Motion and Resistance of a Low-Wat erp lane Catamaran 



Once the loadings at the centerline section of the cross-deck 

 member are known, we can find the loadings at any section of the 

 structural members in the following way. 



For - h < z < h 

 s — — 



V 4 ( Z ) = V 4 (0) + Jm A |{ 2() 



+ X «60" h 



o MO / 



+ « 



: / h -B^ { 



^7n + x *An + (^- n t^A df 



60 



0} 



"E ^ko 



kr2 



(cb d) 



V ^2y V k 



y=b-a v 2y kly- D + a 



JP 



r>. 



<t>j + a, 6 D ) 



) df| 



y=b _o +U o*i + «V^| 



where m A is the mass of the member A, and m!| ( f ) is the 

 mass distribution of the member B. If z > 0, the expression 

 below the dotted line should be discarded. 



M.(z) = M.(0) - w m* (b + z 2 - h + 2h z - 2by - 2zz) 

 11 bo 



dsf 



(48) 



V (0) (h - z) - V_(0) b 

 ^t o O 



+ 0} 



+ u 





m£.(lr)<b-, )( £ 30 -x 



(f - «) 



50 



40 ) d ^ 



{*20 + X *60 + ^ ) * 4 o} 



df 



6 



p£ « 



k:2 



-r 



<*4* * k 



y=b-a 



+ C|> 4x (t) k| h Mr 



- JP 



7 { (w 0^1+ w Vl l + ( " o^t + w *n)| I < ^- z ) d r 



/ I ° i U l y= b-a o I D I / b+a 



Z (49) 



where m^ (^ ) is the mass distribution of the member A. If z > 0, 

 the expression below the dotted line should be discarded. 



For < y < b + a 



V 5 (y) = V 5 (0) 



+ o> I 



m A ( " )( ^30 " X *50 + * 



40' d * 



(50) 



487 



