503
1 INTRODUCTION
The requirements for increasing the safety of bulk
carriers were presented in 1993 by the International
Association of Classification Societies (IACS) and the
International Maritime Organization (IMO). The need
to acknowledge a premier role in the constructive-
elastic optimization of bulk carriers was claimed by the
large number of registered damages, including losses
of ships from this functional-constructive category [43].
Justifiably, the authors of this paper are interested in
limiting the number of ship losses by improving their
constructive structure, respectively the control over the
(general and local) elastic behaviour for the ship’s hull
in the mentioned category. The constructive
restructuring of the bulk carrier’s hull appeared
because of the factors involved in damage losses [32].
The simple comment on the above-mentioned
factors highlights the actual priorities regarding the
constructive structuring of the bulk carrier’s hull. Of
course, two distinct situations arise: for the existing
bulk carriers already in operation, the necessary
structural corrections can only be partially assimilated;
for the bulk carriers to be designed and built, the
structure must be reanalyzed and rationally designed.
FEM Structural Analysis and CAD Hull Modelling
for a Bulk Carrier - a Case Study
A. Pintilie, M.G. Manea, O. Cristea, P. Burlacu, D. Mărăşescu & C.P. Clinci
Mircea cel Bătrân Naval Academy, Constanţa, Romania
ABSTRACT: Due to the frequent damage encountered in the hull of bulk carriers in operation, it is necessary to
analyse the possibilities to increse the performances by structural and dimensional modeling of the central area
of the hull of the vessel under the effect of combined general stresses (and specific local stresses. The present
paper analyzes the response of the central section of the bulk carrier of 165000 tdw for three representative cases
of total stress, re-evaluated by simulation with the help of finite element analysis software. Following the
interpretation of the results obtained by the finite element analysis, the authors propose some solutions to increase
the structural strength of the central area of the bulk carrier of 165000 tdw. The present study shows that the
structure of the cylindrical area of the hull of the analyzed ship, remodeled by finite element, ensures the
compromise between the operational requirements and the design requirements imposed by the norms The
structural characteristics of the central section of the ship were analyzed, the practical validation being provided
by the finding that the bending moments do not exceed the permissible values imposed by the class society. Work
was done on three separate cases of ship loading and corrections were made for 12 sections of the hull. The use
of high-strength steel has led to a weight reduction of 22%.
http://www.transnav.eu
the International Journal
on Marine Navigation
and Safety of Sea Transportation
Volume 19
Number 2
June 2025
DOI: 10.12716/1001.19.02.20
504
Table 1. Factors involved in damage losses ships
Cause
Authors
solution
corrosion of materials
limit the effects either by using
resistant materials or by
intensifying protection measures
grounding and collisions of ships
reevaluating whit FEM to ship hull girder strength
due to grounding and collisions of ships
goods with high
density
FEM analysis of
ship loading
cases
fatigue
redesign the structure
elements of transition from a
framework system
to another
wide cutouts
for the
deck’ s
hatchways
stiffening of
these decks is
required
the presence of
corrugated walls
which
redesign the fixing
system of corrugated
walls to the main deck
the cargo effects on
the double
-bottom
redesigning in
terms of control the
oversizing
2 LITERATURE REVIEW
The design characteristics of bulk carriers have been
the focus of naval classification societies that over time
have been concerned with setting up design and
construction criteria that allow appropriate responses
to the general and local strains upon the hull while in
operation.
2.1 Design requirements of classification societies
2.1.1 American Bureau of Shipping requirements
Since 1991 the American Bureau of Shipping (ABS) has
become interested in investigating the response of the
bulk carrier hull structure to stress, to understand the
causes of the structural weaknesses which may
contribute to ship losses. They proposed a new
complete, flexible, and integrated strength criteria for
the design of bulk carrier hull structures, which involve
loading, strength for minimum scantling requirements,
and strength assessment procedures [18].
The American Bureau of Shipping (ABS) indicates
that most structural deficiencies in bulk carriers are
generated by irrational cargo loading in holds and/or
asymmetric ballasting of trim tanks, necessitating
frequent visits by the ship classification societies so that
flaws be detected before they produce major damage
to the material [40]. According to the ABS Rules, the
following aspects must be considered:
− checking the degree of participation of the efforts in
the general and local demands of the ship’s hull,
idealized as a complex beam (the sectional efforts
resulting from the calculation must be amplified in
order to be sure of taking over the additional loads
due to the cuts in the decks);
− anticipating the loading variant of the goods in the
cargo holds (uniform or alternating,
− the latter producing bending moments and shear
forces which can cause damage to the structure
when combined);
− the participation of dynamic efforts to the hull
stress, with effects on the safety of the structure
(avoided in current design practice by accepting
some covering safety coefficients);
− appreciation of the effects of excessive corrosion
phenomena in various structural areas of the hull (a
fact that sometimes requires the reconsideration of
the materials currently in use).
