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Solving for Unit and Total Run and Rise
Framing Square Tables

Builder 3&2 Volume 02 - Construction manual for building structures
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72 inches long is slightly more than 93.72 inches, but 93 3/4 inches is close enough for practical purposes. Once you know the total length of the member, just measure it off and make the end cuts. To make these cuts at the proper angles, set the square to the unit of run on the tongue and the unit of rise on the blade and draw a line for the cut along the blade (lower end cut) or the tongue  (upper  end  cut). SCALES A  framing  square  contains  four  scales:  tenths, twelfths, hundredths, and octagon. All are found on the face or along the edges of the square. As we mentioned earlier, the tenths scale is not used in roof framing. Twelfths Scale Figure 2-8.-Unit length. 14.4 inches. For practical purposes, you can round this to 14 3/8. To lay out the full length of the brace, set the square to the unit of rise (14 3/8 inches) and the unit of run (12 inches), as shown in figure 2-7. Then, step off this cut as many times as the unit of run goes into the total run (60/12, or 5 times). Determining Line Length If you do not go through the stepping-off procedure, you can figure the total length of the member in question by first determining the bridge measure. The bridge measure is the length of the hypotenuse of a right triangle with the other sides equal to the unit of run and unit of rise. Take the situation shown above in figure 2-7. The unit of run here is 12 inches and the unit of rise is 14 3/8 inches. Set the square to this cut, as shown in figure 2-8, and mark the edges of the board as shown. If you measure the distance between the marks, you will find it is 18 3/4 inches. Bridge measure can also be found by using the Pythagorean theorem: +      = Here, the unit of rise is the altitude (a), the unit or run is the base (b), and the hypotenuse (c) is the bridge measure. To get the total length of the member, you simply multiply the bridge measure in inches by the total run in feet. Since that is 5, the total length of the member is 18 3/4 x 5, or 93 3/4 inches. Actually, the length of the hypotenuse of a right triangle with the other sides 60 and The  graduations  in  inches,  located  on  the  back  of the square along the outer edges of the blade and tongue, are called the twelfths scale. The chief purpose of the twelfths scale is to provide various shortcuts in problem solving graduated in inches and twelfths of inches. Dimensions in feet and inches can be reduced to 1/12th by simply allowing each graduation on the twelfths scale to represent 1 inch; for example, 2 6/12 inches on the twelfths scale may be taken to represent 2 feet 6 inches. A  few  examples  will  show  you  how  the  twelfths  scale is used. Suppose you want to know the total length of a rafter with a total run of 10 feet and a total rise of 6 feet 5 inches. Set the square on a board with the twelfths scale on the blade at 10 inches and the twelfths scale on the tongue at 6 5/12 inches and make the usual marks. If you measure the distance between the marks, you will find it is 11 11/12 inches. The total length of the rafter is 11 feet 11 inches. Suppose now that you know the unit of run, unit of rise, and total run of a rafter, and you want to find the total rise and the total length. Use the unit of run (12 inches) and unit of rise (8 inches), and total run of 8 feet 9 inches. Set the square to the unit of rise on the tongue and unit of run on the blade (fig. 2-9, top view). Then, slide the square to the right until the 8 9/12-inch mark on the blade (representing the total run of 8 feet 9 inches) comes even with the edge of the board, as shown in the second view. The figure of 5 10/12 inches, now  indicated  on  the  tongue,  is  one-twelfth  of  the  total rise. The total rise is, therefore, 5 feet 10 inches. The distance between pencil marks (10 7/12 inches) drawn along the tongue and the blade is one-twelfth of the total length. The total length is, therefore, 10 feet 7 inches. 2-6







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