downwards load at mast base, how much is it?

[mikemonty]

Originally Posted by Avocet

I think this is where we start to diverge. I agree with the sums, so the tension in that shroud times Cos 10 will be the 5.66 tonnes, which must be equal to the compressive load down the mast. However, why should you simply add the initial rig tension to that? The initial rig tension will come from two shrouds (one on each side) and (I believe) that they would each be tightened to an initial tension of about 2.8-ish tonnes. When the boat heels, the tension comes off one and increases on the other, the net compressive force down the mast stays about the same.

Don't get the force due to pre-load tension and force due to gravity mixed up - they can be treated, and should be treated, as separate entities.
Although the tension due to pre-load on the lower shroud disappears, (assuming the lower shroud goes slack) its because of the sagging of the mast and yes, the tension in the upper shroud will increase - but that's the gravity component affecting it.
The compressive force on the mast due to pre-load - using your 2.8 tonnes per shroud is 2.8*cos10 per shroud - which works out about 2.75 Tonnes. This is applicable only to the upper shroud - the lower one has gone slack and cannot "transmit" tension load.
This is in addition to the 5.66 tonnes compressive load due to gravity so the total is about 8.5 tonnes.

I have to say I only used 2 tonnes as a mast weight for simplicity!

Bear in mind that a real mast is a complex system where the lower section is a compressive strut supported by the lower shrouds (because it can "pivot" at the mast base) and the upper section is a cantilever (because it is "fixed" at the hounds) - being a beam which will bend a bit in a controlled fashion to give you mast pre-bend for tuning purposes.
So the above is over-simplified, but the principles are sound.
Or at least they appear to be to me, after the best part of a bottle of very nice red!