (BK-7400) and plotted by x–y plotter BK-2308. The bridge vibrations ambient-ability have been investigated by means of the correlation and spectral analysis by cross-correlation functions Rxy(t) and coherence function γ<sup>2</sup>

Examples of amplitude (a), and spectral (b) analyses results, DAF dependence on lorry velocities (c) and calculated and measured natural frequencies comparison (d) are depictured in

In this section, bridge monitoring process and results are shortly described. Lafranconi bridge over the Danube has been investigated by 24 h of bridge monitoring tests in the summer and

Figure 15. Examples of amplitude (a), and spectral (b) analyses results; DAF dependence on lorry velocities (c) and

xy(f).

A6 and transducers marked as R1–R10.

5.2. Bridge dynamic parameters monitoring

calculated and measured natural frequencies comparison (d).

Figure 15.

132 Bridge Engineering

Bridge testing and experimental procedures: the bridge vibration amplitudes were measured and recorded in selected points of the second (174.0 m) and the third span (172.0 m) of the bridge. The time history of bending vertical amplitude vibration has been recorded by accelerometers at points marked as Al, A2, A5, and A6 (see also Figure 14) that were situated in the same position as during DLT [29]. Output signals from accelerometers were preamplified and recorded by portable computer (PC) with relevant software and hardware facilities for 24 h continuing test. The analysis of the experimental measured data has been carried out in the laboratory conditions. The records obtained in the bridge monitoring tests were investigated by using frequency analyzer BK-2034 and mentioned PC facilities. Figure 16 shows power spectral density example of the monitoring test performed in August, 1994. The damping parameters were found by means of the 3 dB bandwidth method and curve fitting techniques. The amplitude analysis has been used to obtain RMS amplitude value of the bridge vibrations during the monitoring tests. As an example, Figure 17 shows results in the form of dominant frequency, damping for lowest natural frequency in bending vibrations and RMS amplitude value from the monitoring period of years 1990–1997. A 2.7% change in frequency was observed during an year (summer-winter) but it is systematic from 1 year to the next year and is maybe due to changes in ambient temperature. The frequencies measured at the same of the annular monitoring period have changes from year to year small and non–systematic (coefficient of variation of about 0.01).

In comparison with the determined changes in structures natural frequency of about 30% corresponding to advanced failure observed in [31], it may be considered negligible. There are not systematic changes of structure damping but scattering of results are big [29]. These changes are maybe caused by changes in temperatures during the day; also, there are influences of changes in length of bridge which can modify support conditions and structural damping.

From monitoring results follow difference values of the displacement RMS amplitude measured in May 1991 in comparison with other measurements results. It was caused by both side motor traffic flows only on the left bridge. All the following monitoring measurements were performed in conditions of the one-side traffic flow on each of the both Lafranconi bridge. The changes of the amplitude RMS value are caused mainly by changes of the intensity of the regular motor traffic on the bridge.

Figure 16. Power spectral density G33(f) of the bridge vibration displacement amplitude at point A3.

researchers have used the ratio of maximum dynamic response over the maximum filtered

Bridges Subjected to Dynamic Loading http://dx.doi.org/10.5772/intechopen.73193 135

4. Inappropriate position of the pickups on a bridge cross section can give an unreliable

5. Full-scale testing under moving vehicle (DLT, traffic flow) loading is still the only economical and practical way to evaluate the DAF with reasonable certainty [27]. It is also suitable a reliable method for determining bridge structural dynamic properties and fully acceptable mainly for inspection purposes (even in cases of highway bridge dynamic investiga-

We kindly acknowledge the project APVV-14-0508 supported by Slovak Research and Devel-

1 Institute of Competitiveness and Innovations, University of Žilina, Žilina, Slovakia

[1] Willis R. Experiments for determining the effects produced by causing weights to travel over bars with different velocities. In: Grey G et al., editors. Report of the Commissioners Appointed to Inquire into the Application of Iron to Railway Structures. London: W.

[2] Stokes GG. Discussion of a differential equation relating to the breaking of railway

[3] Zimmerman H. Die Schwingungen eines Tragers mit bewegter Last. Centralblatt der Bauver waltung, Berlin. 1896;16(23):249-251, (23A):257-260, (24):264-266, (26):288

[4] Krylov AN. Mathematical collection of papers of the. Academy of Sciences. 1905;61:211 [5] Timoshenko SP. On the forced vibration of bridges. Philosophical Magazine. 1922;6(43):

bridges. Transaction Cambridge Philosophical Society. 1849;8(Part 5):707-735

2 Faculty of Mechanical Engineering, University of Žilina, Žilina, Slovakia

response (e.g., deflections) as a definition of the DAF.

Acknowledgements

Author details

Ján Benčat<sup>1</sup>

References

Clowes; 1849

1018, 707-735

opment Agency and Slovak state budget.

\* and Robert Kohár<sup>2</sup>

\*Address all correspondence to: jan.bencat@gmail.com

experimental value of the DAF from bridge dynamic tests.

tion where DLF for highway bridges is not defined, e.g., in Eurocodes).

Figure 17. Changes in relative frequency, damping, and displacement RMS amplitude values during 1990–1997.
