STRENGTH OF MATERIALS. The relation between force and the distortion it produces in materials of construction (metal, stone, timber, etc.), the harmful effects of force, and the proportioning of materials safely to re sist given forces are studied under this title. For brief notes on the history of the subject see the article ELASTICITY.
Stress and Since forces are dis tributed over surfaces, and not concentrated at points as in the mechanics of rigid bodies, the concept of force-per-unit-area is of funda mental importance; it is called stress in this article although stress is generally used ak be ing synonymous with force; this use is con fusing as well as superfluous. If the stress is normal (perpendicular) to the surface on which it acts it is called normal, or tensile or corn pressive stress; if tangential it is called shear. The deformation resulting from the application of force may be manifested as a change of length, of area or cross-section, of volume; or of angle. The change of length (or area, or volume) per unit length (or area, or volume) is called linear (or areal, or volumetric) strain. Strains are purely numerical ratios; they are not lengths, areas or volumes. If a rectangle drawn on any plane in a stressed material is distorted into a parallelogram the change, in radians, of any one of its right-angles is called the shear strain for reasons which will be evi dent presently. The defotmation produced by stress requires time to develop. Tar, for in stance, is brittle or fragile under quickly ap plied loads and breaks, like flint, with a smooth conchoidal fracture. It behaves like a very rigid solid under sudden blows, but under the smallest forces applied for a long time it flows as if it were a liquid; under gradually applied large forces it is plastic and can be kneaded like dough or putty. Metals behave in the same kind of way but to a decidedly smaller extent. The full effect of stress is not produced im mediately although the greater part arises very quickly. If the stress is removed some of the distortion disappears at once, some takes hours, days or even months to vanish, and some re mains permanently. The property of recover ing from deformation is called elasticity. A
body that recovers completely and resumes its original dimensions is said to be perfectly elastic for the particular stress that acted on it. The slow return to shape, occurring during the second period of recovery, is the elastic after effect discovered by Weber in 1835; some very curious phenomena are associated with it. The after-effect has thus far been of no importance in engineering but it is not unlikely that its study will help to clear up difficulties met with in the molecular derangements resulting from stress. For an exhaustive account consult the article by Braun and Jaeger in Winkelmann's 'Handbuch der Physik,' Vol. I, 1908.
Laws of For many metals and certain other materials the laws of elasticity, i.e., the relations between stress and strain, are quite simple; they date from the time of Hooke in 1678. If a tensile or compressive force F is applied at the end of a rod or bar of length 1 and cross-section A it produces a change of length Al; if the force is not too large these quantities are connected by the experimentally discovered equation F In terms of stress and strain, putting F/A= p and 111/1—s, we have Es where E is a constant called Young modulus ; its value depends on the material and, within cer tain limits, not upon the stress. For iron and steel E is the same for tension as compression; for cast iron and stone this linear relation does not hold at all; for wood E depends upon whether p is along or across the grain. Typical values of E in pounds per square inch are steel (tens. or comp.) 30,000,000; cast iron (tens.) 15,000,000; concrete (comp.) 2,000,000; wood (along grain) 1,500,000.
When a bar is stretched (compressed) longi tudinally its cross-section gets smaller (larger) without change of shape, all transverse di mensions in any plane growing proportionally smaller (larger). If s is the longitudinal strain and s' the lateral strain — the strain of any line in a cross-section— s''== situ where m is constant for a given material and generally independent of the stress. lint is called Poisson's ratio (See article Et.Asncrrv) ; for steel and iron 1/m=0.3 approximately.