Wire Ropes Under Tensile Load - Wire Ropes: Tension, Endurance, Reliability - page 129

x j x cos b j

(+ for lang lay rope) and the twist angle x ij of the wire i in the strand j of the round
strand rope is

x ij ¼ x cos a ij cos b j :

The torsional stress for a wire with the diameter d ij and the shear module G is

s ij ¼ x ij G d ij
2

: ð 2 : 38b Þ

2.4.6.2 Unimpeded Change of Lengths

The unimpeded change of lengths of the different wire and strand helixes means
that the wires and strands can move against each other and a cross-section of the
strands and the rope will not remain plane. For a spiral rope twisted with the rope
twist angle x, the unimpeded change in the length of a wire helix from the wire
layer i in the direction of the spiral rope axis (or a strand axis) is according to
( 2.97 ) for the winding radius r i (presupposed as constant) and the lay angle a i of a
wire i

q

1 2 r i

Dl i
l ¼

x tan a i r i x 2 1 : ð 2 : 97b Þ

In a twisted stranded wire rope with fibre core and one strand layer j = 1, the
unimpeded change of a wire helix of the wire layer i,1 in the direction of the strand
axis of the strand layer 1 is

q

1 2 r i ; 1 x 1 tan a i ; 1 r i ; 1

Dl i ; 1
l 1

x 1 ¼ 1 : ð 2 : 97c Þ

In this equation the strand twist angle is
for lang lay ropes x 1 = x cos b 1 and
for ordinary lay ropes x 1 = -x cos b 1 .
r i,1 is the winding radius of a wire i in the strand 1 and
a i,1 is the lay angle of a wire i in the strand 1.
In a wire rope with steel core or in a multi-strand layer rope, the unimpeded
length change of a strand helix of the strand layer j in the direction of the rope axis
is