For the keel (bolts)-
For simplicity and 'initial estimation', the keel attachment would be a 'cantilever'** (root) subject to beam formulas requiring 1/4th (!!!!) the normal stress levels (shear and 'bending moments', etc.) of a simple beam - a known 'civil engineering' structural requirement.
You'd imaginarily (on paper, etc.) take the intended design, pull the boat over from the top of the mast (boat now imaginarily heeling over at about 45° and with a full estimated 'full load' being carried by the hull) and then calculate the stress-strain reactions (according to 'cantilever' beam formulas, or 'finite element analysis' etc.) of its (torque) 'moment' (= center of mass of the keel 'times' the distance of it center of mass to attachment point). You'd then investigate the tensile loads in shear, bending stress, etc. of all the components and their 'reactions' (stress) and deflections (strain) .... and then apply the appropriate customary/scantling 'factors of safety' - multiply the near finalized entire substructure
connection strength requirements by a minimum of 3 times for an offshore design, or by minimum of 2 times for a 'coastal' design, or by 1.5 times for an inshore design.
If you were a large scale 'major' builder/designer (ie. a very vulnerable 'deep pockets' entity), you'd probably at least build a subsection keel joint system and physically test (statically and dynamically) to failure to see if 'the numbers' agree to where failure occurs (without and without) the applicable safety factors applied.
This would require the total evaluation of not only the keel bolts but also the structural 'attachment' and 'reaction' points to ensure that not only the bolts would not fail; but also, all the mating and support parts of the keel root structure.
I don't know what you precisely mean by mast
'tang'. However all structural mast attachments would be subject to the same '~45° over' analysis and then safety factors applied. Then, a prudent designer would have the connection physically tested for static/dynamic loads, especially for those shapes, etc that are 'statically and dynamically
indeterminate'.
Double or single spreaders would depend on the elasticity and rigidity --- geometric
Moment of Inertia (cubed) of the components under load, and a calculation of the 'deflection' of the 'stiffness' of the mast and rigging under calculated maximum expected sail loading, and the calculated 'combined moment arm / reactions' of the boat over at ~45° ....... plus applied factors of safety. This is usually already done by the spar manufacturer. The designer usually then just 'checks' / verifies the application to his/her hull design (weights, developed moment arms, etc. when the boat is over at ~45° and of course with the added 'factors of safety' applied.
In spar design, the 'worst' and 'easiest' mode of failure is by 'buckling failure' - a very exceedingly complex failure mode involving the possible generation of 'infinite' forces by mathematical 'anomalies' set off by 'deflection' of the spar and compression acting along the long axis of the spar. The primary function of 'spreaders' is to enhance 'stiffness' so that the 'sideways' deflection and the potential of buckling failure remains 'small' (the reason why one should set rig tensions by a gage rather than by eyeball).
The designer, of course, then adds his/her own experience of what historically worked and what didn't work during the further exhaustive refinement process/calculations. Most of the 'math' involved would be primarily plane / spherical trigonometry in 'free-body' (x,y,z direction) diagrams, etc. of each individual connection/interface/load bearing point or surface. A lot of this is done automatically by computer programs involved with 'finite element analysis'. The designer's extensive experience would be the final judgement factor in the actual design selection.
**
https://en.wikipedia.org/wiki/Cantilever
HAHAHA ... your original questions would be similar to someone contacting a large chemical manufacturer, such a DuPont or BASF: "Gentlemen, Kindly reply with
all your information about 'chemistry'". OR ... "Dear Boing Aircraft Company, please explain why the wings don't fall of your 787 airplanes. ... ." ;-)