[Illustration: Fig. 63.
LAY-OUT OF HIP-ROOF WITH DECK.]
THE STEEL SQUARE AND ITS USES.
DIVISION C.
_Introductory._
During my long experience as Editor of several of the leading building
journals in the United States and Canada, I have been asked and have
answered thousands of questions regarding matters concerning building
construction, builders’ materials, tools and processes, and particularly
regarding the “Steel Square and its Uses,” and I have concluded that the
publication of a few of these questions and answers, along with other
matter, in this division will be appreciated by my readers, and to this
end I insert a number of the most useful items in this manual.
Besides these questions and answers, I also publish other up to date
matter, all of which will make this volume one of the most useful little
works to the American carpenter and wood-worker ever published.
[Illustration: Fig. 64.]
[Illustration: Fig. 65.]
I open this division with a few hints regarding the construction, or
rather the laying out of a Hip-Roof where the design has been furnished
by an architect, and which, of course, shows the pitch and the lay of
the timbers. We suppose the roof to have a span of 18 feet and a rise of
6 feet, thus giving the roof a one-third pitch. The fence is used in
this example to its full extent, and when placed on the square and
fastened, the line of fence shows the slope or pitch of roof. Fig. 64
shows the square set to the pitch of the hip rafter. The squares as set
give the plumb and level cuts. Fig. 65 is the rafter plan of a house 18
by 24 feet; the rafters are laid off on the level, and measure nine feet
from center of ridge to outside of wall; there should be a rafter
pattern with a plumb cut at one end, and the foot cut at the other, got
out as previously shown. When the rafter foot is marked, place the end
of the long blade of the square to the wall line, as in drawing, and
mark across the rafter at the outside of the short blade, and these
marks on the rafter pitch will correspond with two feet on the level
plan; slide the square up the rafter and place the end of the long blade
to the mark last made, and mark outside the short blade as before,
repeat the application until nine feet are measured off, and then the
length of the rafter is correct; remember to mark off one-half the
thickness of ridge-piece. The rafters are laid off on part of plan to
show the appearance of the rafters in a roof of this kind, but for
working purposes the rafters 1, 2, 3, 4, 5 and 6, with one hip rafter,
is all that is required.
To proceed, we first lay off common rafter, which has been previously
explained; but deeming it necessary to give a formula in figures to
avoid making a plan, we take 1-3 pitch. This pitch is 1-3 the width of
the building, to point of rafter from wall plate or base. For an
example, always use 8, which is 1-3 of 24, on tongues for altitude; 12,
½ the width of 24, on blade for base. This cuts common rafter. Next is
the hip-rafter. It must be understood that the diagonal of 12 and 12 is
approximately 17 in framing work, and the hip is the diagonal of a
square added to the rise of roof; therefore we take 8 on the tongue and
17 on the blade; run the same number of times as common rafter which
gives the length of hip and plumb and level bevels.
To cut jack rafters, divide the number of openings for common rafters.
Suppose we have five jacks, with six openings, our common rafter 12 feet
long, each jack would be 2 feet shorter. The first, next the hip, 10
feet, the second 8 feet, third 6 feet, and so on. The top down cut same
as down cut for common rafter. For the bevel, cut against hip. Take half
the width of building on tongue and length of common rafter on blade,
and blade gives the bevel. Now find diagonal of 8 and 12, which is 14
7-16 in. Take this length on blade and 12 on tongue, blade gives bevels.
If the hip-rafter is beveled or “backed” to suit jacks, then take height
of hip on tongue, length of hip on blade, and tongue gives bevel. These
figures will cover all bevels for cutting, cornice and sheathing. For
bed moulds for gable to fit under cornice, take half width of building
on tongue, length of common rafter on blade; blade gives cut. To cut
planceer to run up valley, take height of rafter on tongue, length of
rafter on blade; tongue gives bevel. For plumb cut, take height of hip
on tongue, length of hip on blade; tongue gives bevel.
These figures were specially prepared for a hip roof having a one-third
pitch, but will suit other pitches equally well if the difference in
height of ridge is considered.
