A rectangular shaft 10 ft wide by 20 ft long is sunk vertically in ground where the state of premining stress is xx 1,141, yy 2,059, zz 1,600, xy 221, yz 0, zx 0, with compression positive, x east, y north, and z up, in psi Rock properties are E 4 5 10 6 psi, v 0 20, C o 15,000psi, T o 900 psi Find (a) The most favorable orientation of the shaft and (b) The safety factors in this orientation Indicate by sketch where the peak stresses occur in cross section

Question: A rectangular shaft 10 ft wide by 20 ft long is sunk vertically in ground where the state of premining stress is xx =

A rectangular shaft 10 ft wide by 20 ft long is sunk vertically in ground where the state of premining stress is σ_xx = 1,141, σ_yy = 2,059, σ_zz = 1,600, τ_xy = 221, τ_yz = 0, τ_zx = 0, with compression positive, x=east, y=north, and z =up, in psi. Rock properties are: E = 4.5 × 10⁶ psi, v = 0.20, C_o = 15,000psi, T_o = 900 psi. Find

(a) The most favorable orientation of the shaft and

(b) The safety factors in this orientation. Indicate by sketch where the peak stresses occur in cross section.

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