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Mar 162018
 
 

FIU Bridge Collapse: Why Müller-Breslau Matters

Speculation continues to mount regarding the cause of Florida International University’s deadly Pedestrian Bridge Collapse. After a day has passed with no knowledge of the origins of the bridge’s collapse, this article addresses a principal cause of the FIU Bridge Collapse, and why a 19th century German structural engineering principle known as Müller-Breslau Matters Most (as depicted in the above cover diagram of this piece constructed with the help of my fine students at Texas Tech University, Mr. Virgilio A. Gomez (@virgilioAgomez), mechanical engineering masters degree candidate under my guidance inside the Edward Whitacre College of Engineering, and Ms. Alexandria Reeves (https://www.linkedin.com/in/alexandria-reeves-b30760118), undergraduate junior business major inside the Jerry Rawls College of Business).

Video Credit: @OliverMcGee on #FIUBridge Collapse, #FoxNews Your World with Neil Cavuto (3-16-18)

Five dozen kids currently enrolled in my Aircraft Structures, and Aircraft Jet Engines and Rocket Propulsion classes at Texas Tech University, including receiving my Elementary Structural Analysis and Intermediate Structural Analysis principles are entering into a brief introduction to Herr Müller-Breslau.

These students can now understand why Müller-Breslau‘s proven structural engineering principle is as relevant for them to learn today in the wake of the tragic FIU Bridge Collapse in Miami, Florida, as it was for me decades ago. I had my similar training at The Ohio State University Department of Civil Engineering’s elementary and intermediate structural analysis classes and highway bridge analysis and design class of The Late Professor Charles B. Smith. This led me to the privilege to teach similar structural analysis classes at Ohio State, Georgia Tech, MIT, Howard University, and Texas Tech.

But first, let’s take a closer look at the backstory here, specifically at what occurred to cause this catastrophic bridge collapse?

A newly installed bridge heralded days earlier, as an innovation of prefabricated construction engineering suddenly collapsed on Southwest Eighth Street, an eight-lane high-traffic highway near Florida International University’s (FIU) campus in Miami on Thursday, March 15, 2018, at about 1:30pm Eastern, Miami-Dade Fire Rescue Division Chief Paul Estopinan said in a press conference Thursday afternoon.

900 - FIU Bridge Collapse: Why Müller-Breslau Matters

Multiple automobiles were trapped underneath the collapsed pedestrian bridge. Firefighters, who are now in “search and rescue mode,” are utilizing trained canines, search cameras and sensitive listening devices, throughout the night and into the morning. They have pulled out at least six deceased people from the rubble, as of Friday, March 16, 2018, and ten other people were taken to nearby Kendall Regional Medical Center, Miami-Dade Fire Chief Dave Downey said at a Thursday evening press conference and Associated Press.

This is how the FIU Bridge of integrated truss and post-tension prestressed concrete construction appeared in this video days before collapsing.

This surveillance video shows the moment the bridge collapsed and local commentary reveals that the bridge lacked necessary mid-span support as suggested in the cover diagram of this piece. In addition, the local commentary questions why the traffic along Southwest Eighth Street was not halted as construction engineers performed their stress tests on Thursday.

President Trump tweeted: “Continuing to monitor the heartbreaking bridge collapse at FIU – so tragic. Many brave First Responders rushed in to save lives. Thank you for your courage. Praying this evening for all who are affected.”

FIU officials said in a statement: “We are shocked and saddened about the tragic events unfolding at the FIU-Sweetwater pedestrian bridge.”

“This bridge was going to provide a safe transportation for pedestrians to cross between the university and the City of Sweetwater,” said Orlando Lopez, mayor of Sweetwater.

900 - FIU Bridge Collapse: Why Müller-Breslau Matters

FIU, one of the 10 largest American universities with nearly 54,000 students enrolled, has been rocked by this tragic transportation infrastructure collapse.

900 - FIU Bridge Collapse: Why Müller-Breslau Matters

The 174-foot long pedestrian bridge was assembled on-site days earlier on Saturday from prefabricated post-tension prestressed concrete spans along the closed sidewalk of the highway. After which, the assembled prefabricated continuous prestressed concrete beam that was hinging on one support was swung 90 degrees across the highway, and was then hinged on the other support on the other side of the Southwest Eighth Street highway.

“The $14.2 million dollar bridge had been partially assembled by the side of the highway, in order to not obstruct the flow of traffic on the seven-lane highway during construction, and was slated to open in 2019,” according to the Miami  Herald. But its “innovative installation,” which “saw workers move the walkway into place before the main support tower had been installed, was risky,” University of California, Berkeley engineering professor Robert Bea told the Associated Press.

As reported in Time: “The bridge was also unusually heavy, employing concrete elements, such as trusses and a concrete roof, rather than lighter weight steel,” according to Ralph Verrastro, an engineer and expert in accelerated construction projects.

900 - FIU Bridge Collapse: Why Müller-Breslau Matters

Munilla Construction, a family-own firm that worked on the bridge, called the accident a “catastrophic collapse” and promised to conduct “a full investigation to determine exactly what went wrong.”

“Munilla Construction has also been fined more than $50,000 for 11 safety violations over the past five years,” according to Occupational Safety Health Administration records, Time reports.

Two construction workers were on the pedestrian bridge when it collapsed, Miami-Dade Fire Rescue confirmed, and “were believed to be conducting a stress test on the unfinished bridge,” reports the Miami Herald. “Over tightening steel cables that run through the bridge slab sections can lead the structure to “camber,” or buckle,” experts told the Miami Herald.

Construction engineers were performing post-tension moment stress tests across the 8-span continuous prestressed concrete bridge, when it suddenly collapsed onto the 8-lane Southwest Eighth Street highway, akin to what we recently observed with the Amtrak 501 derailment outside of Seattle, Washington!

