Miami Pedestrian Bridge, Part XII 34

[zeusfaber]

A continuation of our discussion of this failure. Best to read the other threads first to avoid rehashing things already discussed.

Part I
thread815-436595: Miami Pedestrian Bridge, Part I

Part II
thread815-436699: Miami Pedestrian Bridge, Part II

Part III
thread815-436802: Miami Pedestrian Bridge, Part III

Part IV
thread815-436924: Miami Pedestrian Bridge, Part IV

Part V
thread815-437029: Miami Pedestrian Bridge, Part V

Part VI
thread815-438451: Miami Pedestrian Bridge, Part VI

Part VII
thread815-438966: Miami Pedestrian Bridge, Part VII

Part VIII
thread815-440072: Miami Pedestrian Bridge, Part VIII

Part IX
thread815-451175: Miami Pedestrian Bridge, Part IX

Part X
thread815-454618: Miami Pedestrian Bridge, Part X

Part XI
thread815-454998: Miami Pedestrian Bridge, Part XI

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[Vance Wiley]

Thank you for confirming what I have sensed for a while.
I have to wonder what Berger found for member 11.

The term "hogging moment" is not familiar to me. It is referring to the load drawn by M/L, right?

 

[SFCharlie]

Conventionally sagging moment is considered positive and hogging moment is considered negative. In simply supported beams the bending moment is a sagging moment. In a cantilever the bending moment is a hogging.Apr 11, 2017


SF Charlie
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[Earth314159]

The term "hogging moment" is not familiar to me

Hogging moment is a negative moment over a support. I think it is more used in the common wealth than the US (I am not too sure how common it is in the US). You usually associate a hogging moment with negative bending and a high shear together at a support. You can use it for a cantilevered beam but it is usually intended for a continuous beam.

 

[Vance Wiley]

Thank you, SFCharlie . EDIT And thank you, Earth314159. Your reply came in while I was typing. END EDIT

The calculation by Earth314159 shows that member 11 should not have failed under self weight only in the independent simple span condition which existed at the completion of Stage 3.
Which seems to leave node 11/12/deck as the suspect.

Apparently the capacity of the joint as given by the code provisions represented on page 31 of the FIGG Power Point presentation of March 15 do not apply after the joint has undergone severe cracking. Not surprising.

 

[SFCharlie]

I still don't trust the little bit of concrete between 11 and 12...

SF Charlie
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[3DDave]

If I've followed it correctly, "hogging" also applies to ships where a wave lifts the center abeam of a long ship, leaving the bow and stern with less support.

 

[Spartan5]

Further to the terms sagging and hogging and its relation to ships:

https://en.wikipedia.org/wiki/Hog_chains

 

[Earth314159]

If I've followed it correctly, "hogging" also applies to ships where a wave lifts the center abeam of a long ship, leaving the bow and stern with less support.

I am not a ship designer but it is the same concept.

 

[Vance Wiley]

You are right on track. This is the place to have focused on. Had the top of that fillet been maybe a foot higher and the little fillet below 11 to the deck been maybe 3 feet longer there could have been room for lots of reinforcing across the construction joint.
But no one was focusing on this joint as loaded at the end of Stage 3.

 

[Earth314159]

I still don't trust the little bit of concrete between 11 and 12...

Once you get a slip failure, the compression stresses between #11 and #12 increases. If you only take the DL case, you end up with a vertical reaction on #11 of about 1100 Kips (factored). You have to factor DL by 1.4 instead of 1.25 when the DL is considered by itself. This makes a horizontal component of 1750 Kips. The concrete is 1.25' high by 1.75' wide for a stress of 5.6 Ksi (38MPa) which is pretty high. Assuming we can get 1% horizontal steel in the cage, you can go up to 30 MPa. However, even at 38 MPa, it isn't going to fail in compression unless there are other contributing factors.

I suspect the cracks parallel (more or less) to the diagonal you see are from varying stress across the slip failure surface. The pour joint is not perfectly flat. The shear stress on some parts of the surface are higher than others and #11 is not well tied together. The differential stress helps initiate the cracks you see. The compression between #11 and #12 makes the cracks worse. In any case, that is what I suspect.

No mater how you cut it, this joint is stressed far beyond acceptable levels.

 

[Earth314159]

I should also mention that the rotation of the base of #12 increases the compression stress of the bit of concrete between #11 and #12. The compression causes a slight rotation at the base of #12 that causes the vertical crack on the south side of #12. This focuses the compression lower to the base of #12.

 

[Vance Wiley]

Capacity of column: 0.8*0.65*8.5ksi*24*21+8*30.6Kips=2230+245=2475Kips<2830Kips therefor NG.

So having 10 bars in member 11 like I think was intended (Section A-A Drawing B-39) would have increased the capacity by 61 kips and the member would still lack capacity from a code standpoint.
It certainly had design capacity for loads when the collapse developed.
Again, thank you for running the numbers.

 

[The Mad Spaniard]

Earth314159 (Structural)15 Aug 19 18:28
I should also mention that the rotation of the base of #12 increases the compression stress of the bit of concrete between #11 and #12. The compression causes a slight rotation at the base of #12 that causes the vertical crack on the south side of #12. This focuses the compression lower to the base of #12.

If the fillet (wedge) is compressed from #11 and from #12, and the PT bar is stressed, isn't it possible that it would "pop-up" vertically? Leaving #11 free to press more to #12. Also, given the sudden failure, don't we have additional forces due to dynamic effects (even from the sudden break of the reinforcing bars)?

Questions, questions...

But at the end on the day, the reinforced concrete was telling from March 11 2018 : I am cracking in a bad place. Please, get the hell out of here.

Live long and prosper.

 

[SFCharlie]

I still don't understand how being in the finished configuration helps 11. If I use a derick to lift a weight, the wire cable to the cab lifts the weight, but the boom is in more compression?

