Structural Reliability Assessment of a Winch Drum for an Offshore Crane

Structural Reliability Assessment of a Winch Drum for an Offshore Crane
Leslie L Moyo
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Structural Reliability Assessment of a Hoist Drum for
an Offshore Crane
Leslie L Moyo
(061140947)
A Dissertation submitted in partial fulfilment for of the
requirements for the qualification of
MSc in Safety, Risk & Reliability Engineering
Supervisor: Dr Dimitry Val
School of the Built Environment, Heriot-Watt University
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DECLARATION
I Leslie L Moyo confirm that this work submitted for assessment is my own and is
expressed in my own words. Any uses made within it of the works of other authors in
any form (e.g. ideas, equations, figures, text, tables, programmes) are properly
acknowledged at the point of their use. A full list of the references employed has been
included.
Signed: …………………………….
Date: 28-Jul-09
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Table of Contents
Contents
Table of Contents __________________________________________________iii
List of Tables _____________________________________________________iv
List of Figures _____________________________________________________iv
Acknowledgements_________________________________________________ v
Abstract __________________________________________________________vi
Glossary of Terms_________________________________________________ vii
Nomenclature ____________________________________________________viii
Project Planning Documents__________________________________________ix
Chapter 1 Introduction_____________________________________________ 1
Chapter 2 Literature review: Design Requirements for Offshore Hoist Drums _ 3
Chapter 3 Hoist Drum Structural Strength Requirements _________________ 23
Chapter 4 Case Study: Auxiliary Hoist Drum on Ruston Bucyrus Crane_____ 32
Chapter 5 Probability of Failure of Hoist Drum ________________________ 41
Chapter 6 Discussion of Results ____________________________________ 65
Chapter 7 Conclusions and Recommendations _________________________ 67
Chapter 8 Suggestions for future work _______________________________ 68
References_______________________________________________________ 71
Appendices ______________________________________________________ 73
Appendix A: MIPEG Rated Capacity Indicators _________________________ 74
Appendix B: MIPEG Data from Ruston Bucyrus Crane ___________________ 77
Appendix C: Project GANTT Chart ___________________________________ 86
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List of Tables
Table 1 Failure Mode & Effects Analysis___________________________________ 31
Table 2 Material Properties______________________________________________ 38
Table 3 FORM Results – Flange Failure ___________________________________ 58
Table 4 FORM Results – Fatigue Failure ___________________________________ 60
Table 5 MIPEG Data___________________________________________________ 85
List of Figures
Figure 1 Diagram showing rope forces on flange for Method 1 (3)________________ 5
Figure 2 Diagram showing rope forces for Method 2 (3)________________________ 6
Figure 3 Relationship between P & P΄ (3) ___________________________________ 7
Figure 4 Load Cell Positions on Drum Flange (2) _____________________________ 9
Figure 5 Flange Design Curves (2)________________________________________ 10
Figure 6 Variation of Flange Force with Number of layers (3) __________________ 11
Figure 7 Asymmetric Deformation of Drum Flange (13)_______________________ 12
Figure 8 T-joint _______________________________________________________ 14
Figure 9 Hoist Drum Requirements according to API 2C (23) __________________ 19
Figure 10 Drum Forces _________________________________________________ 24
Figure 11 Drum Forces _________________________________________________ 25
Figure 12 Flange Loading (33) ___________________________________________ 28
Figure 13 Schematic of the Ruston Bucyrus Crane (34)________________________ 33
Figure 14 Failed Original Drum (34) ______________________________________ 34
Figure 15 Close-up of Failed Flange on Original Drum (34) ____________________ 35
Figure 16 Failed Replacement Drum (34) __________________________________ 36
Figure 17 Close-up of Failed Flange on Replacement Drum (34) ________________ 37
Figure 18 Schematic of Proposed Replacement Drum (34) _____________________ 38
Figure 19 Visual Basic Subroutine for the Monte Carlo Simulation of Flange Failure 63
Figure 20 Results of Monte Carlo Simulation for Flange Failure ________________ 63
Figure 21 Visual Basic Subroutine for the Monte Carlo Simulation of Fatigue Failure 64
Figure 22 Results of Monte Carlo Simulation of Fatigue Failure_________________ 64
Figure 23 Calculation of Flange Force using Roark (33) _______________________ 70
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Acknowledgements
I wish to thank Dr Dimitry Val for his assistance and guidance during this project. I
would also like to thank Dr Phil Clark for his kind assistance and guidance in selecting
an appropriate project. I would also like to thank Lloyd's Register staff in Aberdeen,
namely Mr Manoj Tripathi, Mr Peter Davies and Mr Rubik Allhaverdi for their
assistance in researching some parts of this document. I am also grateful to Mr Ian
Cumming of Specialist Maintenance Services for his assistance in obtaining information
about the hoist drum failures considered in this project. I would like to dedicate this
project to my darling Anna without whose support this project would never have been
completed.
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Abstract
Most hoist drums consist of a drum to wind the rope and where a number of layers are
required, end plates (flanges) are fitted. Whilst the effects of rope pressure on the drum
itself are well researched and understood, the effect of flange forces in hoist drums is
constantly underestimated resulting in the catastrophic failure of the drum. In addition
flanges are also sometimes subjected to forces from band brakes, clutches or both.
These additional forces further complicate hoist drum design, and clear guidance on
how the drum flange is to be designed is not readily available. The difficulty lies in
determining the magnitude and pattern of loading of the drum flange. Once the flange
force has been determined, the stresses can be evaluated.
From the research undertaken during this project, it was found that the magnitude of the
flange force varies significantly depending on various hoist characteristics such as rope
type, drum grooving, rope tension, number of layers and the fleet angle. It was also
found that despite significant research and experiments undertaken on the subject, the
findings are yet to be incorporated into most design standards. It appears that even
though hoist drum design is a complex subject, it is considered trivial by most design
standards. Most design codes and standards do not even specify any requirements for
the drum flange, leaving the designer to decide the best way to proceed based on their
knowledge and experience.
This project looks at the requirements for the design of hoist drums from various design
codes and carries out a literature review on the subject. A case study is considered
where the hoist drum flange failed twice due to poor design, and the reliability of the
proposed replacement drum is evaluated. The reliability of the hoist drum is calculated
based on the probability of failure of a proposed replacement drum using various
methods.
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Glossary of Terms
Fleet Angle Angle at which the rope approaches the drum to the drum centre
line
Lang’s Lay The rope is constructed such that the direction of twist of the
wires in the strand is in the same direction to that of the strands in
the rope.
LeBus Winding system on the drum
Ordinary Lay The rope is constructed such that the direction of twist of the
wires in the strand is opposite to that of the strands in the rope.
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Nomenclature
DNV Det Norske Veritas
FC Fibre Core
FEM Federation Europeenne de la Manutention
IWRC Independent Wire Rope Core
OEM Original Equipment Manufacturer
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Project Planning Documents
These are
1. Project Gantt chart.
2. Project method statement.
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Chapter 1 Introduction
1.1 General
Crane safety is of critical importance today, especially if the HSE are going to achieve
their target of reducing lifting equipment related accidents by 10% by 2012 in the North
Sea(BAE Systems, 2002). The integrity of individual crane elements therefore is critical
as it affects the overall crane safety. Crane design criteria will determine the likelihood
of crane failure and crane approval standards are central in determining the reliability of
the crane and by extension, its mechanisms. There are a number of Standards and
Design Rules for Offshore Cranes with differing requirements. In general, however,
they all leave the determination of the drum strength to good engineering practise.
Hoist drums are single line components whose failure will result in the failure of the
hoisting system. This project looks at the various methods used in industry to determine
hoist drum strength along with the design equations for each failure mode and where
possible the probability of failure associated with each method is calculated. A case
study of the failure of two auxiliary hoist drums of an MK35 AD Ruston Bucyrus
Pedestal Crane is used as an example.
1.2 Scope
A typical hoisting system consists of various components that include the mounting
frame, bolts, shafts, bearings, the drum, the hoist rope, the drive system that will include
a motor (usually hydraulic) and may include a gearing system and the braking system.
This research is limited to the hoist drum which is essentially a component of the
hoisting system.
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1.3 Aims
To assess the different methods used to determine the structural strength of a hoist drum
and establish how the effect of flange forces is considered in hoist drum design. Based
on a Case Study, the probability of failure associated with the effect of the flange forces
will then be determined using various methods. This is then used as an indicator of the
criticality of considering flange forces during hoist drum design.
1.4 Objectives
To achieve the above aims, the following objectives were set;
• Review of crane hoist design standards mainly FEM, BS2573, API2C, AS1418,
DNV and Lloyd’s Register Code of Lifting Appliances in a Marine
Environment.
• Literature review on hoist drum design.
• Outline of hoist drum design criteria in use.
• Strength analysis of hoist drum using a selected method.
• Determine the structural reliability of a hoist drum by calculating the design
probability of failure using various methods.
1.5 Method
A literature review on the subject of hoist drum flange forces is undertaken. The
requirements to design a hoist drum flange from various design codes available are then
outlined and a method selected from the most comprehensive design code. The hoist
drum strength is then assessed based on the selected code and MIPEG data for an
auxiliary hoist drum is then used to calculate the probability of failure of the drum
which is used as an indicator of the hoist drum reliability.
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Chapter 2 Literature review: Design Requirements
for Offshore Hoist Drums
Introduction
2.1 Hoist Drum Design
The drum is made up of a barrel to wind the rope and where it is not practicable to
accommodate all the rope in a single layer, a flange is fitted. Grooved sleeves are
optional, but where fitted aid in guiding the rope onto the drum. The flange is connected
to the drum through various means, with the most ideal being the barrel and flange cast
as a single unit. Other methods include welding the flange to the barrel or bolting it or a
combination of the above. Hoist drums have been in use for a long time on cranes and
winches, with the larger capacity drums being found in the mining industry. Even
though hoist drum failures are rare, when they do occur they have the potential to result
in significant damage to the environment and may also result in harm to personnel in the
vicinity. Hence, the strength of hoist drums has been the subject of many studies in the
past. It is accepted that hoist drums generally fail in two ways(Song, et al., 1979);
1. High rope tensions causing the internal compressive hoop stress in the drum
barrel to exceed the ultimate limit strength of the drum material.
2. The pressure on the wound rope on the drum flanges causes a high stress
concentration at the root or fillet of the flanges. This causes the flange to part
from the drum barrel.
As stated previously, the first mode of failure does not present a novel problem as the
methods for calculating the strength are well researched and understood. It is generally
accepted that the second mode of failure is not well understood. A number of studies
have found that hoist drums failed as a result of poorly designed drums due to a lack of
understanding of the effects of the rope pressure on the flange(Bellamy NW, 1969).
Additionally, as the drum and flange is a single unit, failure of the drum will in some
cases affect the flange as well. An instance has been recorded where the drum hoop
stress exceeded the yield stress at the centre of the drum causing the flanges to deflect
inwards. One of the flanges was geared and the deflection caused the gear teeth to
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disengage resulting in uncontrolled lowering of the load(IMCA, 2009). As a result the
reliability of the hoist drum will be based on an assessment of the strength of the flange.
The literature review looks at published material relating to the strength of drum flanges
as well as design standards that are currently in use. The most common design standards
are;
1. Federation Europeenne de la Manutention commonly referred to as FEM
2. BS2573
3. API2C
4. AS1418
5. Lloyd's Register Code of Lifting Appliances in a Marine Environment
6. DNV Rules for Certification of Lifting Appliances
2.2 Hoist Drum Flange Forces
The forces acting on the drum flange are poorly understood and numerous studies have
been undertaken to determine the size of the flange forces. In cases where the rope is
wound onto the drum in one layer, the flange is not really essential in this instance.
However, in instances where larger quantities of rope are required, it would be
impractical to have the rope in a single layer, and hence flanges are used to contain the
layers of rope. This then introduces the question of how thick the flange has to be. This
question is best answered by considering the magnitude of the forces exerted on the
flange by the rope. Numerous papers have been presented on the subject, with the
earliest being the paper presented by E. O. Waters in 1920.
Waters reported that flange thickness was a function of rope tension and the depth of the
winding. Using two methods, he derived formulae to calculate the total pressure acting
on the flange of a grooved drum with a given initial tension and depth. Two other
formulae were then deduced, which related total pressure to the flange thickness and the
maximum allowable tensile and shearing stress in the material. The second formula
presented by Waters took into account the effect of friction between adjacent layers of
rope and between the rope and drum, as well as the flattening of the rope coils which
relieves the rope of some of the tension and resulting in a reduction in the pressure
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against the flanges. Waters conducted a number of experiments to substantiate his
theory.
Waters First Method
Figure 1 Diagram showing rope forces on flange for Method 1(Waters, 1920)
The formula to calculate flange pressure is given below;
lb
Where;
N Total axial thrust
m No. of layers
P Rope tension
γ Angle as shown in the Figure above
He found this formula to give excessive values of the flange thrust as it did not take into
account rope friction, reduction in rope tension due to rope compression and the cross-
over of the rope.
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Waters Second Method
The second method he proposed took the above factors into account. A diagram
illustrating the forces taken into account is given below;
Figure 2 Diagram showing rope forces for Method 2(Waters, 1920)
This second formula is given below;
lb
Where;
N Total axial thrust
p No. of coils between a and b
μ coefficient of friction between rope layers
γ Angle as shown in the Figure above
P Rope tension in coil
P΄ Tension loss in coil
The relationship between P and P΄ is given in the table below;
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Figure 3 Relationship between P & P΄(Waters, 1920)
He found that the two equations gave significantly different results particularly for a
large number of layers. To simplify the formulae he derived, Waters made the following
assumptions;
• The shear at the surface of the flange is zero,
• The slope of the deflected flange is zero at the shoulder (i.e. a rigid connection
between the flange and the drum),
• The deflection of the flange at the edge is maximum,
• The flange is of constant thickness.
He then considered the flange as a short cantilever beam with a depth equal to the flange
thickness and a length equal to the circumference at the surface of the drum. The
cantilever is loaded with a uniformly distributed load N (Flange axial thrust). Other
loads, such as brake or clutch forces may also be included. The maximum radial stress
(tension or compression) which acts at the shoulder of the flange is then given by;
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lb/in2
Where and;
ri Drum outer radius
ro Outer rope layer radius
ti Flange thickness
N Flange thrust as calculated
The maximum shear stress is given by;
lb/in2
From the experiments he carried out, Waters found that flange pressure increased in
direct ratio to the number of layers (i.e. a straight line relationship), contrary to the
formulae he had presented. He accounted for this by pointing out that the formulae took
into account several variables that may not have been present in the experiment.
Hoist Drums in Mining
Hoist drums were widely used in the mining industry and in 1949; Crawford(Crawford,
1949) presented a series of papers discussing the strength of drums. In them, he
assumed that the supports deflect radially inwards when the shell is loaded. This is
similar to Waters assumption that the drum/flange connection is rigid. He also assumed
that the supported ends of the shell do not rotate.
In 1957, Dolan(Dolan, 1957) carried out experiments similar to those carried out by
Waters and he demonstrated that the approach proposed by Waters results in too thin a
shell. Dolan presented a second paper(Dolan, 1963) where he investigated various drum
failures and proposed formulae to be used to determine the strength of the drum for
design purposes. In 1958, Egawa & Taneda(Egawa, et al., 1958) also presented a paper
with experimental backing on the determination of flange forces. However, their work
as was the work of Dolan, Broughton(Broughton, 1928, Revised 1948) and
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Torrance(Torrance, 1965) was largely concerned with stresses in drum barrels and did
not present significant findings on flange forces.
In 1966, Atkinson & Taylor(Atkinson LTJ, 1966) also presented a series of papers on
the analysis and design of fabricated drums for mine winders. They found that a number
of drums designed using Waters approach had failed. They also found that some drums
which theoretically would have failed under Dolan’s criteria were still operational and
drums which were well below the design limit had failed. They presented a number of
formulae to determine the drum strength taking into account dynamic effects of the rope
under load(Atkinson LTJ, 1967).
Further Research
In 1968, Bellamy& Philips(Bellamy NW, 1969) also carried out a series of experiments
based on Waters experiments to investigate the forces acting on a winch drum during
multi-layered rope winding. They considered the effects of rope construction, rope
tension and the spooling arrangement. Four different types of rope were used and the
test drum was of welded construction made from mild steel and had load cells placed in
the flange to measure exact pressures. The load cells were positioned as shown below;
Figure 4 Load Cell Positions on Drum Flange(Bellamy NW, 1969)
For an identical rope tension, different types of rope constructions were found to exert
significantly different forces on the flange. For example, the force exerted by an 18 x 7
Fibre Core Lang’s lay rope was more than twice that of a 6 x 37 Independent Wire Rope
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Core rope with all other parameters constant. When the results were processed to give
graphs of average pressure exerted by rope on the flange, it was noted that the average
pressure on the flange became constant with an approximately uniform distribution after
a few layers. However, the 18 x 7 Fibre Core Lang’s lay rope had a higher flange
pressure. Ropes with an independent wire rope core were found to present lower flange
forces and fillet strains. From their findings, they presented a series of design curves as
shown below;
Figure 5 Flange Design Curves(Bellamy NW, 1969)
Where;
Rope A Type 6 x 37 Fibre Core, Lang’s Lay
Rope B Type 6 x 37 Independent Wire Rope Core, Lang’s Lay
Rope C Type 18 x 7 Fibre Core Ordinary Lay
Rope D Type 18 x 7 Fibre Core, Lang’s Lay
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They stated that they found it impossible to present an empirical formula for the failure
of drum flanges due to the diverse forms of flanges in existence. They also found that
flange forces were mainly dependent on three main variables;
a) Type of rope construction,
b) Rope tension,
c) Type of spooling.
Other factors they found to be important included rope size, rope lubrication, LeBus
spacing, drum grooving, settling time and variable rope tensions. The curves presented
in Figure 5 above are applicable for the rope constructions specified. To use the curves,
the rope winding stress is calculated from the rope tension and cross-section; then the
flange pressure is obtained for the particular type of rope construction and spooling. A
graph showing the variation of flange pressure with the number of layers is given
below;
Figure 6 Variation of Flange Force with Number of layers(Bellamy NW, 1969)
In 1979; Song, Rao & Childers(Song, et al., 1979) investigated winch drum design in
mooring applications offshore. The drums are generally larger than the hoist drum
found on cranes for instance, as mooring applications generally require ropes of larger
diameter (up to 89mm diameter rope was found, normal hoisting applications on
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average require diameters up to 20mm). They found that flange splitting was the most
common structural failure in the large wire rope mooring winch drums. One of the
reasons they gave for the failures was that designers were using formulae derived for
use with smaller hoist drums. Their study is of interest as it shows that hoist drum
design is a complex area that is affected by a number of variables.
Recent Research
The University of Clausthal in Germany has also done a significant amount of work
