A rectangular shaft 12 ft by 24 ft is planned for deepening from a depth of 3,200 to 4,800 ft in ground where the preshaft stress state relative to compass coordinates (x = east, y = north, z = up) is...

A rectangular shaft 12 ft by 24 ft is planned for deepening from a depth of 3,200 to 4,800 ft in ground where the preshaft stress state relative to compass coordinates (x = east, y = north, z = up) is given by

S_xx
= 2, 000 + 1.1d, S_yy
= 50 + 0.9d, S_zz
= 1.15d, T_xy
= −350 − 0.3d, T_yz
= 0.0, T_zx
= 0.0

where compression is positive and d is depth below surface.

(a) Find the best orientation of the shaft at a planned 3,850 shaft station and show by sketch.

(b) Also show on the sketch where the peak stress concentrations are likely to occur.

(c) Finally, estimate the peak stress concentrations.