Find out extension:
Q: A bar having length 25mm has varying cross section. It carries load of 14KN. Find out extension if cross section is given by (6 + x^{2}/100) mm^{2} where x is distance from one end in cm. Take E = 200 GN/m^{2}.
Sol.: Consider small element of length dx at distance x from small element. Because of tensile load applied at ends, element length dx elongates by small amount Δx, and
Δx = Pdx/AE = Pdx/[(6 + x^{2}/100)]
The total elongation of the bar is then worked out by integrating the above identity between the limits
x = 0 to x = L