stu said:
Take a sling. When loaded with a force of x you'd expect half x on each strand, yes?
[Rummages in memory for long forgotten 'A' level physics knowledge...]
You've not laid out quite all of the parameters, but turning this into a mechanics problem, let's assume the belay is frictionless, the sling is a continuous loop (aka a 'roundsling') which has no mass and is in-elastic, and the sling is simply hung over the belay. In this case the tension in each side of the sling must be equal or the sling would rotate around the belay, so the tension in each side is half the weight which is hung on it (= x/2). This is also the common sense answer.
stu said:
Double the sling up (so four strands). Apply force x and you'd expect 1/4 x on each strand, yes?
Yes, this is correct. Again, all the tensions must balance or the sling will move, so the force due to the weight x is evenly distributed and the tension = x/4.
stu said:
If this thinking is correct (?) will doubling a sling make it twice as strong i.e. if it breaks at max. x when loaded as a single loop of sling, will it be able to bear 2x when doubled? I'm thinking it won't.
You are making life difficult for yourself by a poor use of terminology. The 'strength' of the sling does not change, what changes is the tension in each of the 'legs' and hence the relationship between that tension and the ultimate strength (breaking strain) of the sling. If the tension is only x/2, and x is the breaking strain, then yes, doubling the sling increases the 'strength' of the system by a factor of 2.
The physics of this are the same as those which apply to a hoist system using pulleys - use a single pulley at the top with the rope slung over it and lift the weight directly and the tension in the rope is equal to the weight. Add another pulley and fasten one end of the rope to the ceiling with the weight attached to a pulley in the middle and the tension required to lift the weight is now only a half the weight.
In fact, complexities like friction (especially between any two parts of the sling which come into contact with one another) are very significant and cannot be ignored so the answer is never as simple as it appears in the abstract, but the information given as standard with any CE marked lifting slings might help to give a good feel for the performance of the system in any given configuration. See http://www.tonybeal.com/lift.htm#round
Nick.