Walk The Plank

Here, we develop the ability to measure the natural frequency of a simply supported beam to quickly determine its stiffness so we can estimate the deflection of the same beam when subjected to a large concentrated load at midspan. Our goal is to predict the static deflection from a large applied load based on a natural frequency measurement with no large load in place.

I also used this formula to estimate deflections at the 2024 Pacific Northwest Student Steel Bridge Competition, where I measured the natural frequency of every bridge during aesthetics judging and asked every group how much their bridge weighed.

While there were a couple of outliers, many of the bridges had an aggregate deflection of twice the estimated deflection, which was calculated based on the concentrated load of 2,500 lb. This makes good sense because the aggregate deflection is the summation of deflections measured at two points when the bridge is loaded.

Cantilever Beam

This same approach can be taken with a cantilever beam.

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