Miami Pedestrian Bridge, Part XIII 81

[JAE]

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

Part II
thread815-436699

Part III
thread815-436802

Part IV
thread815-436924

Part V
thread815-437029

Part VI
thread815-438451

Part VII
thread815-438966

Part VIII
thread815-440072

Part IX
thread815-451175

Part X
thread815-454618

Part XI
thread815-454998

Part XII
thread815-455746


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[The Mad Spaniard]

Kestrel42 (Bioengineer)26 Oct 19 20:16
Reading through FIGGs analysis as well, Vance. I find it supremely unconvincing.

Allow me all of you to provide you a piece of information for you to decide if it is relevant or could provide an explanation for the events of the week of march 10, 2018. Read below

Both MCM and FIGG were at the time involved in a lawsuit against the FDOT decision to award the 800million dollar reconstruction of the I-395 viaduct in Miami. At the time, the FDOT had awarded Archer-Western the project. But the MCM-FIGG team complained that the contract had been awarded unfairly. Around May 9, 2018 the team MCM-FIGG withdrew their protest. You can Google all this for further info.

Now, lets especulate a lot, really alot, (you guys can explore other possibilities) :

So, any "bad news" like there is a problem with their "jewel" in Miami like cracks or that now the road has to be closed for a long period of time to repair the structure (remember it was "no closed road" construction) was going to impact negatively the result of their lawsuit. Furthermore, If FDOT structures or construction personnel learnt about the problens (big, huge cracks) in the structure they could shut down inmediately the project and request a extensive a time consuming review. And, the newspapers would had a feast talking about it.

Now, some, hopefully very, very, very few, people, under this situation, may decide to not distribute the bad news and resolve internaly the problem fast and quietly. This may have worked for them in the past in other projects. Did it happen here, I do not know and I have no proof and I am grasping for straws. But at this moment what we have is a set of decisions that do not make any sense in the typical construction project. So, maybe we have to explore explanations that look almost unthinkable under normal circunstances.

Anyway, treat all above with a grain of salt the size of Mount Evrest.

 

[Earth314159]

Earth,
Do you know that? Do you know how it was supported at the time of cracking?

Yes, it was in the field reports at the time and later in the NTSB reports.

Although, unlike the deck, I would say that the PT in #2 and #11 would contribute to the shear cracks.

 

[Earth314159]

My opinion is that this was an indeterminate, non-redundant structure, so we disagree.

How do you have a first order indeterminant and non-redundant structure? It is contradicted by definition.

 

[Vance Wiley]

EDIT - Found the source - finally.
thank you jrs 87.
I was sent to this site by someone here - but I have lost that link and cannot thank him directly. But thank you for the link - kinda tough reading for an old guy but I did glean some jewels there. I now have less confidence in the AASHTO shear friction model. And this structure may have fell somewhere in a danger zone of reliability even if it did meet those design requirements. See what you think - -

https://www.pci.org/PCI_Docs/Public...f_interface_shear_transfer_in_AASHTO_LRFD.pdf

The issue of shear friction in this case may not be so cut and dried as it first seems. The following pieces are from a study of the reliability of AASHTO design for shear friction. It touches on several important things.
I need a statistics guru to help here. Anyone?
First - apparently the target relliability index is 3.5 . That seems to provide a probability of failure of 0.04%. Methinks that means one in 2500 will fail. We have how many bridges in the USA?
pf = failure probability
The probability of failure goes up as the reliability index goes down. Example: “In the latter case, a resistance factor of 0.55 was needed to satisfy the target reliability index of 3.50. The AASHTO LRFD specifications–based resistance factors led to reliability indices of 2.80 (pf equal to 0.3%) “.
Now we are down to one failure in 333 bridges.
Help me here - I am losing confidence rapidly.

Factors which influence this?
The results of the parametric study show that the AASHTO LRFD specifications reliability index values depend on the values of the design variables.

