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Modelling with LUSAS A 3D model was created in LUSAS to examine the dynamic behaviour of the structure. Beam elements represented the deck and pylon members and bar elements modelled the cables. From the LUSAS analysis natural frequencies and mode shapes for the structure were obtained and the first two modes in the vertical direction were found to be within a specified problematic range. As a result a pedestrian loading assessment was carried out based on a draft copy of EN1991-2. This involved assessing three pedestrian loading situations:
Two models of the footbridge, one without a tuned mass damper, and one with, were created and an optimisation of TMD parameters was carried out. Dynamic response of the structure was investigated using the modal superposition method involving step-by-step analysis.
Welded steel structures generally have very low damping. A viscous damping ratio of 0.5% was therefore used for all mode shapes in the dynamic analysis. For pedestrian comfort, and in addition to having to meet specified displacement criteria, an acceleration comfort value of less than 0.7m/s2 had to be met. From LUSAS analyses of the three pedestrian loading types it was seen that this value was greatly exceeded by the group of pedestrian loading (1.8m/s2), let alone a moving stream of people (11m/s2), so the installation of a tuned mass damper was chosen as the best solution to reduce the structural response.
Tuned Mass Damper assessment
In Situ Dynamic Loading Tests After the final construction works had been carried out the bridge was subjected to an in situ dynamic loading test. The aim was to measure the natural frequencies, derive mode shapes, evaluate the response of the structure to different types of human loading and assess initial damping requirements. A variety of walking, swaying and running loadcases were undertaken at critical frequencies of the first and second vertical bending modes and this included a vandalism case of ten people swaying at the location where the displacement in the deck would be greatest for the first vertical bending mode. Measured results were compared against those calculated by LUSAS and found to be in good agreement. At the time of this first loading test the mass of the real footbridge was less than the mass of the LUSAS models but allowance was made for this in the final design of the TMD. The installed tuned mass damper parameters were based upon the results of the first in situ dynamic loading test and on Pontex Ltd’s stated requirements. Four viscous dampers with a combined damping value of 1500Ns/m were employed in a pair of units that were located inside the deck 30.6m from the end furthest from the pylon.
Following the installation of the TMD the same dynamic pedestrian loading as used on the first test was carried out on the footbridge. Measurements showed that, with the TMD fitted and for the critical case of deliberate vandalism, the acceleration in the deck was reduced to just one-tenth of its previous value.
"By using LUSAS we obtained a good correlation of the measured frequencies and successfully designed and tested a tuned mass damper to restrict deck movement for all the pedestrian loadings that were considered." Milan Kalný, Technical Director, Pontex Consulting Engineers Ltd. Find out more
Other LUSAS Bridge case studies:
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Software Information
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