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To: jeffers

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


93 posted on 08/14/2007 2:05:48 AM PDT by kwuntongchai
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To: kwuntongchai

The deck trusses were cantilevered out past the outer edges of the twin truss assembly, and many of these cantilever sections failed on impact. Because of this, it’s going to be difficult for us here to tell whether any of those failed early or whether such failures may have been a trigger for collapse.

The deck trusses wouldn’t even have to fail to impose the kind of point loads you discuss. However...

I’m uncomfortable with the contention that a few piles of gravel or sand, and even ten or 20 cement trucks overloaded the bridge, in general distributed terms, because even though that seems like a lot of weight to a layman, it’s nothing compared to heavy bumper to bumper traffic, times six lanes, times 1500 or so odd feet of the three trussed spans.

In addition to that, the sum total of all that traffic is but a fraction of the dead load that the bridge had to carry, resisting its own weight in order to span the river.

In broad terms, we’re talking construction equipment loads a hundred or more times less than the bridge’s rated load carrying ability.

But you aren’t taking about general, distributed construction loads, you’re talking about point loads, maybe even a single point load.

At first glance, the 27 inch deep cold rolled deck stringers would tend to spread the weight of a cement truck or big pile of gravel out, so that no one deck stringer carried the load. However, each of those rested on a set of floor trusses, and the kind of weight you envision could have at most been distributed to three of the floor trusses, more likely one or two.

While the deck stringers are deep enough to carry deck loads in between floor trusses, I do not think they were deep enough, or designed to carry deck loads to adjacent floor trusses in the event one floor truss deflected out of plane, buckled, or failed.

Further, as you note, the floor trusses were cantilevered in design. They extended out well to either side of the main trusses.

Three general cases:

1. Normal traffic loads greatly exceed total construction traffic loads. Southbound traffic in the far west lane concentrates on the west main truss, and through cantilever action in the floor trusses, actually imposes a lifting force on the east truss. Northbound traffic in the far west lanes imposes loads on both main trusses. Net result, significantly greater load on the west truss than the east truss.

2. Traffic loads roughly equal construction traffic loads. In this case, the live loads are equally distributed on the east and west main truss.

3. Opposite of case 1, construction loads greatly exceed normal traffic loads. Now gravity loads on the east truss exceed those on the west truss.

Note, these are general cases, distributed loads along the full axial length of the main trussed spans.

I have a hard time believing the total weight of construction traffic on the bridge exceeded the heavy normal traffic on the bridge at collapse time, and an even harder time believing that construction loads even approached design limits of the bridge, which include dead loads (weight of the bridge itself) plus live loads, (traffic only).

However...

Couple of big piles of gravel close together, one dump truck dumping more yet, a couple more close by, waiting to dump, add in a cement mixer or 5000 gallon water tank truck and maybe, just maybe, you recreate case three on a single floor truss.

From there, it is possible that floor truss loads a rusted, fatigued, cracked main truss member, held together by cracked welds of poor welding technique, past what it can carry, and if this in one of Jim’s 57 critical members, then yes, you fail the bridge. It could all come down from there.

But...

(getting real deep in the soup here, and pushing me even further out on a limb)

I like the west main truss failing first.

Maybe.

Somehow, something vaporized the pier 6 east main truss panel, and the two main truss panels adjacent to that at the north end of span 6 and the south end of span 7. If what we see in the images atop (barely) the east side of pier 6 is indeed the remnants of the southeast kingpost, then the largest and strongest designed piece of steel on the bridge folded up like wet spaghetti.

If that’s not the kingpost we see in the images, then something up and just threw the largest and strongest piece of steel on the bridge completely out of sight. Either way, bad things happened there.

The simplest way I know of to disappear the SE kingpost is to sever the west main truss somewhere out in span 7. Now you have fully half of all the span 7 load concentrated on the SE king.

And that’s not all.

Now the west main truss can no longer act as a cantilever for span 6, balanced over pier 6, because the counterbalance of span 7 has been removed. So the west truss on span 6 begins to sag, transferring the additional load of a significant fraction of span 6 to the SE kingpost as well.

I think such a speculative sequence as this could easily make the SE king and adjacent main truss vaporize, which is what we see in the pictures, but...

Soon as you sever the west truss mid span 7, you also induce a rotational moment on the SE king, to the WEST, and we all know that the road decks fell to the EAST at pier 6.

Sooooo....the best sequence for vanishing the SE kingpost is to sever the west main truss, but doing so makes the bridge want to fall west, and the pics show it fell east.

