Incorporation of Friction Coefficient in the Design Equations for Elevated Temperature Tanks

Storage tanks operating at elevated temperatures (200 °F to 500 °F) need to consider stresses due to thermal expansions and restraints, due to the tank shell and bottom plate interactions and operating conditions in addition to the design requirements for ambient temperature tanks. Appendix M of API Standard 650 provides additional requirements and guidelines for the design of tanks operating at elevated temperatures. These are based on Karcher's method which gives a simplified procedure for determining the stresses (strain range) in the tank wall and bottom plate. A factor named “C” is used for defining the ratio of actual expansion against free expansion of the tank. Such partial expansion causes significant thermal stresses. API uses these stresses to estimate the low cycle fatigue life of the tanks. At present, a range of C values (0.25–1.0) is allowed by API without clear guidelines for selecting a suitable value. In the absence of such guidelines, a set value (like 0.85) is being used irrespective of the tank dimensions and temperature change. The restraint against free expansion is mainly a result of the friction between bottom plate, the foundation medium and the ring wall (if present). We can estimate the C factor by relating it to the friction coefficient. This is explored in the present study. This paper evaluates the current procedure and suggests an alternate method by incorporating the friction coefficient directly in the stress equations, instead of the C-factor. Use of friction coefficient provides an improved basis for selecting C and avoids some of the difficulties.