So say I have a character with a S24 normal arm and a S56 bionic arm for a combined strength of 80, what effect does this have on the distance they can jump? I assume that the total strength is used to calculate this (for a total of 4 yards). I only ask because it seems odd that a bionic arm should increase the character's ability to jump!
This all falls well within GMs discretion. I would only allow a bonus for a bionic arm if it was being used to perform an action, here defaulting to the character's 'native' strength of 24. This seems very low though - if this represented the weakness of the arm I'd probably average the two. Basically, feel free to 'wing it' to keep things feeling intuitive.
I never let players use the strength of bionic arms when it's not appropriate (which includes for jumps). If they haven't kept a record of their base strength, then I'll usually decree it to be some pretty conservative value. 40 is something of a favourite.
So, I normally have S stats something like: 70-(60/35)-95
Which is base strength, split strengths of L/R arms, then a total respectively.
The character in question should be treated as having a Strength of 48 for the purposes of jumping.
R.