The introduction of friction into the analysis of buckling stability causes problems. For sliding friction, the friction force is fully developed for small lateral motion, while the destabilizing effect of the axial force is proportional to the lateral motion. Because the sliding friction force develops so rapidly and destabilizing effects develop so slowly, buckling is essentially impossible.

But we know that pipe buckles with friction! In conventional analysis, the only possibility for buckling is to have an initial non-zero lateral displacement, so that the axial force contribution may exceed the fully mobilized friction force. This initial displacement cannot normally be accurately estimated, so the force needed to buckle pipe with sliding friction is essentially unknown.

A cylindrical pipe has another possible mode of lateral displacement. Instead of sliding, the pipe can roll. In this case, the friction force developed is static friction. Static friction may take on any value between zero and the peak static friction value, where the value of the static friction is usually determined from a balance of known forces in the problem of interest. Here, the magnitude of the static friction is determined from a balance of torsional forces on the pipe. The key fact is that the friction force develops gradually, so we may determine a critical buckling force in the traditional sense.

The introduction of axial torque adds further complications to the buckling analysis. This paper develops a comprehensive model for pipe with axial forces and torque, and then develops the critical buckling loads for three cases of interest. The first case corresponds to the pipe in the wellbore, as investigated by Dawson, Paslay, He, and Kyllingstad. The second problem looks at a pipe lying on a flat plane, as a pipeline on the seabed. In both cases, a critical buckling load is determined for pipe whose lateral motion is constrained by friction. The third case finds the critical buckling load for rotating pipe. Several sample calculations are performed to illustrate the importance of friction forces in the stability of tubing and in the stability of seafloor flowlines.