Page 302 - Marine Structural Design
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278                                                     Part II Ultimate Strength






























                             Figure 13.24  Deflected Shape in Sagging


                  Since pure  bending  is  applied, it  is  valid  to  assume that  plane  boundaries remain plane.
                  Therefore, only one nodal point is used in the fore end of the tank. Again, this is possible with
                  the transformation for node points out of the neutral axis. The end of the section is loaded with
                  a vertical bending moment that is controlled by the current stiffness parameter method. It is
                  possible to load the hull in pure bending throughout the calculation without knowing the new
                  position of the neutral axis for the hull.  Note that in this procedure, plane sections are not
                  restricted  to  remain  plane,  except  for  the  end  section  described by  only  one  node.  The
                  curvature-moment relationship for the hull is shown in Figure 13.23 and is compared to the
                  full plastic moment.
                  The formulae relating the ultimate moment to the fully plastic moment, imply that the ultimate
                  moment under the influence of a sagging load is 0.86 M, and under the influence of a hogging
                  type load is 0.89 M, (Frieze and Lin,  1991). The present analysis gives results of 0.89 M,
                  and 0.88 MP , respectively. The failure mode in sagging causes overall buckling of the deck as
                  shown in Figure  13.24. The failure mode in hogging causes plate buckling combined with
                  plasticity in the bottom and lower part of the side and limits the load carrying capacity.

                  13.6.5  Quasi-Static Analysis of a Side Collision
                  The next example is a side collision. To be more precise, an infinitely stiff object is forced into
                  the side of a ship hull in a quasi-static analysis. The ship hull is the same as the one used in the
                  hull-bending example; therefore, the  finite element model used in this  example has minor
                  modifications. Shear elements have been added in the deck and at the bottom.
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