Hoop Stress in Spherical Shell 1

[flamby]

Suppose a spherical shell is stressed from inside and hoop stress results. If I consider a small square on the surface of this ball, I see hoop stress in every direction.

Why shouldn't these stresses be combined when we check it against allowable tension, which is a one-dimensional stress? For example (hoop stress * 1.414 < allowable)?

I know I am wrong, but where?

 

[dik]

Consider a tiny element that is 'planar'... do a Mohr's circle of the stress... see what the shear stress is <G>... by symmetry, the forces are the same... all the way around...

 

[flamby]

Now I know where did I goofed it up. I was considering a &quot;square&quot; element on the surface of sphere and led myself to incomprehension.

A circular piece is much better and then I think that the hoop stress acting away from the centre of the element are in fact unidirectional - radial stress. No other stresses are present, so principal stress is the hoop stress itself.

Phew...

 

[dik]

Generally a nice cold beer clears this type of thing up... <G>