This document provides information on various types of hoisting equipment and their components. It discusses theory of hoisting equipment including flexible hoisting appliances like pulleys, chains, and wire ropes. There are three main groups of hoisting equipment - hoisting machines, cranes, and elevators. Cranes combine a hoisting mechanism with a frame to lift and move loads vertically and horizontally. Selection criteria and technical parameters for hoisting equipment like lifting capacity, speed, and dimensions are also outlined. The document also covers wire rope construction, selection, and fastening of chains and ropes. Pulleys are defined as wheels that support movement and change of direction of cables or belts to lift loads or transmit power.

1. Hoisting Equipment
Outlines
 Theory of hoisting equipment
 Flexible hoisting appliance
 Pulleys, sprockets, Drums and
 Load handling attachments
 Arresting gear and brakes
 Hoisting and travelling gear

2. Theory of hoisting equipment
 The hoisting is a device used for lifting or lowering a load by means
of drum or lift – wheel around which rope or chain wraps.
 It may be done with a wide range of equipment from the small hand
operated simple screw or hydraulic – jack to modern high powered
cranes and elevators.
 It may be manually operated, electrically or pneumatically driven
and may use chain, fiber or wire rope as its lifting medium.
 Hoisting equipment can be a stationary, portable or travelling.

3. Cont..
There are three groups of hoisting equipment having the
following main distinctive features.
i. Hoisting machines - a group of periodic action devices
designed for vertical lifting and lowering of freely
suspended unguided load.

4. Cont..
ii. Cranes - a combination of separate hoisting mechanism
with a frame for lifting and/or moving loads
 machines for moving loads vertically and horizontally by
the help of a frame and a hoisting mechanism

5. Cont..
iii. Elevators - a group of periodic action machine intended
for raising loads with guide – ways.

6. Cont..
The main technical parameters are:
 lifting capacity : the maximum safe load a machine is designed to
handle
 Dead weight of the machine : the total weight of the machine
without load
 Speed of various movements: this may be the hoisting speed, the
bridge travel speed and the trolley traveling speed
 lifting height : the height to which the load is intended to be
raised;
 Geometrical dimension of the machine.

7.  Hoisting machines are periodic-action machines and their hourly
capacity can be determined from:
n= number of machine cycles/ hour
Q= weight of live load [tons]
Qhr =Hourly capacity [tons/h]
 When handling bulk material, the weight of live
Q = V x ϕ x ɣ
Where
V= capacity of bucket, [m3]
ϕ = filling factor
ɣ= specific weight [t/m3]
Q
n
Qhr 


8.  The total load lifting capacity of the machine will be:
𝑄𝑡𝑜𝑡= 𝑄 + 𝐺
Where:- Q = live load [tons]
G = weight of bucket, grab, etc. [tons]
 The number of cycles per hour is:
Where
𝑡𝑜𝑝= operation time
𝑡𝑠𝑡=starting time
𝑡𝑐𝑠=constant speed time
𝑡𝑟= retardation time
𝑡𝑖𝑑𝑒𝑙=time lost in grabbing and discharging the load
t= cycle time[second]


t
n
3600
r
cs
st
op t
t
t
t 



idle
op t
t
t 

 

10. Flexible hoisting appliances
Hoisting machineries use different flexible hoisting appliances for
handling materials some of which hemp rope, welded and roller
chains, and steel wire ropes.
1. Hemp – Ropes
 Because of their poor mechanical properties (rapid abrasion,
inadequate strength, rapid damage from sharp materials and
atmospheric effects, etc),
 They can be recommended only for hand- operated hoisting
machinery (rope pulleys with diameters at least10d).

11. Cont..
 By the mode of manufacture and number of strands, hemp ropes are
classified as
i. plain-laid
ii. cable-laid
 The latter being from twisted from three ordinary ropes twisted from
three ordinary ropes.
Where F = load on the rope [kgf]
d = nominal rope diameter [cm]
For white rope σ𝑏𝑟=100 kgf/cm2 and for tarred rope σ𝑏𝑟= 90 kgf/cm2
br
2
4
d
=
F 


12. Cont..
2. Welded loaded chains
 They are widely used in hoisting installations as flexible members.
Fig.3.2 Main Dimensions of a Welded Chain
 Depending on the ratio between the pitch and the diameter of the
chain bar, welded chains are classified into
i. Short – link chains with t ≤ 3d
ii. Long – link chains with t ˃ 3d
where t - pitch of the chain equal to the inside length
of the link
d - diameter of chain bar
B - chain outside width

13. Cont..
Manufacturing accuracy divides welded chains into:
i. Calibrated -with permissible deviation from the nominal size within t +/- 0.03d
and B+/- 0.05d
ii. Uncalibrated -with permissible deviation from the nominal size within t +/- 0.1d
and B +/- 0.1d
 Links for welded chain are formed most commonly hammer (forge) and electric
resistance welding.
Application
 welded chains are used only in some hand –operated mechanism (where Dmin >
20d) and in few power drive mechanism (where Dmin > 30d)
 They are employed for low capacity hoisting machines (hoists, winches, hand –
operated cranes, etc)
 They are also used as the main lifting appliance and as hand driven chains for
traction wheels (d = 5 to 6mm at a speed of v = 0.6 to 0.75m/s).

