Wire Ropes Under Bending and Tensile Stresses - Wire Ropes: Tension, Endurance, Reliability - page 281

Table 3.11 Load collective factor k (estimation for cranes)

D/d 11.2 12.5 14 16 18 20 22.4 25 28 31.5

k 0.3 0.33 0.36 0.39 0.42 0.45 048 0.51 0.54 0.57

3.4.1.2 Simplified Analysis

The wire ropes in cranes will be normally stressed by a collective of tensile forces.
The effective tensile force that represents the different forces, is the collective
force

S ¼ k S 0 :

S 0 is the tensile force from the nominal load. k is the load collective factor.
From the five dimensional limits the awaited numbers of working cycles, the
discarding number of wire breaks, and the optimal rope diameter have to be
calculated with the collective force whereas the Donandt force and the rope safety
factor depend—of course—on the nominal tensile force.
As a first recommendation a load collective factor is listed in Table 3.11 for the
row of diameter ratio D/d of sheave and rope.
The effective bending length is approximately

h
1 þ 2 n

l ¼

with

the nominal stroke h of the load
and the number of sheaves n.

The effective numbers of bendings during one working cycle representing the
collective of load strokes, are for a first approximation

w com ¼ w com ; 0
w sim ¼ w 0 ; 7

sim ; 0
w rev ¼ w 0 ; 7

rev ; 0

In cranes the wire rope normally will be unloaded only in the lower end
position. That means w com = 1. Unloading in a upper position is very seldom and
in that case it is not easy to detect when the wire rope has to be discarded.
For elevators in multi-storied buildings, most car trips start or end on the ground
floor or another main floor. Therefore the most stressed rope piece (bending
length) is that running over the traction sheave and the deflection sheaves when the