Trying to understand what is happening in this bridge report 1

[bojoka4052]

I am reading a report about a multicellular deck bridge and they talk about points of contraflexure, and they say members should be spaced closer than 1/4 of the points of contraflexure which I dont understand?

The bridge has 3 spans as seen below (L1, L2, L3), the middle one has a length of 45.65 m which is referred to in the text above, then they multiply it with 1/4 (?) and 0.6 (?). I know there is not much information, but what could the number 0.6 and 1/4 be referring to? I assume its not a length since it does not have a unit.

The source referred to in the text is Bridge Deck Behaviour by E.C Hambly.

 

[dik]

I'm not into bridges, so I'm not sure of what they want, but I would have thought that L1 = L3 = 40m give or take a bit...

So strange to see the singularity approaching while the entire planet is rapidly turning into a hellscape. -John Coates

-Dik

 

[IDS]

Presumably the 0.6 is the factor of the span length for the distance between points of contraflexure, but the book is talking about the spacing of transverse members in a grillage analysis and it was written in the days when computer models had to be kept as small as possible, consistent with reasonably accurate results.

With modern computers it would make more sense to use a much finer grillage, or use plate elements rather than a grillage model.


Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[dik]

Maybe a little less than 40m... 40m was based on plastic design.

So strange to see the singularity approaching while the entire planet is rapidly turning into a hellscape. -John Coates

-Dik

 

[IDS]

I assume the 0.6 factor is the factor on the central span for the distance between the points of contraflexure in the central span. I don't think the end span lengths are relevant to the question.

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[BridgeSmith]

I agree with IDS that the 0.6*45.65 is likely an approximation of distance between the points of contraflexure for the center span. Contraflexure points in continuous spans of similar length are often assumed to be at 2/10 and 8/10 of the span length.

I believe the 1/4 of that distance as a limit for the transverse spacing of beam elements is either for stability or economy, or both.

Rod Smith, P.E., The artist formerly known as HotRod10

 

[bojoka4052]

I assume the 0.6 factor is the factor on the central span for the distance between the points of contraflexure in the central span. I don't think the end span lengths are relevant to the question.

I think you got it, another thing I was wondering about in the report if I may ask; They have the grillage model under the section "Analysis models for longitudinal design of superstructure". A seperate section "Analysis model for transverse design of superstructure" says "Transverse design will be carried out with a shell model." So it seems logitudinal = grillage and transverse = shell model?

I dont understand why they cant use the grillage model for transverse aswell as the longitudinal analysis? They say that the shell model also includes the substructure (with beam elements) and it can be used for determination of load distribution factors as well as
for the verification of the longitudinal design and design of substructure. Are they perhaps only using the shell model to verify the grillage model?

 

[IDS]

I really don't know why they would do both a grillage and a shell model, maybe they find the longitudinal design actions easier to extract from the grillage, but as you say it provides a cross check so I don't see a problem with it.

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[bojoka4052]

Thank you IDS, I have one more section that has been confusing me if you would have the time:

They say "One of the challenges is to divide the cross-section into individual beams. The subdivision chosen meets the criteria that the longitudinal beams have their "individual principal bending axes aligned with the principal bending axis of the cross section as a whole." This criterion alone will yield infinitely many solutions for the subdivision of the cross section."

They seem to split the entire cross section seen below into 4 equivalent seperate longitudinal beams, but I dont understand what theyre talking about with the principal bending axes, does the text make sense to you?

 

[Settingsun]

I dont understand why they cant use the grillage model for transverse aswell as the longitudinal analysis?

They've referenced Hambly's book. Hambly recommended using spearate global and local models to keep the models and amount of data small. If you use a coarse grillage with the minimum number of elements, the transverse elements are spaced too widely to show local peak stresses.

individual principal bending axes aligned with the principal bending axis of the cross section as a whole.

It means splitting the cellular cross-section into I-beams and J-beams that have their centroids at the same height as the full cross-section. If the webs are all the same thickness, it means each split beam has 1/4 of the top flange (deck) width and 1/4 of the bottom slab width. In your image, they haven't followed this recommendation; they've just split the elements halfway between webs. See image below for a twin-cell case: 1/3 of top slab and 1/3 of btm slab.

 

[bojoka4052]

It means splitting the cellular cross-section into I-beams and J-beams that have their centroids at the same height as the full cross-section.

So for the picture you posted, I would have 2 longitudinal J-beams and one longitudinal I-beam in my FEA model, which will be connected by the transverse members? And if I use say hundreds of transverse elements so I get a very fine grillage I might not have to create a shell model? Sounds like a pretty straightforward way of doing things, and the challenge lies in finding the equivalent cross section.

I could probably go with three longitudinal I-beams?

 

[Settingsun]

You would need additional longitudinal members representing just the top slab to do the local/transverse analysis. If you had lots of transverse members but just the three main longitudinal members, there is no way for the transverse members to share/distribute concentrated wheel loads. They'd just act like beams instead of a deck slab.

 

[rb1957]

man, I'm getting so scared about bridge design ! The cost of modelling these days is so slow that we don't need the short-cuts we used even 10 years ago.

Mesh the cr@p out of it if you want.

For myself I'd model the surface as plate elements with an appropriate bending stiffness. How appropriate ? fine mesh one panel to capture the fine structural details and see how the real structure deflects, then make an equivalent property. Still not sure ? Make a panel and test it.

another day in paradise, or is paradise one day closer ?

 

[IDS]

rb1957 - So what is generating the fear?

Also I'm guessing you meant the cost of modelling was low rather than slow?

But as for modelling the crop out of it, I don't think I agree. It's easy to generate the model these days, but extracting the design actions becomes much slower if you over-complicate it.

These days for the box girder section shown I'd probably use beam elements representing the full depth of concrete at the web locations connected with rigid links to plate elements for the deck and bottom flanges.

I would also generate my own model when verifying, rather than working through the model the designers had used, if that was allowed under the contract verification requirements.

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[rb1957]

yeah, I don't think much about concrete as a structural element (obviously, given my field). I don't mean it's no good, just it is very different to Al.

the discussion seems to be about modelling strategies to represent (or misrepresent) the structural elements.
I'm going to assume you guys know what you're doing.

"Let us hope that all will go well for once" General Paulus, outside Stalingrad after the launch of Operation Uranus.

another day in paradise, or is paradise one day closer ?