This paper presents a methodology to superimpose the American Petroleum Institute (API TR 5C3 2018) uniaxial and triaxial limits on tubular design limits plots. Complications due to a recent change of axis are resolved, producing practical design limits plots that avoid the horizontal shift of the API vertical limits, currently done by the industry. The commonly used slanted ellipse is compared against an adaptation of the circle of plasticity in the form of a horizontal ellipse, showing the convenience of this last one with examples.

After the new collapse formulation was made part of the main body of standard API TR 5C3 (2018), the horizontal axis on the standard industry well tubular design limits plot changed. The present study evaluates this redefinition of the horizontal axis. One consequence of this modification is a difficulty plotting the API tension and compression limits. The API horizontal limits (uniaxial burst and collapse) are found to be independent of load case, while the API vertical design limits (uniaxial tension and compression) are dependent on inside and outside tubular pressures. The approaches used by commercial software and industry publications to solve this challenge are reviewed. A new design methodology is developed to link API uniaxial limits to the triaxial theory.

The main objective of the study is to establish a mathematical relationship between API tubular design limits and the von Mises triaxial theory (API TR 5C3 2018). A methodology that allows plotting the API uniaxial force limits on the design limit plot is developed. The study also shows that the results obtained from the industry standard slanted ellipse are identical to those obtained from the horizontal ellipse and circle. One important difference is that the slanted ellipse is based on zero axial stress datum while the horizontal ellipse/circle uses neutral axial stress datum. The horizontal ellipse/circle is well suited for calculations involving buckling, it is compatible with the information used in field operations and its formulations are less complicated than the tilted ellipse. Therefore, attention is called to it.