14. Cont..
Advantage of welded chain
 Good flexibility in all direction
 Possibility to use small diameter pulleys and drums
 Simple design and manufacture
Disadvantages of welded chains
 Heavy weight
 Susceptibility to jerks and overload
 Sudden failure
 Concentrated wear at the link joints and
 Low safe speed of movement.

15. Selection of Load Chains
 Chains are checked for tension taking a higher safety factor to
take care of the complexity of the problem.
Where:-
o 𝐹𝑏𝑟=breaking load [kgf] (given in manufacturer's catalogue and
in standards)
o K = factor of safety
o 𝐹𝑠=safe load carried by chains [kgf
 the safety factor K should be taken from 3 to 8.
K
F
F br
s 

16. Cont..
3. Roller chains
 Roller chains are composed of plates hinge – jointed by pins and
rollers.
 For light loads, two plates are used. For very heavy loads the
number of plates can be increased up to 12.
 The maximum allowable speed of roller chain is V = 0.25m/s
 Roller chains are used for hand operated hoists, power – driven
winches and hoisting mechanisms of high load lifting capacity.

18. Advantage of roller chains
Roller chains are superior to welded chains in a number of ways such
as:
 The reliability of operation is higher since the plates are solid.
 Roller chain have good flexibility
 The friction in the joints is considerably less than that in the joints
of welded chains.
But roller chains should not be allowed:
 To carry weight acting at an angle to the plate(to prevent excessive
wear and pin breakage)
 To be used in dusty premises (unless the chain is sealed by cover
which would cause excessive wear)
 To a speed greater than0.25m/s
 To wind on a drum

19. Data for the Selection of Chains
Chains Drive Factor of
Safety, K
Ratio
(D/d)
Minimum Number of
Teeth on Sprocket
Welded calibrated and
uncelebrated
Hand
power
3
6
20
30
5
5
Welded calibrated on sprocket
sheaves
Hand
power
4.5
8
20
30
-
-
Welded uncalibrated (sling)
passing around the load - 6 - -
Welded uncalibrated (sling) not
passing around the load - 5 - -
Roller - 5 - 8

20. Cont..
4. Steel wire Ropes
 The steel wire ropes are extensively used in hoisting machinery as
flexible lifting appliance.
Comparing to chains they have the following advantages:-
Lighter weight
Less susceptibility to damage from jerks
Silent operation even at high speeds
Greater reliability in operation

21. Steel Wire Rope Construction
Wire ropes are manufactured first by twisting separate wires, cold
drawn and given heat treatment between drawing stages, into strands
and then into a "round" rope.
Wire ropes consist of 6 or 8 strands and a core. Each strand consists of
19 or 37 wires.

22.  Wire ropes formed from strands are known as double lay ropes.
 They are the most popular types used in hoisting machinery. The lays of
the rope classify the wire ropes into:
i. Cross-of regular lay ropes: the direction of the twist of the wires in the
strand is opposite to that of the strands in the rope (Fig.3.8a).
ii. Parallel or long lay ropes: the direction of twist of wire and strand is
the same (Fig.3.8b). This is more flexible and resists wear better, but
tends to spring and are used in lifts.
iii. Composite or reverse laid ropes: the wires in two adjacent stands are
twisted in the opposite direction (Fig.3.8c).

23. Kinds of Wire Ropes
1. General Purpose Steel Wire Ropes
a. Ordinary (one size-wire) construction: the strands are twisted of
wires of the same diameter. The repeatedly cross over of the inner
wires create zones of increased unit pressure, which shortens life.
b. Warrington type compound rope: is twisted of strands with
different wire diameters keeping the proportional pitch of every
layer, thus crossovers are eliminated.

24. Cont..
2. Non –spinning wire ropes
 Each individual wire and strand being laid is performed to
correspond to its disposition in the rope.
 As a result of unloaded wires are not subjected to internal stresses
and tend to spin.
 Advantages of non – spinning wire ropes over the general
purpose ropes:-
Uniform load distribution over the individual wires,
which reduces internal stresses to a minimum –
Better flexibility
Less wear of the wire ropes running over drum or
sheaves
 Greater operation safety.
The disadvantage of non- spinning wire ropes is that it is more
expensive

