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Unformatted text preview: denoted by PI, Pa,. . . , P n and their magnitude by PI, P2, . . . , Pn. Then the ratios PI : P2 : . .. : P,, remain fixed. When such a set of forces is applied on the body, the body deforms. Let the displacement at an arbitrary point in an arbitrary direction be measured with respect to a rectangular Cartesian frame of reference fixed with the supports. Let this displacement be denoted by u. Then our second hypothesis is (H2) Hookes law; where al, a2,. . . ,a, are constants independent of the magnitude of PI, Pz,. . . , P,. The constants all a2,. . . ,a, depend, of course, on the loca- tion of the point at which the displacement component is measured and on the directions and points of application of the individual forces of the loading. Hookes law in the form (H2) is one that can be subjected readily to direct experimental examination. To complete the formulation of the theory of elasticity, we need a third hypothesis:...
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- Fall '05