Check out the girder farthest right in this photo. Is the beginning of The buckled portion at a splice location? The kink in the top flange at the start of the buckle in the foreground looks very abrupt as well. Maybe that's just what a flange yielded laterally looks like.
I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.
The double curvature buckling behaviour here is indicative of column buckling, caused by restraint against thermal movement. I remember a previous thread about a similar failure, but can't locate it.
Looks like a lateral-torsional buckle under gravity with inadequate bracing. Should lateral horizontal bracing been placed at the top flange as in a curved bridge? Placing the first couple of girders must have been wobbly. I guess it could have been triggered by some thermal restraint, particularly if the girder is wanting to shorten, but the stability must have been borderline.
Thermal restraint doesn't sound right during a girder erection operation -- I don't think the temperature swing would be that significant.
KootK, I think the abruptness is likely due to the end segments having their permanent diaphragms installed, while it looks like the center segments they were picking just have some temporary erection bracing installed. It's tough to tell, but I think the temporary bracing may have only been lean-on style -- so not providing much actual additional stability against LTB/LFB.
It's pretty clear the two outer sections were there first, held up by scaffolding and the cranes hence the missing segment in kootks picture. They were then lowering in the middle bit and then securing it somehow and then bracing against the other sections. the only connection to the ground was at the end of the two initial sections right at the end if you watch the video slowly
note the two cranes holding up the two cantilevered sections. if they went a bit too far up or even not completely vertical then you've got a rather wobbly beam and once it gets even a little out of straight, self weight will force it more and more over.
those bracings are puny.
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We do get some crazy 24hr temperature swings in Alberta. I'd considered thermal induced compression buckling too.
I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.
In the Accidents and Disasters thread on this, I suspected restrained thermal expansion after the bent beams were installed and locked on place - and the other good beams were the proper length and were properly mounted to allow sudden thermal expansion on the first "clear day, bright sunshine" in March.
But look also at the lowest picture, furthest right beam going away from the camera. That beam does NOT look like it is "aimed" at its matching beam on the far side of the bridge by at least 6-8 inches. The beams may have been "encouraged" to connect a "bit vigorously" by bending them sideways so they'd connect.
Vertical weight does not seem to be involved. There's no rotation of the webs.
If thermal expansion - how much temperature change on a completely restrained beam - end-to-end of the whole bridge - is needed to force that large a deflection sideways?
Possible distirtion with the temperature change, but the middle section alone would have had to lengthen by 6" or so to get this kind of lateral distortion in the picture. For the length of the central girder I see, that seems extreme. I think there is something else going on here.
Today's paper indicates they are 40 tonne girders. That seems a bit hefty to me but I'm not experienced in bridge construction. One comment made by Mike Bartlett, a structural engineer and professor at the University of Western Ontario: "My guess is that most of the problem occurred due to the weight of the girders themselves, which is not trivial." He also stated "It sounds crazy to say it when you look at these pictures but the buckling could be what's called elastic lateral-torsional buckling. If you take the load off the girder, the girder may be able to return to more or less its original shape."
Interesting thoughts. Others are wondering if the wind had anything to do with it. Apparently there were fairly strong winds prior to the buckling.
Mike:
You have to be very careful interpreting/reading those photos. Telephoto lenses do some really funny things in foreshortening/lengthening lengths in the line of view, which causes lateral distances or vertical distances (perpendicular to the line of view) to appear far more distorted than they actually are. Take a look at videos of highways, railroad tracks, pipelines, etc., it takes the truck hours to get here (long dist. of view and travel) and it’s climbing mountains not just interstate highway grades in getting here. Those photos are deceptive, if you aren’t careful in studying them.
The end thirds of those girders do have some real construction bracing, offering some lateral stability btwn. them as a framing system, and likely some shoring out near their splice ends, at least during erection. I’ll bet the center third of each girder was as flexible as a wet noddle, and they don’t have any decent erection bracing btwn. those portions to stiffen them laterally. I’ll bet they set the end portions which were stiffer, braced them, and felt pretty confident about how stable everything seemed. Then, they assumed they could just hang the center portions off the two end portions, on any single girder line, just like any other hanging beam. They picked those center portions off a truck, from the top flanges, and this would not have given them much hint of how flexible they were. The splices may not even have been made up completely yet, on all the assembled girders. The center portions did hang there until they started removing the shoring under the end of the girder end thirds, and this added significant compression to the top flgs. of the center portions of the whole girder, and all hell broke loose. BA’s original video does show a side view of the bridge prior to the accident, without much/any shoring under the fully assembled girder lines. The point is, the center portions will hang there just fine, but start removing the shoring and you triple or quadruple the bending stresses in the flgs. at mid span.
