Figure 2-31.-Shortening a hip rafter.Rafter Shortening AllowanceAs in the case with a common rafter, the line lengthof a hip rafter does not take into account the thicknessof the ridge piece. The size of the ridge-end shorteningallowance for a hip rafter depends upon the way theridge end of the hip rafter is joined to the other structuralmembers. As shown in figure 2-31, the ridge end of thehip rafter can be framed against the ridgeboard (view A)or against the ridge-end common rafters (view B). Tocalculate the actual length, deduct one-half the 45°thickness of the ridge piece that fits between the raftersfrom the theoretical length.When no common rafters are placed at the ends ofthe ridgeboard the hip rafters are placed directly againstthe ridgeboard. They must be shortened one-half thelength of the 45° line (that is, one-half the thickness ofthe ridgeboard When common rafters are placed at theends of the ridgeboard (view B), the hip rafter will fitbetween the common rafters. The hip rafter must beshortened one-half the length of the 45° line (that is,one-half the thickness of the common rafter).If the hip rafter is framed against the ridge piece, theshortening allowance is one-half of the 45° thickness ofthe ridge piece (fig. 2-31, view C). The 45° thickness ofstock is the length of a line laid at 45° across thethickness dimension of the stock. If the hip rafter isframed against the common rafter, the shorteningallowance is one-half of the 45° thickness of a commonrafter.To lay off the shortening allowance, first set thetongue of the framing square to the line length ridge cutline. Then, measure off the shortening allowance alongthe blade, set the square at the mark to the cut of therafter (8 inches and 17 inches), draw the actual ridgeplumb cut line. (To find the 45° thickness of a piece oflumber, draw a 450 line across the edge, and measurethe length of the line and divide by 2.)Rafter ProjectionA hip or valley rafter overhang, like a commonrafter overhang, is figured as a separate rafter. Theprojection, however, is not the same as the projection ofa common rafter overhang in the same roof. Theprojection of the hip or valley rafter overhang is thehypotenuse of a right triangle whose shorter sides areeach equal to the run of a common rafter overhang(fig. 2-32). If the run of the common rafter overhang is2-22