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# Curved Deck on Straight Parallel Beam Design

## Curved Deck on Straight Parallel Beam Design

(OP)
Good afternoon. Our next bridge project here will be a single span (133' c/c bearings) steel plate girder on semi-integral abutments on MSE walls. The bridge is a grade separation on an interstate. The skew is in the vicinity of 45 degrees. The horizontal alignment is curved with a radius of 2,830'. We are planning to keep all of the beams straight and parallel. So the deck edge will be variable from about 9" to 4'-9". Currently we only have line girder design software here at the office (Merlin Dash). What is the deciding point on whether the beams can be designed using a line girder analysis or switch over to a grid analysis (ex. MDX or LEAP Steel)? Any certain radius and skew?

Any other insight or reading is also appreciated on this design with this geometry.

### RE: Curved Deck on Straight Parallel Beam Design

I'd go with a grid analysis. You'll get a more accurate prediction of the deflections. I don't recall if you can model a straight grid & curved deck in MDX. If not you use a uniform deck overhang and add in the difference as a variable load. Are you placing the deck in one shot or are you doing staged construction? Staged construction with MDX is tricky.

### RE: Curved Deck on Straight Parallel Beam Design

MDX allows you to input tributary widths at tenth points so the curved deck isn't an issue for line or system girder. Given your parameters, I would do the grid analysis like bridgebuster suggested. Differential deflections can contribute to additional moments in the girders and the cross frames. You can't really account for that in a line girder.

There's a document by AASHTO and NSBA that gives guidance of when to model between a grid or line. I'll see if I can find the document name.

### RE: Curved Deck on Straight Parallel Beam Design

Since the skew is more than 20 degrees, the cross-frames are now primary load carrying members connecting the adjacent girders at different deflection points. Hence the cross-frame acts as a load distributor during service live loads, in addition to lateral wind and seismic loads. Use MDX to model the simple span and use plate and eccentric beam model type. Grid model will give you close to accurate results for the girder, but unusually large cross-frame sizes. Bigger the cross-frames, larger are the connection gussets, bolt numbers etc. So plate and eccentric beam model type will give you reasonable sizes for cross-frames and savings can be realized. The NSBA publication that other members have cited is a good source. In addition, also pay attention to the "type of fit" for the girders. If you dig around the AISC-NSBA website you will find couple of documents on the type of fit to be used for fabrication of the girders and cross-frames as well.

Depending on your girder and cross-frame design, deck pouring sequence may also need to be checked. Since the bridge is a simple span, the girder midspan may have high camber to compensate for the dead load deflection. So, deck may have to be poured starting from the midspan and moving towards the supports. In addition, deck may also have to be poured on a skew so as to load all the girders at the same points along the span and limit differential deflection. All these checks are necessary as you proceed with the design.

Is there a specific reason why you are only considering steel girders ? Considering that you plan to keep the girders straight, you should be able to accommodate a 133 feet span using a straight AASHTO concrete girder or a Bulb-Tee concrete girder. If you are limited to using steel, then you might as well curve it to avoid variable overhang.

### RE: Curved Deck on Straight Parallel Beam Design

(OP)
Thank you all for your input so far. I am trying to make my way through the NSBA document mentioned above. Hoepfully the answer becomes clear on what analysis will be required. I think I know what the answer is already but the people who write check around here will need a solid answer in order to invest in new software.

To answer the questions that have been asked, I'll do my best.

The bridge is actually a set of twin structure separated by a 2" gap between the decks. One deck will be poured all in one phase, the other bridge will be poured in 2 phases, well three considering the closure pour. The bridge aren't true twins since the overhang radii are different so separate analyses will take place. We want to simply the fabrication of the girders, so we hope to provide only one girder design.

Our research has show that the contractor should be able to pour the deck along the skew and load all of the girders concurrently thus eliminating some (most?) of the differential deflections. The length along the skew of the deck will be around 106'.

The DOT requested that we only look at straight beams with the curved deck. Not sure why they requested this. Good question though. Sounds like a slight curve in the beams would eliminate some issues like forming the variable deck edge.

We will definitely be looking into erection process.

We performed a superstructure type study in the 1st phase of this project. We went in thinking that prestressed concrete I's (Wide flange beames) would win hands down from a cost standpoint. With this amount of skew, our DOT requires the semi-integral diaphragm to be 5.8' wide. For the steel option, since we can clip the top flange back to the web, the semi-integral diaphragm only needs to be a little over 3' wide. The wider diaphragm also causes the span to increase by about 5' when compared to the steel option. The prestressed beam required about 360 CY more of concrete in the diaphragm alone. The bridge is also in a sag vertical curve. We checked the haunch thickness and it exceeded 7" in a lot of locations. Anything over 5", our DOT requires the haunch to be reinforced, more cost. When considering life cycle costs, the girders will be galvanized thus eliminating a lot of costly painting in the future. With the wider heavier diaphragm, longer span, and added weight of the prestrssed I's vs. the plate girders, the foundation system cost increased also. So combining all of these, we concluded that the steel option was best fit for this location. It worked out to be about \$700,000 cheaper. Though the DOT could still come back and decide to use the prestressed option. Doubt they will though.

Thanks again! All suggestions and comments are welcome.

### RE: Curved Deck on Straight Parallel Beam Design

In reference to the cross frame "fit" comments above, I believe many of the NSBA and AISC comments on this reference NCHRP report 725, which is available in it's entirety here:

http://www.trb.org/main/blurbs/167646.aspx

It also give guidelines on when different methods of analysis should be used.

The differential deflection at cross frame lines is due to to the cross frames being at a different point along the length of each girder (assuming they are perpendicular to the girders which is what I would expect for a 45 degree skew). Pouring the deck on the skew does not remove the differential deflections - they would exist if every girder was subjected to the same UDL.

On recent projects similar to this, I have seen the move to full plate or shell models of the girders, rather than a grid line analysis. This is for two cited reasons. Generally, beam elements only account for St Venant's and not warping stiffness. This can cause significant differences in cross frame loads (particularly during fit up, depending on the type of fit chosen). I am unfamiliar with MDX though, so I do not know how it treats torsional stiffness of beams. The other is that most firms I deal with are using software capable of 3D finite element analysis already, and the added time in generating a 3D model is small if you are used to the software.

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