When building a stone arch bridge, the question sometimes arises as to how many arches are needed. In some cases the answer is obvious; for instance, a small gap begs for only one arch. But there are times when multiple arches are advantageous, despite the fact that a pier in the waterway is required.
First, it is important to understand the limitations inherent to stone arches.
An arch between 2 feet and 20 feet is fairly easily made and does not present major design challenges. Nor does it have to be very precision-made to stand — a fact borne out by the number of medieval bridges with spans less than 20 feet.
Once the span goes beyond 30 feet, however, challenges begin to arise.
First, the shear weight of the arch becomes enormous, making tight fitting joints more important to prevent stones from crushing.
Secondly, to support this large weight the temporary formwork must be massive. The challenge is worse for flatter arches, as they have a decided tendency to slide out at the ends that must be resisted. Furthermore, they are even more capable of crushing their own ring stones.
Long Span Limitations
For long gaps to be spanned, one arch would often have to be enormous, and very, very flat.
Furthermore, the waterway for a single flat arch is often significantly less than for two more rounded arches on a pier, though, at the same time, the lack of a pier in the stream makes this long, flat arch, less vulnerable to damage in floods.
Adding a pier necessitates some careful planning. At one point it was traditional to use an odd number of arches to prevent having a pier smack in the middle of the stream where it would be capable of the most obstruction, not to mention the most gathering of debris.
A pier is very susceptible to scour, and hence must have a good foundation for long-term stability. Ideally, all bridge foundations should be placed on bedrock, though this is frequently impractical. According to Walter Sharp, pioneer stone arch bridge builder in Kansas, all of the Cowley stone bridges that had ever failed up to 1922 were not resting on bedrock.
Placing the arches themselves on a pier can be tricky. Flat arches on thin piers are simply begging to topple the piers and, furthermore, must be built with a minimum of two at once to prevent accidents. Two identical flat arches on a pier cancel out each other’s thrust, but, if one arch in a chain of flat arches on thin piers ever were to fail, all of the other arches would quickly follow like dominoes.
In medieval times the “piers” were basically robust abutments, and hence could support an arch even without one on the opposite side of the pier; however, this was never a good idea due to waterway constriction.
If the arches are more rounded, it can be possible to build them up one by one without worrying about toppling piers, even if the piers are thin.
For wide streams it is basically a necessity to build multiple arches with a pier. The maximum practical span length for a single-stone arch is about 200 feet (though stone bridges with spans longer than 200 feet do exist — the longest single arch bridge span in the United States is the Cabin John Bridge in Maryland, which has a span of 220 feet).
If the stream is wider than 200 feet, multiple arches on a pier are basically necessary. Long 200-foot spans require some careful planning, and are incredibly difficult to design.
The “Hump” Limitation
For relatively flat, low areas, even if the distance to be crossed is relatively short, the use of a single arch would be impractical, due to the pronounced “hump” in the road. Alternatively, a long, very flat arch to prevent the hump would often be absurdly complicated to design for the area being spanned. For these reasons, several smaller arches make much more sense.
The “hump” factor was likely the largest factor that led to the fairly common use of multiple arch bridges even for small streams. If the ratio of the stream’s bank to the stream’s width is low, one arch is often unacceptable due to the hump.
A classic example of the resulting impossible grade when a multiple-arch bridge is replaced with a single-arch bridge can be found in the story of the Pontypridd Bridge in Wales.
Pontypridd Bridge was originally a triple-arch bridge built by a mason by the name of William Edwards who had a contract that demanded that he pay for any repairs to the bridge out of his own pocket for a period of seven years after the bridge was completed. Unfortunately, a flood completely destroyed the triple-arch bridge before the seven-year period was up, as the piers were scoured out by the water’s action. Apparently to guarantee that this unhappy (not to mention expensive) event would never happen again, Edwards set out to build a single arch with a 145-foot span to cross the river in a single bound. Despite several failed attempts, he finally succeeded. While he no doubt met the letter of the contract, the resultant bridge was practically useless (though it was an inspiration for those determined to build record arch spans). Horses loathed crossing the bridge (the grade made it absolutely impossible to see across the top of the bridge) and, to prevent wagon wrecks, any wagon driver who did manage to coax his draft animals to the top of the bridge had to use a drag chain to get down the other side! Later on a new and much more practical stone arch bridge was built right next to the old, original 145-foot-span Pontypridd Bridge. The new design was a triple-arch bridge — just like the first attempt that washed out! The original Pontypridd Bridge still stands and is used as a pedestrian bridge — steps were later added to make it safe for the pedestrians!