RESISTANCE OF :MATERIALS. When solid bodies are exposed to the action of external forces, they are capable of resisting those forces by reason of the cohesion or of the elasticity they may possess, until their own powers are exceeded, when the particles of which the solid body in question is composed begin firstly to change their respective positions, and finally separate from one another. Within certain limits, the solid bodies in question are susceptible of resuming their original form after their particles have begun thus to change their positions (under conditions depending upon the nature of the external Glee) when the force is withdrawn ; and it is according to the energy and the mode of exhibition of this power that bodies are ranged in the classes of elastic or non-elastio bodies, of highly elastic or perfectly elastic bodies. the force is exercised in a direction parallel to the longitudinal axis of the body in a manner to pull or to extend it, the force is raid to be one of traction, or extension ; when it acts in the direction able to bind the particles of the body into closer contact, it is said to be an effort of compreasies • when it acts in a direction able to cause one part of the body to slide over the other,— or, in other words, to split it,—ths force is said to produce an effort of detrusion ; and when it acts so as to twist the particles or fibres of the material one over the other, the effort is said to be one of torsion. The terms elastic, highly elastic, and nonelastic bodies sufficiently explain themselves • but it may be desirable to acid that bodies arc said to be perfectly ;Jostle when they resist, with equal energy, efforts of compression and of extension. The best wrought iron is an illus tration of this property ; but iu the case of good cast iron, the resist ance to ecmmressiou is equal to nearly 6& times the resistance to extension : the former is nearly a perfectly elastic body, the latter is only imperfectly such. It was formerly considered that the com premien of solid bodies took place equally, or, in the words of Hooke, that et tensio, sic via ; but more recent experiments have shown that, beyond certain limits, the compression and extension take place with a greater degree of rapidity than would be proportional to the increase of the effort. The limits of equable resistance thus alluded to corre spond with the range of the unimpaired elastic powers of the body ; for if the effort should be such as to cause the body to compress or to extend with an accelerated velocity, the original dimensions and form will not be res.a.surned when the effort is withdrawn. Bodies so affected are snid to have had their permanent elasticity interfered with ; or their elasticity has been changed, so as to produce either a permanent elongation, contraction, or flexure, as the case may be.
There is a very important consideration which must always be borne in mind in determining the effort to be applied to any body, namely, that the length of time during which it is so applied has a material influence upon tho resistance; or, in other words, bodies will resist instantaneous efforts of far greater value than they can resist perma nently, without alteration iu their elasticity. It therefore becomes a matter of necessary precaution (in all building or mechanical operations), to keep the forme to which the various materials arc exposed consider ably within the limits of what would be able to produce instantaneous changes of their natural elastic states ; and this is the more necessary because the materials alluded to are, in practice, subject to shocks, jars, or accidental efforts, which may be of a serious nature.
Modulus of Elastieity.—If a prismatic, or cylindrical body of a given length, L, and an area A, be exposed to an effort of longitudinal traction in the direction of its axis P, it would extend under this action by a quantity we may call 1; and if this quantity should be proportional to the total length, in such a manner as that — L should be a constant quantity, it may be represented by i, and will represent the elongation for every unit of length. Now, so long as this quantity does not exceed the limits of the perfect elasticity of the material, i increases proportionally to the load and the area, or to the so that in fact is a constant quantity, called the co-efficient, or modulus of elasticity, and is usually expressed by E. If then, the transverse section were equal to the unity of surface, and the elongation i, for every unit of length, were equal to that unit of length A i = 1, and r = e would be the effort supported by the unity of suriace, and able to produce for the unity of length an elastic elongation equal to that unity. The same remarks will apply to efforts of compression, and it is generally admitted that the co efficient of elasticity has the mane value in the two cases, although in certain granular bodies this law does nut appear always to hold. As the relation T= AZ; becomes T= E i and from thence E when the load I' is supported by every unity of the section A, it ie easy to determine the value of s for every such unity of section, and thence to calculate the value of the load able to produce a given elongation of the body presenting that section, or to calculate the elongation pro duced by a given load, Krtenfion and compression.—A very great number of observations have been made for the purpose of.ateertaining, experimentally, the laws which regulate the extension of solid bodies, the results of which may be briefly stated as fellows. The load which is capable of producing rupture by extension, is directly proportional to the transverse section of the body considered ; and tho load has no reference to the length, provided the material be homogeneous, and the weight of the body be taken into account. The substances which have the highest co efficient of elasticity, are those which resist rupture by extension in the most energetic manner ; that is to say, they are the most tenacious. The temperature of the bodice considered must be taken into con sideration ; for the expansion produced by an increase of temperature in many eubstances acts in such a manner as to produce a longitudinal extension, whereas in others it produces a change in volume ; and this remark may be extended also to the changes which follow upon any alteration in the molecular structure of a body ; because, in the first place, every new crystalline arrangement is liable to produce some change in the volume of the substance, and iu the second, the relative positions of the axes of the crystals may, and often do, singularly affect the powers of resistance to extension. In a great number of the materials used in the arts the resistances to extension and to com pression are nearly equal; but there are cases (as for instance, building stones and cast iron) iu which there are marked differences in these respective powers.