A simple formulation for predicting the ultimate strength of ships

The aim of this study is to derive a simple analytical formula for predicting the ultimate collapse strength of a single- and double-hull ship under a vertical bending moment, and also to characterize the accuracy and applicability for earlier approximate formulations. It is known that a ship hull will reach the overall collapse state if both collapse of the compression flange and yielding of the tension flange occur. Side shells in the vicinity of the compression and the tension flanges will often fail also, but the material around the final neutral axis will remain in the elastic state. Based on this observation, a credible distribution of longitudinal stresses around the hull section at the overall collapse state is assumed, and an explicit analytical equation for calculating the hull ultimate strength is obtained. A comparison between the derived formula and existing expressions is made for largescale box girder models, a one-third-scale frigate hull model, and full-scale ship hulls.List of symbols A_B total sectional area of outer bottom - A_B total sectional area of inner bottom - A_D total sectional area of deck - A_S half-sectional area of all sides (including longitudinal bulkheads and inner sides) - a_s sectional area of a longitudinal stiffener with effective plating - b breadth of plate between longitudinal stiffeners - D hull depth - D_B height of double bottom - E Young's modulus - g neutral axis position above the base line in the sagging condition or below the deck in the hogging condition - H depth of hull section in linear elastic state - I_s moment of inertia of a longitudinal stiffener with effective plating - l length of a longitudinal stiffener between transverse beams - M_E elastic bending moment - M_p fully plastic bending moment of hull section - M_u ultimate bending moment capacity of hull section - M_uh,M_us ultimate bending moment in hogging or sagging conditions - r radius of gyration of a longitudinal stiffener with effective plating [=(I_s/a_s)^1/2] - t plate thickness - Z elastic section modulus at the compression flange - Z_B,Z_D elastic section modulus at bottom or deck - slenderness ratio of plate between stiffeners [= (b/t)(_y/E)^1/2] - slenderness ratio of a longitudinal stiffener with effective plating [=(l/r)(_y/E)^1/2] - _y yield strength of the material - _yB,_yB,_yD yield strength of outer bottom, inner bottom - _yS deck, or side - _u ultimate buckling strength of the compression flange - _uB,_uB,_uD ultimate buckling strength of outer bottom - _uS inner bottom, deck, or side