

Due to 



tern 



Additional 





Masses 



2M 



= SM^ 



SMY 



= sMn,y. 



1 MZ 



= S M^ z„ 



S MY2 = l{MvJ + 1 „„) 

 S MYZ = 2(M y z + I ) 



zz m > 



Due to 

 Longitudinal Members Due to Plates 



at Nodes 



+ p Ax X<^i A. + p Ax 2 d M 



+ p Ax S 4". A.y. + p Ax S Cj tj^^; Y 



+ pAx2CiAiZ. +pAxS<. t.( 



+ p Ax S Ci A. y .2 + p Ax S Cj t^ Cj y 



+ p Ax 2 <j Aj y.z. + p Ax S ^^ t. i^j y 



+ p Ax 2 4. A: z. + p Ax 2 4"j t^^ 



which 



I MZ2 = 2(M^Zm^ + ^zzm) 



In the above, the subscript ni refers to the additional (nonstructural) mass items, for 



M = weight of the item, 



y z = coordinates of the center of gravity of the item, 



■'mm o .; 



1 = weight moment of inertia of the item about an axis through its center of 



yym "^ . 



gravity and parallel to the z-axis, 



I = weight product of inertia of the item with respect to axes through its center 



of gravity, and 



I = weight moment of inertia of the item about an axis through the center of 



zzm '^ . "^ 



gravity of the item and parallel to the y-axis. 



The subscript i refers to the longitudinal structural members associated with node i and the 

 subscript j refers to the plates. Here: 



p = density of structural material (basic). 



Ax = length of hull section for which weights are calculated, 



^. = density ratio, for material at node i, relative to p, 



A. = cross-sectional area of longitudinal structural members associated with node i, 



y.,z. = coordinates of node i 



•'1' 1 



C = density ratio, for material of plate j, relative to p, 

 t. = thickness of plate j, 

 i. = /(Ytj-ynj)^ + (^tj-^hj)" = length of plate j, and 





■[these are the coordinates of the midpoints of the plate j. 



Note that, contrary to the method employed in the calculation of elastic parameters of the 

 cross section of the hull, the weight of the plate j is not combined with the weights associated 



79 



