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 + x²/100) mm² where x is distance from one end in cm. Take E = 200 GN/m².

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 + x²/100)]

The total elongation of the bar is then worked out by integrating the above identity between the limits

x = 0 to x = L