For a hopper the mitre is cut on the same principle. To make a butt
joint, take the width of side on blade, and half the flare on tongue:
the latter gives the cut. You will observe that a hip-roof is the same
as a hopper inverted. The cuts for the edges of the pieces of a
hexagonal hopper are found this way. Subtract the width of one piece at
the bottom from the width of same at top, take remainder on tongue,
depth of side on blade; tongue gives the cut. The cut on face of sides:
Take 7-12 of the rise on tongue and the depth of side on blade; tongue
gives cut. The bevel of top and bottom: Take rise on blade, run on
tongue; tongue gives cut.
SOME QUESTIONS AND ANSWERS
FROM VARIOUS CORRESPONDENTS.
The following questions and answers from practical workmen are
considered among the very best things regarding the use of the Steel
Square, as they are from men who knew of what they were talking about.
They are gathered from many sources, but chiefly from the columns of
Technical Journals with which I have been connected, either as Editor or
contributor.
Jas. Willis, Rochester, N. Y., asks: “How can I get the proper bevel for
a butt joint on an obtuse or acute angle, by the use of the square
only?”
[Illustration: Fig. 66.]
Answer: Suppose Fig. 66 represents an obtuse angle formed by two
parallel boards or timbers. To obtain the joint, A, space off equal
distances from the point 1 to 3, 3, then square over from the lines, R,
R, keeping the heel of the square at the points 3, 3. At the junction of
the lines formed by the tongue of the square at 0 will be one point, and
1 will be the other by which the joint line, A, is defined.
[Illustration: Fig. 67.]
To find the line of juncture for an acute angle, proceed as follows:
Fig. 67 represents two parallel boards or timbers; 1 the extreme angle,
3, 3 equal distances from the angle 1 and are the points where the heel
of the square must rest to form the lines 0, 3; 0 shows the junction of
the lines formed by the blade of the square. Draw a line from 0 to 1,
and the line, A, formed, is the bevel required.
It will be seen, by these two examples, that the bevel of a junction at
any angle may be obtained by this method.
P. McVity, Milwaukee, asks: “How can I draw a circle with the Steel
Square?”
Answer: A circle of any required diameter may be drawn by means of the
square by using it as indicated in the accompanying sketch. Drive two
pins or nails, A and B, Fig. 68, at whatever distance apart the circle
is to have as its diameter. Bring the square against them, as shown, and
use a pencil in the angle as indicated in the drawing. This rule is very
convenient in many instances. Suppose A and B are two points through
which a circle is required to be drawn. By bringing the square against
pins or nails placed in the points, it may be described as indicated in
the sketch.
[Illustration: Fig. 68.]
A “Mechanic,” Tampa, Fla., asks: “Can the steel square be used in laying
out a wreath for a handrail, and if so, please describe how?”
[Illustration: Fig. 69.]
Answer: Some advance in this direction has been made, but not much, but
the outlook is quite encouraging as many experts are trying to obtain
all the lines required for forming circular handrails. It will be
accomplished sooner or later. A few problems and solutions are given
herewith: In getting out face-molds it has generally been considered
necessary first to unfold the tangents and get the heights, and by
construction get the bevels. The method shown is somewhat different,
though results are the same, but are produced more rapidly. Take for
illustration a side wreath mitered into a newel cap. This method will
apply no matter where the newel is placed, or whether the easement is
less or more than the one step of the example illustrated. What is meant
by one step is, that the tangent of the straight rail continues to the
point 2, Fig. 69. The tangent 2-1 is level.
[Illustration: Fig. 70.]
To produce the face mould, lay the steel square in the position,
indicated by the lines 1, 2, 3, 4, not the figure on the square at the
points numbered, and transfer them to a piece of thin stuff, Fig. 70.
Line 3-4 in Fig. 70 is indefinite. Now take the length of the long edge
of the pitch board in the compasses, and with 2, Fig. 70, as a center,
cut the line 3-4 in 4 and draw 2-4. Now 1-2 is the level, and 2-4 is the
pitch tangent on the face mold.
To get the bevels and width of the face mold at both ends, take the
distance 3-4 on the blade of the square, and the height of a riser on
the tongue of the square, apply to the edge of a board and mark by the
tongue; this gives the width of the mold at the lower end.
Next take the distance 4-X on the blade of the square, and the distance
shown on the pitch board by the line squared from its top edge to the
corner, on the tongue of the square; apply to the edge of a board and
mark by the tongue; this gives the bevels for the top end of the wreath.
