A deepwater drilling operation consists of a long "drill string," or pipe, that extends from a floating drilling platform to the wellbore below the se afloor. At the bottom end of the pipe, there is a drillbit that does the actual drilling through rock and sediment. The pipe is subject to the following loads: 1) a torque (to effect the drilling), 2) external pressure (due to the pressure of the mud slurry that surrounds the pipe), and 3) an axial force (due to the weight of the long length of pipe). Regarding this last one, the drilling platform actually exerts an upward force on the drill string equal to two-thirds of the string's weight. The other one-third of the weight is supported by the upward reaction on the drillbit. Please calculate the principal stresses in the wall of the pipe just above the drillbit. Here are the relevant loads and parameters: length of drill string = 4000 m
pipe diameter = 220 mm
pipe wall thickness = 8.0mm
pipe mass = 43.0kg/m
appliedt orque = 7.0kN. m
down-hole external pressure = 41.0MPa

Relevant facts:
1. As always, drawing a sketch will help visualize things here.
2. The loads of interest on the pipe just above the drillbit are the external pressure, the torque, and the axial force due to the upward reaction on the drillbit.
3. For a thin-walled pressure vessel, an external pressure can just be treated as an internal pressure that is negative.
4. The stress states produced by each of the three loading modes just add together. The best way to see how the stress components add is to make a sketch of a small square material element taken from the pipe wall.