Determine elongation because of self weight of conical bar, Mechanical Engineering

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

1414_Determine elongation because of self weight of conical bar.png

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

From similarity of ?ABC and DEC,
1403_Determine elongation because of self weight of conical bar1.png 
As a result of this load, elemental length dy elongates by small amount Dy and
612_Determine elongation because of self weight of conical bar2.png 
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
550_Determine elongation because of self weight of conical bar3.png 
Where ρ is mass density of bar material                                                                              

 

Posted Date: 10/23/2012 1:32:12 AM | Location : United States







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