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# Miami Pedestrian Bridge, Part IX14

## Miami Pedestrian Bridge, Part IX

(OP)

### RE: Miami Pedestrian Bridge, Part IX

Further development from recent court proceedings: https://www.nbcmiami.com/investigations/Engineers-...

I find the statement about conflicting meeting minutes troubling:

But FIGG has challenged the accuracy of the minutes of the meeting, prepared by BP&A, and six weeks after the collapse provided its own version of the meeting to the National Transportation Safety Board, calling them "corrected minutes."

FIGG's version made "significant substantive changes" from the original minutes, according to a lawyer for The Louis Berger Group, an engineering firm also being sued in the civil cases.

I would think that all professional engineering companies require the chair of the meeting to send out a draft of the meeting minutes to all attendees for review and update with any comments or missing information. The final draft isn't issued until everyone agrees, so I find it hard to believe "corrected" meeting minutes issued 6 weeks after the collapse to be considered valid once checked against e-mail records provided by the parties involved.

This also highlights the importance of documentation in our profession.

### RE: Miami Pedestrian Bridge, Part IX

I don't know how they did it there, but most of the meetings I've ever been in, any minutes were pretty rudimentary and were not emailed around until everyone agreed, etc. So I wouldn't doubt that the minutes were incomplete or omitted items that people said, etc., unless they purported to be otherwise.

### RE: Miami Pedestrian Bridge, Part IX

I don't think the Minutes of the Meeting on the day prior to the collapse carried much weight in the case.

FIGG is the designer. Only the designer has the right to modify or repair the bridge. The designer is also charged to evaluate the severity of the cracks and their impact to the structure. He is the sole party to decide if a repair is needed, when and how it is to be executed.

FIGG proposed to re-tension the truss members. The MCM contractor was executing FIGG's repair scheme and FIGG knew traffic was running underneath and did nothing to halt the remedial work. The bridge collapsed "during" the execution of FIGG's repair scheme.

Whatever written on the Minutes can't change the above.

The NTSB published photos, that shows a tape can be inserted to a depth of 4" and then 6" into the cracks of the slab and Member 11 respectively, were taken by the workmen on 13th and 14th so the participants to the meeting on 15th would know full well the severity of the cracking. If FIGG concluded, there is "no safety concern" as recorded in the voice mail then that is enough to demonstrate FIGG's competency in this project.

### RE: Miami Pedestrian Bridge, Part IX

Unless the minutes of the meeting were a condensed version of a recording, it is "he said, she said". There were probably notes taken during the meeting, but the minutes would have been prepared and distributed later, presumably after the collapse, so you would have to question their reliability, just as you would question "corrections" made six weeks later.

### RE: Miami Pedestrian Bridge, Part IX

in order to find core reasons and systemic failures in procedures the true course of actions / nonactions needs to be established
this is beyond the who to blame level,this would save life / health in future

casting of a shadow on things means resources / thoughts are bent elsewhere
engineering maturity is not making the beeline off of the site, not even mentally. but full support to uncover all that may be found out.

in this case, the fact is evident that certain meeting discussions / decisions need to be cast into mutual agreement BEFORE further work is executed.
professionally this should be mandatory for security related issues.

Roland Heilmann

### RE: Miami Pedestrian Bridge, Part IX

I thought I had read that the work crew were already up on the bridge while the meeting was taking place. It raises the question whether they on site to perform work based on the smaller cracks and somehow the word wasn't circulated that a re-think was in the works.

Obviously, the meeting minutes would tell us whether the outcome of the meeting was to tighten the rods.

### RE: Miami Pedestrian Bridge, Part IX

#### Quote (epoxybot )

It raises the question whether they on site to perform work based on the smaller cracks and somehow the word wasn't circulated that a re-think was in the works.

The NTSB photos in the 9 Aug 2018 Update were dated 13 and 14 March 2018. It would be unimaginable the last big known cracks were not discussed at the 15 March meeting held five hours prior to collapse. Any engineer who has worked on site for say a few years and have seen strength tests by crashing concrete cylinders would know the bridge has gone just by looking at the cracking severity in the NTSB photos, one of which shows a tape can be inserted to 25% depth of Member 11 two days before the bridge failed!.

NTSB preliminary report shows the cracks before the bridge was relocated. The last known cracks should be those in the NTSB 9 Aug Update. Three photos were sourced from the Contractor MCM and one from BP&A Consultant most likely sometimes after the PT rod tension was removed in Member 11.

May be I am among the minority disturbed by the magnitude of the cracks. However the majority of the large cracks photos were taken by the workman who carried out work on the PT rods. My speculation is that he was equally surprised too and had gone out his way to record the evidence rather professionally, with a tape inserted as a comparison. He must have been deeply worried if he had done something wrong and the photos were his protection to show the end result of his work was as per instructions/commands. Sadly his employer still sent him out to do more work on the PT rods and he was seriously injured at the end.

### RE: Miami Pedestrian Bridge, Part IX

Don't think this has been mentioned before, but the bridge may have been unknowningly damaged during the move. From the NBC Timeline:

March 10th:
"A document prepared by the claims administrator for the insurer of Bridge Diagnostics Inc. (hired to install and monitor sensors tracking the bridge's position, rotation, strain, tilt and twist during the move) states that the movement had to be stopped 10 to 15 times because the span twisted greater than one half of one degree -- requiring workers to readjust rigging supports each time."

March 15th:
Shortly after the bridge collapsed a Bridge Diagnostics Inc. engineer was called by Barnhart, the company that moved the bridge. The BDI engineer was working on a final report, and told Barnhart that evidently after a work break their monitoring software failed to reload it's stored offset measurements when the computer was turned back on. NBC noted that because the NTSB has prevented all parties from commenting, it's unknown if this malfunction only affected the BDI final report, or if BDI gave the Barnhart engineers corrupted sensor data during the move.

### RE: Miami Pedestrian Bridge, Part IX

Let's see how damage could have inflicted to the bridge during the move.

The FIU bridge has a dead weight of 950 ton. It has 5 bays so roughly each bay weighs about 190 ton. During the move the two end bays were cantilevered out so each might have a maximum of 190 ton hanging freely.

Member 11 has two PT rod each stressed to 280 kips so together the two rods offer about 250 ton resistance.
Since the bridge was tightly monitored and fully rigged with strain gauges I doubt much damage could have occurred.

The Member 11 has a slope of 35 degree (1 vertical:1.427 horizontal:diagonal 1.74) so if the reaction at the support were to be 475 ton then the axial compression in Member 11 due to the dead weight could have been about 950/2*1.74 = 826 ton

To me a real killer could be the omission or the lack of consideration of 250 ton from the PT rod stress, required only during the move, in rebar design of Member 11. 250 ton is an increase of 30% load to member 11.

FDOT had hand written the need of temporary PT rods on FIGG's drawing on 15 Sept 2016. Any engineer looking at the rebar inside Member 11 would know it could not possibly take 1/5 of the bridge dead weight. This raises the alarm about FIGG's competency have to rely on FDOT to tell them something so fundamental. If FIGG had implemented FDOT suggestion of the extra PT rods but did not follow through with the rest of the structure especially the connection design of Member 11 to take the extra 30% load then that might be the smoking gun everybody been looking for.

### RE: Miami Pedestrian Bridge, Part IX

It was FDOT, that asked them to add room for an extra lane just before construction was due to start. I wouldn't have been real happy having to deal with that at the last minute. What I find mysterious is that members one and two were beefed up, but not eleven and twelve?

SF Charlie
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### RE: Miami Pedestrian Bridge, Part IX

The strain gauge data may have been corrupted, allowing the bridge to be over-stressed without a warning indicator. BDI was responsible for installing and monitoring the strain gauges. They acknowledged to the bridge mover, Barnhart, that at one point a computer was turned off and on during a work break, and all their gauge readings were reset to zero instead of reloading the stored values that were present before the break. EDIT ADD: After re-reading the Timeline description, what may have been lost were the inital calibration offsets that were used to zero the gauge readings before the move began. This implies that many of the monitored areas could have exceded 100% of the safety threshold during the remainder of the move, and at least one of the monitored areas may have experienced close to 200%. It's also possible that the lack of concern about the cracks after the move may have been partly influenced by the "good data" provided by BDI showing the bridge hadn't been overly stressed during the move.

Multiple problems with the data collection process. The BDI software apparently wasn't configured to auto-resume after a reboot, or at least indicate a warning. The "meter reader" didn't notice the gauge readings were reset after the work break, possibly because a "new guy" took over. In either case BDI should have anticipated such a problem and trained their personnel. The data discontinuity at the break should have been clearly evident in the charts or readouts, and somebody from BDI or Barnhart should have noticed it during a post-move data review.

### RE: Miami Pedestrian Bridge, Part IX

Given that there were only two load points on the bridge I don't think their issue was changes to the bending of the bridge and in any event the final two bays were hanging off the end so not really impacted by changes in elevation at the support points.

The single line of the columns but wide bottom flange gives rise to twisting of the bridge if the trailers encounter changes to the elevation which as they had to negotiate a verge and the central reservation is not surprising. Hence the limit of 1/2 degree of flex.

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

### RE: Miami Pedestrian Bridge, Part IX

#### Quote (SFCharlie )

It was FDOT, that asked them to add room for an extra lane just before construction was due to start. I wouldn't have been real happy having to deal with that at the last minute.

From record the bridge was moved as one complete unit by 11' to the North. The span was not changed so structurally the structure was the same as before. As construction had not started yet so the impact to the cost should be minimal.

### RE: Miami Pedestrian Bridge, Part IX

#### Quote (saikee119)

The span was not changed so structurally the structure was the same as before
That's the point: The span wasn't changed (enough) but the support during the move was changed fundamentally. Also the construction was scheduled to start within a month. All the adding the PT rods in 11 etc. happened after the support during the move was changed to accommodate the 11 feet of dirt adjacent to the center pier.

SF Charlie
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### RE: Miami Pedestrian Bridge, Part IX

There was a non-trivial charge for the extra engineering for the 11 feet for the extra lane. Moving the center pier closer to the canal required driving extra piles taking more time and delaying the start of pouring the piers, putting the schedule in a time bind with the end of the money availability running out causing the rush at the end causing the panic which may have affected the critical thinking at the time of the move.

SF Charlie
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### RE: Miami Pedestrian Bridge, Part IX

(OP)
Maybe I'm not understanding the legal strategies here - but if the NTSB hasn't determined the cause of it - why, as a contractor, would you settle for $42 million if the cause might end up being totally on the designers? Check out Eng-Tips Forum's Policies here: FAQ731-376: Eng-Tips.com Forum Policies ### RE: Miami Pedestrian Bridge, Part IX #### Quote (JAE) Maybe I'm not understanding the legal strategies here - but if the NTSB hasn't determined the cause of it - why, as a contractor, would you settle for$42 million if the cause might end up being totally on the designers?

