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Chapter 13 Collapse Analysis ofship Hulls                             26 1


                                                                                     (13.27)
                  Here (SM), is the elastic section modulus. Due to the use of greater slenderness ratios for
                  stiffeners and  plate  panels,  and  high  yield  steels,  the  possibility  of  buckling  failure has
                  increased. The initial yield moment may not always be the lower bound to hull girder strength,
                  since the buckling of the individual structural elements has not been accounted for.
                  Due  to  the  simplicity of  the  initial yield  moment  equation, it  may be  kequently used  in
                  practical  engineering.  Vasta (1958) suggested that  the  ship hull would reach its ultimate
                  strength when  the compression  flange in  the upper deck (in  the  sagging condition) or the
                  bottom plating (in the hogging condition) collapses, and that the yield stress in the initial yield
                  moment Eq. (13.24) may be replaced by the ultimate strength ou of the upper deck or bottom
                  plating.
                  Mansour and Faulkner (1 973) suggested the Vasta formula may be modified to account for the
                  shift of the neutral axis location after buckling of the compression flange.
                       M, = (1 + k)  (SM),a,                                         (1 3.28)
                  where k is a function of the ratio of the areas of one side shell to the compression flange. For a
                  frigate, they calculated the value of k to be approximately 0.1.
                  Viner (1986) suggested that hull girder collapses immediately after the longitudinals on the
                  compression flange reach its ultimate strength, and suggested the following ultimate moment
                  equation,
                      M, =a (SM),o,                                                  (13.29)

                  where a is normal in the range of 0.92 - 1.05 (mean 0.985).
                  The findings of Mansour and Faulkner (1973) and Viner (1986) are very useful because of
                  their simplicity  - ultimate moment capacity is approximately the product of the elastic section
                  modulus and the ultimate strength of compression flange.
                  Valsgaard and Steen (1991) pointed out that hull sections have strength reserve beyond the
                  onset of collapse of hull section strength margin, and suggested that a is 1.127 for the single-
                  hull VLCC Energy Concentration, which collapsed in 1980.
                  A further modification was made by Faulkner and Sadden (1979) as:
                                                                                     (1 3.30)

                  where O"  is the ultimate strength of the most critical stiffened panels.
                  13.3.2  Ultimate Moment Capacity Based on Fully Plastic Moment
                  Caldwell(l965) assumed that the ultimate collapse condition is reached when the entire cross-
                  section of the hull including side shell has reached the yield state. The material is assumed to
                  be elastic-perfectly-plastic, e.g. strain-hardening effect is ignored. Also, the effect of buckling,
                  and  the  effects of axial and  shear forces are neglected.  With  these  assumptions,  the  fully
                  plastic collapse moment, M, can be estimated as:
                                                                                     (1 3.3 1)
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