2.1.2 Bureau Veritas requirements
In 1995, Bureau Veritas imposed VeriSTAR, a set of
recommendations regarding ship design, which
considers that fatigue and corrosion are the main
causes of damage observed on ship structures [7].
2.1.3 IACS requirements
For safety reasons, in 2010, a consolidated version
(more complex and time consuming for the design
process) of the Common Structural Rules (CSR) for oil
tankers and bulk carriers was established by the IACS.
To strengthen the IACS CSR design rules, the following
studies were carried out:
− preoccupied by the problem of time, Na and Karr
developed a new structural analysis tool for the
optimum design of ship structure named Efficient
505
Stiffness Method (ESM) trough what reduce the
analysis computing time compared with FEM
method [26];
− to follow the structural design according to IACS
CSR requirements, an original approach has been
presented, proposed by Andric et.al. [3], which uses
an in-house structural design support system,
named OCTOPUS-CSR for the preliminary design
of a bulk carrier;
− others, like Kitarovic, Andric and Piric consider the
rules of IACS CSR to analyze the ultimate strength
of a bulk carrier hull girder at its amidships section,
using the nonlinear finite element method analysis,
the results being compared and discussed on both
local and global level, for sagging and hogging
cases [22];
− to evaluate the Ultimate Limit State (ULS)
performance of a bulk carrier structure designed by
the IACS CSR method, and to certify the quality of
the design, at first, it was necessary to compare this
method with the similar class / type bulk carrier
structure designed by the IACS pre-CSR method
[29].
The conclusion is that the constructive structure
must be established beforehand so that it can be found
in elastic and resistant forms of the ship’s hull
supported by quality materials and efficient
manufacturing technologies, respectively in
shortening the ship’s manufacturing cycle. Right from
the design phase, the multiple, diverse and complex
demands to which the ship’s hull is subjected must be
known and anticipated preventively and
systematically controlled during operation.
2.2 FEM studies of the ship’s structural strength
The elastic-plastic behaviour of the ship is influenced
by certain factors, namely: the geometric and material
properties; the characteristics of the loads upon the
decks; the initial imperfections of the material; up to
the limit conditions; local damage due to corrosion,
cracks and stress concentrators. The Finite Element
Method (FEM) is an advanced method for numerically
solving problems arising in marine engineering and
naval architecture such as structural analysis.
Therefore, various researchers have used this method
both for the ship as a whole and for the analysis of areas
considered critical to the ship’s structure. Yang et.al.
[38] analysed (using 3D FEM to design the dry
structure model and 3D methods in the frequency and
time domain to predict the wave loads) the vertical and
horizontal bending moment together with the torsional
moment caused by the wave loads for a very large bulk
carrier. The hydro elastic responses of ships traveling
on waves were studied and a comparison was
conducted between the numerical prediction results
and experimental data measured from the sea-keeping
basin. Pei, Iijima, Yao et.al. [30] were interested in
examining the influence of the local bending of the
double bottom on the ultimate hull girder strength for
a bulk carrier in alternate heavy loading conditions. For
that reason, they used a nonlinear FEM analysis which
found that bending deformation was produced not
only in the double bottom but also in the bilge hopper
tank, and the ultimate hull girder strength was reduced
by roughly 20% due to this local bending. Two years
later, the same authors concentrated their efforts to
simulate progressive collapse behaviour of a single
hull kamsarmax type bulk carrier [31]. Progressive
collapse behaviour obtained through Idealized
Structural Unit Method (ISUM) analysis (compared
with MARC as a Finite Element Analysis solver)
proved their applicability to structure system by
offering high accuracy and sufficient efficiency. Alie
and coauthors [2] studied the ultimate strength of
ship’s hull considering the cross section and beam
finite element under longitudinal bending (only one-
frame space of the ship was taken into consideration in
the calculation and the cross section of the bulk
carrier’s hull was divided into element-composed plate
and stiffened plate). Knowing that bulk carriers have
been designed with a small safety margin, Frystock
and Spencer present analyses of the strength in flooded
conditions, performed for different loading conditions:
alternate and uniform loading distribution of heavy
cargo [14]. The paper [9] focuses on time-variant
longitudinal strength of bulk carriers under corrosion
wastage, the hull girder section modulus and ultimate
bending moment capacity being determined. The [33]
paper studies the progressive collapse of the hull
girder subjected to pure bending in hogging conditions
for a bulk carrier, using the nonlinear finite element
analysis. The author’s conclusion is that the tripping or
flexural-torsional buckling of the bottom longitudinal
stiffeners after the plate buckling under extreme
hogging condition can be clearly captured by the
nonlinear finite element analysis.
