Wire Ropes Under Tensile Load - Wire Ropes: Tension, Endurance, Reliability - page 88

Table 2.2 Constants A, B and C for calculating the elasticity module of spiral round strand
ropes, Feyrer and Jahne ( 1990 )
Rope condition New Ten times loaded

Load direction Up Up Down

Constant A 35 149 229

Constant B
Two strand layers

90,000 123,000 151,500

Three strand layers 89,000 121,000 149,500

Constant C -1,700,000 -11,200,000 -26,700,000

Coefficient of determination 62 % 75 % 86 %

Standard deviation s 12,000 11,000 11,000

r z

E S ð r z Þ ¼

ln 1 þ

: ð 2 : 48 Þ

B up C up

r z r z

A up þ C up = B up

B up

This rope elasticity module is especially important for the first loading when it
is installed. The constants A, B, and C are listed in Tables 2.1 and 2.2 .

2.2.3.4 Rope Elasticity Module E S Between Two Stresses

The rope elasticity module E S (r 1ower ; r upper ) between the two stresses r lower and
r upper is defined by the secant between these two stresses of the stress-extension
curve with a load reverse at the beginning stress, Figs. 2.9 and 2.14 . The loading
direction changes in most practical applications at the beginning of the considered
loading. This is especially true in cases with a fluctuating load. E S (r 1ower ,r upper )is
therefore the rope elasticity module normally used.
A very good approximation of this rope elasticity module can be obtained by
quasi-turning the stress-extension curve (between r z = 0 and r z = 800 N/mm 2 )in
the ''down'' direction around the origin of coordinate (r z = 0) so far until its
extension at the upper stress is the same as that of the ''up'' direction (between
r z = 0 and r z = 800 N/mm 2 )

e up ð r upper Þ ¼e down ð r upper Þ: ð 2 : 49 Þ

The rope elasticity module E s (r 1ower , r upper ) can be taken from the ''down''
direction stress-extension curve turned as described. The turning will be brought
about by exchanging the constant B down to B down,upper for e down (r upper ). Equation
( 2.48 ) set in ( 2.49 ) gives (with this new constant for the ''down'' direction curve)
the equation for calculating the new constant B down,upper