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.
The Standard Steel Square has a blade 24 inches long and 2 inches wide, and a tongue from 14 to 18 inches long and 1 1/2 inches wide.
The blade is at right angles to the tongue.
The face of the square is shown in Fig. 1. It is always stamped with the manufacturer's name and number.
The reverse is the back (see Fig. 2).
The longer arm is the blade; the shorter arm, the tongue.
In the center of the tongue, on the face side, will be found two parallel lines divided into spaces (see Fig. 1); this is the octagon scale.
The spaces will be found numbered 10, 20, 30, 40, 50, 60, and 70, when the tongue is 18 inches long.
To draw an octagon of 8 inches square, draw a square 8 inches each way, and draw a perpendicular and a horizontal line through its center.
To find the length of the octagon side, place one point of a compass on any of the main divisions of the scale, and the other point of the compass on the eighth subdivision; then step this length off on each side of the center lines on the side of the square, which will give the points from which to draw the octagon lines.
The diameter of the octagon must equal in inches the number of spaces taken from the square.
On the opposite side of the tongue, in the center, will be found the brace rule (see Fig. 3). The fractions denote the rise and run of the brace, and the decimals the length. For example, a brace of 36 inches run and 36 inches rise, will have a length of 50.91 inches; a brace of 42 inches run and 42 inches rise, will have a length of 59.40 inches; etc.
On the back of the blade (Fig. 4) will be found the board measure, where eight parallel lines running along the length of the blade are shown and divided at every inch by cross-lines. Under 12, on the outer edge of the blade, will be found the various lengths of the boards, as 8, 9, 10, 11, 12, etc. For example, take a board 14 feet long and 9
Fig. 1. Face Side of Tongue of Steel Square, Showing Octagon Scale.
Fig. 2. Back of Blade of Steel Square, Showing Rafter Table.
Fig. 3. Back of Tongue of Steel Square, Shoving Brace Measure.
Fig. 4. Back of Blade of Steel Square, Showing Essex Board Measure.
Fig. 5. Use of Steel Square to Find Miter and Side of Pentagon.
inches wide. To find the contents, look under 12, and find 14; then follow this space along to the cross-line under 9, the width of the board; and here is found 10 feet 6 inches, denoting the contents of a board 14 feet long and 9 inches wide. To Find the Mi= ter and Length of Side for any Poly= gon, with the Steel Square. In Fig. 5 is shown a pentagon figure. The miters of the pentagon stand at 72 degrees with each other, and are found by dividing 360 by 5, the number of sides in the pentagon. But the angle when applied to the square to obtain the miter, is only one-half of 72, or 36 degrees, and intersects the blade at 8 23/32, as shown in Fig. 5. By squaring up from 6 on the tongue, intersecting the degree line at a, the center a is determined either for the inscribed or the circumscribed diameter, the radii being a b and a c, respectively,,
The length of the sides will be 8§f inches to the foot.
If the length of the inscribed diameter be 8 feet, then the sides would be 8 X 8 23/32 inches.
Fig. 6. Use of Steel Square to Find Miter and Side of Hexagon.
The figures to use for other polygons are as follows:
Triangle 20 25/32
Nonagon 4 3/8
Decagon 3 7/8
In Fig. 6 the same process is used in finding the miter and side of the hexagon polygon.
To find the degree line, 360 is divided by 6, the number of sides, as follows: 360 / 6 = 60; and 60 / 2 = 30 degrees.
Now, from 12 on tongue, draw a line making an angle of 30 degrees with the tongue. It will cut the blade in 7 as shown; and from 7 to to, the heel of the square, will be the length of the side. From 6 on tongue, erect a line to cut the degree line in c; and with c as center, describe a circle having the radius of c 7; and around the circle, complete the hexagon by taking the length 7 m with the compass for each side, as shown.
In Fig. 7 the same process is shown applied to the octagon. The degree line in all the polygons is found by dividing 360 by the number of sides in the figure:
360 ÷ 8 = 45; and 45 ÷ 2 = 22 1/2 degrees. This gives the degree line for the octagon. Complete the process as was described for the other polygons.
By using the following figures for the various polygons, the miter lines may be found; but in these figures no account is taken of the relative size of sides to the foot as in the figures preceding: Triangle 7 in. and 4 in.
Pentagon 11 " " 8 " Hexagon 4 " "7 " Heptagon 12 1/2 " " 6"
Fig. 7. Use of Steel Square to Find Miter and Side of Octagon.
Octagon 17 in. and 7 in. Nonagon 22 1/2 " " 9" Decagon 9 1/2 " " 3" The miter is to be drawn along the line of the first column, as shown for the triangle in Fig. 8, and for the hexagon in Fig. 9. In Fig. 10 is shown a diagram for finding degrees on the square. For example, if a pitch of 35 degrees is required, use 8 13/32 on tongue and 12 on blade; if 45 degrees, use 12 on tongue and 12 on blade; etc.
In Fig. 11 is shown the relative length of run for a rafter and a hip, the rafter being 12 inches and the hip 17 inches. The reason, as shown in this diagram, why 17 is taken for the run of the hip, instead of 12 as for the common rafter, is that the seats of the common rafter and hip do not run parallel with each other, but diverge in roofs of equal pitch at an angle of 45 degrees; therefore, 17 inches taken on the run of the hip is equal to only 12 inches when taken on that of the common rafter, as shown by the dotted line from heel to heel of the two squares in Fig. 11.
In Fig. 12 is shown how other figures on the square may be found for corners that deviate from the 45 degrees. It is shown that for a pentagon, which makes a 36-degree angle with the plate, the figure to be used on the square for run is 14&8542; inches; for a hexagon, which makes a 30-degree angle with the plate, the figure will be 13 7/8 inches; and for an octagon, which makes an angle of 22 1/2 degrees with the plate, the figure to use on the square for run of hip to correspond to the run of the common rafters, will be 13 inches. It will be observed that the height in each case is 9 inches.
Fig. 8. Use of Square to Find Miter of Equilateral Triangle.
Fig. 9. Use of Square to Find Miter of Hexagon.
Fig. 13 illustrates a method of finding the relative height of a hip or valley per foot run to that of the common rafter. The square is shown placed with 12 on blade and 9 on tongue for the common rafter; and shows that for the hip the rise is only 6 6/17 inches.