Why is this STI shifter cable corkscrewing? I have a roadbike with an older Shimano 105 set of brifters.  The left hand / front shifter has always had problems getting the chain to the big ring, to the point I often have to dismount to reset the chain.
Recently someone pointed out that my shifter outer was &quot;weird-looking&quot;  and I had no idea, because this was all hidden by my stem while riding normally.
 sorry for fuzziness - was a balancing act 
The outer lies normally when untensioned but twists like this when I change to the big ring only.  Shifting to the middle ring from the grannie works fine.
What has caused this?  It used to work acceptably but has never shifted well.
The corkscrew shape of the housing strongly suggests that the cable is under great tension, and putting excessive compression on the cable housing.  Since the cable doesn't completely fill the housing, it will be ever so slightly shorter around a curve than the housing that contains it.  You've put so much tension on the cable that the housing is bending under the pressure.
The most likely cause is that your derailleur is seizing up at the end of its range; normal pressure will move it over the lower part of the range, but it takes extreme pressure to move it the last bit.  I would inspect the pivots for rust or dirt, clean them and apply penetrating oil and see if you can loosen it up that way.
I see some suggestions of a broken cable strand; I wouldn't expect that to cause a problem only at the end of the action.  But if a strand is broken just where the cable exits the cable housing at the bottom of the down tube, it could be hanging up just inside the termination of the housing.  But in that case the other end of the broken strand would be visible in the exposed length of cable, which I assume you've checked.