Mark the width of the rail on the bevel, and this gives the width of the
mold at the top end. An allowance of 6 inches is made at the top end to
joint to the straight rail, and two inches at the bottom end to form the
miter into the newel cap. The springing line is taken from the pitch
board.
Fig. 69, in which are shown the bevels and the pitch board will help to
make clear the methods used. The bevel at the back of the pitch board is
for the bottom end of the wreath. The triangle has for its base the line
3-4 and for its height one riser. The hypothenuse is the length of 2-4,
Fig. 70, and Fig. 70 stands over Fig. 69, level on the line 1-2-3, and
inclined from it in this cast at an angle of nearly 45 degrees.
The top end bevel is shown below the pitch board. The angle has for its
base the distance 4-x, and for its height not one rise, but the length
of a line, from the corner of the pitch board squared from its top edge.
This bevel will be understood better by placing the pitch board on the
line 2-4 and applying the small triangle to it with its base on the line
4-x, and its point even with the top edge of the pitch board. It will
then be at right angles to the top edge of the pitch board.
In practice, a parallel mold is generally used, and the wreath piece is
cut out; both thickness of plank and width of molding being equal to the
diameter of a circle that will contain a section of finished rail.
Jacques Demoux, Winnipeg, Man., wants to know how to lay out braces,
regular and irregular by the use of the Steel Square.
Answer: Braces and trusses are something like rafters and when the run
is known, there should be no difficulty in getting the lengths and
proper bevels.
In the first place it is always best to make a pattern and then mark out
the timber work from the pattern. Suppose we want braces having a
“four-foot run”—that is, the brace is to form a diagonal from points
four feet from the post and four feet from the girt. Take a piece of
stuff already prepared, six feet long, four inches wide and half-inch
thick, gauge it three-eighths from jointed edge.
[Illustration: Fig. 71.]
Take the square as arranged at Fig. 71, and place it on the prepared
stuff as shown at Fig. 72. Adjust the square so that the twelve-inch
line coincide exactly with the gauge line o, o, o, o. Hold the square
firmly in the position now obtained, and slide the fence up the tongue
and blade until it fits snugly against the jointed edge of the prepared
stuff, screw the fence tight on the square, and be sure that the 12-inch
marks on both the blade and the tongue are in exact position over the
gauge-line.
[Illustration: Fig. 72.]
We are now ready to lay out the pattern. Slide the square to the extreme
left, as shown on the dotted lines at x, mark with a knife on the
outside edges of the square, cutting the gauge line. Repeat this process
four times, marking the ends, and you have the length and bevels. Square
over at each end from the gauge line and you have the toe of the brace.
The lines ss, Fig. 72, show the tenons left on the end of the braces.
[Illustration: Fig. 73.]
The cut at Fig. 73, shows the brace in position, on a reduced scale. The
principle on which the square works in the formation of a brace can
easily be understood from this cut, as the dotted lines show the
position the square was in when the pattern was laid out.
It may be necessary to state that the “square,” as now arranged, will
lay out a brace pattern for any length, if the angle is right, and the
run equal. Should the brace be of great length, however, additional care
must be taken in the adjustment of the square, for should there be any
departure from truth, that departure will be repeated every time the
square is moved, and where it would not affect a short run, it might
seriously affect a long one.
To lay out a pattern for a brace where the run on the beam is three
feet, and the run down the post four, proceed as follows:
[Illustration: Fig. 74.]
Prepare a piece of stuff, same as the one operated on for four feet run;
joint and gauge it. Lay the square on the left-hand side, keep the
12-inch mark on the tongue, over the gauge-line; place the 9-inch mark
on the blade, on the gauge-line, so that the gauge-line forms the third
side of a right angle triangle, the other sides of which are nine and
twelve inches, respectively.
Now proceed as on the former occasion, and as shown at Fig. 74, taking
care to mark the bevels at the extreme ends. The dotted lines show the
position of the square, as the pattern is being laid out.
Fig. 75 shows the brace in position, the dotted lines show where the
square was placed on the pattern. It is well to thoroughly understand
the method of obtaining the lengths and bevels of irregular braces. A
little study will soon enable any person to make all kinds of braces.
[Illustration: Fig. 75.]
If we want a brace with a two-foot run, and a four-foot run it must be
evident that, as two is the half of four, so on the square take 12
inches on the tongue, and 6 inches on the blade, apply four times, and
we have the length, and the bevels of a brace for this run.