The prefabricated concrete bridge down at #FIU is called “virtual construction” of structural engineering akin to “virtual manufacturing” used in aircraft designs at #Boeing & #Airbus. Prefabricated Civil Engineering Systems are the future of construction & installation of America’s Infrastructure.

 https://twitter.com/olivermcgee/status/974393367449792512

900 - FIU Bridge Collapse: Why Müller-Breslau Matters

Who is Müller-Breslau?

Let me introduce you to a German  structural designer and classical structural engineering pioneer. 

Heinrich Franz Bernhard Müller (born May 13, 1851 in Wroclaw, Poland and died April 24, 1925 in Grunewald, Germany, “known as Müller-Breslau from around 1875 to distinguish him from other people with similar names”) was a German civil engineer. He made early advances in the structural analysis of continuous beams and rigid frames used in modern pedestrian and highway bridges and tall buildings.

900 - FIU Bridge Collapse: Why Müller-Breslau Matters

Essentially, Müller-Breslau establishes a longstanding principle utilized by structural engineers to sketch qualitative influences of continuous bridge supporting forces, spanwise forces, transverse shear stresses, and transverse bending moment stresses, as a basis for pedestrian and highway bridge design and analysis, including experimental stress testing of bridges.

900 - FIU Bridge Collapse: Why Müller-Breslau Matters

Why Müller-Breslau Matters in the FIU Bridge Collapse.

U.S. Senator Marco Rubio (R-FL) tweeted on Thursday: “The cables that suspend the #Miami bridge had loosened and the engineering firm ordered that they be tightened. They were being tightened, when it collapsed today.”

This FIU Bridge Collapse, I add, is a result of a missing essential center safety support tower mechanism located at midspan across the enormously long 174-foot span of the integrated truss post-tension prestressed concrete continuous beam construction, as shown in the cover diagram of this article. 

Thus, the bridge’s failure collapse mechanism occurred around the center (as shown as a red (failure deflected) dashed line in the cover diagram of this piece), as a result of positive moment distribution stress failure (which could have been mitigated by the missing negative moment distribution stress over the missing midspan support) of the bridge under its own dead-load weight of 950-tons or 5.5 tons per linear foot of bridge span length of uniformly-distributed deadweight loading.

900 - FIU Bridge Collapse: Why Müller-Breslau Matters

Essentially, as shown in the above cover diagram, the post-tension prestressed concrete pedestrian bridge is supposedly fundamentally designed to deflect as a “smile” under positive bending moment stress between end-span supports. 

And,  it is supposedly designed to deflect as a “frown” under negative bending moment stress over middle-span supports – which was apparently missing during Thursday’s stress tests. This essentially caused the FIU bridge to collapse through a huge 140% over traverse bending deflection (as discussed below) during its prefabricated construction and installation. 

Ultimately, the FIU pedestrian bridge’s designed live-loading was to withstand a Category 5 Hurricane over a hundred years!

Müller-Breslau‘s principle demands that a middle support tower mechanism is essential to prevent the FIU pedestrian bridge collapse mechanism, as indicated by the red (failure deflected) dashed line in the cover diagram. The green (true deflected) dashed line in the cover diagram is the properly midspan tower supported equilibrium shape of the FIU pedestrian bridge, carrying its 5.5 tons per linear foot uniformly-distributed deadweight loading. This is shown atop the idealized depiction of the integrated truss post-tension prestressed concrete continuous span bridge.

900 - FIU Bridge Collapse: Why Müller-Breslau Matters

Under the FIU pedestrian bridge deadweight loading, including ideally the properly constructed midspan support tower mechanism, Müller-Breslau’s principle says the bridge’s shear stress distribution is actually proportional to a linear function of the spanswise coordinate (x) shown: V(x)=wL((5/8)-(x/L)) with a midspan support tower maximum shear stress proportional to (5wL/8). 

The bridge’s bending moment stress distribution is actually proportional to a quadratic function of the spanwise coordinate (x): M(x)=wL(Td+(x/L)Tr)(L/8), wherein as first introduced by Müller-Breslau, Td is a sensitivity of the bridge’s bending moment stress undergoing a linearly distributed transverse shear stress, and wherein Tr is a sensitivity of the bridge’s transverse bending moment stress undergoing a constant transverse shear stress distribution. This altogether leads to a midspan support tower negative transverse bending moment stress proportional to (wL)(L/8). 

Finally, the bridge’s properly midspan supported transverse deflection must actually be according to code: Ely(x)=(x/L)(2Wr+Wd)(wL**4)/48, (where L**4 symbolizes now and hereafter the bridge span length, L, raised to the fourth exponent power). And wherein, as first originated by Müller-Breslau, Wd is the bridge’s transverse bending moment stress undergoing a linearly distributed transverse shear stress, and wherein Wr is the bridge’s transverse bending moment stress undergoing a constant transverse shear stress distribution. 

This altogether leads to a maximum transverse deflection according to code at Ely(at x=50 feet from the midspan support equal to (27/5000)(wL**4), or about 0.0054(wL**4), wherein E is the elastic modulus of the bridge’s concrete material and I is the bridge’s moment of inertia or second moment of cross-sectional area transverse to the bridge’s span-wise coordinate (x).

900 - FIU Bridge Collapse: Why Müller-Breslau Matters

Under the FIU pedestrian bridge deadweight loading without the midspan tower support, as it happened during Thursday’s collapse, Müller-Breslau’s principle says the bridge’s transverse shear stress distribution is actually proportional to a linear function of the span-wise coordinate (x) with V(x)=Tr(wL/2) vanishing at the bridge’s midspan. 

The bridge’s transverse bending moment stress distribution is actually proportional to a quadratic function of the spanwise coordinate (x) with M(x)=(wL/2)L, having a midspan non-supported positive transverse bending moment stress maximum proportional to (wL)(L/8). 

