This section is from the book "Cyclopedia Of Architecture, Carpentry, And Building", by James C. et al. Also available from Amazon: Cyclopedia Of Architecture, Carpentry And Building.
Fig. 205 shows the plan of the roof in which there are, in addition to hip and valley rafters, sets of jack rafters. A B and B D are hip rafters, C E is a valley rafter, and the other rafters are common and jack rafters. At B E and E H are shown the ridge boards. Of the jack rafters there are three different kinds: those like I J which run from the valley rafter to the ridge board; those like K L which run from hip rafter to plate; and those like N T, which run between the hip and valley rafters. These jack rafters differ only in respect to the bevels which have to be cut on them. The rafter I J is a simple plumb cut at the top, similar to the cuts at the top of the common rafters, and at the bottom where the rafter meets the valley there are two cuts - a plumb cut and the side cheek cut - which are similar to the cuts in a valley rafter where it comes against a ridge board. This cut has been previously explained.
Fig. 205. Roof Plan Showing Hip and Valley Rafters and Jack Rafters.
The rafter K L has a simple horizontal cut at the bottom like that used on the common rafter, but at the top there are two cuts similar to those at the foot of rafter I J. The rafter N T has two cuts at both top and bottom. All these bevels are obtained just as the bevels for the hip and valley rafters.
The length of a jack rafter is proportional to its distance from the ridge or plate to which it is parallel. The longest jack rafter is equal in length to a common rafter, and the length steadily decreases as the distance of the rafter from its first full length rafter. The exact difference in length between the first jack rafter and the next, is determined by finding how far apart the jack rafters are to be placed, and comparing this distance with the distance from the top of the first full length jack rafter to the point where the hip or valley rafter rests on the ridge board or plate. Suppose, for instance, that the rafters are to be spaced 2 feet apart, and the length of the common rafter is 10 feet. If the distance from the top of this rafter to the point where the valley rafter is fitted against the ridge is 12 feet, it is evident that each rafter will be 2 feet shorter. That is, the second rafter will be 8 feet and the next 6 feet and so on. We use six spaces, although there are only five rafters, there being no rafter used where the valley and ridge join.
Fig. 206. Roof Plan Showing Rafters Cut for Ogee Roof.