160

SCARFING, JOINTS, STRAPS, AND SHOES.

[sect. IX.

284. — Fig. 125 is a slight modification of the last described scarf, where the keys are sup-posed to be of hard wood; if of a curled grain, so much the better. In this form the scarfis easier to execute, and equally as good as the last, when bolts are used.

285. — Fig. 126 represents a very common form, and a very good one, but it appears to beinferior to the two preceding ones (fig. 124 and 125) ; and it is much more difficult to makea sound joint of this form.

When bolts are added, and they are always necessary in pieces exposed to consider-able strains, the scarf represented by Jig. 127 is a very good and strong form fora scarf.

Fig. 128 differs from the last only in having keys instead of being tabled together.

286. — Fig. 129 represents a scarf where the oblique joints in the last examples are avoid-ed, and the same degree of strength is obtained; at the same time it is very simple and easyto execute.

287. —To determine the length of a scarf, in joining beams, it is necessary to know theforce that will cause the fibres of timber to slide upon each other. The researches whichhave been made on this subject have already been laid before the reader in Sect. II. art.115 and 116. To apply them to our present object, let AS, Jig. 130, Plate XXI., be partof a scarfed beam, strained in the direction of its length, and put together without bolts.Now it is plain that the strength of the part c b must be exactly equal to the force thatwould cause the fibres to slide at the dotted line c d-, for, if the part cd were shorter, thejoint would not be so strong as it is possible to make it. Also, if the depth of the indenta c be too small, it would be crushed by the strain; consequently, the parts must have a cer-tain proportion, so that the joint may be equally strong in each part.

288. —In the first degrees of extension and compression the resistance is equal, thereforethe depth of the indent a c must be equal to the part c b, in order that the strain may beequal; and it is evident, that when there is only one indent, as in this example, the deptha c should be one-third of the whole depth. Also, let d be the depth of the beam, and m

the number of indents ; then = the depth of each indent. Or the sum of the depths

of the indents must be equal to one-third of the depth of the beam.

289. —To determine the length of the part cd, we must know the ratio between the forceto resist sliding and the direct cohesion of the material. Let that ratio be as 1 : n ; thenc d must be equal n times c b ; that is, in oak, ash, or elm, c d must be equal to from 8 to 10times c b.

In fir and other straight grained woods c d must be equal to from 16 to 20 times c b.

290. —Hence may be derived some maxims that will be sufficiently accurate for practicalpurposes ;

In oak, ash, or elm, the whole length of the scarf should be six times the depth orthickness of the beam, when there are no bolts.