Finally, as the bridge’s midspan is non-supported, its transverse bending deflection is Ely(x)=(x/L)(Wd-(x/L)Wr(x/L))(wL**4)/24, having a maximum transverse bending deflection of Ely(at x=87 feet, at the non-supported midspan) equal to (5/384)(wL**4) or about 0.013(wL**4).

In conclusion, Müller-Breslau’s principle says the FIU pedestrian bridge collapsed mathematically under an absolute value of (1-(0.013/0.0054))(100%)=140% error in its failure collapse transverse bending deflection mode (shown as a red dashed line in the cover diagram) underneath the bridge’s own deadweight. This is measured relative to its ideally proper midspan tower supported transverse bending deflection mode (shown as a green dashed line in the cover diagram) underneath the bridge’s own deadweight.

900 - FIU Bridge Collapse: Why Müller-Breslau Matters

“My thoughts and prayers are with the victims of this tragedy and their families. Incidents such as this, while thankfully rare, remind us of the complexity of structural systems and the great responsibility that structural engineers and contractors have to public safety,” says Indianapolis-based practicing structural engineer, Michael I. Owings, P.E., S.E. “Many eyes in this industry will be focused on the investigation over the coming weeks to ascertain the cause of the FIU bridge collapse, prevent future loss of life and restore the public’s trust.” 

I wholeheartedly agree with my very dear friend and former masters degree graduate student at Ohio State, Mr. Owings.

We are reminded that the FIU Bridge Collapse is still an ongoing investigation. We all hope to have some definitive answers very soon, that we enable us to better understand structural engineering and infrastructure safety and security threats, whether accidental or resulting from unintentional consequences, so as to avoid this kind of catastrophic and tragic extreme event in the future.

It’s just a matter of time, as people will be thinking about this bridge collapse continuously before we all really know completely all the truths behind this extreme infrastructure event and its aftermath of human recovery.

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Danke Herr Müller-Breslau

Our most compelling interest in pedestrian and historic bridge safety and security in the age of America’s crumbling infrastructure remains an ongoing and essential contemporaneous priority in discussing advanced structural engineering technology and education, as well as, considering the public’s understanding of science, engineering and technology. And, most of all, we must facilitate the diverse cultural participation in structural engineering safety and security by a global workforce of experts, working through the aftermath investigation of a pedestrian bridge collapse on the 10th largest university campus in America at Florida International University.

Besides all the talk of prefabricated concrete bridge construction, midspan tower support mechanisms, innovative bridge installation procedures, German structural engineering, post-tension prestressed concrete materials, and so forth, what investigators also have on their side are basic scientific and engineering principles.

Bridges don’t just collapse, and they don’t just fall onto busy highways. They go up and they don’t fall down.

Like everything else in this world, bridges are bound by fundamental rules of science and engineering — things like transverse shear stresses, transverse bending moment stresses, bridge deadweight to live-load ratios and, not the least, simple gravity of Sir Issac Newton.

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We all owe a great debt of gratitude to Herr Heinrich Franz Bernhard Müller-Breslau for his pioneering innovations in structural engineering analysis and design, and for his fundamental Müller-Breslau principle. This is now aiding America’s ongoing efforts in managing our stressed infrastructure and rebuilding and retrofitting it in preparation for the next generation and the generation after – On Getting to 2076 – America’s Tercentennial!

900 - FIU Bridge Collapse: Why Müller-Breslau Matters

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  59 Responses to “FIU Bridge Collapse: Why Müller-Breslau Matters”

  1. so interesting. thanks for sharing your expertise in this manner. I understand that they had made plans for building a center support. We are all wondering why that wasn’t at least partially built prior to moving bridge into place and then finished once positioned. prayers for all in this tragedy.

    • Great question JED, which is why my students and I initiated this public conversation. Thank you for joining in with your fine question.

      • This is not even remotely relevant to the collapse of this bridge. Dr McGee and Mr Gomez both have it wrong. Please take another look at the drawings for this bridge and you will see two important facts. If you fail to acknowledge them now before it is too late, then you may lose your credibility perhaps permanently. I am trying to help you here, but you do what you want. You guys have jumped to a conclusion and are now embarrassing yourselves with your wild over-confidence.

        1. The bridge section that fell was only HALF of the final bridge. The center support that you are so sure of yourself about is at the end of this first section across the road from FIU. There is a whole section left to be built over the canal, so yes at the end it will appear to have a center support, but in reality it will be two bridges.

        2. The future “cable stays” are not stays at all and are cosmetic pipes mostly for show. The design details show a flat plate welded onto the end of 16″ pipe with a few anchors at the tower and on top of the bridge. Hardly a suitable connection for a cable or even a pipe stay, which would be some kind of heavy duty pinned connection.

        We do not know what happened here and it will come out, but I’ll stake my reputation on the fact that this bridge is not “missing” a center support.

        • “… so yes at the end it will appear to have a center support” quoting you Bryan, as your statement here is the educational purpose of this article.

          This article is not about definite rights or wrongs at all. How can it be written with all the facts still to be determined and the investigation still to be completed.

          The article is for educational purposes only sir.

          Continuous beam (bridge) analysis and design, which I have taught for decades, and which has been outlined in the original 19th century German writings of Mueller-Breslau, of which I own the only existing copies of to-date, and of which I specifically referenced alongside my wonderful students, particularly Mr. Gomez and Ms Reeves, stipulates every statement written inside this educational piece for my students to learn and observe.

          I will defend this higher education purpose for future engineers and engineering education to the floor sir.

          Sometimes education is presenting fundamental questions to discuss with the public and not just about answering those public questions with definitive right or wrong answers that tends to definitely shut down all further questions and answers and further discussions inside the public forum, and most specifically, inside the higher education classroom.

