One consequence of having taught structures for years using failures as examples is that whenever something big comes down my twitter feed and email erupt. Yesterday’s news that a pedestrian bridge at Florida International University collapsed brought a bunch of links and questions, so with the usual caveats (I don’t know anything about its design or construction process, not a licensed engineer, investigations will need to be done thoroughly, etc.), here are some thoughts…
Only a few media outlets reported at first that the bridge was, in fact, under construction when it collapsed–the fatalities appear to have been people in cars underneath it, and workers on it. What was there was only part of a cable-stayed bridge, and that’s the first clue. The picture above is from an FIU press release when the design was first announced, and you can see that–when finished–the structure would be a fairly traditional cable-stayed one, with a compression mast and tension cables connected to raking diagonals below. These have been popular since WWII, when cable-stayed designs were used to quickly replace bridges in central Europe that had been destroyed by bombing raids–Tampa’s Sunshine Skyway bridge and the Millau Viaduct in France are two archetypal cable-stayed designs.
These work by translating the load of the bridge deck into diagonal tension members. This has a couple of consequences. First, the ‘pull’ required in each of these cables isn’t just vertical–it’s also horizontal, meaning that the bridge deck has to be designed to withstand huge compression loads along its length. Second, unlike suspension bridges, there’s no good way to build a cable-stayed span piecemeal. Large sections of the deck have to be brought in at once so that each of the cables has something to pull back against.
And that is exactly what occurred over the weekend, when one whole span of the FIU bridge was brought to the site in one piece and raised into place. Seeing this, a couple of things make sense. First, the shape of the deck itself was probably designed for two conditions: one when the cables were all in place and working with the tower and the deck, and second, when the deck was in place before the tower and cables could be erected to hold it up. That explains the cross section of the bridge, which includes a heavy concrete roof. This, I suspect, was designed to work as one of two flanges in a rough I-beam shape. The floor of the bridge deck would have worked as the other flange, and the raking diagonals that would eventually have continued the lines of the cables were supplemented by more vertical members to create a truss-like web. In other words, the deck appears to have been designed as a giant beam that could self-support until the tower and cables were in place.
This is also a common feature of cable-stayed design–decks that can support themselves before cables are connected. Why put in the cables at all? The decks can be designed to just barely hold themselves up, but often with enormous deflections that would make the bridge unserviceable, and margins of safety that are less than would be required for a fully occupied bridge.
Millau is a great example of this–in this famous shot you can see the deck sagging before the cables were tightened. They’re self-supporting, but you wouldn’t want to drive on such a bridge…yet.
There are a couple of clues in the images above that suggest possible reasons for the FIU collapse. First, you can see that the collapse seems to have happened at joints in the web truss–in other words, the two end triangles seem to be intact, albeit rotated, while the other panels of the truss are smashed. This is evidence for a failure in bending. In some recent collapses, we’ve seen evidence that the cross section twisted or bent in ways that reduced the bridge’s section modulus (the 2004 I-70 collapse in Colorado is the paradigm of this). But here it looks like the top flange fell directly on center and didn’t ‘twist’ out of the way. Failure in bending, as SCI-TECH alums will recall, results when one of the flanges actually fails–either in tension along the bottom edge or in compression along the top edge.
If you look at the image of the deck being placed, you can see that the end of the bottom ‘flange’ has a line of small gray cylinders sticking out of it. These are ducts for post-tensioning cables, ‘super-reinforcing’ that, once tightened, would take the huge tensile force in a bridge deck acting, temporarily, as a beam across its span. These may have been tightened before the deck was put in place, or the bridge may have been waiting for the tower and backspan to be installed, so that cables could be run through the entire length of the bridge and tightened at once, holding all of the pieces together. If that’s the case, then the deck would have been particularly vulnerable to failure along its bottom, tensile flange. Another possibility is that the top flange could have failed in compression. From the images of the collapse, there appears to have been buckling there, but it’s hard to tell whether this occurred before or after the deck impacted the ground.
Collapses like this are always shocking, but invariably contain some lessons within them. Very often they highlight not only structural principles, but also problems of actually constructing such large spans, and this may well be an important example of how the two phases of bridge structures–under construction and in service–present very different static issues.
Update, 17 Mar 2018: Two updates in this morning’s news: 1) There are reports that an engineer saw cracks in the span soon after it was put into place. Depending on where these cracks were (haven’t been able to find more details), this would be consistent with greater-than-anticipated deflection in the lower (tensile) deck. 2) More interesting are reports that the deck was being ‘stress-tested’ when the collapse occurred, and that ‘cables were being tightened.’ Here, I think there’s some confusion–much of what I’ve read assumes that the ‘cables’ mentioned were the stays attached to the tower, but it’s clear that the tower hadn’t been erected yet. More likely they were the post-tensioning cables mentioned above. At least one report mentions a loud ‘pop’ a few minutes prior to the collapse, which would be consistent with a cable (or its anchorage) breaking while being tensioned.