At the last node tlie /-coordinate is compared witli the depth of 

 tlie anclior. If tliere is a difference the initial tension value is ad- 

 justed. Guesses at the first and second tensions are made. From then 

 on a secant (discrete foi-m of Newton Raphson) iteration method is used 

 to compute the subsequent initial tension values. An error of 

 0.0001*depth is allowed. In most cases 4 or 5 iterations yield the 

 desired accurac}'. Some important values are printed for each iteration 

 to aid in troubleshooting. 



Kitiiin UQULIB and SPRING interpolation is required to find the va- 

 lues of tension forces and x coordinates wliicli are between the points 

 computed by BRKMOOR and LINI:2. The linear interpolation routing LTERPS 

 was chosen over higher-order interpolation schemes because of the asymp- 

 totic nature of tlie tension versus X values. If values are requested be- 

 yond the ends of the computer arrays, tliey can be extrapolated, but a 

 warning message will be printed by EQUILIB. 



An iterative procedure is required within EQULIB if the anchor 

 separation condition is selected. Again the secant iteration method 

 is used. EQULIB prints out values at each interation which can aid in 

 troubleshooting but which can normally be ignored. 



Subroutine CHAIN computes the strain in a chain using the basic 

 elastic properties of a steel bar with a total area equal to the area of 

 both parts of the links, and a factor of 6 to allow for tlie deformation 

 characteristics of the links. This factor of 6 came from a finite ele- 

 ment computation. 



Subroutine NYLON computes the strain in a nylon rope using a power- 

 function fit of the form: 



3 

 e = AX , 



where e = Strain, 

 A = 0.02052, 



0.2237, 



X = 



jL 



T = Tension (pound) , 



D = Diameter of rope (inches) • 



This function was determined using a least-squares power- function 

 fit of experimental data provided by Sampson Cordage Works for their 

 2-in-l nylon braided rope. 



An experimental verification test was conducted as a check of the 

 program. A chain was suspended from a spring scale. Measurements were 

 made of the length of the chain, its weight and the tension in two 

 geometrical configurations . The program gave computed values of 

 the tension very close to those measured. 



84 



