Of course there are several different types of arches, not just the semi circle arch and the segmented arch.
At a recent workshop Patrick McAfee and I were teaching last February, we took the opportunity during a huge downpour to go inside and discuss some of these various kinds of arches and vaults and their different applications.
Then our students went back outside and built three segmented arches.
Here are some of these other shapes that can be used in bridges as well.
One example of an elliptical arch.
A superb example of an elliptical dry stone bridge was built in 2013 in Australia by my good friend Gavin Rose. The link to the web site where he describes the building of this bridge is http://www.ttms.com.au/grampians-national-park.html
(photo by John Daley)
There is also the pointed (or Gothic) arch
Here is a flattened Gothic arch stone bridge built over the Sudbury River in Aiken's Park near Hopkinton Massachusetts.
Gothic arches end up needing to be taller than circular or segmented arches and are therefore less useful in going over wide spans. For long bridges they are used in combination. Usually they require a higher approach both sides of the bridge too.
Although I have seen ogee arches, I have never seen one used in a bridge
The catenary arch is very close to a parabolic curve. There are many bridges whose arches approach some sort of parabolic curve. These would be stronger than segmented arched bridges.
The jack arch (or flat arch) is just that - an arch that has little or no curve. A bridge of this type would require the maximum of lateral resistance (in the form of stone mass) on ether side of the span to stop the arch from spreading.
This is a kind of corbelled arch bridge. It relies predominantly on tensile strength, not compression strength, and therefore, even with using massive stones, is a weaker arch.
It and other bridges is found on a very good site where you can see more arches at http://traveltoeat.com/the-arch-in-architecture-and-history/
Through a series of posts in Thinking With My Hands from October 5th to 31st ,2013, I discussed a lot of these different types of arches.
Arch # 1
Arch # 3
Arch # 4
Arch # 5
Arch # 6
Arch # 7
Let's do some exploring along The Catenary Trail
Arch # 8
Arch # 9
Arch # 10
Arch # 12
Arch # 13
Arch # 14
Arch # 15
Arch # 17
Before advent of the arch Part 1
Before the advent of the arch. Part 2
Before the advent of the arch. Part 3
Before the advent of the arch. Part 4