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Hi Everyone,

I’ve been away for a couple weeks, are there any current discussions on the collapse? How about current images from the debris cleanup?

Kwuntongchai

One more bit, here's a diagram of how a cantilever with a suspended span works.

The mens' arms are the tension members, the sticks are the compression members. In my diagrams above, red are tension, blue are compression, and green function as either compression or tension.

So, the failure mode I'm thinking is that, say, the guy on the right looses his grip on his stick with his left hand. What happens? the weight in the middle will make him tip inward, causing a complete failure. How will the middle section fail? The right guy tips inward, everything pivots where left guy and right guy's hands meet middle guy. Depending on the strength of middle guy's connection to left guy, he will either hang and dangle from left guy and pull left guy into the river, or (in the 35W case) bust loose from left guy and drop more or less straight down.

Meanwhile middle guy's falling has town loose left guy's right hand loose from the stick, and the stick drops, then left guy tips over to our left.

(Also, the buckle in the girders on the approach span, now that I look at it, appears to be too uniform from left to right to have been caused by the twisting south span... Must be some artifact of how a continuous girder bridge buckles over an intermediate pier if it loses one abutment)

And, as to what happened? This photo http://www.flickr.com/photos/s4xton/981290582/in/set-72157601157770382/
might explain something. Why is the location the girders buckled **behind** the pier? You’d think they’d have bent right on top of the pier. It’s not exactly normal for a girder to bend a couple feet out into the span.

It looks like a compression buckle. They got shoved, and bent out of shape? What shoved them, why? Did the whole south landside cantilever arm (U8 to U1) bust loose off Pier 5 because of expansion joint issues and crush the approach span?

There needs to be some explanation of this, curious as to what anyone thinks. This is the spot directly “in front” of the burning Tastee Truck and schoolbus.

Here's a few more thoughts:

Check out my diagram below--do I have the labeling right? Now it's a lot easier to talk and see at the same time.

Now, let's establish how the bridge stands up.
* Cantilever bridges are built out from the piers. Chords on top are tension, chords on bottom are compression.
* Truss bridges are built from pier to pier, tension on the bottom, compression on top.
* A Cantilever bridge with a suspended truss span has cantilever arms reaching out from the piers, then a truss span hanging from the ends of each cantilever span.

So, the tension/compression diagrams in the MnDOT doc show that this is a cantilever bridge with a suspended truss span. There's a bit of overlap between the two span types, as can be seen in this labeled diagram. The Cantilever extends out from Pier 6 from U12 to U6, with the compression chords from U12 to U10 and U6 to U4 acting as tension chords. Similarly, the Truss Span extends from L9 to the L9 on the other side of the river (same spot, other side), with the L9 to L11 compression chord also working as a tension (the entire span, except that last 40' segment from L8 to L9 at each end). (Of course, if my whole diagram is backwards, it makes perfect sense, with U6 to U2 and L5 to L1 as "reversal members" -- able to function both ways).

Now, look at where Jeffers determined the failure occurred. U10/L10. It's right at the outer extremity of tension members on the top chord. And, in the video, it looks like the failure at the north end also occurred right at U10/L10.

Now, imagine (hypothetically) the center span standing without the side spans. It now has to function as a truss span, compression across the top, tension on the bottom. What will fail? The compression members on the bottom will probably function pretty well as tension members, they're big and beefy. But the tension members will buckle under compression.

So, I'm thinking, the south arm may have fallen first. Jeffers is exactly right on how the main span fell, but I think the south span triggered the main span. (Mainly because it fell so crooked while the rest of the structure fell straight. With a long, complex set of spans like this, span like this, you'd expect a point failure somewhere to take out one span in an asymetrical way, then the other spans to fall like dominos as they lose their counterbalancing cantilever arms, and the girder spans on each end to be yanked off their piers or shoved off their piers as the main spans go).

So, Jeffers is right on the main span, and this is why.

The south cantilever platform, from U12 to U4, can stand on its own only if its balanced. If, say, the south half (landside) was to collapse, then an unattached north side of the cantilever platform would simply dump itself into the river.

And, the north side, attached to the suspended truss and whole north cantilever platform (over pier 7), wouldn't simply dump itself into the river, it would try to act as a truss span, from pier 6 to pier 7. But, this isn't going to work. It's not designed to hold up that way--it would need a truss network with a continuous compression member across the top. Which it doesn't have--it's tension from U10 to U8. The truss system is fine, actually, from L9 to L9 across the river. But not from L8/U8 to L8/U8.

So it will fail.

Where will it fail?