Having in mind that for bulk carriers, the
longitudinal bending moments induce both
longitudinal and transverse stresses in the hull section,
Ohta conducted some studies to verify that the upper
deck was bent outward or inward horizontally by
using FEM for stress calculations and found that the
transverse stresses was higher than the longitudinal
stresses at the hatch corners, depending on the ballast
loading condition [28]. Nakai and his colleagues [27]
observed the pitting corrosion on hold frames and a
series of tensile tests concluded that the tensile strength
decreased gradually, and the total elongation
decreased drastically with the increase in the thickness
loss due to pitting corrosion. A series of tests were
performed which revealed that compressive buckling
strength of pitted members was smaller than or equal
to that of members with uniform thickness loss in
terms of average thickness loss. The authors provided
an elastoplastic analysis by FEM to simulate the
compressive buckling test to validate the proposed
method of modelling. The buckling / plastic collapse
behaviour of stiffened panels under longitudinal thrust
was investigated by Tanaka et.al. [35] using FEM
analysis; the results were compared with several
existing methods such as CSR for bulk carriers and
PULS (concluding that PULSE method gives a good
estimation).
2.3 Advanced bulk carriers hull design studies
It is a very well-known fact that the loads upon the
ship’s hull in operation can manifest themselves
statically or dynamically. From the static point of view,
the advanced design of a ship structure involves [24]:
the physical-mathematical modelling of the hull
structure, starting from the initial imperfections of the
materials (initial deformations and welding residual
506
stresses); the identification of the working
characteristics of the decks (mode of support and
predominant stresses); the determination of the
expressions that describe the strength of the decks
subjected to combined static loads; the determination
of critical stresses in the case of static loads. Most of the
damage to the hull of bulk carriers is failures in the
plastic area due to the bending of the deck and bottom
panels, and sometimes of the side panels. This is the
reason why the accuracy of determining the bending
stresses and critical stresses in the mentioned decks
becomes a basic requirement for the structure safety.
From the dynamic point of view, the advanced design
of naval structures involves [31]: physical-
mathematical modelling of the ship’s hull structure,
starting from the initial imperfections of the materials;
determining the effects of hindered rotations and
torsional stiffness for backing supports to the naval
decks; determining the breaking strength for any
potential combination of loads; determination of
critical stresses in the case of dynamic loads.
Regarding the design of bulk carriers, the
specialized literature is very rich, with several articles
of very good quality that have been published, and
have made important contributions, and it is
practically impossible to mention them all. For rational
dimensioning of this paper, only a few have been
retained, and are presented in the table below.
Table 2 Bulk carrier hull design studies
Author(s)
Research direction
Liao
et. al. [23]
were concerned with the application of Controlled
Robust Optimization (CRO) methods in solving
conceptual design problems of bulk carriers and the
paper demonstrates the feasibility of the mentioned
approach to find robust solutions for optimizing ship
design for long-term ocean voyages, designer being
able to handle optimization problems with multiple
uncertain parameters
Mohamed
et. al. [25]
the main objective is to design a bulk carrier to
minimize the construction cost, and to maximize the
annual transported cargo. To reach the objective, the
authors have used a method based on Multi-Attribute
Decision Making (MADM), which proves certain
advantage related to construction and voyage cost
(compared to other methods) but remains deficient
regarding the annual transported cargo
Aksu
et. al. [4]
highlighted that the basic design parameters of bulk
carriers could be optimized using the Parameter Space
Investigation method
Zheng
et. al. [36]
studied the data (obtained through an optimization
algorithm) which can be used to find the optimal
solution in hull form design and proposes a set of
knowledge extraction methods suitable for multi-
objective ship optimization. Design aspects of some
components of interest of the bulk carrier hull were
also targeted
Do
et.al. [11]
uses the finite-element (FE) modelling for flat and
curved plates of a ship to assess their safety in
conditions of axial compression, based on the Ultimate
Limit State (ULS) design and analysis concept
Kitamura et
al. [21]
Finite Element Method (FEM), with a numerical
example as confirmation, was used for structural
optimization of a ship’s bottom in this paper, for shape
optimization being considered: the height and width of
the double bottom, the height of the bilge hopper tank,
and the 2 widths of the lower stool
Feng
et al. [13]
the paper studied, through building finite element
model of a bulk carrier’s hold section, the design loads,
boundary conditions and several load cases
The general objective of the research shown in this
paper is to optimize the construction of the cylindrical
area of the 165,000 tdw bulk carrier through structural
and dimensional modelling, under the conditions of
the manifested combined stresses resulting from the
general combined longitudinal-vertical bending stress,
with transverse-vertical bending and longitudinal
torsion.
3 THEORETICAL CONSIDERATIONS
The stress that is common to all categories of ships
comes from the longitudinal-vertical bending;
however, for ships with considerable width, such as
the 165,000 tdw bulk carrier which is the subject of the
present research study, the transverse-vertical bending
and the torsion are significant [24]. In principle, the
stress is the state that determines the general stress
upon the ship’s hull which is represented by the shear
forces, bending moments as well as torsion moments
resulting from the vertical loads (the effect of
horizontal loads can be neglected). Depending on the
effort’s distribution along the transverse section of the
ship’s elastic hull, the following stress cases are of
interest [24]: the pure bending (when the cutting forces
are zero), in the simple variants (with the vector section
moment located on the main inertia axis) or oblique
(with the section moment vector having non-zero
components in accordance with both main inertia
axes); the shear bending (when the shear forces are
non-zero), also in the simple and oblique variants; the
shear and torsion bending (when the loads vary both
along the length and across the width of the ship, and
the shear forces along the two directions are non-zero).
