Common Structural Rules for
Bulk Carriers, January 2006

Background Document
CHAPTER 8 – FATIGUE CHECK OF STRUCTURALDETAILS

NOTE:- This TB is published to improve the transparency of CSRs and increase theunderstanding of CSRs in the industry.
- The content of the TB is not to be considered as requirements.
- This TB cannot be used to avoid any requirements in CSRs, and in cases
where this TB deviates from the Rules, the Rules have precedence.
- This TB provides the background for the first version (January 2006) of theCSRs, and is not subject to maintenance.

COMMON STRUCTURAL RULES FOR BULK CARRIERS − BACKGROUND DOCUMENT
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COMMON STRUCTURAL RULES FOR BULK CARRIERSCOMMON STRUCTURAL RULES FOR BULK CARRIERS − BACKGROUND DOCUMENT
PAGE 3 – CHAPTER 8: FATIGUE CHECK OF STRUCTURAL DETAILSTABLE OF CONTENTS:
SECTION 1 – GENERAL CONSIDERATION.................................................................................... 5
1

GENERAL.................................................................................................................................... 5
1.1
1.2
1.3

2

DEFINITIONS ............................................................................................................................. 6
2.1
2.2
2.3
2.4

3

Application.............................................................................................................................. 5
Net scantlings .......................................................................................................................... 5
Subject members...................................................................................................................... 5
Hot spot................................................................................................................................... 6
Nominal stress......................................................................................................................... 6
Hot spot stress ......................................................................................................................... 6
Notch stress ............................................................................................................................. 6

LOADING ................................................................................................................................... 6
3.1
3.2

Loading condition ................................................................................................................... 6
Load case ................................................................................................................................. 6

SECTION 2 – FATIGUE STRENGTH ASSESSMENT ....................................................................... 81

GENERAL.................................................................................................................................... 81.1

2

EQUIVALENT NOTCH STRESS RANGE.................................................................................. 8
2.1
2.2
2.3

3

Predominant load case ............................................................................................................ 8
Loading "Condition 1"............................................................................................................. 9
Equivalent notch stress range.................................................................................................. 9

CALCULATION OF FATIGUE DAMAGE ............................................................................... 10
3.1
3.2
3.3

4

Application.............................................................................................................................. 8

Correction of the equivalent notch stress range .................................................................... 10
Long-term distribution of stress range.................................................................................. 10
Elementary fatigue damage .................................................................................................. 10

FATIGUE STRENGTH CRITERIA ........................................................................................... 11
4.1

Cumulative fatigue damage .................................................................................................. 11

SECTION 3 – STRESS ASSESSMENT OF PRIMARY MEMBERS .................................................. 121

GENERAL.................................................................................................................................. 12
1.1

2

HOT-SPOT STRESS RANGE.................................................................................................... 12
2.1
2.2

3

Application............................................................................................................................ 12
Stress range according to the direct method ......................................................................... 12
Stress range according to the superimposition method ........................................................ 12

HOT-SPOT MEAN STRESS...................................................................................................... 12
3.1
3.2

Mean Stress range according to the direct method ............................................................... 12
Mean stress according to the superimposition method ........................................................ 13

SECTION 4 – STRESS ASSESSMENT OF STIFFENERS ................................................................. 141

GENERAL.................................................................................................................................. 14
1.1

2

Application............................................................................................................................ 14

HOT-SPOT STRESS RANGE.................................................................................................... 14
2.1

Stress range obtained by the direct method .......................................................................... 14

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PAGE 4 – CHAPTER 8: FATIGUE CHECK OF STRUCTURAL DETAILS

2.2
2.3
3

Stress range according to the superimposition method ........................................................ 14
Stress range according to the simplified procedure .............................................................. 14

HOT-SPOT MEAN STRESS...................................................................................................... 15
3.1
3.2
3.3

Mean stress according to the direct method .......................................................................... 15
Mean stress according to the superimposition method......................................................... 16
Mean stress according to the simplified procedure............................................................... 16

SECTION 5 – STRESS ASSESSMENT OF HATCH CORNERS ...................................................... 171

GENERAL.................................................................................................................................. 17
1.1

2

NOMINAL STRESS RANGE .................................................................................................... 17
2.1
2.2

