Figure 2-38.-Equal-span intersecting roof.Figure 2-40.-Equal pitch but unequal span framing.Figure 2-39.-Ridge-end shortening allowance for equal-spanintersecting valley rafter.hip rafter. The valley-rafter tail has a double side cut(like the hip-rafter tail) but in the reverse direction. Thisis because the tail cut on a valley rafter must form aninside, rather than an outside, corner. As indicated infigure 2-39, the ridge-end shortening allowance in thisframing situation amounts to one-half of the 45°thickness of the ridge.Figure 2-40 shows a framing situation in which thespan of the addition is shorter than the span of the mainroof. Since the pitch of the addition roof is the same asthe pitch of the main roof, the shorter span of theaddition brings the addition ridge down to a lower levelthan that of the main-roof ridge.There are two ways of framing an intersection ofthis type. In the method shown in figure 2-40, a full-length valley rafter (AD in the figure) is framed betweenthe top plate and the main-roof ridgeboard. A shortervalley rafter (BC in the figure) is then framed to thelonger one. If you study the framing diagram, you cansee that the total run of the longer valley rafter is thehypotenuse of a right triangle with the altitude and baseequal to the total run of a common rafter in the mainroof. The total run of the shorter valley rafter, on theother hand, is the hypotenuse of a right triangle with thealtitude and base equal to the total run of a commonrafter in the addition. The total run of a common rafterin the main roof is equal to one-half the span of the mainroof. The total run of a common rafter in the addition isequal to one-half the span of the addition.Knowing the total run of a valley rafter, or of anyrafter for that matter, you can always find the line lengthby applying the bridge measure times the total run.2-27