What is the Most Efficient Arch Shape? It Depends.
Unfortunately, there is no universally optimal shape for precast concrete three-sided structures. Just as every site is different, every site has its own arch shape that fits most efficiently in terms of material use (or cost).
Starting with the stream, some amount of water must be conveyed below a given flood elevation. The road must support a design traffic load, typically at a higher elevation than the water surface. For example, the optimal shape for a 12′ span requiring 60 sf waterway opening with 7′ from stream bed to top of roadway is much different than that of a 28′ span with the same waterway requirement and 30′ from stream bed to top of roadway.
Another question is how is “efficiency” defined? One way is minimal use of materials. But which material? Arches may be designed for minimal concrete (weight) but this may require more reinforcing which would increase the price and possibly decrease the service life. Then there are forming and labor costs. We could design every arch to be the most efficient shape possible in terms of concrete and steel cost, but the labor required to build custom forms for every project would be cost prohibitive. The optimal shape for material may be different that the optimal shape for cost.
Arch shape also affects foundation costs. For example, increasing the span by spreading the legs requires a longer span to provide the same waterway area as an Arch-Box shape with vertical legs. This increased span adds load (and therefore cost) to the foundation.
To add another layer of complexity, consider the laws of supply and demand. A much less efficient shape can often be supplied for a lower price if the producer has lower overhead, is closer to the site, and needs work to keep employees and equipment busy.
In response to the issues described above, ECO-SPAN is organized so that several shapes are available to fit a wide variety of sites. We find that in most cases, the Arch-Box shape is the most efficient in terms of material use, availability, forming, and number of producers (competition). However the Versa shapes are available for high fill situations and long stream enclosures. We keep our overhead low and allow customers to buy direct from local quality precast producers. Our shapes are not proprietary. The ECO-SPAN network is built to provide the most efficient product on the market, all things considered.