Florida International Bridge Collapse

[Peter Dow]

Note: 950 ton weight should be checked.
North side= 950 kips vertical component
Diagonal factor= 1.7
Diagonal force= 1615 kips service load What the diagonal should have carried
...
Diagonal service load= 2015
Ultimate factor= 1.4 Note: 1.2 is only in combination with other loads. If dead load by itself, use 1.4
Ultimate load= 2261 kips ultimate What the diagonal should have been designed for if no post tensioning.

I can't get over 2261 kips using my concrete column spreadsheet calculator unless I use 14 x #10 rebar - diameter 1.25", area 1.23 square inches, in which case I get maximum allowable design factored load of 2312 kips.

So if they had used 14 x #10 rebars, somehow not tensioned the P.T bars with the mainspan in position (by building it in situ, for example) and kept everyone everyone off the bridge, it would have been a perfectly safe architectural folly!

 

[Peter Dow]

...
Diagonal force= 1615 kips service load What the diagonal should have carried
Add post tensioned rods 400 kips service load
Diagonal service load= 2015
Ultimate factor= 1.4 Note: 1.2 is only in combination with other loads. If dead load by itself, use 1.4
Ultimate load= 2261 kips ultimate What the diagonal should have been designed for if no post tensioning.
Add 2 -1 3/4” pt= 480 ult load Check for load factor, 1.2 used. Add post tensioning
Diagonal design load= 2741 Kips ultimate design load

Shouldn't the post tensioning load, because it is variable, be calculated as a live load with a load safety factor of 1.6?
Like -
Factored load = 1.2 x dead load + 1.6 x live load
- as per -

So where you have
bridge @ 1.4 = 2261 kips
P.T. bars @ 1.2 = 480 kips
Total = 2741 kips
(which is still a no-pedestrian factored load may I point out)

Might I suggest, equivalently
bridge @ 1.2 = 1938 kips
P.T bars @ 1.6 = 640 kips
Total = 2578 kips
(which still is a no-pedestrian factored load but it would allow for 163 kips more of a pedestrian load when subtracted from the same total factored load).

 

[Peter Dow]

Rectangular column
Column ID Pu Phi Fy f'c D B Ag # bars Bar size As % Pu
Diagonal 2741 0.65 60 8.5 21 24 504 10 7 6.01 1.19% 2187.19 Kip
Load fact= 1.09

I don't see where you get "2187.19" from?

 

[hardalee]

I don't see where you get "2187.19" from?

It is a pdf of a live spread sheet that calculates 2187.19 by the method I sent you.

1.2 is suggested as the load is well known. It is questionable.

I’m gone and have nothing but an iPhone so can’t doo much.

 

[DaveC426913]

steel is safer ?
steel cable and steel ... ?
burried concrete counter weights...? no canterleavers!

You're an engineer now?

 

[Peter Dow]

Actually, from the appropriate force vector diagram, we can estimate that the compressive force carried by the diagonal truss member which seems to have failed (number 10 in the NCE diagram = number 11 in the MCM-FIGG proposal page 115 and in my diagram below) is better estimated at about 85% of the dead load of the bridge.

With the kind help of a 14 day free trial of an online truss calculator, I modelled the truss of the pedestrian bridge and calculated how 50% of the weight of the bridge (about 950 kips) would be added to the bottom end joint of the truss and onto the north pier by

• the end span of the deck (130 kips - 6.8%),
• truss member #11 (777 kips - 40.9%) and
• truss member #12 (43 kips - 2.3%).

South ---------------------------------------------------------------------------------------------------------------North

Model parameters
I assumed that the canopy and truss members were 1/3 of the weight of the bridge and the deck represented 2/3 of the weight.
I modelled the canopy and truss members as a distributed load of 3.683 kips/foot.
I modelled the deck as a distributed load of 7.373 kips/foot.

Results
The end span of the deck adds half of the span's weight to the end joint - 130 kips, 6.8% of the weight of the bridge.

Member #11 adds 777 kips, 40.9% of the weight of the bridge, which equals an axial compression force of 1367 kips multiplied by the sine of the angle of member #11 to the horizontal.

