Wire ropes are made of strands of twisted steel wires wrapped around a core. They are used to transmit power over long distances in applications like elevators, cranes, and bridges. Wire ropes have advantages like being lighter, more reliable, and durable. They are classified based on the direction of twist of the wires and strands. Design considerations for wire ropes include selecting the type based on application, calculating design load and rope diameter, and ensuring stresses do not exceed the rope's ultimate strength. Sample problems demonstrate designing a wire rope for a mine hoist and selecting a rope to lift debris from a well.

1. ME 571P
Machine Design II
1

2. *Wire Ropes are made from cold-drawn wires that are first wrapped
into strands; then wrapped into helices around a core or central
element, which is usually hemp or pulp.
*Often, the core or central element is an independent wire rope core
(IWRC) which makes the rope much more resistant to crushing.
*IWRC, compared to hemp core, is high-temperature resistant, has
about 7.5% greater strength and has smaller elongation under load.
*Wire ropes are used when a large amount of power is to be transmitted
over long distances from one pulley to another (i.e. when the pulleys
are up to 150 metres apart).
*The wire ropes are widely used in elevators, mine hoists, cranes,
conveyors, hauling devices and suspension bridges.
*The wire ropes run on grooved pulleys but they rest on the bottom of
the grooves and are not wedged between the sides of the grooves.
2

3. Advantages of Wire Ropes
*These are lighter in weight,
*These offer silent operation,
*These can withstand shock loads,
*These are more reliable,
*These are more durable,
*They do not fail suddenly,
*The efficiency is high, and
*The cost is low.
3

4. Classification of Wire Ropes according to the direction of twist of the
individual wires and that of strands relative to each other
1. Cross or regular lay ropes: the direction of twist of wires in the
strands is opposite to the direction of twist of the strands; such type
of ropes are most popular.
2. Parallel or lang lay ropes: the direction of twist of the wires in the
strands is same as that of strands in the rope
3. Composite or reverse laid ropes: the wires in the two adjacent
strands are twisted in the opposite direction.
4

5. Designation of Wire Ropes
*Wire ropes are designated by the number of strands and the number of
wires in each strand.
*For example, a wire rope having six strands and seven wires in each
strand is designated by 6 × 7 rope.
6 x 19 with IWRC
5

6. 6

7. Properties of Wire Ropes (consult also AT 28 of the book by Faires
for English units)
7

8. 8

9. 9

10. 10

11. Wire Rope Sheaves and Drums
*The sheave diameter should be fairly large in order to reduce the bending
stresses in the ropes when they bend around the sheaves or pulleys.
*Large diameters should be employed which give better and more
economical service, if space allows so.
*If the groove is bigger than rope, there will not be sufficient support for
the rope which may, therefore, flatten from its normal circular shape and
increase fatigue effects.
*If the groove is too small, then the rope will be wedged into the groove
and thus the normal rotation is prevented.
Sheave or pulleys for
winding ropes
11

12. For light and medium service, the sheaves are made of cast iron, but for
heavy crane service they are often made of steel castings.
12

13. D
A
d
E
A
S
W
D
d
E
D
d
E
S
.
A
w
W
A
w
W
S
.
w
r
b
b
w
r
w
r
b
d











rope;
on the
load
bending
equivalent
The
drum
or
sheave
of
diameter
wire
of
diameter
rope
wire
the
of
elasticity
of
ulus
mod
:
where
:
ely
Approximat
drum
or
sheave
the
round
winds
rope
when the
stress
Bending
2
rope
the
of
area
sectional
-
cross
net
rope
the
of
weight
lifted
load
:
where
rope
the
of
weight
and
lifted
load
axial
to
due
stress
Direct
1
Ropes
in Wire
Stresses
13

14. l
mat'
wire
of
elasticity
of
modulus
where
ally,
Experiment
ropes
steel
for
84
ropes
iron
t
for wrough
77
rope
entire
the
of
elasticity
of
modulus
l
mat'
wire
of
elasticity
of
modulus
8
3
2
2






E
E
E
mm
kN
E
mm
kN
E
E
E
r
r
r
r
r
section
rope
in the
wires
of
no.
total
is
where
4
:
bending
to
due
rope
whole
on the
load
the
each wire,
in
stress
bending
is
If
2
n
nS
d
W
S
b
w
b
b


14

15. v/t
a
a
v
t
g
a
A
a
g
w
W
S
a
g
w
W
W
W
a
a
a










 








 

by
given
is
’
‘
of
value
then the
known,
is
)
(
speed
a
attain
to
necessary
)
(
time
the
If
on
accelerati
nal
gravitatio
load
the
and
rope
the
of
on
accelerati
:
where
rope.
in the
load
l
add'
induces
This
d.
accelerate
be
to
are
load
supported
the
and
rope
the
stopping,
and
starting
During
stopping
and
starting
during
Stresses
.
3
15

16.  
 