Compressive strength of concrete f�c
For normalweight concrete with fc ' between 41 and 55 MPa (5.9 and 8.0 ksi), the AASHTO LRFD specifications reliability index was 2.75 (below the target reliability index), which is significantly higher than the target reliability index when fc ' is greater than 55 MPa. The reliability indices of Soltani et al.’s model were more consistent than those of the AASHTO LRFD specifications IST model, and averaged around 3.50 for all bins.
So this is a one in 333 bridge except the concrete is 8500 psi and not 8000?

Roughness amplitude of interface R
For the tests with normalweight concrete, the AASHTO LRFD specifications reliability index was 2.70 for a roughness amplitude of interface greater than 3 mm (0.1 in.) and 1.55 for a roughness amplitude of interface less than 3 mm. Thus, the AASHTO LRFD specifications model was 1.74 times more reliable when the interface was roughened compared with smooth interfaces.
Now we are getting downto it - about one in 300if the roughness exceeds 3mm - 1/8" - and probably one on a lot less if roughness is less than 1/8".

Compressive force normal to the shear plane Pc
The AASHTO LRFD specifications reliability indices do not relate to the compressive force normal to the shear plane. The reliability index for tests with normalweight concrete was less than 2.87, with or without the presence of a normal force.
Another reason this is a one in 333 bridge?

Interface reinforcement index ρfy
In the tests with normalweight concrete using Soltani et al.’s model, more interface reinforcement led to higher values of reliability index. The lowest reliability index was 2.62 in the AASHTO LRFD specifications model, when the interface reinforcement index was between 2.8 and 5.5 MPa (0.41 and 0.80 ksi).

Background - -
Per Nowak and Collins12 and Robert,13 the structural reliability or survival probability of structures ps is given by Eq. (10). ps = P(Rm – Q > 0) (10) This is the survival probability of the structural system if the resistance value is more than the load value. Considering Eq. (10), the failure probability pf is determined by Eq. (11). pf = P(Rm – Q < 0) (11) The reliability index β, which is related to the failure probability pf , is defined by Eq. (12). β = –φ–1(pf ) (12) where φ–1() = inverse standard normal distribution function

Calculated the reliability index to be approximately 3.50, which is the target reliability index of most structural design codes, such as the AASHTO LRFD specifications. This target value of 3.50 means that the probability of failure is approximately equal to 0.04%.

The resistance factors of 0.9 (normalweight concrete) and 0.8 (lightweight concrete) in the AASHTO LRFD specifications model led to reliability indices of 2.80 and 5.38 for normalweight and lightweight concrete, respectively. For the tests with normalweight concrete, a resistance factor of 0.55 resulted in the target reliability index of 3.50. The reliability index of the current AASHTO LRFD specifications IST model for normalweight concrete tests is lower than the target reliability index, while the AASHTO LRFD specifications IST model for lightweight concrete is too conservative (no resistance factor needed to satisfy the target reliability index). These results showed the need to revise the AASHTO LRFD specifications IST model and the resistance factors associated with it.

I'm getting the idea bridge engineers do not get paid enough.

 

[Earth314159]

It shouldn't be too difficult for an engineer to figure out redundant load paths that the NTSB discussed.

You can add redundancy but it is a very difficult thing to codify and define exactly how much redundancy is required. The fact of the mater was that there was some redundancy in this bridge. If there wasn't, the bridge would have collapsed sooner. Those cracks gave plenty of warning which is one of the main purposes of redundancy. The #11 sheared at the base and #12 stop it from shearing off completely. That is redundancy.

You can argue that all properly designed and constructed structures have some amount of redundancy (even though it is an infinitesimal amount in some cases). The question really is how much redundancy is required before a structure is considered redundant and that question is not so easy to answer. The bridge that the NTSB gave as an example as being redundant didn't appear to me to be that redundant. They called it redundant because it had two trusses but the failure of one truss would cause the bridge to collapse. So that confused the question even further. They were showing a relatively non-redundant case as being redundant.