under the leadership of Dr Peter Dietz(Dietz, 1972), who presented the principle that
tension reduction occurs due to the flattening of the wire and the radial deflection of the
layer on which the successive layers are wrapped. In 2002, Otto, Mupende &
Dietz(Otto, et al., 2002) using experimental methods and Finite Element Analysis found
that LeBus spooling resulted in asymmetric pressure distribution over the flange.
Conventional methods for determining the strength of a drum flange have assumed a
symmetric load distribution. The effect of this is shown in the picture of a failed drum
shown below;
Figure 7 Asymmetric Deformation of Drum Flange(Otto, et al., 2002)
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2.3 The attachment of Flanges to Drum Barrel
Most researchers consider the drum flange region to be rigid. This would indicate that
the drum and flange are cast as a single unit or the attachment consists of a full
penetration weld. However, this is not the case in some circumstances, the flange is
often attached using partial penetration welds or even bolted to the drum. This is
therefore a critical area in hoist drum design and maybe the weakest area of the drum
unit. The section below considers welded and bolted joints in detail.
2.3.1 Bolting
It is essential that the loading on the flange is modelled correctly so that the required
strength of the bolts can be determined accurately. The maximum force that a bolt is
capable of supporting is basically given by the product of the bolt’s yield or ultimate
stress and the bolt’s stress area. The bolt’s stress area is dependent on the thread pitch
diameter. It is commonly accepted that a minimum Grade of 8.8 for the bolt according
to ISO 898/1 will be used for structural purposes. Black bolts (i.e. bolts of a Grade
below 8.8) are normally not accepted for structural purposes.
Where a bolt is supporting a flange, the point of application of the force is not normally
coincident with the location of the bolts. This is because the force on the flange due to
rope pressure is considered to be a uniformly distributed load as described by Waters,
and the bolts are usually fitted around the drum’s circumference. This will therefore
give rise to a moment that will tend pry the flange from the barrel.
Fatigue is also significant in this case as the loading will be cyclic i.e. the load will vary
as the rope is wound and unwound onto the drum.
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2.3.2 Welding
A welded drum-flange structure, however intricate its shape, is usually composed from
a number of fundamental joint types. Since in most circumstances, the flange and the
drum are at right angles to each other, they are normally joined using a T-joint as shown
below (Hicks, 1999);
Figure 8 T-joint
3.3.2.1 Weld Strength
The basic strength of a butt weld is normally taken as equal to that of the parent
material. A perfect butt weld joint, when subjected to an external force, provides a
distribution of stress throughout its volume which is not significantly greater than that
within the parent metal. This is achieved as long as the following features apply(Oberg,
2008):
• Welds should consist of solid metal throughout a cross section at least equal to
that of the parent metal.
• All parts of a weld should be fully fused to the parent metal.
• Welds should have smoothly blended surfaces.
If any of these requirements are not fulfilled then the weld is imperfect and the stress
distribution through the joint is disrupted.
According to BS2573-1(British Standards, 1983), a continuous partial-penetration weld
welded from one side only or from both sides can be used provided that it is not
subjected to a bending moment about the longitudinal axis of the weld other than that
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resulting from the eccentricity of the weld metal relative to the parts joined or from
secondary moments. A partial-penetration weld welded from one side only shall not be
subjected to any loading that would cause the root of the weld to be in tension if failure
due to such tension would be liable to be progressive and to lead to structural collapse
unless it can be demonstrated that proper attention has been paid to the detailed design
of the joint and testing and operational experience has shown this detail to be
satisfactory. Partial penetration welds have a weld root which acts as a stress
concentration point(Maddox, 1969). Based on this, full penetration welds are therefore
recommended for drum-flange joints.
The weld strength in the case of a partial penetration weld is given by the length of the
weld multiplied by the weld throat. The throat thickness of a partial-penetration butt
weld welded from one side only shall be taken as the depth of penetration and the
adverse effect of the eccentricity of the weld metal relative to the parts joined shall also
be allowed for when calculating the strength.
2.3.3 Fatigue Failure of Welded Joints
Fatigue is considered the most common cause of structural failure for in-service
structural items(Gagg, et al., 2009). It is clear that fatigue is critical in the reliability of
hoist drums as the structure is subjected to cyclic application of stress, the magnitude of
which would normally be insufficient to cause failure(Gagg, et al., 2009). Fatigue
involves the initiation and gradual growth of cracks until the remaining section of
material cannot support the applied service load.
Several methods have been proposed to mitigate the failure of welded members due to
fatigue. One such approach is ultrasonic peening(Jinu, et al., 2009), which was found to
increase fatigue life by up to 35% at 250 Mpa of applied stress.
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2.4 Design Standards
2.4.1 FEM(FEM, 1998)
This is a collection of internationally accepted guidelines for crane design. This code is
split into 9 booklets, each covering a separate element of the crane design. The first
edition of the code was published in 1962 and the second in 1970. The code requires
that only the element that is under unfavourable loading should be verified for strength.
Standard equipment which has been verified once and for all and is under normal
loading need not be verified. The purpose of the code is to determine the loads and
combinations of loads which must be taken into account and to establish the strength
and stability conditions to be observed for the various load combinations.
The code requires the end user to define two elements;
1. The class of utilisation.
2. The load spectrum
The code differentiates between an appliance, a mechanism and a component and
classes these separately based on the class of utilisation and the load spectrum (stress
spectrum in the case of components). The only specific requirement from the Code
relating to hoist drums is the minimum winding diameter which is given below.
Minimum Winding Diameter
The drum’s minimum diameter in FEM is determined by;
dHD ⋅≥
where
D - is drum diameter
H - is a coefficient dependant upon the mechanism group
D - is the nominal diameter of the rope.
The determination of the strength of the drum is left to the designer.
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2.4.2 BS2573(British Standards, 1980)
This is the British Standard for the design of cranes and mechanisms. The code is split
into two parts, BS2573-1:1983 covering the design of structural elements of the crane
and BS2573-2:1980 covering the design of mechanisms and components. As the hoist is
essentially a mechanism, the research is therefore mainly limited to BS2573-2:1983.
The classification of mechanisms in BS2573 is similar to that in FEM and is based on
class of utilisation and the state of loading. The standard only specifies the minimum
winding diameter which is given below. Determination of the strength of the hoist drum
is left to the designer.
Minimum Winding Diameter
The drum’s minimum diameter in BS2573-2 is determined in a similar way as in FEM;
dHD ⋅≥
where
D - is drum diameter
H - is a coefficient dependant upon the mechanism group
d - is the nominal diameter of the rope.
The minimum value of H is 16, which means that the drum diameter has to be at least
16 times the rope diameter.
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2.4.3 AS1418.1-2002(Australian Standards, 2002)
This is the Australian Standard for the design of cranes and associated components.
This code specifies the requirements for cranes, winches, hoists and their components. It
is regarded as one of the most comprehensive available. It states the design life of crane
mechanical components as 10 years unless otherwise specified. Crane mechanisms are
again classified according to the class of utilisation and the state of loading, in a similar
way as in BS2573-2 and FEM.
Basis of Design
The design of power operated mechanisms is based on the following;
1. Strength basis.
2. Life basis based on wear or fatigue (finite or infinite).
Details of the structural strength requirements according to AS1418 are covered in the
next section as they are quite detailed. The calculation of stresses is based on the
approach by Dr Helmut Ernst and Peter Dietz who published detailed papers on the
strength of crane hoist drums. The standard has comprehensive requirements for the
drum barrel but has limited requirements relating directly to the drum flange.
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2.4.4 API 2C(API, 2004)
This standard is produced by the American Petroleum Institute and covers the design of
offshore cranes. The standard also specifies the requirements for hoist drums. It does
not base strength requirements on utilisation or state of loading as does FEM and
BS2573-2.
Basis of Design
The drum is required to provide a minimum first layer rope pitch of 18 times the
nominal rope diameter. This is more onerous than the requirements of FEM and
BS2573-2 where the requirement is 16 times.
API 2C also requires that the flange extend a minimum distance of 2.5 times the wire
rope diameter over the top layer of the rope unless an additional means of keeping the
rope on the drum is provided e.g. keeper plates, rope guards or kicker rings. A minimum
of 5 wraps of the rope are also required to remain on the drum in the operating
condition. This would prevent the rope anchor failure as cases have been documented
where the rope has detached from the rope anchor(Piskoty, et al., 2009). The standard
does not specify particular requirements relating to the drum flange and leaves it to the
designer.
Figure 9 Hoist Drum Requirements according to API 2C(API, 2004)
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2.4.5 Lloyds Register Code of Lifting Appliances in a Marine Environment
(Lloyds Register, 2008)
The requirements for hoist drums are not stated explicitly in the code but the generally
accepted practise is described below. The design of rope drums is based on the BS5500
1982 Code where the hoist drum is regarded as a pressure vessel loaded externally. The
rope around the drum is considered to impart a uniform pressure on the drum and the
drum stresses are then calculated using formulae outlined in the next Chapter.
In addition, the maximum rope tension is considered taking into account dynamic
loading conditions, friction effects and any environmental effects as well as the stalling
force corresponding to the maximum line load attainable due to an overload condition
such as may occur in the event of snagging of the lifting hook or attached load.
The capacity of the drum should normally be designed to accommodate the rope on a
maximum of three layers of rope. Where a greater number of rope layers are required,
suitable spooling arrangements are to be provided. A single layer of rope is acceptable
provided the rope ends are adequately secured to anchor points. A minimum of three
complete turns of rope is to remain on the rope drum at all times during normal
operation. This is less than the API 2C requirement of a minimum of 5 turns of rope.
There are no specific requirements for the drum flange in the code.
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2.4.6 DNV Rules for Certification of Lifting Appliances(DNV, 2007)
The requirements from the Code are quite comprehensive and are outlined below. The
ratio of the drum diameter to hoist rope diameter is not to be less than 18, which is
similar to the requirement in API 2C. The number of rope layers on the drum is also
limited to 3 unless the hoist rope has an independent wire rope core and one of the
following conditions complied with;
• A spooling device is provided
• The drum is grooved
• The fleet angle is restricted to 2°
• A separate traction drum is fitted.
Special consideration will be given when the number of rope layers exceeds 7. The
distance between the top layer of the wire rope on the drum and the outer edge of the
drum flanges is to be at least 2.5 times the diameter of the wire rope, except in cases
where wire rope guards are fitted to prevent overspilling of the wire. This requirement is
also similar to that given in API 2C.
The drum barrel is to be designed to withstand the surface pressure acting on it due to
the maximum number of windings with the rope spooled under maximum uniform rope
tension. The DNV Code also requires that drums are checked with respect to their
overall equilibrium situation and beam action, with the maximum rope tension acting in
the most unfavourable position. The effect of the support forces, overall bending, shear
and torsion is to be considered at the maximum rope tension including any amplification
factors. However, if more unfavourable the situation with forces directly dependent on
motor or brake action is to be considered. The structural requirements for hoist drums
according to DNV are outlined in the next section. There is evidence that DNV Rules
are likely to be revised in future to include methods for estimating target
reliability(Ruud, et al., 2007). The code states that the pressure acting on the flange
varies linearly from zero at the outer layer to a maximum near the barrel surface. A
formula is given to determine the magnitude of the flange pressure.
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2.5 Conclusion
It is clear from the literature review that methods for determining drum barrel strength
are readily available and the mechanism of failure is well understood. Research also
indicates that flange failure is the most common mode of drum failure and as a result
the reliability of the hoist drum will be based on an assessment of the flange’s structural
strength.
It can be seen from the literature review that the most comprehensive standard is the
DNV Rules for Lifting Equipment when it comes to hoist drum design. The code
considers the effects of flange forces, and outlines formulae to be used. The evaluation
of the drum flange structural strength will therefore be based on the DNV approach.
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Chapter 3 Hoist Drum Structural Strength
Requirements
Introduction
There are various approaches to assessing the structural strength of a hoist drum. The
following chapter looks at the various methods of checking the hoist drum as presented
in the various codes or standards. The main drum components are the barrel, the flanges
and the attachment between the barrel and the flange. As has been determined, most
design standards do not specify particular approaches for determining the strength of
hoist drums but leave it to the user to determine which approach would be most suitable
based on sound engineering practise. It is therefore of critical importance to designers
and certifying authorities that the different approaches available are assessed to
determine the most reliable.
3.1 The Barrel
The barrel is subjected to bending, crushing and buckling stresses. The design
calculations therefore have to take all these factors into account. Most of the codes or
standards only specify requirements for some of these stresses and only the Australian
Standard AS1418 specifies requirements for all the stresses mentioned above. The
different approaches to hoist barrel design are outlined below.
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3.1.1 DNV Approach: Hoop stress
The drum hoop stress, which is the stress acting on the drum due to the squeezing effect
of the rope on the drum, is calculated using the formula below must not exceed 85% of
the material’s yield stress;
av
hoop
tp
SC
⋅
⋅
=σ
where;
C - amplification factor (1.75 for more than one layer).
S - rope tension under spooling
P - pitch of rope grooving
tav - average drum thickness
3.1.2 Lloyds Register Approach: Drum Barrel
The Lloyd's Register approach is based on the BS 5500:1982 code as previously
outlined. The approach assumes that the drum is a pressure vessel under external
pressure and calculates the minimum drum barrel thickness required to prevent
buckling. This method is very similar to that outlined in Omer W. Blodgett’s book, The
Design of Weldments, James F Lincoln Arc Welding Foundation (1963)(Blodgett,
1976). This method considers the rope to be applying an external pressure on the drum
due to the line tension as shown in the drawing below;
Figure 10 Drum Forces
The hoop stress is given by;
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t
rP
hoop
⋅
=σ
where;
P - external pressure
r - radius of drum
t - drum shell thickness
The line tension F gives rise to the external pressure acting on the drum shell and can be
expressed as;
tbF hoop ⋅⋅= σ
where;
b - width
therefore;
tb
F
hoop
⋅
=σ
and therefore;
br
F
P
⋅
=
Figure 11 Drum Forces
This method then assumes that each of the succeeding layers will add to the pressure
acting on the drum. However, the outside layers will tend to force the preceding layers
into a smaller diameter, reducing their tension and hence the pressure. Therefore, only
the effect of the outer two layers is considered;
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1++= nnT ppp
The minimum thickness of the drum that prevents failure due to buckling is then
determined using the formula below;
32
3
)1(4 r
tE
pcr
ν−
⋅
=
Where;
Pcr - Critical Pressure acting on barrel and resulting in buckling
E - Youngs Modulus for the material (Modulus of elasticity)
t - Barrel thickness
r - Barrel inner radius
ν - Poisson’s ratio
Therefore, to prevent buckling the minimum thickness will be;
3
32
min
)1(4
E
rP
t cr ν−
=
This method calculates the minimum required drum barrel thickness to prevent drum
buckling. As outlined above it is similar to the Lloyds Register approach. The method is
sometimes used by manufacturers to determine the minimum barrel thickness even
though it only considers failure due to buckling only.
However, from analysis, it has been found that the minimum drum barrel thickness
determined using this method is inadequate to resist the hoop stress as calculated using
the DNV Hoop Stress formula and is much less than the minimum thickness calculated
using the approach presented in the Australian Standard AS1418. This approach is
therefore to be used with caution and its limitations must be fully understood by the
designer.
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3.1.3 AS1418: Drum Barrel
As previously mentioned, this method includes the calculation of drum barrel stresses
presented by Dr Helmut Ernst and Peter Dietz who published detailed papers on the
strength of crane hoist drums. AS1418 presents a method for working out the
recommended minimum thickness of the drum and also presents methods for
determining stresses in the drum barrel. The minimum theoretical thickness of the drum
barrel is determined from;
( )22
min DCDCDBDB TTTTT +⋅+=
where;
TDB - is the minimum theoretical thickness of the drum shell allowing only for
the beam bending stresses given by;
bDM
DB
FD
M
T
⋅
= 2
1250
TDC - is the minimum theoretical thickness of the drum shell allowing only for
the compressive stresses given by;
c
RSRL
DC
Fp
PK
T
⋅
⋅
=
1000
M - is the bending moment due to beam action of unfactored (static) rope
load (PRS)
Fb - is the permissible bending stress in MPa (67% of yield stress)
DDM - is the mean diameter of the drum shell in mm.(DDN-Tmin)
DDN - is the nominal diameter of the drum shell
KRL - is the rope layer factor and rigidity constant for the drum shell (1.6 for
more than three layers)
p - is the pitch of the rope coils
d - is the nominal diameter of the rope
Fc - is the permissible compressive stress in MPa.
PRS - is the maximum unfactored rope load in kN
It can be seen from the formulae presented above that the minimum theoretical
thickness as calculated will take into account the effect of bending, buckling and the
compressive stress.
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3.2 The Hoist Drum Flanges
Most of the codes do not present a way of assessing the strength of the hoist drum
flanges. Only DNV presents a method which is outlined below. The method assumes
that the flanges are under a direct pressure due to the wire rope ‘wedge’ effect. In
determining the strength of the flange this pressure is assumed to vary linearly from a
maximum near the drum barrel to zero at the outer layer. An average value of this
pressure is then taken and assumed to act at a point. The loading of the flange can be
represented as shown below;
Figure 12 Flange Loading(Young, et al., 2002)
In this case the following assumptions are made;
a) The flange is assumed to be loaded at a third of the height.
b) The plate is flat and of uniform thickness.
c) All forces/reactions are normal to the plane of the plate.
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3.2.1 DNV Approach: Flange
The pressure acting on the flange is assumed to be increasing linearly from zero at the
top layer to the value given by the formula below;
D
t
p
hoopav
f
3
2 σ⋅⋅
=
where;
av
hoop
tp
SC
⋅
⋅
=σ
and;
D - outer diameter of barrel
p - wire rope pitch
C,S are defined in the previous section
then;
Dp
SC
pf
⋅⋅
⋅⋅
=
3
2
The maximum force on the flange is then given by the product of the pressure and the
area over which the force acts. This is the area of the flange covered by the rope layers
and is given by;
( )
4
22
DD
A
Outerlayer
flange
−⋅
=
π
therefore the force on the flange is given by; flangefflange ApF ⋅=
or simply;
( )
Dp
DDSC
F outerlayer
flange
⋅⋅
−⋅⋅⋅
=
6
22
π
The force in the flange Fflange shall not be greater than the allowable force in the flange
as determined from the allowable stress multiplied by the area of the flange covered by
the rope layers.
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30
3.3 Hoist Failure Modes
There are several modes of failure associated with each particular element of the drum.
It is apparent from the previous sections that design codes select which failure modes to
specify requirements for, even though there are a number of modes of failure which are
significant. A Failure Mode & Effects Analysis is carried out below to illustrate the
modes of failure possible for the hoist drum. In this instance, failure of a single
component of the hoist drum unit is considered as failure of the whole system.
3.3.1 The Barrel
The barrel is likely to fail due to the modes outlined below;
• Buckling,
• Cracking,
• Fatigue.
3.3.2 The Flange
The flange is likely to fail due to the modes outlined below;
• Elastic failure,
• Cracking,
• Fatigue.
3.3.3 Means of Attachment
The means of attachment can be welding or bolting as outlined in the previous section.
Bolts are likely to fail due to the modes outlined below;
• Elastic failure
Welds are likely to fail due to the modes outlined below;
• Elastic failure,
• Cracking,
• Fatigue.
The results of a Failure Mode and Effects Analysis are shown in the Table overleaf.

