In a mathematics-based investigation, I am trying to estimate the stress through a voussoir (member) of an arch bridge. However, these members have non-uniform cross-sections. I don't need to know how to exactly calculate the stress in each part of the member, only the total stress (unless there is an easy way to do so, but judging from my research, there won't be) The force through it is known, it is just the cross-section that I need to get a reasonable estimate of. A visualisation of the problem is attached here: http://imgur.com/ZiX8JR9
Stress = Force/(cross-sectional area)
The Attempt at a Solution
My idea was to take the volume of the member, and divide it by the length of the object in the direction of the force, to provide an estimate of the cross-sectional area.