In this paper, the symbols σ_iifor the normal stresses
and σ_ijfor the tangential stresses are accepted, where
i and j represent the orthogonal directions.
Figure 1 shows the ship’s hull, idealized by a box-
type beam having thin walls, sectioned by a normal
plane to its axis and to which the Oxyz axis system was
attached.
Figure 1. Distribution of sectional stresses in the ship’s hull
[24]
Additionally, the elementary connection forces
determined by the normal stress σxx are represented,
respectively the components of the tangential stress σxy
and σxz corresponding to the shear bending stress and
507
torsion. They belong to the set of stress components
acting on the elementary rectangular trihedron,
reduced at point P, symbolized by the square matrix
,
xx yx zx
xy yy zy
xz yz zz
T


=






(1)
called the tension tensor, to which corresponds the set
of specific deformation components expressed by the
square matrix
11
22
11
,
22
11
22
xx yx zx
xy yy zy
xz yz zz
T




=







(2)
called the tensor of specific deformations.
From the analysis of Figure 1a) one can notice that
the following sectional stresses are obtained upon
reducing the normal elementary stresses:
− the normal force or the axial force having the
expression
kN ;
x xx
A
N dA
=
(3)
− the bending moments having the expressions
z xx
A
M ydA
=
and
kNm
y xx
A
M zdA
=
(4)
From the analysis of Figure 1b) one can notice that
the following sectional forces are obtained upon
reducing the elementary tangential forces:
y xy
A
T dA
=
and
kN ;
z xz
A
T dA
=
(5)
− the torsion or twisting moment having the
expression:
( )
kNm
x xz xy
A
M y z dA

=−
(6)
The complexity of the stresses results from the fact
that the interaction process, which is carried out on
both waveless and wavy seas, can be deterministic or
random. The general ways of approaching this
interaction process are known [32]; however, the
present paper suggests highlighting the situations that
determined the stress condition in the cylindrical area
within the hull under study, finally causing certain
structural elements in the field of plastic distortions to
cave in.
4 MATERIAL AND METHODS
The bulk carrier (BK) is a ship for dry goods, specially
designed for the transport of cargo with different
specific weights, stowed directly in cargo holds,
without prior packaging [24]. The reference ship
(courtesy of [42]) falls under the category of universal
bulk carriers equipped with bilge tanks and anti-roll
tanks, adapted for the transport of goods with different
densities (grains, coal, coke, phosphates, iron ore, etc.).
It features the following constructive characteristics: it
has a single, continuous deck along the entire hull
length, no longitudinal deck sheer and connected to the
shell plating through the curvature; the engine room
and the superstructure located aft, except the
forecastle, which is located forward; has nine self-
trimming cargo holds; it is equipped with side ballast
tanks, the upper ones located under the main deck, and
the lower ones in the bilge area; the prismatic shape of
the ballast tanks gives the cargo holds their orthogonal
shape (thereby allowing the use of the entire
deadweight space for the transport of goods while
ensuring, at the same time, the stability and trim for
safe exploitation); the general hull framing system is
combined (longitudinal for the deck, bottom, double
bottom and ballast tanks in the cargo holds area;
transversal for the sides, in the cargo holds, the after
end and forwards end, the engine room); the double
bottom of the odd-numbered cargo holds is properly
reinforced for the transport of heavy cargo and for
supporting the loading and unloading operations with
the help of grabs.
Main dimensions and displacement characteristics
are as follows:
−

󰇟󰇠;

󰇟󰇠;
−

󰇟󰇠;
󰇟󰇠; 󰇟󰇠 ;
󰇟󰇠;
−  󰇟󰇠;

󰇟󰇠.
Figure 2. Main dimension of ship
For the hull construction, the following types of
steel were used: ordinary naval steel A (yield strength
235 N/mm
2
), for the shell plating and hull framing;
high-strength naval steel A32, D32, E32 (yield strength
315 N/mm
2
) was used for the deck, in the central area
of the ship; special naval steel B, D and E was used for
the hull elements indicated by the rules of the
classification society. The central section under
investigation is in the cargo holds area, between ribs
C53 and C292, so as to include in its structure all the
constructive units (including the ones in the
transversal bulkhead). The functional and dimensional
diversification, respectively the increase in the
requirements regarding the technical-economic
performances of the current ships, have a limiting role
in the application of classical calculation models, while
in some situations they are even inadequate. Therefore,
there is the need to perfect the modelling in the context
of the facilities offered by the progressive evolution of
the computerized calculation technique. Modern naval
design is dominated by computerized systems based
on the development of complex computer programs.
As of 1990, ABS has been using computer technology
to carry out dynamic technical projects and implement
optimal assessment methods for establishing the
structural requirements of bulk carriers and oil tankers.