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31
Description of unit Description of failure
Component Failure Mode Failure Mechanism
Effects of failure
on System Function
Failure
Rate
Severity
Ranking
Risk Reducing
Measures
Comments
Drum Flange Elastic failure Bending Dropped load
Collapse
High Inspection Design information, Crane
history/records, NDE inspection
records, End of life assessment
Drum Flange Excessive deflection Overload Damaged wire rope
Dropped load
High Inspection
Repair
Replacement
Maintenance
Fatigue failure in parent metal,
weld or connection could result in
a sudden failure leading
to collapse and dropped load/jib.
Drum flange Plastic Collapse Bending Damaged wire rope
Dropped load
High Inspection
Replacement
Drum flange Brittle fracture Stress concentration Damaged wire rope
Dropped load
High Inspection
Repair
Drum Barrel Elastic failure Bending Damaged wire rope
Dropped load
High Inspection
Repair
Drum Barrel Buckling Overload Damaged wire rope
Dropped load
High Inspection
Repair
Drum weld Elastic failure Overload Damaged wire rope
Dropped load
High Inspection
Repair
Drum weld Fatigue Cracking Damaged wire rope
Dropped load
High Inspection
Repair
Drum weld Buckling Overload Damaged wire rope
Dropped load
High Inspection
Repair
Drum weld Brittle fracture Stress concentration Damaged wire rope
Dropped load
High Inspection
Repair
Bolts Elastic failure Shearing Damaged wire rope
Dropped load
High Inspection
Repair
Table 1 Failure Mode & Effects Analysis
It is clear from the above analysis that a lot is left to the discretion of the designer. For instance, none of the design codes specify requirements relating to fatigue,
even though it is a significant mode of failure. In this instance, failure of a single component of the hoist drum unit is considered as failure of the whole system.