Yes, I agree, however, it is not like the contractor really has a role in accepting or rejecting a settlement. Once the insurance co's get hold of the case they and their legal team take it over, and the contractor just follows the lead. Bankruptcy of MGM may have also lead them to this settlement too.

### RE: Miami Pedestrian Bridge, Part IX

This March 14 ENR.com article says MCM had been operating at a loss since 2016 but wanted to make sure they were able to pay out settlements, so they established a trust/fund to cover all claims as part of their bankruptcy reorganization. The $42 million figure was the maximum amount they estimated could be secured from their insurance policies. EDIT ADD: Based on this May 03 Miami Herald article MCM reached an agreement with their insurers, not the families. My impression is that because of their ongoing bankruptcy problems, they wanted to make sure money is available in the future if any claims are eventually settled against them. ### RE: Miami Pedestrian Bridge, Part IX #### Quote (JAE) Maybe I'm not understanding the legal strategies here - but if the NTSB hasn't determined the cause of it - why, as a contractor, would you settle for$42 million if the cause might end up being totally on the designers?

Not a lawyer, but based on what I've seen of past cases I think there's a couple things at work here:

* The NTSB report is pretty much a foregone conclusion at this point. Pretty much everyone who matters knows that it will demonstrate that the bridge was designed with inadequate shear margin to prevent what was essentially a tear-out failure of the 11/12 node. It will probably also demonstrate that it was built as designed, although that is unlikely to provide the builders much cover.

* Early settlement is in accord with two ancient axioms: "The bird in the hand is worth two in the bush," and "The first loss is always the smallest." Dragging this thing out is only going to make it uglier and more expensive to everybody on all sides (excepting perhaps the attorneys), and decrease the amount of money available to compensate survivors.

* Pure speculation, but similar past cases suggest that all involved in the design and construction and underwriting have gotten together, gotten their stories as straight as can be managed, and will present a united front that will limit further culpability to the degree practical.

### RE: Miami Pedestrian Bridge, Part IX

I have the most scorn for those on site who saw the concrete fracturing off in huge chunks and did not declare an emergency, close the road and bail off that bridge. Shades of the Quebec bridge collapse where the on-site engineer kept piling up steel as compression members bowed. After that Wassisname who gave the order to proceed without going on-site and also not pulling everyone off the bridge and closing the road.

### RE: Miami Pedestrian Bridge, Part IX

The contractor's insurance probably settled relatively quickly to avoid litigation. They had liability, so why prolong the proceedings with the attendant costs? As to the designers, I think they were working for the contractor, so that was not an available dodge for the contractor. Typically, construction litigation proceeds with a number of settlements before any remaining defendants have their days in court. There were earlier reports that the insurers of the designers were denying liability, so that will be more complicated to resolve. And then there will be a host of other defendants.

### RE: Miami Pedestrian Bridge, Part IX

The 44-page document was released by FDOT:

https://cdn2.fdot.gov/fiu/14-FIGG-Structural-Analy...

Some interesting stuff. I wonder what exactly FIGG thinks they can dispute in the meeting minutes that look to match up with the presentation. I suppose they could try and take somebody along with them or possibly deny the presentation (initially) since the .pdf doesn't show their name on any of it.

### RE: Miami Pedestrian Bridge, Part IX

This whole presentation shows a scary reliance on their modeling and calculations. I don't care what any of the math says, the bridge is screaming for help and they state there's no safety concern in the same presentation where they say it's not clear how the cracks formed. I'm going to double down on caution if a structure is behaving unexpectedly.

I didn't go through the full presentation but it didn't appear to me that they had any checks of the longitudinal reinforcement anchorage resisting the thrust from the diagonal. I got the distinct impression that they checked most everything but the most obvious limit state.

Ian Riley, PE, SE
Professional Engineer (ME, NH, VT, CT, MA, FL) Structural Engineer (IL, HI)

### RE: Miami Pedestrian Bridge, Part IX

It's difficult to endure the presentation knowing that they completely lost the understanding of basic structural principles while ensconced in the defence of their position.

Shame on anyone that utters the term re-tensioning with regards to the work that was being done. What were they really trying to accomplish? Hang the bridge from itself to relieve the stress?

### RE: Miami Pedestrian Bridge, Part IX

They were trying to use the PT bar to pull the broken sections back together without ever making a diagram that showed the PT line of action would do the opposite. Since the fracturing didn't happen until after the PT load was removed the naive choice was to put it back to stop the fracturing.

Such reliance on the LRFD and not a free-body diagram in sight.

Is there any surprise at the line in the chart "And therefore the is no safety concern ..." An obvious typo and sign of not paying attention to detail?

### RE: Miami Pedestrian Bridge, Part IX

But they had fancy FEA screenshots
(/s)

### RE: Miami Pedestrian Bridge, Part IX

Looking at pages 27 and 28, they clearly gave some thought to shear tear-out of the 11/12 node.

I don't know what went wrong, but I don't think I'm going too far out on a limb to make this guess based on the table on page 28: In assessing the shear resistance contributed by the rebar crossing the shear plane, they assumed that all members were loaded equally in shear. However, the evidence of the cracking shown in the photos suggests that the loading was not uniform; that members were sequentially overloaded and yielded, resulting in even greater loading of the next member along, and its subsequent failure, until the whole thing zippered off the end.

### RE: Miami Pedestrian Bridge, Part IX

I wonder if FDOT engineer Tom Andres' notes were ever seen by the PEER review team.

### RE: Miami Pedestrian Bridge, Part IX

2
They completely missed a potential failure plane in their presentation.

On page 30 a total shear surface area is shown of 23.62 SF. This whole presentation is made assuming shear failure will occur WITHIN the deck, thus the multiple of 2 being used on 11.81 SF. In this presentation they did not check a shear plane happening along surface of deck. Shear surface area in this instance would be roughly 1.75' (width) x 6.33' (length) = 11.1 SF. This is under half of what they've assumed. And, for this failure plane, there will be NO nodal confinement force from transverse PT, as failure plane is deck surface. I didn't run the numbers for the steel--no shop drawings, and I'm just too lazy at this point--but they're likely to be equally worrisome.

### RE: Miami Pedestrian Bridge, Part IX

epoxybot, if you are referring to the suggestions that cracks could form, I think that was due to the observation that differential loading of the various portions from the PT bars would create too much strain in the tension sections in combination with differential shrinkage as the concrete cured.

I don't feel there was worry about immediate catastrophic failure because of the lack of adequate reinforcement but concern about exposure of internal reinforcement to corrosive elements.

Greenlama - that answers a question I would have asked - where did the multiplier come from. How did they not know about the cold-joint between the deck and the truss? For certain the photographs they had access to showed shear displacement along the deck and not damage within the deck beyond the spall-out on the end. It's like they determined at some time that the fracture at the deck end was because of transverse bending of the diaphragm, hence the concentration on the pads underneath.

### RE: Miami Pedestrian Bridge, Part IX

I'd appreciate if someone savvy in structural engineering could clarify a few points in the recently-released"FIGG Structural Analysis Presentation Meeting Minutes" document. (https://cdn2.fdot.gov/fiu/14-FIGG-Structural-Analysis-Presentation-Meeting-Minutes.pdf).

1. The doc uses phrases like "capture the nodal zone" (referring to the 11-12 node). What sort of structure does "capture" imply adding?

2. My non-expert reading is that FIGG seemed more concerned with the vertical load causing problems (hence the shim recommendation) than constraining the horizontal load of #11. Is that a reasonable reading?

3. Page 27 gets to the topic of maintaining the connection of the 11-12 node to the deck, so as to be able to "capture the longitudinal force component of the strut"... ie: connect the strut's horizontal force to the deck's longitudinal PT bars. Page 28 shows some accounting of rebars crossing "assumed shear plane". Which plane would this be?

4. Page 29 assesses "nodal shear stability" in a way that might be problematic. If I understand correctly, this looks at transverse forces across the deck, east-west) compressing ("confining") the concrete in the region of the node. It assumes an even distribution of transverse tendons, spaced at 175/65 ft, or 2.7 feet, then applies the force implied to a 4.75-ft "side" of the region of interest. This 4.75 ft is presumably the length of the oblique connection of #11 to the deck.

However drawings such as this one: https://cdn2.fdot.gov/fiu/13-Denney-Pate-signed-and-sealed-FIU-bridge-construction-plans.pdf page 69 appear to show that there are no transverse tendons (or at most 1) in the end region of the deck or diaphragm, the first one coming at something like 3ft 8in from the end (on the plan view), or maybe 4ft 5in (View B-B), or maybe 4ft (page 71, view B-B) or maybe 4ft 2.5in (page 85).

So it seems to me that not only were there either zero or just one horizontal tendons in this area, but they were not distributed evenly over the area of interest, with the compression effect tapering off rapidly toward the endmost region of the deck where the longitudinal force (and its horizontal component) would be most focused. Certainly there will be some compression from the endmost transverse tendon, and diminishing amounts from the second, third etc, but the compression won't be in a strictly transverse direction.

5. The FEA graphics on pages 36 through 43 I think treat the members as homogeneous objects, and led to the conclusion "the spalled areas have not been replicated by the engineering analysis" (page 44). As it turns out, I guess this is a reminder that if the analysis doesn't predict what is actually happening, then the analysis is wrong. Presumably one or more of the actual members were no longer functioning as homogeneous objects, but instead had internal cracks severe enough to require a more complex model for analysis.

### RE: Miami Pedestrian Bridge, Part IX

The release by FDOT of this meeting record, presumably as recorded by the FIU attendees, is useful in showing the frame of mind of the participants, in particular the FIGG engineers. They were under pressure for sure, but had absolute faith in the correctness of their design. That faith was woefully misplaced, at the expense of a number of lives lost.

The NTSB is taking its time in doing this investigation. I just hope that they don't just focus on the immediate locus of where the truss/frame failed, but rather on the whole flawed concept.

### RE: Miami Pedestrian Bridge, Part IX

gwideman, here are my thoughts.

1) "Capture the nodal zone" is an odd phrase. Took me a while to comprehend. Because this is a concrete truss, and thus unique, I think they were reaching for terms to help them in their discussions, and analysis. Maybe capture means how best to capture the behavior of the truss.

2) Yes.

3) Force here, best I can tell, is the axial force in diagonal. Shear plane is that shaded area on page 27. And there are two areas, one on either side of outside faces of diagonal extending into deck and diaphragm. And it should be noted here that with the slope of the diagonal, the horizontal component of diagonal force will be LARGER than the verticl component.

4) Once transverse PT is stressed and grouted the force cone will tend to evenly distribute across the deck, reaching a uniform distribution near the centerline of the bridge. You are right to question conditions at end of bridge. Here, transverse PT stresses would be expected to lessen. How much is open to discussion.