3

Application ............................................................................................................................ 17
Nominal stress range due to wave torsional moment ........................................................... 17
Nominal mean stress ............................................................................................................. 20

HOT SPOT STRESS .................................................................................................................. 20
3.1

Hot spot stress range ............................................................................................................. 20

APPENDIX 1 – CROSS SECTIONAL PROPERTIES FOR TORSION ............................................. 21
4

CALCULATION FORMULAE .................................................................................................. 21
4.1
4.2
4.3
4.4

5

Torsion Function Φ ................................................................................................................ 21
Co-ordinate system, running coordinate s ............................................................................ 21
Computation of several properties for each part of the cross section.................................... 21
Computation of cross sectional properties for the entire cross section.................................. 21

EXAMPLE CALCULATION FOR A SINGLE SIDE HULL CROSS SECTION ........................ 21
5.1
5.2
5.3
5.4
5.5

Cross section data .................................................................................................................. 21
Determination of the torsion function Φ................................................................................ 21
Determination of the line-segment properties....................................................................... 22
Determination of cross-section properties............................................................................. 22
Notes...................................................................................................................................... 22

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PAGE 5 – CHAPTER 8: FATIGUE CHECK OF STRUCTURAL DETAILSSECTION 1 – GENERAL CONSIDERATION
1GENERAL

1.1

Application

1.1.1
1.1.1.aThe design life considering fatigue is taken as 25 years, same as in other strength
requirements. The assessment is not applicable to bulk carriers under 150 m,
considering that design loads from actual service routes are not appropriate andconsidering the damage results.

1.1.2
1.1.2.aLoad factors other than design loads are taken as out of the scope of applicability
since design loads are based on assessment of external loads due to normal wave
pressures.

1.1.3
1.1.3.a

1.2

Applicable to structural steel with yield point below 400 N/mm2 based on thedesign curves used in the assessment. For steel with yield point higher than 400
N/mm2, data obtained from approved test plans is to be used. Submission of
fatigue design parameters summarized in the data above becomes the condition for
approval.

Net scantlings

1.2.1
1.2.1.a

1.3

In CSR for Bulk Carriers, all strength regulations including those for fatigue
strength assessment are based on the net scantling approach. Please refer to 3.2 ofSection 3, Chapter 3.

Subject members

1.3.1
1.3.1.a

The required locations for fatigue strength assessment have been selected based on
fatigue damage statistics and strength assessment results of bulk carriers withstandard structure.

1.3.1.b

The fatigue damage statistics shows that the almost fatigue damages wereexperienced in a ballast hold.

1.3.1.c

Following a well developed structural detail design is one of the effective fatigue
design methods.

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PAGE 6 – CHAPTER 8: FATIGUE CHECK OF STRUCTURAL DETAILS

2

DEFINITIONS

2.1

Hot spot

2.1.1
2.1.1.a

2.2

Fatigue strength should be assessed based on the assessed results of local stressstates at locations where fatigue cracks are likely to occur (hot spots).

Nominal stress

2.2.1
2.2.1.a

2.3

Multiplying SCF (Stress Concentration Factor) by nominal stress is a simplified
method to obtain hot spot stress.

Hot spot stress

2.3.1
2.3.1.a

2.4

Structural discontinuities or hot spot stresses including stress concentration due toattachments indicate the local stress state. However, crack occurrences are affectedby the existence of weld toe or stress concentration due to the existence of notch, etc.

Notch stress

2.4.1
2.4.1.a

By using notch stress considering the stress concentration due to the existence of
weld toe, fatigue strength can be assessed consistently without discriminating
parent material and weld joints.

3

LOADING

3.1

Loading condition

3.1.1
3.1.1.a

Fatigue phenomena depend on cumulative fatigue damage due to cyclic loads overa long period. Thus, typical loading conditions were selected considering theloading frequency in standard bulk carriers.

3.2

Load case

3.2.1

Load cases

3.2.1.aFor definition of load cases, refer to the explanations in Section 4, Chapter 4.

3.2.2
3.2.2.a

To assess fatigue at hatch corners, the oblique sea state that generates dominantstresses at hatch corner is considered.

