If you read the New York Times today and saw their report on the collapse of the I-35W bridge in Minnesota, you may have been wondering like me exactly what those bends looked like, or for that matter, why did the bridge fail in the first place? For a better explanation than the one given, I went to the National Transportation Safety Board (NTSB) and looked at the reports for more information.

It’s going to be a long post, but more after the jump.

So first of all, what caused the bridge collapse? According to the NTSB, a significant factor in the collapse was the construction of the gussets in specific areas. Gussets are devices used to reinforce the connections between to objects. In the case of the bridge these would be the massive beams the bridge was made of. The NTSB broke down the thickness of each gusset at each connection:

As it turns out, the gussets at joints L3, U4, U10, and L11 were the thinnest by design. Through engineering analysis, the gussets at L3 and U4 were designed correctly. The gussets at U10 and L11, however, were deemed to have a “liberal” and uncommon design that greatly reduced the safety of these segments relative to all others. This was determined through what is called a Demand/Capacity (D/C) ratio comparison of stresses and shear. The Capacity is the theoretical allotted stress or shear that the joint can receive, and the Demand is the stress or shear actually put on the joint through use. A D/C value less than 1 indicates a conservative/safe design; a value equal to 1 represents an efficient design, and a value greater than 1 represents a design that reduces the factor of safety typically desired. In comparing the joints of U10 and L11 to all other joints, only they have a D/C ratio greater than 1:

And in practice, as reported by the New York Times, this lead to undesired wear on the bridge. I modified published pictures by the NTSB to give the images below of the gusset at U10. The red circle highlights the area you should be focused on. The white line represents the outline of the gusset if it was brand new. With the image modified for contrast, you should be able to see the warping of the gusset outside of this theoretical line

Over more time, these plates are subject to even more wear and load. The NTSB asserts that the increased wear and load on the improperly designed gussets were a significant contributor to the overall bridge collapse. The same gusset you see in the image above was salvaged after the collapse and shown in the image below (much more deformed):

So there you have it. Seemingly small deficiencies in design can have dramatic and unintended consequences.