BrokenBridge

The Famous Bay Bridge Crack

Tony Alfrey (tonyalfrey at earthlink dot net)

Page 1.
What's My Motivation?   - "All right Mr. DeMille, I'm ready for my close-up" - - Gloria Swanson.
Introduction   - It's just a little, teeny crack.
Repair 1.0   - A good first attempt that needs improvement.
So What Broke?   - Oooops, back to the drawing board.
Repair 2.0   - "Design enhancements with different elements"
Conclusions
Reader Comments - Repair 1.0 and 2.0

Page 2.
Repair 3.0   - Eyebar repair, finished early on Dec. 22. Click the "next page" button to go to page 2.

In the early evening of October 27, 2009, a repair that had been made on the San Francisco-Oakland Bay Bridge failed spectacularly, and was captured nearly in real-time and posted on Twitter. The subsequent unsatisfying explanation for the failure by Caltrans, the agency responsible for the repair, prompted me to ask "can I figure this out?". Our guesses were pretty close to the official pronouncement issued days later. Now, months after this page was originally posted, the story could be compressed and simplified. But that would miss the point, which is that it was possible to solve a mystery by using photos and pieces of data available on-line. Our writing style can seem a little disjointed because we've written the page in many, many pieces over an extended period of time, and have left some of the parts as originally written without revision to try to display the original style by which the "blog" evolved.

As of the latest update in January, 2010, this is all ancient history! All of these parts are gone, and replaced by Repair 3.0. But it still deserves some consideration: Those who cannot remember the past are condemned to repeat it. - George Santayana.

This is not one of my usual Noon Science experiments, but there's some cool stuff to learn anyway. We'll work on this as the "week" (first posted Oct. 28) progresses and as more info and pictures become available.

OK, so if you're not from the San Francisco Bay area, you might not know that our famous Bay Bridge (a.k.a. San Francisco Oakland Bay Bridge) is undergoing a big earthquake retrofit. Here's a CAD model of the new eastern span (the part that goes from Yerba Buena Island in the middle of the bay over to Oakland), viewed from Yerba Buena Island, that will replace the old eastern span deemed unsafe after the Loma Prieta earthquake.

Below is a photo of the current bridge taken from roughly the same location as above. The plan for Labor Day of 2009 was to install a section (the white thing in the foreground) into the temporary S-section of the bridge so that traffic could be rerouted (to the right) around the portion (to the left) which will be connected to the new Bay Bridge (in the background); a rather remarkable achievement in my opinion. By the way, these dudes should get some credit for this; check out their cool animation.

But while all of this was going on, engineers performed an inspection of the entire eastern span of the bridge, and found a little problem, and everyone forgot all about this cool detour thing. Here is a picture of the Bay Bridge before modifications had begun. The circle shows where our little problem, a crack, was found:

(Picture from here and here. Also, see other fine aerial photography in LA, my hometown, here)

Here is a close-up view of the crack, that rusty-looking opening, in a piece called an Eyebar. The crack is big enough to slip your hand inside.
At 7:07 in this video, you can see what Eyebars look like (albeit for the west span), all stacked up and being prepared for installation.

(Picture here and more broken bridge info from the San Jose Mercury News)

There was a substantial rush to open the bridge after Labor Day weekend, so some "repairs" were made, but not much detail (at first) was available describing what was actually done. On the evening of Oct. 27, in the middle of rush hour, the repair broke. Can we figure out what happened?

As you look at this picture, you'll see two different kinds of stick-like structures that make up the bridge. The first thing is called a Lattice Girder. It is the part that looks like a long, rectangular open-sided box, with a criss-cross-hatching of straps. These parts are generally under compression, that is, they are being pushed from each end with a force that tries to shorten the girder*. The second important part is a so-called Eyebar. They are simple, long, wide, flat straps with big round knobs on each end. They are on the right side of this picture and they go diagonally from the road bed up to the top of the bridge. They are arranged in pairs. There are Eyebars that go in the center and there are Eyebars that connect to the road surface at the bottom and to the Lattice Girders at the top. These Eyebars are in tension, that is, they are being pulled at each end with a force that tries to lengthen the Eyebar. So the crack is in the very top end of the central Eyebar. The crack is big and open, because the tension on the Eyebar tries to pull the crack further apart. And of the literally hundreds of components on the bridge, this eyebar is part of a significant load-bearing assembly.

