|Client:||City of Lucerne, Department of Public Works|
|Reports:||060118, January 18, 2006|
|081231, December 31, 2008|
|Publications:||2009 EMAUG Herzogenrath, Germany|
|2010 IMAC 28, Jacksonville, Florida
2011 IOMAC 4, IOMAC 4, Istanbul Turkey
Fig. 1: Langensand Bridge cross section.
Close to Lucerne Main Railway Station, the new Langensand Bridge carries five traffic lanes plus a pedestrian/cyclist lane on each of the 6 m cantilevers over about a dozen railway tracks. The bridge was built in two halfs in 2008 and 2009 respectively (Fig. 1).
With the bridge still being in the design stage rci dynamics analyzed the possible dynamic behavior of the bridge in 2005. The goal of this analysis was to evaluate whether or not pedestrians walking on the cantilever would be annoyed through traffic excited vibrations. Of course, a comprehensive (and expensive) analytical investigation could have been performed for this purpose. Based on a 30 years experience in bridge dynamics, vehicle dynamics and pedestrian dynamics, the investigation performed by rci dynamics did not involve not much calculation but some respective engineering considerations. However, what is necessary here is some minimum knowledge of, a) the bridge natural dynamic behavior, b) the dynamic forces generated by heavy commercial vehicles, and, c) some mechanical principles of dynamic bridge/vehicle interaction. (EMPA Report 211, Diss. Cantieni, DIVINE Report).
As a consequence of this analysis, the bridge owner refrained from initiating a detailed planning of TMD’s (Tuned Mass Dampers) already in the design stage.
Shortly before opening the first half of the new bridge to traffic end of December 2008, rci performed an experimental dynamic analysis of the structure. An experimental modal analysis was followed by tests including heavy trucks crossing the bridge and determining the cantilever vibrations under this load.
Ambient Vibration Testing Technology (AVT) was used to perform the experimental modal analysis. Excitation through the trains passing underneath the bridge as well as the traffic on the still existing half of the bridge proved to be optimum (i.e. „broad-banded“, „stationary“). Simultaneously using 15 sensors PCB 393B31 In twelve 30-minutes-setups, 152 degrees of freedom were worked through . Two 3D measurement points were kept constant as references, the remaining 9 sensors were roved over structure (Figs. 2, 3).
Fig. 2: Situation of the four measurement axes 111, 113, 114 and 116 (red squares, from the right) as used for the ambient tests; see also Figure 3.
Fig. 3: Plan view of the measurement point layout as used for the experimental modal analysis. Squares indicate the situation for setup 1. References are black squares, rovers are blue squares. Large squares indicate a 3D, small squares a 1D measurment point. The circular point is a 1D measurement point used in setups 1 and 2 only.
21 bridge modes (natural frequency, mode shape and damping coefficient) could be identified in the frequency range f = 1.27 Hz to f = 34 Hz (Fig. 4).
Fig. 4: Modal properties of Mode 4 (as an example): f = 3.52 Hz, zeta = 0.88%.
Subsequently, tests with heavy vehicles crossing the bridge were performed. The vehicles included two 35-kN-trucks with steel and air suspension respectively and a 26-kN-Bus of Lucerne Public Transit. Acceleration in three points at the cantilever tip was measured for 77 vehicle passages with varying loading scheme (number and sequence of vehicles, centric and eccentric driving axis, with and without plank) and vehicle speed (Figs. 5 to 7). As the maximum measured acceleration (for passages without an obstacle) did not pass the a = 0.5…1.0 m/s2 range, the bridge owner decided to open the bridge to traffic without taking special measures as e.g. TMD’s.
Fig. 5: Plan view of the centric driving axis and of the three measurment points.
Fig. 6: Acceleration time signal as acquired during the passage of a heavy vehicle.
Fig. 7: The two 35-kN four-axle trucks, and, in the very background, the Lucerne Public Transit Bus while crossing the bridge in line (here with a 50 mm plank as an obstacle at midspan).