per cent. greater than 23.77 tons the shearing strength of steel.

Moreover it should be observed that the strength of steel rivets was obtained from joints in steel plates, where the friction due to the grip of the rivets (20) must have contributed to the apparent strength, so that the resistance of the rivets alone must have been considerably less than 23 77 tons per square inch, which however must be accepted as the apparent shearing strength of steel rivets in double-riveted joints of steel plates.

(43.) "Proportions of Steel Joints."-The pitch and other proportions of riveted joints with steel plates may be determined on the same principles as those of wrought-iron plates, but the relative weakness of steel rivets will affect the pitch very considerably.

We shall take the tensile strength of the metal between rivetholes in steel joints of all kinds at 41 tons, or 91,840 lbs. (41), and the apparent shearing strain of steel rivets in joints at 53,245 lbs. per square inch (42): hence the rivets are 58 per cent. only of the strength of the plates.

Say we take for illustration 3-inch plates, double-riveted: by col. 3 of Table 14 the rivets should be 1 inch diameter; then the area of the rivets must be 9184053245 = 1.725, that of the plate between holes being 1.0, hence for two }} rivets to each space as with double-riveted joints, whose area = .3712 x 2 = 7424 square inch, we require 7424÷1·725 .43 square inch of plate. The distance between holes will therefore be 433 = 1.146, or 11 inch; the pitch 1 + }} = 1}}; the ratio of metal left between holes, to the solid plate 1}÷ 11, or 1829 = 621; and the strain on the solid part of the plate when the metal between holes is breaking becomes 91840 × 621 57033 lbs. per square inch. Table 12 has been calculated in this way throughout.

=

=

Comparing steel joints with double-riveted wrought-iron ones in Table 8, col. 9 gives for 3-inch plate 34,177 lbs. per square inch hence we obtain 5703334177

=

1.67, or 67 per cent.

in favour of steel for Girder-work: for Boilers see (65), (74).

TABLE 12.-Of DOUBLE-RIVETED JOINTS in STEEL PLATES: for

RIVETED JOINTS FOR STEAM-BOILER WORK.

(44.) In riveting plates for girder-work, we have only to consider the proper proportions of area of rivets to area of plate between rivet-holes, but for steam-boiler joints we have further to consider the space, or distance between rivet-holes with reference to the pressure of steam, otherwise the joint may not be steam-tight. A riveted joint may be abundantly strong enough to resist the strain, but if the pitch of the rivets is too great, it will give trouble by leaking.

(45.) "Space between Rivets."-An ordinary lap-joint, Fig. 16, is made steam-tight by caulking at C, and although the contraction of the rivet in cooling will draw the two plates together, still there will be a small space at D, sufficient to allow the steam to enter, being stopped in its passage by the caulking at C. The plate at E, between two rivets may therefore be regarded as a beam loaded all over by the pressure of the steam, and if that pressure exceeds a certain amount, the effect will be to cause the beam to spring or deflect slightly and thereby to leak at C.

We have now to consider the relations between the thickness of plate, distance between the insides of the rivet-holes, and the pressure of steam.

Let A, B, C, Fig. 17, be three beams, all of the same depth (or thickness) and breadth, but varying in length in the ratio 1, 2, 4; then by analogy these may be regarded as three steam joints having distances between insides of rivet-holes in the ratio 1, 2, 3, &c. Now, if we admit that a crack of any measurable amount will cause leakage, that amount will be the same in all three cases, so that the problem becomes this; to find what the respective loads must be, to give one and the same deflection in all the three cases. By the laws of deflection in (662) it is d3 x b x 8

