Calculating Offsets from Curved Alignment to Straight Beam

[BridgEI]

I'm designing a superstructure replacement, and we have a curved alignment with straight beams in the first span with the curve terminating at the center of pier 2. Although the beams have not undergone final design, I am a little hung up on how we are going to do the screed elevations. When I discussed this with my boss, he said the screed elevations are all going to be given at the same station for each beam in the span. That presents a problem for me because that means the distance between screed elevations for beams on the outside of the curve will be further apart longitudinally along the beams than the elevations on the inside of the curve. Furthermore, I don't understand how you accommodate this at the bearings on end bent 1 because you will have irregular spacings between each screed line at that location. He says it's not an issue because the screed machine will follow the alignment, and while I understand that, it makes the calculation more difficult. I guess my first question would be whether this makes sense or not, even though I assume it does based on the path of travel for the machine.

I was also wondering if anyone had ever gone through the trouble of using the horizontal curve information and the beam orientations to actually calculate (rather than measure) the offsets and positions of where the screed lines intersect each beam. Further, I wondered if anyone had gone through the trouble of also including the vertical curve information and superelevation diagram values to calculate the screed elevations? Probably this is a lot more trouble than it's worth, unless it could be used on longer, more complex bridges in the future. I would presume it would take less time to just draw the superstructure to find out since we're maintaining the substructure. I appreciate any advice and discussion on the matter.

 

[BridgeSmith]

We start by establishing a straight working line that is along a beam, or at least parallel to the beams.

We calculate the screed elevations along the beams and at the edges of the deck. We calculate offsets between the horizontal curve and the beam centerline at the screed elevation points (tenth points of each span at each beam).

We typically start with calculating the screed elevations along the horizontal curved lines that intersect the centerline of the beams at the ends of the beams (or RF abutments or centerline bearing), and then multiply the offset by the superelevation at each tenth point of each span.

The bearing seat elevations are calculated working down from the finished grade/screed for the beams at the supports.

 

[BridgeSmith]

You should probably ask the mods to move this to the Bridge engineering forum.

 

[BridgEI]

I don't know that I understand what you mean. I understand the screeds are calculated along the beams and edges of deck. I know the offsets from the horizontal curve need to be calculated to account for the superelevation or cross-slope, whatever the case might be. I also understand that the seat elevations are calculated from the finished deck elevation down.

How does the straight working line come into play? What do you mean by the horizontal curved lines that intersect the centerline of the beams at the end of the beam? Is there a way you can illustrate what you're talking about? I still don't understand that if the deck is curving, the beams are straight, and the screed lines are perpendicular to the alignment how you can calculate any of this off of a straight working line

Should I send a message to the mods asking to move this thread?

 

[BridgeSmith]

The surveyors and contractors demand a straight working line to use as a reference for setting the locations of substructures, bearing seats, etc.

Theoretically, you can calculate all the finished grade elevations at each beam directly by calculating the offset from the curved reference grade line (AKA the profile grade line) at each span point for each beam, and then multiplying by the superelevation. That hurts my brain too much, though. I prefer to calculate it in 2 steps, for easier verification of the elevation changes.

Step 1) Calculate the change in elevation from the curved reference grade line to parallel curved lines that intersect the beams at the same point on each beam. The elevation change from the reference line is constant value for each parallel curved line along the entire length of the bridge.

Step 2) Calculate the change in elevation due to the offset between the curved reference grade line and the working line at each span point. This will give you the change in elevation due to offset from the straight beam lines to the intersecting curved lines, which is different at each span point, but the same for all the beams.

Then, you apply the changes in elevation from Step 1) to all the points along each beam, and the changes in elevation from Step 2) to each span point of all the beams.

Assuming the edges of the deck follow a curve parallel to the reference grade line, you'd just do Step 1) for those.

Honestly, I'm not sure how to get a thread moved to a different forum. I've never had to do it myself, but I know it can be done.