Fracture-Critical Bridges

The Golden Gate – a fracture-critical bridge

The story of the I-5 collapse continues to evolve. Currently the focus seems to be on the fact that I-5 (not to mention I-35W) was classified as “fracture-critical”, and the danger it and other fracture critical bridges pose. As there’s a great deal of misinformation being spread about the nature of fracture-critical bridges, an explanation of what it actually means is in order.

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The I-5 Bridge Collapse

The I-5 Bridge in Washington

Right on the heels of my last post about structural collapse, we get news that the I-5 bridge in Washington has collapsed.

Information is still limited, but based on the facts available, it looks as if it was caused by a truck carrying a heavy piece of mining machinery striking a cross member. The 50 year old bridge wasn’t classified as “structurally deficient“, but it was “functionally obsolete”, indicating it probably had less clearance height than a modern bridge.

First off, despite what some news outlets are reporting, there are no indications that the bridge was “unsafe”. Functionally obsolete means things like lane width, approach curvature, clearance, and other nonstructural aspects aren’t up to modern bridge code standards. However, none of this has anything to do with the load carrying capacity of the bridge, or the status of the structural members.

So is this just another example of why we need more infrastructure spending? I’m not so sure.

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Collapse and Connections

I-W35 Bridge Collapse

Consider the failure of the I-35W Bridge from several years ago:

During the wreckage recovery, investigators discovered that gusset plates at eight different joint locations in the main center span were fractured. The Board, with assistance from the FHWA, conducted a thorough review of the design of the bridge, with an emphasis on the design of the gusset plates. This review discovered that the original design process of the I-35W bridge led to a serious error in sizing some of the gusset plates in the main truss…On November 13, 2008, the NTSB released the findings of its investigation. The primary cause was the under-sized gusset plates, at 0.5 inches (13 mm) thick.

Or the infamous Hyatt Regency walkway collapse:

…someone looking at the original details of the connection must have said he had a better idea or an easier way to hang one skywalk beneath the other…But no matter how much more convenient to assemble, the new rod configuration effectively doubled the push of the washer on the box beam supporting the upper walkway’s floor, and this made the already under-designed skywalks barely able to support their own weight.

Or the partial collapse of the Centergy parking deck in Atlanta:

First, the connection holding the fourth floor spandrel beam to the column broke. This caused the beam to slide away from the column. The beam moved away from the garage far enough that the T-beams composing the main floor of the parking deck were bearing on a very thin edge on the ledge of the beam. The concrete of the ledge spalled and as the t-beam fell it pushed the spandrel off of the structure. The fourth floor of the deck fell on top of the floor beneath. The weight of the falling floor overwhelmed the capacity of the floor beneath, and initiated a progressive collapse of the entire bay beneath.

Unless they’ve been catastrophically damaged, structural failure in the US tends to occur at the connections between members.

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Accuracy vs. Simplicity in Engineering

Once you move beyond basic statically determinate cases, engineering problems rapidly become very difficult to solve (leading to some creative solutions in the days before computers). An exact solution often requires the aid of either expensive software packages or extensive calculus training. However, while it might be difficult to, say, calculate the exact bending moment in a beam, it’s often easier to put an upper bound on it’s value. And sometimes, a reasonable upper bound is all you really need.

Engineering, in all it's glory.
Engineering, in all it’s glory.

Here’s a real life example I faced recently. A single-story building has a room dedicated to file storage. In this case, the files are stored in large shelves that can be moved along tracks mounted to the floor. I had to design the concrete slab to support the weight of the files.

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Building Codes and Copyright

As I’ve mentioned before, building codes are highly technical documents, reflecting the latest research in structural behavior. As such, building codes are generally authored by private organizations of engineers, architects, and other experts, rather than by the government. If a jurisdiction wishes to adopt one of these codes, they do so by reference[1] (passing a law which states which code will apply) or by obtaining a license. This method goes back to 1905, when the National Board of Fire Underwriters created the first National Building Code.

These organizations, such as the International Code Council (ICC) or the American Society of Civil Engineers (ASCE), fund their operations by selling copies of the codes they develop. However, common sense (and legal precedent[2]) says that you can’t copyright a law – that if someone wants to pass out photocopies of the code, or host it for free on their website, there’s no legal means of stopping them. Someone suing someone else over the issue thus seems almost inevitable. Surprisingly, it took almost 80 years for that to happen, until the case of BOCA v. Code Tech.

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Solving Stress Problems with Soap Bubbles

Serious engineering work.

Calculating the stresses in a member, and determining if they are within it’s capacity, is one of the main tasks of a structural engineer. Often this is accomplished by making simplifying assumptions that allow the use of relatively simple mathematical methods. But for anything other than the simplest shapes under the simplest loading conditions, these approximations don’t work. In these situations, the difficulty of calculating stresses ratchets upward, and requires solving second-order partial differential equations.

Today, thanks to modern computers and tools such as finite element analysis, solving these sorts of problems has become relatively trivial. But before these aids existed, complex stress problems were simply too difficult to solve mathematically. Because of this, alternative methods had to be devised for working out the stresses, methods that didn’t rely on solving intractable equations. One of the more ingenious of these was the soap-film method for calculation torsion stresses.

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The Infrastructure Report Card: What “Deficient” Actually Means


ASCE’s 2013 infrastructure report card was recently released, and can be found here. Once again, the results are dismal. Our infrastructure received a “D+” overall.

Unlike almost everything else that engineers do, the infrastructure report card garners a fair bit of notice. In any discussion of government funding priorities, the state of our infrastructure is frequently brought up, and the infrastructure report card along with it. Because it has such high visibility, there’s also been some skepticism about the accuracy of the ratings. It’s been suggested that the ASCE might be exaggerating the extent of the problem – “juking the stats”, as they say – since a worse infrastructure means more work for engineers.

Because the report card covers a broad swath of infrastructure projects, we’ll just look at one particularly noticeable portion – the bridge section. The salient stat here is the percentage of structurally deficient bridges. The easiest way to pad these numbers would be the inclusion criteria – what qualifies as a “structurally deficient ” bridge. So what does it take to qualify? Are the stats on the level?

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Calculating Period and WEIRD Buildings.

Outside of California, few places in the country are known for having earthquakes. But because the possibility for one exists nearly everywhere, earthquake loads nearly always need to be considered in the design of a structure. During an earthquake, a building will vibrate back and forth, much like a weight attached to a spring. How fast it vibrates dictates how much force the building experiences – this quantity is known as a building’s period, and determining is an important part of calculating the seismic load on a building.

Harmonic motion. My job would be a lot more fun if we were hanging buildings from springs.

ASCE 7 allows the use of several possible formulas for calculating period, depending on the exact sort of building being designed. These equations are very simple, and don’t seem to resemble the equations of simple harmonic motion, the concept that seismic load calculations are based on. So where do they come from?

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ASCE’s Live Load Model

Parts of this are older than me.

(Thanks to Dr. Ross Corotis for help in obtaining some of these original papers.)

The live load on a structure consists of the weight of people, pets, furniture, and anything else that has weight and can be moved around. Despite how heavy concrete, steel, and masonry are, it’s often the magnitude of the live load which governs a structure’s capacity. However, unlike other loadings, live loads are extremely difficult to model accurately. They depend on how people decide to live and where they decide to go, and are thus not very amenable to the sort of mathematical modeling building codes like to be rooted in.

But that hasn’t stopped the codes from trying.

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