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Chapter 4 Case Study: Auxiliary Hoist Drum on
Ruston Bucyrus Crane
Introduction
The Ruston Bucyrus MK35 Crane experienced two hoist drum failures and is an ideal
example of how critical the strength of hoist drums is. The hoist drum originally
supplied with the crane failed due to cracking of the flange. A replacement hoist drum
with a bolted flange also failed during load testing due to failure of the means of
attachment without causing any significant damage. Another replacement drum was
then designed and forwarded to Lloyd’s Register to assess its structural strength. This
project will consider the design of the replacement hoist drum and assess its structural
strength using methods outlined in the previous section. The hoist drum’s probability of
failure will then be calculated based on historical loading records using various
methods.
4.1 Description of Crane
The Ruston Bucyrus MK35 Crane is a pedestal mounted, rope luffing offshore crane
located on the Rough Alpha Platform in the Southern North Sea. The auxiliary hoist is
powered by a closed loop hydraulic system and provides powered lifting and lowering
of the load. The hoist unit is mounted on the roof of the machinery house and operates
on single fall in an open sea environment up to Beaufort Sea State 6. It has a capacity of
4.5 Tonnes on the auxiliary hoist. A schematic of the crane is shown
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below;
Figure 13 Schematic of the Ruston Bucyrus Crane(Specialist Maintenance Solutions, 2008)
The crane was supplied with the platform circa 1975. The crane is fitted with MIPEG
2000 (Sparrows Offshore) data instrument which monitors and records the loading data
over time (See Appendix A).
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4.2 Original Hoist Drum
The original drum consisted of a two piece casting, with a radial weld joining the two
pieces at the centre of the drum. The hoist drum was designed with an integrated wedge
and socket acting as the dead end rope anchor. It was supplied with the crane and was
at least 30 years old at the time of failure.
Figure 14 Failed Original Drum(Specialist Maintenance Solutions, 2008)
The flange failure is shown in the picture above, and other than the part of the flange
that broke off, cracks were also observed on the flange.
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Figure 15 Close-up of Failed Flange on Original Drum(Specialist Maintenance Solutions, 2008)
The darker areas that can be observed from the picture above where the cracks would
have initiated. The mode of failure for the drum would therefore quite likely have been
fatigue, with the machined rope groove acting as a stress concentration point.
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4.3 Failed Replacement Drum
The replacement drum was made up of discrete units with the flange connected to the
drum unit using bolts as shown in the drawing below.
Figure 16 Failed Replacement Drum(Specialist Maintenance Solutions, 2008)
The drum flange can be observed to have parted from the drum at the top of the picture.
From the investigation, it was determined that failure occurred due to the flange bolts
shearing.
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Figure 17 Close-up of Failed Flange on Replacement Drum(Specialist Maintenance Solutions, 2008)
The parting of the flange from the drum resulted in significant damage to the wire rope
as can be observed from the picture above. Had the failure gone unnoticed, which is
possible as the hoist drum is positioned above the crane operator’s cabin, this may have
resulted in an uncontrolled lowering of the load.
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4.4 Proposed Replacement Drum
The proposed replacement drum consists of one piece drum welded to two flange plates.
The drum is similar in dimensions to the OEM drum except the drum length, measured
from flange face to flange face. This is one rope diameter shorter to accommodate a
rope anchor, which is placed outside the flange. The drum does not have grooves and
the wire rope diameter is 19mm. Based on the operating criteria, the minimum number
of layers required on the drum is 3 but it was designed for 5 layers.
Figure 18 Schematic of Proposed Replacement Drum(Specialist Maintenance Solutions, 2008)
The position of the hoist drum as well as the hoist drum specification is as shown
below;
Material
Properties used in making up drum are presented in Table below
Material Standard Min. Yield
(N/mm2)
UTS (N/mm2)
Plate BSEN 10025 345 490
Barrel API 5LX52 345 490
Table 2 Material Properties
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4.4 Structural Strength Assessment of Proposed Replacement Drum
The structural strength of the hoist drum is checked using the DNV method outlined in
the previous section.
4.4.1 The Barrel
The barrel strength is checked by calculating the hoop stress according to the DNV
approach as outlined in the previous section.
av
hoop
tp
SC
⋅
⋅
=σ
Where C = 1.75, S = 45126N, p = 19 mm and the average thickness of the drum
tav = 36mm.
Therefore;
2
/5.115
3619
4512675.1
mmNhoop =
⋅
⋅
=σ
For the barrel to be acceptable, the hoop stress has to be less than 85% of the yield
stress.
2
/3.293345*85.0 mmNhoop ==σ
The hoist drum is therefore acceptable.
4.4.2 The Flange
The flange’s strength is checked by using the DNV approach as well as outlined in the
previous section. The actual force acting on the flange is given by;
( ) N
Dp
DDSC
F outerlayer
flange 1047659
6
22
=
⋅⋅
−⋅⋅⋅
=
π
The maximum allowable force is given by;
weldyflangeAllowable AF ⋅=σ_
Where the yield stress is 345 N/mm2
and the weld area is 22368 mm2
. Therefore;
NAF weldyflangeAllowable 771700822368*345_ ==⋅=σ
The flange and weld strength are therefore acceptable.
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4.4.3 The Means of Attachment
The flange is welded onto the barrel using a partial penetration butt weld. Its strength
has been checked in the preceding section using formulae developed by DNV and is of
sufficient strength. However, as described previously, the means of attachment is still
susceptible to failure through fatigue.
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s safe.
Assumptions
• All aspects of uncertainty associated with strength and loading characteristics
• racteristics have or are assumed to have Normal
• iables are independent.
Chapter 5 Probability of Failure of Hoist Drum
Introduction
The structural strength of the hoist drum replacement has been calculated using various
approaches in the previous section. It can be seen from the results that according to the
various code requirements, the hoist drum should be suitable for service. In this section,
the probability of failure of the hoist drum is calculated using the First Order Second
Moment Method (FOSM), the First Order Reliability Method (FORM) and the Monte
Carlo Method. The methods require a limit state function which is formulated in the
next section.
From the Case Study, it can be seen that the means of attaching the flange to the drum is
critical and this would be the area that is considered most likely to fail. The assessment
of the means of attachment also takes into consideration the strength of the barrel and
flange and the probability of failure of the means of attachment will be a good indicator
of barrel and flange strength.
5.1 The Limit State Function: General
The Limit State function is given by G(x) and is always defined such that when the
function is less than or equal to zero then failure has occurred. When G(x) is greater
than zero then the structure i
DemandCapabilityxG −=)(
can be assessed explicitly.
Strength and loading cha
Distributions.
All random var
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The Limit State function will also have a Normal Distribution with ;
DCG μμμ −= and 222
DCG σσσ +=
where:
DCG ,,μ - Mean value of the function G(x), Capability and Demand
respectively.
DCG ,,σ - Standard deviation of G(x), Capability and Demand function
respectively.
and the probability of failure Pf is given by;
⎥
⎦
⎤
⎢
⎣
⎡
−=
G
G
fP
σ
μ
φ
Where the value of ø is given in Normal Distribution Tables.
G
G
σ
μ
is also known as the
Safety or Reliability Index.
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5.2 Limit State Function: Flange Fillet
The weld fails if the force in the weld exceeds the maximum allowable force given by
the weld area multiplied by the material’s yield stress. The limit state function in this
case is then given by;
FlangeonactingForceStrengthWeldxG ____)( −=
Let;
Aweld weld area given by the product of weld throat(h) and weld length (lweld)
σy flange material yield stress
FAllowable allowable force in weld
The weld strength is given by the allowable force in the weld. The length of the weld is
given by the circumference of the barrel in this case and is equal to;
Dlweld ⋅= π
therefore;
yAllowable DhF σπ ⋅⋅⋅=
If the applied force in the weld area is F, then the limit state function can be stated as;
FDhxG y −⋅⋅⋅= σπ)(
Where F is the force acting on the flange and is dependent on the pressure due to the
rope force and is given by Fflange as defined in the previous section;
Dp
DDSC
F
outerlayer
flange
⋅⋅
−⋅⋅
=
6
)( 22
π
Therefore the complete limit state function is given by;
Dp
DDSC
DhxG
outerlayer
y
⋅⋅
−⋅⋅
−⋅⋅⋅=
6
)(
)(
22
π
σπ
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where;
C amplification factor (1.75 for more than one layer).
S rope tension under spooling
p pitch of rope grooving
D outer diameter of barrel
Each of these parameters is explained further in the following section.
MIPEG Load Data(Specialist Maintenance Solutions, 2008)
The hoist drum load data was recorded using the MIPEG system (See Appendix A) over
almost a 3 year period from August 2005 to March 2007. This is considered to be a
random variable which can be modelled and the variance and mean calculated. The
maximum safe working load is 4.5 Tonnes but it can be seen from the data that this was
often exceeded. The MIPEG load data recorded over the period has the following
parameters;
No. of cycles (n) 1074
Mean (μy) 21127N
Standard Deviation (σy) 8058N
However, the expected number of cycles for the life of the hoist drum (which is taken as
25 years) is approximately 25000 (based on 1000 cycles per year). The maximum load
distribution is assumed to be Extreme Value Distribution and will be approximated by a
normal distribution. Therefore, the mean and variance for the maximum loading
throughout the life of the hoist drum is then given by;
n 25 000
5.4)25000ln(2)ln(2 === nnα
And;
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45
962.3
5.4*2
)4ln()25000ln(ln(
5.4
)ln(22
)4ln())ln(ln(
)ln(2 =
+
−=
+
−=
ππ
n
n
nun
The corresponding mean and variance of the Type I distribution are;
Nu y
n
nyYn
4.540868058*
5.4
577216.0
962.321127 =⎥⎦
⎤
⎢⎣
⎡
++=⎥
⎦
⎤
⎢
⎣
⎡
++= σ
α
γ
μμ
Where γ is Euler’s number, and the variance is given by;
9.5274459
5.4*6
8058*
6 2
22
2
22
2
===
π
α
σπ
σ y
Yn
n
n
Therefore, the standard deviation is given by;
NY 6.2296=σ
The rope tension distribution for the 25000 expected load cycles will be described as
below.
Rope Tension (S)
Parameter Mean (N) Standard Deviation (N)
S 54086.4 2296.6
Yield Stress (σy)
The yield stress depends on the material and in this case, steel to BSEN10025 with a
yield strength of 345 MPa was used. The yield strength is considered a random variable
with a Lognormal distribution.
Parameter Mean (N/mm2) Coefficient of Variation
σy 345 0.05
Where from Course Notes;
2
2
345
ζ
λ
σμ
+
== ey therefore
844.5)345ln(
2
==+
ζ
λ
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And;
22222
25.17
2
=−= +
μσ ζλ
e
Therefore;
69.11)34525.17ln(22 222
=+=+ ζλ
Using the two equations obtained above, we get;
05.0=ζ and 842.5=λ
Outer Barrel Diameter (D)
This will vary with variations in material thickness, measurement error and so on. In
this case, the barrel dimension are taken as a constant.
Parameter Value (mm)
D 356
Pitch of rope Grooving (p)
This will vary with the rope grooving but in this case can be taken as a constant.
p 19
Outer Rope Layer Diameter (Douter layer)
The outer layer rope diameter will vary depending on the rope required to be stored on
the drum and also when the rope winds on/off the drum. In this case a sensitivity
analysis will be carried out for an outer layer diameter from 1 layer to 7 layers.
Douter layer1 394
Douter layer2 432
Douter layer3 470
Douter layer4 508
Douter layer5 546
Douter layer6 584
Douter layer7 622
Weld Throat (h)
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This will vary with material thickness and with welding errors. In this case however it
can be considered a random variable with a Normal distribution.
Parameter Mean (mm) Coefficient of Variation
h 20 0.05
Amplification Factor (C)
This is a random variable with a Beta distribution with a minimum value of 1 and a
maximum value of 2.
Parameter Mean Standard Deviation
C 1.75 0.363
π mathematical constant
The Limit State Function for Layer 1 is then given by;
CSh
Dp
DDSC
DhxG y
outerlayer
y 21.241.1118
6
)(
)(
22
−=
⋅⋅
−⋅⋅
−⋅⋅⋅= σ
π
σπ
For Layer 2;
CShxG y 636.441.1118)( −= σ
For Layer 3;
CShxG y 289.741.1118)( −= σ
For Layer 4;
CShxG y 166.1041.1118)( −= σ
For Layer 5;
CShxG y 267.1341.1118)( −= σ
For Layer 6;
CShxG y 59.1641.1118)( −= σ
For Layer 7;
CShxG y 138.2041.1118)( −= σ
47

