228. Joints for beams and posts are: the vertical scarf—a halved joint (Fig. 229), double halved joint (Figs. 230 and 231), parallel scarf with joggled ends (Fig. 232), splayed scarf (Fig. 233), single fished butt joint when the post is braced (Fig. 234), and the double fished butt joint (Fig. 235) when the post is detached.
Fig. 236.—Tabled Scarf Joint.
Rule for Proportioning Parts of Scarf.—Tredgold gives the following practical rules for proportioning the different parts of a scarf according to the strength possessed by the kind of timber in which it is formed, to resist tensional, compressional, or shearing forces respectively. In Fig. 236 c d must be to c b in the ratio that the force to resist detrusion bears in the direct cohesion of the material—that is, in oak, ash, elm, c d must be equal to from eight to ten times c b; in fir and other straight-grained woods c d must be equal to from sixteen to twenty times c b. The sum of the depth of the indents should be equal to one and one-third depth of beam. The length of scarf should bear the following proportion to the depth of the beam:—
| Wood Used | Without bolts | With bolts | With bolts and indents |
Hardwood (oak, ash, elm)
|
6 times | 3 times | 2 times |
Fir and other straight-grained woods
|
12 „ | 6 „ | 4 „ |
Calculation of a scarfed joint with folding wedges as Fig. 237: —
| Per sq. in. | ||||||
| Working | resistance | to | tearing | = | 12 | cwt. |
| „ | „ | compression | = | 10 | „ | |
| „ | „ | shearing | = | 1.3 | „ | |
Load equals, say, 360 cwt. direct tension beyond that taken by bolts or plates. The joint may tear across a b or d e (Fig. 237), therefore section at a b must equal 36012 = 30, say 10 in. by 3 in. The joint may also shear across b c or g f, therefore section at b c or g f must equal 3601.3 = 277, say 28 in. by 10 in. The joint may also be crushed at b d or g h, therefore section at b d or g h must equal 36010 = 36, say 10 in. by 3½ in. Thus the beam should be about 10 in. by 10 in., with wedges as shown; but in ordinary practice the folding wedges do not exceed one-fourth the depth of the beam, and are usually placed square to the rake of the scarf, the scarf being further strengthened by bolts and plates.
Strength of Joints in Struts and Beams.—If two deals are bolted together, with distance pieces between, they will be stronger than a solid timber strut of the same sectional area, because the dimension of "least width" in the formula for calculation of strength will be increased. There
Fig. 237.—Splayed Scarf with Folding Wedges.
would be no appreciable advantage in making the distance pieces of different thicknesses, to swell or reduce the middle diameter; they should be all alike, and enough to make the combined thickness not less than three-fourths of the width of the deals, and the distance apart in feet should be equal to the length of the deal in feet multiplied by its thickness in inches and divided by the width in inches. Single ½-in. bolts are of no use in rough carpentry, except for very small work; instead, two ⅝-in. bolts should be placed diagonally through each block. Horizontal connecting rods in machinery are sometimes swelled in the middle to allow for the cross strain upon
