## Summary

In this paper we present a methodology to superimpose the American Petroleum Institute (API) uniaxial and triaxial limits on tubular design limits plots (API TR 5C3 2018). Complications caused by a recent change of axis are resolved, producing a practical design limits plot that avoids the horizontal shift of the API vertical limits, which is currently the industry standard. 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 current official 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 situation, whereas 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.

One 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 limits 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 the zero axial stress datum, whereas the horizontal ellipse/circle uses the neutral axial stress datum. The horizontal ellipse/circle is well suited for calculations involving buckling, compatible with the information used in field operations, and its formulations are less complicated than the tilted ellipse. Therefore, attention is called to the use of the horizontal ellipse/circle in well tubular design.