A large vertical shaft is planned for an underground hard rock mine. Laboratory tests on core from exploration drilling show that

Co = 21,500 psi, To = 1,530 psi, E = 6.25(106) psi,

G = 2.5(106) psi, γ = 144pcf

while premining stress measurements can be fit to the formulas

SE = 200 + 0.3h, SN = 600 + 0.9h, SV = 1.1h, where E,N, V refer to compass coordinates (x = east, y = north, z = up) and compression is positive. Premining shear stresses are nil relative to compass coordinates. Find:

(a) The most preferable shape of shaft (elliptical, rectangular, or ovaloidal) when the cross section is 14 × 28 ft and

(b) The resulting factors of safety with respect to compression and tension at a depth of 2,800 ft.