GNGTS 2014 - Atti del 33° Convegno Nazionale

GNGTS 2014 S essione 2.3 441 Structural period. The calculation of the seismic response in the case of a tank is fairly complex. In fact, the structural period needs to be combined with the one of the liquid contents. It was shown that a part of the liquid moves in long-period sloshing motion, while the rest moves rigidly with the tank wall. This part of liquid, also known as the impulsive liquid, experiences the same acceleration as the ground and contributes predominantly to the base shear and overturning moment. The sloshing liquid (or convective) determines the height of the free surface waves, and hence the freeboard requirement to a safety condition. In this paragraph the convective and impulsive periods and the safety height for the Paluzza SIOT buffer tank is calculated, starting from the elastic design response spectra determined in the previous paragraph. Periods of convective and impulsive responses (Eurocode 8: design of structures for earthquake resistance; UNI EN 1998-4: 2006 Part 4: Silos, tanks and pipelines) are calculated through Eq. (1) (1) where H is the design height of the fluid, R is the radius of the tank, s is the equivalent uniform thickness of the wall of the tank, ρ the density of the liquid mass and E the modulus of elasticity of the material. The coefficients Ci and Cc are obtained from an exact model of the tank-liquid system and included intoAppendix 1 in Eurocode 8.4. Ci is a non dimensional coefficient, while Cc is expressed in s/m 1/2 . Replacing the value of R (in meters) in the equation, therefore, the correct value of the convective period is obtained. For tanks with non-uniform wall thickness, s can be calculated by taking a weighted average on the wet height of the tank wall, assigning the highest thickness weight near the base of the tank where the maximum deformation occurs. The impulsive and convective mass m i and m c , which are necessary to calculate the shear stress and the overturning moment, are given again in appendix A of Eurocode 8 part 4, expressed as fractions of the total liquid mass m . Seismic response on theoretical formulations. The oil tank in Paluzza is a vertical cylindrical steel structure, with a capacity of approximately 10000 m 3 . The radius of the tank is 13.72 m (diameter 90 feet), the height 17.07 m (corresponding to 56 feet). The structure has both a fixed coverage and a floating steel roof. The theoretical calculation of impulsive and convective periods and maximum vertical displacement of the fluid in the tank is performed according to the formulations provided by Eurocode 8 part 4. The computation of the period has been carried out considering the worst scenario: upstream pipeline collapse condition and spill of all the fluid in the storage tank until its maximum fill. The height of the tank is 17.07 m, however the maximum filling level is about 16 meters, considering the presence of the floating roof. It is assumed, as fluid density, the minimum and maximum density of the fluids normally transiting in the system, 780 and 900 kg/m 3 respectively. The check is then completed adopting the period value to which corresponds the higher spectral acceleration, for security reasons. Convective periods, on the other hand, being only dependant on the radius, does not change. Tabs. 2 and 3 summarize the computation for the tank in Paluzza with the expected height of sloshing at about 0.07 m. Actually, considering the spectrum calculated with the EC8 formulation, but with the damping at 5%, since it’s not possible to calculate it for a value lower than that, the maximum wave height would be 20 cm. In both cases, if the maximum fluid height is set to 16 m, the security conditions are respected. Single Station top – bottom surveys. One of the most delicate issues about the Malhotra simplified approach is the estimation of the convective and impulsive periods. Thus, the results