Known as "SafeHull", the current trend in register rules
508
differs from the conventional one in that the
requirements are established based on the first
principle of classical mechanics, where the action
criterion is explicitly defined, and the structural
responses are assessed against different types of
potential damage. Therefore, the newly developed
criterion, together with the software developed for its
application, allow the designer to perform the initial
minimum sampling and assess the structure responses
based on the finite element analysis. Naval
competitiveness is based on three reference
coordinates, which ultimately express the essential
requirements, namely quality, cost, delivery date.
These requirements are currently calling for the
exploitation of the fast-processing capacity and the
interaction type facilitated by personal computers.
Computer Aided Design (CAD), Computer Aided
Manufacturing (CAM) and, in general, the Computer
Aided “X” (CAX) concept [15], are current use
technologies. But for their use, the previously stated
desiderata would remain utopian. Understanding the
CAX concept requires examining the various activities
and functions that must be performed in the hull
design/manufacture process. Generically referred to as
the "ship manufacturing cycle", the process comprises
two main activities: design and manufacture. During
these stages, a wide range of software tools have been
used: graphic programming tools (the role of CAD
systems is to create graphic representations of
engineering systems designed by computer
programming, computer-aided drawing and
geometric modelling are necessary); analysis tools
(CAE systems have the role of facilitating the analysis
of the geometry made by CAD techniques, allowing
the designer to simulate and study the product
behaviour so that the project can be optimized). The
sequential programming method, also accepted by the
authors of this paper, uses as operational environment
the Femap finite element analysis program (a finite
element analysis model and post-processing system
that facilitates fast and useful engineering analysis),
made by Enterprise Software Products Inc. [37]. The
finite element analysis model offered by the Femap
program can use two distinct database variants:
internal, which introduces the model geometry step by
step; and external, made with another program
product. For this specific paper, its authors propose an
external program for generating and optimizing the
ship’s shapes, through the AutoLisp programming
environment, specific to the AutoCad program
product. In general, the creation of the finite element
analysis model involves the following stages:
establishing the reference system; identification of
structure nodes; the choice of materials, respectively
their properties; setting up boundary conditions by
introducing the types of restrictions (constrains,
articulations, supports, etc.); establishing loads (forces,
pressures, tensions, efforts, etc.). Finally, having
established all the analysis elements, the post-
processing is carried out, and the model response to the
imposed stress is obtained. Regarding the model made
with the help of Femap for the 165000 tdw bulk carrier
– as the reference vessel for the applicative part of this
research – the following were taken into consideration:
− the central module was identified from the ship’s
hull, including three cargo holds: cargo hold no. 6
(extended on the range limited by the real ribs
C.134-C.160); cargo hold no. 5 (extended on the
range limited by the real ribs C.160-C.186), and
cargo hold no. 4 (extended on the range limited by
the real ribs C.187-C.211);
− the model was initiated with the transversal
framework rib in the amidship section for which the
boundary conditions were established to one single
board (due to symmetry) and the loading of the half
framework rib with loads (Figure 3).
Figure 3. 3D-Model of transversal framework rib for the
reference ship (left side) and the loading of the half
framework rib with loads (right side)
5 CASE STUDY ANALISYS
Checking up the model involved the determination of
the longitudinal strength of the ship beam in the
weakened cross-sections, for 3 representative loading
cases. The initial state of the ship is characterized by the
values of moments and admissible shear forces
calculated according to (courtesy of [42]) and
centralized in Table 3.
Table 3. Admissible shear forces and bending moments in
the initial ship beam on calm sea
Section
(Tsc)a [kN]
(Myc)a [kNm]
Underway
In the
roadstead
In
harbour
Underway
In the
roadstead
In
harbour
C59
46116.54
55339.84
62257.32
2570788
2396443
3244829
C84
48222.13
57866.55
65099.87
3709843
5211920
6338093
C109
55426.41
66508.09
74821.60
4723755
6597066
7689772
C134
56361.28
67633.53
76087.72
4015747
5731620
6688897
C160
70193.98
84232.77
94761.87
4015747
5731620
6688897
C186
70193.98
84232.77
94761.87
4015747
5731620
6688897
C211
53353.50
64002.46
72002.77
4015747
6056162
7064225
C236
40772.68
48927.21
55043.12
4128988
5411829
5667267
C267
37224.04
44668.85
50252.45
3405939
3688044
4863149
C303
45953.19
55143.82
62036.80
3258593
3047126
4309644
Construction-wise, the ship’s hull under study
ensures the compromise between operational stresses
and structural requirements. Therefore, the safety
limits between the structural components cannot be
uniform. The optimal content of the present paper
requires the analysis to be limited only to the structural
changes made in the planks of the watertight
transversal bulkheads, and respectively to the change
of the material and the thickness of the plank covering
for the shell plating.