          We have presented this piece for further Socratic discussions inside my spring semester classroom at Texas Tech University in which I am currently teaching Aircraft Structures, and Aircraft Jet Engines and Rocket Propulsion. In that delightful end, the higher purpose of this piece is immediate and is aimed specifically for future minds and capabilities of future civil, mechanical and aerospace engineers – of which I am each of these. I am only serving as a humble teacher here, and as an actively engaged science, technology, engineering and mathematics role model here – and not as a National Transportation Safety Board (NTSB) Member – of which I have not been called upon to serve as humbly speaking.

          Thank you for your engagement of this article and my website.

          Warmly,
          Oliver

          • Dr. Mcgee — I do appreciate your service and efforts in teaching the next generation of engineers. And while I am no expert in educational methods, the Socratic method has centuries of pedigree.

            However, in my opinion, this post (as written) does not embody the invitation to open discussion you espouse. Rather, it is written from a position of authority, experience (directly relevant or not), and finality. We agree — the full facts are yet to be revealed. And as an educator, I’m sure you can see the wisdom and benefit to being explicit about which statements are authoritative and empirically true, and which statements are opinions or conjecture based on our current knowledge.

            To be frank, the marriage of the causes behind the FIU collapse (as discussed in these comments, and elsewhere) and your obvious passion for the efficiency of continuous beam principles per Mueller-Breslau feels forced here. While it may be effective at driving website traffic (per your impressive statistics, it appears this is an area of great interest for you), or timely use of current events to garner the attention of your students, I fear that it may cause confusion and disinformation among the public — that same public that we have ethically agreed to protect, not only from physical harm, but intellectual harm as well.

  2. I knew nothing about engineering until I read this article. It is very enlightening and well written. Now I have to question, if this information has been around for so many years, why did the companies involved in building it not follow the rules? Poorly trained engineers or just greedy for the money? Sad that people had to die for whatever the reason.

    • Andy, that remains to be seen as the investigation continues, who really knows until then. Me and my students were attempting to do an exercise to share with others to join in our conversation, and thank you for joining in. Above all else, this about encouraging and teaching kids to become fine engineers.

    • I suggest reading different articles. Iamebersole is correct.

  3. Speaking as a structural bridge engineer, this article reads as technical mumbo-jumbo. Lost beneath the factoids and anecdotes is the simple fact that engineers today are entirely capable of designing a bridge able to span the full distance of this bridge without a central support.

    Until we know better whether there was an engineering design issue, a construction sequencing issue, or a material failure at FIU, the assertions here are speculative at best (and not particularly coherent at that).

    • Respectfully, I disagree with you.

    • Speaking as a Mechanical Engineer with a Master’s degree on the vibrations of three-dimensional structures, there is no such thing as a bridge without central support. Even suspension bridges, which do not have a physical central support tower, have central supports in the form of suspension cables. Or even arch bridges, which do not have a central support tower, provide central support by redistributing the dead weight loads horizontally. If you look at the FIU article below, you can see that the proposed design incorporated a type of suspension support. Before rotating the bridge 90 degrees onto the highway, they should have installed a temporary central support until the suspension cables were fully installed. Your statement of being a structural engineer is coming into question. I wouldn’t want you designing a doggy house.
      https://news.fiu.edu/2016/02/fiu-selects-mcmfigg-to-design-and-build-pedestrian-bridge-across-8th-street/97102

      • Awesome points Virgilio! Keep up your great work young man! Warmly, Doc M

      • Virgilio — if you care to define central support as any means of carrying load applied at the center of a bridge span (a substructure, suspension elements, or beam/truss action) — then of course! Without any of those, we would have no such thing as a bridge.

        However, in the context of structural engineering, a “support” is an external element (typically substructure) which provides a reaction to the loads delivered by a primary load carrying element (in this case, the concrete truss).

        As Mr. Kohn also has noted, the “cable stay” elements in this design are clearly serving in a primarily aesthetic function, not as significant load carrying elements. It’s not an uncommon thing in pedestrian bridge design, because owners like to have a flashy, attractive bridge to show for their money (and the marginal cost is small). No matter how impressive or functional they appear, if the connections are minimal (as they are here), they cannot contribute meaningfully to the behavior of the structure.

        And of course, if you wish to verify my credentials, the state board of California (among others) is happy to oblige: http://www.bpelsg.ca.gov/consumers/lic_lookup.shtml

      • I’m not sure if Gomez is being pedantic on purpose or by accident, but I’m fairly certain ianebersole is not suggesting that the center of the bridge has no support. Obviously it must be supported by the structure of the bridge. That does not mean that a physical center support is necessary.

        I suppose that’s the difference between experienced structural engineers and recent grads. Pedantry for the sake of being “correct” combined with willful ignorance of the actual issue under discussion.

      • You may want to go back to school. There are simply supported single span bridges you know. The depth was fine for pedestrian and small live load

    • I am a retired structural engineer (35 years or work). ianebersole is absolutely 100% correct. Dr. McGee should be commended for showing his students the possible advantage of continuous span construction over simple span construction. But in the case of the FIU bridge the simple “truss” span could easily be designed to accomade the bridge dead load and construction live load until the mast and cable stays were completed. I suspect something went wrong when jacking additional tension in the post tensioned tendons.

      • I wholeheartedly agree with you Tom and thank you for getting the point of our educational piece for my students. They are wonderfully energetic kids and they deserve our engagement from the experts like you in structural engineering, kind sir. We so appreciate your reading our piece and your online engagement inside our structural engineering classroom. Our five dozen kids now know you herein and are extremely pleased to meet you, Tom! I am pleased to have you join our social media classroom here – as this website is an online media forum for my Aircraft Structures and Aircraft Jet Engines and Rocket Propulsion classes I am teaching this spring semester at Texas Tech University. Our kids look forward to reading more about your experiences, and what you may further want to offer here, as further investigation continues on the FIU Bridge Collapse.

        Warmly,
        Oliver

    • Ianembersole is correct in what he stated.

