This problem is difficult to solve because of the nonlinear damping 

 due to drag forces on the oscillating load and added mass. A simplified 

 solution has been derived for cable systems."^° It was modified for pipe 

 string analysis and programmed for a computer. By using this program, the 

 normalized amplitude of the maximum dynamic stress was computed. The 

 results are plotted in Figure B-5. This figure presents the axial force induced 

 in the pipe per foot of ship heave versus the period of the suspension point 

 at the surface. For a given sea state and surface vessel, the period and heave 

 can be calculated and the resulting dynamic force determined from the 

 graphs. 



Figure B-5 indicates that for periods up to 15 seconds significant 

 loads can be imposed on the pipe for all depths and loads. Obviously, a 

 floating platform or ship with a long period, say 60 seconds, would minimize 

 the problem to the point of being insignificant. If a ship or platform is to 

 be modified for heavy lift, its response in various sea states should be specified 

 so that a range of safe operating environments can also be specified. In any 

 case, it is apparent that by assuring the surface support vessel has a response 

 of no less than, say 20 seconds in heave for the specified sea states of 

 operation, and that the heave amplitude is 1 foot or less, the forces induced 

 in the pipe string would be negligible. How difficult it would be to design a 

 ship or platform satisfying these requirements is a point worthy of detailed 

 investigation. This topic is discussed in greater detail near the end of this 

 appendix. 



Movement of the Load 



The load will oscillate with the movement of the ship. The amount 

 of oscillation is important during the final placement of the load. Excessive 

 vertical oscillations will make accurate placement difficult and could 

 conceivably subject the load to unacceptable shock loadings. 



The same program used to compute the dynamic loads was used to 

 calculate the movement of the object at the end of the pipe string. Figure B-6 

 shows the vertical movement of the load per foot of ship heave versus the 

 period of the support point. For periods greater than about 1 2 seconds, the 

 load moves with the ship; that is, the load moves the same amount as the 

 ship heaves. 



The effects of the ship heave on the load can be reduced to the point 

 of being negligible. At points along the pipe string, bumper subs, which are 

 simply large shock absorbers, can be installed to reduce the motion of the end 

 of the pipe string and thereby reduce the strain on the pipe. There are various 



110 



