Strength and calculation of dimensions of iron and steel constructions

Many experiments have been lately made in Germany, England, Sweden, and America, to determine the properties of iron and steel. We propose to give in this brochure a general view of the results obtained, and of their consequences, without much detail, but so complete as to place practical engineers at the present stand-point of critical judgment.

These experiments show (what everyone admits) that the methods hitherto employed in calculating the dimensions of iron and steel constructions have been entirely wrong; and that the security of structures, in which their results have been applied, though with great expenditure of material, is much less than supposed.

Several methods for attaining better results have been projected; one of which was adopted by the Bavarian Government. The brief sketch of the several methods, given in the Appendix, shows that Launhardt's deserves the preference. This is so obvious, and meets with so few objections, that it is unsatisfactory only because of its limited application. A formula like that of Launhardt was needed for the case of resistance to alternating tension and compression. Such a formula is here deduced. With it we have all the requisites for a simple and rational determination of dimensions. It is to be hoped that no one will wait to consider it until more bridges are destroyed.

The chief reason that no one of the new methods has been generally employed is, that no one of them is complete. It would be impossible to determine fully the dimensions of a bridge by the use of any one of them, except by the addition of deductions specially made in each case. For this the working engineer has no time.

The systematic and final investigation here presented also includes the cases, so far unconsidered, which occur under shearing stress. Very particular regard is given to the subject of rivet-connections.

The ordinary methods of static calculation are not changed by the new method. Those who prefer graphic solutions will find all that is necessary for the complete determination of stresses after completion of the diagram of forces.

The new formulas are based upon Wohler's law; but the special results of his tests must be applied with judgment; - no more reliance being placed upon them than upon those of Rondelet or Brunei under the old methods. General formulas, old or new, do not change because of new experiments.

In the calculations especial reference is had to bridge and building constructions, in which permanent duration is required. Consideration of the special resistances and experience will serve to determine the coefficients of safety.

Excess of Elastic Limit

The limit of elasticity is generally defined as that stress per square unit beyond which permanent changes of form occur, while under less stresses the body returns to its former condition. Reference is made, not to sudden changes in stress and shocks, but to gradually increasing strains. But the definition is theoretically worthless, for a limit so definite is not probable, and much less is it proven. On the contrary, Hodgkinson and Clark have observed that there are permanent changes of form under very small loads. At present we must be content with defining this limit with Fairbairn, as that stress below which the changes in form are approximately proportional to the forces, while above this they increase much more rapidly. The words "approximately" and "much" are not so indeterminate as might be supposed, for, in the experiments of Bauschinger, the passage beyond the limit of elasticity could be determined very precisely; as for example in tension; "for with the same increase of load a disproportionately great elongation occurred at once, the maximum of which was in every case reached after some time." This sudden elongation must be credited to permanent changes of form; further elongations until near the breaking limit remain proportional to the stresses, and the modulus of elasticity is always found to be independent of the latter. In the first definition the changes of form which are permanent from Bauschinger's point of view are neglected. All experiments, up to the present time, have shown that when the elastic limit is passed, the tensile resistance is considerably increased, while ductility and tenacity diminish; the metal becoming brittle, and having little power of resistance to shock.

Paget found that iron chains after stretching bore a greater dead weight, but had less resistance to shock. Fairbairn thought all these phenomena could be explained by the hypothesis that the resistance of all the parts was not at first called into action, but, like ropes, they became gradually strained in common under sufficient load. "With this accords the fact that Bauschinger observed that increase of resistance, especially in rolled iron, was notably regular when the stress was in the direction of the fibres. The analogy holds further; for a rope, when tense, is more easily broken by shock. And this explains why a rod under sudden increase of stress breaks more readily than in case of gradually increasing pull.

When the limit of elasticity is passed, this limit is again raised. Tresca, in tests of rails, succeeded in pushing the limit of elasticity to near the limit of rupture, so that it was less by about one-tenth. The practice hitherto has been to assume as permissible stress (b) a fraction of the elastic limit. In this case b increases with the number of loads. But the material becomes more brittle, and less resistant to shock, and local passages beyond elastic limits are not excluded. So that we need not assent to the often-advocated opinion that a test of material beyond the elastic limit would be of advantage. It is worth mention that the increase of resistance with the passage beyond each limit cannot go on indefinitely; but a diminution must occur at some time, unless we assume that with very gradual increase of stresses and longer intervals, the original resistance becomes greater than the initial ultimate strength.


Mechanical Treatment, Heating. Hardening.

Elastic limit and ultimate strength are both increased when the limit of elasticity is exceeded; ductility and tenacity diminish. Since under rolling, hammering, and pulling the elastic limit in the affected places is certainly passed, and permanent changes in form take place, the necessary effect of such mechanical treatment is obvious.

Heating and slow cooling has an effect exactly opposite to that caused by passing the elastic limit, for the metal becomes more ductile and loses in ultimate strength. According to Tunner, the brittleness produced by mechanical treatment gradually decreases if the body is allowed to remain at rest. A wire which broke when bent to an obtuse angle, just after leaving the plate, increased in pliability within a few days, and continued to do so during some weeks.

That cold-rolling considerably raises the ultimate strength was clearly shown by Kirkaldy's experiments, t nearly doubling in value, passing from 3,220 to 6,260, while annealing reduced it to 3,580. Styffe had an iron rod, which had been previously annealed, hammered cold to half its original section; the strength was raised from 3,140 to 5,830. According to Kick, United States cold-rolled iron is much more brittle than the common sort. It has often been observed that the ultimate resistance of cold-rolled metal is diminished by removal of the skin, the effect of rolling being materially greater at the surface. These phenomena and many others, having no apparent relation to one another, are all explained upon the hypothesis mentioned.

If the mechanical treatment is with heat, both influences operate, viz.: passage beyond the elastic limit and heating. These must counter-act, entirely or partially, and the metal may gain in strength, the tenacity remaining constant or increasing. In England the working of the metal is often repeated.

A body once annealed is further changed only by higher heat, unless, meanwhile, it has received some treatment with opposite effect. It follows, that the effect of annealing must be greater in the degree that the temperature is higher than that under the previous mechanical treatment. This was observed by Styffe.

Hardening produces upon steel and wrought iron an effect like that due to passing the elastic limit, with this qualification, that in the case of steel, not only ultimate strength and elastic limit, but also brittleness are notably increased. Tempered metal is not suitable for many purposes, because of its slight power of resistance to shocks. The process of tempering consists in plunging the red hot metal into some fluid, oil or water, which suddenly cools it. Brittleness may be somewhat reduced by gradual heating, and may be destroyed by annealing, together with all other qualities due to hardening. The effect of hardening is much greater upon steel than on iron; and in either case depends upon the chemical constitution and other conditions.