Appendix B 

 RESTRAINING MOMENT BY A SINGLE GUIDELINE 



Assuming that wave and current excitations can be completely removed 

 from the guideline system, rotation of the payload must be caused by the 

 torque in the lift line. Such torque is developed in most ropes when 

 under tension. As the guide frame and payload rotate an angle, horizontal 

 components of tensions in both lift line and guideline increase to form a 

 resisting moment until an equilibrium is reached. The amount of rotation 

 as induced by the in-line torque may be solved with the following assump- 

 tions: (1) the weight of either lift line or the guideline is to be 

 neglected; (2) the guideline span is zero; that is, the upper end of the 

 guideline support is directly above the guideline anchor point; (3) hori- 

 zontal current is neglected; and (4) friction at the guide cone is small 

 enough to be disregarded. 



This three-dimensional statics problem is solved with basic free-body 

 diagrams. The problem is defined in Figure B-la (the elevation) and 

 Figure B-lb (the plan view). Line ABC is a single guideline with constant 

 tension T^, and ED is the lift line with tension, T^. The payload is 

 suspended at D having a submerged weight of W. The depth of payload is 

 half of the water depth, where the guideline has least restraining power. 

 The guide frame BD has a length of S and is rotated an angle 9 due to the 

 lift line torque M. 



At equilibrium, a couple F'e is formed to balance the vertical com- 

 ponent of external torque M (Figure B-lc). 



F-e = M 



d/2 



(B-1) 



b2 + 



©^ 



For approximation, 



F = M/e 



From free body Figure B-ld, since S << d, therefore a << d/2. 



F = 2 T, 



From free body Figure B-le, 



V*(s' 



(B-2) 



(B-3) 



31 



