STRENGTH.
The effects of forces of different kinds, on the ma terials employed in the mechanical arts, require to be minutely examined in the arrangement of every work dependent on them ; and of these effects, as exhibited in a solid body at rest., we may distinguish seven different varieties : the extension of a sub stance acting simply as a tie ; the compression of a block supporting a load above it ; the detrusion of an axis resting on a support close to its wheel, and re sisting by its lateral adhesion only ; the flexure of a body bent by a force applied unequally to its differ ent parts ; the torsion or twisting, arising from a par tial detrusion of the external parts in opposite direc tions, while the axis retains its place ; the alteration or permanent change of a body which settles, so as to remain in a new form, when the force is with drawn ; and lastly, the fracture, which consists in a complete separation of parts before united, and which has been the only effect particularly examined by the generality of authors on the strength of ma terials.
The analogy of the laws of extension and com pression has been demonstrated in a former article of this volume, and their connexion with flexure has been investigated : but it is not easy to compare them directly with the resistance opposed to a par tial detrusion, the effects of which are only so far understood as they are exhibited in the phenomena of twisting : and these appear tojustify us in consi dering the resistance of lateral adhesion as a primi tive force, deduced from the rigidity or solidity of the substance, and proportional to the deviation from the natural situation of the particles. The re sistance exhibited by steel wire, when twisted, bears a greater proportion to that of brass than the re sistance to extension or compression ; but the forces agree in being independent of the hardness produced by tempering.
Flexure may be occasioned either by a transverse ar by a longitudinal force : when the force is trans verse, the extent of the flexure.is nearly proportion al to its magnitude ; but when it is longitudinal, there is a 'certain magnitude which it must exceed, in order to produce or rather to continue the flexure, if the force be applied exactly at the axis. But it is equal•
ly true that the slightest possible force applied at a distance from the axis, however minute, or with an obliquity however small, or to a beam already a lit tle curved, will produce a certain degree of flexure; and this observation will serve to explain some of the difficulties and irregularities which have occurred, in making experiments on beams exposed to longitudi nal pressure.
Stiffness, or the power of resisting flexure, is measured by the force required to produce a given minute change of form. For beams similarly fixed, it is directly proportional to the breadth and the cube of the depth, and inversely to the cube of the length. Thus a beam or bar two yards long will be equally stiff with a beam one yard, provided that it be either twice as deep,.or eight times as broad. If the ends of a beam can be firmly fixed, by continuing them to a sufficient distance, and keeping them down by a proper pressure, the stiffness will be four times as great as if the ends were simply supported. A hollow substance, of given weight and length, has its stiffness nearly proportional to the square of the dia meter : and hence arises the great utility of tubes, when stiffness is required, this property being still more increased by the expansion of the substance than the ultimate strength. It is obvious that there are a multiplicity of cases in Carpentry where stiff ness is of more importance than any other property, since the utility as well as beauty of the fabric might often be destroyed by too great a flexibility of the materials.
If we wish to find how much a beam of fir will sink when it is loaded in the middle, we may multi ply the cube of the length in inches by the given weight in pounds, and divide by the cube of the depth, and by ten million times the breadth : but on account of the unequal texture of the wood, we must expect to find the bending somewhat greater than this in practice, besides that a large weight will often produce an alteration, or permanent settling, which will be added to it : a beam of oak will also sink a little more than a beam of fir, with the same weight.