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PAGE 7 – CHAPTER 8: FATIGUE CHECK OF STRUCTURAL DETAILS

3.2.3

Predominant load case

3.2.3.a

The long-term distribution of stress range is characterized by the stress range(maximum value) corresponding to a certain exceedance probability and the shapeparameter. The load case which gives the maximum stress range is selected as the
predominant load case.

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PAGE 8 – CHAPTER 8: FATIGUE CHECK OF STRUCTURAL DETAILSSECTION 2 – FATIGUE STRENGTH ASSESSMENT
1

GENERAL

1.1

Application

1.1.1
1.1.1.a

Fatigue strength assessment is performed by the linear cumulative damage rule
based on fatigue design curves (S-N curves).

1.1.1.b

From our experience with fatigue damage in hull structures until now, it has been
observed that the trend of occurrence of fatigue damage differs from the fatigue
damage in land-based welded structures such as bridges, or in offshore structures,and that its primary cause is the effect of mean stress. In these rules, the assessment
method based on equivalent hot-spot stress range considering the effect of meanstress is used.

1.1.2
1.1.2.a

The fatigue strength of welded joints is affected by the stress concentration due tothe existence of welds. Taking account of this effect enables to assess unified fatigue
strength.

1.1.3
1.1.3.aSince the stress assessment procedure for the fatigue strength assessment isdifferent according to primary members, longitudinal stiffeners connections andhatch corners, the stress assessment procedure is described respectively.

1.1.4

Primary members and longitudinal stiffeners connections

1.1.4.a

The methods to assess hot spot stress of primary members and longitudinal
stiffeners are specified in Section 3 and Section 4 respectively.

1.1.5

Hatch corners

1.1.5.a

The method to assess hot spot stress of hatch corner is specified in Section 5.

2

EQUIVALENT NOTCH STRESS RANGE

2.1

Predominant load case

2.1.1
2.1.1.a

The fatigue strength assessment is performed by calculating the cumulative fatigue
damage based on long-term distribution of stress range. This long-term distribution
has a shape that approximates to the exponential distribution when the long-term
service of the ship is considered. Thus, shape of the long-term distribution can bedecided by using the stress range of load cases assigned to maximum stress ranges
in the design load case.

2.1.1.bMultiple load factors are associated with the stress response of hull structuralmembers. Note that even for the same member, if the loading condition differs, thepredominant load case differs.
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PAGE 9 – CHAPTER 8: FATIGUE CHECK OF STRUCTURAL DETAILS

2.2

Loading "Condition 1"

2.2.1
2.2.1.a

The mean stress effect must be considered when assessing the fatigue strength ofhull structural members. The local mean stress state can be expressed as the sum ofstructural mean stress and residual stress. However, if the maximum stress after
considering the cyclic stress range exceeds the yield stress, the residual stresschanges due to shakedown.

2.2.2
2.2.2.aIf the local mean stress state can be determined from the loading condition at which
the stress on the tensile side becomes maximum, then the assessment can be
performed taking this state as the standard state.

2.3

Equivalent notch stress range

2.3.1

Equivalent notch stress range

2.3.1.a

The hot spot stress is multiplied with the notch factor to estimate the notch stress.
The fatigue strength of welded and non-welded parts can be assessed by aconsistent reference stress.

2.3.1.b

Originally, the notch stress is assessed as a peak stress at the bottom of notch, but if
the crack is found to have propagated to such an extent that fatigue life can be
identified by crack as in the hull structure, stress concentration may be considered
as having eased from the state at the bottom of notch with the propagation of thecrack. This effect is included in the design S-N curves. Thus, the fatigue notch factor
was proposed after considering the stress concentration factors due to structural
discontinuities considered during design and the local stress concentration factors
due to the presence of welding beads, which are generally included in the proposed
S-N curves.

2.3.2

Equivalent hot spot stress range

2.3.2.a

The method used in the MIL-HDBK is followed to determine the effect of local
mean stress state of the hot-spot part and it is assigned as a factor for the sake of
convenience.

2.3.2.b

The local mean stress state can be expressed by structural mean stress and residual
stress, but when the maximum stress exceeds the yield stress when stressfluctuations are loaded, the residual stress varies due to shakedown. Therefore, thelocal mean stress state was assigned a formula considering the variation. In this case,the shakedown was estimated from the relationship between occurrence time of
maximum stress anticipated during the continuous period of navigation in the sameloading condition and its magnitude.