The end column, member #12 adds 43 kips, 2.3% of the weight of the bridge, which equals half the weight of the end span of the canopy and the weight of member #12.

Conclusion
The axial compressive force of member #11 at only 1367 kips is notably less than had been calculated earlier when approximating that the deck only provided a tension force to the end joint and neglecting the real effect of the weight of the end spans of the canopy, the deck and member #12.

 

[RainbowSingularity]

You're an engineer now?

its a question (more precisely a series of questions around the difference between choosing concrete or steel for the super structure)
precisely based on what appears to be the more common use of steel for swing & hanging bridges for pedestrians.
the use of the vast amount of concerte in this bridge is surely something quite odd.
thus... there should be extensive computer modelling done prior to build that should be availible to access and review...
where is it ?

was there any vibration monitoring ?
had it been wind tested ?

with a constant velocity wind from the correct direction matched with the right amount of traffic vibration might it be
also...
possible to build up a harmonic loading that could load many tons of additional pressure ?

just a passing thought....

 

[Peter Dow]

Using the truss calculator again, I changed the support nodes from the end nodes to those 2nd-from-the-end to calculate the difference made to the truss member forces, to model what happens during transport of the bridge from building site for erection in situ.

As expected, when supported by the transporters, 4 of the cantilevered end members of the truss experience reversed compression / tension forces compared to when the bridge ends are supported in situ.

Probably the most relevant result is the tensile force on member #11, which is 304 kip which is the minimum tensile force which must be supplied by the P.T bars. This 304 kip (and more as member #11 experiences strain changes) adds to the compression force before and after the bridge is lifted on to the transporters.

I have summarised my earlier in situ results -

in comparison to the in transit results in this bar graph.

If anyone wants the force data to copy and paste, here is the text -
Truss member forces (KIP)
in transit in situ
M1 68 68
M2 -458 1920
M3 319 -684
M4 868 952
M5 -272 -308
M6 43 117
M7 88 49
M8 -587 -526
M9 634 583
M10 334 -857
M11 -304 1367
M12 43 43
D1 420 -1760
D2 -466 -2398
D3 -498 -2493
D4 7 -2051
D5 250 -1125
C1 0 0
C2 -317 1540
C3 460 2391
C4 465 2475
C5 -452 1642
C6 0 0

 

[hardalee]

Shouldn't the post tensioning load, because it is variable, be calculated as a live load with a load safety factor of 1.6?
Like -
Factored load = 1.2 x dead load + 1.6 x live load
- as per -

So where you have
bridge @ 1.4 = 2261 kips
P.T. bars @ 1.2 = 480 kips
Total = 2741 kips
(which is still a no-pedestrian factored load may I point out)

Might I suggest, equivalently
bridge @ 1.2 = 1938 kips
P.T bars @ 1.6 = 640 kips
Total = 2578 kips
(which still is a no-pedestrian factored load but it would allow for 163 kips more of a pedestrian load when subtracted from the same total factored load).

 

[hardalee]

Peter,

We are beating a dead horse.

The failure of #11 is a given we started with. We know it failed and that it was not heavily reinforced.

In order to know why it failed, we need to know more about the final design, the final construction, the cracking reported and what stressing or de-stressing was going on at the time. It think the visual evidence has given us all it can. We need the information ntsb has gathered from the site to go farther.

Nothing left but food for trolls.

Regards

 

[Peter Dow]

Peter,

We are beating a dead horse.

Speak for yourself.

The failure of #11 is a given we started with. We know it failed and that it was not heavily reinforced.

What we didn't know but now know because I have since calculated it - were the likely axial forces along member #11.
The compression force from the dead weight of the bridge I calculated as - 1367 kip.
The compression force from the P.T. bars - I calculated had to be at least 304 kip but in practice would have been more, perhaps significantly more so we should treat the P.T. bar force as a live load.

So the unfactored load on member #11 was at least 1367 + 304 = 1671 kip.

