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I could really do with some help with this.

First of all, this is NOT a homework question. It is a question that is listed in Benham & Crawford’s 'Mechanics of Engineering Materials' book. I am just reading through my books again and I'm stuck on this problem. As the book is copyright, I have included only the necessities. I wouldn't normally do this and I apologize in advance if I have done wrong but this problem has been bothering me for a week now!

Please see the attached file.

This may sound like a trivial question but I can't seem to see how the formulation of the first equation has been done. I understand part of the first part (force = stress x area, in which case the radial component of stress is 'sigma1 sin theta' and the thickness is 't'), but where does the '2 x pi x r x sin theta' come from? This is somehow the overall surface length of the dome but I don't understand how that has been derived. If I was looking to find the length of an arc of circle, I would use l = r x theta.

Also, in the second part we '2 x pi x r x (r - r cos theta) x q'. Again, I know why we are multiplying by q as q is the force per unit area. But from what I have read in other books, the surface area of the dome should be '2 x pi x r x h' where 'h' is the height. This '2 x pi x r x h' may well have implications on the first part of the equation as well, but I just can't seem to see it.

Please can someone give me some advice in this?

Once again, I apologize as I'm sure that this is a trivial question for all you intelligent people.

Thanks again,

Jus

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# Stresses in a concrete dome

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