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A deck carrying a loading crane in a port is supported by 18 columns as shown in Figure 1. The columns are divided in the three groups shown in the figure (A, B and C) Failure of the entire system can occur in any of the following three ways during operation: (i) Group A fails, (ii) Either one of the two sub-groups (B1, B2) of Group B fails, (iii) Both sub-groups (C1 and C2) of Group C fail. The resulting combined series and parallel configuration of the entire system is shown in Figure 2. Group A and sub- groups B1, B2, C1, C2 fail when all their columns fail (as one of the columns fails, the remaining columns must carry additional loads through redistribution). Assume that the total load S is distributed among the three groups as follows: Group A carries 10% of S, Group B carries 40% of S, and Group C carries 50% of S. The coefficient of variation of these three loads is 15% (including the coefficient of variation in S and variations in load distribution). Assume further that the individual column capacity in the different groups is as follows: Group Mean Capacity Coefficient of Variation of of Each Column Capacity of Each Column A 0. 150 S 20% B 0. 125 S 20% C 0. 125 S 20% Assume that the column capacities and the load S are all normally distributed. Compute the probability of failure of the entire deck system assuming that the failures of groups A, B and C are independent of each other and that the failures of sub-groups B1 and B2 are also independent of each other. [Hint for failure probability of group C: P(Fc) = 2!P(Fc2)P(Fa \\ Fc2)] A C1 B1 B2 B2 A C2 C2 B C Figure 1 Figure 2