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
