hoop stress in spherical shell

huangyhg

hoop stress in spherical shell
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?
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...
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...
generally a nice cold beer clears this type of thing up... <g>