What factors determine the weight limit of a stone arch bridge?
Arch Ring Thickness
The primary factor in the weight limit of a stone bridge is how thick the arch is. Simply, the thicker the arch, the more weight a stone arch bridge can hold. Of course, there is a little more to it than this; how thick an arch ring should be varies depending on the span of the arch. For example, an arch with a 10-foot span and an arch ring thickness of 1 foot can handle more weight than an arch with a 100-foot span and a 1-foot arch ring. For that matter, a 100-foot span arch with an arch ring of 1-foot thickness probably cannot support the bridge’s own weight very easily! Not surprisingly, then, the arch ring needs to be thicker as the bridge’s span increases. This relationship is not linear, however. The 100-foot arch does not need a 10-foot arch ring. An old formula used to determine a good arch ring thickness is:
(The square root of ( ½ arch span + the arch’s radius))/ 4 + .2
Rise of the Arch
This formula also shows that the arch’s radius is an important factor as well. While a Roman arch has a radius of ½ the span, a segmental arch has a radius that becomes longer as the arch gets flatter. This is not surprising, for, as we flatten the arc of the arch, we are utilizing a smaller and smaller section of a circle, which circle, in turn, has to be proportionately larger to keep the span the same. The upshot of all this is that a flatter arch tends to be a weaker arch, which is why the arch ring needs to be thicker.
Another factor in determining an arch’s weight-carrying abilities is how well the load is distributed over the arch. In general, the more material there is above the arch, the more weight the bridge can carry, as the weight of anything atop the bridge is spread over a larger area, rather than concentrated at a single point. This distribution of weight by the fill above the arch becomes more effective when it is a foot thick, preferably two. Fill two feet thick or more above the arch is recognized to be notably effective at distributing the weight of loads on the bridge.
This extra solid mass over the arch does more than just distribute the load of vehicles on the bridge. It also helps evenly push the arch stones together, increasing the rigidness of the structure.
Incidentally, the weight-carrying abilities of a stone arch bridge can be increased if the fill material is replaced with a reinforced concrete slab. This is because such a slab distributes the weight of a vehicle over a much greater area than an equivalent thickness of soil or gravel.
When determining how much weight an existing stone bridge can carry, the structure’s physical condition is important. Obviously, a deteriorated bridge cannot handle as much load as an equivalent bridge in the best of condition. Furthermore, the quality of the construction is important, too — how well are those arch stones fitted? A precisely cut arch is stronger than an equivalent arch which has but loosely fitted stones.
Putting It All Together: The Modified MEXE Method
A common method used to determine the load-carrying abilities of a stone arch bridge is the modified MEXE method, which has proven to be a successful method of evaluating a stone arch bridge’s load-carrying abilities, and takes into account the span, the arch’s rise at the half-span and quarter-span points, how thick the arch is, and how much fill is on top of the arch. The condition of the arch is also factored in.
Incidentally, understanding how the modified MEXE method rates stone arch bridges can also suggest some ideas on how to increase the capacity of a stone arch bridge. An obvious example would be increasing the amount of fill over the top of the arch.