The theories of Glock and Timoshenko present the border cases of buckling failure of circular cross section. From these there results
for the free pipe according to Timoshenko:
for the pipe-in-pipe system according to Glock:
In the comparison of the calculations of the buckling load values of the pipe-in-pipe system by Glock with the maximum loads determined from the FEM calculations, it can be seen that the curves for smaller relationships of t/Dm are very good approximations (Image 220.127.116.11.2.5.1-1). However, the critical load rise is greater from about t/Dm = 3 % in the FEM calculation than is to be expected from the Glock theory due to the fact that the whole pre-buckling behaviour is fully acquired.
The transition of the theoretical statement according to Glock for describing the critical buckling pressure of the circular cross section to the case of failure of an ovoid cross section by means of its maximum radius of curvature in the middle region is depicted in (Image 18.104.22.168.2.5.1-2). The values determined according to Glock for the system without gap for small wall thicknesses lie at 24 % and for large wall thicknesses at 41 % below the FEM results. The bearing capacity of the pipes is under-estimated so that an over-dimensioning of the pipe cross section can be the result. A non-linear calculation is thus to be preferred.