The tension chord from U10 to U8 will buckle. Crunch. Game over. Which is exactly what you've shown, Jeffers, and the video clip shows happening on the other side of the river.

So, it could have been an initial failure on U10, south side. But, you'd think that would have resulted in the main span twisting much more as it dropped. As it is, it fell pretty flat. It seemed to take a few seconds for things to fail. Maybe those tension members handled the compression for about 5 seconds as they slowly got bent out of shape and twisted apart. That's how long it took the same failure to occur in the north landside arm.

So, seems to me, it's much more likely that the initial failure was indeed in the south landside span. Between Pier 6 and Pier 5. Something happened on one side or the other, the west side?? since the deck seems to have flopped to the east. Then the east truss/cantilever arm held for the same 5 seconds, and failed. That makes for the twisted deck. And something in there should also account for the rotating king posts. If the west side, south arm failed (around, say, U6 or U4), then the king post would still be intact. Not sure on the rotational movement, but there's probably a few good reasons.

This brings the initial failure back to a small member somewhere, rather than a massive failure of a main structural member, with a result in s similar failure on the other truss arm, which seems more plausible overall to me.

Hope this makes some sense, I'm staying up *way* too late...

Kwuntongchai

Great analysis--thanks for piecing it all together. You've certainly nailed the point, mechanism and sequence as to how the main span failed.

Couple Qs.

* If you're feeling motivated (insomnia, perhaps), could you redraw that MnDOT diagram so it shows the whole bridge from one side to the other--I'm still never quite sure which are the center spans and which are the landside-spans. And identify what the "king truss"--I'm not sure what a king truss is on a cantilevered tower.

On the diagram, I'm thinking the L9/U10 member on the MnDOT diagram is actually compression, not tension (a typo for MnDOT's consultant). (like the L7/U6 member). For one thing, the photos show it as being a box beam, not an I beam. For another, the bridge wouldn't stand up if it was tension.

* Do you have an opinion as to whether the U10/L10 area failure was or wasn't the initial failure? If the south landside span failed, the center span would be expected to sag and buckle somewhere, is U10/L10 as good as any spot for that?

i.e. if the south landside arm failed somewhere, then the counterweight would be gone from the main span, and the section from U8 to U10 would suddenly be acting in compression, rather than tension. and you'd get a buckling of the tension member somewhere on that stretch, quite possibly at the farthest-extremity of the tension member.

Are there more current bridge collapse threads out there? I’m not familiar with the freerepublic setup, can anyone steer me towards an index, search function, or active thread?

Also, what other discussions have people found elsewhere on the web?

Thanks in advance,
Kwuntongchai

New story from the Star-Trib—MnDOTs discussions from Dec, 2006 of if and when the bridge might collapse.
http://www.startribune.com/10204/story/1370130.html
and
http://www.startribune.com/10072/rich_media/1370367.html

One wonders why
1) they didn’t put a weight restriction on bridge traffic, and
2) why they didn’t pour additional pilings to support the landside cantilever arms. Rather than risk compromising the entire structure to drill in reinforcing plates, simply shorten it into 3 or 4 spans so it can’t possibly collapse.

Kwuntongchai

Thanks for the comments, Jeffers—

Can you post the link to the photo you think you see the east kingpost on?

Kwuntongchai

Movie footage of the bridge under construction. Land-side cantilever arms were constructed first, it looks like they had temporary supports, suggesting that they aren’t designed to stand as a pier-to-pier truss. (and indeed the north main span demonstrated that pretty well)

http://www.mnhs.org/library/bridge/

http://www.flickr.com/photos/s4xton/sets/72157601157770382/

If you haven’t seen this set, you might be able to recognize some bits, especially the close up of that east pier.

Thanks for the comments, Jeffers.

Here’s more food for thought. I haven’t seen these issues discussed.
Look at the big photo at http://fullyarticulated.typepad.com/sprawledout/2007/08/article-are-the.html (Sorry about the political content, but it’s a great photo) and I notice 3 things.

1. South landside span (the one that twisted), the 2 southbound lanes are folded in so as to be almost vertical. A tighter fold than anywhere else in the main bridge system. Why did they fold so vigorously, especially when the main truss that they were on top of seems to have become completely separated? If it had folded down on both sides of the main truss, it would have pinched it, and the main truss wouldn’t be lying down on the riverbank all casual-like.