OK, so what to do? Well, I first speculated that the solution derived from tooling originally used to construct the bridge. But it turns out that when the bridge was first constructed, each girder or eyebar was hung onto the end of the finished portion of the bridge as each section "walked out" (see this) from the twin supports, and this won't work as a repair technique once the bridge is under load. The load (in this case, a tension ) must be removed from the broken piece before repairs can be made. The solution was designed by engineers at C. C. Myers, and the components were fabricated almost overnight by Stinger Welding in Arizona, without much time for a thorough analysis, especially with respect to resistance to vibration. This is how it works.

(Picture from Sacramento Bee here, rumored to have actually originated here)

First, we need a Saddle. This is a half-cylinder-like thing that sits on the cylindrical Pin connecting the Eyebars. Then, on top of the Saddle, they put a large T-shaped slab of steel, that Caltrans calls a Crossbar, that holds the Tie Rods. These Tie Rods (four all together) are just very long bolts with Nuts on the end that are adjusted to tension (tighten by pulling) the Tie Rods (see correction at bottom of page) . They install this assembly at each end of the Eyebar and tighten up the Nuts. Done.

The four Tie Rods (they look like about an inch and a half or two inches in diameter) do the job of an Eyebar (12 3/8" wide and 1 13/16" thick to be exact)? Were they made of the conventional A36 steel used in most bridge construction, and in the Bay Bridge, the Tie Rods would have been way too small. Months after the original failure, we find out that the Tie Rods are Williams Rods, fabricated from a high-tensile-strength steel. In principle, the steel used in these Tie Rods should have tolerated the tensile (stretching) load. See our Tie Rod stress calculations here.

A lot can be learned from this picture. This Saddle (hanging from the crane on the left) fits over the cylindrical Pin that connects the two Eyebars. The Tie Rods must pull on each side of the Saddle to keep the Saddle in place, but the Saddle must be able to slide in between the pair of Eyebars. The big T-shaped Crossbar (on top of the Saddle) holds one pair of Tie Rods, but there must be another Crossbar on the other side of the Saddle which has not been installed yet. It must be installed after the Saddle is slid between the Eyebars. Then the Tie Rods are installed. Look to the right side of the picture where you can see the diagonal Eyebars where the Saddle will be installed. You will see the big crack in the Eyebar just below the Pin.

If you study the picture carefully, and try to visualize assembling the pieces, you will conclude that one needs a little change in the Crossbar that goes between the Eyebars, because the two pairs of Eyebars are too close together to get another Crossbar on top of the Saddle. So an extension must be used under the second Crossbar to clear the upper Eyebar.

Here we're looking at two pairs of Eyebars near the top of the bridge; the pair closest to the viewer has the crack. There is a Saddle (the thing with the three rusty-looking plates side-by-side) at the top of the central Eyebar. On top of the Saddle (between the pairs of Eyebars) is an Extension and a big T-shaped Crossbar that holds the Tie Rods (see previous picture). But there is no Crossbar on top of the Saddle nearest the viewer, where the weld failed, sending it and its Tie Rods down to the roadbed. Note the crack that started all this fuss in the central Eyebar just below the Saddle nearest you.

This photo shows the Crossbar that is supposed to sit on top of the Saddle some 100 feet up in the air at the top of the Eyebar. There are two of these, one possibly hanging down below the bridge and this one that went flying around that took out a car. Both Tie Rods (that look like cable) are still attached to this Crossbar in the photo below (remember, this was sitting on top of the Saddle in the earlier pictures) so it doesn't look like a Tie Rod broke at this end. But we haven't seen the other end. Caltrans now claims (but not originally) that the Tie Rod broke first. If so, it is inevitable that the unbalanced force on the end of the Crossbar will pop the Crossbar off of the Saddle, no matter how good the weld is between Crossbar and Saddle. Clearly the weld between the Crossbar and the Saddle failed, but was that the main problem?

