Engineering+Analysis

Engineering Analysis
Throughout the history of bridges, arches have continuously been used for their strength and stability. Even today, engineers all over the world employ techniques pioneered by the Ancient Romans used in their bridges. The magic of the masonry arch bridges come in its design. Blocks are cut and pieced together in a way in which the arch is in total compression. Being strong in compression and poor in tension, the blocks (or concrete fill that we see in some bridges over the tiber) are used for their strengths instead of its weaknesses. The way the arch improves on the simple beam, is by dissipating some of the vertical forces coming down on it in the horizontal direction. When a load is applied on top of the arch, the base of the arch (footers) try to push out. This makes abutments to stop this outward push necessary. In the case of the Pons Fabricius and other stone bridges seen throughout the Roman Empire, the massive self-weight of the bridge causes a giant thrust, requiring very large and massive abutments to keep the arch in place. Although it is hard to tell what type of abutments the Pons Fabricius had when it was originally built, the ends of the bridge today are kept in place by two gigantic walls with an immeasurable amount of force. Its almost as if the bridge would need to move the entire city in order for it to push out and expand. Because of this, we can assume that if it did fail, it would be very unlikely to do so at the abutments.

To analyze and perform calculations on the masonry arch, we must make certain assumptions to simplify the situation: 1. The masonry units in the bridge (Tuff and Travertine) are infinitely rigid and strong. 2. There will be no sliding at the joints of the bridge. 3. We assume the bridge is a 3 pinned arch. (explained in greater detail below) 4. No tensile strength will be transferred from block to block. 5. The load from the self-weight of the bridge will be treated as a point load instead of a distributed load. Probably the most important of these assumptions is the 3-pinned arch assumption. We can assume this is the case based on the fact that the material is unreinforced and the applied load on the top of the arch will likely create a hinge at the top, or a crack in the case of concrete. The hinge at the top of the arch will not support a moment, however it can support loads in the X and Y directions. This allows the structure to be statically determinant. If the arch was treated as a two pinned structure, it would be statically indeterminate, and finding the support reactions would be much more complicated. Although this may sound like a bad thing, it is perfectly ok, and will not allow the structure to fail. Failure, however, can occur when extra pins appear in an arch. When analyzing a single arch, 4 pins or more can cause failure when the arch simply collapses due to asymmetrical loading. In the case of a multi-span arch bridge such as the Pons Fabricus (two spans), 7 or more pins can cause failure. To make sure these extra pins aren't present, the engineers must make sure the arch is in complete compression and that it supports and abutments are sufficiently strong.