 

[Vance Wiley]

Like Gibbs on the series NCIS, I do not believe in coincidences.
I guess nothing is as simple as it seems. The duplicity runs deep.
For sure, engineers and politics do not mix.
No wonder there was no concern for safety - it did not dare fail - not now! That is beginning to sound less like an engineering decision and more like a business decision.
Thank you for that insight.

 

[Earth314159]

Vance, I read through the same article. I would have to dust off the old stat text books to figure the part with stats in it.

I think the main finding was that you need to have separate factors for the normal forces due to stretching rebar and the dead weight to get a more consistent index. This would alter the code equation. The ratio between the actual failure and the code resistance would be more consistent from case to case. It doesn't actually look like a significant change in terms of difficulty but just changes consistency.

Code writers want consistency. Engineers want ease of use. Contractors want less concrete and steel. Developers want more money.

 

[Vance Wiley]

Regarding AASHTO shear friction design -
Am I reading the report correctly? One chance in 333 that a shear friction design will fail?
I can't believe that. Can I?
EDIT ADD
Maybe I should read one out of 333 would fail if it reaches factored load conditions?
That makes more sense.

 

[SFCharlie]

The WJE report make me so infuriated that I can't think straight, so I'm going to take it one step at a time:
"Concrete Mixture Proportions
For the fabrication of laboratory test specimens, WJE developed a mix to closely match the original mixture
proportions (Class VI 8,500 psi) using materials available in the Chicago area1. The original Class VI 8,500
psi mix had a target slump of 7 to 9 inches, an air content of 0 to 6.0 percent, and a 28-day design
compressive strength of 8,500 psi. WJE developed a mix to closely match these properties, which is
provided in Table 4.1. The following describes the developed mix as it relates to the original:
The water to cementitious ratio was kept at 0.33.
The total cementitious materials (cement, slag cement, fly ash, and metakaolin) was kept at 800 pounds
per cubic yard (lb./yd3)
The portland cement to slag cement ratio was increased in order to facilitate early strength development.
The original mix had a portland cement to slag cement ratio of 0.76, and the mix developed had a ratio
of 2.45."
how is this plausibly a similar concrete?

SF Charlie
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[hokie66]

SFCharlie,
I agree that WJE did their reputation harm by somewhat defending the FIGG design. In many cases, WJE has been retained not by designers, but by the other side. If NTSB had retained them, their report would probably have taken a different tone.

 

[Ingenuity]

If NTSB had retained them [WJE], their report would probably have taken a different tone.

I have been thinking about this too and unfortunately came to a similar conclusion that they were just a 'hired gun' - professionally disappointing.

 

[Brian Malone]

Thank you, Vance Wiley for the shim info. Thanks, Eart314159 for the nuances of redundancy. I did have to reevaluate my black/white consideration of redundancy - the FIU bridge did not fall immediately and considering a bridge like the Ohio Silver Bridge collapsed in 12/1967, like a line of dominoes with the breakage of one eyebar link in a double bar suspension chain. To the average joe, like me I would have thought the Silver Bridge design would be able to stand with one eyebar in the chain and the double eyebar would provide safety margin.

 

[Vance Wiley]

You got it! I am now thinking that report and testing was intended to be a head fake.
I bought into it for a bit until I was so subtly told:
I see this as shortcomings in the WJE report:
Add to that the fact that they did not test a joint prepared to FDOT specs as FIGG istructed the contractor. The head fake comes when FIGG says the tests prove their design was correct. But their instructions to use FDOT specs for joint preparation conflicts with their stated design intent and is the final word chronologically and leaves nothing learned by the tests.
Thanks,

 

[samwise753]

I also don't see how a lab test of an isolated member would be considered one-to-one with the full-size, complete structure. Like hokie66 keeps pointing out, that big beefy deck was being restrained by the twig like diagonals; that interaction doesn't get captured in WJE's test. Obviously, it would be incredibly expensive to rebuild the real thing, but, to me, that's where you'd know if it would really have stood up even with 0.25" roughing amplitude. My gut says you still have major cracking problems. The vast majority of concrete bending application deals with prismatic section for the entire length of bending element; this bridge was a single I-beam with an open web. The stress flowing through this beam was much harder to get a handle on than a prismatic beam.