This is what Caltrans said on the official website:

"Caltrans District 4 closed both directions of the San Francisco-Oakland Bay Bridge to repair the crossbar and two rods that came loose [consistent with 'the weld failed'] from the eyebar repair that afternoon. " [my italics, inserted comments and bold type]

Other early updates (1, 2, 3, 4, 5, 6), which gave remarkably few details, indicated that Caltrans reinstalled the same fix with some "design enhancements with different elements" added to strengthen the connections between the parts. This is also consistent with other statements that blame "metal fatigue" (which means metal breaks when it is bent back and forth enough times). Originally, I thought that Caltrans was refering to metal fatigue in the weld. In other words, when a welded joint is flexed repeatedly, it tends to break rather than bend (see debate below). I originally claimed that welds were "remarkably intolerant" to flexure. I later changed this to "less tolerant" based on a valuable discussion I had with a welding expert (see reader feedback section). I had guessed that the engineers intended to weld on additional pieces of steel over the joints between the parts. Then these steel pieces would tolerate some bending and reduce the stress on the welded joint itself. Or alternatively, extra parts would be welded on to simply minimize the total amount of flexing, that is, to make the whole saddle/crossbar assembly more rigid.

In retrospect, it is impressive to me that they managed to cook up the Repair 1.0 kludge (that what us engineers call an inelegant solution cooked up to solve a problem quickly) in short order, but it was a little underdesigned***. It might have been a better idea to also try to replace the broken Eyebar soon after the repair was installed. Were I responsible for this, I would have ordered new Eyebars at the same time I ordered the parts for this temporary fix and, in the meantime, begun to think about how to replace them. Replacing Eyebars will not be trivial, but the upcoming Repair 3.0 scheme turned out to be an acceptable alternative.

Repair 1.0 lasted two months, yet the crack in the Eyebar has been hanging up there for long enough to get nice and rusty (an anonymous source claims two years); it bends back and forth as the wind blows, as the traffic load changes from rush hour peak to the dead of night, and as the bridge expands and contracts as it heats and cools. So the original bridge design looks pretty good in retrospect. Don't you feel better now as you drive across the bridge (maybe one day soon)?

As time passed, we found more great pictures of the repair work that confirmed some of the guesses made above. There were two principal problems with Repair 1.0:

1. A Tie Rod cracked or broke at the place where it passes through a Crossbar, and
2. The weld broke between the Upper Saddle and a Crossbar; an inevitable consequence of the Crossbar being loaded on only one end by the remaining unbroken Tie Rod.

Here is the modified Saddle Assembly at the lower end of the Eyebar. No Tie Rods yet.

(Original photo screen-grabbed from here)

What is the fix? First of all, in the above photo, you will see that there is now a coupling between the two Crossbars on the lower Saddle assembly. This, along with better welding between Crossbar and Saddle, helps prevent the Crossbar from popping off of the Saddle which was the prior failure at the upper Saddle.

We see that some plates have been added to the bottom of the Crossbars. The purpose of these parts is to try to deal with the side-to-side motion of the Tie Rods caused by wind load, traffic load, and vibration. But how do they do this? Recent Caltrans reports (here is a typical description) say that a Tie Rod broke because of the stress on the Tie Rod induced by bending where the Tie Rod connects to the plate. To reduce the stress on the Tie Rod, the Nut and the plate against which the Nut rests have been "radiused", i.e. rounded, so that they "roll" against each other.

Below is a picture of the Receiving Plates that shows how the inside edge of the hole has been rounded out or radiused (see the shiny ring-like area) to accept the mating surface of the Radiused Nut.

( Original photo screen-grabbed from here)

What is up with all of this? We've drawn some pictures of the parts to show what can happen.

First, consider the ideal situation. Here's a view through the top plate of the upper crossbar (although reports are consistent with a failure at the bottom assembly, both top and bottom assemblies were essentially identical). There is a thick upper plate on the top of the crossbar with a hole drilled through it for the tie rod. The tie rod goes straight through the plate and is held in place with a large nut; there is an identical nut and crossbar on the other end, some 80 feet below. The tie rod is being pulled from each end by the loading on the bridge. The load on the tie rod pulls the nut flush against the surface of the crossbar. The hole in the crossbar is a little larger than the diameter of the tie rod and the tie rod sits roughly in the center of the hole.