25. 3. Steel Wire Ropes with Flattened Strands
 They are usually made from five flattened strands with a flattened wire core; the
strands are laid on the hemp core Thus they experience more uniform pressure.
 Such ropes are used where the rope is subjected to intensive abrasion and wear.
4. Locked-coil Steel Wire Ropes
 A locked coil rope consists of an outer layer formed of specially shaped wire and
an inner single lay spiral rope
 Locked-coil wire ropes are used in cable-ways and cable cranes; they are never met
within hoisting machines.
(a) (b)
Fig.3.9 Ropes with Flattened Strands

26. Selecting Steel Wire Ropes
 Wires in a loaded rope experience complex stress consisting of
tension, bending, twisting and compression.
 The rope life is inversely proportional to the number of bends
 where one bend equals the transition of the rope from a straight
position into a bent position or vise versa.
Depending on the number of bends, the corresponding rope life can
be found from the ratios:
𝐷𝑚𝑖𝑛
𝑑
=
𝐷𝑚𝑖𝑛
ẟ
Where:
𝐷𝑚𝑖𝑛= minimum diameter of pulley or drum
d = rope diameter
ẟ= wire diameter

28. Table3.4 Values 𝐷𝑚𝑖𝑛 /d as a Function of Number of Bends
No. of bends
1 2 3 4 5 6 7 8
𝐷𝑚𝑖𝑛/d 16 20 23 25 26.5 28 30 31
No. of bends 9 10 11 12 13 14 15 16
𝐷𝑚𝑖𝑛/d 32 33 34 35 36 37 37.5 38

29. Strength of Wire Rope
• Total stress in the loaded wire rope in its bent part is the sum of the
tensile and bending stress.
Where
σ𝑏𝑟 =breaking strength [kgf/cm2 ]
K = rope factor of safety
S = tension in the rope [kgf]
A = useful area of the cross-section [cm2]
I = moment of inertia [cm4]
M = bending moment [kgf.cm]
c = centroid [cm]
= Corrected rope elastic modulus  800,000kg/cm2
E = elastic modulus of rope wire material = 2,100,000kg/cm
I
Mc
A
S
ben
ten 



 


min
min D
E
2
I
M
EI
M
1
D
2





min
min
ben
D
E
2
D
E
2
I
Mc
2
c










min
br
D
'
E
+
A
S
K


 


E
8
3
'
E 

30.  The area of the wire rope is the sum of the cross-sectional area
of each individual wire multiplied by a filling factor of 2.25.
Where:
i = number of wires in the wire rope
ẟ = diameter of wire rope
d = rope diameter
Thus
Rewriting the equation for the required useful area:
K
d
D
i
1.5
'
E
A
S
D
i
5
.
1
d
'
E
A
S
D
'
E
A
S br
min
min
min


 
















25
.
2
i
4
4
d 2
2



 i
1.5
d 

i
E
D
d
K
S
A
br
5
.
1
'
min





31. Ropes subjected to only tensile forces
𝐹𝑏𝑟= breaking strength [kgf]
𝐹𝑆 =maximum permissible tensile force in the rope [kgf]
K = factor of safety
Values of K for Different Operating Conditions
K
F
F br
s 
Drive Duty K e
Hand Light (L) 4.5 18
Power
Light (L) 5.0 20
Medium (M) 5.5 25
Heavy (H) 6.0 30
Very Heavy (VH) 6.0 30

32. cont..
4. Fastening of chains and Ropes
 Various methods are used to secure the ends of chains and ropes.
a) Fastenings of Welded Load Chains

33. b) Fastenings of Roller Chains

34. c) Fastenings of Wire Ropes

35. Pulleys
 A pulley is a wheel on an axle or shaft that is designed to support
movement and change of direction of a rigid cable or belt, or
transfer of power between the shaft and cable along its
circumference.
 Pulleys are used in a variety of ways to lift loads, apply force, and
to transmit power.

36. Classification of pulleys
 Pulleys are either fixed or movable in design.
1. Fixed Pulleys
 Fixed pulleys are used to change the direction of the flexible appliance.
 Disregarding the resistance of the pulley, the pulling force Zo equals Q (weight to
be pulled) i.e Zo = Q, without considering pulley resisting.
 But in reality due to the pulley resistance, Z0 > Q,
 the resistance being partly due to the stiffness of wire rope and partly due to
frictional resistance in the bearings.

