1. Introduction
This paper investigates the behavior of the first mode resonance in the liquid storage tanks with the single-deck type floating roof. In the Tokachi-Oki Earthquake in 2003, the floating roof of the large-sized oil tanks received damage by sloshing. One of the reasons is considered to be out-of-plane deformation of the pontoon by the first mode resonance in the past report. In this paper, the behavior of the floating roof is simulated by the proposed numerical analysis method, and the deformation and stress in the pontoon are investigated in detail.
2. Analysis Method
The pontoon of the floating roof is modeled by beam elements, and the deck is modeled by membrane elements. The potential fluid element which was developed by author by using the ALE method is applied to internal fluid. All the elements have consideration of geometric nonlinearity. Analysis models are three tanks of volumes 30,00kL, 40,000kL, and 100,000kL which are created by referring to the tanks damaged by the Tokachi-Oki Earthquake (see Fig. 4, Fig. 5 and Table 1).
3. Influence of Liquid Depth
The liquid depth is changed to 5m, 10m, 15m, and 20m, and each response under sine wave loads is analyzed. As a result, it is found that the out-of-plane deformation of the pontoon is large, as the liquid depth is low. Moreover, the regression curve proposed for free surface by the past work16) is compared with the relation between the liquid depth and the out-of-plane deformation by the analysis, and it is shown that both are well in agreement (see Fig. 13).
4. Response Reduction Rate by Pontoon and the Response Amplification Rate by Deck
The models without the deck of the floating roof under the sine wave loads are analyzed, and the results are compared with the results of the models with the deck. And it is found that the tension of the deck affects the deformation of the pontoon largely. Furthermore, the floating roofs with the various rigidity of the pontoon are analyzed, and the relation between the rigidity of the pontoon and the out-of- plane deformation is investigated in detail. A regression curve is presented for the relation in Fig. 19.
5. Evaluation Formula for Cross-Sectional Force
The evaluation formula for the cross-sectional force notified by the Fire Defense Agency4) is modified by the results in Chapter 3 and 4. The flow chart of the modified evaluation formula is shown in Fig. 20.
6. Seismic Response Analysis
The response analysis of the floating roofs under artificial earthquake motions is performed and the response results are compared with the modified evaluation formula. Although the modified evaluation formula shows the small moment than the value of the response results, it is shown that the modified evaluation formula could express the gross tendency of the response results, in Fig. 24 and Fig. 25.
7. Conclusion
The out-of-plane deformation of the floating roof pontoon is investigated by the proposed numerical analysis, and the influences of the liquid depth and the deck tension on the deformation are clarified. The evaluation formula of the cross-sectional force of the pontoon is shown, and the validity is confirmed.
