A tapered (structural steel) column with a circular cross-section varies linearly from a radius of 25 mm to 15 mm over a length of 250 mm. If the column is hanging from its broad end, determine the maximum stress and the total change in length due to the weight. If there is an additional axial force of P applied at the bottom end, determine the maximum stress. When is the stress due to P of the same order of magnitude as that due to the weight of the bar? When can you ignore the stress induced in the bar due to its own weight?