 
A
w
W
S
w
W
W
v
h
L
h
a
ah
v
Lg
S
ahE
w
W
W
st
st
r
r
a
r
st




















2
is
stress
ing
correspond
The
2
starting,
during
load
Impact
therefore
,
0
and
0
then
rope,
in the
slackness
no
is
When there
rope
the
of
length
rope
the
of
slackness
rope
the
of
on
accelerati
2
rope,
of
velocity
2
1
1
rope.
on the
load
impact
an
induces
This
load.
on the
pull
a
exert
to
starts
and
stretched
or
taut
is
rope
the
before
overcame
be
must
which
(h)
slack
a
has
rope
when the
is
starting
of
case
general
The
16

17.  
safety.
of
factor
by the
divided
strength
ultimate
than the
less
be
should
stresses
these
of
sum
the
rope,
wire
a
designing
When
load
the
of
on
accelerati
during
rope
in the
Stress
Effective
starting
during
rope
in the
Stress
Effective
working
normal
during
rope
in the
Stress
Effective
rope
in the
Stress
Effective
.
5
in w/c
3
similar to
obtained
be
may
stress
l
add'
This
speed
of
change
to
due
Stress
.
4
1
2
a
b
d
b
st
b
d
S
S
S
S
S
S
S
t
v
v
a









17

18. Procedures in Designing a Wire Rope
1. Select a suitable type of rope from Tables for the given
application.
2. Find the design load by assuming a factor of safety 2 to 2.5
times the factor of safety given in the Table.
3. Find the diameter of wire rope (d) by equating the tensile
strength of the rope selected to the design load.
4. Find the diameter of the wire (dw) and area of the rope (A)
from the Table.
5. Find the various stresses (or loads) in the rope.
6. Find the effective stresses (or loads) during normal working,
during starting and during acceleration of the load.
7. Lastly, find the actual factor of safety and compare with the
factor of safety given in the Table. If the actual factor of safety is
within permissible limits, then the design is safe.
18

19. Sample Problem 1
*Select a wire rope for a vertical mine hoist to lift a load of 50 kN from
a depth 150 meters. A rope speed of 250 metres / min is to be
attained in 10 seconds.
19
s
; t
m/
m; v
N
kN
W 10
min
250
150
depth
;
50000
50
:
Given





Step 1. Select a suitable type of rope from Tables for the given application.
Either 6x7 or 6x19 rope can be used. Say, we use 6x19

20. 20
Step 2. Find the design load by assuming a factor of safety 2 to 2.5 times the
factor of safety given in the Table.
 
  N
N 900000
50000
18
rope
for the
Load
Design
18
8
2.25
safety
of
Factor





21. 21
Step 3. Find the diameter of wire rope (d) by equating the tensile strength of
the rope selected to the design load.
mm
mm
d
d
38
89
.
38
900000
595 2




22. 22
 
  2
2
2
550
38
38
.
0
38
.
0
4
.
2
38
063
.
0
063
.
0
mm
d
A
mm
d
dw






Step 4. Find the diameter of the wire (dw) and area of the rope (A) from the
Table.

23. 23
Step 5. Find the various stresses (or loads) in the rope.
  N
d
w
w
a
6
.
7862
150
0363
.
0
rope
of
length
X
length
unit
ave.wt.per
rope
of
weight
)
2





24. 24
 
 
2
2
3
.
66
3040
4
.
2
84000
ropes;
steel
for
84
:
3040
38
80
sheave
dia.of
;
80
Say
)
mm
N
S
mm
kN
E
D
d
E
S
mm
D
d
D
b
b
r
w
r
b 








25. 25
  N
W
A
S
W
b
b
b
36465
550
3
.
66
load
bending
equivalent




 
   
    N
w
W
W
h
d
N
a
g
w
W
W
W
s
m
t
v
a
c
st
a
a
115725.2
6
.
7862
50000
2
2
given)
(not
0
starting,
to
due
load
Impact
)
2459.6
417
.
0
81
.
9
6
.
7862
50000
on
accelerati
to
due
load
l
add'
417
.
0
10
60
250
60
load
and
rope
of
on
accelerati
)
2
















