We ended Part 3 of our Miami Bridge failure series with a quote from Bruce Landsberg of the National Transportation Safety Board (NTSB): “A bridge-building disaster should be incomprehensible in today’s technical world. We have been building bridges in this country for over two hundred years, and long before that in other parts of the world. The science should be well sorted out by now – and for the most part, it is.”
But if the science was so well sorted, what went so wrong in Miami?
We now examine the tragedy of 15 March 2018 from a technical perspective.
How Bridges are Designed
To understand how the engineering design process failed for the Florida International University Bridge, we first need to step through how engineers design bridges. (And apologies to any structural engineers reading – we’re going to dramatically simplify the very complex process of bridge design.)
The bridge was meant to be designed in accordance with the AASHTO LRFD design code provisions, and we can break this process down to a number of core steps:
- Sizing: Select preliminary sizes for all the members in the bridge. This is carried out by making educated guesses, using experience, and/or applying rules of thumb.
- Loading: Determine the loads that the structure is required to carry. Loading will include the bridge’s own weight (self weight or dead load), the loading applied from pedestrians (live load), as well as a range of other load types, such as earthquake and wind.
- Action: Calculate the actions that each member and connection of the bridge is required to withstand. This is calculated by applying the loading – determined in the previous step – to the bridge, either in a computer model or using hand calculations. This process essentially determines how the bridge’s overall loading is carried by its individual members and connections.
- Capacity: Determine the capacity (strength) of each member and connection in the bridge. The capacity is a measure of how much action can be applied to a member or connection before its considered overstressed.
- Design Check: Determine if each member and connection in the bridge is subject to an action that’s lower than its capacity to resist that action. If this is the case, the bridge’s design is considered compliant with the relevant design code. (As a side note, the actions and capacities are adjusted by factors in the design process to ensure the bridge has an appropriate safety margin, and we’ll return to this concept in the next part of our series.)
So, ignoring many other aspects of bridge design, such as stability checks, the process of designing a bridge is essentially about ensuring that the action in each member or connection of the structure is lower than its capacity to resist that action.
So, was this process undertaken correctly for the FIU bridge?
Through the course of their investigation, the NTSB found that there were multiple connections where the actions were significantly higher than the capacities.
The Action Calculation Error
The key action we’re interested in is the action in the Member 11 and 12 deck joint, which is the connection that failed explosively on the afternoon of 15 March 2018 and led to the collapse the bridge (see Part 1). In particular, we’ll focus on what’s known as the interface shear force at this connection. This is an action that’s essentially trying to slide members 11 and 12 horizontally relative to the deck.
The bridge’s designers, FIGG, calculated this interface shear action by building and analysing computer models of the bridge. (Think of a computer model as a virtual representation of the bridge that replicates – or approximates – its behavior and performance in real life.)
Based on these models, it appears FIGG determined that the interface shear at this key bridge connection was circa 1000 kips, with a kip being a measure of force.
How accurate was this value of 1000 kips?
As part of the investigation, the Federal Highway Administration (FHWA) built their own computer models of the bridge, and they determined that FIGG’s value was not reasonable. FIGG should have used a value circa 1800 kips. This was almost twice what they assumed – see the comparison of the FHWA value of 1800 kips in orange, as opposed to the FIGG’s 1000 kips in blue. (Although we won’t discuss the other connections, note that that the interface shear action for many other connections was also underestimated by FIGG – this was not an isolated error.)
Several Computer Models
Why did FIGG pick this low value for interface shear?
To answer this question, it’s worth stepping back and discussing why FIGG built multiple models of the bridge. And the reason is that they needed to analyse the behavior and performance of the structure through four different construction stages. In each of these stages, the manner in which the bridge was required to support its loading was quite different:
- After the bridge was poured and the falsework removed, the structure was required to carry its own weight, spanning end to end in the casting yard.
- While it was being moved from the casting yard to its position over the highway, it was supported on transport platforms, which meant the ends of the bridge were overhanging (cantilevering) in mid-air (Stage 2).
- In its final configuration – which never eventuated because the span collapsed – the bridge was intended to form part of a larger structure that mimicked a cable-stayed bridge (Stage 3 and 4).
FIGG analysed these models to determine the interface shear at the Member 11 and 12 deck joint. As expected, the results from the different models differed from one another because each model had different support conditions. FIGG should have selected the largest action from each of the models – in other words, the most onerous action on the connection, the worst-case scenario.
As you know, FIGG selected a value of 1000 kips.
But when the NTSB examined the results from FIGG’s own models, not only did they find a model predicting a value of 1000 kips for the critical connection, but they also found a model predicting a much higher value, of circa 2000 kips.
This shows FIGG had a model that predicted an action that was considerably higher than the value they appear to have used in their design, with this higher value being very consistent with the value of 1800 kips determined by FHWA.
In other words, FIGG had a computer model that predicted the correct action in the joint, but instead of using that value, they used a lower value from one of their other models.
Why would they do that?
And the answer is we don’t, unfortunately, know. The NTSB don’t appear to have gotten to the bottom of why FIGG used this lower value of 1000 kips.
Which raises a key point that many of us engineers will find uncomfortable. We like to believe that engineering failures are primarily technical failures, but this illustrates that behind every technical failure, there are organisational reasons why these technical failures go undetected and result in collapses.
The Only Design Error?
So, we’ve seen the action that the key member 11 to 12 deck joint connection had to withstand was much greater than that anticipated by the designers. It should come, then, as no surprise that when the bridge was forced to carry its own weight for the first time, when it was in the casting yard, it cracked, even before it was placed over the freeway.
But there were even more design errors.
Not only were the actions in the connections wrong, FIGG also miscalculated the capacities of the connections to resist these actions. The bridge had considerably less strength in real life than it had on paper – a subject we’ll examine in Part 5 of our series.
Photo: Miami-Dade Fire Rescue