37. Momentum equilibrium
a.Due to the stiffness of the wire rope
 The rope is first deflected by an amount e to the outside on the
running-on part and approximately the same amount to the inside on
the running-off part.
(Rcosϕ  e)Q (Rcos ϕ –e)Z
The Deflection of the Wire Rope on a Pulley
e
R
e
R
Q
Z





cos
cos


cos
1
cos
1
R
e
R
e














cos
2
1
R
e
Q
Z

38. b. Resistance due to friction
The resisting moment due to frictional resistance
Frictional resistance in the bearings:
d ' = pulley axle diameter
 = coefficient of friction
where
Q
Z
Q
P 2
0 


2
'
d
P
M 

 
( )
R
d
Q
R
2
d
Z
Q
N
'
'







c. Total pulling force
( )
friction
to
due
resistance
regidity
to
due
resistance
Q
Z 

 1













R
d
cos
R
e
2
1
Q
Z
'

39. .
where is stiffness of rope
where d - rope diameter [cm]
D - pulley diameter [cm
 The magnitude of is called pulley factor of resistance, and


Q
Z



1
is the pulley efficiency
Thus
R
d
cos
R
e '






2
1

cos
2
R
e
10
1
.
0
cos
2


D
d
R
e

it can be empirically determined by experiment and was found
to be

40. Cont...
2. Movable pulley
 Movable pulleys are used to gain mechanical advantage or speed/force.
Movable pulleys are classified into two
a. Pulleys for gain in force:
 Used to increase amount of force applied and it doesn’t change direction
of the force.
 The distance that effort moves is double that of the load, and the speed at
which the load is raised is half of that of the effort.
S = 2h, C = 2v
Where: C= Speed of force
v = speed of load
s = distance the force moves
h = distance the load moves
Figure : Single movable pulley for a gain in force

41. • Resistance:
Z + So = Q , Z =  So =  (Q –Z)
Z = Q -Z
• where for   1.05,   0.975
Q
Z




1 




2
1
1
2 




Q
Q
Z
Zo
2
Q
Zo 

42. Cont..
b) Pulleys for gain in speed
 Used to increase amount of load speed and it doesn’t change
direction.
 The effort is applied at the axle of the pulley and moves at half
the speed of the load.
 The distance moved by the load is twice that of the effort.

43. Cont..
3. Block and Tackle pulley
 A block and tackle is a pulley system made up of fixed and movable
pulleys.

44. Cont..
Pulley Systems
 Several fixed and movable pulleys are combined in order to form a
pulley system for a gain in force or a gain in speed.
Figure: pulley system for a gain in force Figure: pulley system for a gain in Speed

45. Pulley systems for gain in force
 Pulleys for a gain in force can further be divided into rope running
of a fixed pulley and rope running of a movable pulley
a. Rope running off a fixed pulley
The number of parts of the line on which the weight is suspended is
also equal to the number of pulleys Z. The transmission ratio i of the
system is equal to z. Neglecting pulley resistance
and the actual effort Z is given by
Z= z
Q
z
Q 





48. b. Running off a movable pulley
 When the rope runs off a movable pulley in a pulley system of z
pulleys, the number of rope parts on which the load is suspended is
equal to one plus the number of pulleys.
Transmission ratio:
The ideal effort:
The actual effort:
1

 z
i
1
0


z
Q
Z
)
( 1




z
Q
Z

50. Pulley System for a Gain in Speed
 is usually used in hydraulic and pneumatic lifts to move the load
faster
 The working effort Z provided by a hydraulic or pneumatic means
is applied to a movable frame while the load is suspended at the
free end
 For the case shown

51.  Sheaves :- Used for ropes and welded chains
 Sprockets:- Used for welded chains and Roller chain
 Drums:- used for Hemp rope and steel wire ropes
Flexible hoisting appliances
- Hemp – rope
- Welded loaded chains
- Roller chain
- Steel wire ropes

53. Sheaves
 A sheaves is a pulley with a grooved wheel for holding belt, wire
rope or rope.
 A sheaves are grooved rims used for guiding ropes or chains.
 The sheaves are usually mounted freely on their axles.
 To increase rope life, sheave grooves are lined with aluminum,
rubber, and plastics.

54. Design of sheaves and Sprockets Rope Sheaves
The minimum diameter 𝐷𝑚𝑖𝑛of the sheave should be at least ten times
the diameter of the hemp rope. Whereas 𝐷𝑚𝑖𝑛for wire rope should be
Where
𝑒1= factor depending on the hoisting device and its service
𝑒2= factor depending the rope construction
d= wire rope diameter
Where =deviation of the rope from the plane of the sheave.
d
e
e
D 2
1
min 


K
7
.
0
D
1
tan
2
tan max





55. 1. Sheaves for welded chains:
These sheaves are usually made of cast iron. They are mainly used for
hand operated hoists and rarely they are used for power driven devices.
The minimum diameter of the chain sheave may be calculated by:
𝐷 ≥ 20𝑑 for hand driven
𝐷 ≥ 30𝑑for power driven
where d= diameter of the chain bar
The efficiency of a chain sheave is 𝜂 = 0.95.
The resistance of welded chains running over sheaves to bending is
ordinarily determined from the formula:
𝑊 = 𝑄
𝑑
𝑅
𝜇 (4.16)
where R = radius of the sheaves
𝜇 = coefficient of friction in the line joints (  0.1 to 0.2)
Q = tension in the chain.