5.1 Remodeling the planks of watertight transversal
bulkheads
The optimization by modelling the plank in the
watertight transversal bulkhead envisaged two
aspects: increasing the rigidity of the upper part of the
plank, by introducing a support structure into the
model, and respectively reducing the weight of the
509
bulkhead plank by changing the geometry of the
corrugation system and, implicitly, reducing the
number of corrugations. To reduce the weight of the
plank in the watertight transversal bulkhead, the type
of corrugation has been modified, (see Figure 4.
Figure 4. Structural remodelling of side panel corrugations
For the proposed variant, keeping the same
thicknesses, the normal stress in the wall floor exceeds
the admissible value, correction being made by
increasing the wall thickness from t=13 mm to 14 mm,
the normal stress in the deck becoming
σyy=218.52N/mm
2
, falling within the admissible limits.
To stiffen the wall deck at the top, the constructive
solution from Figure 5 is adopted.
Figure 5. Structural remodelling of the upper support of the
side panel
5.2 Remodeling the side panels
Remodelling the side panels is based on the analysis of
the behaviour of the ship’s cylindrical area analyzed in
three representative flooding situations: unloaded and
unflooded cargo holds; loaded and successively
flooded cargo holds; unloaded and flooded cargo
holds. To establish the thickness values for the shell
plating in the three flooding cases, based on the
principle of effects superposition, only the maximum
effective and admissible absolute values of the shear
forces in calm water are kept on the same diagram. The
authors’ proposal was represented by two types of
steel: ordinary naval steel, with c = 235 N/mm
2
; high
strength naval steel, with c = 315 N/mm
2
.
The analysis of the diagrams resulting from the
effects of superposition of the shear forces and the
admissible values recommends the variant in Figure 6
as acceptable (to ensure the compromise between the
ship safety and the technological implications),
corresponding to the worst situation (the case of
unloaded and flooded cargo holds). In the areas where
the admissible values of the shear forces are exceeded,
a shell plating covering made of steel is proposed:
thickness 19.0 mm, quality A32, between C83 and C86;
thickness 16.5 mm, quality A32, between C238 and
C241; thickness 19.0 mm, quality A32, between C270
and C280.
Figure 6. Diagram resulting from the effect of superposition
of the shear forces and admissible values, for the case of
unloaded and flooded cargo holds
Following the change in the quality of the materials,
the thickness of the component elements and the
changes in the structure, the values of moments and
admissible shear forces in the weakened sections will
have the values in Table 4, calculated according to [42]
requires.
Table 4. Shear forces and admissible bending moments -
remodeled ship beam, in calm water
Section
(Tsc)a [kN]
(Myc)a [kNm]
Underway
In the
roadstead
In
harbor
Underway
In the
roadstead
In harbor
C59
70800
70800
86900
3189140
3497730
3960620
C84
60880
70490
84910
5017010
5636760
6397130
C109
73770
83380
97800
5765000
6612730
7884320
C134
78050
85430
96500
4499550
5600730
7251600
C160
78070
85440
98940
3901630
5122040
6952640
C186
78710
85950
96820
4434020
5547950
7218830
C211
70940
79760
92990
5511090
6416150
7761460
C236
52940
63100
78360
4980000
5622400
6574010
C267
52890
63050
78310
3591000
3971370
4541930
C303
59690
64040
70560
2964170
3190590
3430170
The local stress on the ship’s hull in the cargo holds
area depends on the usual loading options in
operation. Each load variant (Table 5) of the cargo
holds was associated with a stress model (which
responds to the type of cargo, environmental
conditions, dynamic responses and representative
stress rates), finally resulting in the design proposal.
Table 5. Representative load situations
Situation
Loading situation
Draft
1
Ship having ballast in cargo hold
T1 = 0.45T
2
Ship having high-density ore in cargo hold
T2 = T
3
Ship having heavy ore in cargo hold
T3 = 0.67T
Particular features for loading situation 1 (see
Figure 7): if the tanks in the double bottom, bilge and
below deck are intended for ballast, then they are
considered full; the adjacent watertight compartment
has empty cargo holds and associated tanks; the
external load exerted by the sea water on the structure
is determined by the rules of the naval classification
registers, for draft T1, excluding the dynamic pressure
exerted by the wave; the internal load exerted by the
ballast (sea water) on the structure is also determined
by the Rules of the Naval Classification Registers,
considering only the static pressure.
510
Figure 7 Loading situation 1
Particular features for loading situation 2 (Figure 8):
the cargo partially takes up the volume of the cargo
holds, the bilge and under-deck tanks are empty, and
the double-bottom tanks are full of fuel; the adjacent
watertight compartment has empty stores as well as
empty associated tanks; both the external and internal
loads on the structure was determined according to the
specific Rules of the classification register.
Figure 8. Loading situation 2
Particular features for loading situation 3 (see
Figure 9): in the analysed watertight compartment, the
bilge, under-deck and double-bottom tanks are empty;
the adjacent watertight compartment has empty stores
as well as the associated tanks; the external load
exerted by the sea water on the structure is determined
by the Rules of the naval classification register for the
specified draft, excluding the dynamic pressure caused
by the wave; the internal load, exerted by the load on
the structure, is determined with the specific rules of
the naval classification register.
