Page:The New International Encyclopædia 1st ed. v. 18.djvu/722

* STRENGTH OF MATERIALS. 624 STRENGTH OF MATERIALS. stresses such as flexure and torsion are capable of being resolved into tension, compression, and shearing stresses. A unit stress: is the stress per unit of area; the unit of area is the square inch iu English-.spcakinjj countries and the square centimeter in countries where the metric system of measures prevails. In all cases of direct stress the total stress is supposed to be uniformly distributed over the area of the cross-section. When a tensile or compressive force is applied to a bar of metal it elongates or is shortened, and up to a certain limit the elongation or short- ening is proportional to the load. Beyond this limit the elongation or shortening increases more rapidly than the load. The unit stress at which the deformations begin to increase in a faster ratio than the stress is called the elastic limit, or less commonly the elastic strength. 'hen the unit stress in a bar is less than the elastic limit, the bar returns, when the stress is removed, to its original dimensions. When, however, the unit stress is greater than the elastic limit, the bar does not fully return to its original dimensions, but a permanent distortion remains. Therefore, if a material is strained beyond its elastic limit, a permanent injury results to its elastic prop- erties; and for tliis reason it is the universal practice in designing engineering structures to make certain that the unit stresses never exceed the elastic limit of the material. When a ma- terial is under a stress exceeding its elastic limit it is usually in an unsafe condition. If the stress be increased the deformation rapidly increases until finally the material ruptures. The unit stress which occurs just before rup- ture takes place is called the ultimate strength of the material. The ultimate strengths of ma- terials are from two to four times as great as their elastic limits. The strength of materials is determined by straining a piece of the ma- terial to rupture and ob.serving the elastic limit, ultimate strength, and other coordinate phenom- ena. Tension. In testing a material under tension a 'test piece' or 'test specimen.' usually eight inches long and one square inch in section, is broken by direct pull. The loads are gradually applied. At first each increment of load pro- duces a proportionate increment of elongation, but after the load has reached a certain amount the elongation begins to increase more rapidly than the load. The unit load recorded just as this change in the rate of deformation takes place is the elastic strength or the elastic limit of the material. As the load continues to in- crease the elongation increases more rapidly than the load and is commonly accompanied by a reduction in area of the cross-section of the te.st piece. Finally the test piece breaks and it3 ultimate strength is recorded. Record is also taken of the total elongation of the piece and of the total reduction of area. These last two rec- ords are indices of the ductility of the material. The usual records of a tensile test of materials consist, therefore, of figures showing the elastic limit, the ultimate strength, the percentage of elongation, and, often, the percentage of reduc- tion of area. These values vary greatly for dif- ferent kinds of materials and considerably for different qualities of the same material. In printing figures for illustration, therefore, the best that can be done is to select rough average values. The following figures are taken from Prof. Mansfield Merriman's The Strength of Ma- terials (New York. 1897). which will be found an excellent discussion of the subject for the non-technical reader : MATERIAL. Elastic limit. Ibe. per eq. inch. Ultimate strength, lbs. per BQ. inch. Ultimate eloni^ation, per cent. Timbpr. 3,000 6.000 25,000 50,000 10.000 211.01 III 5.'). lino 100. ouo 1 5 Cast iron 5 Steel Compression. In testing for compressive strength the test piece used is short and thick, a cube and a short cylinder being the common forms of test pieces. The phenomena which oc- cur are substantially as in tension, first a dis- tortion proportional to the load until the elastic limit is reached, and then a distortion increasing more rapidly than the load increases until rup- ture occurs. The manner in wiiicli rupture oc- curs is quite different from the manner in which it occurs in tension. In tension the material draws down to a smaller diameter and finally parts by a more or less ragged fracture at ap- proximately right angles to the direction of the pull ; in compression the test piece first bulges to an increased diameter and then ruptures with a fracture oblique to the direction of the pressure. This method of fracture occurs only when the test piece is thick compared with its height; when the height is great comjiared with the thickness lateral flexure or bending occurs and the conditions of rupture are no longer those of simple compression, as it is explained in the suc- ceeding pai'agraph on the strength of columns. As was the case with tension, only rough average figures of comparative strength can be given, owing to the fact that this strength varies for different materials and with different qualities of the same material. The following figures are quoted from the work of Professor Merriman which is named above: .MATERIAL Timber Stone Cast iron Wrought iron Steel EliiBtic Ultimate limit. strenprth. lbs. per sq. lbs. per sq. inch inch 3.000 8.000 6.000 20.000 90.000 2.^,000 55,000 50,000 150,000 Shear. Shear is the stress produced by two parallel forces acting on the material in opposite directions, as. for example, do the blades of a pair of shears. If a weight be suspended by a bar which is composed of two shorter bars connected at one end by a rivet or bolt passing through them, the stress brought upon the rivet is a shearing stress. The same stress is exerted by a punching machine in punching holes in metal plates. The shearing strength of materials often differs according to the direction in which the shearing forces are exerted. Thus the shearing strength of timber is much less along the .grain than at right angles to the grain. The follow- ing figures taken from Professor Merriman's book named above give the average ultimate shearing strengths of the more common struc- tural materials: