Above is the situation in a perfect ring - i.e. without the compessive load due to the tangential force.  The stress is tensile at one face and compressive at the other, with a "neutral axis", where the stress is zero at the centre of the section.  These stresses rise from zero at the gap and increase proportionately to Sin(sqd) theta to a maximum at 180degs, though I have shown only the first 20degs or so.

   Next, the situation with the compressive stress due to the wedging force added.   For the first 8 - 10degs the stress is compressive only, right across the section - there is no "neutral axis".   Thereafter the tensile stress slowly increases, but the neutral axis lies well away from the geometric centre of the section, and even at 30degs it is still some 6% of the half-thickness away.  See below.  (With aplologies for the illegible figures)
  The result is that the ends of the ring will, when installed, bear more heavily at the gap and so exert a higher wall pressure in that region.  Further, the reaction to this higher pressure at the ends causes a further high area about 120degs away on either side.