Analysis

Failure In An Expected Pattern

by Don Friedman on September 20, 2017


The animated picture above is from The General, a 1926 Buster Keaton movie. (Click on the picture to enlarge it.) In the era before computer graphics, and when the use of scale models for special effects led to disappointing results, Keaton got a realistic train crash in the obvious manner: he crashed a train and bridge. This is one of the reasons that the movie was, for its time, considered incredibly expensive.

If you watch the clip frame by frame, or simply watch it a few dozen times, you’ll see the way the bridge fails: the left end lifts up off its vertical supports and then breaks, triggering the failure of the main span. This raises the question of why? Why does the bridge fail in that particular manner? Common sense – which is, of course, so often wrong – says that if the main span is overloaded that should fail first.

The bridge, probably by design but maybe by accident, is continuous across the left support, meaning that bending moments and shears are transmitted across that support. One of the interesting results in analysis is that the “negative* bending” moments at supports tend to be higher than the positive bending moments at midspan. So, if the bridge was of equal strength and stiffness along its length, as it probably was**, then it would deflect fastest at the continuous support and break there first, which is exactly the behavior we see. Using the same logic, the righthand support is probably not continuous, as it simply bends down as the main span sags and then breaks after the collapse has already begun.

 


* A fellow student during my second year of college introduced me to a mnemonic to help remember which moments are positive and which are negative. Positive moments cause a beam to bend downward in the middle and upward at its ends, so that it looks like it’s smiling; negative moments cause a beam to bend downward one either side of an unmoving support, so that it looks like it’s frowning. This is an oversimplification of the difference between positive and negative moments, but it’s also unforgettable.

** This was an old and primitive bridge for a branch railroad. It’s easier to design and build a girder bridge that is the same strength for its whole length than it is to design one where the strength reflects the requirements at any given point.

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