test frame except that the frame could be rotated to angles up to = 34° from the horizontal. Three 

 angles, 6 = 0°, 20° and 34°, were selected for the experiments. An important feature of the inclined 

 cable analysis described above is that all frequencies should collapse onto a single curve if the span and 

 sag are measured in the appropriate inclined coordinates (B7). This was indeed the case in the present 

 experiments as shown in Fig. B6 and this finding justifies the simplified approach. If these same fre- 

 quencies are plotted against the tension H, then a separate curve for each inclination angle is obtained 

 as indicated by equation (B18). 



Although the ranges of the inclination angles and the sag-to-span ratios are somewhat restricted, 

 one can generalize the present results to larger angles by using the quantity e . In the tests conducted at 

 NRL 6 was as large as 0.48, which includes substantially greater values of s/l and 6 than are implied by 

 equation (B18). For example, e < 0.48 implies that the linear analysis is adequate for sag-to-span 

 ratios at least as large as 0.06 and 0.035 at 9 = 45° and 6 = 60° respectively. 



B.4. The Slack Cable Computer Code. The finite element slack cable code which was originally 

 written by Henghold, Russell and Morgan (B8) has been adapted for marine cable studies. The result- 

 ing FORTRAN source program, called SLAK, is available to interested users. The remainder of this 

 appendix is devoted to a further discussion of the slack cable problem and to brief descriptions of the 

 method, code, the input and some typical results. Extensive comparisons between numerical, theoreti- 

 cal, and experimental results for inclined slack cables are contained in the final section of this appendix. 



A sketch of an inclined slack cable is presented in Fig. B7 along with the appropriate nomencla- 

 ture. The numerical problem is defined by the locations of the two ends of the cable (left end always at 

 X = >' = z = 0), by the unstretched initial length of the cable L, by the physical properties of the cable 

 grouped together as AE/ mgL, and possibly by the number and location of (any) applied loads and 

 attached discrete masses. The loads and masses must be concentrated at the nodes of the finite ele- 

 ment model. Important derived parameters are the cable span / (i.e. chord length) and the cable incli- 

 nation angle (i.e. chord inclination). The principal results are the equilibrium shape of the cable. 



129 



