Millennium Legacies - Pushing the Limits: New Adventures in Engineering - page 71

feet of walkers. The Pont de Solferino, a 106-meter-long narrow steel arch spanning the Seine near
the Louvre, was closed shortly after it opened.
Clearly, it was the footsteps of pedestrians that were exciting the Millennium and other bridges,
but why they were doing so was not immediately obvious. The expectation was that large crowds
of people would subject the bridge to random vertical forces, favoring no particular frequency and
hence exerting no strong forcing function on any particular natural frequency of the bridge struc-
ture. But people on a crowded narrow bridge cannot walk at random speeds; they must fall in step
with the general flow.
Investigating the misbehavior of the Millennium Bridge fell to Arup and the consultants the
firm engaged. The resources of the Institute of Sound and Vibration Research at the University of
Southampton were called upon, and a physical model of a sideways-moving walkway was con-
structed at Imperial College, London. The effects of a person walking over it helped engineers un-
derstand the nature of the forces of interaction. A mechanical shaking device was installed on the
actual bridge to excite and verify the nature of the vibration modes. At one point, a corps of Arup
employees was dispatched to the Millennium Bridge to conduct tests upon it. They grouped togeth-
er and moved in unison, presenting a sight reminiscent of the load test of a section of the galleries
of the Crystal Palace conducted 150 years earlier in London's Hyde Park. Over the Thames, it was
found that it took only five hundred to six hundred walkers to set off the wobble observed on open-
ing day, when there had been as many as two thousand people on the structure at one time.
As it turns out, a normal walking pace is about two strides per second. Thus, the two footfalls per
second exert a vertical force at a frequency of two cycles per second on the surface over which ped-
estrians walk. This is the force that was taken into account in the design of the bridge. There is also
a backward horizontal component of force exerted at the same frequency by a walker; otherwise
there could be no forward movement. Another component of force, however, is more subtle: a side-
ways horizontal push to counter the natural side-to-side motion of the human body walking. This
sideways force alternates left and right, so in each direction it is exerted at only half the frequency
of the other forces, and normally it is relatively small. However, the frequency of this one-cycle-
per-second force matched a natural frequency of the Millennium Bridge and set it into vibration in
an unexpected S-shaped mode in the plane of the walkway.
The principal finding of the various studies was that the Millennium Bridge exhibited a
pedestrian-structure interaction, or “crowd-induced dynamic pedestrian loading.” When the bridge
was being used by walkers moving in random ways, it was possible that by chance a sufficient num-
ber of them were in step and so caused the walkway to move sideways, if only slightly. However,
since the motion takes place at a relatively high frequency, and since humans tend to be sensitive to
higher-frequency motion, the slight movement was amplified in their minds and bodies. Reacting
to the motion sensed, the people on the bridge at the time began to move side-to-side in synchrony
with the bridge deck, thus amplifying the motion much as a parent pushing a child in a swing in-
creases the arc with each cycle. In time, the amplitude of the movement of the bridge became vis-
ibly more and more noticeable and psychologically more disconcerting to those on its walkway. On
the bridge's opening day, there was also a high crosswind that caused walkers to brace themselves
against it and so exert in opposition to the wind a stronger-than-normal horizontal-force component