5) I think your take on the FEM is a good one. Concrete with large cracks should NOT be modeled homogeneously.

### RE: Miami Pedestrian Bridge, Part IX

#### Quote (TheGreenLama)

Shear plane is that shaded area on page 27.

Ah, that makes sense, thanks.

And interestingly, that same figure shows the arrangement of transverse tendons, somewhat speaking to my question 4 about transverse forces containing the region where the axial forces of #11 are "captured". That endmost transverse tendon does not seem ideally placed to help, though it's not clear whether this drawing is to scale.

#### Quote (TheGreenLama)

You are right to question conditions at end of bridge
And on that topic, page 29 shows a calculation resulting in 520kips of confinement force. But that would be for a region of the bridge that has transverse tendons both north and south of it, and at 2.7ft spacing. Since the region of node 11-12 has only a tendon to the south, and only at the edge of this region of 3 or 4 feet length, I would guess that the actual confinement force resulting from the tendon would be reduced by a factor of at least three of four, so more like 130 to 170kips.

Following this to page 31, this would make the (Phi)(Vni) (without c) = (1908 + 1.4 x 130) x 0.9 = 1881
Which is less than the (page 32) factored Demand Nodal Shear of 1983.

This is a relative pessimistic version of the calculation, but it doesn't look encouraging.

### RE: Miami Pedestrian Bridge, Part IX

#### Quote (1) "Capture the nodal zone" is an odd phrase. Took me a while to comprehend. Because this is a concrete truss, and thus unique, I think they were reaching for terms to help them in their discussions, and analysis. Maybe capture means how best to capture the behavior of the truss.)

Want to emphasize this isn't a truss; truss members only carry axial force and nodes do not carry moment. For this concept, the open web members have to carry moment, shear, and axial force, and the nodes have to restrain these forces.

And therein lies the rub. The design itself was very ambitious. How they would practically design a giant, simply-supported, all-concrete I-beam relying on frame action between the angled "web" members and the top and bottom flange is beyond me. I truly wonder if there was ever a sound way to pull this concept off. If they wanted concrete so badly, a solid web would have made more sense.

### RE: Miami Pedestrian Bridge, Part IX

"...if the analysis doesn't predict what is actually happening, then the analysis is wrong."

BINGO! I think you hit on the crux of the failure to anticipate the imminent collapse of the bridge, gwideman.

### RE: Miami Pedestrian Bridge, Part IX

The question now is this - will claiming total incompetence at understanding the mechanics of the failure with direct observation of the failure be enough for a manslaughter conviction for certain engineers at FIGG and the other companies or will it be a shrug that mistakes were made? How could they see the horizontal displacement at the bottom of 11 and the spalling of the faces and conclude the shims on the pylon were the problem?

I think the meeting notes hint that they knew what was really wrong and they were trying to cover for it when they indicated a desire to tie 11-12 back to the 9-10 node with steel channel until the backspan and pylon were finished; the "capture" mention in the notes.

CEI to FIGG: Do we need temporary shoring?
o FIGG responded that it was not necessary. Rather than carry weight, carry load off that number/node. Steel channels to 10/9 node & PT Bars to capture some of that force which is better than vertical support. The diagonal member is what needs to be captured

I think they believed the reapplication of post tension would pull the end of 11 back somehow and that the steel channels would be better than putting cribbing under the bridge as cribbing would make the failure plain to everyone.

### RE: Miami Pedestrian Bridge, Part IX

#### Quote (3DDave)

tie 11-12 back to the 9-10 node
Ah, I had seen "Steel channels to 10/9 node & PT Bars to capture some of that force which is better than vertical support.", but had misunderstood that this was addressing some separate issue they had with 10/9. Your answer filled in that this means channels/PT bars FROM 11/12 TO 10/9. So something like this sketch, which also includes the proposed shim in the gap left directly under 11/12:

And "which is better than vertical support", because just supporting near the end of bridge, doesn't deal with the fact that, as a truss, the top member is in compression, which needs to be resisted by the horizontal component of compression of 11. So plausible vertical support would need to have been inboard, say under 9/10 like when the bridge was moved. And that would block traffic, and might require yet more calculations unless the other support used during moving was also put in place.

### RE: Miami Pedestrian Bridge, Part IX

(OP)

#### Quote:

Want to emphasize this isn't a truss; truss members only carry axial force and nodes do not carry moment.
Tell that to a Vierendeel truss.

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### RE: Miami Pedestrian Bridge, Part IX

Many of the comments here deal only with axial forces, which mirrors the problem with the design concept. As samwise753 described above, this was a concrete frame. The Vierendeel action of the frame was not adequately considered.

But it is worse than that...the internal restraint stresses were apparently not well thought out either.

### RE: Miami Pedestrian Bridge, Part IX

Looks like I was typing at the same time as JAE was posting.

### RE: Miami Pedestrian Bridge, Part IX

About "comments here deal only with axial forces" and "Vierendeel" action, and "this isn't a truss".

Clarification please: Are you guys saying that the FIU bridge structure is being discussed here (and perhaps designed) as though it was a truss, but in fact lacks the compliance at joints to be considered as such; that the concrete joints will attempt to resist rotations (as in Vierendeel designs), but not being appropriate to do so will be damaged under certain conditions?

### RE: Miami Pedestrian Bridge, Part IX

#### Quote (hoki66)

But it is worse than that...the internal restraint stresses were apparently not well thought out either.

At some level the 11/12 failure appears to be insufficient ability to transmit axial forces to the deck's longitudinal PT bars. Those tendons are positioned in a way that they won't do much to support the deck by itself, so their main objective is to resist the horizontal tension "of a truss's lower members", a substantial amount of it imparted by the two end diagonal members.

Evidently 11 was supposed to transmit the horizontal component of its axial force across the end diaphragm to the PT bars (and the vertical component across the diaphragm to the support pads which were not directly under 11/12).

Has any documentation been released on diaphragm structure, and how 11/12 was connected to it? To what extent does it rely on the integrity of the concrete (possibly damaged by one or another effect, such as rotation of the joint during transportation), as opposed to the capability of the rebar unaided?

(And I note that this ties in to my comment a couple of posts ago that the confinement force for this area seems to have been calculated based on an unrealistic contribution from the transverse tendons, at least for the March 15 2018 meeting.)

### RE: Miami Pedestrian Bridge, Part IX

Not the way I would have said it, but yes, this bridge was a frame, and the members and joints needed to take a lot of bending moment, which I don't believe was adequately considered. Rigid joints in concrete are not easily achieved, in fact never achieved 100%. And the other issue I have raised numerous times was about the internal restraints. Understand that problem?

### RE: Miami Pedestrian Bridge, Part IX

(OP)
Yes, agree with hokie66.

The "truss" as it was, had all diagonal members and thus - stable triangular shapes along its length.

For most historical truss design (with steel) engineers traditionally assumed that there would be a bit of give in the diagonal end connections, or that if you ignored the fixity at the diagonal ends, there would be some slight inelastic response that would allow you to assume the diagonal ends were moment free (pinned). This also simplified analysis prior to our handy PC's.

However, with this "truss", there was true fixity and the ability of the diagonal ends to be axially connected to the decks depended on the integrity of the diagonal-to-deck connection, which appeared to have been significantly compromised by non-uniform shears though the deck....due to moment perhaps.

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### RE: Miami Pedestrian Bridge, Part IX

This structure was unique, in the history of the world. Sure, it was built with concrete and steel reinforcement, but the conceptual form was unique. And there was no testing of the concept. No matter how clever or innovative it was thought to be, it was illogical to jump headfirst into this concept without any physical testing. In my previously expressed opinion, that testing should have been load testing of the actual frame while it was still at the casting location.

### RE: Miami Pedestrian Bridge, Part IX

Touche, JAE. I didn't remember a Vierendeel Truss, though it is a truss in name only.

Well said, hokie66. Rigid joints with members at odd angles was just crazy.

### RE: Miami Pedestrian Bridge, Part IX

From the presentation, they relied on shear friction to tie the members together. Not sure if their computations or the actual details comply with accepted practice, but if so, then the whole concept of shear friction would need reexamination. We have had lots of arguments in the structural forums about shear friction theory, and I for one have not accepted its validity.

### RE: Miami Pedestrian Bridge, Part IX

#### Quote (gwideman)

At some level the 11/12 failure appears to be insufficient ability to transmit axial forces to the deck's longitudinal PT bars. Those tendons are positioned in a way that they won't do much to support the deck by itself, so their main objective is to resist the horizontal tension "of a truss's lower members", a substantial amount of it imparted by the two end diagonal members.

I would say, "all of it imparted by the two end diagonal members."

Here's a thought experiment. Look at member 11 as a column framing into a slab. If member 11 was vertical we would check the "punching shear" capacity of the slab for the axial load in the column, similar to what was done in the recent FIGG presentation. And assuming no moments were in the column, only nominal longitudinal steel would be required. But once the column enters the slab at an angle, as is our case, longitudinal steel from member 11 is going to be required to get the axial load into the slab (and thus the longitudinal PT). That's what's so puzzling about the FIGG presentation. Why didn't they also run numbers for the horizontal component of member 11? They've also failed to detail hairpins tying member 12 back into the slab. So is this a case of people at FIGG not seeing beyond a FEM model?

### RE: Miami Pedestrian Bridge, Part IX

#### Quote (hokie66)

this bridge was a frame

Ahem, just now catching on that "frame" has a technical meaning that distinguishes it from "truss", in that frames have joints that can transfer moments (resist rotation), whereas in a truss the members are considered to be pinned, and this able to rotate (at least a little) at the joints, conveying only axial forces.

So if I understand the discussion properly, the idea is that the FIU bridge could work fine as a truss, say made of steel, where some (small) amount of rotation at the joints would be acceptable. Or with steel some or all joints could be made rigid, and achieve some joint-bending-resistance frame properties. But implemented in concrete+rebar, significant trussly bending at the joints would cause damage, and framesque resistance to bending would be difficult to implement.

#### Quote (hokie66)

And the other issue I have raised numerous times was about the internal restraints. Understand that problem?

By "internal restraints" are you referring to (competing) forces/moments operating within the concrete in the 11/12/diaphragm region that could cause internal cracking, for example during concrete curing and shrinkage, or loading?

And that would shed light on whether or how the concrete would maintain its integrity and be able to perform, with the rebar, as simple homogenous components?

Are there docs which bear on this?

### RE: Miami Pedestrian Bridge, Part IX

The pessimist in me says they were clearly understanding the horizontal shear failure and that's why they wanted to tie back to 9/10 with the steel channels until they could cast in place a stop in the form of the other span and the pylon.

FIGG's is the presentation I would make if I wanted to point the audience in a different direction from the actual failure; however it seems like anyone who did the FEA should have been smart enough to realize the fundamental flaw and not provide anything else that could be used to distract.