56. Sprockets
 A sprocket or sprocket-wheel is a profiled wheel with teeth, that
mesh with a chain, track or other perforated or indented material.
 As a rule , sprockets are manufactured with a small number of teeth
and are small in size ensuring compactness and low cost of the
driving mechanism.

57. 1. Sprockets for Welded Chains:
 Sprockets are used as driving chain wheels of hand operated hoists
and winches.
 The diameter of the sprocket can be found as follows
From triangle AOC
𝐴𝑂 = 𝑂𝐶
2
+ 𝐴𝐶
2
𝑅 = 𝑎2 +
𝑡+𝑑
2
2
𝛼 =
3600
𝑧
where z = number of teeth

58.  Expressing the value of a in terms of 𝛼, t and d, for small z = (  z )
2𝑅 =
𝑡
𝑠𝑖𝑛
900
𝑧
2
+
𝑑
𝑐𝑜𝑠
900
𝑧
2
where t = inside length of the link
d = diameter of the chain bar
z = number of sprocket teeth; the minimum number of teeth z = 4
 For z > 9 and for sufficiently small chain bar diameter (d  16) then the
second terms in the previous formula can be neglected and
𝐷 ≈
𝑡
𝑠𝑖𝑛
900
𝑧
2
=
𝑡
𝑠𝑖𝑛
900
𝑧

59. 2. Sprockets for Rollers chains:
 Sprockets are manufactured from cast iron and forged steel of steel
castings.
 They are mainly used for hand-operated hoists and winches.
 From triangle AOC
 𝐷 =
𝑡
𝑠𝑖𝑛
180
𝑧
; 𝐴𝑂 =
𝐴𝑐
𝑠𝑖𝑛
𝛼
2
; 𝛼 =
360
𝑍
where t = pitch measured along the cord
z = teeth number; 𝑧𝑚𝑖𝑛
𝜂 = 0.95
Fig. 4.14 Sprockets for Roller Chains

60. Drums
 Drums is a grooved wheel on which the rope is wound in more than
one layer.
 During operation the drum is subject to the combined action of
torsion bending and compression.
 The machined grooves increase the drum bearing surface, prevent
friction between the adjacent rope turns and consequently reduce the
contact stresses and rope wear.

61. Rope Drums
 Drums for steel wire rope are made of cast iron and rarely of steel
castings.
 Helical grooves are always used for wire ropes.
 Number of turns on the drums (z)
𝑧 =
𝐻𝑖
𝜋𝐷
+ 2
where i = ratio of the pulley system
D = drum diameter
H = height to which the load is raised
The value 2 in equation 4.16 is added to account for the
idle (or holding) turns.
 Length of the helix on the drum:
𝑙 = 𝑧 × 𝑡
where t is the pitch
Fig.4.15 Helical Grooves in Rope Drums

62.  Leaving a length of about 5t for both sides flanges, the full length of the
drum L is:
𝐿 =
𝐻𝑖
𝐷𝜋
+ 7 𝑡
 If two ropes are coiled on the drum, the full length of the drum will be
𝐿 =
2𝐻𝑖
𝜋𝐷
+ 9 𝑡 + 𝓁1
where 𝓁1 is the space in the middle of the drum (minimum of 3t).
 The wall thickness of cast iron drum can be approximated by using the
following formula:
w= 0.02D  (0.6 to 1.0) cm

63.  One-half ring is separated from the body with the thickness of w and
with the width equal to the pitch s.
 The tension forces S are effective on the separated ring.
The force bearing on an element of an area is
dA = sR d and dS = (d A) p.
Where:- p is the normal pressure on a unit drum surface.
S is the sum of dS on the vertical projection
Fig.4.16 Forces Acting on a Drum

64. 2𝑆 = 2
0
𝜋
2
𝑅𝑑𝜙 ⋅ 𝑠𝑝 𝑐𝑜𝑠 𝜙 = 2𝑅𝑠𝑝
0
𝜋
2
𝑐𝑜𝑠 𝜙 𝑑𝜙
2𝑆 = 2𝑅 ⋅ 𝑠𝑝
𝑝 =
𝑆
𝑅𝑠
=
2𝑆
𝐷𝑠
From Lames formula: At the inner surface
𝜎𝑖𝑛 = 𝑝𝑖𝑛
𝐷2+𝑑0
2
𝐷2−𝑑0
2 − 2𝑝𝑜𝑢𝑡
𝐷2
𝐷2−𝑑0
2
At the outer surface
𝜎𝑜𝑢𝑡 = 2𝑝𝑖𝑛
𝐷2+𝑑0
2
𝐷2−𝑑0
2 − 𝑝𝑜𝑢𝑡
𝐷2
𝐷2−𝑑0
2
where 𝜎𝑖𝑛= internal stress
𝜎𝑜𝑢𝑡= external stress
𝑝𝑖𝑛= internal pressure
𝑝𝑜𝑢𝑡= external pressure
𝐷 = internal diameter
𝑑𝑜= outside diameter