Factoring the load as 1.2 x DL + 1.6 x LL suggests they should have designed for a
Maximum allowable design factored load of 1367 x 1.2 + 304 x 1.6 = 2127 kip

I estimated from the NTSB video that member #11 used 10 x #7 bars which would suggest it was suitable for a factored load of only 2006 kip. which corresponds to a ratio of factored to unfactored load of 2006/1671 = 1.2.

To get to a factored load of at least 2127 kip, as my table suggests, member #11 would have needed 14 x #8 or 12 x #9 or 10 x #10 rebars.

Even if member #11 was not designed or constructed within code we cannot conclude that the failure of the bridge's bottom northern end joint was caused by a failure of member #11 per se.

The failure which the evidence of the video and photographs suggests is more likely to be with the design of the joint itself, an insufficiency of reinforcement in anchoring member #11 to the deck, leading to, I might suggest, shear fractures along the 2 planes either side of member #11 where they intersect with the deck which I have illustrated by annotating sheet B-8 as follows.

In order to know why it failed, we need to know more about the final design, the final construction, the cracking reported and what stressing or de-stressing was going on at the time. It think the visual evidence has given us all it can. We need the information ntsb has gathered from the site to go farther.

I may not know with 100% certainty but I can offer my expert opinion on the basis of the available evidence, which is worth doing meantime.

 

[Peter Dow]

Summary

A picture paints a thousand words so I'll summarise by adding a few sentences in red ink to this picture which I have extracted from the FIGG - MCM design-build team's own document pdf proposing to FIU that they get the contract to build the bridge.

What caused it to fail?

The bridge designers innovated (incompetently) a new I-beam design of bridge but where the I-beam's upright-supports (called an "open truss") join the deck of the bridge, the designers should have specified the necessary reinforcement to stop the severely stressed joints breaking apart - "should have" but negligently didn't and so the weakest link - the northern bottom end joint - failed first and it caused a catastrophic collapse of the whole bridge.

 

[Peter Dow]

The table of "P.T. BAR REQUIREMENTS" which I have quoted from the engineers' drawing sheet B-17 from the MCM-FIGG proposal for FIU pedestrian bridge pdf,

is not accurate and the requirements must have been recalculated and updated before construction because member #11 did have 2 P.T. bars fitted - as the photographic and video evidence of them taken in the ruins of the collapsed bridge proves.

I have recently posted here results of my own calculations of the truss member forces (compression or tension, in transit and in situ).

Now I have calculated what the appropriate P.T. bar tensioning requirements really were and produced this table and bar chart.

I calculate the P.T. requirement as a factor of about 1.3 times the greatest tension force that the member experiences, being half-way between the minimum tension acceptable and that times the load safety factor of 1.6 for a live load. 1.3 x is half way between the two acceptable extremes.

As you can see there is little agreement between my calculated P.T. bar tensioning requirements and what was initially proposed in B-17.

Here is my blow by blow analysis of each of the P.T. bar requirements of truss members 1 to 12.

M1 - Our figures agree that no P.T. bar force is required. Having said that, any concrete column that is being moved around or subject to vibration, side loads or possible earthquake forces would resist tensile fracture far better by prestressing so "no P.T. bar required" should not be taken to mean "no prestressing is required". For this kind of job, I would assume that some kind of prestressing is a "must" throughout.

M2 - B-17's "400" is even lower than the calculated tension in transit and this would cause a failure of M2 in tension. M2 also experiences more compressive force than any other member and so one might be curious as to why M2 was not the weakest link in the bridge that failed first?

As this photograph of the south end of the collapsed bridge shows, M2 was constructed 150% of the width of M3 and of all the other members.

We may presume that it was as a consequence of the special reinforcement which M2 received which allowed it to survive at least until M11 had failed.

M3 - B-17's "960" is higher than I calculate it needs to be.

M4 - Is always under compression so M4 doesn't need the P.T. bars that B-17 recommends.

M5 - Our figures agree that "400" is the correct P.T. bar force. However, because M5 is always under tension, I don't agree that a concrete column is required at all. The design would save weight by replacing the M5 reinforced concrete column with a M5 suspension cable.

