Probabilistic Method for Predicting Ship Collision Damage

More documents

Recommendations

Info

where P i and T i are referred to the particular leg L i . If the applied force, P i , is greater than the maximum elastic capacity ofthe flanking web, P wf , the particular web frame is deformed as shown in Figure 7. The change of angle, g c , at the distortedweb is then:Pwfγ ci ≅(12)TiRosenblatt [1975] proposed an approach to determine whether P i exceeds the capacity P wf , and to estimate the value of P wf .First, the allowable bending moment and shear force of the web frame at each support, the crushing load of the web, and thebuckling force of supporting struts are calculated. Then, the load P i is applied to the web frame, and the induced moments,shear forces and compression of the web frame and struts are calculated, considering the web frame as a beam with clampedends. The ratios of the induced loads to the allowable loads are determined using equation (13). If the maximum ratio, R m , isgreater than unity, the load, P, exceeds the capacity, and the web frame deforms. R m is also used to estimate the number ofdistorted web frames.RmP= (13)PwfSide Shellw1wg cPwfWeb FrameWeb FrameL 1L 2LsFigure 7. Deflection and forces in web framesThe deflection at the outermost distorted web is:where:wnLs1= { w −γ c2[nLi+ ( n −1)nLs]}(14)L + nL2isn -L s -number of deformed web frames on L i sideweb frame spacing (m)The deflection at other deformed web frames is:1wj= ( n − j + 1) wn+ ( n − j)(n − j + 1) γc2L(15)s210
where j is the number of webs counted from the striking point. The elongation in adjacent webs is:ej= w j − w j+22s( 1) + L − L(16)sand the elongation in the struck web is:e20 i = w − w1)2i( + L − L(17)iWith these elongation and deformation results, the rupture criteria given in equations (9) and (10) are applied to all deformedwebs. The total elongation on the L i side is:eti= e+n∑e0 i ji(18)j=1and the energy absorbed in membrane tension and web deformation is:Ei= T eiti+ Pn∑wfj=1wji(19)For right angle collisions, T i always equals T m as calculated in equation (6). In oblique angle collisions, T i equals T m if L i ison the side behind the strike. Based on experimental data, Rosenblatt [1975] suggests using ½ T m ahead of the strike and thisis used in SIMCOL.For double hull ships, if the web frames are distorted because of bending, shearing and buckling of supporting struts, thedeformed web frames push the inner skin into membrane tension as shown in Figure 4 (right), and the right angle collisionmechanism is applied to the inner hull. Inner skin integrity is checked using equations (9) and (10), and the energy absorbedin inner-skin membrane tension is calculated using equation (6).In the simulation, the energy absorbed in membrane tension and web deformation during the time step is:∆ KE n = ( E1,n+ 1 + E2,n+1)− ( E1n+ E2,n)(20)Considering the friction force, F f , shown in Figure 6, and assuming the dynamic coefficient of friction is a constant value of0.15, the reacting forces and moments are:∆KEFηnFξnMnn= N= F= N ( wnfn( llξnn + 1n + 1nn+1( E=( w1, n+1n + 1= −Fd + F l− w ) + Fnηnnn+ E2 , n+1nfn− ln)= 0.15F− lηn[(w − w ) + 0.15 l − l ]In addition to the friction force, another longitudinal force, F R , the force to propagate the yielding zone, is considered, asshown in Figure 6. McDermott [1974] provides an expression for this force:11n + 1) − ( E( ll1n− w ) + 0.15 lln+1n+1n+1− ln+ E− l2, nnn− ln)− l= N)n+1nn + 1n(21)
Page 2 and 3: ABSTRACTThis paper describes a meth
Page 7 and 8: Web frames acting as a vertical bea
Page 9: where:e i - strain in leg iq bi - b
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

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?