fea hull structures

GUIDANCE NOTES ON

FINITE ELEMENT ANALYSIS OF HULL STRUCTURES – LOCAL 3D MODEL ANALYSIS

DECEMBER 2004

American Bureau of Shipping Incorporated by Act of Legislature of the State of New York 1862

Copyright 2004 American Bureau of Shipping ABS Plaza 16855 Northchase Drive Houston, TX 77060 USA

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ABS GUIDANCE NOTES ON FINITE ELEMENT ANALYSIS OF HULL STRUCTURES – LOCAL 3D MODEL ANALYSIS . 2004 iii

GUIDANCE NOTES ON

FINITE ELEMENT ANALYSIS OF HULL STRUCTURES – LOCAL 3D MODEL ANALYSIS

CONTENTS SECTION 1 Local 3D Model Analysis .......................................................1

1 General ..................................................................................1 3 Model .....................................................................................1

3.1 Watertight (WT) Structural Details..................................... 1 3.3 Non-tight (NT) Structural Details ....................................... 1

5 Failure Criteria – Yielding ......................................................2 7 Failure Criteria – Fatigue .......................................................2

SECTION 2 Oil Carrier................................................................................5

1 Global Model..........................................................................5 3 Transverse Web.....................................................................6

3.1 Transverse Web in Global Model ...................................... 6 3.3 Transverse Web in Local 3D Model (Yielding) .................. 7 3.5 Transverse Web – Bracket Toe at Location 3 (Simplified

Model) ............................................................................... 8 3.7 Transverse Web – Bracket Toe at Location 3 (Detailed

Model) ............................................................................. 11 3.9 Transverse Web – Bracket Toe at Locations 2 and 4 ..... 13

5 Transverse Web – Access Openings ..................................15 7 Horizontal Girder..................................................................17

7.1 Global Model Analysis of Horizontal Girder..................... 17 7.3 Local 3D Fine Mesh Model for Horizontal Girders........... 19 7.5 Location 1: Large Opening for Inclined Ladder ............... 19 7.7 Location 2: Bracket Toes ................................................ 20 7.9 Location 3: Connection of Inner Skin and Transverse

bulkhead ......................................................................... 21 7.11 Locations 4 and 5: Horizontal Girder Intersect with

Longitudinal Stiffeners..................................................... 21

9 Buttress Structures ..............................................................22 9.1 Buttress Structure – Global Model .................................. 22 9.3 Buttress Structure – Local 3D Fine Mesh Model ............. 23

11 Vertical Stiffeners on Transverse Bulkheads.......................25 13 Hopper Knuckle Connection ................................................29

13.1 Hopper Knuckle Connection Model with Mesh Size 1/4Sp ....................................................................... 31

iv ABS GUIDANCE NOTES ON FINITE ELEMENT ANALYSIS OF HULL STRUCTURES – LOCAL 3D MODEL ANALYSIS . 2004

13.3 Hopper Knuckle Connection Model with Mesh Size 1/8Sp........................................................................32

13.5 Hopper Knuckle Connection Model with Mesh Size 1/16Sp......................................................................33

13.7 Yielding and Buckling ......................................................34

15 Double Bottom Floor Structures ..........................................35 15.1 Double Bottom Floor and Web Stiffeners ........................35 15.3 Cutouts ............................................................................38 15.5 Opening on Double Bottom Floor ....................................41

17 Tripping Bracket...................................................................42 FIGURE 1 Global Frame Arrangement .........................................5 FIGURE 2 Transverse Web – Global Model .................................6 FIGURE 3 Transverse Web...........................................................7 FIGURE 4 Radii and Web Depth of Lower Web and Openings....8 FIGURE 5 Bracket Toe – Simplified Fatigue Model ......................9 FIGURE 6 Stress Distribution and Dynamic Stress Range.........10 FIGURE 7 Bracket Toe – Detailed Model....................................11 FIGURE 8 Type A – One Large Radius ......................................12 FIGURE 9 Type B – Two Small Radii..........................................12 FIGURE 10 Stress Distributions of Bracket with Different