M6 & M7 - Like M4 are always under compression, though the compressive force is so small (117 kip at most) I might speculate that calculations might reveal that the truss could hold up well enough without any M6 or M7 members at all and weight saved by a redesign involving

• removing M6 & M7 from the design altogether,
• moving the bottom node of M5 to the node where M8 meets D4,
• D2&D3 merging to become one member and
• C3&C4 merging to become one member too.

M8 - As per M3, B-17's "960" is higher than it needs to be and as per M5 this is a member that is always under tension and should be replaced by a much lighter suspension cable.

M9 - As per M1.

M10 - Remarkably close agreement.

M11 - The "bad boy" member #11 that B-17 forgot. We don't know what P.T. bar tension had been set or was being set when the bridge collapsed happened. I would recommend 390 kip, all other things being equal.

M12 - As per M1.

 

[Peter Dow]

What caused it to fail?

The bridge designers innovated (incompetently) a new I-beam design of bridge but where the I-beam's upright-supports (called an "open truss") join the deck of the bridge, the designers should have specified the necessary reinforcement to stop the severely stressed joints breaking apart - "should have" but negligently didn't and so the weakest link - the northern bottom end joint - failed first and it caused a catastrophic collapse of the whole bridge.

How hard can it be?

Here's my concept for a high shear strength steel joint for this sort of application.

Here's a closer look at my computer aided design images for the joint

So my concept is to use an steel I-beam to make something like a clevis joint.

The link is designed accept a cable connector.

 

[Railman]

Newbie 1st timer here...
The said crack most likely happened at the short 24 wd x 10" long x 8" horizontal block between #11 & #12. The crack most likely wasn't there before they transported, because if it was, they surely would have addressed it. It very likely happen'd while doing the 90' turn in bridge transport with one corner on elevated sidewalk area, & the diagonal corner going over the 10"? road divider. Their technique was to drive up on 10"? high road divider, & then re-position load, both vertically, & if you look closely at the time lapse video, the load shifted horizontally as well. While it shifted horizontally, ALL the north end load was on the inboard transporter, which put way more load on #11 tendons than they accounted for. The end result most likely would have been a vertical/diagonal crack in the 10" x 8" x 24" horizontal block, due to #12 & deck weight on said block. The Block had a grand total area, less than 1/2 of the #11 cross section. There simply isn't another crack location that fits the situation.

Why is this so critical?
#11 bottom had very little interaction with the deck to hold back the 1.7 million lb load, because it was poured as a cold joint after the deck was poured. Pretty much all that held #11 force was #12 bottom, which seemed to be working until it was decimated by #11 abrasion pushing past it. If #12 was a solid connection to deck, and #11 had soft connection by way of small amount of somewhat flexible rebar soft shear, virtually all of #11 would have been pushing on the short horizontal block. Consider that block had 2 big plastic conduits, & most likely a diagonal crack in it. Also consider when bridge failed. It failed while de-tensioning #11 bottom tendon which was providing a very large amount of friction between #11, & deck. Once that friction was lessened, I believe the block additionally split vertically, out the end of deck. I believe it climbed up on #12 because the crack was most likely at an angle. The rebar and pipe at the end of the deck was pretty much in tact. The explosive force was mostly above deck. That tells me the the block split, & climbed up #12, resulting in what looked like a dynamite explosion on two sides of #12. The rebar would have guided #11 along both sides of #12. This scenario fits all the videos, including the timing of failure points.
The #11 bottom tendon with hydro jack still attached can be seen ejecting out of blister past worker. When canopy slammed into top 1/3 of #11, it stretched and snapped tendon for ejection. The bottom of tendon zippered out bottom of #11 as soon as it started to slide across deck. At this point the tendon was in tact.

Everything in this analysis is evident in all the videos. The evidence is there, & it all adds up. I don't know how to post videos, or picts on here, but I suspect you guys have seen them all.

