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Rio de Janeiro, Brazil is currently stunned by the fact that yesterday a span of a brand new (innaugurated in January) bicycle bridge along the coast collapsed when struck by a wave, killing some people that were on it at the time.

A few videos have surfaced:

  • This one is of the moment it collapsed, but the man behind the camera didn't notice what happened until a few moments later, so you don't can't clearly see the wave impacting the structure, but you can see how the waves are redirected and slam against the structure almost vertically.
  • This one is from after the collapse, but clearly shows the aftermath. At 2:15 you can see an example of another wave running up the rocks, spraying up higher than the road. At 2:30 you can see the columns (including their topping, where the beam was supported are in perfect condition and don't seem to present any damage.
  • This article shows a video representation of what is believed to have happened: the waves lifted the beam off the pillars and caused a rigid-body rotation around its own axis. This, along with the mint condition of the tops of the columns implies that the project probably did not adopt a beam-column connection which could resist tension, which would therefore have impeded the beam's "liftoff".

Now, my actual question is: how does one calculate a structure to resist such a load? I've done some searching and have found some articles ([A] [B] [C] [D]) regarding wave action on bridges, but they all consider the more common case of a wave moving in a horizontal direction striking the side of a bridge. Now, how should one translate this to this case, with the wave being thrust (and possibly sped up) vertically?

Are there any codes which consider such cases? Also, more generally, are there any codes which define even standard wave action? International codes are fine. (I'm leaning a bit on Rick Teachey's position on the "recommendations/finding stuff" meta post for this part).

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  • $\begingroup$ That seems like a very uncommon load case. I have checked spans over rivers for buoyancy, but I haven't ever thought about the vertical energy of waves. $\endgroup$ – hazzey Apr 23 '16 at 1:44
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    $\begingroup$ I"m betting there'll be a rapid analysis of vertical lift resistance and new code added to bridge design :-( . In the meantime, why not take the design rules for horizontal shock (wave attack) resistance and apply them in the vertical direction? That is, consider redesigning vertical fastenings to be more like the horizontal ones. $\endgroup$ – Carl Witthoft Apr 25 '16 at 11:14
  • $\begingroup$ @CarlWitthoft: With a lack of other options, I think that's what I'd do, but I'm just not sure how valid that is. After all, in this case the wave didn't really behave like a wave, since it was diverted and became more like a jet of water slamming into the bridge. But yeah, I can't think of a better solution. Just wanted to know if some code had something closer to this reality, as unusual as it is. $\endgroup$ – Wasabi Apr 25 '16 at 11:26
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    $\begingroup$ I would start by doing a survey and find out how high the column of water is known to shoot up vertically in that area. Using bernoulli's equation I would simplify this, assuming that the ground level below the bridge is where an orifice is located. From that I assume a vertical column of water reaching an apex, as discussed. Bernoulli does the rest. This is very basic, but it should give an excessively conservative result, which will be on the safe side of reality. $\endgroup$ – NamSandStorm Apr 27 '16 at 14:54
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    $\begingroup$ I will need to take some time to prepare it properly, will do. $\endgroup$ – NamSandStorm Apr 27 '16 at 16:22
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I understand this question is about an event in Brazil and not the US. However, section 3.7.4 (Wave Loads) of the 2012 AASHTO LRFD Bridge Design Specifications simply says:

Wave action on bridge structures shall be considered for exposed structures where the development of significant wave forces may occur.

(This isn't a summary; that's literally the entire section.)

The commentary recommends referring to the Shore Protection Manual from the Coastal Engineering Research Center. Copies of the manual (at least older editions) seem to be available via a quick Google search; it is very lengthy and I am not familiar with it myself, so it may or may not have specific recommendations for calculation of load cases for vertical wave action. Perhaps someone more familiar with the manual can edit my answer with more information.

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I think in this particular case the tensions force on the bridge should be calculated by regarding the bottom surface of the bridge as a water pump's impeller or the drag induced on the tip of a submarine or torpedo. The Entire bottom of the bridge geometry should offer the least resistance to flow of wave break. Dynamic drag forces are very similar to already exiting methods to design submarines! if the geometry of the abutment is potentially capable of creating explosive impact that has to be accounted for too. Surely there will be new research and code added for this particular case in the future. It is only that this is a new phenomenon. I had designed a concrete deck including a suspended swimming pool supported by 6 concrete cassions 45" deep into bedrock. And after some years visiting the job I noticed some of the caissons had cracks on top where they met the slab which was due to seasonal uplift and settlement force of clay soils. One has to think about all eventualities when designing theses kind of structures!

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