However, if the crossbar and tie rod are not absolutely perpendicular (hard to achieve on such a structure), or if vibration causes the tie rods to slide around a bit inside the hole (as chairs on a hardwood floor might slide around during an earthquake), the tie rod can rub up against the side of the crossbar. Repeated wear at the contacting surfaces can lead to a failure of the tie rod. Or in the second picture, because the pressure on the surface of the nut is now not uniform (greater pressure at the corner in contact with the crossbar), the nut itself is also more prone to failure. Our drawing is exaggerated to more clearly show the effects.

So one approach is to radius the nut and the plate onto which the nut rests. Then, the tie rod is free to take on a tilted orientation while still providing uniform contact between nut and plate surface, and the tie rod can be kept centered on the hole and away from the sides of the hole in the plate. The existing nuts can be radiused, or one can purchase nuts from Williams Form Engineering that look like the nuts in the picture below-left that have a broader foot with greater surface area. This larger foot was not used on the Bay Bridge nuts because the severe tilt which we display in our graphic was not expected, so the radiused surface was simply milled onto the surface of the existing nuts. In the bridge repair, an extra plate with a spherical "cutout" has been added to the top of the existing crossbar because it would be impractical to try to machine these spherical surfaces onto the unwieldy crossbars/saddles. A larger hole (extra clearance) is also drilled into the mating plate that has been radiused.

So it is not as if the radiused nut and plate are continually rolling against each other, but there can be some vibration or changes in traffic loading that would otherwise cause the nut and rod to drift. The radiused surfaces prevent this. We expect these new parts will be periodically checked and retrofitted if necessary, during the three Fridays per month that the bridge is to be closed (note on Nov. 5: now daily inspections).

The lower Crossbar has been fitted with pedestals, i.e. each radiused Receiving Plate sits up on a pedestal or raised platform. There are some other photos floating around the web that indicate that an earlier idea was to install some sort of pneumatic cylinders on the ends of the lower Tie Rods that required this pedestal. We thought that this scheme has been abandoned, because there were pictures without the cylinders installed. This pedestal affair is weaker than simply welding together two fat, flat plates (as they did on the upper Crossbar), and it also puts more "leverage" on the weld between the Crossbar and Saddle. So we can conclude that this project is really evolving and changing even as I write this.

On the morning of Nov. 2, we found out what Caltrans was doing with the pedestals:

"During stress test late Sunday, workers used a mechanism to pull at the entire assembly, which allows them to measure the amount of strain it can withstand."

They add hydraulic actuators (the cylindrical things that look like coffee cans with the tubing coming out of the sides) to the end of the Tie Rods. These are like the pistons used on heavy construction equipment, such as on a bulldozer to move the blade around. Here, they are used to give the Tie Rods a pull and then allow engineers to watch what happens. Engineers can then calibrate their strain gauges and watch the Tie Rods stretch. My guess is that they would like to see the crack in the Eyebar close up a bit so that they know some load has been removed from the cracked Eyebar, but they also want to know that the amount of tension required to do this is less than the known strain limits of the Tie Rods and Nuts.

As seen on our drive across the bridge, these hydraulic actuators became part of the permanent installation of Repair 2.0. So now we have radiused Receiver Plates and Hydraulic Actuators at the lower Saddle assembly.

Now, what was modified at the upper end? Below is a picture of the Saddles and Crossbar at the Upper part of the Eyebar, prior to any modifications. The Eyebar with the crack is on the opposite side (not visible) and is the lower of these two sets of bars. Two Crossbars are in place; the upper Crossbar has an extension between it and the Saddle so that everything fits correctly. No Tie Rods are installed.

We see that radiused Receiver Plates have been added to the tops of the Crossbars without the Pedestal used for the hydraulic actuators on the lower Saddle.

But more important, there is no visible coupling between the two Crossbars on the upper assembly because the Crossbars are not lined up side-by-side as in the lower Saddle assembly, making such a modification tricky!! So hiding between the Eyebars is (hopefully) a coupling that we cannot see that helps prevent the upper Crossbar from popping off like it did just a few days ago! This is a major component that we will look for in future photos! The Caltrans review says that the original tack weld used between the Saddle and Crossbar (two pieces welded together at small points in several locations) which broke, has been replaced with a more thorough weld - "Enhanced Welding" - between the two surfaces. So this is consistent with not seeing a coupling between the upper Crossbars! Caltrans thinks they need cross-couplings at the lower assembly but not the upper assembly?

