As a general rule, it is more important in the arts to know the limits of the resistance of the substances employed to efforts of com pression, and it thus happens that the majority of the experiments, made upon the physical properties of those bodies, have been made with a view to the solution of that class of investigations. The law before stated, as applying to the resistance to extension, sensibly holds with respect to compression, and it is expressed by the formula N= A n, in which N = the total effort exercised normally to the direction of the base, A = the sectional area of the prism, and it = the resistance for every unity of the section. When, however, the bodies pass certain lengths, compared with the dimensions of their sides, the resistances to compression cease to follow the ordinary Law, and it becomes necessary to divide the theoretical results, obtained by the application of the tables of resistance, by a co-efficient varying with the propor tionate length of the prism to the diameter of the polygon circum scribed upon its base. Thus, when the diameter of the polygon is in a lesser ration than 1 to the following tabular numbers, representing the height, the co-efficient becomes, in each ease, as under : Again, the form of the body experimented upon, and the relative positions of its molecules, have an important influence on its resistance, for \lent has shown (` Annales des Ponta et Chaussdes,' 1S33) that the resistance of a cylinder of stone to compression, in a direction at right angles to its bedding, is rather greater iu proportion than that of the circumscribed square; a cylinder laid flat crushes under a weight which does not exceed of the one required to crush it when loaded on end ; and the inscribed sphere will crush under of the load of the cylinder. Compound substances were found to crush more readily than homogeneous ones; that is to say, that cubes of stone built up of several pieces were found to crush more easily than monoliths did ; but the general conditions of their resistance to compression were, after clue allowance for this law, pre cisely analogous to those of solid bodies. In fact, in large masses of masonry, the resistance to efforts of compression is regulated by the resistance of their weakest parts, that is to say, by the resistance of the mortar used ; and if it were required to calculate within safe limits the condition of the stability of a lofty pier, it would also be necessary to apply the co-efficient for the relative heights and base.s just quoted. Vicat observes that in many eases loads. which for as much as 95 days were not able to produce any perceptible effect upon the bodies exposed to their compressive action, were able ultimately to destroy them ; and he thence inferred that it was not safe to employ any materials, under efforts of permanent compression exceeding of the effort required to produce instantaneous rupture. In the case of substances possessing very imperfect elasticity a diminution of volume may frequently be produced by an effort of compression, which would not be recovered if that effort were withdrawn, even though the substance had not begun to disintegrate, nor its molecules had lost their cohesion. The clays and helms, so frequently met with in foundation works, are exposed to this peculiar action ; and it requires to be taken seriously into account in building operations. Water is one of the imperfectly elastic bodies, but it resists compres sion with very great energy.
Temperature has a decided influence upon the powers of resistance of bodies to efforts of compression. For an increase of temperature, beyond the atmospheric average, diminishes in a gradually accelerating ratio the solidity of the bodies, whilst a decrease of temperature, below the freezing point, by affecting the powers of cohesion (or in common phrase by its rendering the bodies more brittle), causes the bodies to break up more rapidly. In materials obtained from stratified
deposits, such as the decidedly laminated building stones, itc., Vicat found that the resistance to compression was much greater when the effort was applied in a direction perpendicular to the bedding, than when it was applied in a direction parallel to the beds; and in fibrous materials the resistance to efforts, either of extension or of compres sion, is the greatest when those efforts are applied in the direction of the fibres. In this last-named class of materials it is especially necessary to preserve them from flexure in their length ; and thence also the necessity for observing the proportions before stated between the various conditions of base, height, and load. As it has been ascertained, theoretically and experimentally, that when the mass of a body is arranged in the form of a hollow body, the resistance is nearly doubled, (when the thickness of the cylinder is made about as of the diameter,) it becomes an additional reason for using hollow columns of metal to support heavy loads, because, in the first place, the powers of resistance to compression are increased, and, in the second, there is less danger of flexure, when the diameter of the body is thus made as large as possible.
In the works of Tredgold, Ilodgkinson, Tate, Barlow, Moseley, Willis, Whewell, Morin, Navier, l'rony, Breese, Claude], Bourdaie, Daguin, Jamin, &c., the various conditions of the resistance of solid bodies, and of the forms of greatest resistance, are discussed in great detail; and the reader is referred to them, should he require to examine any complicated problem of this description. It may suffice here to say that the condition most commonly occurring in practice is, when a rectangular beam is exposed to a load acting either longitudinally, or transversally, to its axis. In the former case the whole action is either of compression or of extension, as the case may be, and in addition to what has been before stated, it is only necessary to observe that it is essential, in order that the action should be uniform, that the load should be brought to bear evenly over the whole area. When beams are, however, exposed to efforts acting transversally to their axes, the laws of their resistance become more complicated, for the deflections produced cause sonic of the fibres to pass into a state of tension, whilst some of the others are compressed, and some of them remain in a neutral state, as long as the limits of elasticity of the extended or compressed fibres are not exceeded. The modes of loading solid bodies are usually considered to be classed under the following heads, and the fornmhe for calculating their resistances have been deduced from the known laws of mechanics. 1. When one extremity of the beam is firmly embedded hi masonry at one end and acted upon by a force, r, applied at the other; then, calling the lever of the beam L ; the resistance to compression and extension, n; the moment of Inertia of the beam at the point of its bedding. I; and the distance of the line of the neutral fibres from the most distant point of the section of the part fixed, n ; E I L = ; As in a regular prism of a rectangular section n = and the moment of inertia is i — —; this formula becomes P L = n6 — in 6 12 which 6 = the transverse section of the prism perpendicular to the direction of the force P, and h = the section parallel to that direction.
The deflection f would be represented by f = ; in which the new e term E represents the modulus of elasticity.