Fig. 73. - Diagram for Finding the Lengths and Bevels of the Jacks on the Rear Side of the Long Hip.

Fig. 74. - Plan of Roof having Three Gables of Varying Pitches.

Fig. 75. - Finding Lengths and Devels of Jack Rafters on the Front Side of Right and Left Gables Shown in Fig. 74.

In Fig. 74 is represented a plan of a roof having three gables of varying pitches. The right gable A B C is 16 feet wide and has a rise of 8 feet. The front gable D F G is 18 feet wide and has a rise of 8 feet. The last gable J I H is 21 feet wide and has a rise of 8 feet. It will be noticed that the left gable has two different pitches. This plan shows as much irregularity as can be desired and as much as is generally encountered in actual practice. We will now proceed to find the lengths and different cuts of the various rafters required in this roof. The dotted lines represent lines plumb under the ridge of the gables. The lengths of the common rafters and their proper cuts may be taken from each of the three gables separately, and are so plain and easily understood from the diagram that further explanation is unnecessary. The roof has two valleys of different pitches, of which the lines N L K are the seats or runs. To find the length of the valley rafter on the right side of the front gable on the line K L, square up the rise of the roof from L to M, connect M with K, and we have the length of the valley after. A bevel set in the angle at M will give the down bevel at the top and the angle at K the bottom cut fitting the plate. To find the length of the valley rafter on the left side of the front gable on the line N L, square up the rise of the roof from L to O and connect O with N for the length of the valley rafter. A bevel set in the angle at O will give the down bevel at the top and the angle at N the bottom cut fitting the plate. Now, if we were to draw all the lines in Fig, 74 necessary to show the lengths and proper cuts of all the different jack rafters required in this roof, there would be such a number crossing each other at various angles as to cause confusion. In this roof there are four different cuts of jack rafters, and it is better not to have them mixed up with the valleys and common rafters, hence wc will make separate diagrams.

Referring now to Fig. 75, to find the lengths and bevels of jacks on the front side of right and left gables, draw a horizontal line, J A, representing the entire length of front plate line. Next set off the exact location of the front gable N K. From the center of the front gable draw a perpendicular line, S O, the length of the common rafter on the front side of the left gable, the same as J I in Fig. 74. Connect O with N for the position of the valley rafter for finding the lengths and bevels of jacks on the front side of the left gable. Square up the length of the common rafter on the front side of the left gable J I and connect I O for the ridge line. Space the rafters on the ridge line and draw perpendicular lines to the plate and valley, which will give the lengths of the jacks on the front side of the left gable. A bevel set in the angle at W where they join the valley will give the bevel across the back. The plumb cut or down bevel will be same as that of the common rafter on the front side of the left gable. To find the lengths and bevels of jacks on the front side of right gable, set off the length of common rafter from the center of the front gable S M, which is the same as A B of Fig. 74. Connect M with K for the position of the valley rafter for finding the lengths and bevels of the jacks on the front side of the right gable. Square up the length of the common rafter on the right gable A B and connect B M for the ridge line. Space the jacks on the ridge line and draw perpendicular lines to the plate and valley, which will give the lengths of the jacks on the front side of the right gable. A bevel set in the angle at Z where they join the valley will give the bevel across the back. The plumb cut or down bevel will be the same as that of the common rafter on the right gable. The lines N F K show the length of the common rafter on the front gable.

Fig. 76. - Finding Lengths and Bevels of the Jack Rafters on the Bight Side of the Front Gable.

To find the lengths and bevels of the jacks on the right side of the front gable draw a horizontal line G C, Fig. 76, representing the plate line. On this line set off the location of the right gable K C. From the center of the gable set off the length of common rafter on the front gable T M, which is the same as G F of Fig. 74. Connect M with K for the position of valley rafter for finding the lengths and bevels of jacks on the right side of the front gable. Square up the length of the common rafter on the front gable, G F, and connect F M for the ridge line. Space the jacks on the ridge line and draw perpendicular lines to the plate and valley, which will give the lengths of the jacks on the right side of the front gable. A bevel set in the angle at Y will give the bevel across the back. The plumb cut or down bevel will be the same as that of the common rafter on the front gable. The lines K B C show the length of the common rafter on the right gable. To find the lengths and bevels of the jacks on the left side of the front gable draw a horizontal line, as H D of Fig. 77, representing the plate line. On this line set off the location of the left gable, H N. From R, the point directly under the ridge of this gable, set off the length of the common rafter on the front gable R O, which is the same as D F of Fig. 74. Connect O N for the position of the valley for finding the lengths and bevels of the jacks on the left side of the front gable. A bevel set in the angle at x will give the bevel across the back. The plumb cut or down bevel will be the same as that of the common rafter on the front gable. The lines H I J show the lengths of the common rafters on the left gable.

Fig. 77. - Finding Lengths and Bevels of Jacks on the Left Side of the Front Gable.

Fig. 78. - Diagram Showing More Clearly the Different Cuts of Jack Rafters.

In order to throw as much light as possible upon the subject and present a choice of methods, we will give another diagram showing the different cuts of the jack rafters in a much plainer manner, and which to many, perhaps, will be more satisfactory. Fig. 78 shows the wall plate lines exactly the same as in Fig. 74, except it is divided on the ridge line of the front gable, and spread so far apart that when the roof is developed, showing the different jack rafters in their various positions, there will not be a series of lines crossing each other to cause confusion. Let H, C, A, K, G, D, N, J, represent the wall plate lines. The dotted lines R L S and S2 L2 T are the lines plumb under the ridge of the gables. We will now proceed to find the jack rafters and their proper cuts : Taking the left gable first on the line J H, set off the length of the common rafter from J to I ; from I, at right angles, draw the line IO, which is the ridge proper and extends to the center of the front gable represented by the dotted line L S ; connect O with N for the valley rafter; on the line IO space off the jacks and draw the lines connecting them with the valley N O, as shown in the diagram. This will give the lengths of the jacks in the left gable, and a bevel set in the angle at W will give the bevel across the backs of the same. The down bevel will be the same as that of the common rafter on the front side of the left gable. A similar plan is followed for each gable or each side of a gable, where the jack rafters are of different lengths or have different cuts, as will be readily seen by referring to the diagram. The valley lines N O and N 0s are of the same length and show the valley rafters in different positions for finding the lengths and cuts of the two divisions of jacks - namely, the left gable and the left side of the front gable. The valley lines K M and K M2 are of the same length, but show the valley rafter in different positions for finding the lengths and cuts of the other two divisions of jacks - namely, the right gable and the right side of the front gable.

Now elevate the four sections of the roof containing the different jacks to their proper pitch, and move the two divisions of the diagram together till the dotted lines L S and L2 S2 meet plumb under the ridge of the front gable. What is the result ? N O and N O2 join as one line and constitute the left valley. K M and K M2 also join as one line and constitute the right valley. This would also bring every jack into its required position in the roof, as can be plainly seen in the diagram. The cuts of the two valley rafters must be taken from Fig. 74, as shown and described before. The cuts could be shown in Fig. 78, but as they would only serve to make the diagram more complicated, they are omitted. If any one would like to see a diagram showing all the rafters and different cuts in a roof of this kind, they can draw the lines of Figs. 74 and 78 in one diagram. If they will imagine one of these diagrams placed over the other, the result will probably be satisfactory.