      Since we are speaking of credentials, I am an engineer licensed in both mechanical and civil, with 48 years of real world experience.
      The bridge was designed as a 174 ft truss, simply supported at each end. There was no center support, and the bridge would never have one.
      It was not cable stayed and no structural support would ever be provided by the “esthetic” tower nor cables. The “cable stayed” appearance was, in fact, just for appearance.
      Perhaps the bridge “should” have been designed with a center support. That discussion could have occurred during a design review.
      I believe my comments above are factual. My opinion, however, is that it was wrong to design the bridge to appear what it was not.

  4. You’re wrong. The bridge did not break in the middle. The video of the actual collapse shows that the bridge first broke at the bottom of the last angled roof support on the right end of the bridge in the last picture. All of the angled roof supports were of similar angle except that the angle of the support where the bridge broke was more vertical than the others.

  5. I was a registered designer of industrial systems(Wisconsin).I agree with Mr McGee’s analysis.
    There is no doubt this collapse could have been easily avoided if QUALIFIED engineers had reviewed the methods planned for this installation.

    • On behalf of our fine young engineers at Texas Tech (who’s basketball athletes have just made the NCAA Sweet 16 in Basketball), Thank you so much, Peter.

      My above replies to others gives the purpose(s) of offering this piece to a wanting public wanting to discuss this publicly tragic accident, as they naturally would. We are humbly only one such article among so many others in which similar discussions and learning are taking place. Warmly, Oliver

  6. The original design shows a central support tower with cable stays with the angled web members being in Tension. (You can see the substantial attachment points on the roof.) The section was installed as a “simple span” Without the cable suspension. Wouldn’t that put the top and bottom “flanges” (roof and deck) in excessive and possible opposite stress forces? Seems it would be more difficult/ costly to design a structure both ways?
    I also disagree with the narrator in the collapse video who stated the bridge was a “bad design” when it appears the more likely cause to be an Incorrect installation sequence? I’m sure this case will be extensively studied in Civil Engineering classes from now on. So sad at the loss of innocent lives. Details Matter!

    • We so appreciate your thoughtful comments, your fine questions raised and your suggestive contributions to our discussion here, J.W. Jones! Thank you, Oliver

  7. No plans? Unprofessional. Confused analysis. Incorrect “true deflection” curve. Given that it was designed as a cable stayed bridge and I suspect the stresses were high in the interim and a center support is an easy way out. Without plans I would not draw any conclusions. I love Mueller but he was all about deflection and your curve is discontinuous for a continuous beam. Brian Blum PE, MSME MSCE former aircraft stress analyst.

    • “a center support is an easy way out”

      Not an easy way out Brian, the safest way! Construction and installation and retrofitting America’s Crumbling Infrastructure must always be about safety first at all cost always, sir.

      “your curve is discontinuous for a continuous beam”

      I beg to differ here Brian, and so does the original 19th Century German works of Mueller-Breslau, which I own inside my library, sir.

      Continuous beam (bridge) analysis and design, which I have taught for decades, and which has been outlined in the original 19th century German writings of Mueller-Breslau, of which I own the only existing copies of to-date, and of which I specifically referenced alongside my wonderful students, particularly Mr. Gomez and Ms Reeves, stipulates every statement written inside this educational piece for my students to learn and observe.

      • Dr. McGee, I believe I understand Mr. Blum’s point about the discontinuous deflection. In the title diagram of this article, the green “true def” curve shows a “kink” at the proposed center support. For a continuous beam or truss (like the FIU bridge), this “kink” requires a hinge in that beam — which does not exist. Rather than the single, sharp point of inflection shown, the deflection curve should have two smooth points of inflection near the center support.

        While the intent of showing the reduced deflection, shear and moment benefits of a continuous beam is still valid, Mr. Blum is technically correct.

    • Brian, hard to believe but the bridge was NOT designed as cable stayed. It is a 174 ft. simply supported continuous truss. The cable stayed appearance was for show, in other words, fake.
      Bill Wells PE

  8. I This question is directed to Dr. McGee-
    The bridge was to be supported by cables linked to a vertical”post” located at “curb” side . The length of the section supported over the street is approximately 2x the length towards the curb.
    Would the support post eventually fail due to greater stresses on the street side?

    • Great question Peter! Tell us more about what you think?

      • If I may interject in Dr. McGee’s stead:

        1. For this particular bridge, the “cables” (actually steel pipe members) are aesthetic, and not part of the primary load carrying structure. See related comments above.

        2. Speaking hypothetically about a different bridge where a true cable-stay system was a primary load carrying element (but with the same geometry):

        You are partially correct in that there is the potential for load imbalance between the two spans of different lengths. (Imbalances can actually be minimized by a clever design, although that’s usually not the most cost effective solution).

        However, a cable stay system (unlike its cousin, a suspension system) does not ever act alone. Cable stays have two purposes — to carry some of the vertical loads, and to enable a separate horizontal structural system (a beam or truss) to carry the remaining loads more efficiently than it could by itself. This horizontal system has it’s own structural capacity.

        As such, an imbalance in a cable stay bridge does not mean the horizontal structure or the cable stays and tower (“post”) themselves will fail. Cable stays carry away a portion of the imbalance (and are designed to carry that portion through cantilever bending of the tower) — while reducing the imbalance that needs to be carried by the horizontal structure’s own inherent capacity.

        3. Returning to the FIU bridge, because the “cable stays” are aesthetic with very little capacity of their own, they take a very small (essentially zero) portion of the load. Hence, the horizontal structure would be intended to carry the entire design load. In this case, the two spans (over the roadway, and over the waterway) appear to be effectively separate structural systems, so no real imbalance exists.

        4. Based on the facts to date, I believe this discussion of structural systems, while hopefully informative, is not related to the failure mode of the FIU bridge.