However if I did understand the true failure mode the last thing I would authorize is retensioning the PT bars in 11. So I don't know how Pate got himself to that presentation, except brutal ignorance. He knows 11 and 12 are sliding out, has a plan to stop them from sliding out, yet has no grasp on how the are sliding out. And, apparently, neither does anyone else in the room or about to apply the hydraulic jacks to the PT bars.

I think the critical question that might have worked is - why aren't they sliding any faster? That brings focus to the re-bar and from there the loads that have to be acting on the re-bar, which should produce a free-body diagram showing that the diagonals are not actually tied to the deck except by the re-bar; which the PT bars cross. If they had put extensiometers across the cracks in the direction of the movement they would have been able to get a feel for if the failure was speeding up or slowing down and therefore if the re-bar or re-bar anchorage was failing or the re-bar was aligning itself to better resist the load.

In the meantime someone would certainly have called for at least one crawler to come back and shore up the bridge since all it would take for a cascade catastrophic failure is one strand of re-bar to give and transfer it's load to all the others, zippering though them in quick order.

### RE: Miami Pedestrian Bridge, Part IX

gwideman,
That's the gist of it. The various members of the bridge wanted to change volume at different rates and at different times. Therefore, shortening due to shrinkage and prestress, as well as perhaps temperature, would have meant that the web members were acting as struts to prevent the shortening of the decks. Restrained shortening places concrete in tension, and it cracks. But this structure was never "homogeneous", as it was cast bit by bit.

### RE: Miami Pedestrian Bridge, Part IX

I have atttempted to recreate the "total nodal shear stability" accounting on page 28 (and following) of the FIGG presentation https://cdn2.fdot.gov/fiu/14-FIGG-Structural-Analy....

The table lists "Rebar crossing assumed shear plane", where the "assumed shear plane" is that which is important in conveying the axial force of member 11 to the deck's longitudinal tendons.

I have cross-referenced the listed bars to the rebar list and detail drawings in https://cdn2.fdot.gov/fiu/13-Denney-Pate-signed-an....

Some of these rebars don't appear to me to cross the shear plane.

From page 28:

Correlated to the rebar list, and color coded by diameter:

My attempt to find them on the construction drawings. For a larger version see the attachments. Likely you'll need to look at the PDF to see the shape and extent of the rebars in detail.

And here are my comments on each rebar line:

In short, of the 22.72 in^2 called out in the presentation, I only found 9.99 in^2. Have I missed something here? Perhaps these were not the final construction drawings?

Now considering the calculation on page 31:

...I commented before that the Mu x Pc component looks overestimated by a factor of three or four due to the geometry relative to the endmost transverse tendon. Now the accounting of the rebars crossing the shear plane(s) looks to be about only 40% of what the presentation counts.

That line of thinking would lead to total Vni being mostly dependent on the Cohesion portion, and without that, significantly less than the factored Demand Nodal Shear of 1983 kips (page 32).

### RE: Miami Pedestrian Bridge, Part IX

#### Quote (gwideman)

Perhaps these were not the final construction drawings?
Even though these were 100% sealed, there must have been later construction drawings, because these do not show the span shifted to the north, with the pylon base in the SFWMD canal. I am not an engineer but rather know waters well, and I've always wondered about how the shift affected the stability of the north end, considering that a new retaining wall and fill were needed; previously spec'ed concrete piles were now used in the canal instead of on the bank; and whether dredging in that canal location (which was occurring during construction) had any effect. The shift was dictated by FDOT in October, so it's weird that plans signed in December still show the pylon on dry land.

### RE: Miami Pedestrian Bridge, Part IX

Oh sorry, those were the April plans, not the December ones. Maybe they did show the shift?

### RE: Miami Pedestrian Bridge, Part IX

Gwideman, For the transverse PT, they're not talking about how many PT tendons run thru the diaphragm. They're talking about the stress the transverse PT generates along the centerline. And for this you need to consider all the PT. Say you conservatively assume a stress cone extending out at 45 deg. from each anchorage, and the spacing of anchors is 2' - 8". That means that only in the outer 2' - 8" of the deck is there a reduced stress. Looking at the drawings again, the first transverse PT comes in 4' - 0" from the end, and then the 2' - 8" spacing begins (Dwg B-60). Based on this, I think I'd like to modify what I told you earlier about forces lessening near the end. I think that for the purposes of what FIGG is attempting to demonstrate in that calc, using a 54.8 k/ft as an approximation of the transverse tendon force along the centerline is OK.

As far as whether these are the final drawings, the answer is no. There are shop drawings, which are prepared by the mild reinforcement provider, and reviewed by the designer, which detail exactly size and placement of steel. Since these are created based on the design drawings, they're generally identical. But we don't have these. Then, once the bridge is finished, an as-built set of drawings is usually created, which includes any modifications that were made to the original design plans during construction. We don't fully know what these are either.

Lacking shop drawings is one reason I refrained from delving into that very crowded area of the diaphragm. Not sure I want to try and tackle it without them.

#### Quote (3DDave)

FIGG's is the presentation I would make if I wanted to point the audience in a different direction from the actual failure; however it seems like anyone who did the FEA should have been smart enough to realize the fundamental flaw and not provide anything else that could be used to distract.
Misdirection--that's something I hadn't considered. FIU, the owner, was an attendee. 3DDave, you may be on to something.

### RE: Miami Pedestrian Bridge, Part IX

GreenLama - I want to clarify that it's very likely that Pate & Co initially mislead themselves, the presentation was a continuation of that process; before this presentation they'd already set the PT crew do exactly what would increase the forces in the direction of failure.

I said a similar thing for the failure of MCAS - it all started with a convincing presentation. This follows that pattern.

Gawd how I hate PowerPoint. It's like people switch off their brains when they make them and when they watch them. Just because it's on a screen does not mean it's true. Make a real report, unroll actual blue-prints. Put an actual pencil to actual paper. Convene at the failure site.

### RE: Miami Pedestrian Bridge, Part IX

#### Quote (TheGreenLama)

For the transverse PT, they're not talking about how many PT tendons run thru the diaphragm. They're talking about the stress the transverse PT generates along the centerline.

Yes, exactly, that's what I was talking about with relation to the Mu x Pc component of the overall page 31 calc.

I don't know the theory that governs how the transverse tendon tension translates into a distribution of compression at the (longitudinal) midline of the bridge. However, my naive assumption is that away from the ends of the span, each point at the midline receives a sum of forces from the transverse tendons to its north and south, most from the closest tendons, and diminishing force from those further away. The further away the tendon, the more those forces are not perpendicular to midline, but the north-south components of the numerous contributions will cancel.

So it's as though each 2ft-8in section of bridge is compressed by one tendon; each tendon serving 1ft-4in region to its south and to its north. Construction drawings show tendon force after tensioning of about 160 kips, distributed over 2.7ft = 59 kips/ft, pretty good agreement with the presentation's value of 54.8.

But the end of the deck is only adjacent to a tendon to its south, with obviously no tendons to its north. So, again naively, that last region of 4ft is covered primarily by "one side" of the last tendon, and no tendons to the north. So the force that the tendon would normally apply to 1ft 4in of midline is instead distributed to 4ft, resulting in only one third the compressive force per unit length.

Clearly this is simplistic. No doubt the material complies somewhat to redistribute the forces a bit more evenly. But I am fairly convinced that the end region can't be seeing the same compressive force (from the transverse tendons) as a region in the middle of the span.

### RE: Miami Pedestrian Bridge, Part IX

Since the failure did not happen within the material of the deck and there is not a good way to generate 1.5 Million pounds of resistance with transverse containment in this configuration, it's a moot point as to what the effect is.

### RE: Miami Pedestrian Bridge, Part IX

#### Quote (3DDave)

it's a moot point as to what the effect is
I infer you're responding to my post, inquiring into the effect the transverse tendons would have in the region of 11/12?
It may be moot if one's position is that this was a flawed design from basic principles, no need to analyze the details to get to that conclusion. Fair enough.

However, it's not moot in trying to understand FIGG's reasoning. As you pointed out "it's very likely that Pate & Co initially mislead themselves". I think it is valuable to understand how engineers (or management, or whoever) gets into that position. In this case, were these qualitative mistakes (wrong type of structure for the job), or errors of magnitude (should have been 50% beefier), or of construction (drawing said X, but Y got built) and so on.

The recently-released presentation gives a little insight into the model they were using to analyze the 11-12 connection, and the numbers they were plugging into it. Was that a sensible model? Did those numbers properly apply to what was built (or at least drawn)?

#### Quote (3DDave)

the failure did not happen within the material of the deck
I'm not quite sure what you mean here. I think one of the prominent theories in this forum is that the failure did involved the intersection of deck and 11/12, with pictures before the collapse showing significant spalling of the deck surface adjacent to 11/12. Granted that was not the only spalling, and this is not the only theory, of course.

### RE: Miami Pedestrian Bridge, Part IX

Third post in a series looking at the FIGG presentation Total Nodal Shear Stability calculations, page 23. This time, the Cohesion contribution.

The cohesion contribution is based on a shear plane area of 23.62 sqft, which is the shaded area on page 27. Here's how that number is arrived at:

#### CODE -->

A:  2 x 1/2 x 4.71 x 4.08 = 19.2
B:  2 x 1/2 x 1.75 x 2    =  3.5
C:  2 x        0.2 x 2    =  0.8
Total = 23.5168 
, which agrees with the presentation (23.6).

However, that shear area is interrupted by two sleeves (around vertical reinforcing bars). These are shown in this figure:

The sleeves are each 4 inches in diameter, and have an intervening gap of 2.75 inches (lighter pink), which I think would not contribute to any shear force. So I suggest that the entire 0.9ft x 4.3 ft should be discounted from the shear plane area. (I have also marked a gray "???" area that I think also would not provide useful shear force, but I did not deduct it from the area).

Revised shear plane area: 23.6 - (2 x 4.3 x 0.9) = 23.6 - 7.7 = 15.9 sq ft.
Revised as percent of presentation = 15.9/23.6 = 67%

For orientation, here is the area under discussion. The sleeves marked with yellow arrows in the top picture are the ones also shown in the bottom picture. The sleeves marked with red arrows are on the other side of 12, and protruded from the deck only a couple of inches (as other pictures elsewhere in this thread show).

Shearing (or at least lack of cohesion) looks to have occurred around and between the sleeves. (Though this doesn't necessarily imply that this was the very initial part of the failure.)

### RE: Miami Pedestrian Bridge, Part IX

The intersection, not the embedment. Since 11/12 weren't actually captured in the deck pour they could not be retained by the deck no matter what. Only the re-bar crossing that boundary could be captured and it looks like the portion in the deck remained there when the rest was sheared off. There's no reason to believe that the few bits of re-bar at the deck edge which carried the loads that spalled the deck could have been reinforced enough to make a difference considering that there were about 26 sections of re-bar joining the deck to the truss at that location; sections that all failed.