Leslie L Moyo
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5.3 Limit State Function: Weld Fatigue
The assessment of weld fatigue will be based on the JCSS Probabilistic Model Code
Part 3: Resistance Models (3rd
draft/ November 2006). Using the S-N lines approach in
combination with Miner’s Damage Rule, the Limit State Function is given by(Joint
Committee of Structural Safety, 2006);
ncr DDxG −=)(
Where Dcr is Miners’ Damage Sum at Failure and;
⎥⎦
⎤
⎢⎣
⎡
Δ= )(
1
)( m
n SE
A
nED
Where n is the expected number of cycles and A and m are the material parameters and
is the stress range.SΔ
The Limit State Function is then given by;
⎥⎦
⎤
⎢⎣
⎡
Δ−= )(
1
)()( m
cr SE
A
nEDxG
The above parameters have the following characteristics [56];
Parameter Distribution Mean Coefficient of variation
Dcr Lognormal 1.0 0.3
A Lognormal 1.0E13 0.58
m 3
The expected number of cycles E(n) is 25000 as stated in the previous section. Since the
distributions are lognormal, the parameters to and s are calculated as below;
For Dcr;
[ ]
959.0
3.01
1
1
22
=
+
=
⎥
⎦
⎤
⎢
⎣
⎡
+
=
μ
σ
μ
ot
Therefore;
042.0)ln( −=ot
48