For a three by four foot run, take 12 inches on the tongue and 9 inches
on the blade, and apply four times, because, as three feet is ¾ of four
feet, so 9 inches is ¾ of 12 inches.
A young carpenter, Toronto, wants to know how to find the center of a
circle by aid of the Square.
[Illustration: Fig. 76.]
Answer: In Fig. 76 is shown how the center of a circle may be determined
without the use of compasses; this is based on the principle that a
circle can be drawn through any three points that are not actually in a
straight line. Suppose we take A, B, C, D for four given points, then
draw a line from A to D, and from B to C; get the center of these lines,
and square from these centers as shown, and when the square crosses the
line, or where the lines intersect, as at x, there will be the center of
the circle. This is a very useful rule.
Ed. McDonald, Cincinnati, Ohio, says: “I want to know how much can be
done with the square towards setting out stair railing?”
Answer: In a previous page a few remarks on this subject will be found
and the following is further submitted:
[Illustration: Fig. 77.]
[Illustration: Fig. 78.]
Fig. 77 shows a plan of a stair well having three winders. The rail in
this case will have two different pitches. These rails are a little more
complicated than those having equal pitches, as in the latter the major
axis is parallel off the diagonal line B D (Fig. 77). When the pitches
differ the major axis ceases to be parallel; and the greater the
difference in the pitches, the greater will be the difference in the
axis and diagonal line. This fact can be easily demonstrated by cutting
a model bed block out of 2-inch by 2-inch stuff to equal pitches.
Procure a board, and draw a parallel line, say 8 inches off the edge.
Now square over a line to cut the first line; set the bed block on, with
the back corner touching the intersection of the lines. Lay a piece of
cardboard on the inclined face of the bed block, and let it slide down
until it touches the board. Make a mark along this edge, and it will be
seen, on removing the card, that this line is equidistant from the
corner (see Fig. 78). In Fig. 78 the cardboard is shown as though it
were transparent. What has just been done is that the plane in which the
rail lies has been projected to intersect the horizontal plane which
contains the plan of the wreath. The name by which this line is
generally known is the horizontal trace (shown at C, Figs. 78 and 79).
The minor axis (Figs. 78 and 79) is always parallel off this, and always
touches A as in Fig. 77. The major axis (Figs. 78 and 79) also touches
this point A, and is always square off the minor axis and off the
horizontal trace. It will be seen by this that the rail is pitched
equally both ways; therefore the face mold will be of equal width at the
ends.
[Illustration: Fig. 79.]
When rails are cut by bandsaw on bed blocks, bevels are not necessary,
as they can always be obtained by applying a bevel as shown at Fig. 80.
The stock should lie solid on the block and square off the sides. When
the block is thin it is best to apply the bevel near the corner, when a
greater surface is obtained. These bevels are applied after the joint is
squared off the tangent lines. To demonstrate a rail with unequal
pitches, cut another piece of stuff 2x2 inches, as shown in Fig. 79,
repeat the process with the cardboard as before. It will be found that
the horizontal trace has departed from the angle of 45 degrees (see Fig.
79) and has approached nearer one corner and gone farther away on the
other. The major axis B will have done likewise, as it is always square
off the horizontal trace C. The wreath having two pitches, the face mold
will obviously be wider at one end than at the other; and if bevels are
required, they must be set off on the face of each side of the block.
The width of the face mold is to be applied on the tangent line; this
makes it slightly in excess on the joint, but it is better to have a
little margin in thickness for working. Where thickness of stuff is a
secondary consideration, it is preferable to take the rail out of stuff
which is as thick as the diameter of a circle that will enclose the
section of rail; the corners will then be left complete.
[Illustration: Fig. 80.]
[Illustration: Fig. 81.]
The following method shows the least thickness the rail can be cut out
of, and also gives width of face molds on the joint. Set the bevel to
the bed block as shown at Fig. 80, and apply at the side of the block.
Draw a section of rail level; apply the bevel again, touching the bottom
corner of the section. The distance between the marks is the thickness,
a plumb line marked on shows the width of the face mold on the bevel
line. Where the pitches are different the foregoing method has to be
applied to each side of the bed block.
