Figure 2. An oblique scarf; bolted in three places. Allow ing the utmost cohesion of the at of the joint A a, to be the same as whole timber, and that the transverse parts, A n or B c, arc one-fourth of the breadth, D E. the compound timber will possess three-fourths of the strength of a solid piece.
Figure 3. A scarf with parallel joints and a single table upon each piece. here the cohesive strength is diminished in an additional degree to that of Figure 1, by the projection of the table ; but this gives an opportunity of driving a wedge through the joint, between the ends of the tables and thereby- forcing the abutting parts to a joint. This mode requires the scarf to be longer than those which have no tables ; and the transverse parts of the scarf must also be strapped and bolted.
Figure 4. Allows of the same opportunity of wedging as before : if we would suppose the parts A B and c n to be com pressed by bolts as firmly together as if they were but one piece they would be, by the continuity of the fibres, and if the projection of the tables be equal to the transverse parts of the joints at A and D; the loss of strength, compared with that of a solid piece, will be no more than what it would be at A and D.
Let it be here observed, once for all, that the strapping across the transverse part of the joint is the most effectual mode of preventing the pieces from being drawn from each other, by the sliding of the longitudinal parts of the scarf; and thereby giving the bolts an oblique position.
Figure 5. A scarf formed by several steps. In this, if all the transverse parts of the steps be equal, and the longitudinal parts as strongly compressed by bolts as the fibres of whole timber would adhere laterally, the loss of strength would only be a fourth, compared to that of a solid piece; there being four transverse parts, that is, the part which the cod of a step is of the whole.
Figure 0. The end of each piece is formed by three steps, and the abutting parts of the middle step being greater than that at either extremity, the loss of strength in the compound timber is the part which the middle abutting surfaces are of the whole section.
Figure 7. A scarf consisting of six steps, the abutting parts being equal, and th.• longitudinal parts inclined in a small degree to the sides ; so that when the two parts come to be bolted together. the pieces Will dovetail each other. and thereby prevent their being drawn ; lint as all timber is liable to shrink in proportion to the dimensions its section, no dependence can be put in dovetailing. for the shrinking may be so great, that the thickest parts of the solids at the :dun went of the joint may pass through the narrower cavities. and reinter the dovetails useless. We may also observe. in
the case of bolting, that when the longitndinal shrink front other, the bolts will be drawn obliiptily, unless the transverse parts on the sides be stripped and bolted, both opposite to the scarf and through the solid at each end of it. The strength of t lie compound beam may likewise be assisted by the iron ; the dovetailing therefore can only give greater adhesion at first ; at the same time, it occasions a small loss of strength, equal to the difference of the extreme end of the outer step and the nearer end of the section.
Figure S. The method of forming a compound timber, when the two pieces are not of sufficient length to allow them to lap, by means of a third piece, connected with both by a double scarf, firmed of several degrees, or steps; the pieces abutting upon each other, with the middle of the connecting piece over their abutment.
When girders are extended beyond a certain length, they bend under their OW11 weight in the middle. and the degree of curvature will increase in a much greater degree than their lengths. An excellent method to prevent this sagging, with out the assistance of uprights or posts from the or floor below, is, to make the beam in two equal lengths. and insert a truss, so that when the two pieces are bolted, the truss may be included between theta, they forming its tie. To prevent any bad etli•ets from shrinking, the truss-posts are generally constructed of iron. screwed and nutted at the ends; and to give a firmer abutment. the braces are let in with grooves into the side of each flitch. The abutments at the ends are also made of iron, and either screwed and nutted at each of the ends, and bolted thrarigh the thickness of both pieces, with a broad part in the middle. that the braces may abut upon the whole dimension of their section ; or. the abutments are made in the tarin of an inverted wedge at the bottom, and rise cylindrically to the top, where they are screwed and nutted. These modes may be either constructed with one king-bolt in the middle, or with a truss-bolt at one third of the length from each end. When there are two bolts, they include a straining place in the middle. The two braces may either be constructed of oak. or cast or wrought iron ; the latter material is, however, very seldom employed. As wood contracts less in length than most metals, oak is better tar the purpose than cast iron, but then the parts of the core must be so much stronger. As to the bolts, wrought iron is indispensable. It is obvious, that the higher the girder, the less will the parts be atl'eeted by the stress, and conse quently there will be less risk of their giving way under heavy weights, or through long bearings.