Optimum span length 2

In that length, the decision of 1, 2, or 3 spans generally comes down to clearance (allowable depth of superstructure) and the height, depth and size of the piers required.

If it's over a deep canyon, with plenty of freeboard, where piers would have to be fairly massive, single span may be the most economical choice.

If it's over a roadway, or railroad, where the depth of the superstructure is fairly limited, most likely a 3 span bridge is going to be the preferred option. Multiple span bridges with continuous concrete girders is not a straightforward design. If both steel and concrete are available options, generally steel girders would be preferred.

Where I'm at, we don't find many places where a 2 span bridge is feasible. Usually having a pier in the middle of a stream gets a flat no from the maintenance crew.

For steel girders, we find a depth to span ratio between 0.04 and 0.045 to be the most economical, with the 0.04 being the best for composite girders, and the 0.045 being better for non-composite. That being said, we've done composite steel girders with a depth to span ratio of 0.032 without adding significantly to the steel weight. If it's a choice between a shallow girder and cumbersome or expensive grade raise, the overall less expensive option may be the shallow girder.

Some of the deeper prestressed bulb tee sections are suitable for a 50m (or 60m) simple span. They're heavy, and therefore expensive to transport, so to be competitive, there would need to be a plant that cast them somewhere in the region.

Thank you BridgeSmith for the detailed reply.
I agree with the points you mentioned.
This bridge is over a river whose water level fluctuates due to the presence an upstream dam, and it freezes in winter. So, freeboard (consequently, shallow superstructure depth) is an important parameter. But at the same time, construction of two piers in the stream is discouraged from river flow / ice jam / river bed disturbance considerations. A big single span arch bridge with large freeboard is also out of question from cost perspective. It seems, one pier in the middle of the river is unavoidable.

Your 3 spans do not have to be equal length, something like 10 - 30 - 10 could work to improve the spacing over the river. It would be much better than central!

The 10m-30m-10m span arrangement is a good option. The downside with a 3:1 span ratio is that there will be uplift that will need to be mitigated, both during construction (the girders will need to be clamped down to the abutments), and in the final condition.

It may be possible to provide enough counterweight in the abutment itself, or with concrete infill between the girders. Our preferred method to mitigate uplift is with steel H-piles embedded inside of a drilled shaft, to increase the skin friction area and coefficient of friction. Typically, the top 3m under the abutment would be ungrouted, to allow for thermal translation of the fully integral abutment.

At a span ratio of about 2.35:1 (11.5m-27m-11.5m), we can typically eliminate the uplift during construction, and find the final uplift to be minimal.

On the other end, we've gone as high as a 4:1 span ratio, but the uplift is fairly large, requiring a fairly extensive combination of measures to mitigate it.

Why would you have uplift with simple spans? You did say that continuity is not straightforward.

Why would you have uplift with simple spans?

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I was talking about continuous steel girder spans. Highway bridges are rarely done as a series of simple spans, anymore. It requires joints in the deck over the piers, which pretty much always leak and damage the bearings and piers. Continuous decks with integral abutments move the expansion joints off the bridge, so that when they fail and leak, it doesn't result in damage to the superstructure. We take it one step further, and attach the approach slabs to the abutment, moving the expansion joint to a sleeper slab at the roadway end of the approach slab.

You did say that continuity is not straightforward.

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I said (or meant to convey) that making prestressed concrete girders continuous for live load requires a more involved design process, and a significant amount of extra care and attention to proper construction, to function properly.

Continuous steel girders are very common, and straightforward to design and construct.

Thanks for the explanation. Makes sense to an engineer who does not design bridges.

The biggest obstacle to using concrete girders for bridges, particularly for spans over 20m, is mitigating the initial camber, and handling the additional camber that develops over the long-term. Even if you can figure out a good way to get the shape of the girder to match the finished grade required initially (by placing a variable thickness CIP deck, etc.), you also have to consider the additional camber that will develop over the next few years.

This can be minimized by allowing the concrete to cure longer before transfer (releasing of the prestressing strands from the anchors, transferring the force to the concrete), but the precasters are typically an impatient lot, and don't like to wait that long.

BridgeSmith said:

Highway bridges are rarely done as a series of simple spans, anymore. It requires joints in the deck over the piers, which pretty much always leak and damage the bearings and piers. Continuous decks with integral abutments move the expansion joints off the bridge, so that when they fail and leak, it doesn't result in damage to the superstructure.

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Ever been to Texas?

BridgeSmith,

My 10-30-10 was approximate questimate (something like!) at a balance between a cantilever and an end span. Better to use your 11.5 - 27 - 11.5 if it balances fully with moving loads so no uplift on the end abutments.

Ever been to Texas?

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Not for quite a while. Are you telling me that Texas still designs and constructs new multiple span bridges as a series of simple spans?

It's common in Australia to have a series of simply supported spans, although the deck is normally cast continuously over the joints (link slab). Steel girders are not common anywhere here, because road authorities do not like the maintenance issues with them. These bridges are usually prestressed planks or prestressed trough girders ("Super Ts").

The link slab adds some very minor degree of continuity to the girders, but this effect is usually ignored. The link slab is usually only designed as a tension member to sustain the imposed deformation due to the rotation of the girders, and to remain serviceable to avoid the water ingress issue.

I think wherever you are, Texas included, single spans would be typical for trestles. Probably not 50 meter long bridges, but for trestles over kilometers of flood prone land below.

hokie66 said:

... single spans would be typical for trestles. Probably not 50 meter long bridges, but for trestles over kilometers of flood prone land below.

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And over salt water marsh and freshwater swamps in coastal regions.

I knew Texas, like many other states, has a significant inventory of multiple simple span bridges, but I didn't think anyone was still building new ones. I suppose in areas that don't use salt on the roadways, leaky intermediate joints would be less detrimental.

We've rehabbed some bridges that had double-bearing piers and deck joints, and replaced portions of the deck to with link slabs, to eliminate the joints. As far as I know, all of those have been fairly recent, so we have yet to see how they hold up.

The maintenance of joints is certainly a problem, but single span trestles make sense for bridges like this.

Of course there's a limit to the length of jointless bridges. Tennessee has pushed that limit to well over 1000' feet in some of their designs, though.

I was not trying to make broad statements encompassing the whole of bridge design everywhere. I didn't think I needed to qualify my statements, assuming that my comments would be taken in the context of the bridges of the length the OP inquired about. Apparently, I should have, in order to avoid this rabbit trail.

As the starter of this thread, it's good to see that it has generated discussion on bridge span length and presence (or absence) of joints. These are valuable comments.
In Ontario, jointless bridges are preferred (at the priers and also at the abutments).
End span to interior span ratio is preferred to be 0.75 for medium span steel bridges, as this proportion is expected to result in positive dead load moments being approximately equal in all spans. Possibly, the same holds true for concrete bridges.

End span to interior span ratio is preferred to be 0.75 for medium span steel bridges, as this proportion is expected to result in positive dead load moments being approximately equal in all spans. Possibly, the same holds true for concrete bridges.

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It generally holds true for 3 span continuous bridges. For multiple simple span bridges, especially concrete one, having the spans the same length is usually the most economical. The simple for dead load, continuous for live load (girders made continuous after erection) is usually the same, just due to the economy of scale (same girders for all spans, with only minor differences in strand arrangements.

For shorter 3 span steel girder bridges, though, we sometimes find it more efficient to push the span ratio to around 0.6 (or 1.67 for center/end ratio, the way we refer to span ratio), allowing us to have only 2 field splices (around the 2/10 and 8/10 points of the center span).