Greenhill's Formula and the Mechanics of Cable Hockling

: In the application of marine cables as tension members, serious structural failures have occurred as a result of hockling (forming of a loop under torsion combined with insufficient tension). This report endeavors to establish a criterion on end torques and forces for preventing hockling. It is shown that for rods in tension the torque corresponding to Greenhill's 100-year- old formula defining the onset of bending is also the maximum torque which can be sustained at that tension. Thus, a straight rod or cable loaded by tension and the Greenhill torque is unstable, and Greenhill's formula modified by an appropriate safety factor provides the desired no-hockle criterion. For long straight rods or cables under tension T and twisting moment M, this criterion for stability is M sq. 4TEI, where EI is the bending stiffness under load. The approach used was to numerically solve in nondimensional form the two-point boundary-value problem of the rod under axial end torques and forces. The report includes curves showing torques and forces for the possible range of deflection curves.