Text-book of mechanics . re inch. Strain. — When a bar is stressed it invariably changesin length. This deformation is called the total longi-tudinal strain. Instead of considering the total defor-mation, it is usual to specify the deformation per unitof length, and this is called the unit strain. Thus if abar / inches long is put in tension and lengthens Al inches,the unit longitudinal strain or simply the longitudinal strain = s = — • Relation between Stress and Strain. — The relationbetween stress and strain can be established only byexperiment. The machines used for this purpose areadmirab
Text-book of mechanics . re inch. Strain. — When a bar is stressed it invariably changesin length. This deformation is called the total longi-tudinal strain. Instead of considering the total defor-mation, it is usual to specify the deformation per unitof length, and this is called the unit strain. Thus if abar / inches long is put in tension and lengthens Al inches,the unit longitudinal strain or simply the longitudinal strain = s = — • Relation between Stress and Strain. — The relationbetween stress and strain can be established only byexperiment. The machines used for this purpose areadmirably described in Martens Handbook of TestingMaterials.* * English Translation by G. Henning. Wiley & Sons, N. Y. C. SIMPLE STRESSES 5 The diagramatic sketch, Fig. 2, will illustrate the gen-eral principle involved. By means of hydraulic pressureat A the test piece BC is put in tension, the force appliedbeing measured by means of the weight W. The lengthof a portion / of the test piece, well away from its ends,. Fig. 2 is measured (by means of micrometer screws) undervarious conditions of loading. Thus the total stress andthe corresponding total longitudinal strain are deter-mined experimentally. The results of experiments such as described above canbest be represented graphically. Consider, as an exam-ple, wrought iron. The curve obtained by plotting unit 6 MECHANICS OF MATERIALS stress and unit strain as ordinates and abscissas is repre-sented in Fig. 3. Fig. 3 shows that the strain is pro-portional to the stress up to the point marked point is known as the elastic limit. If the stretch-ing force be diminished to zero at any time before theelastic limit is reached, the test piece will return to its 40000 30000 ?aa §a 20000 10000 A U. r^ Y. // / /// / /// 0—^ Strain in inches per inchFig. 3 original length; that is, the strain will wholly disappear,and in plotting the results the line of return will followthe line to O. The point marked at which a s
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