Newbie, Railman, Joe

 

[Railman]

Too much to repost, so here's a link with better description......
http://www.contractortalk.com/f11/fl-bridge-collapse-389874/index8/

Joe

 

[Peter Dow]

I apologise because many of the images which I had posted above remain "hidden" because I have been let down by a service problem with an unreliable image hosting website. I'll re-post a few of my images using another hosting site and I can do the same for other images on request.

I have summarised my earlier in situ results -
in comparison to the in transit results in this bar graph.

The failure which the evidence of the video and photographs suggests is more likely to be with the design of the joint itself, an insufficiency of reinforcement in anchoring member #11 to the deck, leading to, I might suggest, shear fractures along the 2 planes either side of member #11 where they intersect with the deck which I have illustrated by annotating sheet B-8 as follows.

A picture paints a thousand words so I'll summarise by adding a few sentences in red ink to this picture which I have extracted from the FIGG - MCM design-build team's own document pdf proposing to FIU that they get the contract to build the bridge.

Now I have calculated what the appropriate P.T. bar tensioning requirements really were and produced this table and bar chart.

I calculate the P.T. requirement as a factor of about 1.3 times the greatest tension force that the member experiences, being half-way between the minimum tension acceptable and that times the load safety factor of 1.6 for a live load. 1.3 x is half way between the two acceptable extremes.

As this photograph of the south end of the collapsed bridge shows, M2 was constructed 150% of the width of M3 and of all the other members.

Here's my concept for a high shear strength steel joint for this sort of application.

 

[Railman]

I apologise because many of the images which I had posted above remain "hidden" because I have been let down by a service problem with an unreliable image hosting website. I'll re-post a few of my images using another hosting site and I can do the same for other images on request.

 

[Peter Dow]

Too much to repost, so here's a link with better description......
http://www.contractortalk.com/f11/fl-bridge-collapse-389874/index8/

Joe

I joined that "contractortalk" forum to post in that topic, which I did successfully, but on my next visit when I logged in I got the message

"You have been banned for the following reason:
Not a contractor
Date the ban will be lifted: Never"​

Charming.

I noticed you had a question about forces Joe but it wasn't clear what you were asking and I wasn't too hopeful that I could answer your question.

What I can do is post these two images which show the detailed results of my truss force calculations.

The first is when the bridge is supported at the ends, after it has been placed in position.



The second is when the bridge is supported at the nodes which are 2nd from the ends, like when the bridge is on the transporters when it is being moved into position.



These results don't tell me or anyone else the detail of what is happening inside the nodes. The node is a model, a simplification which allows for a mathematical analysis, which treats the junctions between truss members as single points and does not distinguish between parts of the junctions so could not, for example, tell us where precisely the forces were concentrated, where the weakest point was and where the failure occurred.

The best I can do in that regard is draw a diagram with purple ink showing where I think the weak points which failed were, but there are not any more detailed force numbers which are more detailed than the truss force calculations already given.

What was the exact force in that particularly purple bit, right next to that slightly less purple bit? I don't know.

 

[hardalee]

Peter,


Finally, new information.


The NTSB said the workers were tightening the post tension rods as we suspected, adding compressive stress to the first diagonal south of the north end. This was likely to help close the currently reported but unknown cracking at the north end.


The rods usually would have been loosened as the member that failed , number 11, was a compression member and the additional compressive stress would not have helped.


It is said that one rod was already stressed and they were stressing the other one of two.


The likely failure was at the anchor in member 11 in the area of cracked concrete at the bottom of the diagonal. This highly stressed concrete would have failed as the wedges of cracked concrete moved against each other in an area that had openings for drains. Once the anchor failed, the column would have lost area at its base on one side and the other stressed rod would have introduced bending in the column which together with the loss of compressive area caused an explosive failure.


The next diagonal to the south then became a compression member taking load down into a member that was no longer a truss at its north end and failure was assured.


The quantity and placement of mild steel reinforcing in the area of the anchor and if any voids existed behind the anchor is currently unreported. I would have expected to see the area of the anchor highly reinforced with bursting steel to distribute the high compressive stress over a larger area.


I await more information.


Regards,