65. Considering the forces in we have:
pin = 0 , pout = p , do = 𝐷 − 2𝑤
𝜎𝑖𝑛 𝑐𝑜𝑚𝑝 = −2𝑝𝑜𝑢𝑡
𝐷2
𝐷2+𝑑0
2
𝜎𝑐𝑜𝑚𝑝 = −2
2𝑆
𝐷𝑠
×
𝐷2
𝐷2−𝑑0
2 =
−4𝑆𝐷
𝑠 𝐷+𝑑 𝐷−𝑑0
𝐷 + 𝑑0 ≈ 2𝐷 and 𝐷 − 𝑑0 ≈ 2𝑤
𝜎𝑐𝑜𝑚𝑝 =
−4𝑆𝐷
𝑆2𝐷⋅2𝑤
=
𝑆
𝑠𝑤
Allowable compressive stresses:
For cast iron 15-32 𝜎𝑎𝑙𝑙 = 1,000 kgf/cm2
cast steel 𝜎𝑎𝑙𝑙 = 1,600 kgf/cm2
welded drums (St 42) 𝜎𝑎𝑙𝑙 = 1,800 kgf/cm2
Allowable bending stresses:
For cast iron 𝜎𝑎𝑙𝑙 = 230 kgf/cm2
steel casting 𝜎𝑎𝑙𝑙 = 1,800 kgf/cm2
welded drums 𝜎𝑎𝑙𝑙 = 1,400 kgf/cm2

66. Friction Drums
 Friction Drums for Ropes: are rope-driving drums in which
motion is transmitted by friction between the rope and drum. There are
three types of friction drums.
a. Simple friction drums are provided with helical grooves for the
rope, which coils around them in one or several turns.

67. Tension ration between on coming and running off parts of simple rope is
described by Euler’s formula:
𝑆1
𝑆2
= 𝑒𝜇2𝜋𝑛
where:- 𝑆1 on coming force
𝑆2 running off (can be regulated by hand)
 coefficient of friction
n  number of coils
e  2.718 the base of the natural logarithm
𝐹 = 𝑆1 − 𝑆2 peripheral force on drum
Simple friction drums are used for
 the drives of trucks in rotary cranes with variable radius
 load transfer bridges
 cable cranes
 moving ratio and cars at docks and ports
-hoisting anchors and hauling various loads

68. b. Double-Drum Friction Drive: In this case the rope is wound several
times around two parallel drums rotating in the same direction and
driven by a single motor.
 The tension force in the parts of the rope is
𝑆2 =
𝑆1
𝑒𝜇𝜋𝜂1
; 𝑆3 =
𝑆1
𝑒𝜇𝜋⋅𝜂1
2
(4.27)
𝑆𝑛 =
𝑆1
𝑒𝜇𝜋⋅𝜂𝑛−1 𝑆𝑛+1 =
𝑆1
𝑒𝜇𝜋⋅𝜂𝑛
where 𝑆1= tension on the on coming leg of rope
𝑆2, 𝑆3= tension in the intermediate parts
𝑆𝑛+1= tension in the running off parts
𝜋 = arc of contact of the rope on one drum
n = bearing areas in contact between the rope and both drums
η1 = 0.995 = efficiency taking into account the rigidity of the rope in one
encirclement (disregarding the losses in the bearings).

69. c. Capstan: are usually arranged vertically, driven by an electromotor
through a worm gear drive and used to move railway cars.
𝑆2 =
𝑆1
𝑒𝜇2𝜋𝑛
s1
s2
where n is the number of turns.
Capstan

70. LOAD HANDLING ATTACHMENTS
 The load is usually handled by various methods.

71. Cont..
 They are three most commonly used load handling attachment
i. Hook’s
ii. Electric lifting magnets
iii. Grabs
i. Hook’s
 The load is usually handled by means of chain or rope slings
attached to hooks.
 One – piece forged hooks are used for lifting loads up to 100 tons
while triangular and laminated hooks can be employed to carry
over 100 tons.
 Hook are forged from low carbon steel.

72. Cont..
 Generally hooks have trapezoidal section made wider on the inside
for better material utilization.

73. Cont..
ii. Electric Lifting Magnets.
 Lifting magnets are used to handle magnetic materials of diverse
form (ingots, beams, rails, steel sheets and plates, scrap, metal chips
etc.).
 These drastically reduces the time required for manual suspension
of loads.

74. Cont..
iii. Grabs
• These are the holding attachments which are special type of buckets
which mechanically grab and automatically dump the materials.
• The grabs are designed considering the type of material to be bold.

