Relative deflection of girders on horizontally cruved bridge 1

[Noopur]

I have a question regarding the deflection of curved girders. The bridge I am working on:

Has skewed supports (not radial)

Supports are not parallel to each other

Span is a simple span (167’ longest girder, 158’ shortest girder)

The supports are skewed such that the outer girder is actually the shortest. And the girder on the inside of the curve is the longest.

Radius of all girders is 605.22’

I am getting larger deflection (8.6”) for the outside girder and about 5” less (3.7”) for the inside girder.

For a normal curved girder bridge with radial support, it is understandable that the outside girder (longest) would deflect more. But for this bridge, with the outside girder being shortest, is this still true?

Does anybody of you had a similar situation like this. I am designing a curved girder bridge for first time and really do not know where to look for answers.

Your valuable input from experience is much appreciated.

thanks.
Njain





Noopur Jain
Bridge/Structural Engineer

 

[civilperson]

The girders of curved bridges MUST be connected with rigid diaphragms to make the deflections equal at the diaphragm location, (including the abutments). The stiffer beam will receive the most load and the deflections at the diaphragms will be equal.

 

[Noopur]

In other words rigid diaphragm takes the stresses/loads due to differential deflections of the adjacent girders?
Correct me if I am wrong.

Also my question is still unanswered...why the outer girder is delfecting the lost, although it is shortest? Is this normal?

Noopur Jain
Bridge/Structural Engineer

 

[civilperson]

Your problem is suspect: All girders with same radius, (this means a varying space between the girders); calculated deflection of 8.6",( What is load case and arrangement of the lanes giving this deflection? Is the same load case and load pattern used for the other girder calculations which give 3.7"? How did you calculate the deflections? What assumptions of fixed ends or simple span, what portion of the deck is assumed composite with the girder?

 

[Drumchaser]

Are your girders steel? I am guessing yes, due to horiz. curve. Size?
I am one click above a novice, but 8" inch deflection (mid span?) sounds extreme.

Can you attach a .pdf or screen shot of this span?

 

[graybeach]

As civilperson pointed out, your girders should not all have the same radius. Whatever your configuration is, you need to do a 3d computer analysis with all members, including the diaphragms accurately modeled. The deflections will not necessarily be equal along each diaphragm, but they should vary linearly.

 

[Noopur]

I have attached a pdf of the bridge. It shows all girders with two supports and edge of deck, gutterlines etc.

I am sorry, the girders are not all same radius. I intented to call them concentric and mistakenly called them same radius. They are at a spacing of 7'-8" constant not variable along the lengjht of the bridge.

I am doing computer analysis. When I do a line analysis, the girders behaves as anticipated: Longest (inside) girder delfects the most and shortest (outside) girder the least.

but when I run a grid model, the beahavior is exactly opposite. Does anybody have a clue why so?

Noopur Jain
Bridge/Structural Engineer

 

[Qshake]

The layout you've shown is not a particularly complex curved bridge, what software are you using? I would recommend that you use the grid analysis and focus on getting the diaphragms accurately modeled as for a curved bridge these are no longer secondary members.

I also recommend that you discuss with a more senior bridge engineer in your group.

Regards,
Qshake

Eng-Tips Forums:Real Solutions for Real Problems Really Quick.

 

[Noopur]

I am using an inhouse program? Would you recommend any particular software which is better over others?

Have you experienced anytime: that shorter girders have more deflections (just beacuse they are on outside of the curve?)

Thanks,


Noopur Jain
Bridge/Structural Engineer

 

[graybeach]

Noorpur,
The behavior you describe makes sense to me. Due to the curvature each girder wants to twist as gravity loads are applied. The direction of the twisting is such that the outside curve gets pushed down and the inside curve gets pushed up. The diaphragms keep the girders from twisting individually, but the loading on the diaphragms causes the global twisting. In your configuration, the tendency of the longer girder to want to deflect more is overcome by the twisting.

 

[miecz]

Noorpor,

I would expect that the vehicular centrifugal force would cause this type of deflection. Can you load your model without the CE loading?

 

[Noopur]

Yeah, but if you think about it...it is a simple supported span. The mid span deflection is directly proportional to lspan lenght to the power 4.

5/384 * w * l**4 /EI

My outside girder is 10' shorter then the inside. How would you convince that the shorte girder would deflect more? Due to some combined action due to curvature?

Software generated the Live loads and I do no think that Centrifugal force is incorporated. morever in my first post the deflections that I have listes are due to dead load only applied to non-composite section.

