How To Cross A Bridge

In 1831 cavalry troops were marching in step across a suspension bridge near Manchester, England, when the bridge collapsed. Since then troops have been ordered to break step (not to march in cadence) when crossing bridges. Does this really help? If so, why?

• A. Yes, it does help. In this case all of the troopers happened to step down at exactly the same instant producing a very large impulse on the bridge and causing it to collapse.
• B. Yes, it does help. Marching in step to one of the natural frequencies of vibration a bridge may have can cause the bridge to absorb energy cumulatively from marching troopers resulting in bridge damage or destruction.
• C. No, marching in step makes no difference one way or the other. The bridge was simply overloaded.
• D. No, It might make a difference on old swinging bridges, but not on a modern concrete suspension bridge.

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Answer

How To Cross A Bridge - Answer = B

Yes, it does make a difference. When troopers march in cadence across a bridge, the marching may match a natural resonance frequency of the bridge. Although only a small amount of energy is added with each step, because of the resonance effect this energy will be stored. As a result, the bridge will cumulatively absorb energy from the marching men, increasing the oscillation amplitude in the bridge (just as pushing someone on a swing, in cadence, increase the amplitude of the swing). Enough energy may be added this way to damage or destroy the bridge. In fact, a concrete suspension bridge, the Tacoma Narrows Bridge, was destroyed by resonance vibrations set up by winds acting on the bridge. Today's bridges are constructed to prevent or minimize this type of wind resonance effects. (Some information from The Flying Circus of Physics by Jearl Walker)

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