Adding a open-end gable roof to an existing L-shaped brick home at a 45-degree angle tangent to the inside corner of building. The existing 2 roofs have rafters and ceiling joists that are perpendicular. The ridge will tie into the second story top plate at the same inside corner and it's height is as the other ridges. All roofs have a 3/12 pitch. Are the valleys sufficient enough or do I need a roof beam to span the hypotenuse (open-end)? Use collar ties instead? Trying to achieve a cathedral ceiling appearance.