Curvatures..................................................................13 FIGURE 11 Transverse Web – Bracket Toe at Locations

2 and 4 .......................................................................14 FIGURE 12 Access Openings .......................................................15 FIGURE 13 Stress Distribution for Access Openings with and

without Reinforced Web Stiffeners.............................16 FIGURE 14 Horizontal Girder – Global Model...............................17 FIGURE 15 Horizontal Girder – Fine Mesh Model ........................18 FIGURE 16 Typical Critical Locations ...........................................19 FIGURE 17 Large Opening for Inclined Ladder and Stress

Distribution .................................................................20 FIGURE 18 Bracket Toes..............................................................20 FIGURE 19 Intersection with Longitudinal Stiffeners ....................21 FIGURE 20 Buttress Structures: Deformation and Stress

Distribution from Global Model Analysis ...................22 FIGURE 21 Connection of Bulkhead Vertical Stiffener with

Double Bottom Longitudinal.......................................23 FIGURE 22 Local Fine Mesh Model for Buttress Structure and

Stress Distribution......................................................24 FIGURE 23 Vertical Stiffeners on Transverse Bulkheads.............25 FIGURE 24 Stress Distribution of Location 2 ................................28 FIGURE 25 2nd Zooming................................................................28 FIGURE 26 Types of Bilge Corners ..............................................29 FIGURE 27 Varied Mesh Sizes .....................................................30 FIGURE 28 Stress Calculation and Distribution............................31 FIGURE 29 Stress Calculation and Distribution............................32

ABS GUIDANCE NOTES ON FINITE ELEMENT ANALYSIS OF HULL STRUCTURES – LOCAL 3D MODEL ANALYSIS . 2004 v

FIGURE 30 Stress Calculation and Distribution............................33 FIGURE 31 Yielding and Buckling Check .....................................34 FIGURE 32 Local 3D Zooming Analysis .......................................35 FIGURE 33 Web Stiffeners on Double Bottom Floors ..................36 FIGURE 34 Stress Distribution of Web Stiffener on the Double

Bottom Floor...............................................................38 FIGURE 35 Cutouts.......................................................................38 FIGURE 36 Finer Mesh Models (Cutout) ......................................39 FIGURE 37 Stress Distribution (Cutout)........................................40 FIGURE 38 Stress Distribution in Floor Plate ...............................42 FIGURE 39 Tripping Bracket Stress..............................................43 FIGURE 40 A Finer Mesh Analysis for the Indicated Area of

Figure 39....................................................................44 SECTION 3 Bulk Carrier...........................................................................45

1 General ................................................................................45 3 Global Model........................................................................45 5 Local Fine Mesh Model for Lower Stool Structures.............46 7 Local Stress for Transverse Lower Stools ...........................48 9 Fatigue Evaluation for Transverse Lower Stools.................50 11 Connection of Lower Wing Tank and Inner Bottom.............51 13 Double Bottom Floors ..........................................................57 15 Corrugated Bulkhead...........................................................61 17 Hold Frames ........................................................................64 19 Hatch Opening Structures ...................................................66

19.1 Hatch Side Coaming – End Brackets .............................. 66 19.5 Hatch Opening Corners .................................................. 70 19.3 Hatch Side Coaming – Drain Hole .................................. 69

FIGURE 1 Sample Global Model.................................................45 FIGURE 2 Critical Structure Details ............................................47 FIGURE 3 Mesh Size and Surface Stress Distribution ...............48 FIGURE 4 Fine Mesh Model for Simplified Fatigue Strength......50 FIGURE 5 Stress Fluctuations ....................................................51 FIGURE 6 Built-Up Type Connection Structure of Inner-Bottom