Leslie L Moyo
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And;
294.0)3.01ln(1ln 2
2
=+=
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
+=
μ
σ
s
For A;
[ ]
1265.8
58.01
130.1
1
22
E
E
to =
+
=
⎥
⎦
⎤
⎢
⎣
⎡
+
=
μ
σ
μ
Therefore;
79.29)ln( =ot
And;
539.0)58.01ln(1ln 2
2
=+=
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
+=
μ
σ
s
Stress Range SΔ
Assuming the flange does not bend, the weld is primarily under a direct stress due to the
drum flange force. This stress has a minimum of zero when there is no force acting on
the flange and the maximum stress in the weld is given by;
AreaWeld
Fflange
_
max =σ
The weld area is given by the weld throat multiplied by the length of the weld. These
parameters were detailed in the previous section. Therefore;
2
14.22368 mmDhAweld == π
The flange force (with 5 rope layers) is given by;
Dp
DDSC
F outerlayer
flange
⋅⋅
−⋅⋅
=
6
)( 22
π
Therefore;
2
2
22
max /
6
)(
mmN
hDp
DDSC outerlayer
⋅⋅⋅
−⋅
=σ
The stress varies from zero (when there is no loading) to the maximum value given by
the formula. The expected value [ ]m
SE Δ is obtained using Appendix B of the JCSS
49

Leslie L Moyo
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Document (Joint Committee of Structural Safety, 2006), which requires an evaluation of
the standard deviation. The standard deviation is evaluated below;
Differentiating the function with respect to each variable;
1.32
6
)(
2
22
max =
⋅⋅⋅
−
=
∂
∂
hDp
DDS
C
outerlayer
σ
001.0
6
)(
2
22
max =
⋅⋅⋅
−⋅
=
∂
∂
hDp
DDC
S
outerlayer
σ
8.2
7.1122
2max −=−=
∂
∂
hh
σ
The variance is then given by;
2222222
2
1
max2
1*)8.2(6.2296*001.0363.0*1.32])[(max
−++=−⎥
⎦
⎤
⎢
⎣
⎡
∂
∂
= ∑=
ii
n
i i
xE
x
μ
σ
σσ
Therefore;
2
/2.12max
mmN=σσ
Assuming a Rayleigh Distribution and a Gaussian stress spectrum which is narrow
banded according to the JCSS document, then;
[ ] ⎟
⎠
⎞
⎜
⎝
⎛
Γ=Δ
2
)22( max
m
SE mm
σσ where m = 3 as described above, then;
[ ] 2
*)2*2.12*2( 33 π
=ΔSE where
22
3 π
=⎟
⎠
⎞
⎜
⎝
⎛
Γ
Therefore; [ ] 6.365283
=ΔSE
The Limit State Function is therefore;
A
E
DSE
A
nEDxG cr
m
cr
081.9
)(
1
)()( −=⎥⎦
⎤
⎢⎣
⎡
Δ−=
50

Leslie L Moyo
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5.4 First Order Second Moment Method (FOSM)
The FOSM is a Level I method based on the limit state function. According to the
Structural Reliability Course Notes (Heriot Watt University), this was one of the first
structural reliability methods to be used. This method gives exact answers to certain
types of structural problems but will suffer from the ‘lack of invariance’ problem. This
is because this method assumes that the limit state function is linear. However, in some
cases the limit state function is not linear and the FOSM approach is considered to give
only an approximate answer.
A summary of how the method is applied is given below;
1. The Limit State function for a particular problem is generated.
2. The Mean Value of the Limit state function is then calculated using the means of
the variables.
3. The Limit State Function is then differentiated with respect to all the variables in
turn.
4. The variance for the Limit State Function is the calculated using the formula
below;
])[(
)( 2
2
1
2
ii
n
i i
G xE
x
xG
μσ −⎥
⎦
⎤
⎢
⎣
⎡
∂
∂
= ∑=
5. The Safety or Reliability Index is then calculated from
G
G
σ
μ
.
6. The probability of failure is then obtained from Normal Distribution Tables.
In this case, the limit state function and the variables have been defined in the preceding
section. The calculation steps continue below with the evaluation of the mean value of
the limit state function.
51

Leslie L Moyo
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Flange Fillet Failure
The limit state function is given by;
Dp
DDSC
DhxG
outerlayer
y
⋅⋅
−⋅⋅
−⋅⋅⋅=
6
)(
)(
22
π
σπ
The values for the variables are given in the table below;
Parameter Mean Value Standard Deviation
σy 345 17.25
C 1.75 0.363
S 54086.4 2296.6
h 20 1
The values for the constants are given below;
Constant Value
π 3.14
D 356
Douter layer 546
p 19
The mean value is then given by;
Dp
DDSC
DhG outerlayer
yG
⋅⋅
−⋅⋅
−⋅⋅⋅==
6
)(
)(
22
π
σπμμ
Therefore;
5.6461321=Gμ
Next, differentiating the Limit State function with respect to each variable;
14.22368
)(
==
∂
∂
hD
xG
y
π
σ
and;
52

Leslie L Moyo
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22.23
6
)()(
22
=
−
=
∂
∂
pD
DDC
S
xG outerlayerπ
4.385850
)(
==
∂
∂
yD
h
xG
σπ
And;
2.717535
6
)()(
22
=
−
=
∂
∂
pD
DDS
C
xG outerlayerπ
2^1*2^4.385850363.0*2.7175356.2296*22.2325.17*22368])[(
)( 2222222
2
2
+++=−⎥
⎦
⎤
⎢
⎣
⎡
∂
∂
= ∑=
ii
n
i
G xE
x
xG
μσ
1i
G
Therefore;
2.604654=σ
The Safety or Reliability index is then given by;
7.10
3.468578
5.6461321
=== G
σG
μ
β
and the probability of failure from Normal Distribution Tables is given by;
2709.5)( −=−= Epf βφ
The hoist drum flange fillet therefore has a very low chance of failure with 5 layers
according to the FOSM method.
53

