Reliability estimation of ship's hull girder in probabilistic terms when ultimate strength is used as a failure mode

Using the ultimate strength as a failure mode, the hull girder reliability is calculated as the probability of the total bending moment (BM) acting on the ship's hull being greater than the ultimate hull girder moment. Both individual amplitude statistics and extreme value statistics are employed to derive the probability density function of the total hull girder BM as a sum of the still water and wave-induced bending moments probability density functions applying the convolution integral. The annual and lifetime probability density functions of the hull girder elastic and plastic section modulus are also derived and used as a base for determining the probability density functions of the first-yield and pure plastic BM. It is shown that the use of the first yield BM as a representative of the hull girder ultimate strength is reasonable only in the case when it is greater than approximate to 85% of the pure plastic BM. An example is given for a 25K DWT bulk carrier.