and Sloping Bulkhead ................................................52 FIGURE 7 Maximum Stress Range.............................................53 FIGURE 8 Small Bent Type Connection .....................................53 FIGURE 9 Mesh Size 1/4Sp.........................................................54 FIGURE 10 Mesh Size 1/8 Sp........................................................55 FIGURE 11 Mesh Size 1/16Sp.......................................................56 FIGURE 12 Stress and Large Access Openings ..........................57 FIGURE 13 Floor Plate with Openings and Cutouts .....................58 FIGURE 14 Details at Ends of Web Stiffeners ..............................58 FIGURE 15 Associated Cutouts Reinforced by Collar Plates .......59

vi ABS GUIDANCE NOTES ON FINITE ELEMENT ANALYSIS OF HULL STRUCTURES – LOCAL 3D MODEL ANALYSIS . 2004

FIGURE 16 Buckling Evaluation by Eigen Value Approach..........60 FIGURE 17 Fine Mesh Model Yielding Check ..............................61 FIGURE 18 Yielding Check From SafeHull Load Case 9 .............62 FIGURE 19 Buckling Check ..........................................................63 FIGURE 20 Hold Frame Analysis from Global Model ...................65 FIGURE 21 Fatigue Strength ........................................................66 FIGURE 22 Edge Stresses............................................................67 FIGURE 23 Drain Hole ..................................................................69 FIGURE 24 Hatch Opening Corners .............................................71

ABS GUIDANCE NOTES ON FINITE ELEMENT ANALYSIS OF HULL STRUCTURES – LOCAL 3D MODEL ANALYSIS . 2004 1

S E C T I O N 1 Local 3D Model Analysis

1 General

The SafeHull global model finite element analysis should evaluate the yielding and buckling strength of all of the primary (watertight in general) and main supporting (non-tight in general) members. The local 3D fine mesh analysis is required if the global model analysis indicates high stress at the critical areas, which cannot be evaluated using the fine mesh global 3D models of standard mesh sizes. Note: The same procedure for local 3D model analysis as specified in this Guide may be used for the analysis of

membrane tank SH LNG carriers, however, no examples of modeling, analysis, etc. are specified in the Guide. This information will be provided with the next edition of the Guide.

3 Model

Various local 3D models with different mesh sizes are to be employed for the structural analysis, depending on the structural details, which include:

3.1 Watertight (WT) Structural Details This is the evaluation of the effects of structural discontinuity in the watertight boundaries. The typical locations, which necessitate this evaluation, are the periphery of the inner-bottom structures and hopper knuckle locations. Tertiary stress is to be considered in this analysis. Mesh size for this analysis is usually 1/4 of one-stiffener spacing or less, and different criteria are to be applied depending on the mesh sizes.

3.3 Non-tight (NT) Structural Details This is the evaluation of the effects of structural discontinuity in the non-tight structures, which can be grouped in one of the following ways:

3.3.1 Openings in the Structures • Manholes in the double bottom and double side structures

• Cutouts for longitudinal stiffeners

• Pipe holes

• Traffic openings in horizontal girders

3.3.2 Peripheries of the Structures Structural discontinuity always exists whenever two members are connected. In general, either large or small brackets are fitted in order to minimize the abrupt changes of stiffness in these connections. The bracket connection areas are to be analyzed. The critical locations will be explained in this document.

Section 1 Local 3D Model Analysis

2 ABS GUIDANCE NOTES ON FINITE ELEMENT ANALYSIS OF HULL STRUCTURES – LOCAL 3D MODEL ANALYSIS . 2004

3.3.3 Local Structures Subjected to Buckling Evaluation Buckling strength of intact plates of rectangular shapes can be easily evaluated. However, for non-rectangular panels, with or without openings, it requires a different analysis method for buckling evaluation. One of the typical locations subject to buckling analysis is the panel of the double bottom floors with manholes and cutouts for longitudinal stiffeners.

5 Failure Criteria – Yielding

Different yielding criteria are applied, depending on the models, with different functions and mesh sizes. The allowable stress (kg/cm2) to be used for different materials is as follows:

Mesh Mild HT32 HT36

Global model Stress 1*sp 2400 3040 3269

Local Stress (NT) 1/4*sp 3000 3800 4086

Local Stress (WT) 1/4 *sp 4100 4500 5000

Detail Stress 1/16*sp 4100 4500 5000

Fine Stress 1/64*sp 6000 7600 8170

Note: sp is the typical spacing of longitudinal stiffeners (800~900 mm).

