Probabilistic Method for Predicting Ship Collision Damage

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e tnt -B e- total elongation of shell or bulkhead structure within the damaged web spacing- smeared thickness of side shell or bulkhead plating and stiffeners (m)- effective breadth (height) of side shell or bulkhead (m)Side ShellWeb Frame2qb1w2qb2Web FrameL 1 L 2LdFigure 5. Membrane geometryFigure 5 illustrates the membrane geometry for calculation of elongation where e 1 and e 2 are the elongation of legs L 1 and L 2respectively:and:eeit=12i= e + e22L + wLd=2L L12w22w− Li≅2Li(7)L d -distance between adjacent webs (m)w n -transverse deflection at time step n (m)Side shell rupture due to membrane tension is predicted using the following criteria:• The strain in the side shell reaches the rupture strain, e r , which is taken as 10% in ABS steel; or• The bending angle at a support reaches the critical value as defined in equation (8) [Rosenblatt 1975].where:e m -s m -s u -q c -D -mm = 4 σε sin θctanc= 1. 5D3 σ − σ cosθθ(8)umaximum bending and membrane-tension strain to rupturemembrane-tension in-plate stress (MPa)ultimate stress of the plate (MPa)critical bending angletension test ductilitymcThe resistance of the membrane is only considered up to the point of rupture:eiε i =Lθbii1=≤ εrarctan2wLi≅8w2Li≤ θc(9)
where:e i - strain in leg iq bi - bending angle of flanking web framesSince the striking bow normally has a generous radius, the bending angle at the impact location is not considered in therupture criteria. From these equations, it is seen that only the strain and bending angle in the shorter leg need be consideredfor right angle collisions. Based on material properties of ABS steel, the critical bending angle q c from equation (8) is19.896, 17.318 or 16.812 degrees for MS, H32 or H36 grades respectively. Once either of the rupture criteria is reached, theside shell or longitudinal bulkhead is considered ruptured, and does not continue to contribute to the reacting force.For collisions at an oblique angle, the membrane tension is only fully developed in the leg behind the strike, L 2 in Figure 5.This is demonstrated in the force diagram shown in Figure 6, where T 1 is much smaller than T 2 . It is also assumed that all thestrain developed from membrane tension is behind the striking point. Therefore, the first rupture criterion in equation (9) becomes:where e b and L b represent the strain and length of the leg behind the strike.etεb= ≤ ε(10)rLbT 2 – tension in leg L 2N - reacting forcecomponent normal tostruck shipTheoretical resultantneglecting propagation ofyielded zoneT 1 – tension in leg L 1Theoretical resultantconsidering propagationof yielded zoneFR - force required topropagate yielded zoneFf - nominal frictionFigure 6. Oblique collision force diagram [McDermott 1974]Web failure modes include bending, shear, and compression. Web frames are allowed transverse deformation while keepingtheir longitudinal locations. The resisting force is assumed constant at a distorted flanking web frame, and the transverse deformationof the web frame is assumed uniform from top to bottom. The magnitude of this force is its maximum elastic capacity.From Figure 6, the applied force on a rigid flanking web frame is:wP i = T(11)iLi9
Page 2 and 3: ABSTRACTThis paper describes a meth
Page 7: Web frames acting as a vertical bea
Page 11 and 12: where j is the number of webs count
Page 13 and 14: collision angle, and extents of dam
Page 15 and 16: Striking ShipBow HEACollision Angle
Page 17 and 18: Figure 11. Striking ship displaceme
Page 19 and 20: applied to each of the four ships.
Page 21: Giannotti, J.G., Johns, N., Genalis

Probabilistic Method for Predicting Ship Collision Damage

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