MATERIALS, STRENGTH OF. The strength of any material object, as a rod, bar, beam, chain, or rope, is that power by which the substance resists an effort to destroy the cohesion of its parts. It evidently depends on the disposition of the particles relatively to each other, on the iutenaity of the force by which the particles cohere together, and on the manner in which the straining power is applied. The inquiry Into the laws by which the materials employed in the con struction of edifices or machines resist the strains to which they aro subject is of considerable importance, because upon a just adaptation of the strength at any one point to the strain there experienced (and an excess or deficiency of the former is sometimes equally injurious) depends the stability of the whole structure.
Whatever be the constitution of a rod or of a beam, the relation between its strength and tho strain to which it may be exposed can be made the subject of mathematical investigation only by imagining the material to consist of an infinite number of particles arranged in lines (like fibres or threads) parallel to each other in the direction of its length. The particles in each line must be supposed to cohere together by powers exerted in that direction, and the several lines to cohere laterally with forces which may or may not be equal to those exerted longitudinally. In homogeneous bodies, as glass and some of the metals, the particles may be supposed to be symmetrically disposed throughout the masses, and to attract each other in every direction with equal powers : but the case is different in other bodies, particu larly in timber; for in such bodice the lateral cohesion of the fibres is much less powerful than the longitudinal cohesion of the particles in each fibre. In ropes the fibres have no lateral cohesion, and the strength depends on the twisting of the fibres together; in consequence of this, as the latter can scarcely be separated from each other in this direction of the length of the rope, the cohesion of nearly all the particles in any transverse section must be destroyed befol-e a disruption can take place.
A rod of any material, consisting of parallel fibres as above supposed, being placed in a vertical position, and strained by a weight applied at the lower extremity, the particles in every fibre will bo separated from each other by the action of the weight, and consequently its length will be increased. The cohesive power by which the particles are kept together will, in most cases, be diminished by the separation ; and if the weight be sufficiently great, or if it be allowed to act during a sufficient length of time, the cohesive power will be eventually over come ; that is, the rod will in some parts of its length be torn asunder.
But before this occurs, since all bodies possess a certain degreo of elas ticity, on removing the weight the attraction of cohesion will cause the separated particles to return towards their original positions; or the rod will become nearly of the same length as at first. That it does not exactly become so, in general, arises from the imperfect elasticity of the material, ou which account the particles come to a state of rest at augmented distances from each other. The elongation of the red when strained by a weight, and the amount of the weight necessary to produce fracture, will depend on the nature of the material ; and, from a want of uniformity in the constitution of materials even of the same kind, though the rods be of like dimensions, groat Irregularities are found to exist in their power of resisting direct strains. Numerous experiments performed on each of the different kinds of material can alone afford a mean value on which reliance may be placed when it is required to determine the capability of a bar or beam to resist the strain arising from the action of any given force. • H the material* were perfectly elastic, so that the length of the rod became the same after the:removal of the suspended weight as before that weight was applied, the force of cohesion would evidently be pro portional to the Intensity of the straining power; and this is generally adopted as an hypothesis in investigations concerning the equilibrium between strengths and strains; it being understood that the latter have only that moderate degree of intensity, compared with the former, which is consistent with the permanent stability of the edifice or of the machine. The law just mentioned appears to have been discovered by Dr. Ifooke ; and as the separation of the particles in any fibre is proportional to the straining power, it follows that, within certain limits, the cohesive power between two particles of en elastic body is proportional to the distances to which one of them is removed by the straining force from the place where it was before at rest. The same law is considered to hold good when the particles of an elastic body are made to approach each other by the action of a compressing force like that of a weight on the top of a vertical pillar.