For example: sp = 840 mm; 1/4*sp = 210 mm; 1/16*sp = 52.5 mm; 1/64*sp = 13.1 mm

“Global Model Stress” is a stress determined by the “Global 3D FE Models” with mesh size nearly equal to one-longitudinal-spacing. Such a mesh size is adequate to determine stress distributions in local structures. However, it is inadequate to determine stress concentrations in structural connections and discontinuities. Tertiary bending stress is not included.

“Local Stress” is a stress determined by models with a mesh size nearly equal to 1/4-longitudinal-spacing. Such a mesh size is adequate to determine stress distributions in local structures. However, it is still not adequate enough to determine stress concentrations in connection with fatigue strength evaluation. Tertiary bending stress is to be considered, if it exists.

There are two different criteria, “(NT)” and “(WT)”, under “Local Stress”. Higher permissible stresses are allowed, equal to “Detail Stress”, provided that the maximum surface stresses on both sides of the plate are evaluated. This includes the tertiary stresses arising from plate bending under lateral load for watertight members.

“Detail Stress” is a stress at a critical point in structural details with finer model analysis. This is where a fatigue crack is expected to initiate. This limiting value is nearly equal to the “Hot Spot Stress”. The hot spot stress in the details may be allowed up to the minimum tensile strength of the material, provided that the fatigue strength of the detail is satisfactory based on SafeHull fatigue criteria.

“Fine Stress” is allowed in small openings, which are free from structural discontinuity and/or weld beads.

Section 1 Local 3D Model Analysis


7 Failure Criteria – Fatigue

Tables of permissible stress ranges specified in the Rules for Fatigue Classification for Structural Details (e.g., 5-1-A1/Table 1 of the Rules for Building and Classing Steel Vessels) are based on the assumptions:

i) A linear cumulative damage model (Palmgren-Miner’s Rule) has been used in connection with the S-N data extracted from UK DEN.

ii) Cyclic stresses due to SafeHull standard loading have been used and the effects of mean stress have been ignored.

iii) The target design life of the vessel is taken at 20 years.

iv) The long-term stress ranges on a detail are characterized using the modified Weibull probability distribution parameter (γ).

γ = 1.4 – 0.2αL0.2 for 150 ≤ L ≤ 305 m

γ = 1.54 – 0.245α0.8L0.2 for L > 305 m

For internal structures, such as transverse webs, bulkheads, etc., where stress distribution is not governed by hull girder load, the uniform distribution zone factor (α = 0.80) can be applied, regardless of their vertical location.

Example: L = 238.000 m

γ = 1.4 – 0.2αL0.2

Permissible Stress Range (kg/cm2)

α γ C Curve D Curve E Curve

1.00 0.845 5913 4352 3833

0.90 0.900 5330 3890 3420

0.86 0.922 5163 3758 3306

0.80 0.956 4904 3554 3129

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S E C T I O N 2 Oil Carrier

1 Global Model

The sample global model used for the discussion of the “Local 3D Approach” is taken from the “Guidance Note on SafeHull Finite Element Analysis of Hull Structures”, as shown in Section 2, Figure 1.The global model analysis identifies the critical areas and provides the boundary displacement conditions for local model analysis.

FIGURE 1 Global Frame Arrangement

One transverse web space (4.300 m) is cut into 3 divisions in this sample model, however, users are recommended to apply 4 divisions for the models with wider web spacing in order for better element aspect ratio.

Section 2 Oil Carrier


3 Transverse Web

3.1 Transverse Web in Global Model It is required to select at least two sections of transverse web structures (one in the mid-hold and one in the end-hold) for a detailed evaluation of the transverse web frames. Section 2, Figure 2 shows the faceplate axial stress distribution from the global model analysis. The faceplate stress values in the global model analysis provide the information for local 3D model selections.

