STRENGTH OF MATERIALS. The force with which a solid body resists an effort to separate its particles, or destroy their aggregation, can only become known from experiment ; nevertheless, if we assume an hypothesis to represent the manner in which the elementary particles are arranged and cohere, general formulas may be deduced, which will represent the comparative strength of bodies of differ ent forms and dimensions, or submitted to the action of forces applied indifferent manners, and will consequently be of great use in practical mechanics.
There are four different ways in which the strength ofa solid body may be exerted: first, in resisting a longitudinal tension, or force tending to tear it asunder ; se condly, in resisting a force to break the body by a transverse strain; thirdly, in resisting compression, or a force tending to crush the body ; and I fourthly, in resisting a force tending to wrench it asunder by torsion. We consider these separately.
1. Longitudinal Tension.—The resist ance opposed by a solid body to a longi tudinal strain is usually termed the ab solute strength, or force of direct cohe sion, of the body. Two points may be proposed for investigation : first, to de termine the quantity by which a body of a given length is stretched or elongat ed under the action of a given force or weight ; and secondly, the effect required to separate the parts or produce rupture. Experiments have usually been directed to the last of these only, but the first may be determined indirectly from ex periments on flexure. In bodies of a fibrous structure, as the woods, the co ve force differs greatly, according as the effect is applied in the direction of the fibres, or at right angles to it. When the strain is exerted in the direction of the fibres, the cohesive force obviously depends on two circumstances only—the strength of each fibre, and their number; and, in general, in bodies of the same substance and structure, the strength is proportional to the transverse area of the body, and to a certain constant which must be determined by experiment. Although the longitudinal tension is, with respect to mechanical action, the simplest of all the strains to which a solid body can be subjected, it is the most difficult to submit to experiment, by reason of the enormous forces required to produce rupture, and, in the case of fibrous bodies, the difficulty of applying those forces in the direct line of the fibres. If the fibres are not all subjected to the same strain, it is obvious that the direct cohesion will be estimated at less than its real value; and, as Mr. Barlow remarks, it is probably owing to this cir cumstance that so little agreement is found in the results of experiments.
2. Transverse Strength.—When a body suffers a transverse strain, the mechani cal action which takes place among the particles is of a more complicated nature. Galileo was the first who attempted to give a rational explanation of this action, and to submit the strength of the mate rials used in the mechanical arts to the measures of geometry and arithmetic.
He assumed that all solid bodies are com posed of numerous small parallel fibres, perfectly inflexible and inextensible ; and that when they break, the several fibres give way in succession, the body turning on the last, which give way as on a hinge, and the strain on each fibre, previous to the rupture, being proportional to its distance from the quiescent fibres.
From the table of data given by Bar low the following mean results of experi ments (on beams supported at both ends), made in the dock-yard at Woolwich, for determining the elasticity and strength of various species of timber, are ex tracted: From the mean of a number of experi mekts by Tredgold, the values of E and S, for rectangular cast iron bars, were found to be E=2214000, S=7620.
Resistance of bodies to farces tending to crush them.—The resistance of a body to a crushing force might be supposed, a priori, to follow the same law as the ab solute force of cohesion, and, consequent ly, to depend only upon the area of the section and the force of aggregation of the particles. It is found, however, by experiment, that the thickness of the body (or length, if the force is applied endwise), has an important influence on the amount of pressure it is capable of bearing. Very thin plates are readily crushed ; and the resistance appears to increase with the thickness up to a cer tain maximum, after which it diminishes. The theory of the resistance of pillars, which is of great importance on account of its application to architectural pur poses, was investigated by Euler ; and, according to the hypothesis adopted by him, the strength varies directly as the fourth power of the diameter or side, and inversely as the square of the length. This is confirmed by the recent experi ments of Mr. Hodgkinson, in respect of pillars of wrought iron or timber; but in the case of pillars of cast iron, the powers of the diameter and length were some what different. Mr. Hodgkinson found from a mean of experiments, that a solid, uniform pillar of cast iron, whose trans verse section is one square inch, is de stroyed by a weight of 98922 lbs., or 44.16 tons. Assuming this as a unit of measure, he gives the following formula (as representing his experiments), in which s is the strength or weight in lbs. that would crush the pillar, d the diameter, and 1 the length, viz., s-98922 xd 1 ". This formula applies to pillars of which the lengths are twenty five times the diameter and upwards, and which are perfectly flat at the ends. When the ends of a pillar are rounded, so that the load bears only on the middle fibres, the strength is greatly reduced. In pillars whose length is thirty times the diameter, or upwards, Mr. Hodgkinson found the strength of those with flat ends to be about three times greater than the strength of others of the same dimen sions with round ends, the mean ratio being 3.167. In shorter pillars the ratio was not constant. The strength of a pillar is slightly increased by placing disks on the ends to increase the bearings.