= = = 21.69 But the Then, each rivet giving 4 tons of friction, we have 4.75 x 7 = 33.25 tons, and the total breaking weight of the joint 117.2833.25 150.53 tons, or 150.536.94 tons per square inch of metal between rivet-holes. solid plate yields 20 6 tons only, hence we have 21.6920.6 = 1.053, or 5.3 per cent. in excess of the solid plate, agreeing with Mr. Fairbairn's result in col. 4 of Table 5, which gives 1.0526, or 5.26 per cent. excess. Here the actual strength of metal between rivet-holes is 18 per cent. less than the normal strength or that of the solid plate, but the apparent strength is 5.3 per cent. in excess, the difference being due to friction. = (23.) These calculations are not given as absolutely correct, but as serving to illustrate the principles on which the strength of riveted joints depends, and to explain the differences in the apparent strength of various kinds of joints in Table 5. For instance, by col. 6 the mean strength of a solid plate of average British plate-iron 48,454 lbs. per square inch; by punching, the loss is 18 per cent. as in (21), and the strength of the metal left between rivet-holes is reduced to 48454 × 82 = 39723 lbs., and will be the same with all the different joints in that column. The oblique action of the strain in an ordinary single-riveted joint, as shown by the broken centre line o, p at A, in Fig. 6, reduces the apparent strength to 36,898 lbs., and with one back plate as at B, to 39,248 lbs. per square inch, both being less than that of a punched but unriveted plate with a fair central strain, which, as we have seen, is 39,723 lbs. But with a front and back plate, friction becomes more influential and increases the apparent strength to 46,070 lbs. (24.) "Kinds of Riveted Joints."-There are six principal kinds of riveted joint, which are shown by A, B, C, D, E, F in Fig. 6, and are described or specified in Table 5, which also gives the apparent strength of the metal between the rivetholes in each kind of joint, and with three different kinds or qualities of plate iron, namely, Yorkshire, Staffordshire, and the general average of British iron. Staffordshire is the weakest of the three, but is more extensively used than any other, and may be taken as a basis for calculation in ordinary cases. Taking it as a standard, British iron gives 48454 44800 = 1.082, or TABLE 5. Of the STRENGTH of RIVETED JOINTS in WROUGHT-IRON 8.2 per cent., and Yorkshire 56264 ÷ 44800 per cent. greater tensile strength. (25.) "Proportions of Riveted Joints."-In fixing the proportions of riveted joints, it is necessary to consider the subject under two different heads; 1st for girder-work, where we have simply to secure equality between the shearing strength of the rivets and the tensile strength of the plate between rivet-holes, so that both may fail simultaneously; and 2nd, for steam-boiler work, where we have not only to consider the question of strength, but also the maximum pitch of rivets consistent with tightness of the steam-joints. This will vary with the pressure of the steam and the thickness of the plate; if with a given thickness and pressure the distance between rivet-holes exceeds a certain amount, it will be difficult, or perhaps impossible, to make the joint permanently steamtight (45). On the other hand, if the pitch is unduly reduced, the proportions of the metal left between the holes to the solid part of the plate are reduced also, and a loss of strength will ensue. With girder-work we have the choice of any of the six kinds of joint in Table 5, but for boilers we are practically confined to two, namely, single and double riveted; these alone being easily made steam-tight by caulking. (26.) “Diameter of Rivets."—The proper size of rivets in proportion to the thickness of plate is to some extent arbitrary, and within certain limits may be varied considerably, so long as the great principle is observed, namely, so to adjust the pitch and thickness as to secure equality between the tensile strength of the plate and the shearing strength of the rivets. Nevertheless, practice has dictated as expedient, certain proportions between the diameter of rivet and thickness of plate which should be followed in ordinary cases, and may be expressed by the rule: (27.) d = (tx 1) + 1 or d = (t x 1.25) + ·1875. In which t = the thickness of plate, and d = diameter of rivetholes, both in inches: col. 2 of Table 14 has been calculated by this rule. It should be observed that the diameter of the hole should be taken rather than that of the cold rivet: the rivet is always made smaller than the hole for facility in inserting it; but when riveted hot in the usual way it fills the hole completely, and the strength is therefore governed by the size of the hole itself. (28.) It is a practical dictum that the diameter of the rivets shall be proportional to the thickness of the plate irrespective of the pressure of steam and other considerations. This leads to no difficulty with girder-work, because we can always adjust the pitch so as to obtain equality between the strain on the rivets to that on the plate (25). But for boiler-work the pitch is restricted by the pressure of steam (45), and we are conducted to the anomaly, that as the pressure is increased, the diameter of the rivets should be reduced, a result precisely contrary to that expected (53). RIVETED JOINTS FOR GIRDER-WORK. (29.) "Pitch of Rivets in Single-riveted Joints."-The main principle in riveting, as we have stated, is so to proportion the space between rivet-holes to the area of the rivet as to obtain equality of strength, that is to say, that, theoretically at least, the rivets shall be sheared and the plate ruptured simultaneously. In a simple single-riveted joint, if the shearing strength of rivets per square inch and the tensile strength of boiler-plate were equal, the area of plate between two rivet-holes should be equal to the area of a rivet-hole, and it is commonly assumed that such is the proper proportion. But by col. 6 of Table 5 the mean strength of the metal between the rivet-holes in singleriveted joints is 36,898 lbs. per square inch, whereas the shearing strain of rivets by (19) is 49,280 lbs.: hence the area of the rivet in this kind of joint should be 36898÷49280 ⚫75 of the area of metal between rivet-holes. (30.) Thus, with = = = plate, and rivets, as per Table 6, the area of 3712, hence the area of metal between two rivetholes should be 371275 = 495 square inch; the distance between rivet-holes = 495 ÷ 3 = 1.32 or 1 inch, and the pitch 1+ 2 inches. The ratio of the metal between holes to the solid plate is 1.32 ÷ 2 = ·66, hence the strain on the solid plate, when the joint is breaking through the line of rivet-holes, is 36898 × 66 24353 lbs. per square inch. This reduced strain on the solid plate as thus found, is useful for the purpose of calculation, as we shall find when we come to apply these results to girders, boilers, &c. = The general proportions of single-riveted lap-joints calculated on these principles are given by Table 6; with steam-boilers the pressure of the steam has to be considered in fixing the pitch of the rivets (44), but for girder-work the proportions given by the Table require no correction. (31.) "Single-riveted Joints with Back and Front Plate.”—The advantage of a single back-plate, as at B, Fig. 6, is inconsiderable, as shown by col. 4 of Table 5, but with a front and back plate, as in Fig. 8, it is very great, which is due not only to the greater apparent strength of the metal, but also because |