FIGURE 2 Transverse Web – Global Model



In general, the following locations need to be considered for detail stress analysis:

Location 1 Structural details in curved parts. Built-up, L2 or L3 type faceplates.

Locations 2 – 4 Bracket ends.

Location 5 Structural details in curved parts.

3.3 Transverse Web in Local 3D Model (Yielding) Section 2, Figure 3 shows the faceplate axial stress distributions from local 3D fine mesh analysis. The maximum stresses in the faceplates from the local 3D fine mesh analysis usually indicate a good agreement compared with those from the global model analysis, except in Location 1. The reason for the difference in Location 1 is that the mesh size of the global model is not fine enough to provide reliable stresses for such curvature. However, it is not advisable to apply finer meshes in the global models because this area must be checked by detail analysis in order to justify the way how faceplates and radii are fitted to the curved parts.

When built-up faceplates are applied, we can assume the full effectiveness of their sectional areas. However, if it is designed with an L2 type or unusually wide faceplate, there is a possible reduction in their effectiveness.

Another consideration is the radii applied to the openings in the hopper bilge webs. Balanced models are created when the web depth and corner radii are in good proportion. It is recommended that the ratio (Radius/Depth) not be less than 0.5. Section 2, Figure 4 shows the radii and the web depth for calculating the ratio (Radius/Depth). The investigation of an effective width may be necessary if a smaller ratio is used.

Resultant stresses are significantly affected by this ratio, and changing the radii is usually difficult when the “Midship Section” drawing has been completed. It is a good practice to always check this ratio in the early design stage.

FIGURE 3 Transverse Web



FIGURE 4 Radii and Web Depth of Lower Web and Openings

D2

D1=1400

D3=1300D2=1400

R3=750R2=750R1=750

R3R1

D1

R2D3

R1=500R2=500R3=500

D2

D1=1400D2=1400D3=1300

R1 R3

D1

R2

D3

3.5 Transverse Web – Bracket Toe at Location 3 (Simplified Model) Fatigue strength evaluation at the bracket toes is generally applied at the end of the faceplates. Faceplates are modeled by plate elements in association with the actual shape of tapering in the width. The free edges of the web plates beyond the ends of the faceplate are to be divided into at least two segments, as shown in Section 2, Figure 5. Dummy rod elements are applied at the free edges of the web plates.

Maximum stress at the end of the faceplates must comply with the “Detail Stress” criteria in Subsection 2/3. The associated stress ranges with permissible stress range use the “E” curve.



FIGURE 5 Bracket Toe – Simplified Fatigue Model



FIGURE 6 Stress Distribution and Dynamic Stress Range

Resultant Stress Range: fR = Cf (Cw × MSR) kg/cm2

where

MSR = MAX_STRESS RANGE

= 0.95 × 0.75 × 5013 = 3572 > 3129 kg/cm2

Cf = 0.95 (adjustment factor to reflect a mean wasted condition)

Cw = 0.75 (coefficient for the weighted effects of the two paired loading patterns)

Permissible Stress Range = 3129 kg/cm2 (Class E)

L = 238.000 m

α = 0.800

γ = 1.40 – 0.036 α L1/2 = 0.956

Detailed analyses may be required when the maximum stresses and the associated stress ranges are estimated by the “Simplified Method” and are close to or above the permissible values. This is illustrated in 2/3.7.



3.7 Transverse Web – Bracket Toe at Location 3 (Detailed Model) Faceplates are modeled by solid elements. The tapering width and thickness of the faceplates are represented in the model. Weld beads are modeled by triangular elements. Maximum stresses and stress ranges are estimated by interpolation or extrapolation, depending on the size of the weld beads.

FIGURE 7 Bracket Toe – Detailed Model

The bracket ends of deep supporting members are usually designed as one of two types. Type A is with one large radius and Type B is with two small radii, as shown in Section 2, Figures 8 and 9.

