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Strain measurements are made on a wide, flat bench in a dimension stone quarry using a 0-45-90 rosette. The 0-gauge is oriented N60E. Specific weight of the stone (a granite) is 162 pcf (25.6 kN/m3); Young’s modulus E = 12.7(10)6 psi (87.59 GPa) and Poisson’s ratio ν = 0.27. Tension is considered positive. Measured strains in micro units per unit are:

(0) = −1480, (45) = −300, (90) = −2760 Find (where x = east, y = north and z = up):

1 the strains xx, yy, xy (tonsorial shear strain);

2 the stresses σzz, τyz, τzx (in psi or MPa);

3 the stresses σxx, σyy, and τyx (in psi or MPa);

4 the strain zz (micro inches per inch or mm/m);

5 the strains yz and zx (tonsorial shear strains);

6 the direction of the true principal stresses σ1, σ2, σ3, Where σ1 ≥ σ2 ≥ σ3 (tension is positive) and sketch;

7 the magnitudes of the principal stresses σ1, σ2, σ3; Where σ1 ≥ σ2 ≥ σ3 (tension is positive);

8 the magnitudes of the principal strains 1, 2, 3;

9 the directions of the principal strains; and sketch;

10 the change v in volume per unit volume that would occur if the stresses were Entirely relieved, that is reduced to zero, for example, by over coring the rosette.

(0) = −1480, (45) = −300, (90) = −2760 Find (where x = east, y = north and z = up):

1 the strains xx, yy, xy (tonsorial shear strain);

2 the stresses σzz, τyz, τzx (in psi or MPa);

3 the stresses σxx, σyy, and τyx (in psi or MPa);

4 the strain zz (micro inches per inch or mm/m);

5 the strains yz and zx (tonsorial shear strains);

6 the direction of the true principal stresses σ1, σ2, σ3, Where σ1 ≥ σ2 ≥ σ3 (tension is positive) and sketch;

7 the magnitudes of the principal stresses σ1, σ2, σ3; Where σ1 ≥ σ2 ≥ σ3 (tension is positive);

8 the magnitudes of the principal strains 1, 2, 3;

9 the directions of the principal strains; and sketch;

10 the change v in volume per unit volume that would occur if the stresses were Entirely relieved, that is reduced to zero, for example, by over coring the rosette.

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