usual way the metal is damaged and its strength reduced by the maltreatment experienced: thus by Table 1, Mr. Kirkaldy gives 26 tons per square inch as the mean tensile strength of rolled rivet-iron; but Mr. Fairbairn found it to be 22 tons only in single-riveted joints of boiler-plate (19); hence we have 2226·846, or say 85 per cent. realised; therefore 15 per cent. is lost by riveting hot.

With steel rivets the loss is very great, as shown by (42); the tensile strength of bar steel is 47 84 tons per square inch, but that of steel in riveted joints is 23.77 tons only: hence 23.7747.8450, or 50 per cent. only, is realised, and 50 per cent. is lost by riveting hot.

With treenails of English oak, commonly used in shipbuilding, the shearing strain across the grain by experiments at H.M. Dockyard was 4000 lbs. per square inch, and as by Table 79 the mean tensile strength of oak

ratio is 3.1 to 1.0.

=

12,332 lbs., the

(124.) "Rectangular Bars."- Experiments recorded by the Institute of Mechanical Engineers show that in shearing flat bars, the shearing strain is nearly the same whether the bar is flat or on edge; thus bars inch by 3 inches gave on the flat 22.3 and on edge 23 1 tons per square inch. Others 1 inch by 3 inches gave 23.1 and 22.7 tons per square inch respectively in these experiments the shear blades were parallel.

(125.) "Oblique Shearing."-When the blades are fixed at an angle so as to shear a plate obliquely, the strain is less than with parallel shearing to an extent which varies with the angle of the blade and the thickness of the plate. Say, for illustration, that Fig. 29 is a blade 12 inches wide, with four steps in it, each 3 inches wide, and B the plate to be sheared, the thickness of the plate and the height of the steps being inch. Now, it will be observed that the steps act one after the other, thus C will have done its work and passed through the plate before D begins to act, &c., hence the strain is th only of that due to a parallel blade 12 inches wide, but of course the travel is 4 times as much; therefore the mechanical power is the same in either case. The line E, F, G at a slope of 1 to 12 or 1 to 8 would

evidently give the same result as a blade with steps, that is to say, with a 4-inch plate as in our case. But the slope would vary with the thickness; thus for 4-inch plate it might be 1 to 16; with 1-inch plate 1 to 4, &c.; the strain being then 4th of that with a parallel blade. For ordinary and general purposes a slope of 1 in 8 to 1 in 12 is commonly used.

"Strain for Punching."-An ordinary punch may be regarded as a circular cutter or shearing blade whose length is equal to the circumference: then by Table 1 the mean strength of plateiron is 48,454 lbs., or 21.63 tons per square inch: hence a punch 1 inch diameter with a plate 1 inch thick would require

TABLE 30.-Of the STRAIN for PUNCHING RIVET-HOLES in

a force of 21.63 x 3.1416 = 68 tons, and we have for wroughtiron plates the rule:

In which d = the diameter of punch, and t = the thickness of the plate, both in inches; Sp being the punching strain in tons: thus, for example, with 2-inch punch and -inch plate we obtain 2 × 1 × 68 = 25.5 tons.

Sp

=

With steel plates the mean tensile and shearing strength by Table 1 = 85,977 lbs., or 38.38 tons per square inch; hence a punch 1 inch diameter with 1-inch plate requires 38.38 x 3.1416 120 tons, and we have for steel plates the rule :—

=

Thus for say-inch punch and 4-inch steel plate the punching strain becomes Sp = × × 120 = 15 tons. Table 30 has been calculated by these rules.

DETRUSION.

(128.) This term has been applied to the shearing strength of timber in the direction of the fibres. Experiments have shown that, 1st, This is practically the same as the tensile strength perpendicular to the grain which is given at the end of Table 1; and, 2nd, That both are very small and very variable: with

Poplar

Oak

Larch Scotch Fir Memel

the mean resistance to detrusion with the grain and tensile strain across the grain is :

In practice, simple detrusion is easily avoided by bolts through the bar, hence the great weakness of some kinds of timber to that particular strain is a matter of small importance.

CHAPTER VI.

ON THE CRUSHING STRAIN.

(129.) We are indebted to Mr. Hodgkinson for almost the whole of our exact knowledge of the strength of materials in resisting crushing strains, and from his experimental investigations we obtain the following laws:

1st. That for specimens whose height is between 1 and 3 times the diameter or side of square, the crushing strain is simply proportional to the area.

2nd. In that case the plane of rupture is inclined at an angle with the base, and therefore with the axis, which angle is constant for the same material, but is different for different materials.

3rd. That for heights less than 1 times the diameter, the crushing strain becomes greater irregularly with the reduction in height (130).

4th. For very great heights, the specimen becoming a pillar of considerable length in proportion to the diameter, failure takes place by lateral flexure, with a load very much less than that necessary to crush the material (306).

5th. For intermediate heights, the pillar fails with an intermediate load, partly by flexure, and partly by incipient crushing (163).

(130.) "Cast Iron.”—The effect of height is well illustrated by some experiments by Mr. Hodgkinson on cylinders inch diameter, the heights being

tons; the equivalent strains per square inch were

69.3 63.5 60.0 55.0 53.3 53.3 49.6 34.4 tons. It appears from this that when the height is equal to the diameter the resistance to crushing is 5553.3 1.032, or 3.2 per cent. greater than when the height is between 1 and 2 with diameter 1.0.

(131.) Table 31 gives the general results of Mr. Hodgkinson's experiments on the crushing strength of cast-iron cylinders inch diameter; those in col. 1 were 1 inch in height, or double the diameter; those in col. 4 were inch high, and they show an excess of 5.8 per cent. over those in col. 1.

Most of the old experiments on the resistance of materials to crushing by Rennie, Bramah, and others, were made on cubes, and it has been objected that this fact vitiates their results, but we have seen that in cast iron at least the difference is from 3.2 to 5.8 per cent. only, so that the earlier experiments on cubes may be accepted as correct enough for practice.

TABLE 31.-Of the TENSILE and CRUSHING STRENGTH of CAST IRON, in Tons per Square Inch.