The bevels may be also obtained by the steel square. Take the width of
prism face (shown by dotted lines) by laying the square with blade on
the line C D (Fig. 82) and tongue, cutting at the center A. Note the
length on the tongue of the square. Make a mark of this length on the
edge of board. Now take the width of A to D (Fig. 84) which is 6 inches
off the blade; keep this 6-inch mark fair at the end of this line made
on the board (Fig. 81) and push on square until the tongue touches the
end of the line; mark by the tongue, and this gives the bevel required.
[Illustration: Fig. 82.]
[Illustration: Fig. 83.]
To obtain an example of unequal pitches refer to Fig. 84. To set this
out, run a line parallel off the edge of the board, and off this line
square another. With the intersection A as a center, describe a
semi-circle of 6 inches radius. This indicates the center of the rail.
Run lines radial from A as shown; these are the riser lines. Draw the
lines B C and C D, which are the tangents. Draw the diagonal B D. To
make the bed blocks, procure a piece of one inch stuff; take it to the
width shown at B C; square on a mark about 3 inches from the end (this
is to allow for the shank to clear the saw table; the block is shown at
Fig. 83 without the 3-inch allowance). Take on the steel square the rise
on tongue and going on blade of the straight flight of stairs; mark on
the inch board at tongue; this is pitch of the first tangent. Take the
height at D, which is one and a half risers—10½ inches; deduct the
height of the first tangent from 10½ inches; take the difference on the
tongue and width from C to D on the blade; the tongue gives the cut for
the second tangent. Mark the pitch of the first tangent on the edge of
the second and cut to this; the pitch of the second tangent gives the
edge cut of the first. Cut and fix together with stretcher as previously
described.
[Illustration: Fig. 84.]
To get out the face mold, procure a piece of thin stuff. Three-ply wood
is excellent, as though it is liable to warp it does not shrink
perceptibly. Shoot on edge and gauge on a center line; take the distance
from B to D (Fig. 84) (the hypothenuse of 6 and 6) on the blade and the
rise (10½) at D on the tongue; lay on the edge of the board to this. Lay
off this length on the three-ply at B D (Fig. 82); take the width B C
(Fig. 84) on the blade, rise at C on the tongue; find the hypothenuse,
and apply with a pair of compasses at Fig. 82 with B as a center cutting
at C. Then apply at D as a center, cutting at A. Now find the
hypothenuse C to D (Fig. 84), and apply the compasses as before, with D
and B as centers, cutting at A and C. Connect up the points where the
arcs intersect to B and D; this is the face of the inclined prism, and
contains the true shape of rail. Continue the tangent line C B, 3 inches
or whatever is required for the shank, and square the joints of the
lines B and D. In order to locate the major axis the horizontal trace is
now required. Stand the bed block on the plan (see Fig. 83). Run the
blade of the square down until it touches the board; mark this, and
remove the block. It will be seen that the bed block has not got the 3
inches allowed at the bottom, but the horizontal trace is as easily
found with as without the allowance; all that is required in the former
case being to turn the blade to B (still keeping the heel at the top of
the bed block), make a mark where the square touches and lay on the
square as shown at Fig. 83. Mark at the blade, and slide back the square
until the tongue touches at B, and also at the center A. This gives the
true horizontal trace and major axis. Note the size indicated by the
arrow lines on the tongue (from heel to B). Transfer the square to the
three-ply board (Fig. 82), placing it as shown, with the blade touching
A, and the distance of the arrow lines at B. Mark along the inside of
the blade of the square and slide the square back until the tongue cuts
at A. This gives the minor axis. Now continue this line downwards to
guide the position of the square shown at Fig. 84. Describe a circle as
wide as the rail on the minor axis (Fig. 82). The distance from A (Fig.
84) to the center of the rail is the distance to apply at Fig. 82 for
the center of the rail, as this is the point where the center of the
rail is fair with the plank. Obtain the width of the face molds, and
apply at B and D; lay the square on the major and minor axis as shown at
Fig. 84. Lay a lath on the square, with the point touching the outside
of the circle at C; drive in a nail at the heel of the square; shift the
lath until the point lies at B, and drive in another nail at the side of
the square. This trammel is now ready to sweep the outside of the mold,
which is done by reversing the square, as shown by dotted lines. Pull
out the nails and repeat the process for the inside of the mold.
[Illustration: Fig. 85.]
