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.