Wire Ropes Under Tensile Load - Wire Ropes: Tension, Endurance, Reliability - page 89

r upper
B up

C up
B up

r upper
A up þ C up = B up

ln ð 1 þ Þ

: ð 2 : 50 Þ

r upper
B down ; upper

r upper
A down þ C down = B down ; upper

C down
B down ; upper

¼ ln ð 1 þ Þ

The constant B downup has to be calculated by iteration using ( 2.50 ). The rope
extension e lower,upper can be calculated with ( 2.47 ), the constant B down,upper , and the
constants A down and C down using Tables 2.1 and 2.2 . Then the rope elasticity module is
E S ð r lower ; r upper Þ ¼ r upper r lower
e lower ; upper

ð 2 : 51 Þ

or

r upper r lower

E S ð r lower ; r upper Þ ¼ :

r upper r lower
B down ; upper

ln r upper þ A down þ C down = B down ; upper
r lower þ A down þ C down = B down ; upper

C down
B down ; upper

ð 2 : 52 Þ

Calculating the rope elasticity module without the aid of a computer involves a
certain amount of effort. For some chosen rope stresses r lower and r upper , the rope
elasticity module E S (r lower , r upper ) is listed in tables. Table 2.3 shows the rope
elasticity module for 6-strand ropes with two wire layers and for spiral round
strand ropes. In case of rope oscillations with the middle stress r m and small
amplitude stress r a , the elasticity module required is E S (r m ± 0). This rope
elasticity module is listed for some middle stresses in Table 2.3 as

E S ð r lower ; r upper Þ ¼E S ð r m ; r m Þ:

For example, for a rope 6 9 19—IWRC with r m = 200 N/mm 2

E S ð 200 0 Þ ¼E S ð 200; 200 Þ ¼117 kN/mm 2 :

Table 2.4 gives correction constants DE for 8-strand ropes and for one and three
wire layers. With this, the rope elasticity module E S (r lower , r upper )is

E S ð r lower ; r upper Þ ¼E S ð Table 2 : 3 Þþ DE : ð 2 : 53 Þ

The standard deviation can be taken from the Tables 2.1 and 2.2 .
The elasticity module between two stress levels and the rope elongation can be
calculated with the help of the Excel-program SEILELA2.XLS.

Example 2.4: Wire rope elasticity module
Data:
wire rope IWRC + 8 9 19
rope tensile stresses between r z = 100 and r z = 220 N/mm 2 .