The strength of materials and structures

PART I. - The strength of materials, as depending on their quality, and as ascertained by testing apparatus.
PART II. - The strength of structures, as depending on the form and arrangement of their parts, and on the materials of which they are constructed.

This elementary treatise is divided into two distinct parts.

The First Part treats of the natural properties of various materials employed in construction, more especially in regard to their strength and elasticity, and their adaptation for particular practical purposes in the arts. The object of this portion of the work is to describe the qualities and characteristics of materials, so far as they are of importance to the engineer, or are exhibited in the results of experiments made with the testing-machine.

An acquaintance with the natural properties of materials, as forming part of the great field of applied mechanics, is indispensably necessary for the young mechanic or engineer, who desires to be something more than an artisan. That real knowledge, which consists in understanding the materials which he handles, and in a familiarity with their points of agreement or difference, both in regard to elasticity and strength, cannot fail to give a charm to his daily duty.

As it cannot be expected that all will have the opportunity of making experiments for themselves, the first three chapters are devoted to the testing of materials, and to the practical manipulation of a testing-machine. In these chapters reference is made to the physical properties of some common materials, by which the student will be able to comprehend the nature of such experimental investigations, and the labour and care needed in order to arrive at true results; and it is hoped that he will find the subject treated in such a clear and simple manner, that he may understand it without much difficulty.

The fourth, fifth, sixth, seventh, and eighth chapters refer more especially to cast iron, wrought iron, steel, copper, alloys, and timber, and are intended to describe their qualities and leading peculiarities.

The ninth, tenth, and eleventh chapters treat, more generally, of the resistance of materials to torsion, shearing, and punching, and to transverse strains, conjoined with impact and vibration.

The first eleven chapters, therefore, have regard to the nature of materials, and the remaining six chapters which constitute the second part of the volume are devoted to the strength of structures, when made of the materials previously treated of.

In the Second Part, the student will learn the correct forms which must be given to the various structures in order to obtain the requisite strength, and likewise the best arrangement of materials, as depending on their respective properties, so that by the practical application of correct principles, the maximum of strength may be attained with the minimum of weight and cost

The experiments most frequently referred to, and which are quoted as ‘Woolwich experiments,’ have all been made in the Royal Arsenal for various purposes during the past eighteen years, and chiefly with the American testing machine, which is described in the third chapter, the only exception being certain experiments, to ascertain the strength of ropes under various conditions, which were carried out with a hydraulic testing-machine, recently transferred from Her Majesty's Dockyard to the Royal Arsenal.

The sources from whence the results of other experiments have been drawn, or from which extracts have been made, are generally quoted. Reference has very frequently been made to the Blue Book, containing the Report of the Commissioners appointed to enquire into the Application of Iron to Railway Structures,

The resistance of a long column, to loads acting in the direction of its axis, depends mainly on three conditions: first, on the proportion which its length bears to its least transverse dimension; second, on the form of the ends of the column; and, third, on the direction in which the load acts, with reference to the axis of the column.

In the case of short columns that is, columns whose length is only slightly in excess of their transverse dimensions the material is ruptured by simple crushing alone; but when the height exceeds from three to eight times the least transverse dimension, according to the nature of the material, the rupture is caused partly by bending and partly by crushing; and, when the length exceeds from twenty-five to thirty times the transverse dimension, then the column will fail by bending, and the material will be subjected to strains, similar to those of a beam, when under a transverse load; one side will be crushed and the other will be extended.

There is, at the present time, no completely satisfactory theory of the ultimate resistance of long columns. Euler investigated the law of resistance, on the assumption that the elasticity of the material remained perfect up to the point at which rupture was imminent. On this assumption, he found that the resistance of long cylindrical columns would be proportional to the fourth power of the diameter and inversely as the square of the length.

Hodgkinson found, however, by his experiments, that the ultimate resistance was proportional to a power of the diameter rather less than the fourth, and decreased in a much less ratio than the square of the length.