Figure 9. Loading situation 3
The effective values of shear forces and bending
moments, for the load cases analyzed, were
determined in 12 verification sections and the obtained
results were centralized in Tables 6 –8. Also, the stress
states on the framework rib are illustrated in Figures 10
- 12.
Figure 10. Stress state on framework rib for Loading
situation 1
Figure 11. Stress state on framework rib for Loading
Situation 2
Figure 12. Stress state on framework rib for Loading
Situation 3
Table 6. The effective shear forces in the calculation sections for loading case 1
Section
Myc [kNm]
Tzc [kN]
Remarks
Det.value
[kNm]
Adm. value
[kNm]
Ratio [%]
Det.value [kN]
Adm.value [kN]
Ratio [%]
C59
1528040
3189140
47.9
64220
70800
90.7
accepted
C84
2801880
5017010
55.8
43800
60880
71.9
accepted
C109
3584100
5765000
62.2
21750
73770
29.5
accepted
C134
3903570
4499550
86.8
3540
78050
4.5
accepted
C147
3911930
4153490
94.2
-5000
78050
6.4
accepted
C160
3781040
3901630
96.9
-13480
78070
17.3
accepted
C173
3599800
4167830
86.4
-19210
78390
24.5
accepted
C186
3308610
4434020
74.6
-24410
78710
31.0
accepted
C211
2644480
5511090
48.0
-32000
70940
45.1
accepted
C236
1858460
4980000
37.3
-35190
52940
66.5
accepted
C267
1020050
3591000
28.4
-34050
52890
64.4
accepted
511
C303
296390
2964170
10.0
-26360
59690
44.2
accepted
Maximum bending moment: (Myc)max = 3930030 [kNm[ (90.2%), corresponding to C134 + 5.12 [m]
Table 7. The effective shear forces in the calculation sections for loading case 2
Section
Myc [kNm]
Tzc [kN]
Remarks
Det.value
[kNm]
Adm. value
[kNm]
Ratio [%]
Det.value [kN]
Adm.value [kN]
Ratio [%]
C59
-774010
3189140
24.3
-47540
70800
67.2
accepted
C84
-353930
5017010
7.1
81430
60880
133.8
unacceptable
C109
-491010
5765000
8.5
-95080
73770
128.9
unacceptable
C134
-660890
4499550
14.7
99630
78050
127.6
unacceptable
C147
-3030
4153490
0.1
62100
78050
8.0
accepted
C160
-513990
3901630
13.2
-87500
78070
112.1
unacceptable
C173
-1045680
4167830
25.1
23900
78390
3.0
accepted
C186
-422750
4434020
9.5
101980
78710
129.6
unacceptable
C211
-98360
5511090
1.8
-74490
70940
105.0
unacceptable
C236
-71030
4980000
1.4
94600
52940
178.7
unacceptable
C267
71340
3591000
2.0
-80910
52890
153.0
unacceptable
C303
-380190
2964170
12.8
41800
59690
70.0
accepted
Maximum bending moment: (Myc)max = -1266290 [kNm] (24.6%), corresponding to C109 + 11.60 [m]
Table 8. The effective shear forces in the calculation sections for Loading Situation 3
Section
Myc [kNm]
Tzc [kN]
Remarks
Det.value
[kNm]
Adm. value
[kNm]
Ratio [%]
Det.value [kN]
Adm.value [kN]
Ratio [%]
C59
-263960
3189140
8.3
-68970
70800
97.4
accepted
C84
-266900
5017010
5.3
67030
60880
110.1
unacceptable
C109
-671970
5765000
11.7
-103510
73770
140.3
unacceptable
C134
-981390
4499550
21.8
96020
78050
123.0
unacceptable
C147
-354460
4153490
8.5
4640
78050
5.9
accepted
C160
-872850
3901630
22.4
-87330
78070
111.9
unacceptable
C173
-1392350
4167830
33.4
3990
78390
5.1
accepted
C186
-741480
4434020
16.7
104700
78710
133.0
unacceptable
C211
-333160
5511090
6.0
-70500
70940
99.4
accepted
C236
-205160
4980000
4.1
98700
52940
186.4
unacceptable
C267
27820
3591000
0.8
-77870
52890
147.2
unacceptable
C303
-369380
2964170
12.5
42740
59690
71.6
accepted
Maximum bending moment: (Myc)max = -1530070 [kNm] (30.0%), corresponding to C109 + 12.32 [m]
6 RESULTS AND DISCUSSIONS
The analysis of the obtained data revealed that the
admissible shear forces were exceeded in several
verification sections (for two of the three load cases
analysed). In this situation, the effective shear forces in
all the verification sections are reduced, and the
obtained values are compared with the admissible
values.
The results are summarized in Tables 9 and 10. As
can be seen from the tables below, following the
reduction of shear forces in the calculation sections, the
effective values fall within the admissible values so
that the longitudinal strength of the ship beam is
verified. Furthermore, considering the total loads
reassessed, the central section of the 165 000 tdw bulk
carrier is remodelled in accordance with the
requirements of [44] and considering the
recommendations of [41], for the GL 100 A5 class.