 

[Earth314159]

The stress flowing through this beam was much harder to get a handle on than a prismatic beam.

The truss should actually be easier than a beam to determine the force distribution since there is less redundancy in a truss than a prismatic beam member. There is really only one place for the north end reaction to flow to and that is #11. 99% goes to #11 and 1% goes to bending in the canopy and deck. You don't have to make a planes sections assumption to analyze a truss.

The bending stiffness of the truss was orders of magnitude stiffer than the deck or canopy. multiple means of analysis from FHWA also matched up with computer models which gives a high level of confidence.

 

[Mark R]

I just saw these video on another forum I frequently visit. I don't believe I've seen these here previously:

https://www.youtube.com/watch?time_continue=348&v=hBjntrebxj8

https://www.youtube.com/watch?time_continue=8703&v=fdUf-_el9vA

 

[SFCharlie]

The bending stiffness of the truss was orders of magnitude stiffer than the deck or canopy.

Maybe it's just my inexperience, but the curved canopy looked as if it could be very stiff?

SF Charlie
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[Earth314159]

SF charlie,

In order to act as any strong back at all (so the diagonals could resist the deck PT forces), the bending stiffness of the canopy would have to be stiff relative to the bending stiffness of the truss as a whole. Another way to put this (assuming material were infinitely strong so we are only looking at the elasticity issues) is to ask how much would the canopy deflect over 174' with the same load as the truss as a whole? The deflection of the canopy would be in 10s of feet (if not more) and the truss would only be a couple of inches. If the stiffness of the canopy was more like a foot or two (with the same load as the truss as a whole), it could contribute significantly as a strong back but there is no way the canopy is that stiff. This is why you need a truss or another deep structural element to minimize deflections. This is also why the member axial loads are easy to predict with simple hand calculations. If the canopy or deck were that stiff, the structure would be significantly redundant and indeterminate.

As the base of 11 failed, the load was shifted to the bending of the canopy and deck (the canopy and deck try to rack vertically to resist the load). You can see how far and rapidly these elements bent. The elastic stiffness was negligible. The rotation quickly progressed to plastic hinges in the canopy and deck.

The truss cambers upward rather than the diagonals resisting the shortening from the deck. This is typical for PT beams. They will camber upwards rather than shearing the web.

If you have a determinant structure, you can PT all, some, none of the members and you will see that none of the member forces change. There is nothing to restrain the PT force except the individual member itself. I have had colleges try to run PT on light structurally determinant structures and wonder why the computer was giving them zero member forces. They asked me what they were doing wrong with their model. It is deflecting but there are no forces. I told them nothing is wrong. That is what happens.

 

[Earth314159]

I should also mention that the moment of inertia is approximately proportional to the cube of the depth (bd^3/12 for a rectangle). The canopy is much shallower than the truss).

 

[samwise753]

Earth314159, under uniform dead load (which is basically what the structure was under at the time of collapse), every single node had to handle shear, moment, and axial forces; a truss, by contrast only cares about axial forces in the members (get out of here, Vierendeel; you're not a real truss!). Aside from it probably being impractical due to insane weight, had this bridge been a prismatic section (just have constant thickness web instead of open web verticals and struts), I can wL^2/8, wL/2 and My/I all day to get the moments, shears, and stresses at the critical sections. That's back-of-napkin, Mickey Mouse stuff. What FIGG put out was incredibly more complicated to assess than a prismatic concrete beam or a true, bolted gusset plate steel truss; it required FEA to be accurate. It might be a successful design concept with enough material, but it put concrete at a disadvantage.