The elasticity and resistance of the materials of engineering . stress, and E^ the corresponding coefficient. Hence: /, =r EJ,, or, ^, = y (2) ELASTICITY IN AMORPHOUS SOLID BODIES. [Art. 3. E^, consequently, is the coefficient of elasticity for compres-sion. The characteristic strain for a shearing stress may be deter-mined by considering the effect which it produces on the layersof the body parallel to its plane of action. In Fig. I let ABCD represent one face of a cube, anotherof whose faces is fixed along AD, If a shear acts in the faceBC^ whose plane is normal to the plane of thepaper, all
The elasticity and resistance of the materials of engineering . stress, and E^ the corresponding coefficient. Hence: /, =r EJ,, or, ^, = y (2) ELASTICITY IN AMORPHOUS SOLID BODIES. [Art. 3. E^, consequently, is the coefficient of elasticity for compres-sion. The characteristic strain for a shearing stress may be deter-mined by considering the effect which it produces on the layersof the body parallel to its plane of action. In Fig. I let ABCD represent one face of a cube, anotherof whose faces is fixed along AD, If a shear acts in the faceBC^ whose plane is normal to the plane of thepaper, all layers of the cube parallel to theplane of the shearing stress, ^ BCy will slideover each other, so that the faces AB and DCwill take the positions AE and DE. Theamount of distortion or strain per unit of lengthwill be represented by the angle EAB = cp. Ifthe strain is small there may be written ^, sm cpor tan cp , therefore, the intensity of shear, coefficientand strain by 5, G and q)^ respectively, Eq. (i) of Art. i be-comes :. 5 = Gcp^ or, G = 9 (3) It will be seen hereafter that there are certain limits ofstress within which Eqs. (i), (2) and (3) are essentially true,but beyond which they do not hold ; this limit is called the limit of elasticity, and is not in general a well definedpoint. Art. 3.—Lateral Strains. If a body, like that shown in Fig. i, be subjected to ten-sion, all of its oblique cross sections, such as EE and GH, willsustain shearing stresses in consequence of the componentsof the tension tangential to those oblique sections. These Art. 3.] LATERAL STRALNS. 5 tangential stresses will cause the oblique sections, in bothdirections, to slide over each other. Consequently tJie normalcross sections of the body will be decreased; and if the normalelasticityresist00burr
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