(Original photo screen-grabbed from here)

Here is a photo of the improved welding (before the receiver plates are added on top). While it is clear that the weld is more substantial than before, there are some obvious problems to consider. The first is that the contact area between the Crossbar and Saddle occurs in only the spots where the sets of bars (two for the Crossbar and three for the Saddle) overlap. So the welds are only as large as the overlap, perhaps 3" square, since the plates in the Saddles and Crossbars appear to be about 3" thick. It's hard to get a welding torch between the plates so most likely only the edges of the bars are welded. I hope this does not leave an open seam at the back of the joint that will allow salt water to creep in between the joint. But it is still a better joint than Repair 1.0, and remember, the Crossbar and Saddle are being pulled together by the Tie Rods anyway.

The second is to ask why Repair 1.0 broke in the first place. The two long arrows show how the Tie Rods will pull equally on each end of the Crossbar when they are installed, like the weight of two children on either side of a seesaw. If one Tie Rod breaks (the previous failure), then there is a very large force (a rough calculation gives a number of over 100 tons) that is unbalanced on the end of the Crossbar that tends to pop the weld off. The hydraulic actuators may be used to insure that there is uniform tension on the Tie Rods, thereby balancing the force on each end of the Crossbar, and minimizing stress on the improved weld. But all bets are off if a Tie Rod breaks.

Finally, there are some other devices (which we have not seen in photos) used to reduce the vibration of the Tie Rods themselves, along with monitoring strain gauges (these measure Tie Rod stretching) which tells me that the engineering crew wants to know just how much load they have on the Tie Rods. The vibration dampers are attached to these bolts (below) between pairs of adjacent Tie Rods. We don't have pictures of the strain gauges, also attached to the Tie Rods. As the Tie Rod stretches, it pulls on the Strain Gauge, and directly measures the actual lengthening of the Tie Rod (it's like attaching a measuring tape to the Tie Rod).

How does this assembly work? The tie rods are on the outside; the eyebars are in the middle. They have taken large slabs of what appears to be high-density foam or a material called Sorbothane, which is a dense, rubber-like material used for a variety of vibration-damping applications. They bolt big slabs of this to the eyebars with a simple clamp. Then the slabs that are furthest out simply press against the sides of the tie rods. Further, all four tie rods are attached together in sets by using long turnbuckles. Here is another view:

See how the Sorbothane slabs simply press against the side of the tie rods. This allows the tie rods to move, but oscillatory motion (like a guitar string) that would develop because of wind or road vibration is dampened or absorbed by the Sorbothane pads. Also note that foam rubber tubes of the kind that can be purchased in your local hardware store for insulating the water pipes that go to your hot water heater, have been added over the tie rods (slice the side, slip it over the tie rod, add lots of tape) to prevent them from banging against the eyebar joint.

All of this tells me that the Bay Bridge moves a lot! A reader has pointed out this article which indicates that vibration of the Tie Rods has been a concern at Caltrans after Repair 1.0 was installed and before the failure:

"We didn't get the modifications put in place in this for the latest windstorm," Fey said. Gusts of more than 50 mph Tuesday were a 'contributing factor,' increasing vibrations in the metal rods, he said."

I've lived in the Bay Area for 20 years. It blows like this every year, several times a year. It is becoming more and more clear that the implementation of the Tie Rods is a substantial challenge and a work-in-progress.

Below we see the upper Saddle assembly with Tie Rods being installed. Hiding under those nuts (right above the yellow jacket of the center ironworker) on the Tie Rods are the radiused surfaces that allow the Tie Rods to tip side-to-side a little more freely and not bind against the inside of the plates.

Here we are getting a little more serious about tightening the Nuts. One ironworker has his hands on the wrench, and another is applying some extra force.
But why? It is simply not necessary to crank on the nuts like this, because the hydraulic actuators on the lower crossbar/saddle are going to do the real work of tensioning the Tie Rods. So in spite of the dates on the photographs, this may be Repair 1.0.