75. Forged Standard Hooks
Hook Dimensions
 For the shank:
𝜎𝑡 =
4𝑄
𝜋𝑑1
2 ≤ 𝜎𝑎𝑙𝑙 =500 kgf/cm2
 The unit stress on the saddle of the hook
𝜎 =
𝑄
𝐴
+
𝑀
𝐴𝑟
+
𝑀
𝐴𝑟
⋅
1
𝑥
⋅
𝛾
𝛾 + 𝑟

76. where
  = unit stress for the fibre at a distance y from the neutral axis
[kgf/cm2]
 Q = load on the hook kgf
 A = area of the critical cross-section here cross-section I cm
 r = radius of curvature of the neutral axis at the critical cross-section
cm
 x = factor depending on the shape of the cross-section and the
curvature of the beam
 y = distance from the fibre to the neutral axis.
 y is negative if the fibre is between the centre of curvature and the
natural axis; and is positive if the fibre is on the other side of the neutral
axis,cm

77. )
Since the load tends to open the hook,
𝑀 = −𝑄. 𝑟 = −𝑄 0.5𝑎 + 𝑒1
𝜒 = −1 +
𝑟
𝐴
𝑏2 + 𝑏1 − 𝑏2
𝑅2
𝑑
𝑙𝑛
𝑅2
𝑅1
− 𝑏1 − 𝑏2
𝜒 = −
1
𝐴
𝑦
𝑦+𝑟
𝑑𝐴
The Critical Cross-section I-II
 M = bending moment kgf.cm.
 M is positive if it causes the hook curvature to increase (its radius
decrease) or negative if the curvature decreases.

78. 1. Tensile Stress in the Inner Fibre
Substituting
𝑀 = −𝑄 0.5𝑎 +𝑒1
𝑟 = 0.5𝑎 + 𝑒1
𝑌 = −𝑒1
and h = a
In the equation 4.26 for , we obtain
𝜎𝐼 =
𝑄
𝛢
−
𝑄 0.5𝑎 + 𝑒1
𝛢𝑟
− 𝑄
0.5 + 𝑒1
𝐴𝑟
⋅
1
𝜒
⋅
𝑦
𝑦 + 𝑟
=
𝑄
𝐴
1 −
0.5𝑎+𝑒1
𝑟
1 +
1
𝜒
⋅
𝑦
𝑦+1
𝜎𝐼 =
𝑄
𝐴
⋅
1
𝑥
⋅
2𝑒1
𝑎
≤ 𝜎safe all - maximum tensile stress
i.e. the maximum unit tensile stress of the inner fibres of the section is:
𝜎𝑡 =
𝑄
𝐴
⋅
1
𝜒
⋅
2𝑒1
𝑎
 𝜎𝑎𝑙𝑙

79. 2. Compressive Stress in the Outer Fibre
Substituting
𝑀 = −𝑄 0.5𝑎 + 𝑒1
𝑟 = 0.5𝑎 + 𝑒1; ℎ = 𝑒1 + 𝑒2
𝑟 = 0.5𝑎 + ℎ − 𝑒2
and 𝑦 = 𝑒2
In the equation 4.26 for , we obtain
𝜎𝐼𝐼 = −
𝑄
𝐴
⋅
1
𝜒
×
𝑒2
𝑎
2
+ℎ
 𝜎𝑎𝑙𝑙 - maximum compressive
stress
In the above calculations the maximum tensile, 𝜎𝐼 and compressive,
𝜎𝐼𝐼 stresses, the allowable stress 𝜎𝑎𝑙𝑙 should not exceed 1500
kgf/cm2.

80. Solid Triangular Eye Hooks
Solid triangular eye hooks are usually employed in cranes with high
lifting capacity (over 100 tons) and occasionally in medium power
cranes
Bending moment in the bow (from investigation):
𝑀1 ≈
𝑄𝑙
6
Bending moment where the sides adjoin the bow
𝑀2 ≈
𝑄𝓁
13

81. Tensile force acting on the sides:
𝑃 =
𝑄
2 𝑐𝑜𝑠
𝛼
2
where 𝛼 = angle between the inclined sides
𝓁 = bow spans measured along the neutral line of the sections.
Q = load
Compressive force 𝑃1 acting on the bow is
𝑃1 =
𝑄
2
𝑡𝑎𝑛
𝛼
2
Maximum stress in the bow
𝜎 =
𝑀𝑏𝑒𝑛𝑑
𝑤
+
𝑃1
𝐴
< 𝜎𝑎𝑙𝑙
where 𝑀𝑏𝑒𝑛𝑑 ≈
𝑄𝑙
6
+ 𝑃1𝑥 [kgf.cm]
w = Sectional modulus[cm3]
A = Cross-sectional area [cm2]
x = moment arm of the compressive force𝑃1
The safe stress 𝜎𝑎𝑙𝑙 = 800kgf/cm2

