# Relationship between curvature of an arch and bending moment.

1. Sep 17, 2012

### Scintillation

1. The problem statement, all variables and given/known data
A bridge has two arches, with one abutment in the center labeled A connecting the two arches, and a point b on the right.

I have calculated that the maximum bending moment in the structure would be at point A, right on the abutment that is connecting the two arches. I am to consider whether or not the bridge designer made the correct decision in placing the abutment at the point where the maximum moment would be located, and whether or not it has the appropriate thickness.

Here is a picture of the structure. Note that there is a roadway on the arches.

3. The attempt at a solution
The professor mentioned something about how curvature of the arch is related to the moment that is applied. He used the example of the diving board. The diving board is less thick near the jumping end, because more movement is desired. It is thicker near the ladder, since less movement is desired there.

However, I am not sure how this relates to the bridge. I understand that the bridge has the greatest moment at point A. I understand that we want to minimize the actual bending taking place, meaning that we counteract the bending moment applied by the maximum load.

There are two interpretations:
1. Because we want to reduce the amount of bending at point A, making it thicker there makes sense. Thickness mitigates the effects of bending moment. Having the ends of the arches, with its high curvature, also helps to decrease the effect of the moment.

2. Because the maximum amount of bending is at point A, we should have made point A the center of an arch. That way, it should be able to best counter the bending moment.

I am not too sure #2 is correct. If curvature and thickness both help to reduce the effects of bending moment, then having a thin, uncurved section at the center of the arch would not help. Is this even a correct analysis?