This section is from the book "Spons' Mechanics' Own Book: A Manual For Handicraftsmen And Amateurs", by Edward Spon. Also available from Amazon: Spons' Mechanics' Own Book.
A strut meeting a tie, as in the case of the foot of a principal rafter in a roof truss, is generally tenoned into the tie by an oblique tenon, as shown in Fig. 499; and the joint is further strengthened by a toe on the rafter bearing against a shoulder in the tie Tredgold strongly advised this joint being made with a bridle instead of a tenon, as shown in Fig. 500, on account of the abutting surfaces being fully open to view. A strut meeting a post as in Fig. 501, or a strut meeting the principal rafter of a roof truss (Fig. 502), is usually connected by a simple toe-joint. The shoulder should be cut square with the piece containing it, or it should bisect the angle formed between the two pieces. It is sometimes made square with the strut, but this is incorrect, as there would in some cases be a possibility of the piece slipping out. In ledged and braced doors or gates this joint is used, the pieces being so arranged as to form triangles, and so prevent the liability to sag or drop, which is difficult to guard against in square-framed work without.struts or braces.
When a structure is triangulated, its shape remains constant so long as the fastenings are not torn away, because, with a given length of sides, a triangle can assume only one position; but this is nott the case with four-sided framing, as the sides, while remaining constant in length, may vary in position. A mansard roof contains various examples of a toe-joint; it shows also the principle of framing king-post and queen-post roof trusses, each portion being triangulated to ensure the utmost stability.