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.
When jacks are placed between hips and valleys as shown at 1, 2, 3, 4, etc., in Fig. 14, a better method of treatment is shown in Fig. 29, where the slope of the roof is projected into the horizontal plane. The distance from the plate in this figure to the ridge m, equals the length of the common rafter for the main roof. On the plate a n n is made equal to a n n in Fig. 14. By drawing a figure like this to a scale of one inch to one foot, the length of all the jacks can be measured and also the lengths of the hip and the two valleys. It also gives the bevels for the jacks, as well as the bevel to fit the hip and valley against the ridge; but this last bevel must be applied to the hip and valley when backed.
It has been shown before, that the figures to be used on the square for this bevel when the timber is left square on back as is the custom in construction, are the length of a foot run of a hip or valley, which is 17, on tongue, and the length of a hip or valley that will span over 17 inches run, on blade - the blade giving the bevel.
Fig. 30 contains all the bevels or cuts that have been treated upon so far, and, if correctly understood, will enable any one to frame any roof of equal pitch. In this figure it is shown that 12 inches run and 9 inches rise will give bevels 1 and 2, which are the plumb and heel cuts of rafters of a roof rising 9 inches to the foot of run. By taking these figures, therefore, on the square, 9 inches on the tongue and 12 inches on the blade, marking along the tongue will give the plumb cut, and marking along the blade will give the heel cut.
Bevels 3 and 4 are the plumb and heel cuts for the hip, and are shown to have the length of the seat of hip for one foot run, which is 17 inches. By taking 17 inches, therefore, on the blade, and 9 inches on the tongue, marking along the tongue for the plumb cut, and along the blade for the heel cut, the plumb and heel cuts are found. Bevel 5, which is to fit the hip or valley against the ridge when not backed, is shown from o w, the length of the hip for one foot of run, which is 19 1/4 inches, and from o s, which always in roofs of equal pitch will be 17 inches and equal in length to the seat of a hip or valley for one foot of run.
Fig. 31. Method of Finding Bevel 5, Fig. 30, for Fitting Hip or Valley Against Ridge when not Backed.
Fig. 32. Method of Finding Back Bevel 6, Fig. 30, for Jack Rafters, and Bevel 7, for Roof-Board.
Fig. 33. Determining Miter Cut for Roof-Board.
These figures, therefore, taken on the square, 19 1/4 on the blade, and 17 on the tongue, will give the bevel by marking along the blade as shown in Fig. 31, where the square is shown applied to the hip timber with 19 1/4 on blade and 17 on tongue, the blade showing the cut.
Bevels 6 and 7 in Fig. 30 are shown formed of the length of the rafter for one foot of run, which is 15 inches, and the run of the rafter, which is 12 inches. These figures are applied on the square, as shown in Fig. 32, to a jack rafter timber; taking 15 on the blade and 12 on the tongue, marking along the blade will give the back bevel for the jack rafters, and marking along the tongue will give the face cut of roof-boards to fit along the hip or valley.
It is shown in Fig. 30, also, that by taking the length of rafter 15 inches on blade, and rise of roof 9 inches on tongue, bevel 8 will give the miter cut for the roof-boards.
In Fig. 33 the square is shown applied to a roof-board with 15 on blade, which is the length of the rafter to one foot of run, and with 9 on tongue, which is the rise of the roof to the foot run; marking along the tongue will give the miter for the boards.
Other uses may be made of these figures, as shown in Fig. 34, which is one-half of a gable of a roof rising 9 inches to the foot run. The squares at the bottom and the top will give the plumb and heel cuts of the common rafter. The same figures on the square applied to the studding, marking along the tongue for the cut, will give the bevel to fit the studding against the rafter; and by marking along the blade we obtain the cut for the boards that run across the gable. By taking 19 1/4 on blade, which is the length of the hip for one foot of run, and taking on the tongue the rise of the roof to the foot of run, which is 9 inches, and applying these as shown in Fig. 35, we obtain the backing of the hip by marking along the tongue of the two squares, as shown.
Fig. 34. Laying Out Timbers of One-half Gable of 3/8-Pitch Roof.
Fig. 35. Finding Backing of Hip in Gable Roof.
It will be observed from what has been said, that in roofs of equal pitch the figure 12 on the blade, and whatever number of inches the roof rises to the foot run on the tongue, will give the plumb and heel cuts for the common rafter; and that by taking 17 on the blade instead of 12, and taking on the tongue the figure representing the rise of the roof to the foot run, the plumb and heel cuts are found for the hips and valleys.
By taking the length of the common rafter for one foot of run on blade, and the run 12 on tongue, marking along the blade will give the back bevel for the jack to fit the hip or valley, and marking along the tongue will give the bevel to cut the roof-boards to fit the line of hip or valley upon the roof.