the rivets are subjected to a double-shear, and their area in proportion to the plate may be reduced to half.

The apparent strength of metal between holes being by col. 6 = 46070 lbs. per square inch, the area of the rivets should be 460704928093 of the area of metal between two holes. Taking plate, and rivets as before, the area of the rivet with double shear = • 3712 × 2 7424 square inch; ·7424·93 = ·8

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the area of metal between two holes square inch; the distance between the holes inches, and the pitch = 2 + 1 = 213; the ratio of the metal between holes to the solid plate 21÷218, or 34 ÷ 45 = ·756, and the strain on the solid plate = 756 × 46070 = 34829 lbs. per square inch, which is 3482924353 = 1.43, or 43 per cent. more than with a simple single-riveted joint (30). Table 7 gives the general proportions and strength of single-riveted joints, with front and back plate calculated in the manner we have illustrated.

(32.) “Amount of Lap."-A riveted joint may give way 1st, by the rivets shearing; 2nd, by the plate breaking across through the line of the rivet-holes; and 3rd, by the rivetholes tearing out: we have considered the two former, and have now to consider the latter. Theoretically, the metal a, b, c, d, in Fig. 10, should be torn out, but the rivet would be flattened and deformed by the plate, and we may assume a starting-point for the line of fracture at m, say midway between a and n then the sum of the distances m, o and p, r should be equal to the space c, e between two rivets. Taking, therefore, half the distance c, e, and setting it from m to o, we obtain the lap for single-riveted joints, as in col. 5 of Table 6.

(33.) With a double-riveted joint, Fig. 11, the plate F might break on the line of rivets A, B; in that case the plate E and all the rivets may remain intact; conversely, the plate E may break on the line C, D, the plate F and all the rivets remaining firm.

If, as in Fig. 12, we make the space T = half S, fracture might take place on the zig-zag line J, K as easily as on the line A, B, or C, D, in Fig. 11, because the breadth of plate strained is the same in both cases. This shows that T should be half S. In another case all the rivets might be torn out, as in Fig. 13,

both plates being torn, but if the lap be adjusted, as in Fig. 12, so that the area of metal torn out in each half is equal to that on the line A, B in Fig. 11, the breaking weight will be the same in all three cases, Figs. 11, 12, 13.

In yet another case all the rivets might be sheared, and both plates remain intact.

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1.2026

(34.) "Pitch of Rivets in Double-riveted Joints.”—Say that we take the case of -inch plate, double-riveted with 7-inch rivets: the area of '6013, or for two rivets ·6013 × 2 square inch. In a common double-riveted joint, the apparent strength of the metal between the rivet-holes, by col. 6 of Table 5, is 45,208 lbs. per square inch, and taking the shearing strength of rivets (19) at 49,280 lbs. per square inch, the ratio is 4520849280 91; hence for 1.2026 square inch of 1.32 square inch of plate. The distance between two rivet-holes will then be 1.32÷ = 2.64, or 2 inches, and the pitch P in Fig. 11, = 2§ + 7 = 3 inches the ratio of the metal between rivet-holes to the solid plate is 2531, or 21÷28 751, hence we have 45208 x 751 33951 lbs. per square inch on the solid plate.

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rivet we require 1.2026·91

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Comparing this result with that given for the same plate single-riveted by col. 8 of Table 6, we obtain 33951 ÷ 23984

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1.42, or 42 per cent. more with a double than with a single-riveted joint. This great advantage is partly due to the improved conditions of the strain by which the apparent strength is increased from 36,898 to 45,208 lbs. per square inch, as shown by col. 6 of Table 5; and partly to the greatly increased pitch, by which the ratio of metal between holes to the solid plate is increased from 650 to 751.

For girder-work this increased strength may be realised, but for steam-boilers the great pitch precludes the use of such proportions, except for very low pressures of steam, for instance,

-inch plate, 3 inches pitch, with rivets, would give 2ğ space, with which, by the rule (46), the working pressure of steam = 7.4 lbs. per square inch only.

Table 8 gives the general proportions of double-riveted joints, calculated on the principles we have illustrated.

TABLE 8. Of the PROPORTIONS and STRENGTH of DOUBLE-RIVETED JOINTS in WROUGHT-IRON PLATES: for GIRDER-WORK ONLY.

NOTE.-The rivet-holes marked are the most suitable for the given thickness of plate,

in ordinary cases.

(35.) "Double-riveted Joints with Back and Front Plates.”With a plate on both sides, as in Fig 9, a double-riveted joint has an apparent strength of 51,000 lbs. per square inch by col. 6 of Table 5, and taking the shearing strength of rivets at 49,280 lbs. (19) the shearing area of the rivets should be 5100049280 = 1.035, that of the metal between holes being 1.0. Taking the case of -inch plate with rivets, each space being now matched by two rivets subjected to doubleshear, and the area of 13 = 5185 square inch, we have 5185 x 4 = 2.074 square inches of rivets, requiring 2.074 1.035 = 2 square inches of plate: hence the distance between the insides of two rivet-holes 4 inches; the pitch 4+ 18 41 inches: the ratio of metal between rivet-holes to the solid plate 4413, or 64÷77·831, giving on the solid plate 51000 × 831 = 42381 lbs. per square inch, being 4238123172 1.83, or 83 per cent. greater strength than the same 2-inch plate with simple single-riveted joint, as given by col. 8 of Table 6. Table 7 has been calculated throughout in this manner.

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(36.) "Chain-Riveting."-The various Tables 6 to 8 show that with every kind of ordinary joint there is a considerable loss of strength, due to the metal being punched out to take the rivets, varying from 588, or a loss of 41.2 per cent. with single-riveted joints in Table 6, to 857, or a loss of 14.3 per cent. in double-riveted ones with front and back plates in Table 7. By what has been termed Chain-riveting the loss from this cause may be entirely avoided, and the full tensile strength of the entire area of the solid plate may be utilised.

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Say we take plates, double-riveted with 14 rivets 4 inches pitch, as in Table 8, the space between rivet-holes being 21; then the ratio of the metal between rivet-holes to the solid part of the plate or space÷pitch, becomes 21841, or 4765723, hence 1.0 ·723·277, or 27.7 per cent. of the strength, is lost. Now if instead of arranging the rivets in two rows, as in Fig. 11, we place them in five rows, as in Fig. 15, we have on the line Q, R, 4 × 3 = 12 inches pitch, and the space 123 - 11 11, then the ratio or space pitch becomes 11123, or 177 195·91, or 100

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