Daily max/min temperatures can been in link below. There were some warm days leading up to the girders buckling (buckled morning of the 16th). They said the day before they couldn't work because of wind...so if the outer girders were installed on the 14th there was a max/min temp of +16.8/+2.1 C. When the girders buckled the temperature was closer to -3 C. It looks the temperature was trending downward in the 24 hrs leading up. Seems that would tend to put the center span in tension.
It does look like only the center portion has buckled. And looking at the very beginning of the video in the article that BA linked to, you can see there are 6 girders in place. Only the 3 shown in the pictures above have buckled. Maybe faulty bracing between the 3rd and 4th girder?
BA:
40 tonnes is only 500-600lbs./ft., the girders are about 135' long aren’t they, maybe not so outlandish, 1.2 cu.ft./(ft. of length). I didn’t exactly have the term ‘elastic buckling’ on the tip of my tongue, but I’ll buy that. I don’t see any sharp kinks anyplace or local bucking in the top flanges, so I was certainly thinking, not much real yielding, localized yielding, had taken place. The top flanges have nice clean curvatures in their rolled over distortions. The top flgs. of the middle portions also seem narrower than the flgs. on the end third portions, thus less stiff laterally. The webs and stiffeners look pretty good and straight, and the bottom flg. rolled right with the webs. The bottom flg. saw almost no yielding or high stresses, so they’re good, but I’ll bet they bent the hell out of parts of the splice pls., and maybe a little bit of the girders right at the splices. If the City, County, Province will give them a bit of a break, I’ll bet those center portions can be heat straightened with no loss in ultimate strength of the girders or final bridge. The top flgs. will req’r. the most work, localized yielding and residual stresses from the heating, but they’ll finally be encased in the deck haunches/conc. Furthermore, as you load the girders, in the final bridge, you essentially just stress that local region back up to its previous max. on a slightly shifted stress/strain curve (elastic portion of the curve) before it continues up the original stress/strain curve, but the conc. is there to help with that too.
These plate girders/bridges are at their most dangerous during erection. Nobody wants to spend too much money on temp. bracing, it’s only going to be there for a short time. There won’t be any strong winds during that short time period. Do we really need all that bracing, flip a coin. And, the worst of the worst is the first two girders, until you get some real solid bracing btwn. them, then the rest can be braced back to the first two while a crane hold them in place for a short time.
Continuing CANPRO's thoughts, the centre segment wouldn't just be in axial tension. The bearings, where the restraint would likely occur, are well below the neutral axis leading to positive bending and additional compression in the top flange.
Would the bearings have been fixed against sliding during erection?
In Missouri they'd call it good and just stripe the lanes to match. Just kidding - but there was a Saint Louis contract for demolition of a multiple arch bridge over RR tracks that they 'staged' only forgetting the resisting forces still needed to be applied. (
In this case it looks like there was a conversion from bending to torsion as some minor deviation in the straightness or loading got amplified by the self-weight of the girders. Looks exactly like the failure one gets from a simply supported vertical strip of cardboard with a bending load.
Is it uncommon to place the cross bracing before the crane releases the weight to the supporting structure?
500 - 600 plf for a plate girder is pretty common. The exterior girders are not buckled and they have cross-frames or temp bracing installed between them along their entire length. The girders that buckled don't have the same bracing between them in the center sections that buckled. My armchair analysis says the bracing wasn't adequate.
The permanent cross-frames I design for straight plate girders are usually K braces made of at least a L4x4x3/8. If the girder spacing to height ratio becomes to low I will switch to X braces. I also specify hardwood 4x4 struts at 4' maximum spacing for the bottom flanges and 1/2" tension ties at 4' maximum spacing for the top flanges. This helps to keep everything braced when the deck is being placed. After seeing this I don't think any of it is overkill.
It's most common to have a reduced number of braces required before the crane releases the girder (enough to provide stability with a minimum lateral load during the work period), and then more braces that need to be installed before the end of the shift or before winds exceeding X mph occur.
Of course, that requires the contractor plan in advance to know how long a weather window they need to get a girder and bracing up, compare that to their weather forecast, and make the right go/no-go call.
It's very possible that pair of braces at the center were the release bracing, that they were planning to install additional bracing prior to the end of the shift, and couldn't because the wind speeds exceeded their crane's specs. Either poor planning or just unlucky.
Although that doesn't explain why the buckling didn't occur until monday morning.