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PAGE 10 – CHAPTER 8: FATIGUE CHECK OF STRUCTURAL DETAILS3CALCULATION OF FATIGUE DAMAGE

3.1

Correction of the equivalent notch stress range

3.1.1
3.1.1.a

Factors other than mean stress that influence the fatigue strength must be
considered when design S-N curves are used in the assessed stress range. In thisrule, the effects of corrosive environment, material strength, and plating thickness
are considered.

3.1.1.b

The design S-N curves give the fatigue strength in air in a non-corrosive
environment or in a state protected from the corrosive environment. The Guidelines
for Offshore Structures of the UK HSE specifies 1/2 the service life in a corrosive
environment. In this rule, the factor was set considering that paint is effective inprotecting from a corrosive environment for 20 years out of the design life of 25
years. The effective period of paint was set as 22 years for compartments that are
difficult to identify as having an easily-corrosive environment.

3.1.1.c

The fatigue life of parent material is enhanced according to the enhancement inmaterial strength. On the other hand, the fatigue strength of welded joints does notchange regardless of the differences in material strength when weld residual stressclose to the yield stress exists in the welds. However, if the weld residual stress canbe inhibited, the fatigue strength can be enhanced according to the material strength.
In this rule, the magnitude of the residual stress due to shakedown according to theyield stress of the material is estimated, and the effect of the mean stress is
considered. Accordingly, the effect of enhancing the fatigue strength according toyield stress is given by a factor that is based on the experimental results of fatigue
strength. If weld residual stress close to the yield stress is assumed in the welded
condition, the same fatigue strength can be assigned regardless of the type ofmaterial used.

3.1.1.d

The description of degradation in fatigue strength when plating thickness increases,
given in the Guidelines for Offshore Structures of the UK HSE has been
incorporated.

3.2

Long-term distribution of stress range

3.2.1
3.2.1.a

3.3

The long-term distribution of stress range can be approximated by a Weibull
distribution close to an exponential distribution. The value of shape parameter
expressing the shape of the Weibull distribution cannot be fixed at a uniform level
because of the differences in external load conditions and stress response
characteristics, such as wave environment, loading conditions during assessment,
size of ship, and type and position of member to be assessed. For the sake of
convenience, it was decided to use an exponential distribution.

Elementary fatigue damage

3.3.1
3.3.1.a

The cumulative fatigue damage is calculated according to the Palmgren-Minerlinear cumulative damage rule. However, elementary damage in the large
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PAGE 11 – CHAPTER 8: FATIGUE CHECK OF STRUCTURAL DETAILS

frequency, small stress range is calculated according to the Haibach’s rule. The
design S-N curves used in calculating elementary damage are the B curves for theparent material proposed in the Guidelines for Offshore Structures in the UK HSE,
and are the lower limiting lines of double the standard deviation, which include thesafety margin.
3.3.1.b

Damage calculation is performed for the cycles of wave fluctuations in 25 years,
which is the design life. However, 85% of the full life was taken as effective
considering that the ship may be at anchor because of reasons such as cargoloading/unloading, inspection and maintenance, and considering voyage in calm
areas in the vicinity of cargo loading/unloading areas.

3.3.1.c

The frequency of typical loading condition of standard bulk carriers is set based onquestionnaires given to the shipping companies and on the comments received.

4

FATIGUE STRENGTH CRITERIA

4.1

Cumulative fatigue damage

4.1.1
4.1.1.a

The criterion for assessed fatigue damage for all cases is taken as 1.0, but since thecurve used includes the safety margin, the assessed results also includes the safetymargin implicitly.

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PAGE 12 – CHAPTER 8: FATIGUE CHECK OF STRUCTURAL DETAILSSECTION 3 – STRESS ASSESSMENT OF PRIMARY MEMBERS
1

GENERAL

1.1

Application

1.1.1
1.1.1.a

The assessment procedure for hot-spot stresses is described here for performing
fatigue strength assessment of primary members.

2

HOT-SPOT STRESS RANGE

2.1

Stress range according to the direct method

2.1.1
2.1.1.a

Design loads must be applied in the hold model using fine mesh to assess thestresses in the hot-spot parts of primary members. In the direct model, the hull
girder moment and loads due to design waves are simultaneously applied on themodel and stress assessment is performed. The stress range is determined from thedifference in the stress values at two conditions - at the crest and the trough.

