RonnyRaygun: I know this thread is old but....
I understand what you're getting at in your post, and agree that according to your analysis the hip beam will have a low load due to the 3D truss type action, however, I think there's more to it…
The truss forces you describe depend on the jack rafters working in axial compression which, at wall plate level, will resolve into vertical AND horizontal thrust components. This is just like a pair of opposing common rafters, where compression is generated in the rafters and the resultant forces at the wall plate resolve into the vertical load (taken by the wall) and opposing horizontal thrusts taken via the ceiling joist (acting as a tie) to cancel each other out.
In the hip situation, however, rafters on one side of the hip will (probably) be running perpendicular to ceiling joists so - even assuming there is a set of opposing hip jack rafters on the other end of the roof - there are no tie members to connect and cancel out these opposing thrusts at wall plate level. As such, the system relies on the wall to resist the thrust of the hipped jack rafters - not ideal. Suitably detailed ties perpendicular to the ceiling joists (often found forming double duty as ceiling binders) can address this.
Whether they know it or not, the approach by many structural engineers to say the hip rafter takes half the vertical load of each jack rafter means that (if the bottom of the jack rafter is birds-mouthed onto the wall plate) no net axial load exists at supports and so the wall only receives vertical load. It would be interesting to see what restraints were used in your model, and what the horizontal reactions were at the base of the untied jack rafters.
Taking things a step further, in the case of an asymmetric (single) hip arrangement, if you assume no load taken by the hip rafter (and that the jack rafters develop compression as above) then in-plane diaphragm action of the main roof pitches is required for overall stability as there's no equalising thrust from an opposing hip. Diaphragm action does no doubt exist, with in-plane distortion of the roof being resisted by tile-batten to rafter connections (forming vierendeel-like truss resistance), in-plane bracing/sarking (if present) and the friction of overlapping tiles. Good luck quantifying some of those though. You could also say the wall plate receiving hip jack rafters (parallel to CJ's) is working as a beam to resist horizontal thrust, but if taking this approach you'd need to make sure the wall plate is man enough and that it's ends can pass the reactions developed into something that can take it (maybe strap it to the perpendicular wall plate and pass load down into the wall below to resist it in shear). Another alternative is to strap hip jack rafters across enough ceiling joists to satisfy yourself that 'diaphragm' action of the ceiling deck will suffice (although note that in the symmetric hip case, the diaphragm needs to be continuous for opposing forces to reach and cancel each other out, and in the asymmetric case the unbalanced load does actually need to go somewhere). You don't need to strap every jack rafter as the thrusts from unstrapped rafters can be transferred via the wall plate spanning between strapped rafters if suitable fixings exist. This diaphragm principle is also in use when ceiling joist spans change locally at the end of a roof to pick up the hip jack rafter feet. These approaches can also be used with balanced (symmetric) hips to avoid the need for long connecting ties (useful in loft extensions when there's no room for binders or ties would clash with nested floor joists).
I'm sure unintentional combinations of all/some of these above load-paths and resistances are the reason so many roofs stand up, even though the design analysis doesn't represent the real behaviour and load paths.
Could be wrong though, so interested to hear your thoughts.
and yet the roof will not be taking any etra load in that area, This is proving troublesome as i cannot gey timber that size and will also cause me problems with boarding out the corners.