Leslie L Moyo
______________________________________________________________________________________________
Weld Fatigue Failure
The Limit State Function is given by;
A
E
DSE
A
nEDxG cr
m
cr
081.9
)(
1
)()( −=⎥⎦
⎤
⎢⎣
⎡
Δ−=
Therefore, the mean value is then given by;
9999.0
130.1
081.9
1)( =−==
E
E
GG μμ
Therefore; 9999.0=Gμ
Next, differentiating the Limit State function with respect to each variable;
1
)(
=
∂
∂
D
xG
cr
and; 2
081.9)(
A
E
A
xG
=
∂
∂
2
2
2
222
2
1
2
128.5*
131
081.9
3.0*1])[(
)(
E
E
E
xE
x
xG
ii
n
i i
G ⎥⎦
⎤
⎢⎣
⎡
+=−⎥
⎦
⎤
⎢
⎣
⎡
∂
∂
= ∑=
μσ
Therefore; 3.0=Gσ
The Safety or Reliability index is then given by;
333.3
3.0
9999.0
===
G
G
σ
μ
β
and the probability of failure from Normal Distribution Tables is given by;
00043.0)( =−= βφfp
The hoist drum therefore has 0.043% chance of failure with 5 layers from weld fatigue
according to the FOSM method.
54

Leslie L Moyo
______________________________________________________________________________________________
5.5 First Order Reliability Method (FORM)
The FORM Method is a Level II Method that is considered to give a reasonable
approximation of the failure probability. According to the Structural Safety Module
Course Notes (Heriot Watt University), this method overcomes the ‘lack of invariance’
problem. This is done by expanding the Taylor series around the failure point and
converting the expansion from basic variable space to standard Normal space. The
Safety Index, in this case referred to as the Hasofer and Lind Reliability index is then
expressed as the distance from the origin in standard Normal space to the closest point
on the failure surface where G(x)=0. The Hasofer and Lind Reliability Index is then
estimated through iteration. A summary of the method is given below;
1. The Limit State Function for the problem is generated.
2. The Limit State Function is expressed in the form of standardised normal
variates, i.e.
i
ii
i
x
x
σ
μ−
='
Any variable that is not normally distributed must be converted to the equivalent
Normal variable using the Normal Tail Approximation.
3. The starting values of the standardised normal variates are selected as 0, i.e. the
origin in the standard Normal space.
4. The partial derivatives of the limit state function G(x) at the current value of
are calculated.
'
x
5. The direction cosines αi are then calculated using the formula below;
∑=
⎥
⎦
⎤
⎢
⎣
⎡
∂
∂
⎥
⎦
⎤
⎢
⎣
⎡
∂
∂
=
ni xi
xi
i
x
xG
x
xG
,1
2
'
'
'*
'*
)(
)(
α
6. The value of l is calculated from;
55

Leslie L Moyo
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∑=
⎥
⎦
⎤
⎢
⎣
⎡
∂
∂
=
ni xix
xG
l
,1
2
'
'
'*
)(
7. The limit state function is then evaluated.
8. The first estimation of the Hasofer and Lind Reliability Index β is then estimated
from;
∑=
−=
ni
ix
,1
'*
αβ
9. New values of are then computed using the equation below;'
x
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
+−=+
l
xG
x mxm
mmm
'
)(
)( )(
)()(
'
)1( βα
10. Steps 4 through to 9 are then repeated until convergence is achieved or G(x) is
equal to or close to zero.
56

Leslie L Moyo
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57
As the Limit State Function has been generated in the previous section, this is then
expressed in terms of the standardised normal variates below;
Dp
DDSC
DhxG
outerlayer
y
⋅⋅
−⋅⋅
−⋅⋅⋅=
6
)(
)(
22
π
σπ
CShxG y 3.134.1118)( −=
Where the variables are σy and S. This can be simplified to;
σ
And the standardised normal variates are;
y
yy
y
σ
σ
σ
μσ
σ
−
='
,
C
CC
σ
C
μ−
=' ,
h
hh
h
σ
μ−
='
and
S
SS
S
σ
μ−
='
34525.17 '
+= yy σσ 363.075.1 '
+= C 20'
+= hh 6.22964. '
+= SS
)'363.0746.22964.54086(3.13)'20)(25.17)( '''
CShxG y ++−++= σ
Therefore;
And;
And the partial derivatives are;
And;
*6.22964.54086(*363.0*3.13
)(
'
'
C
xG
+−=
∂
∂
20(*25.17*4.1118
)(
'
'
xG
y
=
∂
∂
σ
)25.17345(4.1118
'
)( '
'
y
h
xG
σ+=
∂
∂
345(4.1118
, C , and 54086
)'h+
)'75.1(*6.
)(
'
'
C
S
xG
+−=
∂
∂
,
2296*3.13
)'S
.1)(
363.0

Leslie L Moyo
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58
As stated the starting point is chosen as the origin where the variables equal zero. The iterative calculations are then computed in an Excel
spreadsheet inserted below;
Variable Iteration 1 Iteration 2 Iteration 3 Iteration 4 Iteration 5 Iteration 6 Iteration 7 Iteration 8 Iteration 9
y_1 (Sig_y) 0.0000 -6.7666 -6.8635 -6.3465 -6.3960 -6.3966 -6.3971 -6.3970 -6.3970
y_2 (h) 0.0000 -6.7665 -6.8634 -6.3464 -6.3959 -6.3965 -6.3970 -6.3969 -6.3969
y_3 (C) 0.0000 4.5677 7.2801 7.2956 7.2245 7.2251 7.2241 7.2244 7.2243
y_4 (S) 0.0000 0.9350 2.7914 3.3514 3.2539 3.2468 3.2474 3.2472 3.2472
(dg(y)/dy_1) 385851.4500 255307.5271 253439.5807 263412.2840 262457.6213 262446.0075 262437.2333 262439.1574 262438.5978
(dg(y)/dy_2) 385848.0000 255304.0771 253435.5253 263407.9695 262453.2535 262441.6072 262432.8175 262434.7343 262434.1713
(dg(y)/dy_3) -260465.0312 -270806.3305 -291337.8303 -297531.3130 -296452.0163 -296374.3976 -296380.5063 -296377.9960 -296378.7261
(dg(y)/dy_4) -53318.5259 -103836.5551 -133834.9628 -134006.0374 -133219.8133 -133227.0906 -133215.3940 -133218.4711 -133217.5731
l 606996.6378 463120.0752 480885.3452 495229.5327 493352.8452 493295.7990 493286.9660 493288.3322 493287.9311
alpha_1 0.6357 0.5513 0.5270 0.5319 0.5320 0.5320 0.5320 0.5320 0.5320
alpha_2 0.6357 0.5513 0.5270 0.5319 0.5320 0.5320 0.5320 0.5320 0.5320
alpha_3 -0.4291 -0.5847 -0.6058 -0.6008 -0.6009 -0.6008 -0.6008 -0.6008 -0.6008
alpha_4 -0.0878 -0.2242 -0.2783 -0.2706 -0.2700 -0.2701 -0.2701 -0.2701 -0.2701
beta 0.0000 10.6448 12.4501 12.0422 12.0249 12.0240 12.0240 12.0240 12.0240
g(y) 6461343.5878 836078.7710 -196171.1257 -8553.5341 -424.4711 -0.9624 -0.0283 -0.0019 -0.0003
Probability of failure 5.000E-01 9.221E-27 6.984E-36 1.067E-33 1.315E-33 1.329E-33 1.329E-33 1.329E-33 1.329E-33
Table 3 FORM Results – Flange Failure
The probability of failure is therefore taken when the value of G(x`) approaches zero. The probability of failure with 5 rope layers according to
the FORM method is therefore very low.

Leslie L Moyo
______________________________________________________________________________________________
As the Limit State Function has been generated in the previous section, this is then
expressed in terms of the standardised normal variates below;
A
E
DSE
A
nEDxG cr
m
cr
081.9
)(
1
)()( −=⎥⎦
⎤
⎢⎣
⎡
Δ−=
Where the variables are σy and S. This can be simplified to;
A
E
DxG cr
081.9
)( −=
And the standardised normal variates are;
y
yy
y
σ
σ
σ
μσ
σ
−
='
and
A
AA
A
σ
μ−
='
Therefore;
13.0 '
+= crcr DD and 131128.5 '
EAEA +=
And;
131128.5
081.9
13.0)( '
''
EAE
E
DxG cr
+
−+=
And the partial derivatives are;
3.0
)(
'
'
=
∂
∂
D
xG
cr
and 2''
'
)131128.5(
213.5)(
EAE
E
A
xG
+
=
∂
∂
As stated the starting point is chosen as the origin where the variables equal zero. The
iterative calculations are then computed in an Excel spreadsheet inserted below;
59

Leslie L Moyo
______________________________________________________________________________________________
Variable Iteration 1 Iteration 2 Iteration 3 Iteration 4 Iteration 5
y_1 (Dcr) 0.0000 -3.3330 -3.3330 -3.3330 -3.3330
y_2 (A) 0.0000 -0.0006 -0.0006 -0.0006 -0.0006
(dg(y)/dy_1) 0.3000 0.3000 0.3000 0.3000 0.3000
(dg(y)/dy_2) 0.0001 0.0001 0.0001 0.0001 0.0001
l 0.3000 0.3000 0.3000 0.3000 0.3000
alpha_1 1.0000 1.0000 1.0000 1.0000 1.0000
alpha_2 0.0002 0.0002 0.0002 0.0002 0.0002
beta 0.0000 3.3330 3.3330 3.3330 3.3330
g(y) 0.9999 0.0000 0.0000 0.0000 0.0000
Probability of
failure 5.000E-01 4.295E-04 4.295E-04 4.295E-04 4.295E-04
Table 4 FORM Results – Fatigue Failure
The probability of failure is therefore taken when the value of G(x`) approaches zero.
The probability of failure with 5 rope layers according to the FORM method is therefore
0.043%.
60

