Determine elongation because of self weight of conical bar:

Sol.: Consider conical bar ABC of length L with the diameter d fixed rigidly at AB. Let attention be focused on small element of length dy at distance y from lower end point C. Total tension P at the section DE equals weight of bar for length y and can be given by

Where ω is the specific weight of the bar material and ds = DE is diameter of elementary strip.

From similarity of ?ABC and DEC,
 
As a result of this load, elemental length dy elongates by small amount Dy and
 
The total change in length of conical bar because of self weight is worked out by integrating above expression between limits  y = 0 to  y = L
 
Where ρ is mass density of bar material