shown that W =

In our case d3, b, 8, and C are

case 1, 2, 4, the loads But in our case, the

constant, therefore W will be inversely proportional to L3 simply, hence the lengths C, B, A, being in our will be in the ratio 43, 23, 13, or 64, 8, 1. surfaces over which these loads are spread are also in the ratio 1, 2, 4, and our special object is to find the pressure or load per square inch; with A we have a load of 1 spread over a length of 4, hence 1÷4= per unit of length; with B, a load of 8 spread over a length of 2, or 8÷2 = 4 per unit of length; and with C, a load of 64 spread over a length of 1, or 64 per unit of length. Thus, with lengths 4, 2, 1, we obtain pressures †, 4, 64 ; or in the ratio 1, 16, 256, which are inversely as the fourth power of the lengths, for 1a, 2*, 4* are 1, 16, 256, and we thus find that with constant thickness, the pressure tending to produce leakage of steam will be inversely proportional to S1, or the fourth power of the space, or distance between the insides of the rivet-holes. The formula in (662) shows that W is directly proportional to t3, hence we have the rules :

(46.)

(47.)

(48.)

In which S = the space between insides of rivet-holes in inches.

t = thickness of plate in ths of an inch.

p

=

MI

working pressure of steam in lbs. per square inch.

= a constant from practice

iron; 6-2 for steel plate.

=

5.5 for wrought

To find the value of ML we may take a standard case, say plate, rivets, 2 inches pitch, 1 space, and 50 lbs. per square inch; these are common proportions, and have been proved to be satisfactory by universal experience.

5

54

We may find 1 by the square of the square of that number; thus 11%2 1.723, and 1.7232 2.969, which is the fourth power of 1; then the rule M, S x p÷t, becomes 2.969

=

Ꮮ

=

=

X 50275-48, say 5.5, the value of ML.

(49.) Again: to find S for say 150-lb. steam with 4-inch plate, the rule (47) becomes S 5.5 x 43150 = 1·238, or say 1 inch. For example, 5·5 × 64 ÷ 150 = 2.35; then we may obtain the 4th root of 2.35 by finding the square root of the square root of that number: thus √2.35

=

=

1.533, and 1.533 1.238 inch as before, this being the 4th root of 2.35. We should obtain the same result direct by the use of logarithms: thus the log. of 2.35 or 3710684·092767, the natural number due to which = 1.238 inch as before.

Again: to find p for say space, therefore +12 5.5 × 31315

plate with rivets, 1-inch pitch, the rule (46) gives p = 80-lb. steam. Thus 12 = 1.72, and 1.722 2.96, which is the 4th power of 1%. Then 313 being

=

=

16

=

42.87, we obtain p = 5.5 x 42.872.96

as before.

=

80-lb. steam

=

The London and North-Western Railway Co. at Crewe, for their 4-foot locomotive boilers, use 3-inch plates, rivets, 12 pitch, therefore 1-inch space; then p 5.5 × 31311 189-lb. steam; the actual ordinary working pressure is 120 lbs.; occasionally 150 lbs. per square inch.

(50.) Table 13 has been calculated by rule (46). It should be understood that these rules are approximate only, giving a fair working pressure. Possibly a pressure double or even treble that given by the rule, would not cause the joint to leak instantly, but in all probability it would eventually do so, and as it is essential that boilers should be perfectly steam-tight, it will be advisable that the working pressure should not much exceed those given by the rules, and Table 13. When a steam joint or anything else is overstrained, failure is always more or less a question of time.

TABLE 13.-Of the MAXIMUM PRESSURE of STEAM with RIVETED JOINTS, as governed by the Space between Rivet-holes.

Average Working Pressure of Steam: Lbs. per Square Inch.

(51.) We have admitted in (28) that the diameter of the rivets shall be governed by the thickness of the plate alone, irrespective of the pressure of steam or other considerations; and in (44) we have allowed that the space between rivet-holes (and thereby the pitch of the rivets) shall be dominated by the pressure of the steam. But under these two conditions it is impossible to secure that equality between the shearing strain on the rivets and the tensile strain on the plate, which is an essential principle in riveting, as shown in (29). For instance, in Table 14, the pitch is allowed to be the same whether the joints are single or double-riveted: but obviously if the area of the rivets is properly proportioned for the