Given The Stresses Relative To Compass Coordinates

Given the stresses relative to compass coordinates (x = east, y = north, z = sup), σxx = 2,155, σyy = 3,045, σzz = 4,200, τyx = −1,222, τxz = 0, τyz = 0 in psi with compression positive, find the principal stresses σ1, σ2, σ3 (magnitude and orientation). Show with a suitable sketch. Then consider an unlined shaft that will be 13 ft by 26 ft in section, chose the best opening shape (ellipse, ovaloidal, or rectangle) and best orientation from the rock mechanics perspective, assuming the given stress state is critical to the design. Sketch

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