The elasticity and resistance of the materials of engineering . d to any state of stress whatever. At any point as O^Fig. I, let there be assumed any three rectangular co-ordinateplanes; then consider any small rectangular parallelopipedwhose faces are parallel to those planes. Finally let thestresses on the three faces nearest the origin be resolved into Art. 5.] STJ?£SSES IN TERMS OF STRAINS. components normal and parallel to their planes of action,whose directions are parallel to the co-ordinate axis. The intensities of these tangential and normal componentswill be represented in the usual
The elasticity and resistance of the materials of engineering . d to any state of stress whatever. At any point as O^Fig. I, let there be assumed any three rectangular co-ordinateplanes; then consider any small rectangular parallelopipedwhose faces are parallel to those planes. Finally let thestresses on the three faces nearest the origin be resolved into Art. 5.] STJ?£SSES IN TERMS OF STRAINS. components normal and parallel to their planes of action,whose directions are parallel to the co-ordinate axis. The intensities of these tangential and normal componentswill be represented in the usual manner, ,^ p^y signifies atangential intensity ona plane normal to theaxis of X (plane ^F),whose direction is paral-lel to the axis of F,while pxx signifies theintensity of a normalstress on a plane nor-mal to the axis of X(plane ZY^ and in thedirection of the axis ofX. Two unlike sub-scripts, therefore, indi-cate a tangential stress, while two of the same kind signify anormal stress. From Eq. (3) of Art. 2 and Eq. (7) of Art. 4, there is atonce deduced :. 5 = E 2(1 + r) q) — Gq) (I) Now when the material is subjected to stress the linesbounding the faces of the parallelepiped will no longer be atright angles to each other. It has already been shown in that the angular changes of the lines, from right angles, arethe characteristic shearing strains, which, multiplied by G, givethe shearing intensities. Let 9?j be the change of angle of the boundary linesparallel to X and Y. Let ^2 be the change of angle of the boundary linesparallel to Fand Z. 10 ELASTICITY IN AMORPHOUS SOLID BODIES. [Art. 5. Let ^3 be the change of angle of the boundary linesparallel to Z and X, Eq. (i) will then give the following three equations: ^- = W^) ^- •••••• (2) A«=^(I^)«3 (4) In Fig. I let the rectangle agfh represent the right pro-jection of the indefinitely small parallelopiped dx dy dz. IfM^ V and zv are the strains, parallel to the axis of x, y and z, of the origina
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Keywords: ., book, bookcentury1800, booksubjectbuildingmaterials, bookyear1883