82. Hinged Triangular Hooks
In handling heavy loads, preference is given to hinged triangular hooks.
Unit stress in the links (assuming the bow in suspended on four links)
𝜎𝑡 =
𝑄
4 𝑐𝑜𝑠
𝛼
2
⋅𝐴′
(4.30)
Permissible value of 𝜎𝑡 is 𝜎𝑡,𝑎𝑙𝑙 =1,200 kgf/cm2.
The unit stress in the bow (assumed as a curved beam)
𝜎 =
𝑝1
𝐴
+
𝑀
𝐴𝑅
+
𝑀
𝑥𝐴𝑅
⋅
𝑒1
𝑅−𝑒2
(4.31)
where 𝑀 =
𝑄
2
+ 𝑃1 ⋅ 𝑥
𝑃
1 =
𝑄
2
𝑡𝑎𝑛
𝛼
2
𝑒1 = distance between the neutral axis
and the fibres carrying the greatest load

83. Three-Joint Built-up Hooks
For an ellipse 𝑥 =
1
4
𝑎
𝑅
2
+
1
8
𝑎
𝑅
4
+
5
64
𝑎
𝑅
6
(4.32)
where a is the major axis of the ellipse or the diameter of a
circle.
The shank eye stress is check by Lame Formula of equations
4.25 and 4.26.
𝜎𝑡 =
𝑝 𝐷2+𝑑2
𝐷2+𝑑2
where 𝑝 =
𝑄
4 𝑐𝑜𝑠
𝛼
2
𝑏⋅𝑑
b = eye width

84. Arresting Gear and Brakes
Arresting Gear
 Arresting gear is used to hold the being lifted without interfering in
the hoisting process but preventing the load from coming down
due to gravity.
 They are three most common arresting gear types:-
i. Ratchet gearing
ii. Friction arresters
iii. Roller ratchets Arresting gear and brakes

85. Cont..
i. Ratchet gearing
• Ratchet gearing consists of ratchet gear and pawl.
• The teeth in the ratchet(internal teeth or external teeth) and so
arranged that the ratchet gear runs free when the load is being
raised.
• The pawl engaging the ratchet assist its motion when the load is
being lowered.

86. Cont..
ii. Friction Arresters
• Friction arresters operate noiselessly compared to the operation of
toothed arresting gear.
• However, the pressure on the pawl pivot and shaft is considerably
high. They have a limited application.
• To avoid unidirectional action, the arrester is always provided with
two pawls arranged at diametrically opposite points.

87. Cont..
iii. Roller Ratchets
• This mechanism arrest the load within a minimum distance.
• The whole system relies on friction for its successful operation.
• A roller wedged between the follower and the driver is subjected to
the action of normal forces N1 and N2 and tangential friction forces
µ1N1 andµ2N2.
• With the roller in equilibrium, the resultant force R1 = R2. for
equilibrium N1= N2

88. Brakes
• A brake is a mechanical device that inhibits motion by absorbing
energy from a moving system.
• It is used for slowing or stopping of moving vehicle, wheel axle or
to prevent it’s motion, most often accomplished by means of
friction.
• In hoisting machinery, brakes are employed for controlling the
speed of load lowering and holding the suspended load at rest.

89. Cont..
• Depending on the purpose, brakes can be classified as
i. Stopping brakes – These bring the drive at rest at the end of
motion.
ii. Regulating brakes – These are serving to maintain the speed of
motion within prescribed limits.
• From operational aspect they can be classified as
i. Automatic brakes – These brakes are applied automatically
irrespectively of the operator’s will at the- instant the motor of the
mechanism is de-energized.
ii. Controlled brakes – These are set and released by the operator
irrespectively of whether or not the relevant drive is in operation.

90. Hoisting and Travelling Gear
• In any lifting drive the hoisting mechanism is considered to be the
vital element.
• Hoisting mechanisms are subdivided into three groups
a) Hand power drives
b) Individual power drives
c) A common drive for several mechanisms

91. Cont..
a) Hand power drives
• A hand drive" is employed in mechanisms with a low lifting
capacity, or where the load has to be moved a short distance, or for
occasional lifts;
• Application area of Hand drives are:- winches with small lifting
height, in jacks, and sometimes in travelling overhead and gentry
cranes and in light-duty rotary cranes.

92. Cont..
b) Individual electric drives
• An electric motor driven hoist has one or two rope drums for
coiling and uncoiling the hoisting wire rope.
• The hoisting motor drives the drum through a planetary
gearing system.
• Electrically driven cranes designed to handle up to 2000 tons are
available. The drives can be hydraulic drive , pneumatic drive ,
diesel electric drives etc.

93. Cont..
 Electric motor is generally preferred in most hoisting installations
owing to the following advantages.
1) Immediate readiness for operation.
2) Possibility of driving every motion by a separate motor.
3) Higher economic efficiency as compared with other drives.
4) The ease of speed control over a wide range.
5) Convenient reversing of motions.
6) Safe operation, simplicity of construction, and high reliability of
safety devices.
7) Ability to cope with short-time overloads of significant
magnitude.