2. No cars on the SB lanes or on the ground on the twisted south landside span. You’d think if there were cars on that span when it collapsed that you’d see them on the ground. And there was the schoolbus and semi truck just ahead of them, which you’d normally get cars queing behind. If the main span fell first, thes cars would have gotten off without any additional cars coming on. No cars visible in http://www.flickr.com/photos/thecurseofbrian/981931600/in/set-72157601159020144/ either. Maybe there just weren’t any cars, the traffic cam video should show this.

3. The west truss is lying horizontally on the pier, and it’s in pretty good shape. It’s still pretty much all in plane, it has a couple web members all intact, in fact, it’s the only non-mangled piece of the whole supertructure.

Another shot of the relative good condition of the west truss over the south pier http://www.flickr.com/photos/s4xton/980394803/in/set-72157601157770382/

and 2 other things:
* South approach girder spans failed due to compression—they got shoved back away from the river. South side http://www.flickr.com/photos/s4xton/980437381/in/set-72157601157770382/ and north side was plainly tugged, as one span even got tugged off its foundations a couple spans back from the RR tracks. (Though it looks like the south spans slid backwards after it kinked on the pier, so it could be a post-collapse feature (slipped on the way down). In any case, the south side girder span that fell on the Tastee truck cab seems to have fallen in a different sort of way than the north side approach girder span that fell on the train cars.

* High survivorship is really remarkable. Lots of folks dropped 105’ into the river and walked away from it. 3 of the folks that died did so after they fell—one drowned rescuing people, one had a lampost hit them, one had a sign land on their car. And the truck driver had the fire to contend with.

http://www.flickr.com/photos/s4xton/980407219/in/set-72157601157770382/ this pic shows the plastic pylons still rightside up...

*************

So, seems to me the south approach cantilever arm (from pier 5 to 6, I think) with the twisted roadway almost has to be where it started. Everything else failed symetrically across a cross-section of the deck. The cars are all where they were on the road, so the main span didn’t twist on its way down to the river.

And it was just good luck that there weren’t cars going south at that instant in time, or they’re hidden under the bridge in the one photo. But with a sideways fall seems like you’d have lots of fatalities.

The intact west-side truss suggests that it simply fell down, didn’t fail at all, wasn’t crushed.

So somehow the main deck over the river didnt get twisted, even though the underlying truss did...

Anyhow, more stuff for everyone to think about, piece together.

Kwuntongchai

Rotational stress due to construction on the east side of each truss?

Looking at the collapsed bridge deck in the river, the deck sagged down on each side of each underlying truss stucture.

The design of the bridge puts one truss structure under each half of the bridge, close to the center of each 4-lane road on the deck.

Since the construction had the east side of each side of the bridge closed to traffic, and the west side of each side open, there is an assymetric loading of each truss structure.

If the under-construction areas had heavy loads of sand and equipment, it would have added rotational stress to each truss structure and could have caused the cross-members tying the two main truss structures together to fail, and the truss structures to tip over sideways to the east, as happened.

Very interesting discussion all, I hadn’t seen this come up anywhere, so I’m throwing it in.

Kwuntongchai

Clark857

Not to hyjack the thread, but it’s interesting that you consider all these to be “trusses.” Are there bridges in the world that you *would* call “Cantilever bridges?”

i.e. at http://en.wikipedia.org/wiki/Cantilever_bridge it lists the longest cantilever bridge spans in the world, but you refer to these as trusses. These all have compression members on the bottom, tension on the top (except in the suspended truss span). Compare to the examples at http://en.wikipedia.org/wiki/Truss_bridge where every bridge has the tension members on the bottom and the compression members on the top.

Not to belabor an issue, but can you steer me to a lexicon used by bridge engineers where these are defined as “continuous through trusses” rather than cantilevers? It’s always been something I’ve been curious about, how different groups use different terminology for the same bridge.

Or, what is a typical “basic text” used by bridge engineers that I could go dig up at the university library?

Thanks,
Kwuntongchai

Clark857

Here’s terminology question for you:

I find it curious that people are calling this a “truss” rather than a “cantilever” My understanding is that a cantilever is suspended out from the piers, tension on top, compression on the bottom. A truss, on the other hand, has the compression members on the top, the tension on the bottom.