2.1.1.b

For details of stress analysis of hold model using fine mesh, refer to Section 4,
Chapter 7 of the Rules.

2.2

Stress range according to the superimposition method

2.2.1

Hot spot stress range

2.2.1.aIn the superimposition method, stress due to hull girder moment determined
separately is superimposed on the stress assessed by applying the load due todesign waves on the model, and the combined stress is assessed.

2.2.2

Stress due to hull girder moments

2.2.2.aThe stress due to hull girder moment is determined by considering the bending
moment on the hull girder. The nominal stress determined from beam theory andthe stress concentration factors are considered when determining the hot-spot stress.
However, for primary members the stress concentration factor corresponding to thestress due to hull girder moment is almost equal to 1.0, and therefore, the stressconcentration factor corresponding to stress due to hull girder moment is
considered as 1.0 in these Rules.

3

HOT-SPOT MEAN STRESS

3.1

Mean Stress range according to the direct method

3.1.1
3.1.1.a

To assess the mean stress in the hot-spot part of primary members, the mean valueof stress from design loads and hull girder moment in two conditions - wave crest
and wave trough - applied in the hold model using fine mesh, is determined.

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PAGE 13 – CHAPTER 8: FATIGUE CHECK OF STRUCTURAL DETAILS

3.2

Mean stress according to the superimposition method

3.2.1

Hot spot mean stress3.2.1.aIn the superimposition method, the mean stress is found by adding the mean valueof stresses assessed by loading the model with loads due to the design waves in thetwo conditions of wave crest and wave trough, to the stress due to still watervertical bending moment determined separately.

3.2.2

Stress due to still water hull girder moment

3.2.2.aFor details of the still water vertical bending moment, refer to Section 3, Chapter 4of the Rules.

3.2.2.b

The assessment method in each loading condition using the permissible still watervertical bending moment is shown for the case when the still water vertical bending
moment has not been set at the initial design stage.

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PAGE 14 – CHAPTER 8: FATIGUE CHECK OF STRUCTURAL DETAILSSECTION 4 – STRESS ASSESSMENT OF STIFFENERS
1

GENERAL

1.1

Application

1.1.1
1.1.1.a

The assessment procedure for hot-spot stresses is described here, for performing thefatigue strength assessment of end connections of longitudinal stiffeners.

2

HOT-SPOT STRESS RANGE

2.1

Stress range obtained by the direct method

2.1.1
2.1.1.a

2.2

Refer to 2.1 of Section 3, Chapter 8.

Stress range according to the superimposition method

2.2.1
2.2.1.a

Refer to 2.2 of Section 3, Chapter 8.

2.3

Stress range according to the simplified procedure

2.3.1

Hot spot stress ranges

2.3.1.aThis is a procedure in which the nominal stress is assessed by beam theory, andmultiplied by the stress concentration factor to assess the hot-spot stress. The stressassessment is performed by determining the stress by beam theory for each load
component and superimposing the stresses. In this case, it should be noted that thesign of the stress varies with the direction in which the lateral pressure is applied.

2.3.1.b

For details of each component of load, refer to the relevant section of Chapter 4 of
the Rules.

2.3.1.cAt positions where longitudinal stiffeners pass through transverse bulkheads, thedeformation of the entire cargo hold or tank is constrained. Thus, secondary
bending stress due to relative deformation occurs at the penetrating position of thebulkhead, and the penetrating positions of the forward and aft transverse bulkheads.

2.3.2

Stress due to hull girder moments

2.3.2.a

Refer to 2.2 of Section 3, Chapter 8.

2.3.3

Stress due to wave pressure

2.3.3.a

When longitudinal stiffeners are connected by flat bars or brackets at the position
where they pass through transverse bulkheads or transverse webs, the stressconcentration due to structural discontinuity at the connections is to be considered.
In the simplified procedure, assessment is performed by multiplying the nominal
stress with the stress concentration factor. Since there have been many instances ofdesign and construction of structural details of joints of longitudinal stiffener at
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PAGE 15 – CHAPTER 8: FATIGUE CHECK OF STRUCTURAL DETAILS

these locations, stress concentration factors for these typical detailed joints are given
for design assistance. The values of these factors are the results of FE analysis
according to the detailed models. From the assessment points shown in the table,
for points that are evidently not severe considering stress, the difference in thefactor due to the difference in whether the penetration is blocked by collar plate or
not can be ignored, and is thus omitted.
2.3.3.bIn the assessment of stress due to waves, the effect of increase in stressaccompanying the tripping of stiffeners of asymmetric cross section is consideredseparate from the stress concentration factor due to the shape of the detailed joint,
and the stress concentration factor determined from elastic beam theory is
considered.

