Sloshing effects on the seismic design of horizontal-cylindrical and spherical industrial vessels

The present paper investigates sloshing effects on the earthquake design of horizontal-cylindrical and spherical industrial vessels. Assuming small-amplitude free-surface elevation, a linearized sloshing problem is obtained, and its solution provides sloshing frequencies, modes, and masses. Based on an "impulsive-convective" decomposition of the container-fluid motion, an efficient methodology is proposed for the calculation of seismic force. The methodology gives rise to appropriate spring-mass mechanical models, which represent sloshing effects on the container-fluid system in an elegant and simple manner Special issues, such as the deformability of horizontal-cylindrical containers or the flexibility of spherical vessel supports, are also taken into account. The proposed methodology can be used to calculate the seismic force, in the framework of liquid container earthquake design, and extends the current design practice for vertical cylindrical tanks stated in existing seismic design specifications (e.g., API Standard 650 and Eurocode 8). The methodology is illustrated in three design examples.