### RE: Miami Pedestrian Bridge, Part IX

I'm glad new information is available now. Hopefully soon we will have a mathematical explanation for the failure.

I found reviewing MCM original technical proposal interesting > Link (Link typo corrected May 12 2019)

FIU bridge project homepage > Link

FIU documents homepage, includes calculations > http://facilities.fiu.edu/projects/BT-904-PRR.htm

### RE: Miami Pedestrian Bridge, Part IX

Summary of series of posts examining the FIGG presentation calculations around node 11/12/deck "Total Nodal Shear Stability".

The equation has three contributions, each of which I've discussed in a previous post, and noticed that there are reasons to believe that each one is overstated in the presentation:

1. Cohesion component: Presentation uses 23.6 sqft as the area of the shear planes (total of the two sides), but that area is interrupted by sleeves that reduce this to 15.6.
Presentation overstates by 50%.

2. Rebar shear component. Presentation uses 22.7 sqin for the rebar crossing the shear planes (total two sides). I was able to find only about 10 sqin of the listed rebar (ie: only about 45% of it). That would put the presentation overstatement at over 120%. However, it's possible that the large bars that I either couldn't find, or that appeared not to cross the shear plane, were perhaps detailed in on some other drawing. (It might be feasible to correlate the drawings with post-failure photos.)

3. "Clamping" component: The deck's transverse tendons squeeze on the 11/12/deck node clamping it in place. The force used in the presentation is the average effect that the transverse tendons would have away from the ends of the span. My critique is that there is a uniquely large gap from the end of the deck to the first tendon, and that the area in question is only subject to the tendons on its south, with none on its north, unlike the middle of the deck. As a consequence, I (admittedly naively) think that the presentation overstates the clamping force by a factor of two or three. (Ie: Actual clamping force is only 33% to 50% of the presentation value.)

Summary of the Total Nodal Shear Stability components:

#### CODE -->

.           Presentation      Revised
Cohesion       1360            910
Rebar shear    1980            890?  (But there may be additional bars detailed elsewhere.)
Clamping        730            240 - 320 

If the observations I've made here are valid, then obviously it's disappointing that such errors were made for the presentation to the crucial meeting, especially if they reflect the calculations done in designing the bridge in the first place, regardless of whether they turn out to be the root of the failure.

However, I reiterate that this is not my field of expertise, so certainly should not be taken as gospel.

### RE: Miami Pedestrian Bridge, Part IX

#### Quote (3DDave)

The intersection, not the embedment.

I understand your points. I've not yet seen a photo from an angle that completely convinces me that 11/12 sheared off at the level of the top of the deck, but not an expert.

Regardless, I thought it useful to try to follow the reasoning and calculations in the presentation, because even if they were looking at the wrong place (vertical shear planes beside the projection of 11 into the slab, instead of the horizontal 11-12 to slab interface), it shows what they were and weren't taking into account.

### RE: Miami Pedestrian Bridge, Part IX

And thanks to jrs_87's post of links, here we have some nodal zone calculations for the beefier 1/2/deck connection.

This pdf doesn't include any calculations for the 11/12/deck connection.

http://facilities.fiu.edu/projects/BT-904-PRR.htm > Calculations (zip).
> UCPP_Final_Calculations_Superstructure (1).pdf
PDF page number 1299 and following.

... and a couple more pages.

And there are also pertinent calculations and design notes in document UCPP_Final_Calculations_Superstructure Misc Details.pdf
Section I Deck End Diaphragms.
"A strut and tie model was developed for the Type I and Type IV diaphragms to determine the steel area required for the tension tie at the bottom of the section between the two bearings. The tension tie, compressive strut, and node regions were designed per AASHTO LRFD 5.6.3.4, 5.6.3.3, and 5.6.3.5 respectively. Crack control reinforcement and shrinkage and temperature reinforcement were provided in accordance with AASHTO LRFD 5.6.3.6 and 5.10.8 respectively. The bearing replacement case was also checked, but found not to govern the design. Shear friction at the interface of the diaphragm and typical deck section was checked per AASHTO LRFD 5.8.4.1. A similar analysis was performed for the Type II diaphragm during casting (section supported by bearings) using construction loads. The results of this analysis were conservatively applied to the Type III diaphragm design. [...]"

### RE: Miami Pedestrian Bridge, Part IX

#### Quote (gwideman)

But the end of the deck is only adjacent to a tendon to its south, with obviously no tendons to its north. So, again naively, that last region of 4ft is covered primarily by "one side" of the last tendon, and no tendons to the north. So the force that the tendon would normally apply to 1ft 4in of midline is instead distributed to 4ft, resulting in only one third the compressive force per unit length.

Yes, but the tendons near the end of the bridge are acting over a smaller area of deck, thus the generated stresses increase. In other words, a tendon at the centerline of the diaphragm would, if it existed, generate twice the stress than one at midspan.

### RE: Miami Pedestrian Bridge, Part IX

Gwideman, just as a matter of comparison, if you use the FIGG calc you've shown as a guide to calc the area for node 11/12, and not the hashed area shown in the presentation, the approximate shear area would be:

6.33' L x 2' D = 12.66 SF x 2 sides = 25.32 SF

In this case the conduit area would account for a smaller percentage of total area. Still, I think it would be correct to discount that area.

This is the first I've heard of the calculations being available online. I will have to look at when I get time.

And just a thought on rebar disparities between drawings and presentation. It's possible the shop drawings use different call numbers to identify the bars, and those call numbers are what they're showing in the presentation.

### RE: Miami Pedestrian Bridge, Part IX

#### Quote (TheGreenLama)

In other words, a tendon at the centerline of the diaphragm would, if it existed, generate twice the stress than one at midspan.

Are you sure about that? If what you say is true, that seems to make the total stress higher than the total force applied by all the transverse tendons.

If there were N tendons, equally spaced X distance apart (with the end ones at X/2 from each end), each applying force F, then the force applied would be NxF, and according to your discussion, the resulting stress would be (N+2) x F.

Or have I fallen into some reasoning trap?

### RE: Miami Pedestrian Bridge, Part IX

Gwideman, Assume distance from edge of deck to centerline is 10', and force from tendons distribute out at 45 deg. Tendon in center of bridge would have force distributed over 20' of deck. Tendon at end of bridge is only distributed over 10' of deck. Assuming same tendon force, stress would double.

### RE: Miami Pedestrian Bridge, Part IX

#### Quote (TheGreenLama)

Assume distance from edge of deck to centerline is 10', and force from tendons distribute out at 45 deg. Tendon in center of bridge would have force distributed over 20' of deck. Tendon at end of bridge is only distributed over 10' of deck. Assuming same tendon force, stress would double.

I believe your point is illustrated like this:

... where this is a considerable simplification in that the forces won't distribute evenly over the entire +/- 45 degrees, and won't stop abruptly at the edge. However, OK for this illustration.

I understand your point, however, in the middle (longitundinally) of the span the midline points are receiving forces from PT bars within +/- 45 degrees, whereas at the end of the span they only receive forces from half that amount of PT bars [*], cancelling out the doubling that you state. Like this:

[* or less in the FIU bridge, due to the non-uniform wider spacing at the end of the deck].

I still might not understand something about this, but this is the way it seems to me.

### RE: Miami Pedestrian Bridge, Part IX

[Edit: A few posts down, IceNine corrects my mistaken impression. The calculations I reference here are not for the endmost strut nodes per se, they are for the end diaphragms transmitting vertical force from those nodes to the support pads under the diaphragms. See later discussion.]

I'm sure everyone is enjoying their Saturday studying the Plans and Calculations docs at http://facilities.fiu.edu/projects/BT-904-PRR.htm

Pursuing further the design of the 11-12-deck area, document UCPP_Final_Calculations_Superstructure Misc Details.pdf presents some calculations.

However, despite this being a "Final" document, the numbers used seem disturbingly at odds with the actual bridge.

End Diaphragm I, PDF page 11

Struts 1 and 2, South end, not the ones that failed
Fc = 1336 kip
alpha s (theta s in the accompanying drawing) = 39 deg, compared to actual angle of strut 2 = 23.9 deg.

End Diaphragm II PDF page 31
Strut 11, North end (the one involved in failure).
Diaphragms II and III are considered together, despite dissimilarities.

Fc = 729 kip (this is half of what's reckoned elsewhere, for example in "the FIGG presentation" PowerPoint.
alpha s (theta s in the accompanying drawing) = 53 deg, compared to actual angle of strut 11 = about 32 deg.

Of course, the actual angles being much smaller in both cases than the ones in the calculations cause the actual forces to be considerably larger than those in the calculations.

There must surely be some later calculations, since these are dated September 2016, and don't seem applicable to the bridge as built.

### RE: Miami Pedestrian Bridge, Part IX

gwideman,

These are strut and tie models of the end diaphragms. Because the centerline of the truss isn't supported with a bearing directly beneath it, the end diaphragm must span between bearings. So the angles in these calculations are the the angle from the centerline of truss to the bearing, not the angle from the truss member to the deck.

### RE: Miami Pedestrian Bridge, Part IX

#### Quote (gwideman)

this is a considerable simplification in that the forces won't distribute evenly over the entire +/- 45 degrees, and won't stop abruptly at the edge
The distribution does stop abruptly at end of bridge. That's the whole point. Less deck area to capture force means higher stresses.

#### Quote (gwideman)

whereas at the end of the span they only receive forces from half that amount of PT bars
Yes, but the stress from those bars is higher than at midspan.

### RE: Miami Pedestrian Bridge, Part IX

#### Quote (IceNine)

These are strut and tie models of the end diaphragms. Because the centerline of the truss isn't supported with a bearing directly beneath it, the end diaphragm must span between bearings. So the angles in these calculations are the the angle from the centerline of truss to the bearing, not the angle from the truss member to the deck.
Ah, thanks for that comment, I see you're right. So the calculations in UCPP_Final_Calculations_Superstructure Misc Details.pdf on PDF page 31 and following correspond to the meeting presentation slides thus:

... and the results compare like this:

... with the presentation's unfactored 593 (652 factored) considerably higher than the calculations' value of 439 which appears to be the factored value. This is I guess due to changing from one pad on each side of the support close to center line to two pads each side, somewhat further away, especially the outboard pads, hence more acute angles.

Luckily, the the eight #11 bars anticipated in the calculations (8 x 11S01, drawing B-47) are enough for the load. Though the presentation calculation adds in an additional 2 x 0.31 sq in for a slightly improved result.

Anyhow, this does not seem to be an element that failed, but it does mean I'm still not seeing where in the calculations the connection of #11/12/deck was analyzed.

