The following technique is sometimes used to connect tubular

The following technique is sometimes used to connect tubular components down oil wells. As manufactured, the smaller of the two tubes has inner and outer radii (b, c), while the larger has inner and outer radii (c, a), so that the end of the smaller tube can simply be inserted into the larger tube. An over-sized die is then pulled through the bore of the inner of the two tubes. The radius of the die is chosen so that both cylinders are fully plastically deformed as the die passes through the region where the two cylinders overlap. As a result, a state of residual stress is developed at the coupling, which clamps the two tubes together. For a/b = 1.2, calculate the value of c that gives the strongest coupling. Both steel tubes have the same material properties and, in particular, the same yield stress, sigma_Y = 500 MPa.

Solution

In this case,

a/c = c/b

so, c = (ab)^0.5

= (a*1.2a)^0.5

c= 1.095445a

or c = 1.314 b........Ans