Umair,
In simple terms: Imagine the bahavioural changes in a beam when it is loaded by a lateral force and when it is loaded by a tensile force as well as the lateral force. Is it not the case that it is easier to bend it with the lateral force alone? Instead of tensile force if you use compressive force the bahaviour is just the opposite ( recall bifurcation buckling) .
The above phenomenon is what is known as geometric stiffening , this is a type of non linearity knwon as geometric non linearity.The addition or reduction in stiffness is not a function of the material and dimensions of th beam while the conventional stiffness ( AE/L, EI/L^3,GJ/L etc )of the beam is a function of these parameters. Stress stiffening is this phenomenon.
Bourdon effect on the other hand is extension of the pipe due to pressure loading. A very simple case: If the pipe is a loaded with a force at each end= PXA, is its axial extension not equal to:PD/4ET ( considering poisson ratio =0)? Treat it like displacement induced loading.
Regards
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anindya