408. Beams to resist cross strains require to be lengthened more frequently than any others, and, from the nature of the strain, a different form must be adopted for the scarf from that which is best for a strain in the direction of the length. There are cases where beams are exposed to both strains at the same time, but -the cross strain is generally that of the most importance. Of this we have an example in the tie-beam of a roof, where the strain in the direction of the length is very small compared with the cross strain.

Let C D, Fig. 136, represent a beam strained by a load at E, and supported at the ends. All the parts above the middle of the depth, b c, will be compressed, while those below will be extended; therefore, the square abutment a e is better for the upper side than any kind of complicated joint; and it is evident that all oblique joints should be avoided on the compressed side. In this figure the whole of the strength of the lower side depends on the bolts and straps.

Fro. 136.

409. Fig. 137 shows another form, where the lower, or extended side, is indented so as not to depend wholly on the strap and bolts; and a key is introduced to tighten the scarf.

FIG. 137.

It will readily appear that had the joint been cut to the dotted line instead of the oblique line, the strength would have been much impaired.

Fig. 138 is another form with some slight alterations.

Fig. 138.

410. Fig. 139 represents an angular view of a scarf where it is jointed the contrary way. An iron plate at abcd is supposed to be removed, which shows the tongue at e. This method appears to employ more of the strength of the timber than any other, and is very well adapted for a tie-beam where it is strained both across and in the direction of its length.

Fig. 139.

In all these cases the depth of the indents and the length of the scarf will be obtained by the same rules as for beams strained in the direction of their length (see Arts. 405 to 407).

In scarfing beams to bear a cross strain it would be a great advantage to apply hoops or straps instead of bolts, as the coachmakers and ship-carpenters do. It would be easy to form the scarf so that hoops might be driven on perfectly tight.

There is no part of carpentry that requires greater accuracy in workmanship than scarfing; as all the indents should bear equally, otherwise the greater part of the strength will be lost. Hence we see how very unfit some of the complicated forms shown in the old works on carpentry were for the purpose. It is certainly very absurd to render the parts difficult to be fitted, when the whole of the strength depends on their fitting well. " But many," says Professor Robison, "seem to aim at making the beam stronger than if it were of one piece; and this inconsiderate project has given rise to many whimsical modes of tabling and scarfing." *