Dynamic Analysis of Large Steel Tanks

Transcription

1 Transactions of the 17 th International Conference on Structural Mechanics in Reactor Technology (SMiRT 17) Prague, Czech Republic, August 17 22, 2003 Paper # K14-1 Dynamic Analysis of Large Steel Tanks Alejandro P. Asfura 1), Basilio N. Sumodobila 2), Farzin R. Beigi 2) 1) APA Consulting, Moraga, California, USA 2) ABS Consulting, Oakland, California, USA ABSTRACT Dynamic non-linear fluid-structure interaction analyses were performed for two large diameter steel tanks with floating roofs. The diameter of the tanks varied between sixty and one hundred meters with a height of approximately twenty meters. The tanks wall and roof were modeled with plate elements, the soil with equivalent non-linear spring elements, and the fluid with non-linear fluid elements. Hoop and buckling stresses in the tanks wall, uplifting of the tank bottom, and sloshing height were calculated. Stresses and sloshing heights were compared to the same quantities given by the API [1] and New Zealand recommendations [2] for the design of tanks. KEY WORDS: tank, fluid-structure interaction, sloshing, non-linear, dynamic analysis. INTRODUCTION The most commonly used design code/recommendations for the seismic design of flat bottom tanks are the API [1] and New Zealand recommendations [2] (referred to as NZ code here on after in this paper). They are relatively simple codes and their application is expected to result in successful designs. This paper presents the comparison between the application of these two codes and the results obtained by a more elaborate analytical methodology. Even though it is clearly understood that engineering analysis methods, no matter how sophisticated they are, have also implicit simplifications and assumptions, they will give results that can be considered more accurate for a specific case than the application of a general code. This is true especially for localized responses. Non-linear dynamic analyses were performed for two large steel tanks. Selected results from these analyses were compared to the quantities obtained by the application of the design codes mentioned before. This comparison will give an indication of the accuracy or conservatism of these codes in the calculation of the selected results. TANKS CHARACTERISTICS The two tanks included in this study have steel plate walls with flexible flat bottoms and flexible floating roofs. The first tank (Tank 1) has a diameter of 92.3 meters, a wall height of 21.4 meters and a maximum fluid height of 20.0 meters. Its foundation consists of a reinforced concrete ring. The second tank (Tank 2) has a diameter of 60.5 meters, a wall height of 19.8 meters and a maximum fluid height of 18.0 meters. Its foundation consists of a reinforced concrete pad on piles. SOIL CHARACTERISTICS The foundation soil for Tank 1 consists of a 10-meter thick soil layer with shear wave velocity of about 200 mps overlaying a half space of firm soil with shear wave velocity of about 500 mps. Tank 2 is founded on deep soil with shear wave velocities ranging from 175 to 200 mps. SEISMIC ENVIRONMENT The maximum surface ground accelerations at the site of Tank 1 are 0.66g in the horizontal direction and 0.40 in the vertical direction. For Tank 2, the maximum ground acceleration is 0.30g in the horizontal direction and 0.20 in the vertical direction. Using the acceleration response spectra defined for these sites, acceleration and displacement time histories were developed to match the spectra. The energy content of the seismic input for Tank 1 is in the 3.0 hz to 8.0 hz frequency range. For Tank 2, the energy content is in the 2.0 hz to 6.0 hz frequency range. FINITE ELEMENT MODEL Each tank s wall, bottom plate, and floating roof were modeled using plate elements with beam elements for stiffeners. The pad and ring foundations were modeled with plate and beam elements, respectively. The fluid inside the tanks was modeled using non-linear fluid elements (ANSYS element Type FLUID80). This element is incompressible and it is free to move relative to the tanks shells in the vertical and tangent directions. This fluid element is also free to move relative to the floating roofs in the horizontal direction. 1

2 The tanks are not connected to their foundation, so they can slide and uplift, thus the contact between the bottom of the tank and the foundations was done using a non-linear contact-friction element (ANSYS element Type CONTACT52). This element acts only in compression and provides the sliding resisting forces between the tank bottom and the foundation. Since Tank 1 is founded on a concrete ring; most of the tank bottom is in direct contact with the soil. The contact between the tank bottom and the soil and the soil itself were modeled by a combination of elements that allow for uplift and friction (combination of ANSYS elements Type CONTACT52 and COMBIN40). For Tank 2, which is supported on a concrete pad on piles, the soil was modeled by linear equivalent horizontal and vertical soil springs (ANSYS element Type COMBIN40). They do not allow for the uplifting or sliding of the pad. The interface between the tank bottom and the pad was modeled by non-linear contact-friction elements. The stiffness constants of these springs included the effects of the piles and the soil and were estimated using soil-pile interaction analysis using computer code SASSI (Reference 3). A typical tank model is shown in Figures 1, 2, and 3. Figure 1: Tank finite element model Shell and Fluid Figure 2: Tank shell and base plate 2