Type B is preferred because of better fatigue strength behavior. End stress is reduced by about 20%, from 1059 kg/cm2 to 827 kg/cm2, as shown in Section 2, Figure 10.



FIGURE 8 Type A – One Large Radius

FIGURE 9 Type B – Two Small Radii



FIGURE 10 Stress Distributions of Bracket with Different Curvatures

3.9 Transverse Web – Bracket Toe at Locations 2 and 4 Structural details in the lower part are governed by total strength instead of stress ranges. Maximum stress (–5190 kg/cm2) is too high, even with this mesh size. Changing the bracket type from A to B would significantly reduce this stress.



FIGURE 11 Transverse Web – Bracket Toe at Locations 2 and 4

Permissible Stress Range = 3129 kg/cm2 (Class E)

L = 238.000 m

α = 0.80

γ = 1.40 – 0.036 α L1/2 = 0.956



5 Transverse Web – Access Openings

Large access openings are usually reinforced by partial heavy insert plates. Fatigue classification around the openings is defined by “C”. However, this can be upgraded to “B”, if their edges are well ground. No weld beads are allowed in the curved parts of the openings. Section 2, Figure 12 shows the local 3D model and stress distribution of an access opening in a transverse side web.

FIGURE 12 Access Openings

Resultant Stress Range: fR = Cf (Cw × MSR) kg/cm2

where

MSR = MAX_STRESS RANGE

Cf = 0.95 (adjustment factor to reflect a mean wasted condition)

Cw = 0.75 (coefficient for the weighted effects of the two paired loading patterns)



In addition to the partial heavy insert plates, large access openings are usually reinforced by web stiffeners parallel to their edges. These stiffeners are added for protection against tripping of web plates and do not need to be included in the model because they only reduce the stresses along the edges of the opening by about 5%. However, this reduction can be taken into consideration when the resulting stresses exceed the criteria. Section 2, Figure 13 shows the access opening with and without web-reinforced parallel stiffeners and corresponding stress distribution.

FIGURE 13 Stress Distribution for Access Openings

with and without Reinforced Web Stiffeners



7 Horizontal Girder

7.1 Global Model Analysis of Horizontal Girder Edge stresses along the faceplates of horizontal girders have been evaluated during the global stress checking, and their scantlings were checked against the “One Step Stress” criteria in Subsection 2/3. It is important to check the maximum bracket end stress (1526 kg/cm2), as shown in Section 2, Figure 14, if the stress value in the global model analysis exceeds the target value of 1000 kg/cm2. Designers must be notified of this problem as early as possible during the initial design stage since solving this problem is extremely difficult later. The bracket type needs to be changed from type A to type B, as introduced in Section 2, Figure 8.

FIGURE 14 Horizontal Girder – Global Model



FIGURE 14 (continued) Horizontal Girder – Global Model

FIGURE 15 Horizontal Girder – Fine Mesh Model



7.3 Local 3D Fine Mesh Model for Horizontal Girders Most critical locations of structural details for No.2 horizontal girders are selected among both the aft and forward transverse bulkheads. Usually, the first step of zooming analysis of horizontal girders is done by the “Carried-over Load” process. No local load has been applied to the model, and the resultant stresses may be under-estimated. Section 2, Figure 16 shows the stress distribution, and the five (5) typical locations need to be evaluated for the horizontal girder.

FIGURE 16 Typical Critical Locations

7.5 Location 1: Large Opening for Inclined Ladder The stress distribution around the openings in horizontal girders is significantly affected by their locations. Ideally, they should be positioned at the mid-point of the beam span length. The corner radius may be required to be increased, unless it conflicts with the installation of the inclined ladders and smooth passage. Maximum stress must be less than the tensile strength of the material, provided the associated dynamic stress ranges comply with fatigue requirements.



FIGURE 17 Large Opening for Inclined Ladder and Stress Distribution

7.7 Location 2: Bracket Toes Section 2, Figure 18 shows the stress distribution of the bracket toe at Location 2 of the horizontal girder. Both yielding and fatigue evaluations should be performed for this location, and the design consideration should be applied here, as discussed for the bracket toe in the transverse web.

