Efficient estimation of extreme long-term stresses by considering a combination of longitudinal bending stresses

Abstract

Longitudinal stresses due to combined horizontal and vertical bending moments in ships, corresponding to a return period of 20 years, are estimated by linear response analysis. In principle, the stress should be obtained by combining the stress in all sea states that can occur over a long-term period. A method to determine the desired long-term extreme stress by considering only a few short-term sea states is presented. The sea states have a certain probability of occurrence, and are each identified by a contour line in the (Hs, Tp)-plane. This approach makes it possible to estimate the extreme loads on the vessel in a practical and accurate manner. Moreover, it is shown that the long-term stress can be estimated by combining the individual long-term extreme stresses due to vertical and horizontal bending moments by using the sum-of-squares approach and accounting for the correlation between stresses. It was found that the correlation coefficient can be taken as the largest of the ones calculated along the contour line. It is shown that this correlation coefficient can even be approximated by the normalized phase angle at the wave length where the dominant response has its peak value. A comparison with the results obtained using well-known combination rules is presented. While linear analysis has been used here, it is believed that the approach can be generalized to stresses with nonlinear behavior, and hence represent a significant improvement in calculation efficiency.