The ultimate stress, for a hollow steel column which carries an axial load of 1.9 MN is 480N/Sq(mm). If the external diameter of the column is 200mm. determine the internal diameter. Take factor of safety as 4?

Explanation: permissible stress = ultimate stess / factor of safety = 480/4 = 120N/Sq(mm),,also stress= force/area ,,, hence 120N/Sq(mm) = 1.9 x 1000000 N/ area of hollow steel column,, hence ,, Area of column= 1.9 x 1000000/120 = 15833.33 Sq(mm) ,, also Area = 0.785(external diameter^2 - internal diameter^2),,,hence by comparing area we get,,,15833.33 = 0.785 x (200 x 200 - internal diameter^2),, hence by solving we get,, 20169.85 =40000 - internal diameter^2,, also Internal diameter = (40000-20169.85)^0.5 =140.82 mm