September 2021 Newsletter: Twist and Shout

Hit a tuning fork on a table and it will ring at its natural frequency; point a speaker playing that frequency at the tuning fork and the fork will resonate. Resonance, an amplification of vibratory motion, occurs when an external force is applied to an object at or close to its natural frequency, which is a function of the mass and stiffness of an object or system. For buildings and structures, resonance is carefully considered by designers because it can lead to catastrophic outcomes. Read on to learn more about how things can fall apart.

External forces are constantly applied to structures by mechanical equipment, people walking, earthquakes, and even heavy winds. When the forcing frequency of the external source and natural frequency of a structure align, that structure will resonate.

A jogger (blue circle in picture on left) coaxing out a resonant response in a bridge here in Philadelphia during a recent site survey.

Examples of catastrophic failures due to resonance go at least as far back as 1831, when a group of British soldiers marching in stride across the Broughton Suspension Bridge in England created a resonant condition; the bridge collapsed beneath their feet and threw the soldiers into the water below. Walking step rates are approximately 1.5 Hz, 2.0 Hz, and 2.8 Hz corresponding to slow, medium, and fast walking. Harmonics of these frequencies are 3.0, 4.0, 4.5, 5.5, 6.0, and 8.25 Hz. Any of these frequencies can set a floor or footbridge into resonance if they align with the natural frequency of the structure. As a result of the Broughton Bridge collapse, soldiers now stagger their stride on footbridges so their steps do not act as an oscillatory force. Avoiding harmonics of vibration created by common human activities is a good reason to design floor structures with a natural frequency above 8.5 Hz.

The dramatic, rhythmic twisting that resulted in the 1940 collapse of “Galloping Gertie”, the original Tacoma Narrows Bridge, is sometimes characterized in physics textbooks as a classic example of resonance. Relatively recent research contradicts this claim; prevailing theories on the collapse indicate that – while similar to resonance in results – the catastrophic vibrations that destroyed the bridge were likely due to an oscillation caused by interactions between the bridge and the prevailing winds passing through the strait, a phenomenon known as aeroelastic flutter. Videos of this catastrophe are amazing to watch.

Closer to modern day, Metropolitan Acoustics was involved in a project with a concert venue over occupied space. Even though a floating floor was installed in the concert venue, patrons of the space below experienced their floor “waving” when people jumped up and down on the dance floor above during concerts. In this case, the walls, which were not supposed to be rigidly connected to the slab above, were and transmitted vibration between floors. The forcing frequency from above was creating a resonance situation in the floor slab below. Very unsettling!

 

Columns marked above with “F” and “G” connect between floors.

No one wants a building or bridge to suddenly start moving unexpectedly. Careful consideration of the natural frequency of structures is key to their design. Oh and making sure that they are not subject to flooding which could result in a Bridge Under Troubled Water!

Street and bridge scene in Philadelphia following flooding from Hurricane Ida.
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