In this paper, the buckling equation and natural boundary conditions are derived with the aid of calculus of variations. The natural and geometric boundary conditions are used to determine the proper solution that represents the post-buckling configuration. Effects of friction and boundary conditions on the critical load of helical buckling are investigated. Theoretical results show that the effect of boundary conditions on helical buckling becomes negligible for a long pipe with dimensionless length greater than 5π. Velocity analysis shows that lateral velocity approaches infinity and lateral friction becomes dominant at the instant of buckling initiation. Thus, friction can significantly increase the critical load of helical buckling. However, once buckling is initiated, axial velocity becomes dominant again, and lateral friction becomes negligible for post-buckling behavior and axial load transfer analysis. Consequently, it is possible to seek an analytical solution for the buckling equation. To verify the proposed model and analytical results, the authors also conducted experimental studies. Experimental results support the proposed solutions.

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