Now run parallel lines off the tangent B for the shank; this completes
the face mold, which is now ready for the face of the plank. Wreaths for
stairs with flights which stand at either acute or obtuse angles to each
other may be set out by the methods that have been here described. The
only difference, practically, is that the bed block is made acute or
obtuse to suit plan of tangents. The device shown at Fig. 85 has been
found to answer excellently for striking out ellipses. To make this,
procure two screws ¾ inches long, also a piece of brass tube that will
just slip on the plain part of the screw without shaking. Counter sink
out the ends until the screw heads are flush; cut two pieces off the
tube three-sixteenths and file up true—these pieces are best held by
sinking them with a bit in a piece of hardwood. Now when about to strike
an ellipse, drive these screws in with the collars on to half major and
minor, measured from the point of the trammel to the inside of the
collar for the major, and to the outside of the collar for the minor. It
will be found that if the collar has been made true, the trammel will
slip around the curve without causing the square to slip about, the
collars acting as rollers.
W. T. Jones, Boise City, Idaho, would like to know of a ready way to
frame hip roofs and roofs of irregular or different pitches with the
steel square, including lengths and bevels of all rafters.
Answer: These problems along with many others are discussed and
explained at length in my larger works on the Steel Square, but the
following, which is somewhat condensed, does to some extent cover Mr.
Jones’ inquiries:
[Illustration: Fig. 86.]
Suppose A, B, C, D, Fig. 86, to represent one end of a hip roof with a
span of 24 feet and a 10-foot rise. The side rafter I D shown in top
sketch will have a run of 12 feet. The common rafter at the end of
building, I L, has a run of 16 feet, with the same rise, so that the
ends and sides of the roofs have different pitches. The lengths and cuts
of the common rafters are obtained as shown in Fig. 87, by taking 12 on
the blade and 10 on the tongue of the square and measuring across,
giving the length of the side rafter, from which one-half the thickness
of the ridge, measured square back from the plumb cut, must be deducted.
The blade gives the foot cut and the tongue the plumb cut. The length of
the end rafter is obtained by taking 16 on the blade and 10 on the
tongue, which will of course give the respective cuts also. The same
results may be obtained by applying the square to a straight edge and
marking along the blade and tongue, which will give a gauge line to
which a bevel may be set. By taking 16 on the blade and 12 on the
tongue, as shown in Fig. 90, the run of the hip rafters, 20, is
obtained.
[Illustration: Fig. 87.]
[Illustration: Fig. 88.]
[Illustration: Fig. 89.]
Referring to Fig. 88, it will be seen that 20 on the blade and 10 on the
tongue give the seat and plumb cuts of the hip together with the length,
after one-half the thickness of the ridge has been deducted from the
side cut. The side cut is found in a slightly different way from that of
a regular hip or valley on an ordinary roof. The common method is to
take the length of the hip on the blade and run on the tongue, but this
will not work in this case, as the run of the hip does not be at an
angle of 45 degrees as in ordinary roofs. The line B J in Fig. 86 must
first be obtained, as shown in Fig. 89. Joint one edge of a board and
square up the line B L. Measure one-half the width of building—in
inches—on this line, 12 in this case, and with the heel of the square at
the point B, move the square until 20 on the blade touches the edge of
the board at E. The tongue will then give the point J 15 inches; which
is the length of the line required.
[Illustration: Fig. 90.]
Then take this line on the tongue and the length of the hip on the
blade, Fig. 90, and the blade will give the bevel of the hip to lie
against the ridge. As a general rule, hip rafters are not backed, but if
such is desired the lines for backing can be found by setting it to the
foot cut of the hip rafter. Make O R square with S O and gauge back as
shown in the diagram A. Do the same on the other side, using the
distance T R instead of P S. The point O is of course at the center of
the line T P.
[Illustration: Fig. 91.]
For lengths and bevels of jacks, proceed as follows: For end of roof,
and set 2 feet on centers, take a board and apply the square to it, as
shown in Fig. 91, with the length of the end rafter on the blade and the
run of the side rafter on the tongue. Space off 2, 4, 6, 8 and 10 in. on
the tongue after marking along both blade and tongue. The lines, AA, BB,
CC, DD, EE, will give the length of the jacks, as well as the side cut
to fit the side of the hip, the square being moved down along tongue
line, while the run of the end rafter on blade and its rise on tongue
will give the seat and plumb cuts. For the side jacks, Fig. 92 gives the
same method, only that the length of the side rafter is taken on the
blade and the run of the end rafter on the tongue. If it is so desired,
the length of the jack rafter A¹ A¹ may be deducted from the length of
the common rafter, which will give the difference in the lengths of the
jacks.