    • Peter – you have pointed out the probable reason a cable stayed system was not intended. The unbalance due to different spans would introduce other conditions which would require solutions.
      If you search for the MCM proposal and preliminary drawings, and if you dig deep enough into those documents, you will see the statements that the cable stay system is for aesthetics and is intended to dampen vibrations only.
      The engineer who designed this bridge has a patent for cable stay installation features and it is doubtful that he detailed the faux stays of this project with the intent of supporting the structure.

  9. My understanding is that the design was 2 spans, and it was the 1st span that has collapsed. The ‘suspension’ element looks to be cosmetic rather than structural, so span 1 should be capable of supporting its own weight without suspension or a central support tower.

    The nature of the failure though looks like a combination of possible structural failure during transport to its final destination, lack of safety protocol (close traffic while post tensioning) and a significant post tensioning failure on truss beam #11 where a PT rod looks to have failed while under significant tension load.

    If you review the various videos of the collapse frame by frame, you will see the initial failure starts at the top and bottom of truss beam #11 where the PT rod failed with enormous outwards loads and force.

    The bridge did not fail in the middle, did not fail because is sagged in the middle, and probably not any inherent design flaw regarding span width. However there will be questions about the all concrete design, ABC approach, construction and transport methods (including possible last minute changes) and fundamental questions on post tensioning design, procedure and safety.

    Can’t see why a 50m span concrete bridge is a problem per se. Here’s 2 examples of similar length spans, albeit different designs:

    http://penerbit.uthm.edu.my/ojs/index.php/IJSCET/article/viewFile/388/310

    https://www.pci.org/PCI_Docs/Publications/PCI%20Journal/2006/November_and_December_2006/Nebraska%20Precast%20Record%20-%20204th%20Street%20Bridge%20Spans%20Single-Point%20Interchange.pdf

  10. This is a lot to digest (I’m electronics related engineer.. was in school 37 years ago), but I agree the span needed a temporary support until the second span, pylon, and cables/struts were in place. This bridge was designed to last 100 years through a Cat 5 hurricane, but failed after 5 days.

    I noticed the asymmetrical “W” truss structure and ran some numbers using an online truss application. Node distances were estimated from artist’s drawing of the completed bridge – main issue being the angle of members that would be in line with cables from the pylon. I estimated load distribution using 1000 kN across the bridge with 20% from canopy and 80% from walkway – loading this way, or all on top or bottom, didn’t affect stress directions, though had minor affect on magnitude. The forces within this span REALLY look different than with a symmetrical design.

    A difference with this span is there’s only one truss in the middle, instead of on both sides – seems it would be more susceptible to twisting if tightening cables, under stress, wind, etc.

    A random factor might be vibration from traffic. There’s an overpass across Hwy 70 by my house (6 lanes total), which bounces a bit when semi-trucks pass underneath – it hasn’t fallen in 20 years when fully loaded with stopped traffic, so it’s obviously built to withstand the impulse. Traffic is fairly close to the spans supports so they could transmit impulses to the span.

    I can’t post a diagram, but it can be seen by clicking my screen name/twitter account. I’m wondering if anyone knows if this asymmetrical design might cause a stability problem without the final support structures. [I’m not even sure if the diagram makes sense/software is okay… seems tension and compression would be opposite]. Any feedback would be appreciated.

  11. Using approximate numbers–Street side– 475Tonsx 87″=41325 Curb side 240Tonsx 44’= 10560
    Street side stresses are 4x curb side . If the vertical tower is concrete(with steel rods) i think it would eventually crack and fail -falling toward the street . Does this make sense to you?

  12. Its been many years since I took structures in college and have been in the business end of engineering since then. I and have observed a fair number of structural failures fortunately without any one getting hurt. Generally there is more than one factor leading up to the mishap. The above analysis discusses that a midspan support of the span that failed would have prevented the collapse. (Even a layman could have deduced this) This support would have been in the center of the highway and would have supported the span until the tower and suspension cables were installed. This support structure would have had to have been installed using some type of costly foundation such as friction piles or spread footings necessitating interruption in traffic flow. Also this structure would likely have interfered with rotating the span into place all of which would have compromised the advantages of the ABC method.
    Thus the designers used another means of providing a continuous beam for temporary support in a cost efficient manner. In time we should learn what the cause of the failure. Since it reportedly happened during tightening of the post tension cables a failure of the cable end attachments may have occurred.

  13. I’m a bridge engineer with 30+ years of experience, including prestressed concrete beam design.

    The author of this essay is declaring that the reason that this Florida bridge fell down is because it’s a single 170 foot simple span instead of two 85 foot continuous spans.

    Unless the bridge was designed as two continuous 85 foot spans and improperly constructed as a 170 foot simple span, this conclusion is incorrect.

    It’s true that the bending moment and deflection are lower in two 85 foot continuous spans than in a single 170 foot simple span.

    However, it is an easy task to design a safe 170 foot simple span. The loads are higher, so the the engineer simply uses larger, stronger beams to carry the larger loads.

    Next time you go out driving, observe that most existing highway and rail bridges are simple spans. This is because continuous span bridges are sensitive to foundation settlement of the supports. The state DOTs back in the 1930s, 1940s, and 1950s thought of continuous spans as a needless complication. Most preferred simple spans and would say, “simple spans, simple problems.”

    Even today, railroads don’t build continuous through-girder and multi-beam bridges, they almost always build simple span bridges. Rail loads are VERY VERY large, so if they build continuous spans, then they will have problems with uplift of beams at the end supports. The beams at the ends of the bridge will try to lift up off the abutments as the adjacent spans are loaded.

    Also, the vast majority of the typical prestressed concrete multi-beam bridges out there are simple spans, even when multiple spans are needed. And when they are made continuous, they are continuous for live traffic loads only. The continuity is done to eliminate deck joins, which tend to leak rainwater, not to lower the bending moment in the beams.

    To summarize:

    170 span = commonplace, no problem at all.

    Simple span = very commonplace, no problem at all.

