Risers anchored in a floating system and excited by a moderate sea state are often subjected to dynamic compression near the touchdown point, since the static tension in this region is usually very small. An analytical expression for the critical load of dynamically compressed risers was recently derived by Aranha et al. [1], whose results were compared with numerical simulations, showing a good agreement in several cases. This paper extends Aranha’s results by showing that the well-known Greenhill formula can be used to predict stability conditions in cables/risers having an initial curvature and subjected simultaneously to dynamic compression and twisting. This is done by extending Aranha’s reasoning, of a “local buckling length scale,” a little further, therefore creating a general procedure that enables one to obtain the buckling number $n$ appearing in the classical Greenhill formula. An application to rigid risers is presented and discussed.

1.
Aranha
,
J. A. P.
,
Pinto
,
M. O.
, and
Silva
,
R. M. C.
,
2001
, “
On the Dynamic Compression of Risers: an Analytic Expression for the Critical Load
,”
Appl. Ocean Res.
,
23
, pp.
83
91
.
2.
Atanackovic, T. M., 1997, Stability Theory of Elastic Rods, World Scientific Publishing Co., Singapore.
3.
Stump
,
D. M.
,
Fraser
,
W. B.
, and
Gates
,
K. E.
,
1998
, “
The Writhing of Circular Cross-Section Rods: Undersea Cables to DNA Supercoils
,”
Proc. R. Soc. London, Ser. A
,
A454
, pp.
2123
2156
.
4.
Love, A. E. H., 1959, A Treatise on the Mathematical Theory of Elasticity, 4th ed., Cambridge University Press.
5.
Rosenthal, F., 1976, “The Application of Greenhill’s Formula to Cable Hockling,” ASME J. Appl. Mech., pp. 681–683.
6.
Coyne
,
J.
,
1990
, “
Analysis of the Formation and Elimination of Loops in Twisted Cable
,”
IEEE J. Ocean. Eng.
,
15
(
2
), pp.
72
83
.
7.
Lu
,
C. L.
, and
Perkins
,
N. C.
,
1994
, “
Nonlinear Spatial Equilibria and Stability of Cables under Uni-axial Torque and Thrust
,”
ASME J. Appl. Mech.
,
61
, pp.
879
886
.
8.
Ramos Jr., R., 2001, “Analytical Models for the Structural Behavior Study of Flexible Pipes and Umbilical Cables” (in Portuguese), Ph.D. thesis, University of Sa˜o Paulo, Sa˜o Paulo.
9.
Gottlieb
,
O.
, and
Perkins
,
N. C.
,
1999
, “
Local and Global Bifurcation Analyses of a Spatial Cable Elastica
,”
ASME J. Appl. Mech.
,
66
, pp.
352
360
.
10.
Fe´ret
,
J. J.
, and
Bournazel
,
C. L.
,
1987
, “
Calculation of Stresses and Slip in Structural Layers of Unbonded Flexible Pipes
,”
ASME J. Offshore Mech. Arct. Eng.
,
109
, pp.
263
269
.
11.
Witz
,
J. A.
,
1996
, “
A Case Study in the Cross-Section Analysis of Flexible Risers
,”
Mar. Struct.
,
9
, pp.
885
904
.
12.
Pesce, C. P., 1997, “Mechanics of Submerged Cables and Pipes in Catenary Configuration: an Analytical and Experimental Approach” (in Portuguese), “Livre Doce^ncia” Thesis, University of Sa˜o Paulo, Sa˜o Paulo.
13.
Pesce
,
C. P.
,
Aranha
,
J. A. P.
,
Martins
,
C. A.
,
Ricardo
,
O. G. S.
, and
Silva
,
S.
,
1998
, “
Dynamic Curvature in Catenary Risers at the Touch Down Point: an Experimental Study and the Analytical Boundary Layer Solution
,”
Int. J. Offshore Polar Eng.
,
8
(
4
), pp.
302
310
.