Also the inside girder has an overhang of 5'-8" and outside girder has an overhang of 2'-8". Comman sense makes me beleive that the longer inside girder with 5'-8" overhang should delfect more?


Noopur Jain
Bridge/Structural Engineer

 

[bridgebuster]

graybeach's explaination is correct; and as Qshake said you need to do a grid analysis.

Remember your girders are stupid; they don't know they're part of a system; they don't know they're curved; each one thinks it's a straight girder with an eccentric load.

Draw chord from centerline of bearing to centerline of bearing for one girder and it might be easier to visualize how the system works.

 

[VoyageofDiscovery]

What is preventing you to skew your diaphragms, your diaphragm as shown will intersect your pier diaphragm generally used for others things as well as jacking for maintainance, will help for splice locations and fatigue checks.

 

[VoyageofDiscovery]

On second thought your skew looks to much to skew your bracing.

 

[Drumchaser]

*inside girder has an overhang of 5'-8"*???????
This also sounds extreme.


The few Plate Girder (steel) bridges I have seen had a unique conc. slab placement sequnce due to the tension flange areas. Could this possibly be your problem?

Also have not seen any deflection diagrams that were even close to 8".

 

[gwynn]

Drumchaser

It's a bit of an aside, but over the past decade or so overhang widths have tended to increase. In the past six months I have seen a couple of 6' overhangs and one with the overhang peaking at 8'. The contractors were not happy.

 

[Noopur]

Thank you all for your thoughts.

Qshake: I agree that diaphragms are primary members for this case.

Please elaborate on what would you consider while modeling diaphragms? How the stiffness and location/orientation of diaphragm could affect how the girders will behave? Any thoughts......??

Graybeach: The global twisting of the bridge makes sense.

I am planning to do a 3D analysis modeling the girders/diaphragms/slab in STAAD and/or SAP to verify this and the deflections I am getting. Any recommendation on which is the best software to do this kind of analysis?

Bridgebuster: Drawing chords from CL to CL of bearing is a good idea. I will try that as well.

VoyageofDiscovery: Guide specification and research done so far recommends using radial diaphragms. Moreover all curved bridge designs that I looked for example used radial girders. My skew from radial is significant: about 40 degree at abutments and about 60 degree at piers.

Drumchaser: This is a rehab bridge. To avoid extending/widening pier (pier is existing), a 5’8” overhang is used. And that is the reason the overhang is not same on both sides.

Previous designs done for curved bridges shows DL deflections of up to 14”. The bridges are constructed recently (7-8 years back) and are in service without any issues so far.

I think I am going to do a grid analysis using a 3D modeling software. More thoughts from all of you would be appreciated. If you have a similar design done previously, I would appreciate any details, which you could forward.

Thanks again. This discussion is giving lot of new ideas that I can use. Please continue to provid more thoughts....


Noopur Jain
Bridge/Structural Engineer

 

[Qshake]

Noopur -

MDX is one of many curved girder progrmams available on the market. It is widely used and accepted by the bridge engineering community and has excellent technical support.

If you are not experienced in FEA modeling of bridges, using SAP (I would not use STAAD) can be difficult do to so many modeling issues seemingly unrelated to the deflection but which have a direct impact on those deflections. For example, there is a matter of continuity or strain compatibility at the concrete slab girder interface which must be accounted for in areas of composite action and for those areas where no composite action occurs other modeling techniques need to be employed. Other examples include eccentricity if you are using plate elements for the deck and frame elements for the girders. If you don't use frame elements for the girders but model them with plate elements for the web and beam elements for the flanges the problem get much more intricate and complex.

On the matter of providing a 5'-8" overhang, this is excessive and should be re-evaluated. One consideration if you'd like to avoid pier widening is to use an exterior girder that is supported off the first interior girder (assuming it is also new) using tapered diaphragms to connect the two. This has been successfully used in many applications.



Regards,
Qshake

Eng-Tips Forums:Real Solutions for Real Problems Really Quick.

 

[Noopur]

Qshake

I was thinking of modeling the beams as a system of small (may be 5') curved beams (STAAD has capility to define curved members) joined together. Essentially all software model curved beams as such (to my best knowledge). Also
I will have joints at diaphragm locations so that I can easily connect diaphragm to my beams. I have to figure out how would I model my diaphragm to depict actual. One thought is to use an equivalent I-beam with same stiffness and area as the angles used in a X type diaphragm connected to the main cirved girders. I would model the slab as plate elements also joined to the beam at each joint.

You have raised some good points to be considered, and I will keep them in mind.

If you happen to find a example for tapered diaphragm, would u mind forwarding it?

Noopur Jain
Bridge/Structural Engineer