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HIP RAFTER EXAMPLE 
(INCREASING LOAD FROM ZERO TO A MAXIMUM)

Through common practice it has been shown that there is some buttressing effect from steep rafters pushing against each other at a hip rafter, however there isn't any provision for this in the building code and hips must be designed as a common beam as if it were horizontal.

ROOF LOAD
LL = 25 PSF (SNOW), DL = 15 PSF, TL = 40 PSF

ROOF PITCH = 9:12 (9 INCH RISE PER FOOT)
Dead Load has been increased to account for the slope of the rafters.
As the slope increases the rafters are longer and the amount of roofing increases.

SPAN  The length of the hip rafter (the hypotenuse of the triangle) is 1.414 x the side of the right triangle formed by the outside walls, which in this case is 10 feet.
The hip (horizontal) span is 10' x 1.414 = 14.14'
The true length of the member is longer because it is sloping on a 9:12 pitch.