Transactions . Fig 7 -Strain Produced by Torsional Stress. The value of 3s the linear component of volumetric elasticity, is,for glass, 17,400,000,1b. per square inch a8 If a shear is applied to a unit cube, Fig. 7, it winshown, by -f. This is equivalent to compressing it along the diago- 104 THE LAWS OF JOINTING. nal BD by an amount f l/2/i and expanding it by an equal amount along the diagonal A C. The proportional compression and expan-sion along the direction of these diagonals are respectively obtainedby dividing the deflection by the length of the diagonals. As theselengths are approxima
Transactions . Fig 7 -Strain Produced by Torsional Stress. The value of 3s the linear component of volumetric elasticity, is,for glass, 17,400,000,1b. per square inch a8 If a shear is applied to a unit cube, Fig. 7, it winshown, by -f. This is equivalent to compressing it along the diago- 104 THE LAWS OF JOINTING. nal BD by an amount f l/2/i and expanding it by an equal amount along the diagonal A C. The proportional compression and expan-sion along the direction of these diagonals are respectively obtainedby dividing the deflection by the length of the diagonals. As theselengths are approximately j/jj in each case, the proportional compres- f 1 f sions and expansions are —r= X —7=- = o~- From an inspection of the stress relations in Fig. 8 it will also beseen that a shearing stress f on the unit diagonal is equivalent to two f * compressive forces —7^ and two expansive forces - = on the sides of 1/2 1/2. • Fig. 8.—Kelation of Torsional, to Direct Stresses. the cube. As the sides of the cube on which these forces act is 1 —7= the corresponding compressive and expanding stresses are f in each case. The value of 2 /*, the linear component of rigidity, is, for glass,5,800,000 lb. per square inch. Stress in One Direction Only.—The modulus of elasticity, used inengineering problems, is a combination of « and fi. In finding it adirect stress is applied in one direction only. In the diagram Fig. 9 presume a fluid compressive force f is firstapplied equally in all directions on the unit cube shown. The dimi- THE LAWS OF JOINTING. f 105 nution of each single dimension is — Now apply shears such that there are no resultant forces on the cube in the y and ^directions. fThis will be equivalent to expanding the cube by — in each of these directions and compressing it in the x direction by equal amounts. f fThe stress in the x direction is then 3f and the strain _ ?] The ratio of thes
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