Seismic Analysis of Cylindrical Ground Liquid Storage Tanks Incorporating the Effects of Rotational Components of Earthquake

The present study deals with the seismic analysis of cylindrical liquid tanks, taking the rotational components of the earthquake into account for various ratios of reservoir height to diameters of tanks. While defining actual kinematic behavior of any point requires incorporating the rotational components of ground motions, as well as the translational components, however majority of studies ignore the effects of rotational components. Here we propose a methodology to evaluate the rotational components of the earthquake based on the translational components. Since the earthquake waves are mainly created by ground movements in fault direction and such kind of movements leads to creation of the shear waves, potential functions of SV and SH waves are used to evaluate the rocking and torsion components, respectively.
For this purpose, a transitional component of ground motion using frequency discrete Fourier transformed to discrete frequency and G value for each frequency determined. Then, the incident angle of the wave was calculated for each frequency. After determining the incident angle, Fourier spectrums of rocking and torsion components of ground motion were calculated. Finally, the inverse of Fourier conversion time histories of rocking and torsion components of ground motion were calculated. The methodology introduced to evaluate time history of rocking and torsion components of ground motion was coded in MATLAB software. In order to verify the proposed methodology, the rotational components of San Fernando earthquake were determined based on the proposed model and compared to Li and Liang's results. The results differed only for about 3% which could be attributed to the different wave velocities and incident angles. In Li's model, the incident angle and apparent wave velocity was supposed to be constant while in the present study the incident angle and apparent wave velocity were variable based on each frequency Then, the rotational components of San Fernando, Tabas and Taft earthquakes were calculated based on the proposed model and the results were used in dynamic analysis of the tanks. Finally, seismic analyses of cylindrical liquid tanks were presented to evaluate the effects of rotational components on the seismic response of the tanks. The time history method was employed for dynamic analysis of the structure considering fluid-structure interaction. The complete fluid structure interaction was considered in analyses taking account the compressibility of fluid . Fluid domain behavior implies small displacements of inviscid compressible fluid with irrotational motion. Water compressibility has a significant impact on the fluid-structure interaction for a wide range of ratios in natural frequencies of structure to fluid domain.
It is evident that the distribution of displacements and stress is very sensitive to the rotational components of the earthquake. Applying rotational components of earthquake may alter the maximum displacement values, as well as the pattern of displacements distribution in all three directions. Incorporation of rotational components will lead to decreases in the maximum stress and displacement. This reduction in responses is more obvious in the empty tanks. An increase in the height of the tanks can boost the effects of rotational components on the structure. Results indicate that it is necessary to take rotational components of the earthquake into account while designing and analyzing cylindrical liquid tanks.