Determine the elongation of plate, Mechanical Engineering

Determine the elongation of plate:

Q: A steel bar AB which is having uniform thickness 2 cm, tapers from 1.5 cm to 7.5 cm uniformly in a length of 50 cm. From 1st principles determine the elongation of plate; if axial tensile force of 100 kN is applied on it. [E = 2 x 105 N/mm2]

Sol.: Consider small element of length dx of plate, at a distance x from larger end. Then at this section,

Width wx=   1667_Determine the elongation of plate.png 

Cross-section area A = thickness × width =  236_Determine the elongation of plate1.png 

1061_Determine the elongation of plate3.png

100_Determine the elongation of plate2.png

∴ Elongation of elementary length,
925_Determine the elongation of plate4.png 
The total change in length of plate can be worked out by integrating above identity between the limits  x = 0 and x = 400 mm. That is:
1567_Determine the elongation of plate5.png 

Posted Date: 10/20/2012 8:56:27 AM | Location : United States

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