Strength and determination of the dimensions of structures of iron and steel

The methods of calculation of the forces which act upon the various members of our bridges and other structures have, within the last ten years, owing to the united labor of European and American engineers, gained most remarkably in clearness and reliability. These advances can, however, attain their greatest value, only when the question as to what forces these members can sustain with the desired degree of security is satisfactorily disposed of.

That the method of dimensioning thus far in use is an entirely arbitrary one, cannot be denied. In spite of numerous attacks no defence of it has ever been heard. What has for the last hundred years justified the assumption that a piece which has once successfully resisted a certain stress, must necessarily resist equally, well an indefinite number of repetitions of that stress? How can it be held that it is a matter of indifference whether a piece is subjected always to the same constant load, or is alternately loaded and then unloaded, or is even subjected to alternate strains of tension and compression? Every layman knows that he can more readily break a piece by bending to and fro than by a steady pull, even though the force exerted in each case be the same.

By assuming the strength, which is not constant, as nevertheless constant for every member of a construction, the degree of safety of the different members varies. The least safety of any place in the structure is, however, the measure of the security. of the whole. If one member gives way, it is a matter of little moment whether, in falling, the other members hang together or not, and the structure comes to the ground in two or more pieces.

The admirable investigations made during the last eighteen years at the instance of the Prussian Government, have led to results in complete accord with practical sense. The method by which, even before the publication of these results, in the construction of the bridge over the Rhine at Mayence, the strength of the web members was estimated, appears to have been, in all its essentials, correct. The most important result of the investigations alluded to, however, is “Wohler's law” a principle which is, indeed, self-evident, and upon which, in future, every rational method of dimensioning must be based. Immediately after the publication of Wohler's investigations, the results of which were further confirmed by Spangenberg, new methods of dimensioning were proposed in Germany and Austria. These methods are reviewed and criticised in the Appendix to the present work. These proposed methods are, all of them, not sufficiently developed, and are all, moreover, too closely fitted to the numerical results of Wohler.

The present little work gives a systematic presentation of a new method of dimensioning, based upon two formulae deduced by Professor Launhardt and by the Author, respectively. It will be noticed that this method, which leaves as to simplicity nothing to be desired, gives considerable economy of material as well as increased security, while the ordinary methods of staticalcalculation, in general use, remain unaffected by it.

As the resistance of riveted constructions depends directly upon the quality of the rivet connections, I have gived special attention to this hitherto somewhat neglected subject. Without denying the numerous advantages of bolt connections, European engineers use rivets even in frame work, almost exclusively.

In order to make the work serviceable to the practical engineer, I have subjected the numerous experiments upon the strength properties of Iron and Steel recently made in various countries to careful comparison and scrutiny, and thus given a concise presentation of the present state ot knowledge in this respect. Everything is thus given which after the completion of the statical calculation, may be desired.

Finally, I must take occasion to express my best thanks to Professor Du Bois for his kind compliance with my wishes in the preparation of this Translation, which will, I hope, meet with as favorable a reception from the Profession in America as has already been so justly accorded to the Translator's “Elements of Graphical Statics.”

In recent times, most admirable experiments have been made upon the properties of iron and steel in Germany, England, Sweden, and America. In the present brochure, it has been attempted to present the tangible results and consequences of these experiments, as free from detail as possible, but to such an extent that the practical engineer may be put in possession of the results thus far obtained. Numerous foot references to the literature of the subject point out the sources of more detailed information upon special topics.

The experiments alluded to have proved, among other things, what is by this time all but universally admitted, that heretofore the method of dimensioning iron and steel constructions has been entirely incorrect, and that the safety of the structures thus proportioned, in spite of liberal expenditure of material, is considerably less than that relied upon (Chaps. 3, 13, 29).

Various methods have been proposed for the attainment of better results, one of which has even been adopted by the Bavarian government. A short presentation of these methods in the Appendix will show that of them, that due to Launhardt deserves the preference. This method is so clear, and open to so few objections, that only its limited applicability is to be regretted. The strength relations for alternate stresses of tension and compression are, however, not included by the formula of Launhardt. Such a formula is deduced in the present treatise. With this lack supplied, all the necessary data for a simple and rational method of dimensioning are at hand. It is to be hoped we shall not delay its acceptance until still more bridges come to grief.

One of the chief reasons why thus far none of the new methods have met with better favor, is that none of them have been sufficiently developed. It has not been possible to proportion a bridge by any one of these methods completely, without instituting special discussions. For such discussions the practising engineer has, in general, little time. A systematic presentation is therefore imperative.

The systematic presentation, complete in itself, here given, includes also the hitherto neglected cases of construction-pieces submitted to shear. Special and much needed attention has been given to rivet connections. Although here also the present condition of theory finds full recognition, I do not consider that it has been at the expense of simplicity of application.

The customary methods of statical calculation remain unaffected by the new method of dimensioning. Those who prefer the graphical methods for such calculations, will find in the present brochure everything which remains necessary to be done after the preparation of the strain-sheet, in the calculation of a structure. By the previous rude methods of dimensioning, very exact statical calculations are rendered rather useless.

In the setting forth of the new formulae, Wohler's law has of course been premised. The special experimental values of Wohler are, however, to be used with caution, and scarcely more weight can be laid upon them relatively than, for example, upon the results of Rondelet or Brunei or others, with regard to the previous methods. The general formulae are, however, affected as little by such new results as, in the time of Brunei, the early method of procedure was by new and later series of experiments (Chaps. 2, 29).

In the values for the allowable stress per square centimetre, we have had special reference to bridges and other constructions from which unlimited life is expected. Study of strength properties and practical experience will furnish sufficient grounds for the proper selection of the coefficient of safety in other cases.

Notwithstanding the simplicity of the contents of the present work, I have endeavored to give with care, perhaps with rather too anxious care, credit, where I have borrowed from others that which has not long been common property, and to indicate authorities and sources of information. Better thus, than to imitate those who preserve a discreet silence upon such masters, and concerning whose works we do well to take for granted that all is compilation.

In works upon iron and steel constructions, there is generally but little to be found upon the strength properties of the materials themselves, and for reasons already alluded to the new methods of dimensioning find no place. I may therefore hope, in this little work, which may serve as an appendix to every text-book, to have supplied a real want.