Table XL. p. 203, gives the mean results of a number of experiments, made by Hodgkinson, and shows clearly that the strength of pillars depends greatly on the secure fixing of their ends. With both ends rounded, the strength is only 1/3 of that afforded by similar pillars, having both ends flat, and abutting on flat surfaces. Pillars, with one end round and the other flat, have 2/3 of the strength of those with both ends flat. These facts show the advantage derived from correct bearing surfaces in structures exposed to compression. The table also shows that pillars of timber, when the length exceeds seventeen times the diameter, are destroyed by bending, and that even those of seventeen diameters are partly bent as well as crushed.

It was found in these experiments that a deflection was visible, in one case, with a little under 1/9 of the destroying load, and that, generally, there was a considerable deflection with between 1/3 and ¼ of the destroying load.

The visible result of the crushing strain upon short columns varies with the nature of the material, and rupture is caused either by splitting, shearing, or bulging; the former is characteristic of the hardest cast iron, the hardest description of stones, and also of timber. Crushing by shearing is exhibited by cast iron, when the height of the column is about one and a half time the transverse dimension, whilst crushing by bulging takes place with short specimens of wrought iron, mild steel, gun-metal, lead, and other ductile metals.

There are two other forms of crushing: first, crushing by wrinkling up, commonly called crippling or buckling; and, second, by cross-breaking. The former is sometimes seen in columns of wrought iron, which are too long to be crushed by bulging, and too short to be bent by flexure; and the latter occurs in cast-iron columns, when the length exceeds thirty times their diameter.

The manner in which the column gives way depends upon the form of the ends of the column, in so far that, if the ends are rounded, the column is as liable to flexure as one of the same diameter and twice the length, with both ends flat and firmly fixed. Hence, if we break two similar columns, the one with the ends rounded, and the other with the ends flat, the length being about twenty times the diameter, the material in the one with rounded ends will be ruptured entirely by cross-breaking or transverse strain, while that of the other will be ruptured partly by crushing and partly by cross-breaking.

The way in which the column yields also depends upon the direction of the load, which has heretofore been supposed to pass along the axis of the column. If the direction of the action of the load forms only a very small angle with the axis of the column, it induces a strain upon the column at right angles to the direction of its axis, and it is then in a precisely similar condition to a beam supported at each end and loaded at the centre.

In short columns, possessing sufficient rigidity to resist the bending strain caused by this indirect action of the load, the material is liable to be ruptured in detail, from the fact that the whole of it has not the opportunity of taking its full share of the work in resisting the load, and therefore cannot give due support to the smaller portion, upon which the load acts.

There are a few practical deductions to be drawn from these three considerations: First, that a column should be made as short as possible, in proportion to diameter; in other words, it should be capable of maintaining itself vertical by its stiffness. Second, that the ends of cast-iron pillars should be cast with broad bracketed flanges, considerably larger than the transverse dimensions of the columns at the centre, for although the flanges may not add to the strength, in a direct manner, yet they certainly add to the stability, and will prevent the column from bending; that is, if the ends are made sufficiently stiff and strong to resist the thrust. Third, that the ends should be at right angles to the axis of the column, and placed so that the load may act upon the whole surface of the capital and base, and its resultant may pass directly along the axis of the column.

As a matter of economy, all long columns should be of the form recommended for cylindrical beams namely, that of a parabolic spindle but this is a form which does not please the eye so well as the graceful outline of a taper column, and hence, no doubt, strict economy is often sacrificed to appearance.

In considering the strength of columns, the probability of crushing by splitting or by shearing may be entirely neglected, because, practically, columns are never made so short that these forms of rupture are called into play, and, so far as timber and cast-iron columns are concerned, rupture will always take place by cross-breaking, and wrought-iron plate columns should either be properly stayed, to prevent buckling or bulging, or else sufficient material should be put into the section to resist the stress tending to cause local distortion or wrinkling up of the metal, until the cross-breaking or bending strain can come into play.

The most reliable experiments upon the strength of columns are those of Hodgkinson, who carried out an elaborate series of experiments to determine the laws which govern the strength of cast-iron columns, and who also made a considerable number of experiments for the Railway Commissioners, in order to determine the best form of section of a wrought-iron tube, to resist compression, when the load is applied in the direction of its length.