General expression for stress within cone.

1. Nov 14, 2012

peripatein

Hello,
I am supposed to find an expression for the general stress wrt height within a truncated cone of lower and upper radii a and b (a>b), pulled down from its vertical axis by a force of the same magnitude as that pulling it up. The diagram implies that the height between the upper and lower base is h (see attached diagram).

Attempt at solution:
I did (a-b)/h = (a-r)/h' (since the slope is similar even at height h' from lower base of radius a),
From which I could find r and hence the difference in the stress: F(1/A_a - 1/A_r) where A_x denotes the surface area of radius x.

I am really not sure this is how it should be done. My initial inclination was to use integrals.
Should it indeed be done the way it is presented above? Please advise.

Attached Files:

• Cone stress.JPG
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2. Nov 14, 2012

peripatein

I was hoping someone could possibly comment on my attempt at solution and advise how to solve this. Did I happen to post it to the wrong place?

3. Nov 14, 2012

haruspex

The stress is just the force per unit area of cross-section, yes? So what you did sounds right. What actual equation did you get?