Leslie L Moyo
______________________________________________________________________________________________
5.6 The Monte Carlo Method
The Monte Carlo Method is considered a Level III Method that can, in principle,
provide exact solutions for the probability of failure [Ref Course Notes]. It also has the
advantage that there is no need to transfer the variables into the standard Normal space,
as with Level II Methods, e.g. the FORM Method which was considered in the previous
section.
The Monte Carlo Method of determining the probability is conducted as follows;
1. Once the mean and standard deviation as well as the type of distribution of the
parameters have been determined, the initial values to be used in the analysis are
determined as follows;
For a Normal distribution;
)2cos()ln(2 211 uux xx πσμ −+=
And;
)2sin()ln(2 212 uux xx πσμ −+=
For a Lognormal distribution;
))2cos()ln(2)exp(ln( 211 uustx o π−+=
And;
))2sin()ln(2)exp(ln( 212 uustx o π−+=
For a Beta distribution;
Where u1 and u2 are the generated random numbers.
Since the Extreme Value Distribution is used for the rope tension, the initial
value is calculated from the Asymptotic distribution;
61

Leslie L Moyo
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62
))ln(ln(
11
u
x
n
x
−−=
nx
−
α
μ
σ
μ
2. The generated values are then substituted into the Limit State Function G(x) and
the value calculated.
3. The number of trials nf for which G(x) ≤ 0 are then counted. The estimate of the
probability of failure is then given by;
N
n
p f
f =

Leslie L Moyo
______________________________________________________________________________________________
Due to the large number of trials that have to be carried out, a Visual Basic program is
developed in Excel and the calculations carried out. The subroutine for the simulation
solution for the flange fillet for Layer 5 is shown below;
Private Sub CommandButton1_Click()
' Simulation solution for Flange Fillet
mean_C = 1.75
sig_C = 0.363
Var_C = sig_C ^ 2
alpha = (mean_C - 1) * ((mean_C - 1) * (2 - mean_C) / Var_C - 1)
beta = (2 - mean_C) * ((mean_C - 1) * (2 - mean_C) / Var_C - 1)
u_1 = Rnd
Numfails = 0
Ntrials = 100000
Numfails = 0
Ntrials = 100000
Randomize
For x = 1 To Ntrials
Sy = exp(5.842+0.05*Sqr(-2*log(Rnd))*cos(6.284*Rnd))
h = 20 + Sqr(-2 * Log(Rnd)) * Sin(6.284 * Rnd)
C = Application.WorksheetFunction.BetaInv(u_1, alpha, beta, 1, 2)
S = 8058 * (3.962 - (Log(-Log(Rnd))) / 4.5) + 21127
Gx = 1118.41 * Sy * h – 13.3 * C * S
If Gx < 0! Then
Numfails = Numfails + 1
End If
Next x
Pf = Numfails / Ntrials
COV_Pf = Sqr((1# - Pf) / (Ntrials - 1) / Pf)
Range("C8").Value = Ntrials
Range("C10").Value = Numfails
Range("C12").Value = Pf
Range("C14").Value = COV_Pf
End Sub
Figure 19 Visual Basic Subroutine for the Monte Carlo Simulation of Flange Failure
The results of the simulation are shown below;
Number of simulation trials 100000
Number of times G(x) < 0 0
Probability of failure 0
COV_Pf
Monte Carlo Simulation
Flange Fillet
Start simulation
Figure 20 Results of Monte Carlo Simulation for Flange Failure
The probability of failure of the flange fillet according to the Monte Carlo Method is
0% with 5 layers of rope.
63

Leslie L Moyo
______________________________________________________________________________________________
The subroutine for the simulation solution for weld fatigue is shown below;
Private Sub CommandButton1_Click()
' Simulation solution for Weld Fatigue
Numfails = 0
Ntrials = 1000000
Randomize
For x = 1 To Ntrials
Dcr = exp(-0.042+0.294*Sqr(-2*Log(Rnd))*sin(6.284*Rnd))
A = exp(29.79+0.539*Sqr(-2*Log(Rnd))*sin(6.284*Rnd))
Gx = Dcr-9.1E08/A
If Gx < 0! Then
Numfails = Numfails + 1
End If
Next x
Pf = Numfails / Ntrials
COV_Pf = Sqr((1# - Pf) / (Ntrials - 1) / Pf)
Range("C8").Value = Ntrials
Range("C10").Value = Numfails
Range("C12").Value = Pf
Range("C14").Value = COV_Pf
End Sub
Figure 21 Visual Basic Subroutine for the Monte Carlo Simulation of Fatigue Failure
The results of the simulation are shown below;
Number of simulation cycles 1000000
Number of times G(X) < 0 0
Probability of failure 0
COV_Pf
Monte Carlo Simulation
Weld Fatigue
Start simulation
Figure 22 Results of Monte Carlo Simulation of Fatigue Failure
The probability of failure due to weld fatigue according to the Monte Carlo Method is
0% with 5 layers of rope.
64

Leslie L Moyo
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Chapter 6 Discussion of Results
The results obtained from the previous are summarised in the Table below;
For the flange fillet failure with 5 layers of rope;
Method Probability of Failure
FOSM 5.09E-27
FORM 1.33E-33
Monte Carlo 0
For the weld fatigue failure with 5 layers of rope;
Method Probability of Failure (%)
FOSM 0.043
FORM 0.043
Monte Carlo 0
The results indicate that the probability of failure of the hoist drum flange is very low,
which implies a very high reliability of the hoist drum. However, the probability of
failure of the hoist drum is higher for the fatigue limit state using FOSM and FORM but
the Monte Carlo Simulation did not indicate any failures for weld fatigue failure, even
after the number of trials was increased to 1million.
It is possible that the hoist drum has been over designed since the probability of failure
is quite low. However, the previous failures of the drum indicate that failure is possible
and it is therefore quite possible that the formulae used do not model the flange loading
accurately. It is quite clear from the research that the drum flange forces are critical to
the reliability of the hoist drum, given the failures reported by Song & Rao which
further reinforces the possibility that the formulae used in determining the strength of
the drum flange do not give a true indication of the drum flange loading model.
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Leslie L Moyo
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Unfortunately, there is no clear guidance on how the flange forces are to be evaluated,
and it appears that most design standards consider the issue of hoist drum design to be
trivial. Further work will need to be done to develop formulae that will model the drum
flange loading accurately.
66

Leslie L Moyo
______________________________________________________________________________________________
Chapter 7 Conclusions and Recommendations
The reliability of a hoist drum is subject to many factors and the results only give an
indicator of the probability of failure of the hoist drum assuming all other variables are
acceptable. Due to the large number of failures associated with the drum flange, the
flange strength has been selected as the most critical in this instance. However, the
results obtained seem to indicate that the failure of the hoist drum flange is unlikely in
this instance. It would have been worthwhile to apply the same approach to the failed
hoist drums with a view of verifying the accuracy of the formulae. The results therefore
are not conclusive, but indicate that further work needs to be done to come up with
substantive conclusions.
The differences in the pattern of loading are also quite significant. Waters suggests a
uniform loading of the flange, whereas DNV propose that the flange force increases
linearly from zero at the outer layer to a maximum near the barrel surface. Song & Rao
found that the flange thrust increased with the number of layers and Bellamy & Phillips
found that the flange force increased linearly with the number of layers but observed
non-linearity for one type of rope. Bellamy & Philips also observed that LeBus spooling
only had an effect on flange force for certain types of ropes, whilst the effect was
negligible for others.
Unfortunately, it appears as if none of the design standards have taken the work and
findings of the researched authors into account. It is accepted that the results from the
experiments carried out may now be out of date as the stiffness of steel wire ropes has
changed significantly(Lange, 2007) over the years. However, the research can be used
as a basis for future study on the subject.
67

Leslie L Moyo
______________________________________________________________________________________________
Chapter 8 Suggestions for future work
A similar study can be undertaken taking into consideration the failed drums to verify
the accuracy of the design code formulae. The magnitude of the flange forces as
calculated using approaches can also be compared. The project outlined the challenge
facing the hoist drum designer. Whilst the drum barrel can be designed based on clear
procedures and guidelines, the same is not true for the drum flange. The difficulty lies in
determining the magnitude and pattern of loading of the drum flange. Once the flange
force has been determined, the evaluation of the flange stresses is relatively straight
forward.
The approach proposed by Waters, the graphs presented by Bellamy and the DNV
formula can be compared to come up with a clear, verified procedure for determining
drum flange forces. Song & Rao also found significant variations in the flange forces
for small drums compared to large drums and it would be helpful to clarify these
variations. A common design code covering the design of winch drums can then be
developed. A considerable amount of research has been carried out on the subject of
drum flange forces, but unfortunately it does not appear as if any of the work has been
used in any of the design standards reviewed.
The University of Clausthal in Germany has also carried out a number of experiments to
determine the strength of drums in recent years. Unfortunately the papers they have
published are in German and the author did not have the resources to translate the
documents. It would be useful in future if the work was translated to English and the
findings combined with other research findings.
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Leslie L Moyo
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8.1 Fleet Angle
The effects of rope fleet angle do not appear to have been considered in past
experiments. Industry practise normally limits the fleet angle to 2 degrees for grooved
drums and 1.5 degrees for smooth drums(Shapiro, et al., 1991). It is not clear what
effects larger fleet angles will have and the significance of the fleet angle may be
underestimated as a result. Dynamic effects due to braking(Perry, et al., 1932) and
dynamic loading due to the rope snatching also need to be considered(Imanishi, et al.,
2009).
8.2 Calculation of Stresses
Once the pattern and magnitude of the flange forces have been determined, the
determination of flange stresses is relatively straightforward. A way of calculating the
flange stresses is presented below. This would require the flange to be considered as an
annular ring as in Roark(Young, et al., 2002). This magnitude and pattern of loading
will need to be determined, in this instance the flange force is considered to be a point
load acting at a distance that is 1/3 of the distance from the outermost layer to the drum
surface, measured from the drum surface. Going forward, this approach could be
adopted into the design codes. An excel spreadsheet for the calculation is included
overleaf;
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Structural Reliability Assessment of a Winch Drum for an Offshore Crane

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