Bridge analysis, design + assessment

Case Study

Pilsen Footbridge

  • Analysis and assessment of the behaviour of a dynamically sensitive footbridge
  • Pedestrian load modelling to EN 1991-2 (Draft version)
  • Optimisation and installation of a tuned mass damper for pedestrian comfort

Pilsen footbridge: Image courtesy of Pontex Consulting Engineers Ltd

Pontex Consulting Engineers Ltd. used LUSAS Bridge to assist with its analysis and assessment of the dynamic behaviour of a slender decked, steel cable stayed bridge on behalf of the Roads and Motorways Directorate of the Czech Republic. Finite element analysis and dynamic loading tests showed that the structure was susceptible to pedestrian loading, and especially by vandalism, meaning that an energy dissipation device needed to be installed. After the design and installation of a tuned mass damper a second dynamic loading testwas carried out, proving the effectiveness of the installed unit.


Pilsen Footbridge is a cable stayed footbridge that spans around 65m across the D5 motorway near Plzen in the Czech Republic. The steel box girder deck is supported by three pairs of 40mm diameter fore-stays anchored into a 24m high, steel pylon which, in turn, is anchored by three pairs of 50mm diameter back stays into a substantial piled concrete foundation. The pylon has a ball and socket joint at its base. The box girder is supported by articulated steel bearings. During tender design (by others) a tuned mass damper was seen to be necessary. Final detailed design saw some re-design to parts of the bridge but it remained very dynamically sensitive to live load, showing that some form of passive damping was still required.

Pilsen Footbridge: schematic cross-section

Pilsen Footbridge: schematic elevation

Schematic elevation of footbridge

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:

  • A group of pedestrians modelled by a pulsating single force. (Loading type 1)
  • A constant stream of pedestrians modelled by a pulsating constant uniform load (Loading type 2)
  • Vandalism where a group of ten people are effectively jumping up and down together at problematic frequencies. (Loading type 3)

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.

Pilsen Footbridge: first vertical bending mode

Pilsen Footbridge: second vertical bending mode

1st vertical bending mode (without a TMD installed). 
Natural frequency = 1.33 Hz

2nd vertical bending mode (without a TMD installed). 
Natural frequency = 2.93 Hz

Calculated dynamic responses to pedestrian loading

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.

Pilsen Footbridge

Pilsen Footbridge

Displacement response from a group and flow (stream) of pedestrians (loading types 1 and 2) Acceleration response from a group and flow (stream) of pedestrians (loading types 1 and 2)

Pilsen Footbridge

Pilsen Footbridge: Summary of maximum accelerations and displacements for pedestrian loading types 1,2 3 and 3

Acceleration response from vandalism loading 
(loading type 3)

Summary of maximum accelerations and displacements for pedestrian loading types 1,2 3 and 3

Tuned Mass Damper assessment

A LUSAS analysis to assess the installation of a tuned mass damper was carried out using TMD parameters that were chosen according to Bachmann and Weber (1995). This resulted in a modal mass of 2 tonnes being used along with a frequency of 0.95 of the natural frequency of the structure that was to be damped. The results showed that vertical acceleration at the critical location in the deck would be reduced to just 0.1m/s2 for the pedestrian group loading and 0.56m/s2 for the flow (stream) of pedestrians. Acceleration response due to vandalism was similarly reduced to a value of 0.5m/s2, satisfying this particular comfort criteria. Maximum vertical displacement values were also substantially reduced. The maximum displacement caused by a flow of pedestrians, for example, reduced from 158mm to just 6mm.

Pilsen Footbridge

Calculated acceleration response from vandalism loading 
(with a TMD installed)

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 Ltds 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.

Pilsen Footbridge: Installation of Tuned Mass Damper

Pilsen Footbridge: Tuned Mass Dampers in place

Tuned Mass Damper installation

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. 

Pilsen Footbridge: Vandalism response without TMD fitted

Pilsen Footbridge: Vandalism response with TMD fitted

Measured response of the deck to vandalism loading (without and with TMD installed)

Completed structure

"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 Kaln, Technical Director, Pontex Consulting Engineers Ltd.

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