### RE: Miami Pedestrian Bridge, Part IX

#### Quote (gwideman)

this is a considerable simplification in that the forces won't distribute evenly over the entire +/- 45 degrees, and won't stop abruptly at the edge
The distribution does stop abruptly at end of bridge. That's the whole point. Less deck area to capture force means higher stresses.

Perhaps the sentence you quoted was not quite clear. I am saying that for this discussion I accept your simple model of the PT force being distributed over a +/- 45 degree triangle, but I note that the nature of the simplification is that at the bridge midline the force won't actually distribute evenly over the +/-45 degrees, and also won't stop abruptly at the edge of the 45 degrees.

Yes, agreed, the forces will not exit the edge of the concrete, as I diagrammed right before the part you quoted.

Anyhow, the more important part is this:

#### Quote (gwideman)

whereas at the end of the span they only receive forces from half that amount of PT bars
Yes, but the stress from those bars is higher than at midspan.

So at this point I think you agree that the two effects I diagrammed are indeed at work. And hopefully that in an "ideal" case where the transverse PT bars are evenly spaced, (so a half-space at the end), the two effects cancel out, resulting in uniform distribution of force to the midline of the bridge, and not an increased distribution of force toward the ends.

The one step further that I take it is that the actual bridge is "missing" the final tendon, so the transverse force at the midline near the end (at the 11/12/deck node) must be reduced.

### RE: Miami Pedestrian Bridge, Part IX

I found a hint about shear with the deck on page 1382 of the calculations report. It refers to "Traction Force location from F.E." which doesn't seem to be mentioned anywhere else. There's something promising on page 1388, but it doesn't track with any force values I've run across.

### RE: Miami Pedestrian Bridge, Part IX

#### Quote (3DDave)

page 1382 ... page 1388 ... doesn't track with any force values I've run across

I think you are on to something there. I'll try to elaborate.

### RE: Miami Pedestrian Bridge, Part IX

As 3DDave has noted, pages 1382 through 1388 present some calculations that appear to calculate the forces at a horizontal shear plane that more or less matches the leading proposal for that actual failure location. But the numbers in those calculations don't match very well what we think we know about the bridge.

To try and correlate them with other numbers, I will look first at the #1/#2/deck connection, because those calcs almost correlate. Then look at the #11/#12/deck calcs.

First, here's what the forces should look like at 1/2/deck, I think.

These are based on assuming that there's a vertical component of 950 kips, half the weight of the bridge, through each of the end diagonal members. This matches the approach in the "presentation" PowerPoint.

Here's the shear plane referenced in the calcs:

(Yellow is in the pdf. Red and blue added by me.)

And the analysis results.

(Yellow is in the pdf. Red and blue added by me.)

No explicit angle is provided. However, I have added a sketch of the vectors from which to infer an angle.
The angle doesn't match what we might expect. But at least the vertical component is more than half the weight of the bridge. Possibly coincidentally, the horizontal component almost matches half the weight of the bridge. But is far less than the horizontal force one would expect from the angle of ~24 deg

A further oddity is the large Mxx value, which I assume is moment around the X axis. This perhaps corresponds to the offset between the center of the shear patch and the supporting column? (The small blue and red squares in the previous figure). 2.6ft x 1235 kips = 3211 ft-kips, very close to Mxx = 3113.

Comments: Very odd that the angle is so unexpectedly tall, but at least it has a vertical component that is in the same range as the half-weight of the bridge. (Though the concern of the analysis is to assess the horizontal component, that looks very understated.) I don't fully understand the analysis, but the force numbers are somewhere near the expected ballpark, if not actually in it.

For additional comparison, here's an excerpt from the analysis on page 1299:

Here again, puzzlingly, the vertical component is significantly less than the half-weight of the bridge.

### RE: Miami Pedestrian Bridge, Part IX

[Part 2] Now for the 11/12/deck analysis from UCPP_Final_Calculations_Superstructure (1).pdf page 1388.

Here's the analysis diagram of the shear plane considered, and the forces involved, based on the assumption that member 11 has to include the vertical force of half the weight of the bridge. (Notably, that assumption accords with page 27 of the FIGG presentation PDF.)

(Yellow is in the pdf. Red and blue added by me.)

Here is the analysis result. Again I have added a vector diagram from which to infer an angle.

(Yellow is in the pdf. Red and blue added by me.)

The obvious issues are:
-- The analysis vertical force of 646.7 kips is substantially less than the 950 kips half-weight of the bridge. But oddly similar to the vertical force of 673.6 in the hand-written page 1299 notes.

-- The angle of about 48 degree is far steeper than the actual angle of about 32 degrees.

-- The horizontal force of 570.9 kips is far less than the expected 1531 kips.

These numbers are so extraordinarily different that I would expect someone to jump in and say that I've completely misunderstood the analysis, if it weren't for the results of the #1/#2/deck analysis, which, while still using an unexpected angle, at least had somewhat recognizable sizes of numbers. So I don't know what to conclude.

### RE: Miami Pedestrian Bridge, Part IX

The other puzzle is that there are several areas where the number and spacing stirrups was done to keep the diagonals from rupturing, yet nothing about the amount of re-bar to take the shear loads at these locations.

### RE: Miami Pedestrian Bridge, Part IX

I would like to make a friendly suggestion that any posters that markup calculation drawings and sketches come up with a method to distinguish original and contributed elements. I make this point only because the originals are by nature marked-up already.

### RE: Miami Pedestrian Bridge, Part IX

#### Quote (3DDave)

The other puzzle is that there are several areas where the number and spacing stirrups was done to keep the diagonals from rupturing, yet nothing about the amount of re-bar to take the shear loads at these locations.

Agreed! There are such calculations of forces and comparison to the quantity of rebar in the calculations for the end diaphragms. Maybe there are some somewhere for the shear plane we're talking about here.

Also, I edited my 1/2/deck post to add a calculation that appears to confirm that the Mxx=3113 is moment attributable to the offset of the center of the shear patch from the support column.

If that's a correct understanding, then the structure would also need to withstand that moment, with appropriate calcs for the concrete and steel. Or the effective shear patch would be considerably smaller and more towards the end of the deck.

A bit of a sidebar at this point though, since it's 11/12/deck that's of most interest.

### RE: Miami Pedestrian Bridge, Part IX

#### Quote (jrs_87)

I would like to make a friendly suggestion that any posters that markup calculation drawings and sketches come up with a method to distinguish original and contributed elements. I make this point only because the originals are by nature marked-up already.

Agreed, and good point. For my part I try to add any markup in a distinctive color, usually red or blue. Of course, readers may not be aware that these are my markups, but I also try to reference the original docs, which are readily available, and where the contrast will be obvious.

### RE: Miami Pedestrian Bridge, Part IX

#### Quote (3DDave)

"Traction Force location from F.E."

The horizontal locations of the south and north edges of each of the shear plane patches are annotated in terms of "Global Z" from the south end of the bridge.

Perhaps the comment you quoted is saying that those Z values came from the F.E. model?

### RE: Miami Pedestrian Bridge, Part IX

I was hoping that if they went to the trouble of mentioning where the force was located that they would mention what the force was.

### RE: Miami Pedestrian Bridge, Part IX

FDOT documents page, updated May 6, 2019 to allow access to files previously blocked by NTSB.

https://www.fdot.gov/info/co/record.shtm

### RE: Miami Pedestrian Bridge, Part IX

In the May 16, 2019 ENR article linked by jrs_87 it has this quotation from Bill Gamble:

#### Quote (Bill Gamble)

William L. Gamble, professor emeritus of civil and environmental engineering at the University of Illinois in Urbana, told ENR that he was “dumbfounded, greatly surprised and appalled” at the documents detailing the meeting, adding: “Yes, reinforced concrete structures often crack, but no, the cracks should not be large and growing day by day.

I still find it hard to believe that anyone who had taken, and passed, a course on reinforced concrete design and behavior could not be greatly concerned,” he added. “Cracks that one can stick the end of a tape measure into are a collapse waiting to happen.”

### RE: Miami Pedestrian Bridge, Part IX

[Revised to add image of spreadsheet calcs, which correct a miscalculation in previous version. Basic conclusion remains the same].

OK structural people, could you take a look at this and tell us whether I've understood the following?

If I'm right, the crucial page of calculations that verifies sufficient strength of the strut-to-deck nodes seems to have some conspicuous problems.

#### Quote (3DDave)

The other puzzle is that there are several areas where the number and spacing stirrups was done to keep the diagonals from rupturing, yet nothing about the amount of re-bar to take the shear loads at these locations.

I and others had been puzzled by not finding the calculations where the assessments of horizontal shear forces at 11/12/deck are compared to horizontal shear resistance provided across that plane by concrete friction and rebar.

The relevant page appears to be: UCPP_Final_Calculations_Superstructure (1).pdf PDF Page 1284 (labeled 1283) where there are three tables listing and calculating several variables for each of the deck-to-member nodes.

It's a bit of a chore to understand all the variables, but they are described on pages PDF 1295 and following, though the example there is for vertical shear planes, and page 1284 is about horizontal shear planes.

(I also found a PDF 2012 copy of the AASHTO bridge manual which covers the same material, and is searchable for variable names:

Description of variables and reasoning:

bvi: width of interface (21")

Lvi: Length of interface. For most of the nodes this matches the lengths shown on the drawings on PDF pages 1440 and 1441. Oddly, the lengths used for the end nodes are conspicuously shorter than the length on the drawings, but do correspond to the length over which the rebar is distributed, plus a modest amount. That oddity would underestimate the cohesion component of stress resistance, but that's zeroed out by c = 0.

Acv = bvi x Lvi Area of interface

Pc: Compression force perpendicular to the shear interface. So in this case, the vertical component of Compression force in the diagonals. For the end diagonals 2 and 11, we would expect this to be half the bridge weight, or 950 kips. For 2 and 11, Pc is overstated at around 1250 kips, which I will come back to.

VDC, VLL, VPT, VTU+TD. These are apparently components of horizontal stress. VDC (stress due to dead load of structural components and any nonstructural attachments) looks extremely understated for members 2 and 11. Given a vertical load of 950 kips, and member angles less than 45 degrees, the horizontal component VDC has to be more than 950, not 589. And if Pc is supposedly around 1250, then VDC has to be more than that. (And in previous calcs I have shown it to be even higher.)

Vui: This is a crucial variable -- the total horizontal stress to be resisted.
Vui = the sum of VDC, VLL, VPT, VTU+TD multiplied by their respective load factors (provided in the "Load Factors" table.)

Needless to say, if VDC is understated, then so is Vui, by an even larger amount since DC load factor is 1.25.

Avf: Area of rebars passing through the shear plane. Avf tells the number of rebars, which are all #7 whose cross section is 0.6 sq-in. These correspond to the bars seen on PDF page 1448. None of the rebar area Avf figures look correct, and several of them are negative!