Again, we see no connection between the Crossbars (Dude, the brim of the hat goes over your forehead and the chin strap goes under your chin! Is this an OSHA violation?? Maybe not: my anonymous source says the welders always wear their hats backwards. How do we know he's a welder? Because he has those protective welding pants on).

So the conclusion so far is that the repair is essentially the same scheme as fabricated on Labor Day weekend, with some important improvements, hopefully some of which are hidden from view.

1. Engineers are putting a lot of effort into understanding the forces on the Tie Rods. They are, and have been, worried about how much they vibrate, about what they rub up against as the bridge moves and as the rods vibrate, and about the stress on the Tie Rods as they pass through the Receiving Plates. They are constantly monitoring the forces on these Tie Rods and are using hydraulic actuators to provide a known tension, or pull, on the Tie Rods (presumably uniform between all rods) . If a Tie Rod fails, there's a good chance that some of the components of the Saddle/Crossbar assembly will once again come loose. Also, see our calculation of the stress in the Eyebar and Tie Rod here.

2. They have improved the weld between the Crossbar and Saddle and even added some extra pieces to hold the Crossbars on at the lower Saddle, but they've done different things on the upper and lower Crossbars, adding hydraulic actuators to tension the Tie Rods.

They have essentially replaced an Eyebar (that lasted 70 years) with an arrangement of rods and brackets (whose first version lasted 2 months). And the cracked Eyebar is still there.

Caltrans (November, 2009) closes the #1 lane of the bridge every day for an hour and a half just after lunch to monitor the strain gauges and observe the parts. My guess is that they need to do it in mid-day because they want to monitor the repair under traffic conditions. I think it's a good idea that the same engineers monitor the repair each day (not just a crew that goes out and takes notes) so that any trends that might point to deterioration become obvious. So monitoring needs to be done during the day so that the engineers also get a good night's sleep.

The operator in front is holding a Panametrics-NDT Epoch LT ultrasound flaw and thickness detector (you can do a Google search to find out about this device). It sends out a pulse of sound at extremely high frequency (inaudible) from a transducer being held against the pin by the operator in the rear (think earphone connected to an iPod). The sound propagates through the material, in this case, the big steel pin that you see running horizontally between the eyebars (not that silly little bolt sticking out), and bounces off of the far end of the pin (to the left) and is reflected back to the transducer. The sound is also reflected off of any cracks or perturbations (like a change in pin diameter at a flange). This is similar to ultrasonic imaging used for medical applications.

What you see on the screen is a plot of the reflected sound amplitude versus the depth within the material. The big burst of hash on the left side is sound being reflected from the poor mechanical interface between the transducer and the pin itself, and the spikes on the right side show reflections from the opposite end of the pin. The cursor is set on the second big spike and the number at the top of the display, 45.800 inches, corresponds to that spike, indicating a place in the pin that reflects a lot of sound, and appears to be the total length of the pin. The first big spike, easily calculated to be at 42.6 inches, could be from a big crack or it could be from a flange or a counterbore machined into the end of the pin, like this one:

(Photo source)

"Whew," he says, as he compares the counterbore depth on the tape measure with the number on the ultrasound tester, "no crack!" "Let's put the cap back on [held on with a big nut] and go have a beer!" What does "UTOK 10/09" mean? I guess "ultrasound test OK, Sept. 9". So since this is Nov, '09, is this a second test?

(Photo source)

Stress Monitoring

Late in December, after Repair 3.0 had begun, we grabbed this screenshot from a Caltrans video, clearly shot from the inside of a van. We see a big screen displaying the output from a bunch of strain gauges placed who knows where on the bridge. Each readout is in thousands of pounds. It looks like this particular application has been written in LabView, an application particularly useful for reading sensors and performing real-time control of actuators. The positive numbers are probably measurements of tension as would be found in elements like the eyebars or tie rods and the negative numbers are probably measurements of compression as would be found in the lattice girders or roadbed elements. The graphical plots in the middle allow the monitoring of trends, which can provide a clue of something beginning to fail; straight lines are a good sign. The "1954" number (representing 1,954,000 pounds) is pretty darn substantial (977 tons) and most likely represent the tension in some of the massive upper eyebars at the top of the bridge (see our analysis).

