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I recently stumbled across this article "Why are soldiers ordered to break their marching steps while crossing a bridge?" (The Times of India) where a claim is made:

When soldiers march in three files over a bridge, they generate a rhythmic oscillation of sine waves on the bridge. At a certain point, the bridge would start oscillating to the same rhythm as that of the marching steps.
This oscillation would reach a maximum peak when the bridge can no longer sustain its own strength and hence collapses. Therefore, soldiers are ordered to break their steps while crossing a bridge. (my emphasis)

Is it true that column of marching soldiers has to break their rhythm while crossing a bridge to prevent its collapse?

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    Note to the would be answerers: Mythbusters is not a scientifically valid source. They did try it here, but we would like answers based on something more reputable.
    – Sklivvz
    Commented Dec 23, 2012 at 20:33
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    Personally I suspect that this is more of an issue for old, damaged, field-expedient and intended-for-foot-traffic bridges than for modern bridges intended for vehicular traffic.
    – dmckee --- ex-moderator kitten
    Commented Dec 23, 2012 at 22:05
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    I can say that we marched across plenty of modern bridges in the ARMY. In a combat environment a bridge is a vulnerable point so you break formation and spread out to reduce the number of casualties should the bridge be taken out while crossing.
    – Chad
    Commented Dec 25, 2012 at 4:49
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    It depends on the bridge. Albert Bridge in London is known to resonate at marching pace and has signs ordering troops to break step
    – Henry
    Commented Dec 25, 2012 at 10:27
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    I know it happens sometimes that the floor of concerts break of that reason. People jump up and down to the rhythm of the music. I remember my physics teacher in high school explaining it, that the force increased by quite a bit than if people just was standing on it, and that they doesn't always calculate for the increase of force when people jump in rhythm.
    – Wertilq
    Commented Apr 24, 2013 at 16:54

1 Answer 1

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Mechanical Resonance

Certain types of bridge are susceptible to mechanical resonance effects even when marching soldiers are not involved.

Mechanical structures usually have one or more frequencies at which some part of the structure oscillates. A tuning fork has a well-defined natural frequency of oscillation. More complex structures may have a dominant natural frequency of oscillation. If some mechanical inputs (such as the pressure of feet walking in unison) have a frequency that is close to a natural frequency of the structure, these inputs will tend to initiate and, over a short time, increase the oscillating movements of the structure. Like pushing a child's swing at the right time.

London Millenium Bridge

One example is London's Millennium Bridge which was closed shortly after opening because low-frequency vibrations in the bridge were causing large groups of pedestrians to simultaneously shift their weight and reinforcing the oscillation. Dampers were fitted.

enter image description here
Maths in the city

All 690 tons of its steel-and-aluminium deck began to sway left and right like a giant, executive desktop toy, so much so that pedestrians, suspended above the Thames on slender steel cables, began to clutch at handrails to steady themselves, and throw themselves against the sway, to stay upright. As they did, so the swings began to get increasingly violent.

Report in The Guardian

Soon after the crowd streamed on to London's Millennium Bridge on the day it opened, the bridge started to sway from side to side: many pedestrians fell spontaneously into step with the bridge's vibrations, inadvertently amplifying them.

Crowd synchrony on the Millennium Bridge - Nature 438, 43-44 (3 November 2005)

other bridges – with completely different structures to the Millennium Bridge – have also moved laterally under large crowds. An example of this is the Auckland Harbour Road Bridge which has a box-girder structure. This bridge was filmed vibrating laterally at 0.7 Hz when a large crowd of demonstrators walked over it in 1975.

This is particularly significant because the Auckland Harbour Bridge is a large road bridge with a conventional structure.

Stabilising the London Millennium Bridge

Other Bridges

There are reports of small suspension bridges collapsing partly due to resonance effects

Broughton Suspension Bridge

Angers Bridge Catastrophe

Studies

There's at least one PhD Thesis on the subject

Instructions to Soldiers

bridges should be crosssed at a slow gait, and marching men should break step.

The Examination & Repair of Bridges WITH PRINCIPLES RELATING TO THEIR DESIGN, Captain C. O. SHERRILL, Corps of Engineers Instructor, Department of Engineering, 1909

companies of soldiers must break step when crossing bridges due to the risk of creating large motions at resonant frequencies.

EVALUATION OF CONDITION OF LAKE SUPERIOR REGULATORY STRUCTURE SAULT STE. MARIE, MICHIGAN. 1981

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    The Tacoma Narrows brinde famously failed due to a wind driven resonance.
    – dmckee --- ex-moderator kitten
    Commented Dec 23, 2012 at 22:01
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    +1 for a good answer but is there any evidence that military organizations actually change their marching behavior to avoid this kind of resonance (as the actual question is asking)?
    – KutuluMike
    Commented Dec 25, 2012 at 4:01
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    Actually every structure has an inherent resonance (based on its structural design). It's a common concept in earthquake engineering. e.g. tall buildings often have higher resonance. There's also more than one in complex structures, e.g. multistorey buildings.
    – j riv
    Commented Dec 27, 2012 at 13:22
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    @Brian: Thanks for the suggestion. I've added some links and a brief (though inexpert) discussion of the point. I'll dig out my old textbooks later :)
    – RedGrittyBrick
    Commented Jul 9, 2014 at 15:46
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    It doesn't happen often but it does happen, and when it does it's a really stupid way of losing millions of dollars' worth of infrastructure plus the loss of life of people on the bridge when it collapses, and the military feels that's too high a price to pay for its parade marching pride, so they play it safe.
    – Shadur-don't-feed-the-AI
    Commented Feb 16, 2016 at 14:30

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