Since one of the purposes is to determine whether the rebars are sufficient, the fact negative rebar areas were not noticed seems to me a rather significant indication of the level of scrutiny this vitally important calculation underwent.

Lest we disbelieve that Avf is maybe not what I just described, continue on to the third table on the page.

Here the crucial variable is Vni, Nominal Interface Shear Resistance. One of the most crucial design checks is that shear resistance is greater than shear force, or Vni > Vui.

Vni = c x Acv + mu (Avf x fy + Pc) where

c (cohesion coefficient) = 0 for this analysis (making Acv moot, as previously noted)

mu = coefficient of friction = 1

Avf = area of rebar passing through the interface

fy = 60 ksi (shear resistance of rebar per area)

Pc = force normal to interface = 1233 for member 11. So note that overstating Pc by 30% means the shear resistance will be overstated by 30%

So Vni = 1 (-2.28 X 60 + 1233) = 1096.

Note that this matches the third table, showing that the calculation blithely subtracted the shear resistance of the negative rebars, verifying that Avf is indeed what I surmised!

The negative rebars error understates the shear resistance, hence would have made the bridge safer, but it also shows that effectively the shear resisting rebars were simply not calculated at all. So the calculations supposedly "validate" that all the shear resistance can come from the concrete friction resulting from the normal force, with no rebars.

The following image shows several versions of the calculation of the shear force (Vui), and the implications when compared to Vni (shear resistance), and resulting rebar requirement.

Of note:

1. So far as I can tell, the bridge should have been designed according to the "factored all" row, in which case the provided 4.8 sq-in of rebar is 15.4 sq-in short of the requirement.

2. But as a better idea of whether the bridge should be able to stand up at all, we might neglect the live load, and the load factor, and just use raw VDC as the horizontal shear. That would result in a requirement for 9.7 sq-in of rebar, double what was provided. (The calculations page conservatively omits any reliance on concrete cohesion, so presumably there some additional shear resistance from that source not counted here.)

Summary:

• The horizontal shear force VDC was stated as 589, clearly less than the 950 it would be for a 45 degree member (ie: no-calc reality check should fail), and hugely less than the 1531 I calculated for #11's actual angle of 32 degrees.
• The horizontal shear resistance concrete friction component was overstated by 30% by overstating Pc. (But that error was reduced by the contribution of the "negative rebars".)
• The rebar area was negative, which essentially means that so far as the calculations are concerned, the rebars were unnecessary for shear resistance, a clearly absurd result.
These problems appear so conspicuous that it seems hard to believe that these are the calculations actually used, or that these issues went unnoticed. Hence my interest in having someone with a structural background take a look.

### RE: Miami Pedestrian Bridge, Part IX

An undergraduate engineering student from my time as a student, without any computing device, would easily have been able to arrive at the following result on the back of an envelope:

I think this tells us what has happened to college education in this field since the introduction of computers. Nobody today can "see" where the maximum forces and stresses in a structure are located. Engineers today wait for the color coded printout, without understanding that a back of the envelope calc. MUST be done in all cases to check that the order of magnitude is correct.

Tragedies will continue until colleges go back to teaching the old method of visualization and hand calculation of structural forces and stresses.

### RE: Miami Pedestrian Bridge, Part IX

The calculation below took less than 10 minutes. The calculation is an "order of magnitude" check. It ignores live load, to provide a rapid check for absolute minimum steel required to tie diagonal 11 load to the deck load.
The calculation confirms the calculation above almost exactly. One could add factors and the like, but the correct answer is somewhere close to 28 square inches of steel needed to tie the compressive forces in diagonal 11 to the tensile forces running in the deck. NOT the 5 square inches actually provided.

### RE: Miami Pedestrian Bridge, Part IX

#### Quote (FortyYearsExperience)

... 23.4 sq-in...

Thanks for commenting. As it happens I was in the process of tidying the spreadsheet I used, and discovered that I had applied the load factor for VDC twice. I have corrected that error in the post you commented on.

The general conclusion is the same. Just that the 23.4 sq-in should be "only" 15.4 sq-in.

And I think your sketch assumes that shear resistance is provided only by the steel, at 53 kips/sq-in, whereas the calculations page (and my calcs) get 950 kips of resistance from concrete friction under load of 950 kips, and use 60 kips/sq-in for the steel.

For what it's worth, 950 kips would be equivalent to 16 sq-in of steel. So that puts us both in the same ballpark.

### RE: Miami Pedestrian Bridge, Part IX

Thanks for your interesting and thoughtful observations.

I believe however that the shear force between the tie and the deck is 1,450 kips, not 950 kips. (= one half weight of bridge, times cotan 32 degrees).

Also, I am puzzled that you find a reduction in shear can permissibly be attributed to concrete friction. The way I understand the shear capacity of reinforced concrete is to ignore the concrete when analyzing the steel. Then, do a separate check to see if the concrete can withstand the compression. In this case, I believe it cannot withstand the compression, but my check ends with the steel because it is hugely inadequate.

Appreciate any further thoughts.

### RE: Miami Pedestrian Bridge, Part IX

#### Quote (FortyYearsExperience)

I believe however that the shear force between the tie and the deck is 1,450 kips, not 950 kips. (= one half weight of bridge, times cotan 32 degrees).

First, I think the 950 kips you're looking at is for Vni (resistance) not for shear force.

So the figure for plain horizontal force that I used was 1531 (not 1450), as follows:

I actually did it in two steps: 950 kips vertical --> 1802 kips diagonal --> 1531 kips horizontal. (This way I could match the diagonal force with a slide in the FIGGs "crack meeting" presentation).

However, to go directly:

Angle = 31.82 deg

Cotan(31.82 degrees) = 1.6115

Vertical force = 950

950 x 1.6115 = 1531 horizontal shear force.

### RE: Miami Pedestrian Bridge, Part IX

#### Quote (FortyYearsExperience)

Also, I am puzzled that you find a reduction in shear can permissibly be attributed to concrete friction. The way I understand the shear capacity of reinforced concrete is to ignore the concrete when analyzing the steel.

I have very little background in this kind of analysis for actual materials. I'm just following what I recall from a first course in static forces, plus the calculations laid out on the referenced calculations page 1284, plus the description of the method in the AASHTO manual excerpt on pages 1295 and following.

So all I've really demonstrated is that the intended calculations suffer from wrong input data and wrong execution of the formulas that should have been calculated, producing results that seem so wrong (like negative rebar area) that they should have immediately triggered alarm.

I am not qualified to have an opinion on whether this was a suitable approach in the first place.

I think I have learned in this exercise that the shear resistance is seen to be composed of three parts:

1. Rebar shear resistance.
2. Friction at the shear interface (perpendicular force x friction coefficient)
3. Cohesion of the concrete, which is apparently not well characterized and thus controversial (and in calculations under discussion here, omitted).

I could certainly see how steel is the only component useful in tension. And maybe for assessing shear, there's a very conservative approach that again assumes the entire shear resistance would come from steel. But apparently that's not the approach taken here.

### RE: Miami Pedestrian Bridge, Part IX

FIGG's calculations are extremely opaque, and this is evidently one of the sources of the problem. They could not even explain to themselves, in a checkable form, what they were calculating and why.

### RE: Miami Pedestrian Bridge, Part IX

#### Quote (FortyYearsExperience)

FIGG's calculations are extremely opaque, and this is evidently one of the sources of the problem. They could not even explain to themselves, in a checkable form, what they were calculating and why.

Well I found the calcs a bit opaque at first. But after looking up what all the variables mean, it seems straightforward. It's also the same set of steps used on pdf page 1299, and also on the slides in the FIGG "cracks" meeting, albeit examining different shear planes. I infer that people who work with these variables everyday would find this easy to follow.

Though it is curious that the cracks meeting presented an examination (meeting PDF slides page 27 and following) of a different shear interface, rather than using the ones for which calculations were already available. (And as I've discussed earlier, the slides appear to overstate the shear interface areas, the perpendicular ("clamping") force and the rebars crossing the interface.)

### RE: Miami Pedestrian Bridge, Part IX

I would even question the use of the 4 - #7 stirrups as contributing to the area of shear steel, the way they are detailed. The requirement states that the steel should cross the expected shear plane perpendicularly, AND that the steel be fully developed on either side of that plane. It's not clear from the design drawings how far the stirrups extend above the top of deck. Simply extending them above the deck construction joint (1" or 2" or 3") is not enough. To be fully developed (90-deg. bend) they'd need to extend at least 11" above the deck. And, if you wanted to use the steel coming from the diagonal for this purpose (that's assuming those J-bars are placed properly and fully developed), because they're crossing the shear plane at an angle, I would reduce the effective area based on the angle of the incoming diagonal--say use only 32/90 of those bars.

Is it clear where FIGG is pulling the numbers from for doing these calcs? I've looked through parts of the calcs only briefly. Page after page of tabular data cause my eyes to glaze over. Any thoughts on why 2 computer models were done. I haven't looked at the FEA at all, except to note that it's undated, done by someone else (not the LARSA modeler), and models only stage 1 of construction.

### RE: Miami Pedestrian Bridge, Part IX

#### Quote (TheGreenLama )

I would even question the use of the 4 - #7 stirrups as contributing to the area of shear steel, the way they are detailed. The requirement states that the steel should cross the expected shear plane perpendicularly, AND that the steel be fully developed on either side of that plane.

I entirely agree. There is, in reality, zero amount of steel provided to tie diagonal 11 to the deck.

### RE: Miami Pedestrian Bridge, Part IX

Reinforced concrete beam resisting bending - BE of Reinforced Concrete with Prof Ibell Pt2

https://youtu.be/GPOAelSOLFs?t=69

Insightful explanation of how to control failure mode of reinforced concrete beams.

Has anyone here seen any evidence the emergency center-line shims were actuality installed and when? Is it possible the shim jack was being operated in conjunction with the PT rod operation? Obviously the diagram would have to be lifted some order of magnitude to fit the shim effectively.

Bear with me for a moment... I have faith in Figg in so far as engineering goes. I argue they think just like us and it rarely is useful to underestimate people. When they decide it's necessary to shim center-line, implement an "exoskeleton" to add confinement to 11/12 node, and get CIP tied in ASAP, I believe them on that. These recommendations suggest they knew what was wrong even if candor may have been lacking to some extent.

It's my opinion most structure engineers and construction managers would have resisted group-think and taken action to get road closed immediately upon examining that diagonal no matter what. It's just by fate none on this project quite reached that level. Possibly because closing the road was paramount to realizing structure was doomed and un-repairable.

### RE: Miami Pedestrian Bridge, Part IX

GWIDEMAN: Here are some excellent lectures to assist in your quest.