[Illustration: Fig. 92.]
[Illustration: Fig. 93.]
The rules and diagrams, given herewith will apply to valley as well as
hip rafters, and may be relied upon as being accurate if closely
followed.
RULE—See Fig. 87.
Tongue. Blade.
12″ 16″ gives run of hip.
10″ 12″ gives length of side rafter.
10″ 16″ gives length of end rafter.
10″ 20″ gives length of hip rafter.
RULE—See Fig. 91.
Blade. Tongue.
Common End Rafter 19″ 12′
Longest Jack “ 15 10/12″ 10′
4th “ “ 12 8/12″ 8′
3d “ “ 9 6/12″ 6′
2d “ “ 6 4/12″ 4′
Shortest “ “ 3 2/12″ 2′
Blade gives Side Cut of Jacks.
RULE—See Fig. 92.
Blade. Tongue.
Common Side Rafter 15′ 7½″ 16′
Longest Jack “ 13′ 8″ 14′
6th “ “ 11′ 8½″ 12′
5th “ “ 9′ 9″ 10′
4th “ “ 7′ 9½″ 8′
3d “ “ 5′ 10″ 6′
2d “ “ 3′ 10½″ 4′
1st “ “ 1′ 11″ 2′
Blade gives Cut of Jacks, also Sheathing.
These matters have been discussed at length, in trade journals and also
in my larger volumes on The Practical Uses of the Steel Square, but the
foregoing treatment of the subject is on somewhat different lines and
will prove interesting.
John Wilberforce, Toronto, Ont., wants to know if a wreath piece for a
single-pitch rail with level landing can be set out with the Steel
Square.
Answer: Yes, the problem can be solved as follows:
[Illustration: Fig. 94.]
Set out on a board the plan of the wreath A (Fig. 94). Draw the outside
circle and the inside and center line of same, showing also the joints.
Set out the pitch off the shank; square up the center outside and inside
lines from the plan on to the pitch. The thickness of the wreath piece
is found by drawing a section of rail under the pitch line B. Set out
again the half-width of the well; square off the pitch lines to the half
width; this gives major and minor axes of the ellipse, as shown in the
development (Fig. 94). Lay the square on the axis. Get a light piece of
lath, drive in a nail at the half major, and one at the half minor;
describe the inner ellipse line on the piece of timber from which the
wreath is to be formed; pull out the nails, and repeat the process for
the center and outside lines. Draw the shank and also the point as shown
on the board.
[Illustration: Fig. 95.]
Now cut at the joints, allowing an ⅛-inch for the fitting of the joint
after the wreath is cut and roughed out. Use another piece of timber
about 2 inches thick, to form the bed block, and cut it to the pitch
accurate and square in thickness. Screw or pin it to the under side of
the wreath piece (see Fig. 95), taking care to get it parallel with the
shank, and the nails in clear of the saw. Then proceed to cut the wreath
with the band saw, beginning at the circular part, and work it to the
shank inside and outside. This operation should be performed most
carefully with a narrow band saw, having a strong set and strained
tight, feeding very slowly. The wreath should require hardly any spoke
shaving. Knock off the block and draw a chalk mark across the table,
just in front of the teeth. The use of this line is to assist the
operator to get the outside of the wreath always touching this spot in
front of the saw. He must carefully lower his hand until it is down
level at the shank end. The top is cut first, and the saw should skim
along the outside top arris, giving a sweep that cannot be excelled in
graduation of curve. Then set a gauge to the thickness of the rail, mark
a line on the inside of the wreath, and cut as before. With a little
practice a wreath can be turned off the band saw ready for molding. When
the shank is too long, it is always better to nail the bed block on top
of the wreath, and cut it upside down, thus getting the curve portion
near the table. Then the shank can be run in with the band saw when the
block is knocked off. The foregoing is for a single-pitch wreath as used
for stairs with level landings and narrow wells. Where the rails are
pitched both ways, the bed block has to be cut at the double
inclination. (See preceding answers.)
[Illustration]