Hoop Stress in Spherical Shell

Question

Hoop Stress in Spherical Shell

flamby (Structural)

(OP)

25 Aug 03 07:29

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 (Structural) · Answer 1 · 2003-08-25 08:39:02

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 (Structural) · Answer 2 · 2003-08-27 01:22:43

Now I know where did I goofed it up. I was considering a "square" 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 (Structural) · Answer 3 · 2003-08-27 13:23:34

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

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Hoop Stress in Spherical Shell