or crossways to have an ultimate tensile strength of not less than 26 and not exceeding 32 tons per square inch, with an elongation of 20 per cent. measured on a length of 8 inches; the beam, angle, bulb, and bar steel to withstand such forge tests as may be sufficient to prove soundness and fitness. Strips cut lengthways or crossways, 1 inch wide, heated uniformly to a low cherry red, and cooled in water at 82° Fahrenheit, must stand bending in a press to a curve of which the inner radius is one and a half times the thickness of the steel tested. The strips for bending should be planed on the edges, and the sharp edges taken off.

The percentage of elongation in the Admiralty test might just as well have been measured on a length of 10 inches. Rivetsteel, being softer and more ductile, may be taken at, between 24 and 30 tons per square inch for tensile strength, and 25 per cent. elongation. The steel used in the construction of tension members in the Forth Bridge was specified to have a strength of from 30 to 33 tons, with 20 per cent. elongation; for tubular columns and struts, the steel was specified to have a tensile strength of from 34 to 37 tons per square inch, and an elongation of 17 per cent. The elongations were specified to be measured on 8 inches.

Working-stress and Factor of Safety.-Working-stress signifies the intensity of stress-generally expressed in tons per square inch-to which a piece of material may be subjected without ceasing to fulfil its purpose efficiently under the conditions on which the stresses are applied.

The factor of safety is the ratio of the ultimate strength to the working-load. Sir William Fairburn proved that a riveted girder, loaded to one-third of the load which would have broken it if gradually applied, failed after 313,000 applications of this load.

The experiments of Herr Wöhler and Professor Spangenberg demonstrate the following law, known as "Wöhler's Law: " "Rupture may be caused, not only by a steady load which exceeds the carrying-strength, but also by repeated applications of stresses none of which are equal to this carryingstrength. The difference of these stresses are measures of the disturbance of the continuity, in so far as by their increase the maximum stress which is still necessary for rupture diminishes."

Professor Bauschinger has made a long series of experiments which confirm those made by Herr Wöhler. Professor Bauschinger's experiments are the most valuable on this subject which have ever been made, and the results are summarized in Table V.

In England, Sir B. Baker has made various experiments which also confirm Wöhler's original experiments. For example, he found that when a shaft was loaded with one-half its gradually applied breaking-weight, and set rotating, about five thousand reversals of stress produced fracture. He mentions an experiment with a bar of cast iron loaded with a weight which, according to Fairbairn's experiments, it should have carried for a long series of years, broken in two minutes when set gently rotating; also, a bar of fine tough steel so changed in constitution at fracture after a few months' rotation as to offer no advantage over a new cast-iron bar of the same section. Sir B. Baker has proved, by experimenting on flat bars of steel by repeatedly bending them, and subsequently testing them in direct tension and direct crushing, that the effect of repeated stresses is more prejudicial in tension than in compression.

The change which a piece of material undergoes when subjected to repeated stresses has been termed "fatigue." It is most marked in the case of stresses alternating between tension and an equal compression, as seen in the fracture of railway axles.

The strength of a piece of material when subjected to a gradually applied load, as in a testing-machine, is termed its "statical strength." When subjected to a load which is entirely removed before being reapplied, the load which will ultimately break the piece is termed its "primitive strength." When subjected to stresses which alternate between tension and an equal compression, the ultimate breaking-stress is termed its "vibrating-strength." Approximately, the vibrating-strength is to the primitive is to the statical as 1 is to 2 is to 3.

The values of the strengths for a variety of materials are recorded in Table V.

Several methods have been proposed which have for their object the representation of the results of the experiments made by Wöhler and Bauschinger, and their extension to the various ranges of stress which occur in engineering practice, among

which may be noticed Gerber's parabola. If the ranges of stress given in Table V. are plotted as ordinates, and the

TABLE V.

BAUSCHINGER'S ENDURANCE TESTS.

Stresses requiring fifteen million repetitions to cause fracture. Tons per square inch.

LIMITS OF STRESS FROM WÖHLER'S ENDURANCE-TEST.

Stresses in tons per square inch for which fracture occurs only after an indefinitely large

number of repetitions.

minimum stress as abscissæ, the points fall on a parabolic curve, which Professor Unwin expresses thus:

Let f max. and ƒ min. denote the limits of stress, and ▲ the range of stress; then

A =ƒ max. ƒ min.

The upper sign is to be taken when the stresses are of like kind, and the lower sign when they are of opposite kind, as in alternating stresses. Let f denote the statical breaking-strength; then the equation to Gerber's parabola is—

If the statical strength ƒ be known, and the value of ƒ min. and ƒ max. for any range of stress at which the bar stands. a practically unlimited number of repetitions before breaking, then k can be determined, and the limits of stress for all conditions of loading can be calculated. The parabolas are

с

drawn from the above equation, using the results recorded in Table V.

Soon after Wöhler's results were published, Professor Launhardt published a formula which applies to the cases in which the stresses are either tensile or compressive, which may be represented as follows:

Let b denote the breaking-strength.

If, in the end lattice-bar of a bridge, the stress produced by

Minimum stress in tons per square inch.

40

FIG. 6.-Wöhler's and Bauschinger's endurance tests.

the live load were nine times the stress produced by the dead load, then

and, using the results given in Table V. for wrought iron, we have

so that 14.07 tons is the ultimate breaking-strength of the bar; and, if the working-stress be taken at 4.69 tons per square inch, the factor of safety is

In order to meet the cases which include stresses alternating between tension and compression, Professor Weyrauch proposed the following formula, in which the vibrating-strength is denoted by v

If the greatest tension on a bar be 5 tons, and the greatest compression 10 tons, then

and, using the same material as before, we have—

b=13.10 (13·10 - 7·15) = 10.125 tons

and the factor of safety, with a working-stress of 3.375 tons per square inch, is

The effect of "fatigue" is considered to be purely local, as it is not possible to discover any change in strength, elasticity, or ductility in material which has been fractured in this way, by retesting it in the ordinary way by means of the testingmachine.

There is no difference in the results obtained from testing specimens cut from an axle broken in ordinary use, or by means of the drop-test, than would be obtained from testing specimens cut from the axle when new. Retesting specimens cut from old structures does not show any measurable change in the material. It is known, however, that the fracture of specimens by repeated stresses in Wöhler's machines and that of railway axles from the fatigue and impact occurring in ordinary work are short and crystalline, showing no sign of ductility; hence the reason given by Professor Unwin, that fatigue is primarily a loss of power of yielding in the particles near the plane of weakness at which fracture occurs. There is, however, no evidence to show that materials which were originally fibrous and ductile may become granular and crystalline when subjected to such conditions as exist in a railway axle, excepting in the plane of the fracture itself.

As stated by Kirkaldie, the crystalline appearance appears