397. The simplest and perhaps the best method of lengthening a beam is to abut the ends together, and place a piece on each side; these, when firmly bolted together, form a strong and simple connection. Such a method of lengthening a tie is shown by Fig. 125, and is what ship-carpenters call fishing a beam. It is obvious, however, that the strength in this case depends on the bolts, and the lateral adhesion and friction produced by screwing the parts tightly together.

FIG. 125.

The dependence on the bolts may be lessened by indenting the parts together, as shown by the upper side of Fig. 126;

Fig. 126.

The only reasons for not depending wholly on bolts arc, that should the parts shrink ever so little, the bolts lose a great part of their effect; and the smallness of the bolts renders them liable to press into the timber, and thus to suffer the joint to yield.

The sum of the areas of the bolts should never be less than one-fifth of the area of the section of the beam; and they should not be placed too near to the ends of the pieces.

398. The most usual method of joining beams is that called scarfing, where the two pieces are joined so as to preserve the same breadth and depth throughout; and wherever neatness is preferable to strength, this method should be adopted.

From Fig. 127 to Fig. 134 various methods of scarfing are shown. The first (Fig. 127) is the most simple; it depends wholly on the bolts, and in this and like cases it is best to put a continued plate of iron on each side to receive the heads of the bolts. The ends of the plates may be bent and let into the beams.

Fig. 127.

399. Fig. 128 is another very common, but not so good a combination, as the bolts do not press the surfaces in a perpendicular direction: and an oblique pressure, such as would be likely to take place in this example, must have some tendency to separate the joint, and it has no advantage in other respects.

Fig. 128.

400. Fig. 129 is a joint where bolts would not be absolutely required, but it is clear that the strength would not be quite so great as half that of an entire piece; the key, or double wedge in the centre of the joint, should only be driven so as to bring the parts to their proper bearing, as it would be better to omit it altogether than to drive it so as to produce any considerable strain on the joint. It is not necessary that there should be a key, except when bolts are to be added, and then it is desirable to bring the joints to a . bearing before the bolts are put in. The addition of bolts and straps, however, makes this an excellent scarf.

Fig. 129.

401. Fig. 130 is a slight modification of the last, where the keys are supposed to be of hard wood; if of a curled grain, so much the better. In this form the scarf is easier to execute, and equally as good, when bolts are used, as that shown by Fig. 129.

Fig. 130.

402. Fig. 131 represents a good and very common form, though inferior to the two preceding ones (Figs. 129 and

Fig. 131.

130), and it is much more difficult to make with it a sound joint.

When bolts are added, and they are always necessary in pieces exposed to considerable strains, then the form represented by Fig. 132 becomes a very good and strong scarf.

Fig. 132.

Fig. 133 differs from the last only in having keys instead of being tabled together.

Fig. 1:3.

403. Fig. 134 represents a scarf where the oblique joints in the last examples are avoided, and the same degree of strength is obtained; it is at the same time very simple, and easy to execute.

FIG. 134.

404. To determine the length of a scarf, in joining beams, it is necessary to know the force that will cause the fibres of timber to slide upon each other. Some information on the subject has been already laid before the reader in Sect. II., Arts. 133 and 134. To apply it to our present object, let A B, Fig. 135, be part of 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 that would cause the fibres to slide at the dotted line c d; for if the part c d were shorter, the joint would not be so strong as it is possible to make it. Also, if the depth of the indent a c be too small, it would be crushed by the strain; consequently the parts must have a certain proportion, so that the joint may be equally strong in every part.

Fig. 135.

405. Where the amount of extension and compression is very small, the resistance may be considered as equal, therefore the depth of the indent a c must be equal to the part c b, in order that the strain may be equal; and it is evident, that when there is only one indent, as in this example, the depth a 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 d/3m = 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.

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

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

407. Hence may be derived some maxims that will be sufficiently accurate for practical purposes:

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

2. In fir the whole length of the scarf should be about twelve times the thickness of the beam, when there are no bolts.

3. In oak, ash, or elm, the whole length of a scarf depending on bolts only, should be about three times the breadth of the beam; and for fir beams it should be six times the breadth.

4. When both bolts and indents are combined, the whole length of the scarf for oak and hard wood may be twice the depth; and for fir or soft woods, four times the depth.