2.3.3.c

For definitions of effective span and center distance, refer to Section 6, Chapter 3 of
the Rule.

2.3.3.dDuring assessment of stress range according to fluctuating wave pressure,sometimes pressure may not be received (negative pressure may not be generated)because of positional relationships such as position of member to be assessed andposition of wave surface fluctuation near the water line. Assessment must be
performed considering the effect of this positional relationship of fluctuating
surface of wave and the position of member to be assessed, and also considering theeffect of height of the fluctuating surface, or the magnitude of acceleration and its
occurrence frequency. These effects are considered in the Rules, and a correction
coefficient was assigned to treat the non-linear stress range for fluctuations of waves
as probabilistically equivalent linear stress range.

2.3.4

Stress due to liquid pressure

2.3.4.aStress due to liquid pressure is assessed according to the same procedure as one
assessing stress due to wave pressure.

2.3.5

Stress due to dry bulk cargo pressure

2.3.5.aStress due to dry bulk cargo pressure is assessed according to the same procedure
as one assessing stress due to wave pressure.

2.3.6

Stress due to relative displacement of transverse bulkhead

2.3.6.aIn these Rules, the equivalent formula for stress was developed from relative
deformation by correcting the coefficients from the results of FE analysis in theformulation of rules by elastic continuous beam theory. The relative displacement
must be determined from FE hold analysis for applying the equivalent formula.

3

HOT-SPOT MEAN STRESS

3.1

Mean stress according to the direct method

3.1.1
3.1.1.a

Refer to 3.1 of Section 3, Chapter 8.

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3.2

Mean stress according to the superimposition method

3.2.1
3.2.1.a

Refer to 3.1 of Section 3, Chapter 8.

3.3

Mean stress according to the simplified procedure

3.3.1

Hot spot mean stresses

3.3.1.aThe structural mean stress is assessed by evaluating stress in the still watercondition in the simplified procedure.

3.3.1.b

For assessment procedures of stress for various load factors, refer to 2.3, Section 4,
Chapter 8.

3.3.2

Stress due to still water hull girder moment

3.3.2.a

Refer to 3.2 of Section 3, Chapter 8.

3.3.3

Stress due to hydrostatic pressure

3.3.3.a

Refer to 2.3 of Section 4, Chapter 8.

3.3.4

Stress due to liquid pressure in still water

3.3.4.a

Refer to 2.3 of Section 4, Chapter 8.

3.3.5

Stress due to dry bulk cargo pressure in still water

3.3.5.a

Refer to 2.3 of Section 4, Chapter 8.

3.3.6

Stress due to relative displacement of transverse bulkhead in still water

3.3.6.a

Refer to 2.3 of Section 4, Chapter 8.

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PAGE 17 – CHAPTER 8: FATIGUE CHECK OF STRUCTURAL DETAILSSECTION 5 – STRESS ASSESSMENT OF HATCH CORNERS
1

GENERAL

1.1

Application

1.1.1
1.1.1.a

It is considered that for this topic, no information in addition to that shown in theRules is necessary to explain the background.

2

NOMINAL STRESS RANGE

2.1

Nominal stress range due to wave torsional moment

2.1.1
2.1.1.a

The calculation is based on the evaluation of the stresses induced in the hatch cornerby cross deck bending following torsional deflection of the ship hull. The
calculation of the displacement of the hatch corner in longitudinal direction(warping deflection) u is done by using an empirical formulae derived byparametric FE-studies of cargo-hold models under constant torsional moment
which was scaled to the maximum moment acc. to Ch 04 Sec 03 of CSR. The
displacement u is dependent of the relation between the hatch opening and the shipsize. Therefore an Deck Opening Coefficient was introduced in the calculation of u.
The relationship of the calculated displacements and the Deck Opening Coefficientis shown in figure 1.
7.00006.0000-1.0405

warping FE / theory

5.0000y = 12.683x
2
R = 0.9899

4.00003.0000-0.9583

y = 11.587x
2
R = 0.9464-1.0124

y = 11.697x2
R = 0.9972

2.00001.00000.0000
2.0

2.2

2.4

2.6

2.8

3.0

3.2

3.4

3.6

3.8

4.0

4.2

4.4

4.6

4.8

5.0

5.2

5.4

deck opening coefficient
SSS-BC cape-size
Potenziell (DSS-BC cape size)

