Problem:
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 ? = 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 szz, tyz, tzx (in psi or MPa);
3 the stresses sxx, syy, and tyx (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 s1, s2, s3, Where s1 = s2 = s3 (tension is positive) and sketch;
7 the magnitudes of the principal stresses s1, s2, s3; Where s1 = s2 = s3 (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.