Here’s a diagram, of the Quebec Bridge, a cantilever bridge with a suspended truss. The diagram shows the reversal of tension and compression members where the cantilever arms end and the truss section begins. http://www.brantacan.org.uk/QuebecSide2A.jpg

The transition between the truss segments and cantilever segments of cantilever bridges with suspended spans is pretty easy to see. In “through cantilevers” like the Quebec bridge or the first Carquinez Strait bridge in California, the truss sections are arched in typical truss fashion. With “deck cantilevers” the truss sections can be spotted where the thick compression members of the cantilever transition into the thin tension members of the truss, see http://www.cvrma.org/pictures/MISC/
dfrr5_170_so_young’s_high_bridge_tyrone_ky_1977.jpg (cut and paste link)

So, here’s a terminology question: What would you call
* The Quebec Bridge in Quebec? (I’d call it a “through cantilever with suspended truss”) http://www.hvq.com/fr_location.htm
* The Queensborough Bridge in New York? (I’d call it a “through cantilever without suspended truss”) http://www.brantacan.co.uk/QueensBoroughB.jpg
* The Aurora Bridge in Seattle? (I’d call it a “deck cantilever with suspended truss”) http://www.art.com/asp/display-asp/_/id—6725/Seattle.htm
* And I’d call the 35W bridge a “deck cantilever without suspended truss.”

So, back to your statement that it’s not a cantilever, seems that a truss would have the compression members on top, tension on the bottom, which is clearly not the case. So I’m curious as to the terminolgy used by bridge engineers—can you elaborate? If it was a “through” bridge rather than a “deck” bridge so it looked like the Queensborough Bridge in profile, would you still call it a “truss” or would you call it a cantilever?

Inquiring minds want to know
Kwuntongchai

BTW, posting links is easy—just paste in the location info of the page you’re steering us to.

>>I haven’t been able to determib\ne if that was a moving train or spotted cars. The railroad people I know are debating if the line under the southern approaches was active at all.<<

In 1967, Northern Pacific ran under a south approach span, the Great Northern ran under the north side approach span (where the RR cars are today). Neither was a heavy freight line, used mainly for passenger trains to access the Great Northern Station (at Hennepin and the river).

The RR line clearance was the reason the bridge was so high. It had to have a fair bit of clearance over the river channel (30’, 40’?), and if it went under the RR tracks it wouldn’t have enough river clearance. So it ramped up over the RR tracks at both ends, making it extremely high over the river gorge.

Today, the bridges used by both RR lines are ped bridges, the tracks on the south have been abandoned, and the tracks on the north are just a spur line to the grain elevators. Used for storage. If there was a train in motion there at the time of collapse, it was probably switching cars at about 5 mph, with a 10 mph speed limit.

Since the collapse started on the south cantilever platform or in the middle of the span, it’s unlikely a train under a north approach span had anything to do with it.

Right on the money with the cantilever diagnosis and diagram of compression and tension members.

You can confirm it in the photo—the chords along the bottom and the ones angled upwards from the piers are box girders with oval holes—a compression member. The ones angled down from the top of the piers are I beams—tension members.

It’s curious that people call it an “arch” or a “deck truss” when it’s so clearly a cantilever—a truss would have tension members along the bottom, and would be tallest midspan, not around the piers. And arch would need a beefier arch for such a massive bridge. (Like the 494 bridge over the Mississippi or the Cedar Ave Bridges over the Minnesota River elsewhere in town—these are 3 or 4 lane bridges and have much fatter tubular steel arch members.) I can see most people getting it wrong, but surely there must be a few people that the media has found that actually understand bridges. (But, when they keep saying cars fell 64 feet to the river and any dummy can tell it’s more like 100’, I guess I’m overoptimistic)

Note also the views from MS Earth, the on-shore cantilever arms are one segment longer than the arms making the central span. So unlike classic cantilevers that have anchored on-shore ends as a counterweight to a suspended truss in the middle, this cantilever has extended on-shore arms, which probably function as something of a “suspended truss” on shore.

Jeffers—the diagrams from p. 49 and 50 of the MnDOT report—can you tell if the “reversal members” are on the center span or the on-shore arms? I’m guessing the on-shore arms.

On that same note, has anyone found a diagram in the MnDOT report that identifies where all the locations (pier 6, L4, etc.) are on the bridge itself?

>>So far, investigators say they have ruled out nothing and will consider everything from the expansion and contraction of the bridge in the extreme weather conditions of Minneapolis to the possible corrosive role of bird droppings.
You gotta be kidding me!<<

Look at the oval panels in the compression chords—the ovals used to be open, but now they’ve been retrofitted with a perforated screen. Why? Pigeons were roosting in them.

When I was a kid I climbed the Northern Pacific railroad truss bridge, about 3 miles upriver from the 35W bridge, with similar oval-holed compression chords. You could climb right up the diagonal beam like a ladder using those holes. All was well until I scared up a bunch of pigeons that just about hit me in the head as they were bailing out, good thing I was hanging on tight...

I’m thinking 30 years of pigeon dung and urea packed in around your welds and rivets is not a good thing for a bridge.