Figure 1:

DSS-BC cape size
Potenziell (SSS-BC cape-size)

SSS-BC panmax
Potenziell (SSS-BC panmax)

Relationship between normalized displacement u and deck opening coefficient

COMMON STRUCTURAL RULES FOR BULK CARRIERS

5.6

5.8

6.0

COMMON STRUCTURAL RULES FOR BULK CARRIERS − BACKGROUND DOCUMENT
PAGE 18 – CHAPTER 8: FATIGUE CHECK OF STRUCTURAL DETAILSThe displacements of the FE-analyses shown in figure 1 are normalized by using atheoretical value, based on St.-Venant Torsion-Theory (equation (1)).
u = −φ ′ ⋅ ω(1)where:
Φ´
Ω
MT
IT
G

torque of the cross section = MT /(IT G)
sector coordinate
torsion moment
torsion moment of inertia of the cross section
shear modulus of the material

The analysis of the results in figure 1 yields to the following formulation for the
calculation of the hatch corner displacement due to torsion.
u=

M WT ⋅ ω
31.2⋅
1000 I T ⋅ E ⋅ DOC(2)

where:
MWT
maximum torsion moment acc. to JBP rules Ch.04 sec 3.4[kNm]
IT
torsional moment of inertia of the cross section at the hatch
corner calculated within cross deck area (closed cross section) by neglecting
upper and lower stool of the bulkhead [m^4]E
elastic modulus of the material [N/mm²]
LC ⋅ Bn∑L

H ,i ⋅ B H ,i

DOC
deck opening coefficient =ωsector coordinate calculated at the same cross section as IT and at the Y
and Z location of the hatch corner [m²]i =1

The deck opening coefficient is the quotient of the deck area (Length between engine
room bulkhead and collision bulkhead (LC) times ships breadth B) and thesummation of the area of the cargo hatch openings (n = number of hatches, LH,ilength of Hatch i, BH,i breadth of hatch i).
The shear force within the cross deck can calculated by the following formulae:Q=u(B H + bs )3
12 EI Q

where:
u
BH
bs
IQ

AQ

+

2.6 B H
EAQ

(3)

displacement of hatch corner as derived in equation (2)breadth of hatch opening [m]breadth of remaining deck-strip [m]moment of inertia of cross deck, including upper stool and hatchcoaming near the hatch corner (see figure 13 for components theyshould be considered) [m^4]
shear area of cross deck section, including upper stool near thehatch corner [m²]COMMON STRUCTURAL RULES FOR BULK CARRIERSCOMMON STRUCTURAL RULES FOR BULK CARRIERS − BACKGROUND DOCUMENT
PAGE 19 – CHAPTER 8: FATIGUE CHECK OF STRUCTURAL DETAILSWith the shear force now the stress at the hatch corner can be calculated based on crossdeck bending acc. to the following formulae:
σ WT = FS ⋅Q ⋅ BH
WQ

with:
FS

(4)

stress concentration factor FS=5 - this factor is caused byneglecting
thetorsion
of
the
cross
deck
and
simplifying/neglecting the transition zone between the crossdeck and the wing tank, which gives a large discontinuity instiffness at the location of hatch cornershear force calculated acc. eq. (3)bending resistance of cross deck section (bending around verticalaxis of the ship, hatch coamings will act as flanges of theconsidered cross section) [m³]Q
WQ

For the consideration of the stress distribution related to the position of the hatch
cover in ships longitudinal direction, the stress obtained by equation (4) has to be
multiplied by Factor FL which is given as follows:
FL = 1.75 x/L for 0.57 < x/L < 0.85
FL = 1.0
for x/L < 0.57 and x/L > 0.85
The factor FL (shown at figure 2) was determined by comparison of stress results ofthe 2 hold cargo-hold-model used for the parametric investigation with stresses
determined by calculations for the whole ship as shown in figure 5 for example.
1.8

