This method of joining timbers is sometimes used in heavy frame work,
but can be used to advantage in light frame work that has to be taken
apart, such as curtain frames, etc.
In Fig. 74 is shown the assembled and the detailed drawings of this
piece of work. The experience gained from the previous exercises can be
used to advantage in working this problem.
The requirements in this exercise are that all pieces be square and to
dimensions.
That the upright and cross-pieces when keyed be square to each other.
That the brace fit snugly, and form two angles of 45 degrees back at
its junction with the upright and cross-piece.
That all joints fit closely, and the whole work be smoothed off and
made true.
The method of laying out the keyed joint is somewhat similar to that in
the third exercise.
[Illustration: FIG. 74.]
On the upright locate the cross-piece (on the face edge), which is 1½
inches from the end to the upper edge, and measure the width of the
piece, which is 1½ inches; draw the lines square to the face side,
deduct the amount of splay or bevel that is given to the mortise and
tenon from the lower end of the mortise, and add to the upper end the
width of the key; draw the lines, and mark them in some manner so that
they will be known as working lines. Figs. 75 and 76 will show how this
may be done.
From the line which locates the lower edge of the cross-piece (using
the square on the face edge) mark the position (on the opposite
corner) of the lower line on the outside edge, by the method given in
the previous exercise (see Fig. 66), and square this line across the
outside edge; then measure the width of the tenon, plus the width of
the key, and square the line across.
[Illustration: FIG. 75.]
[Illustration: FIG. 76.]
(Where work is to be finished on the faces, care should be taken not to
mark the work with knife lines, but if auxiliary lines must be used,
then mark them with a pencil so that they may be cleaned off when the
work is being smoothed.)
Having laid out the keyed mortise lay out the brace mortise, the lower
end of which is located 3½ inches below the lower edge of the cross
piece; the drawing gives all the dimensions for this.
Take the cross-piece and lay out the tenon in the same way that the
tenon in Exercise Number 3 is prepared, using the dimensions that are
given in the drawing for the work on hand.
After marking the shoulders of the cross-piece lay out the brace
mortise, which is 3½ inches from the shoulder to the farthest end, and
mark the other lines as called for in the drawing. Use the single gauge
as directed in Exercise Number 3 to mark the side lines of the mortise
and tenon, and cut the mortise with the mortising chisel, taking care
to cut the ends to the proper angle.
Saw the tenon as previously directed, and after the sides have been cut
off, mark the splay on the lower side of the tenon and cut it off with
a paring chisel.
The method of finding the length of the brace is of importance, as it
will give the student some idea of the application of square root to
practical work of this kind.
The hypotenuse of a right-angled triangle equals the square root of
the sum of the squares of its sides. For example, take the triangle
that is formed by the upright, the cross-piece, and the outside of the
brace. We have a triangle that has two sides of equal length and wish
to obtain the length of the brace on its longest side.
We will designate the angle where the cross-piece meets the upright,
A, and the lower point of the brace on the upright, B, and the outside
point of the brace on the cross-piece, C. Then we have the side AB, and
the side AC, which we will square and add together, then extract the
square root of this sum, which will give us the length of the brace on
the longest side, to which we must add the length of the tenons that
go into the upright and the cross-piece. The angles at each end of the
brace will be 45 degrees, as the opposite angles of the triangle are
equal, there being 180 degrees in the sum of the three angles; one of
the angles is a right angle (90 degrees), which we subtract from 180
degrees; the remainder divided by two will give the number of degrees
contained in the angle at the ends of the brace.
The lines at the outside of the tenons on the brace are parallel with
the upright and the cross-piece respectively.
A method often used by practical men to get the length of short braces
is to take a steel framing square and a rule, and find the length of
the brace by applying the rule to the square as shown in Fig. 77. On
the short leg of the square will be found a brace measure which gives
the length of the sides of the triangle and the length of the brace,
thus, ⁵⁴″/₅₄″ = 76.31″.
[Illustration: FIG. 77.]
Bevels and tapers are found by applying the bevel to the square
according to the bevel or the taper required, such as 1 inch on one
side and 4 inches on the other side of the square; this would be called
a taper of 1 inch in 4 inches.
Having cut the pieces to dimensions as called for in the drawing, put
them together, and finish smooth.