  14. As a bridge engineer with a Master’s degree from Texas Tech, it makes me sad to see this post from a Texas Tech University professor. While this article shows an understanding of the theory behind some aspects of structural analysis, it does not show an understanding of the real-world practice of bridge design today. This span length can be easily and safely constructed without the need for a center pier. I have personally designed unsupported post-tensioned concrete bridge spans up to 250 ft in length. I urge you to walk over to the civil engineering department and discuss this with the knowledgeable professors over there.

  15. There are a number technical inaccuracies in this post.

    YOU SAID: “The 174-foot long pedestrian bridge was assembled on-site days earlier on Saturday from prefabricated post-tension prestressed concrete spans”.

    ACTUALLY: The design plan called for the main span truss to be prefabricated in the staging area as a single unit for the entire span. It was not assembled from prefabricated concrete spans.

    YOU SAID: “the assembled prefabricated continuous prestressed concrete beam that was hinging on one support was swung 90 degrees across the highway, and was then hinged on the other support”.

    ACTUALLY: The concrete truss was not “hinging on one support”; it was supported entirely by the 4 transporters while being lifted and moved. Once it had been moved into place, it was then lowered onto the supports. You can see this quite easily from the timelapse videos of the move.

    YOU SAID: “This FIU Bridge Collapse… is a result of a missing essential center safety support tower mechanism located at midspan across the enormously long 174-foot span”.

    ACTUALLY: The bridge did have a mid-support tower, positioned between the highway and the adjacent canal, at the north end of the span which collapsed. The finished bridge was actually designed to be 274′ in length, consisting of a 175′ span crossing the highway, to be constructed in a staging area and moved into place, and a 99′ span crossing the canal, which was not yet built but scheduled to be constructed in-place after the first span had been placed. The main, 175′ span collapsed after being placed in its location, prior to completion of the second span. It was, obviously, designed to be more than capable of supporting its own weight as a single span without a mid-section. This design, just as obviously, failed. The investigation will hopefully determine where and why.

    If your point is that “every span needs a center safety support tower”, well then you’ve created two spans and they both need a center support, creating four spans, and so on. Obviously this is not the case. Spans are designed to be capable of supporting their own length. While it is true that supports can be used to shorten the length of individual spans, reducing the amount of stress on the structure, you cannot simply jump to the assumption that the lack of one in that section is why this bridge failed.

    YOU SAID: “Thus, the bridge’s failure collapse mechanism occurred around the center”.

    ACTUALLY: The collapse did not occur around the center; it occurred at or very near to the second node from the north end of the span. If you cannot tell just from looking at the rubble, there are multiple security camera and dashcam videos of the collapse which clearly show that the collapse occurred in that location, not in the center.

    FINALLY, a number of people have posted comments believing that the bridge was supposed to be suspended by stay cables. This is simply not the case, and you would do well to correct their misconception. The bridge was designed as two truss sections supported at both ends. The center pylon with its stays was designed to provide some stiffness to avoid harmonic vibrations under pedestrian loading, and to “create dramatic signature aesthetics that tie directly to the rhythm of the strut pattern” (of the truss).

  16. Dr. Oliver, When will we be seeing you on Fox news commenting on this subject?

  17. what a crock of shit.

  18. That structure should work as a truss or as six single beams supported by cables, or both. So, the old an good theory on continuous beams does not apply to it. What is incredible is the speech about “decorative” or “dramatic” cables… However, if such a structural piece was actually supposed to stand alone under its own 950 tons and the overload should be mere pedestrians, a truss would be enough, with no poles and cables…
    Failure has happened at bottom plate between bars 2 and 3 (from north). Frames of fail show entire structure with no issues, all triangles ok, except that one between bars 2 and 3. The angle between those bars increases, as if that segment of bottom plate had elongated. For me, the traction rupture at that segment is evident on video.

  19. Your writing is really hard to follow. Are you essentially saying that the bridge would not have collapsed if there was a central support? Doesn’t that seem obvious? How does this discussion add to the collective conversation among the public and among engineers?

    Also, could you please explain this sentence:

    “the FIU pedestrian bridge collapsed mathematically under an absolute value of (1-(0.013/0.0054))(100%)=140% error in its failure collapse transverse bending deflection mode … underneath the bridge’s own deadweight.”

    If the bridge collapsed solely from its own self-weight, how was it stable for the several days before the collapse after it was moved into place? The bridge failed due to some sort of external construction load placed on the system, not due any internal stresses. Is this not correct?

    Either I am wholly misunderstanding you or my comprehension of undergraduate mechanics is suspect.

  20. Please help doctor. I live near this single span truss bridge with no central support. When is it going to collapse?

    http://c8.alamy.com/comp/B01RK3/bridge-over-salt-river-arizona-state-road-288-steel-truss-bridge-desert-B01RK3.jpg

  21. What the heck are you guys smoking?

    So a 174ft simple span requires a central support? Are you insane? Have you left your office and looked at a few bridges recently?

    Did you even look at the pictures of the bridge collapse? Even better, there’s actual video of the collapse occurring. Can you seriously watch that video and claim that the failure point was in the center of the bridge?

  22. Hi thanks for this article.

    I’ve Very basic questions and I’m not quite sure how to ask them:
    If a support is needed at the middle, what happens the next middle? Or in the 1/4 position?

    Also when I was looking up the design of the bridge I saw that it v was called a truss and not a beam, how does that effect what’s down here?

    Good to see an article with references!