Video lectures are by David Garber, PhD, assistant professor at FIU (coincidence, link not submitted to be provocative)

### RE: Miami Pedestrian Bridge, Part IX

I must have missed this earlier, but FIU is a research hub for ABC - Accelerated Bridge Construction - and does research sponsored by the US Dept of Transportation. David Garber, mentioned by jrs_87 above, is an Assistant Professor of Structural Engineering and a member of the Accelerated Bridge Construction University Transportation Center.

Whenever "FIU" has been mentioned in conjunction with the design of this bridge, I just assumed it meant the university administration, but now it looks like the bridge may have been intended to be some sort of recruiting showpiece for the FIU Engineering Department. In any case, I wonder how many of their faculty have left after this debacle.

EDIT ADD: This Miami Herald Article from 2018 March 15 reported that a university spokesman said, just after the span was installed, that the FIU ABC center was not formally involved in the bridge project. Below is a section from the article:
FIU’s engineering school has become a hub for accelerated bridge construction training and research in recent years.

In 2010, after recognizing the need for more engineers trained in the method, FIU started a center focused on the approach. It has drawn 4,000 people to its webinars since launching in 2011, according to a center website, and in 2016 became one of just 20 programs nationwide to receive federal funding amounting to \$10 million over five years.

The center’s director, Atorod Azizinamini, recognized by the White House in 2016 as one of the world’s leading bridge engineers, said the method is safer and more efficient than conventional construction.

“We are able to replace or retrofit bridges without affecting traffic, while providing safety for motorists and workers who are on site,” he said in a 2016 press release about the program. “The result is more durable bridges.”

### RE: Miami Pedestrian Bridge, Part IX

At this point I'm fairly satisfied that, as described in my earlier post, UCPP_Final_Calculations_Superstructure (1).pdf PDF Page 1284 (labeled 1283) is where the stress resistance is supposedly checked against the stress demand, and wrongly passed due to wrong input numbers.

So I agree with:

#### Quote (TheGreenLama)

Is it clear where FIGG is pulling the numbers from for doing these calcs?
... that one point of interest now is where did those numbers come from?

In summary, the numbers that I think are of most interest are the red ones in the following table:

Here I show what I think are the correct values for key variables, and the four calculations that we've seen presented. (I've included the calculations pertaining to member #2, because it allows comparison to the handwritten notes page.)

Clearly the biggest puzzle is how the half-weight of the bridge was not the number used in the key calculations. The angles of the members were also wrong with a comparably harmful effect on the calculations.

A related issue is how the rebar area on page 1284 came out negative, which is impossible. That didn't help the bridge to pass muster, but it does imply incorrect formulas behind the result table, and thus a flawed process in setting up this critical design-check report and also the checking of it, both of which would make illuminating lessons.

### RE: Miami Pedestrian Bridge, Part IX

Some general thoughts on approach and speculation on load disparities.
Two different shear planes, two different approaches to design.

Shear Plane 2 (as imagined on p.1298 of calcs)

External loads are applied to hand-drawn free body diagram.
Easy to visualize. Easy to get a feel for relative load magnitudes.
Presume loads are taken from 2D LARSA.

Shear Plane 1 (as shown on p.1381 of calcs)

Member 11-12 area is modeled as a 3D block in the FEM.
From within this concrete block a "slice" is defined.
Loads are extracted for this "slice", taken as gospel, and used for design.
No attempt made to gauge relative magnitudes of extracted values to real world numbers.

From the table on p.1283, Acv (concrete shear area) = 882 sq in, with Lvi = 42 in
This 42 in corresponds only to the area where the #7 stirrups are situated.
Could it be that Shear Plane 1 was checked using only the load over this area, excluding the Member 12 area?
Could it be that Shear Plane 1 was checked for fixed pylon case?
Could it be that the unaccounted for Member 11 load, which needs to be designed for, is just not crossing this plane slice due to modeling irregularities?
[Edit: Using this internal slice method to extract loads, is it conceivable that the longitudinal PT in the deck is impacting (i.e. incorrectly reducing) the design shear load on this internal slice?]

And, Gwideman, I agree that when looking at this puzzle it's good to incorporate Member 2 in the summaries, for comparison purposes.

### RE: Miami Pedestrian Bridge, Part IX

#### Quote (TheGreenLama)

p1298 of calcs... Shear Plane 1... Presume loads are taken from 2D LARSA.
(aka PDF page 1299)

I agree that the free body diagram is satisfyingly visualizable. But it uses a vertical load of only 674 kips (and correspondingly low axial force).

#### Quote (TheGreenLama)

p1381 of calcs ... Could it be that Shear Plane 1 was checked using only the load over this area, excluding the Member 12 area? Could it be that Shear Plane 1 was checked for fixed pylon case?
(aka PDF page 1382)

I wondered those points too. But the vertical load on #12, while substantial, would surely be only a small fraction of the 950 kips half-weight of bridge.
And somewhat countering the pylon speculation is that the interface length chosen is only 5'-5.8", which includes the entire dashed red line, excluding the fixed pylon.

I did search the entire calculations PDF for the key numbers I've highlighted previously in red, and found none of them. (And when looking for "647" for example, I searched for "647", and also "646.", on the basis that the page 1382 calc might round up.)

### RE: Miami Pedestrian Bridge, Part IX

Member 11 is offset from diaphragm support. Would areas I marked in orange also be subject to shear? Does anyone know where the steel for this is detailed? And would not the PT bars have messed with this?

Also, does not the offset of 11 and diaphragm greatly reduce vertical vector of clamping force against shear in yellow area? The diaphragm on south size was much larger because it did not share space with CIP wire stay pylon/tower.

### RE: Miami Pedestrian Bridge, Part IX

#### Quote (jrs_87)

Member 11 is offset from diaphragm support. Would areas I marked in orange also be subject to shear? Does anyone know where the steel for this is detailed?

I guess the thinking is that almost any area is subject to shear. The "shear interfaces" looked at in analyses are not necessarily actual physical joints (but could be), but rather just places where the engineer thinks there may be a high level of shear stress, and thus a place to make some calculations. The chosen interface is usually (always?) flat, to make the calculations easy. I would certainly agree that the vertical line you drew would be a good place to analyze. The only drawings I've seen that detail that area are B-60 and B-61, and maybe B24A.

#### Quote (jrs_87)

And would not the PT bars have messed with this?

Which PT bars were you thinking? Axial in member 11? Not sure what to think about those.
Longitudinal in the deck? Those are off to the sides of the 11-12-dec connection.
Or maybe the transverse PT bars across the deck? In the drawing you used (from B-61), there are two oval-ish symbols just below the red/yellow line. I believe those are the channels for the transverse PT bars. But this is the only drawing where there's such a transverse PT bar located where your vertical orange line is. Other drawings, for example B-60, omit this endmost PT bar.

### RE: Miami Pedestrian Bridge, Part IX

gwideman, I agree we should think that shear can express itself almost everywhere. I was just looking at load path of node and diaphragm and it vaguely reminded me of Hyatt hanging rod. But I digress until photos or drawings are released that show exactly where deck and node separated.

I was thinking about temp PT bars in 11. I knew transverse strands pass through node, thanks for telling me about location (ovals). Thanks for your post, I will study it more now...

PS. After watching some lectures I can see how negative values for re bar area are legitimate (assuming the re-bar is placed anyway).

### RE: Miami Pedestrian Bridge, Part IX

#### Quote (jrs_87)

PS. After watching some lectures I can see how negative values for re bar area are legitimate (assuming the re-bar is placed anyway).

Really? That's intriguing. Which lecture(s) pertain? BTW, I did look at some of the links you posted previously -- thanks for those.

#### Quote (jrs_87)

I knew transverse strands pass through node, thanks for telling me about location (ovals).

... but according to other drawings, that last transverse PT strand is omitted and does not go through that 11-12-deck node. (Which I noted in a previous post would mean that the FIGG "crack meeting" presentation overstates the clamping force on #11's extension through to the end diaphragm.)

### RE: Miami Pedestrian Bridge, Part IX

#### Quote (jrs_87)

Member 11 is offset from diaphragm support. Would areas I marked in orange also be subject to shear? Does anyone know where the steel for this is detailed?

It occurs to me that your vertical shear interface might be seen as "safe" immediately as follows:

They are using a coef of friction mu = 1. Since the angle of #11 is less than 45 degrees, the horizontal force, (and thus the friction), must be greater than the vertical force.

And the flipside of this same reasoning is that it would be obvious that for the horizontal shear interface we've been discussing, a significant amount of rebar would be required.

### RE: Miami Pedestrian Bridge, Part IX

#### Quote (gwideman)

Really? That's intriguing. Which lecture(s) pertain?
(re: negative rebar area)

Sorry, I don't know yet exactly what I saw and where. Perhaps we can get more specific and compare notes later. The NTSB report is months away so plenty of time remains. The idea was iterative adjustments and checks with the primary goal of not making structure stand, but determining how it would fail i.e. provide warning. Figg seems to have used same codes in presentation to present a case structure would not collapse because it passed design checks. But the codes don't mean that exactly. Figg had the warning the code provides but seems to have discounted it.

You may have seen in lectures where, for the sake of simplified equations, steel (in the equation) is replaced with equivalent (more area) concrete. Side point> We have all heard concrete is strong in compression and weak in tension. One Phd said that is wrong, it is weak in both. I'm losing focus and need to take a break for a week or so.

### RE: Miami Pedestrian Bridge, Part IX

#### Quote (gwideman)

They are using a coef of friction mu = 1. Since the angle of #11 is less than 45 degrees, the horizontal force, (and thus the friction), must be greater than the vertical force

I have to make a point here. Nowhere, absolutely nowhere, in reinforced concrete design does "friction" come into any analysis. Concrete does not provide any frictional resistance. It is not a "thing." You will not find friction mentioned anywhere in any learned treatise on reinforced concrete design. The only structure that can resist shear or tension in a reinforced concrete structure is steel. In this case, no steel was provided to restrain the diagonal #11 from moving to the north (right, in the figure above), away from the tensile force that was trying to develop in the deck cables to move to the left. Those stirrups you see are not long enough to develop any tension load within the concrete, and even if they were long enough, they are totally inadequate in sectional area. This has been demonstrated above.

### RE: Miami Pedestrian Bridge, Part IX

(OP)
I'm assuming you are discounting the Shear Friction method described in ACI 318 as "not really friction"?

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### RE: Miami Pedestrian Bridge, Part IX

#### Quote (FortyYearsExperience)

I have to make a point here. Nowhere, absolutely nowhere, in reinforced concrete design does "friction" come into any analysis.

AASHTO LFRD Bridge Design Specs 2014 page 5-82 and following (included as PDF pages 1297 and following of the FIU "Final calculations" PDF):

### RE: Miami Pedestrian Bridge, Part IX

#### Quote (JAE)

I'm assuming you are discounting the Shear Friction method described in ACI 318 as "not really friction"?

JAE, maybe FortyYearsExpereince is hokie66

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