EXERCISE NUMBER 4.
KEYED MORTISE AND TENON,
WITH BRACE.
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.
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.
Fig. 75.
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″.
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.