The response of the central section, subjected to the
3 representative load cases, together with the diagrams
of bending moments and shear forces on the structure
nodes, can be visualized in Figures 13-15.
Table 9. Values of reduced shear forces (Tzc)red for loading case 2
Section
Determined value
Tzc[kN]
Reduction factor
Reducedvalue
(Tzc)red [kN]
(Tzc)a
[kN]
Ratio
[%]
C59
-47540
0.2845
-47540
70800
67.2
C84
81430
0.2825
44740
60880
73.5
C109
-95080
0.3130
-45210
73770
61.3
C134
99630
0.2825
46770
78050
59.9
C147
62100
-
6210
78050
8.0
C160
-87500
0.3130
-34640
78070
44.4
C173
23900
-
2390
78390
3.0
C186
101980
0.2825
52130
78710
66.2
C211
-74490
0.3130
-24640
70940
34.7
512
C236
94600
0.2915
43430
52940
82.0
C267
-80910
0.2290
-52810
52890
99.9
C303
41800
-
41800
59690
70.0
Table 10. Values of reduced shear forces (Tzc)red for loading case 3
Section
Determined value
Tzc[kN]
Reduction factor
Reducedvalue
(Tzc)red [kN]
(Tzc)a
[kN]
Ratio
[%]
C59
-68970
0.2845
-68970
70800
97.4
C84
67030
0.2825
28340
60880
46.5
C109
-103510
0.3130
-55330
73770
75.0
C134
96020
0.2825
44220
78050
56.7
C147
4640
-
4640
78050
5.9
C160
-87330
0.3130
-35530
78070
45.5
C173
3990
-
3990
78390
5.1
C186
104700
0.2825
55210
78710
70.1
C211
-70500
0.3130
-21010
70940
29.6
C236
98700
0.2915
47230
52940
89.2
C267
-77870
0.2290
-50250
52890
95.0
C303
42740
-
42740
59690
71.6
Figure 13. Response of the central section subjected
reassessed total loads for situation 1
Figure 14. Response of the central section subjected
reassessed total loads for situation 2
Figure 15. Response of the central section subjected
reassessed total loads for situation 3
7 CONCLUSIONS
This paper analyses the response of the central section
of the 165 000 tdw bulk carrier to the total loads
reassessed by simulation using FEMAP finite element
analysis software. The structural-constructive
characteristics for the initial and final variants of the
central section subjected to remodelling are
highlighted and compared. Thus, structurally and
constructively, the authors made qualitative and
dimensional changes to the planks that make up the
watertight transversal bulkheads and the bulkheads in
the central area of the ship’s hull. The practical
validation of the research results was based on the
verification of compliance with the registry rules and
the application of corrections for 12 calculation sections
of the ship’s hull, selecting three representative load
cases. It was found that the bending moments do not
exceed the admissible values, while critical situations
are recorded for the shear forces for four of the selected
load cases. Consequently, the effective cutting forces
were subjected to reduction, to be within the
admissible values. Through these corrections, the
safety of the longitudinal strength of the ship's hull
becomes certain. The structure of the cylindrical hull
area of the 165,000 tdw bulk carrier, remodelled in
accordance with the rules of the registry and verified
by finite element analysis programs, ensures that the
compromise between operational demands and
structural requirements is met. Also, in addition to the
fact that the structure meets the safety criteria, by using
high-strength steel, its weight has been reduced by
22%.
As stated at the beginning of this paper, the general
objective was to optimize, through structural and
dimensional modelling, the construction of the central
area belonging to the hull of bulk carriers, under the
effect of combined general stresses of longitudinal-
vertical bending, transverse-vertical bending, and
longitudinal torsion, complemented with specific local
stresses.
The fulfilment of the stated general objective
required a step-by-step process and the solution of the
following problems:
− theoretical, consisting in the identification,
processing and adequacy of the physical-
513
mathematical support, based on the analytical
support of the dominant ship exploitation
situations;
− practical-experimental, consisting of: creating
programs for the calculation and computer
simulation of elastic behavior; verification and
experimental or practical-statistical correction of the
results, in order to validate the research.
The authors remain convinced that the application
of numerical methods, based on the power of the
computerized calculation technique, offers the
possibility of almost complete ship modelling and
estimation. Major marine classification societies give
due importance to online vessel assessment and
assistance systems that respond to this concept. Thus,
detailed numerical ship models (in terms of volume
and structure) are built, fully supported by the
calculation technique. Limit states are evaluated taking
into account the actual operation of the structure,
including the effect of corrosion, loading and damage
situations, as well as changes in the technical state
(generated by: accidents; flooding of compartments;
loss of cargo or reserves, as a result of failure or
collision; changes in the condition of materials, as a
result of major fires on board, etc.). Thus, the ship can
be assisted and followed in its evolution throughout its
operation, anticipating possible safety risks.
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