Skewed Bridges

[penpal97]

I have seen a few things to worry about w/ highly skewed bridges (over 30 degrees). One is increased shear on some of the girders, and I can understand that since the load path can be kind of odd given the geometry of the loading relative to the abutment. The other is uplift at the bearings. Where is the uplift? Why is there uplift? I would appreciate your thoughts.

 

[crossframe]

There can be uplift (not necessarily net uplift) at the acute corners.

 

[penpal97]

Thank you. Why?

 

[graybeach]

Hmm. How to explain? I think its because the diaphragms can act as supports to the fascia girders near the acute corners. As the girders rotate to take on the positive moment shape, the girder ends pop up at the acute corners.

 

[bridgebuster]

Also, as a truck is moving across the bridge the girder deflections aren't uniform across the bridge at any given section. The girder twists and creates the potential for uplift.

 

[penpal97]

Thank you for your responses. I have some further questsions and would like to continue the discussion to try to get to a relatively definitive answer. Everyone I have talked to only has "thoughts".

graybeach - please let know me if I am interpreting this incorrectly: truck on fascia girder 1 midspan causes positive moment deflection in fascia girder 1. however, the diaphragms near the acute corner of fascia girder 1 acts as an intermediate support (because of the high skew), resulting in uplift at the bearing of fascia girder 1.
Doesn't this mean that the diaphragm is being canitilevered from interior girder 2 (or 3 or whatever)? Then I would expect to see uplift on the backside of the diaphragm at the opposite fascia girder N. Does this then result in uplift at the obtuse corner as well (in additoin to at fascia girder 1 mentioned above)?

bridgebuster - I agree. differential deflection is an issue for pretty much any bridge when the truck is out by the fascia. For skew bridges, the differential deflection from one side to the other is worse. a truck on fascia girder 1 causes the most deflection at fascia girder 1, so fascia girder 1 will twist if the deflection is high enough. However, doesn't this twist get resisted by the diaphragms? This would be a concentrated moment at the diaphragm end at fascia girder 1. I would expect uplift on the opposite fascia girder N. Seeing as how I would get the most differential displacement at the acute corner of fascia girder 1, I would then expect uplift at the obtuse corner for fascia girder N, not at the acute corner.

 

[paddingtongreen]

If you load a flat, square plate, uniformly, the corners do lift or try to lift. Consider the curvature of a middle strip, maximum deflection is at the center. There is a similar center strip in the other direction. Consider the next strip adjacent to the center strip, it would like to take the same shape as the center strip, but cannot because of the curvature of the strip in the other direction.
If you continue to the outermost strip, it wants to take a similar curvature, but can only do that by raising the corners.

If you skew the plate, the effect is exacerbated at the sharp ends.

If you substitute beams in two layers, one going N<>S and the other E<>W, and connected at every crossing, but only one direction being supported, then sketch your expectation of their deflected shapes and it may be clearer that the corners will lift. Then try a skewed equivalent.

Michael.
Timing has a lot to do with the outcome of a rain dance.

 

[penpal97]

paddingtongreen, I do not follow the analogy for a grillage beam setup. Simplifying the setup, place several girders N<>S and one floorbeam in the top layer going E<>W. If the floorbeam is infinitely stiff, then all N<>S girders deflect the same, all girders in positive bending, no uplift. If the floorbeam is not quite infinitely stiff, then the girders may not deflect as much as the center girder, but I do not follow how any of them will have uplift. If the floorbeam is infinitely flexible, only the central (or loaded) girder goes into bending, and the other girders do nothing; still no uplift. I also do not see how adding more floorbeams (to simulate flat plate) would create uplift. Any clairification would be appreciated. Thanks.

 

[paddingtongreen]

@penpal, I didn't explain that at all well. When I was young and Icame on a mystery like this, I used to try these thought experiments to gain understanding.

Consider a flat plate skewed bridge. Intuitively one thinks that a line from the halfway point on the left side of the bridge to the halfway point on the right hand side would be level and would be the line of greatest deflection. But, the stiffest elements of the plate would be between the obtuse angles, and those beam strips would cross the line we originally picked and reduce the deflection. This, in turn, reduces the load at the acute angle, even lifting them.

If you have Roarke, look at the behavior of a square or rectangular flat plate, the corners lift up.


Michael.
Timing has a lot to do with the outcome of a rain dance.

 

[penpal97]

Thank you for talking this through with me.

The system you have described seems similar to a 2span beam w/ an interior spring support. The "beam" running from obtuse angle to obtuse angle would be the spring support. So if a truck were at the beginning of the bridge, the bearing at the end of the bridge would experience uplift. Then I would guess that from a more global perspective, if I put the truck halfway between the acute corner and the "beam", then the opposite acute corner would experience the most uplift. Correct?

Unfortunately, I am not familiar with the Roarke text that you mentioned. The only thing I have found are Roark equations for sterss and strain, but the formulas did not seem applicable to the discussion.