3 Figure 3: Floating roof elements GRAVITY ANALYSIS To verify the models, gravity analyses were performed for both tanks. The pressure obtained using the mathematical model was compared to the static pressure for the liquid-floating roof weight. Table 1 lists the comparison of the maximum pressure. As expected, the effect of the floating roof on the pressure is negligible. Table 1: Comparison of maximum gravity pressures calculated at center of gravity of bottom element Tank Gravity Analysis (ton/m 2 ) Static Pressure (ton/m 2 ) Tank Tank MODAL ANALYSIS The fundamental frequencies of the tanks, which mainly correspond to sloshing and impulsive modes, are listed in Table 2. Table 2: Main frequencies Tank Sloshing mode (hz) Impulsive mode (hz) Tank Tank DYNAMIC ANALYSIS Dynamic non-linear time history analyses were performed for the two tanks using the non-linear finite element code ANSYS [4]. In this paper, only some key results from the dynamic analysis are presented and then compared with the results obtained by using the procedures in the API and New Zealand codes. The results shown here are the maximum hoop stress in the tank wall, elephant-foot buckling stress, slosh height, and tank wall uplift. Table 3 presents the maximum wall uplift displacements for both tanks. Figures 4 and 5 show the wall uplifting time histories for Tanks 1 and 2, respectively. Table 3: Non linear analyses results Shell Uplift Maximum uplift height (m)

4 Tank 1 - Uplift Time History Uplift, m Time, sec Figure 4: Uplift time history, Tank 1 Tank 2 - Uplift Time History 6.00E E E-02 Uplift, m 3.00E E E E Time, sec Figure 5: Uplift time history, Tank 2 CODE ANALYSIS Using the API and NZ codes for the design of tanks, hoop stress, elephant-foot buckling stress, and slosh height were calculated and compared to the analytical results. The established site-specific response spectra for both sites were used as the input motion. For the API method, the product ZIC 1 was set to the response spectrum ordinate corresponding to the impulsive frequency of the tanks. Per API, the spectrum for the factor ZIC 1 corresponds to a damping coefficient of 2 percent of critical. Since API does not include a method for calculation of tank impulsive frequency, this frequency was obtained using the method in the NZ code, which includes the soil effects. Similarly, the factor ZIC 2 in the API method was set equal to the spectrum ordinate corresponding to the first sloshing period, as calculated by the API method. The spectrum for calculation of factor ZIC 2 corresponds to a damping coefficient of 0.5 percent of critical. Since the site-specific horizontal and vertical spectrums were also used for the NZ code method, the product of αβα P and α βα P defined in that code are set equal to 1.0. In the NZ method, the spectra for calculation of impulsive and convective loads correspond to 10 and 0.5 percent of critical damping, respectively. The spectrum for vertical modes of vibration corresponds to 5 percent of critical. Figures 6, 7, and 8 show the comparison of the results of rigorous analysis of Tanks 1 and 2 to those using API and NZ codes.. 4

5 Hoop Stress Hoop Stress (Ton/m2) 40,000 30,000 20,000 10,000 0 Analysis 31,400 31,000 API ,500 29,800 NZ 30,100 27,500 Figure 6: Comparison of Tanks Hoop Stresses Buckling Stress Buckling Stress (Ton/m2) 1,500 1, Analysis API ,062 NZ 861 1,360 Figure 7: Comparison of Tanks Buckling Stresses Maximum Slosh Height Slosh Height (m) Analysis API NZ Figure 8: Comparison of Tanks Slosh Height 5

6 CONCLUSION For the two tanks studied in this paper, the hoop stresses calculated using dynamic non-linear time history analyses and those calculated using the approaches given in the API and NZ codes are similar differing only by about 10%. The buckling stresses and the sloshing height calculated using the API and NZ codes are higher than the values calculated with the more rigorous method. The buckling stresses are overestimated by as much as 114% using the NZ method, and by 36% using the API method over that obtained by the rigorous analysis. Similarly, the wave height is overestimated by a maximum of 104% from NZ method, and by 71% from API method over the analysis results. The comparisons shown here, even though corresponds to a very limited number of cases, indicate that the approaches in the API and NZ codes give reasonable seismic demands and are adequate for the seismic design of large tanks. REFERENCES 1. American Petroleum Institute, Welded Steel Tanks for Oil Storage, API Standard 650, 10 th Edition, Washington D.C., National Society for Earthquake Engineering, Seismic Design of Storage Tanks, Recommendations of a Study Group of the New Zealand National Society for Earthquake Engineering, December Computer Code SASSI. A System for Analysis of Soil-Structure Interaction. Geotechnical Engineering Division, Civil Engineering Department, University of California, Berkeley, Computer Code ANSYS. A General Purpose Finite Element Program. ANSYS Inc. 6