26. 26
Step 6. Find the effective stresses (or loads) during normal working, during
starting and during acceleration of the load.
Step 7. Lastly, find the actual factor of safety and compare with the factor of
safety given in the Table. If the actual factor of safety is within permissible
limits, then the design is safe.
ry.
satisfacto
is
diameter
mm
-
38
of
rope
19
x
6
therefore
Safe,
3
.
9
96787.2
900000
safety
of
factor
Actual
96787.2
2459.6
36465
6
.
7862
50000
load
Effective
load,
of
on
accelerati
During
91
.
5
152190.2
900000
safety
of
factor
Actual
152190.2
36465
115725.2
load
Effective
starting,
During
54
.
9
94327.6
900000
safety
of
factor
Actual
94327.6
36465
6
.
7862
50000
load
Effective
operation,
normal
During



























N
W
W
w
W
N
W
W
N
W
w
W
a
b
b
st
b

27. Sample Problem 2
*Select a suitable wire rope to lift a load of 10 kN of debris from a well
60 m deep. The rope should have a factor of safety equal to 6. The
weight of the bucket is 5 kN. The load is lifted up with a maximum
speed of 150 metres/min which is attained in 1 second. Find also the
stress induced in the rope due to starting with an initial slack of 250
mm. The average tensile strength of the rope may be taken as 590 d2
Newtons (where d is the rope diameter in mm) for 6 × 19 wire rope.
The weight of the rope is 18.5 N/m. Take diameter of the wire (dw) =
0.063 d, and area of the rope (A) = 0.38 d2.
27
d
.
d; A
.
; d
wire rope
x
m
N
w
d
mm
h
s
t
m
v
;
m; FS
N
kN
W
N
kN
W
w
bucket
debris
2
2
38
0
063
0
19
6
;
5
.
18
;
590
strength
Tensile
;
250
;
1
;
min
150
6
60
depth
;
5000
5
;
10000
10
:
Given














28. 28
 
 
mm
d
mm
d
d
N
20
Use
;
53
.
18
202500
590
202500
5000
10000
5
.
13
rope
for the
Load
Design
5
.
13
6
2.25
safety
of
Factor
2








 
  2
2
2
152
20
38
.
0
38
.
0
26
.
1
20
063
.
0
063
.
0
mm
d
A
mm
d
dw






 
 
 
  N
A
S
W
mm
N
S
mm
kN
E
D
d
E
S
mm
D
d
D
d
N
m
m
N
w
b
b
b
r
w
r
b
26812.8
152
4
.
176
4
.
176
600
26
.
1
84000
ropes
steel
for
84
:
600
20
30
sheave
dia.of
;
30
20
1110
60
5
.
18
rope
of
weight
2
2
















29. 29
 
   
 
     
  
N
W
Lg
S
ahE
w
W
W
W
mm
m
depth
L
mm
h
mm
N
A
W
S
N
a
g
w
W
W
W
W
s
m
t
v
a
st
a
r
bucket
debris
st
a
a
bucket
debris
a
a
60542.7
81
.
9
60000
27
84000
250
5
.
2
2
1
1
1110
5000
10000
2
1
1
60000
60
;
250
starting,
to
due
load
Impact
27
152
4105.5
4105.5
5
.
2
81
.
9
1110
5000
10000
on
accelerati
to
due
load
l
add'
5
.
2
1
60
150
60
load
and
rope
of
on
accelerati
2
2










































30. 30
2
398.3
152
60542.7
mm
N
A
W
S st
st 


   
 
 
31
.
4
47028.3
202500
safety
of
factor
Actual
47028.3
4105.5
26812.8
1110
5000
10000
load
Effective
load,
of
on
accelerati
During
32
.
2
87355.5
202500
safety
of
factor
Actual
87355.5
26812.8
60542.7
load
Effective
starting,
During
72
.
4
42922.8
202500
safety
of
factor
Actual
42922.8
26812.8
1110
5000
10000
load
Effective
working,
normal
During































N
W
W
w
W
W
N
W
W
N
W
w
W
W
a
b
bucket
debris
b
st
b
bucket
debris

31. Homework:
*Suggest the suitable size of 6 × 19 hoisting steel wire rope for an
inclined mine shaft of 1000 m length and inclination of the rails 60°
with the horizontal. The weight of the loaded skip is 100 kN. The
maximum acceleration is limited to 1.5 m/s2. The diameter of the
drum on which the rope is being wound may be taken as 80 times the
diameter of the rope. The car friction is 20 N / kN of weight normal to
the incline and friction of the rope on the guide roller is 50 N / kN of
weight normal to the incline. Assume a factor of safety of 5. The
following properties of 6 × 19 flexible hoisting rope are given : The
diameter of the rope (d) is in mm. The weight of the rope per meter =
0.0334 d2 N; breaking load = 500 d2 N; wire diameter = 0.063 d mm;
area of wires in rope = 0.38 d2 mm2; equivalent elastic modulus = 82
kN/ mm2. [Ans. 105 mm]
31