nnnnah, its easy to calculate all the 'joints' as individual 'free
bodies', even when simplifying by omitting elastic strain (of mast
etc.) and then simply balance all the free body connections as sums.
The original poster's question was "calculating stress in the standing
rigging" ... not necessary to calculate wind/sail loads as they can be
equated as reactions via their CE's and resultant distributive loads
as moments versus the 'connections' ... just like you do with any
'beam' calculation (mast).

The above will work as a close approximation ... at least that was the
method of most designers that Ive asked this direct question ... all
have replied: (paraphrased) ... mathematically pull the boat over onto
a 45 degree heel, calculate the restorative loads ... the moment arm
of mass versus center of buoyancy which will result in an close
approximation of the cap shroud tension ... then calculate all the
rest of the shrouds based on trigonometric relationship to the cap
shroud tension, etc. etc.; add/multiply by appropriate factors of
safety, etc. to account for sailing at beyond normal sailing angles
(GT 45 degress), etc. Those scantilings when back calculated seem
to still be appropriate in most cases. :-)