In principle, one could actually automate the system and provide active feedback on the hydraulic actuators used on Repair 2.0, but I'm betting they don't. I'm guessing that a Windows crash (the Blue Screen of Death) in such a case might not be a good thing.

(Photo source)

I am surprised at the interest this page has generated. Many readers have sent me a variety of comments, questions and links to other information. Most recent comments get added to the top of the list.

My Snail Mail Comment.
a) Don't do a search on my snail-mail address and send me things without sending me a note by e-mail first! It's way creepy! Please use my e-mail address above to send a comment or question.
b) Don't send me snail-mail unannounced; how do I know that you're not some kinda nut that would send me anthrax in your letter? I'm not even going to open your mail; it goes straight to the trash!
c) Don't send me reams of paper because I'm not going to read them; while it might appear otherwise, I have a life, too. If you feel compelled to send a lot of stuff, please post it on-line somewhere, and send me a link to it.
d) Stay on-topic and stick to the subject, which is "what was the repair", "why did it break", "is the new repair going to work", "is there a better way" and "where can one get a really good martini in San Francisco (besides Zuni Cafe) or Santa Fe (besides Coyote Cafe)". I can't comment on the new Bay Bridge design; I haven't studied it yet, therefore I can't speak intelligently about it. Please ask this guy; he will have a lot to tell you.

Radiused Nuts. A member of the Stanford University community has pointed out that the KRON article says that the purpose of the radiused nuts/plates is to center the tie rods in the receiver plates while I've alternatively emphasized the Caltrans claim that the nuts and plates are radiused to allow rotation (more accurately, "pivoting"). I claimed that that latter would not work very well; the reader thinks I should emphasize the former. I now think that Caltrans means exactly what they say; they did it for both reasons. But I began thinking why? Did the Tie Rod snap because it flexed against the Crossbar? Or did it snap at the Nut itself? The weakest point anywhere on a threaded bolt is at the thread and where the nut and thread "connect". Are the Tie Rods too small in diameter to tolerate the stress at the Nut. Is the solution simply to use larger diameter Tie Rods? Will larger diameter Tie Rods not fit because there is not enough space between the two parallel plates that form the Crossbars?

Hydraulic Actuators. A reader (P. T.) has mentioned that the hydraulic actuators might be used to compensate for the different thermal expansion of Tie Rods and Eyebars. This is possible if the Tie Rods and Eyebars are made of different types of steel. And since an unbalance in the tension of Tie Rods was partly responsible for the failure of the weld between Tie Rod and Crossbar, keeping the Tie Rod tension uniform is also important. This can be monitored with the strain gauges that have been installed, and controlled with the hydraulic actuators.

Corrosion Prevention. Have any of you seen any painting on the Bay Bridge lately? One of the reasons that the bridge gets painted is to help stop corrosion that might lead to cracks. Sometimes you need to do more exotic things (like on pins and eyebars) because you have to get in between the small spaces (like on the cracked eyebar). One experienced viewer (William L.) familiar with Bay Bridge Paint Crew says that this sort of maintennance is no longer performed on the Bay Bridge, assuming that the eastern span would be removed in 2013, hence no longer needing the paint. Would paint and corrosion work have prevented the eyebar crack? I certainly do not have the background to tell you.

Stability of the Repair. I've been having an interesting discussion with an engineer (E. F.) who has also discussed this issue with some UC Berkeley faculty and also with another reader (Mark M). The issue is one of the inherent stability of the repair. This is comparable to the idea of balancing a pencil on it's point: it may actually be possible to do that (for a very short time) but any perturbation sends the pencil to the table. It has been proposed that the repair (saddles, crossbars, tie rods) has this same inherent problem, one of stability, and depends critically on the friction between the big fat pins (that connect the ends of the eyebars) and the saddles that sit on these pins. I've been doing these calculations myself and don't see that problem, but I'll work on it a bit more and see what I find. I've not heard back from him, so after reviewing his calculation, he may have come to the same conclusion as I.

