Cross-posted from streets.mn: The Fall and Rise of the I-35W Mississippi River Bridge – Part 2: Structure :
Bridges are designed to overcome gravity. They take travelers over a trench, river, or chasm of some kind to reduce the costs of travel. In their absence, travelers would need to descend, and ford a river, take a ferry, or make some other less convenient accommodation. Bridges are networks, sometimes simple, sometimes complex, for transmitting forces from the air to the ground. These networks may be of stone, concrete, wood, steel, or other materials. The network elements are connected in various ways.
The I-35W Bridge was constructed as part of the Interstate Highway System. It was not the first crossing of the Mississippi River in the City of Minneapolis, one can see many other crossings from the photos and maps. Immediately upstream we find the oldest extant crossing, the curved Stone Arch Bridge, dating from the 1883, which originally brought trains of the Great Northern Railway across the Saint Anthony Falls from Old St. Anthony on the east bank of the River to the Mill District on the West Bank, and now acts as a pedestrian crossing. Immediately downstream is the 10th Avenue Bridge, opened in 1929, and still carrying vehicles. The first river crossing in Minneapolis was the 1855 Hennepin Avenue Bridge, a tolled suspension bridge, which lasted at least 20 years.
In principle engineers know (or knew) how to build long lasting structures, that with proper maintenance could last centuries. In fact the Pons Fabricius in Rome was originally constructed in 62 BC, more than 2,000 years ago, and has remained in continuous use. So something went wrong on I-35W for it to last only 40 years, and something has gone wrong in civil engineering practice if we are designing bridges to only last 50 years.
The National Transportation Safety Board, the federal government agency for investigating failures, engaged in an extensive one-year study of the collapse. Inadequately sized gusset plates, sheets of steel that connect truss members, beams, girders, and columns in bridges and other structures, were the proximate cause. While the gusset places were too thin for the design, they were not so thin that the Bridge collapsed earlier. As can be seen from the pictures, the Bridge was undergoing some construction at the time of the collapse, only two of the four lanes were open to traffic, while the others were being resurfaced. It was the combination of the undersized gusset plate with increased weight of the Bridge over time (due to things like pavement resurfacings), and in particular, the loading of construction materials on the Bridge, above the gusset plate that day was the proverbial “straw that broke the camel’s back”. Once one gusset place cracked and could not support the loads, cascading failures led to the collapse (A summary of the NTSB report can be found at “NTSB releases report on I-35W bridge collapse” in Roads\&Bridges, November 17, 2008 (Accessed April 19, 2012)). The Bridge was fracture critical or “non-load-path-redundant”, meaning that once one critical element failed, there was no redundant element to take the load.
Tom Fisher says that fracture-critical design has four characteristics: lack of redundancy, interconnectedness, efficiency, and sensitivity to stress (Fisher, Thomas (2009) Fracture Critical. Places: Design Observer.(Accessed April 19, 2012)). Beyond that, it has long been known the Bridge was structurally deficient, and it had been investigated for other possible failure modes.
A report by my late colleague Bob Dexter is interesting in that it said
“As a result, Mn/DOT does not need to prematurely replace this bridge because of fatigue cracking, avoiding the high costs associated with such a large project.” The report was correct as far as it went, since fatigue cracking was not the source of failure. It did not identify the problems with the gusset plates, nor did any inspections after construction. (Robert Dexter, Heather O’Connell, Paul Bergson (2001) Fatigue Evaluation of the Deck Truss of Bridge 9340. Report no. Mn/DOT 2001-10 . The full report NTSB/HAR-08/03 PB2008-916203.)
The US still has about 18,000 fracture critical bridges (America’s Broken Bridges
By Carol Wolf on March 22, 2012). Some 465 have similar designs to the I-35W Bridge. There are about 72,500 structurally deficient bridges according to USDOT, out of about 600,000 bridges (Transportation Statistics Annual Report, U.S. Department of Transportation, Bureau of Transportation Statistics, 2008). Another 80,000 are functionally obsolete, which does not imply a bridge safety problem, but means they are not to standard, for instance with narrow lanes, or are under-capacity for demand.
Bridge failures on the Interstate are not as uncommon as one might think. The list below shows major Interstate bridge failures and their causes.
- Tampa Bay, FL – May 9, 1980 – I-275 – ship collision
- Greenwich, CT – June 28, 1983- I-95 – metal corrosion, fatigue
- Oakland, CA – October 17, 1989- Bay Bridge- earthquake
- Oakland, CA – October 17, 1989- I-880- earthquake
- Milwaukee, WI – December 13, 2000- I-794 – weather, traffic?
- Webbers Falls, OK – May 26, 2002- I-40 – barge collision
- Bridgeport, CT – March 2003 – I-95 – car-truck fire
- Oakland, CA – April 29, 2007- MacArthur Maze – truck explosion
- Minneapolis, MN – August 1, 2007 – I-35W – design, construction
Other bridges have been closed before failure, and repaired or replaced. The Sherman Minton Bridge across the Ohio River was closed in 2011 after cracks were discovered, and repaired. While some causes seem to be acts of nature (earthquakes) or difficult to predict (barge collision, truck explosion), good design will defend against even those failures, at least to a point. The trade-off inherent in all design is the amount of failure to be accepted. Will we accept one Interstate bridge failure in the US every day (no), every month (no), every year (no), every decade (yes), or every century (yes)? Nine failures in 27 years indicates about one every three years is somehow acceptable.
Each higher standard is increasingly expensive. At some point, money spent on reducing fatalities by making ever safer bridges outweighs the same money spent on reducing deaths some other way (e.g. increasing traffic safety or reducing air pollution). For instance, a billion dollars annually spent on reducing expected fatalities from bridge collapses by one person per year is 200 times more than would be spent reducing traffic fatalities (where the “statistical value of life” is on the order of 5 to 6 million dollars per person), and would be a misallocation of resources from a safety perspective.
We can of course potentially add the costs of infrastructure replacement avoided, but we currently spend more per life saved on safety in structures than on safety in traffic. As with aviation crashes, bridge collapses are highly visible and are perceived as more common than they really are.