1.6

stress (real loadcase/hold model)

1.4

1.2

1

0.8

0.6

0.4

0.2

0
0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

x/L

Figure 2:

distribution of hatch edge stresses along the ship length (PANMAX Single-Side BC –Maximum Torsion Moment acting at the fore part of the ship)

COMMON STRUCTURAL RULES FOR BULK CARRIERS

1COMMON STRUCTURAL RULES FOR BULK CARRIERS − BACKGROUND DOCUMENT
PAGE 20 – CHAPTER 8: FATIGUE CHECK OF STRUCTURAL DETAILS

2.2

Nominal mean stress

2.2.1
2.2.1.a

The mean stress due to still water vertical bending moment within the cross deck is
set to 0.
The correction factor for mean stress fmean is set to 0.77 which was determined byverification of the calculated results with results calculated acc. to the GL-rules. The
mean stress factor is relatively large caused by the expectation of compressive
residual stresses induced by thermal cutting of the hatch corner. It is expected, thatthese compressive stresses will remain during the ship life and no reloading effects
are expected.

3

HOT SPOT STRESS

3.1

Hot spot stress range

3.1.1
3.1.1.aThe determination of the stress concentration factor Kgh is based on an adaptationof the formulation for the stress concentration factor for a stepped flat tension bar
with fillet shoulder as given by Heywood [ Heywood, R. B., “Photo-elasticity for
Designers”, Pergamon, New York, 1969 ] to the hatch corner geometry by NK.

COMMON STRUCTURAL RULES FOR BULK CARRIERSCOMMON STRUCTURAL RULES FOR BULK CARRIERS − BACKGROUND DOCUMENT
PAGE 21 – CHAPTER 8: FATIGUE CHECK OF STRUCTURAL DETAILSAPPENDIX 1 – CROSS SECTIONAL PROPERTIES FORTORSION
4

CALCULATION FORMULAE

4.1

Torsion Function Φ

4.1.1
4.1.1.a4.2

It is considered that for this topic, no information in addition to that shown in theRules is necessary to explain the background.

Co-ordinate system, running coordinate s

4.2.1
4.2.1.a

4.3

It is considered that for this topic, no information in addition to that shown in theRules is necessary to explain the background.

Computation of several properties for each part of the cross section

4.3.1
4.3.1.a

4.4

It should be considered that the symbols used under this topic are only valid for the
calculation of the properties of the parts of one cross section. They should not be
confounded with the symbols and expressions used in 1.4.1

Computation of cross sectional properties for the entire cross section

4.4.1
4.4.1.a

It should be considered that the symbols and expressions used under this topic are
only valid for the calculation of the properties of the whole cross section.
Expressions at the right hand side of the formulas (under the sum signs) are related
to the results of 1.3.1. The results of this table should not be confounded with thesymbols and expressions used in 1.3.1

5

EXAMPLE CALCULATION FOR A SINGLE SIDE HULL CROSS SECTION

5.1

Cross section data

5.1.1
5.1.1.a5.2

It is considered that for this topic, no information in addition to that shown in theRules is necessary to explain the background.

Determination of the torsion function Φ

5.2.1
5.2.1.a

It is considered that for this topic, no information in addition to that shown in theRules is necessary to explain the background.

COMMON STRUCTURAL RULES FOR BULK CARRIERSCOMMON STRUCTURAL RULES FOR BULK CARRIERS − BACKGROUND DOCUMENT
PAGE 22 – CHAPTER 8: FATIGUE CHECK OF STRUCTURAL DETAILS

5.3

Determination of the line-segment properties

5.3.1
5.3.1.a5.4

It is considered that for this topic, no information in addition to that shown in theRules is necessary to explain the background.

Determination of cross-section properties

5.4.1
5.4.1.a5.5

It is considered that for this topic, no information in addition to that shown in theRules is necessary to explain the background.

Notes

5.5.1
5.5.1.a

It is considered that for this topic, no information in addition to that shown in theRules is necessary to explain the background.

COMMON STRUCTURAL RULES FOR BULK CARRIERS