Rigging Techniques. A welding rigger (T. R.) commented on how one could weld on various pieces (dogs and shaped saddles) onto the unbroken eyebars above and below the failed one. These pieces would be used to hold a "stopper" in place (essentially a loop of cable around the undamaged eyebars). Block-and-tackle are added (cables and a way to tighten them), the load on the cracked eyebar is removed and the eyebar replaced.

About Replacing Eyebars. This comment from Patti B. get a Pulitzer Prize:
"I've been wondering why they don't just bite the bullet and replace the eyebar as well. I can certainly see how doing so would be a significant engineering effort, but no more so than slicing out a chunk of the bridge and swapping in a new one."

Comparison with the Silver Bridge. Several readers have pointed me to webpages that describes the Silver Bridge collapse in Ohio, a bridge of about the same vintage as the Bay Bridge, in which the collapse was caused by the failure of an Eyebar.

http://labspace.open.ac.uk/course/view.php?id=3350&topic=all

and

http://en.wikipedia.org/wiki/Silver_Bridge_%28bridge%29

Now I must point out that the type of bridge described in the above document is of a type more like the west span of the Bay Bridge (a suspension bridge) and not like the east span of the Bay Bridge (a double cantilever). It does appear that there are many parallel Eyebars in the Bay Bridge at the location of the cracked Eyebar that share the same load. So if one breaks, there are others that act as a backup. But it is interesting to see that Eyebars are a common component in many different bridge styles and that they have been known to crack before, and in fact, the very top section of the Bay Bridge is full of Eyebars.

Corrosion-induced Cracks. One reader points out that on the Silver Bridge
"the corrosion crack likely was the result of water collecting in the
eyebar hole in a spot where it was inaccessable to painting, as well as the
fact that there's a greatly increased (2-3)x concentration of stress around
the eyebar hole."

    One could imagine the same problem, exacerbated by salt water, on the Bay Bridge.

Other Bridge Failures. And while the Bay Bridge has not actually "failed" yet, here is a large
list of failures offered by a reader:       http://en.wikipedia.org/wiki/List_of_bridge_failures

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A Debate! I've had a lively discussion with a welding instructor at a community college in New Hampshire who claims that a properly-welded joint can have tensile strength (the measure of strength that matters in bridge structures) equal to the basic material used on either side of the weld if the welded region is made oversized and properly designed. We know that the original Caltrans welds were only tack welds (not the full surface between the two metal elements) so these sorts of welds are unquestionably not as strong as if the weld were "full". It may imply that if the weld is "enhanced" to use Caltrans words, that the weld can be successful. However, as I read "Fatigue Strength of Welded Structures" by Stephen John Maddox, and other references on-line, I see that, in general, a welded joint is less tolerate to fatigue (repeated bending) than the starting material. So while the original weld may be strong, it weakens faster than the rest of the material as it is bent back and forth. The instructor has pointed out that virtually all large structures have welded joints and survive well for extended periods. While I agree, my counter is that engineers compensate for the greater rate of fatigue failure of welded joints by designing the structure to place bending forces at places within the structure that better tolerate these forces. For example, bridges are designed so that forces that bend the structure are placed at places where the joints are pivoted. For the meantime, I've rephrased my statement to say that welded joints are "less tolerant" of repeated bending, and meanwhile I'll try to find a definitive reference in the literature. Also, the instructor has assured me that portable equipment exists (as opposed to some large, fixed welder within a factory environment) that is sufficient to do the best possible weld 100 feet up in the air at the end of a 'cherry picker'.

**A Correction
Originally I thought that the repair had used a combination of Tie Rods connected to Cables, or what is known in the rigging industry as Wire Rope. There are Federal Standards for the manufacture of this stuff and it is incredibly strong and tolerates flexure (bending). Fittings can be crimped (squeezed) onto the ends of the cable and the crimp, if made properly, is actually as strong as the wire rope itself. I supposed that the Tie Rod was hollow at one end and the cable was fitted inside and welded or crimped on, like this device. It now appears that the Tie Rods are indeed one long continuous rod, with threads on the outside. I don't see any seam in these Tie Rods (below) that would show a separate rod and cable connection.

Months after this article was first started, we discovered that the Tie Rods are made by Williams Form Engineering Corp. and are available here. This is strong stuff but it does not like being bent. One day, we may discover if and/or why one of these failed.