Minneapolis Bridge Collapse: Engineering aspects

OK, so I am not a civil engineer, nor am I a bridge expert in any way. However, I do have degrees in both mechanics and materials engineering, and I have to say, this morning the news is full of increasing nonsense about the bridge collapse. For example: from the BBC,

Such complete bridge collapses are a very rare occurrence.

If they happen, it is either because the load is too heavy, or the connections between the bridge’s structural elements are too weak, Keith Eaton, chief executive of the UK’s Institution of Structural Engineers, told the BBC.

“The engineers will have to see where the collapse started. Clearly a failure occurred somewhere which imbalanced the whole thing,” he said.

This adds no information whatsoever. All failures occur because the extrinsic loading (stress) exceeds a part’s intrinsic ability to withstand loading (strength). When that happens, something fails or fractures. So yes, “clearly a failure occurred somewhere here.” The news is starting to be full of words that may or may not be used in a technically correct sense: as the Minneapolis Star-Tribune headline reads, “Cracking, vibration possible culprits.”

So I thought a little engineering primer might be in order here, to at least start to clear the confusion in terminology. I’m purposefully keeping my books on the shelf and trying to do this in layman’s terms off the top of my head, so please don’t be surprised that some of this is a bit of a generalization.

Flaws: It is virtually impossible to obtain the theoretical strength of any real, macroscopic-sized engineering component, because the component will have some distribution of intrinsic, tiny flaws. This is critical to remember: no steel beam is perfect to start out with, and part of engineering design is in knowing and understanding this in the first place, and knowing how to safely design around these intrinsic flaws.

Stable and unstable cracks: Small cracks in a structure are not unlike the intrinsic flaws in that engineering design accounts for the fact that there will be small cracks in a structure. Small cracks can be stable, like a crack in your windshield that stays the same for years. Something breaks catastrophically when a small crack under external loading transitions from stable to unstable and rushes across a part with no real warning.

Strength: as noted above, strength is the maximum external stress a part can withstand, and the strength of a component is determined by its “weakest link” or its largest crack or flaw. Macroscopic failure is fundamentally related to the rupture of atomic bonds but it can be difficult to model all length-scales of a process from atomic to km-span bridges in the same mechanical model. When the stress on a part exceeds its strength, macroscopic failure occurs. Failure can thus be considered in two complementary ways: a part’s intrinsic strength can decrease and/or the extrinsic stress on it can increase. This is complicated by the fact that tiny cracks or defects are actually “stress concentrators” in a material: the stress at the edge of a circular hole in a plate is three times greater than in the bulk of the plate. Tiny cracks and flaws can thus grow at subcritical stresses because their local stresses are greater than those on the bulk specimen.

Fatigue cracks: Fatigue failure is the progressive failure of a component that is exposed to cyclic stresses. Any part in service that is loaded repetitively is a candidate for fatigue failure; the accumulation of damage over many years and many cycles of loading can cause a failure at stresses lower than expected. The opposite of fatigue failure is a failure caused by a clear, single obvious event of stress overload (bridge failure when a ship hits a pier, for example). It’s probably true that the cracks in the 35W bridge were “fatigue cracks” since the bridge had been there for 40 years and thus had been subjected to plenty of loading, both mechanical and thermal, over the years. It also appears true that there was no single landmark event that caused the bridge to fail, that small applied loadings (perhaps related to the vibrations of the train passing underneath or the jackhammering of construction work) of a sort that were not out of the ordinary caused the bridge to fall into the Mississippi.

The events of this week, while truly tragic, are not without precedent. Two sets of prior bridge failures keep coming up due to their similarity with this week’s: the Silver Bridge and the Mianus Bridge. In both cases, a steel part failed that was relatively small, but the structures were not designed robustly such that one small failure initiated a chain reaction of subsequent failures and the eventual catastrophic collapse of a large physical structure. When a redundant structure experiences a failure of one of its components, the stress previously withstood by that component is distributed to a number of other components, and even with the additional stress “burden” the remaining components stay below their strength threshold and as a result the structure does not fail catastrophically. For this reason most suspension bridges have bundles of steel cables instead of a single monster cable: one small cable can fail but the bridge does not fall down.

The role of inspections is another topic that does not seem to easily die down. I’m not sure that it’s fair in this case to put the blame on the inspections system. People will, politicians especially. But all of the inspections in the world do not make up for poor initial design. As discussed above, parts in service will fail. Inspections are designed to try and identify the potential for failure by identifying flaws and cracks that might become critical. If we tried to identify every mm-scale sub-critical crack or flaw in every steel structure in America by human inspection, we would need to put a hell of a lot of people on full time employment in this field. The real problem at the root of this failure is the lack of redundancy. Good structures can undergo a failure of one part without causing a catastrophic collapse. The failed part then serves as a much greater and more obvious sign to the outside world that the structure needs work. I said it in the comments, but I’ll say it again here: read the chapter on Redundancy in “Why Buildings Fall Down” by Levy and Salvadori. A quote from them to leave you pondering:

“… the amount of redundancy the designer puts into a structure to avoid total failure in case of local failures … varies with the type of structure. Structural redundancy essentially allows the loads to be carried in more than one way–i.e. through more than one path through the structure–and must be considered a needed characteristic in any large structure or any structure whose failure may cause extensive damage or loss of life.”

So in a way, we DO need more inspections, but not of the sort people keep talking about in the context of this week’s bridge collapse. It is unlikely that an inspection would identify with 100% accuracy the sorts of cracks that brought the 35W bridge down. Instead of focusing on tiny flaws in a steel beam, we need to inspect the structure of bridges and other large components and take them out of service if they are not designed to be sufficiently redundant. That is how we can prevent catastrophic failure and loss of life of the dramatic sort that we saw earlier this week.