The connection of a binding joist to a girder is an example of this kind of joint. The greatest strains upon the fibres of a girder are at the upper and lower surfaces, and they gradually decrease towards the middle of the depth, where they become neutral; hence the most suitable place for a mortise is at the middle of the depth.
To find in what proportion a beam is weakened by a plain rectangular mortise cut in the middle of the depth, let D be the depth, and B the breadth of the beam, D' the depth of the mortise, and B' the distance to which it penetrates into the beam; then the beam is weakened in the following ratio:* -
The upper side being compressed, it is imagined by some writers that the tenon might be made to fill the mortise so completely that the strength of the girder would not be impaired by it, but this is a mistake; for any one who understands the practice of carpentry, knows that it cannot bo done in an effectual manner: besides, the shrinkage of the joist would soon render it loose, however tightly it might be fitted in the first instance.
Assuming then the best place for a mortise in a girder, or other beam in a like position, is at the middle of its depth, the next point to consider is the best form and place for the tenon.
If the tenon were to be placed near the lower side of the joist, it would obviously be in the strongest position; but as the mortise would also have to be cut near the lower side of the girder, this cannot be adopted; therefore the form in general use, and that which appears to combine most of the advantages, is represented by Fig. 72, Art. 211, which is called a " shouldered tenon," the tenon being one-sixth of the depth of the joist, and placed at one-third of the depth from the lower side. The shoulder 6 should penetrate the side of the girder also about one-sixth of the depth. The length of the tenon beyond the shoulder should be about double its own depth. An iron screw, called a " bed-screw," is often used to secure a joint of this kind.
414. Binding joists, or any other beams in a like position, should never be made with double tenons; for, as Price has judiciously remarked, it weakens the timber into which it is framed, and both tenons seldom have a bearing at the same time; besides, it rarely happens that they can be pinned so that both may draw alike, unless the pin be as tough as wire.*
* Raukine, 'Engineering,' 1869.
All horizontal timbers for bearing purposes should be notched upon the supports rather than framed between, whenever it can be done, and much additional strength is gained by keeping timbers in continued lengths. The same observation applies to inclined timbers, such as common rafters (see Sect. II., Art. 107).