I have attached a graphic showing the loading on a common rafter and a hip valley rafter. Most of the time the hip valley rafter is the same size as the common rafter. In this graphic the common rafters are 17 feet long spaced at 16" on center. The hip valley rafter is 22’-8" long with the attached jack rafters at 16" on center. The yellow shaded areas show the area loading that is transferred to the common rafter and the hip valley rafter. Just by visual observation you can see the hip valley rafter carries significantly more load than the common rafter. I did the calculations and the common rafter carries 7.42#/linear foot deal load (DL) and 20.48#/linear foot snow load (SL). The loading is based on a shingle roof, 1/2" plywood on #2 D.Fir-L 2x6 rafters. Based on the loading the common rafter without intermediate bracing fails in bending and deflection. By adding a mid-span support the 2x6 common rafter passes. The hip valley rafter failed in all combinations including two 2x12s, which was modeled without intermediate supports. The two 2x12s failed 220% in bending and 6% in deflection.To make the hip valley rafter a clear span beam it needed to be one LVL beam 1-3/4" x 11-1/4" , 2.0E, 2950Fb or two LVL beams 3-1/2" x 9-1/4". Total deflection was 73% of the maximum allowable by code for the single LVL and 65% for the double LVL beam.
I have added pictures of Friday’s inspection where the 2x6 hip valley rafter had about a 4" deflection mid-span. The jack rafters were pulling away from the hip valley rafter due to the excessive deflection. In general the hip valley rafter needs to be one to two sizes larger than the jack rafters, if you can add a few support braces. However there is typically no load bearing wall under the hip valley rafter needed for support. Where the hip roof is attached to the main roof at the ridge board both valley rafters and the hip roof ridge board transfer approximately 2400 lbs. So a vertical support at this point is needed.