# How do I estimate stress in a non-prismatic shape?

• maxf11

## Homework Statement

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

## Homework Equations

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.

The applied down force is reacted by components of the contact forces between the block in question and the adjacent blocks to left and right .

Have a think about this and try to draw the free body diagram for the block .

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maxf11
I see what you mean, thanks. However, the components of the contact forces don't act perpendicular to any uniform cross-section either, so my question remains. Is there any good way to estimate the stress you could propose (e.g. finding the average stress).

For basic estimate of stress assume that the contact forces act in a direction normal to the contact surfaces and that contact stress = contact force / contact area .

There is section in one of those papers that I gave a link to in your previous thread that tells you in detail how to calculate all the forces and stresses in an arch bridge .

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