  23. Professor McGee – I think you have provided a clue to something I
    have wondered about for years. Earlier in my career we had an
    Architect as a client (now deceased). He often spoke of working in
    the 1930s for an Engineer in San Francisco named Nishkian, as I
    recall. He spoke of Nishkian drawing moment diagrams and sketches
    and solving structural problems that way. I did not learn the details –
    and I doubt that he could have accurately relayed them – but I now
    suspect Nishkian was using the principles of Muller-Breslau.
    I applaud your efforts to bring outside discussion into your classroom.
    I am sure your students will gain insight thru the process.
    I fear we are in something that might be called a circular discussion.
    It seems we always return to needing a center support. Could that be
    because Muller was addressing two span structures and elements
    which spanned over a center support? Should each of the two spans
    created by the center support require an additional support? How long
    can we divide the span by 2 before we have a solid wall under the
    structure?
    I may have misunderstood you, but am surprised that you disagree
    with the statement that engineers today can design a bridge that
    would span 174 feet. I understand that if Muller is the only design
    method and criteria, then a center support must be provided. As Mark
    Twain is supposed to have said , “ When the only tool you have is a
    hammer, everything looks like a nail”.
    But we have gained many tools since Muller’s days. And I see it as the
    nature of engineering to use those tools.
    I propose that your students learn the Muller methods – they may
    provide them insight into things that data entry and a computer
    printout cannot. The ease of computer solutions masks the actual
    thing that may be critical – it isolates the engineer somehow and
    requires much deliberation to remain involved with what is happening
    in the design. And no computer can tell you that something may just
    be a bad idea. I wonder if the computer program for the FIU Ped
    Bridge told them that the single truss lacked redundancy? The failure
    certainly emphasized that point.
    At the time of a comment you made, you probably had not seen the
    videos of the collapse. The structure clearly failed at the north end,
    and I suspect failure began at the heel joint of the truss over the north
    pier. The last diagonal has about 1600 Kips compression, causing a
    1300 Kip shear thru a pour joint.
    From a human interest angle, consider the following: Suppose the
    failure was somehow imminent but without any manifestation of a
    pending problem – yet. And consider that there are concerns that the
    “adjustment” of the PT in the last diagonal triggered this collapse, by
    adding compression in the diagonal and thereby increasing shear
    across a suspected deficient joint. That increase in PT force would be
    less than the increase from by a full live load of students and
    dignitaries at a ribbon cutting ceremony. That happy event then could
    have triggered the collapse with much greater consequences. The
    failure we have endured has been horrible, but it may have prevented
    an even worse tragedy.

    Now to comments by Virgilio. I appreciate the vigor of youth. Really.
    But even your Professor lauds the knowledge of a guy who died almost
    a hundred years ago. So old guys can sometimes have something to
    contribute. I think your dog house would be structurally sound if the
    bridge engineer built it.
    But I have a question for you that is right up your cable stay. The
    proposal and preliminary drawings are clear that the intent is the
    trussed structures span without support from any cable stay system.
    The intent of the mast and ‘cables’ is to dampen vibrations (your
    specialty) and is a visual statement.
    My question is – the ‘stays’ are 16″ dia pipe sections. The longest is
    145 feet long. What is the possibility that vortex shedding will create
    vibrations in those ‘stays’? I can envision gentle breezes causing
    significant vibrations in the stays and transferring those into the
    bridge structure. The result could be exactly the opposite of that
    desired.
    Thank you,
    Vance Wiley

    Link to Proposal and preliminary drawings.
    http

  24. Dr McGee, with respect, your article is balderdash. Your insistence that the problem with this bridge was that it had no center support is making you the butt of jokes on engineering websites. This was simple span truss. With a central support, it would have been a continuous truss, and a completely different bridge concept.

    It was not a cable stayed bridge, as the pipes and tower were there for aesthetics.

    The bridge design can be faulted for many reasons, but your explanation is nonsensical.

  25. Muller-Breslau was born in Wroclaw, Poland and not in Portland.

  26. Your analysis is incorrect. This bridge, and many others, was designed to span the entire roadway. The planned 175’ clear span is not remarkable or unusual. A center pier, as you have described, was neither needed nor advisable given the presence of the roadway below.

    The bridge did not initially fail in flexure, near mid span, as you have suggested. It is clear that the critical initial failure occurred in the northernmost web diagonal, which in turn led to a progressive collapse. Any flexural failures came only later as the bridge struck the pavement.

    While Müller-Breslau is an important principal which we structural engineers use routinely, it’s application to this tragic failure is misinformed.

    I practiced structural engineering for over 35 years, most of which time was spent designing bridges. I am very confident that my criticism of your assessment of the FIU failure is appropriate.

  27. If this situation was simplified to considering it a “Teeter Toter” both sides would balance when weight x distance from the fulcrum is equal. On that basis, the street side has 4X greater down force than the the curb side. The vertical support column would have the able to withstand the unequal stresses indefinitely. If it is as slender as depicted in the design pictures i’ve seen, I don’t think it will.
    Does this make sense??

  28. The problem smells like a human problem.

    Clearly the bridge was incomplete. It is very likely that when complete, the bridge would design as intended for decades to centuries.

    The engineers would have detailed the construction sequence in a sound manner. I would presume:
    1. the central pillar
    2. supporting pylons
    3. short section
    4. long section
    5. cable stays
    6. tensioning

    The long span looks marginally engineered to stay up without cable stays or temporary support under its centre (there is a traffic island where a temporary central pylon could have been if needed – but it wasn’t needed and the bridge was supporting its own weight).

    So in the construction sequence, why place the longest span first???

    It seems that someone in charge without requisite knowledge was being pressured to do something. Schedule running behind. Cracks reported a couple of days earlier. A decision is made to tension, but surely in the design documents this would have been after the cables are installed. Clearly the evidence suggests the tensioning caused it, but there is a long back story.

    Major failure require multiple small errors or coincidences and people who would have known what to do were not consulted or unavailable.

  29. I left a comment before, but it was censored. The idea that you cannot design and build a footbridge to span 175′ without central support is nonsensical. The problem here is that the wrong system was selected. Concrete trusses are rare, and for good reason.

  30. Peter, as I stated above the post and cables were only for show, to give appearance of a cable stayed bridge.
    The bridge was designed as a continuous truss supported only at ends.

    In my opinion, they should have found some other way to give their bridge a “stunning appearance”.

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