Getting around this is complex.

Let’s say you fail one member of the east truss out in span 7, not far north of pier 6. Just for a point of reference, say it is a diagonal main truss member in tension, running down towards the base of the vertical strut under the floor truss and construction traffic point load we discussed earlier.

Pop, it’s no longer doing its job. The vertical strut it was carrying begins to sag. In a simple truss, the bottom chord nearby goes into tension, top chord goes into compression, but this was not a simple truss for its full span. If close enough to pier 6, it acts as a cantilever, top chord in tension, bottom chord in compression. Either way, you could easily envision significant axial loading on the SE kingpost, differiential axial loading comparing top to bottom, and dynamic axial loading as different parts of the span 7 east truss let go, especially if either the top or bottom chord suddenly reversed stress or was subject to a sudden jerk.

Now, you have a mechanism which might deflect or even buckle the SE king. Once it’s no longer dead vertical, yes, bad things happen. To do their jobs, compression members like to be straight. Even if you don’t buckle the SE king by jerking span 7 east truss loose, you have a severed east main truss, or it’s still in the process of severing itself, which is affecting the ability of the east truss to cantilever the north end of the span 6 east truss, again concentrating loads on the SE kingpost.

Okay, nine miles out on a half inch limb here, but bear with me, because now, you have a mechanism to rotate the pier 6 decks to the east. Not the best mechanism, but a viable mechanism.

When the SE kingpost buckles, the sway bracing between it and the SW king goes into tension and pulls the SW king to the...wait for it....east.

So, where does that leave us?

If you followed me through this rambling, highly speculative narrative so far, you can see:

1. A concentrated gravity load imposed by a LOT of construction materials and equipment, spacially localized, could have transferred to a single floor truss and thereby, could have overloaded a single, rusted, cracked, poorly welded, corroded main truss member past its tensile limits. Same goes for a gusset at an adjacent connection.

2. Severing the west main truss, midspan span 7 gives us an easy mechanism to explain why the SE king ceased to exist as a viable (and visible) entity.

3. Severing the east main truss, midspan span 7, gives us a handy mechanism to explain why the pier 6 superstructure rotated east.

Why is this important, and why did I lead you into this dark and lonely forest?

Because severing the west truss on span 7 makes the most likely case for obliterating the SE kingpost, AND gives us a viable (though still not my favorite) explanation for the east rotation of the pier 6 superstructure.

Yes, the loads of span 6 and 7 tend to rotate the SE king west if the span 7 west truss is severed, but if the SE king buckles before it leans west, the sway bracing pulls the SW king to the...east.

And that brings us full circle back to your question.

If construction loads greatly exceeded normal traffic, at any given point on the trussed span, the load imbalance would affect the east truss more than the west truss. The cantilevered floor trusses amplify this effect.

If we like the west truss severing first, then point construction loads do not help us buckle the SE king, but point construction loads do give us the best chance to rotate the pier 6 superstructure to the east.

Now...before you take this to any banks, remember, we’re talking about VERY slight POSSIBLE differences in probabilities here, in a foolhardy attempt to explain something we didn’t see, and haven’t got to look at yet in detail, in an event where bad things happened so quickly and successively that critical members were probably still failing in the span 7 truss assembly, even after it broke loose and was in free fall.

The point of all this is not to say what happened, or even what might have happened.

The point is to show you what any answer to the question you raise will entail.

The point is to show you some basic structural dynamics processes, in the hope that your gut level “feel” for how bad things happen will increase.

If somebody else posted this answer to you, I could poke a million holes in it without even going for a second cup of coffee.

But you asked, and I think it was a good question.

I like the idea of point construction loads failing the bridge.

I like the idea of frozen bearings failing the bridge.

I like the idea of bad welds, fatigue cracking, broken bolts, and lingering damage failing the bridge.

The differences in probabilities related to these possible causes are insignificant in my opinion. I don’t have enough information to say yes or no.

I won’t till the final report comes out, and even then...

But if it makes you feel any better, I don’t like resonant vibration, as a mechanism for failing the bridge.

I don’t like construction traffic overloading the bridge.

I flat can’t stand scouring as mechanisms causative in this bridge collapse.

Construction traffic point loads? Exacerbated by the cantilever design of the floor trusses, and possibly the west lane construction traffic, east lane normal traffic scheme?

Yeah, maybe.

You’re still in the running, good question.


94 posted on 08/14/2007 4:47:13 AM PDT by jeffers
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