SF Charlie
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[Vance Wiley]

Again, you are on the right track.
Actually, by developing the "hogging moment" through the addition of PT C-1 and C-4 in the canopy AFTER the backspan is complete, more load is added to member 11. That additional load is about 311 kips, unfactored.
So the completion of the structure does not help member 11. It may have added capacity to node 11/12/deck by supporting/resisting some of the blow out forces.

 

[Earth314159]

I still don't understand how being in the finished configuration helps 11. If I use a derick to lift a weight, the wire cable to the cab lifts the weight, but the boom is in more compression?

It actually makes #11 worst (more compression on a highly stressed #11) but it makes the shear transfer at the base better. The shear transfer is the horizontal component of #11 minus the horizontal component of #14. This puts less shear across the pour joint. This assumes you could have gotten to the finished state without over stressing the joint.

I am not a lawyer but I think the issue was that the shear was the cause of the failure. There are all kinds of issues with the bridge. When comes to damages, it doesn't mater what the other issues were. I suspect the legal question is did the negligence of Louis Berger contribute to the failure mode that killed the people (or caused other damage). They were hired to review the completed structure. They missed multiple code issues for the final configuration but I suspect they will argue, all the missed items are not relevant since it was the shear failure that caused the failure. The other omissions could have lead to a failure but they did not lead to this failure. I can speed down the highway. I may get a ticket but I won't be charged with a crime. I can speed down the highway go out of control and kill someone. I will get charged with a crime. All the other times I was speeding did not mater to the final crime and charges. Each omission is likely considered a separate incident that did not happen to have a consequence (even though there could have been future consequences).

 

[Earth314159]

If the fillet (wedge) is compressed from #11 and from #12, and the PT bar is stressed, isn't it possible that it would "pop-up" vertically? Leaving #11 free to press more to #12. Also, given the sudden failure, don't we have additional forces due to dynamic effects (even from the sudden break of the reinforcing bars)?

The PT added to the shear stresses which I did not account for in the above calculations. Re-tightening the PT was the final straw.

You can not lift #11 with the PT. It is like standing on a skipping rope and pulling on it in hopes that it will lift you up. For lift up to occur, the rest of the frame would have to be strong (with an independent load path) and stiff enough to support the bridge. The bending in the deck and canopy are orders of magnitude too weak and flexible to support the bridge. If the canopy and deck were strong and stiff enough to do this, there would not have been a failure (or perhaps at the very least a very slow progressive failure would have occurred).

 

[Earth314159]

So having 10 bars in member 11 like I think was intended (Section A-A Drawing B-39) would have increased the capacity by 61 kips and the member would still lack capacity from a code standpoint.
It certainly had design capacity for loads when the collapse developed.
Again, thank you for running the numbers.

Correct.

Adding vertical steel to a column has little effect on it's capacity. 1% is minimum to take the full section into account and anything more than 4% is not practical. When there is a compression issue in a diagonal or column, it is much better to increase the area, then the strength, then as a last resort the vertical steel.

 

[The Mad Spaniard]

Quote (The Mad Spaniard)
If the fillet (wedge) is compressed from #11 and from #12, and the PT bar is stressed, isn't it possible that it would "pop-up" vertically? Leaving #11 free to press more to #12. Also, given the sudden failure, don't we have additional forces due to dynamic effects (even from the sudden break of the reinforcing bars)?

The PT added to the shear stresses which I did not account for in the above calculations. Re-tightening the PT was the final straw.

You can not lift #11 with the PT. It is like standing on a skipping rope and pulling on it in hopes that it will lift you up. For lift up to occur, the rest of the frame would have to be strong (with an independent load path) and stiff enough to support the bridge. The bending in the deck and canopy are orders of magnitude too weak and flexible to support the bridge. If the canopy and deck were strong and stiff enough to do this, there would not have been a failure (or perhaps at the very least a very slow progressive failure would have occurred).

I was taking about the "fillet" , the concrete wedge in between 11 and 12.

Regarding having the other truss built in the final stage, it confines the node horizontally. Then it is only a matter of #11 to be able to transfer horizontal loads to #12 which is now restrainded on the other side by the shorter truss with forces (may be smaller) in the oposite direction. But again, the "wedge" has to be there to transfer the load. If the wedge pops-up, then here we go aging with the dynamic effects. Ball park, many times these dynamic effects are 2 times the force that is being let go.

 

[Earth314159]

I was taking about the "fillet" , the concrete wedge in between 11 and 12.

I see.

You could get an apple seed type failure. Most compression failures are shear failures. It is a plane at an angle to the longitudinal compression axis that shears (the angle varies with the amount of ties etc). It is really a shear friction failure through a monolithic section at an angle to the axis. It is pretty much like a concrete cylinder test failure plane (except rotated 90 degrees).

The piece of concrete between #11 and #12 can shear and pop out just like any concrete columns or cylinder. However, in the final stage (assuming there was no damage in intermediates stages) the compression would not be high enough to do this. The compression stress is high but there would be some shear fiction capacity through the pour joint that would help reduce the compression.

If the intermediate stages are ignored, the whole joint design in the final stage is unnecessarily tenuous and barely meets code (perhaps a little under code). Even in the final stage, you really have to scratch to make this joint work. Anyways, I think this is what Louis Berger is clinging too. The only other factor is the tube stays that Lois Berger could argue as an alternate load path for the joint. They may argue that the joint was allowed to be over-stressed since the tube stays could add some support and prevent that one failure mechanism. It is tenuous but it is up to the prosecution to prove the shear friction mechanism in the joint would have been too weak which would then cause a failure in the final stage. Damage to the joint in the intermediate stages would be immaterial to their case (if the lawyers would make this argument).