Page:Elementary Text-book of Physics (Anthony, 1897).djvu/130

116 stress these forces are normal to their respective faces, and the tetrahedron will be in equilibrium when the components of the force $$X$$ are equal respectively to the forces applied to the other faces; that is, when $$Xa. l = P. al, Xa. m = Q. am, Xa. n = R. an$$; that is, when $$X = P = Q = R$$.

It has been stated that the stresses in a body may always be represented by the combination of three longitudinal stresses at right angles to each other. Since a longitudinal stress may be replaced by a hydrostatic stress and two shearing stresses, it follows that any stress in a body may be replaced by a hydrostatic stress and a proper combination of shearing stresses.

'''102. Relations of Stress and Strain. Modulus of Elasticity.'''—When a body serves as the medium for the transmission of stress it experiences a deformation or strain, the type of strain depending upon the stress applied. The resistance offered by a body to deformation is ascribed to its elasticity. If the body be deformed in a definite way by a given stress, and recover its original condition when the stress is removed, it is said to be perfectly elastic. If the deformation of a body do not exceed the limits within which it may be considered perfectly elastic, it may be proved by experiment that the strain is of the same type as the stress and proportional to it. This law was proved for certain cases by Hooke, and is known as Hooke's Law.

The ratio of the stress applied to the strain experienced by a unit of the body measures the elasticity of the substance composing the body. This ratio is called the modulus of elasticity of the body, or simply its elasticity; its reciprocal is the coefficient of elasticity. It is of course understood that the stress and strain are of the same type. Thus, for example, the voluminal elasticity of a fluid is measured by the ratio of any small change of pressure to the corresponding change of unit volume. The tractional elasticity of a wire stretched by a weight is measured by the ratio of any small change in the stretching weight to the corresponding change in unit length.

Since all stresses may be reduced to hydrostatic stresses and