Marine Technology - October 2007 - Page#61

<BODY> <span id="lblContents">Table 3 Probabilities that the bending stresses due to overall bending are smaller than the critical buckling stresses Time Period T 0 to 25 years Corrosion Protection T1 T1 T1 T1 T1 T1 T1 T1 T2 T2 7, T2 7, T2 T2 T2 7, T2 7, T2 0 0 9 years 9 years 0 0 9 years 9 years Distribution W exp W exp W exp W exp Bells 3.90 4.23 4.46 4.84 2.81 3.55 3.23 4.08 T 15 to 25 years W exp Weibull probabilistic distribution. exponential probabilistic distribution. Fig. 18 Corrugation's reliability versus T2 Fig. 17 Corrugation's reliability R = P ( < cr) versus T2 Fig. 19 Reliability R = P ( < cr) and probability P (tf > tf, corrugated bulkhead permissible) for the 9. Comparison between the reliability and the probability of meeting given geometry-based renewal criteria The probability that tf or tw meet given geometry-based renewal criteria becomes the true representative of the corrugation reliability when the following condition (in mathematical terms) is fulfilled: R=P cr = P tf tf,permissible . (9) In geometrical terms, this condition is fulfilled at the crossing line of the two surfaces in Fig. 17 (i.e., R P( < cr)) and Fig. 12 (i.e., P(tf > tf, permissible)) as shown in Fig. 19. For the example, equation (9) takes the form: Weibull: Exponential: 0.062T2 + 3.89 = n + w 0.068T2 + 4.22 = n + w 2.5 2.5 (10) . (11) When T2 is fixed (or assumed), equations (12) and (13) allow for finding the permissible reduction of the corrugation flange, for which the probability P(tf > tf, permissible) becomes equal to the corrugation's reliability R P( < cr). The results for this example are given in Fig. 20 and Table 4. Weibull: Exponential: % = 0.062T2 + 3.89 - n w % = 0.068T2 + 4.22 - n w 0.4 0.4 (12) . (13) The graphs in Fig. 20 (calculated with Weibull and exponential distribution for the lateral pressure) represent the pro232 OCTOBER 2007 jection of the crossing line of the two surfaces corresponding to R P ( < cr) and P(tf > tf, permissible) on the horizontal base surface. It is worth mentioning that the corrugation's reliability changes with the change of the longevity of the corrosion protection, but not as much as the curves for P(tf > tf, permissible). The reason is that the corrosion affects the corrugation geometric properties but not the loads. The probability P(tf > tf, permissible) is not the corrugation reliability R P( < cr), but can be used as its representative only when the condition in equation (9) is fulfilled. P(tf > tf, permissible) is a function of two parameters: (maximum permissible reduction of tf) and T2 (longevity of the corrosion protection plus transition period). There is an endless number of points with coordinates and T2 that lie on the surface of P(tf > tf, permissible). However, only those combinations of and T2 that correspond to points on the cross line of P(tf > tf, permissible) and R P( < cr) ensure that P(tf > tf, permissible) is the true representative of the calculated corrugation reliability R P( < cr). As an example, let us assume T2 9 years. If we allow 15.5 to 16% reduction of tf, we control the corrugation reliability and do not allow it to become smaller than 4.46 to 4.84 Bells (see Table 4 and Fig. 21). If we allow reduction of tf greater than 15.5 to 16%, the error will be on the nonconservative side because then P(tf > tf, permissible) will be greater than R P( < cr). If we allow reduction of tf smaller than 15.5 to 16%, the error will be on the conservaMARINE TECHNOLOGY</span> <br /> <br /> <a href="http://www.digitalwavepublishing.com/" title="Digital Magazine">Digital Wave Publishing</a> </BODY>