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This paper considers the frequencies at which synchronised human loading from jumping and stamping can occur.
The consensus view from 1993 onwards was that the range of frequencies that a large group of people could jump and keep in synchronisation was 1.5 to 2.8Hz. However, as part of an extensive test programme monitoring different forms of grandstands during pop concerts it was noted
that, on several occasions, significant responses of the structures occurred when the frequency of the loading appeared to be faster than 2.8Hz. The paper discusses the types of human loading observed at pop concerts and the range of song beat frequencies that occurred. The paper also considers a night-club dance floor where the maximum response was measured with people jumping to a song with a beat frequency of 3.1Hz.
Following these monitoring exercises, a series of tests were performed to ascertain the first three Fourier components of the loading as a group of four people jumped to beat frequencies from 1.0 to 3.4Hz. These showed that jumping in good synchronisation at frequencies faster
than 2.8Hz was not particularly difficult, at least for a small group. Similar tests were conducted with the group stamping. The Fourier components obtained from the stamping were considerably lower than those from the jumping were but the group was able to maintain good synchronisation up to beat frequencies of at least 5Hz.
Although only a single set of tests was conducted, the results are in good agreement with those in other experiments and those measured during public events. The paper considers whether the 2.8Hz upper bound currently being used for human loading should be raised, particularly
for dance floors and areas of comparable or smaller size.
John D. Littler, PhD
Centre for Structural and Geotechnical Engineering, BRE, Watford, UK
In recent times a number of footbridges have suffered from lateral vibration induced by pedestrians. Field measurements were carried out on a Japanese pedestrian suspension bridge, the M-bridge, to clarify the dynamic properties of this lateral vibration. The bridge vibrated in either the third asymmetric mode with a natural frequency of 0.88Hz or the fourth symmetric mode with a natural frequency of 1.02Hz, depending on the distribution of the pedestrians on the bridge. The maximum lateral displacement reached about 45mm. The measurements showed that
when a pedestrian walked on the vibrating girder, the person synchronised to the girder frequency with a phase shift between 120° and 160° ahead of the girder. According to the ambient vibrations, the synchronisation is unlikely to occur at the girder natural frequency under 0.6Hz.
By analysing the vibration data of the three pedestrian bridges which suffered from lateral vibration, it is ascertained that the smaller bridge mass and damping produces the largest girder response. When the girder response reached about 45mm, equivalent to the velocity of
250mm/sec or the acceleration of 1350mm/sec2, pedestrians felt unsafe and could not walk normally. This condition is thought to be the serviceability limit for the lateral girder vibration.
Shun-ichi Nakamura, PhD, DIC, PE, MIABSE, MASCE, FJSCE
Professor, Department of Civil Engineering, Tokai University, Japan
Visiting Professor, School of Engineering, University of Surrey, UK