Civil Engineering Reference
In-Depth Information
B ¼ C 0 þ X
n
C i x i
and with
C ¼ C 1 ;
i¼2
the tangent elasticity module for the rope tensile stress r z on the stress-extension
curve between the tensile stresses r z = 0 and 800 N/mm 2
in an ''up-and-down''
direction is
C
r z þ A :
E t r ðÞ ¼B þ
ð 2 : 46 Þ
The constants A, B and C are listed in Tables 2.1 and 2.2 . The constant B for
wire ropes with fibre-covered steel cores in Table 2.1 has been changed unlike
constant B in Feyrer and Jahne ( 1990 ).
2.2.3.3 Rope Elasticity Module with the Lower Tensile Stress r z = 0
The extension e of a wire rope is
e ¼ Z 1
E t ð r z Þ dr z :
Using ( 2.46 ), the extension of a wire rope between the two stresses r lower and
r upper —in the stress-extension curve coming from r z = 0—in the ''up'' direc-
tion—is
r upper
r upper
e ¼ Z
dr z ¼ Z
1
r z þ A up
dr z
C up
r z þ A up
B up
r z þ A up
B up þ C up
B up þ
r lower
r lower
and after integration
e ¼ r upper r lower
B up
C up
B up
ln r upper þ A up þ C up = B up
r lower þ A up þ C up = B up :
ð 2 : 47 Þ
According to ( 2.47 ), the important rope elasticity module with the lower stress
r lower = 0 and the upper stress r upper is
E S ð r z Þ ¼E S ð 0 ; r z Þ ¼ r z
e
or
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