Elastic collapse is an important piece of the tubular collapse formulation in API TR 5C3 and ISO 10400. Elastic collapse is significant because it is independent of the strength of the tubing, e.g. K-55 and Q-125 have the same resistance to elastic collapse. Advanced collapse models, such as Klever (2006), require a thick-wall collapse result as part of their formulation.
What would the effect of a thick-wall have on elastic collapse? There really is no way to tell from the classic formulation. What is needed is a formulation that is based on an elastic solution for a thick-wall cylinder, but that can derive the classic solution for a thin-wall.
The elastic equations for a thick-walled cylinder exist, known as the Kirsch equations. This elastic solution was expanded in a series as a function of t/D. Using terms of order t/D only, the boundary conditions were set, and balance of moments yielded the classical result. This shows that the Kirsch equation is a valid starting point for a thick-wall collapse result.
A new set of physically reasonable boundary conditions was proposed for the Kirsch equation, which were then used to determine the collapse resistance for thick-wall pipe. This result also yielded the classic result in the limit as t/D is small.
Number of Pages
Bresse, M: Cours de Mechanique Applique'e, 2nd edition, p334, (1866).
Kirsch, Ernst Gustav (1898): Die Theorie der Elastizität und die Bedürfnisse der Festigkeitslehre, Zeitschrift des Vereines deutscher Ingenieure, 42, 797-807.
Timoshenko, Stephen P. and Gere, James M. (1936): Theory of Elastic Stability, 2nd Edition, McGraw-Hill Publishing Co., New York, 289-293.
Housner, George W., and Vreeland, Thad (1966): The Analysis of Stress and Deformation, The Macmillan Co., New York, 211-214.
ISO/TR 10400 (2007): Petroleum and natural gas industries - Formulas and calculations for the properties of casing, tubing, drill pipe, and line pipe used as casing or tubing.
ANSI/API Technical Report 5C3, 1st Edition (2008): Technical Report on Equations and Calculations for Casing, Tubing, and Line Pipe Used as Casing or Tubing; and Performance Properties Tables for Casing and Tubing.
Klever, F.J., and Tamano, T. (2006): A New OCTG Strength Equation For Collapse Under Combined Loads, SPE Drilling and Completions, 164-179, September 2006.
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