FIGURE 18 Bracket Toes



7.9 Location 3: Connection of Inner Skin and Transverse bulkhead This location may need to be considered if the global model analysis indicates a high stress value.

7.11 Locations 4 and 5: Horizontal Girder Intersect with Longitudinal Stiffeners Stresses in the faceplates of longitudinal stiffeners must comply with the “One Step Stress” criteria in Subsection 2/3 (2400 kg/cm2 for Mild Steel, 3040 kg/cm2 for HT32). If the faceplates are modeled by plate elements, the “Local Stress” criteria in Subsection 2/3 are applicable. The “Detail Stress” criteria in Subsection 2/3 are not applicable, except at the ends of the faceplates. Fatigue evaluation may be also necessary, especially for the bracket toes.

FIGURE 19 Intersection with Longitudinal Stiffeners



9 Buttress Structures

Fitting of partial girders is used to restrict the vertical displacements of the bottom floors adjacent to transverse bulkheads. The structural details of bottom and inner-bottom longitudinal stiffeners, as well as bulkhead vertical stiffeners on the transverse bulkheads, are significantly affected by the behavior of partial girders, as shown in Section 2, Figure 20.

Fitting buttress structures above the partial girders will transmit the lateral load acting on the transverse bulkhead to the double bottom structure through the partial girder and full girder. It is obvious that part of the buttress structure, if not connected to the lower horizontal girder, will not help transmit this load and may be questionable from a cost-wise viewpoint. These structural details at the ends of brackets may necessitate closer examination. It is difficult to justify bracket end stress as high as 1744 kg/cm2. This is found in the results of the global model.

9.1 Buttress Structure – Global Model Section 2, Figure 20 also shows the deformation from global model evaluation when the middle hold is filled and side holds are empty under sagging condition. As mentioned above, the high stress is found at the end of the bracket connected to the inner bottom.

FIGURE 20 Buttress Structures: Deformation and Stress Distribution

from Global Model Analysis



Section 2, Figure 21 shows the connection of the bulkhead vertical stiffener with the double bottom structure.

FIGURE 21 Connection of Bulkhead Vertical Stiffener

with Double Bottom Longitudinal

9.3 Buttress Structure – Local 3D Fine Mesh Model All stresses in the faceplates must comply with the “One Step Stress” criteria in Subsection 2/3 (3040 kg/cm2 for HT32), if the faceplates are modeled by rod elements. If they are modeled by plate elements, the “Local Stress” criteria in Subsection 2/3 (3800 kg/cm2, HT32) is applicable.

Free edge stresses along the brackets are checked against the “Detail Stress” criteria in Subsection 2/3 (4500 kg/cm2, HT32), provided that the resultant stress ranges are within the permissible ranges required by fatigue evaluation.

If longitudinal stiffeners are designed with ordinary T-type built-up construction, no big differences are expected between modeling faceplates with rod or plate elements.



FIGURE 22 Local Fine Mesh Model for Buttress Structure and Stress Distribution



11 Vertical Stiffeners on Transverse Bulkheads

Section 2, Figure 23 shows the model for analyzing the vertical stiffener on the transverse bulkhead and the stress and deformation. The connection of vertical stiffeners and double bottom longitudinal stiffeners has been shown in Section 2, Figure 21. The critical areas are the connection of the vertical stiffeners to the upper deck longitudinal (Locations 1 and 2) and to the double bottom longitudinal structure (Locations 3 and 4), which are indicated in Section 2, Figure 23. This figure also shows the stress distribution for all four locations.

FIGURE 23 Vertical Stiffeners on Transverse Bulkheads



FIGURE 23 (continued) Vertical Stiffeners on Transverse Bulkheads



FIGURE 23 (continued) Vertical Stiffeners on Transverse Bulkheads

Among the four locations, Location 2 is the most critical one, which is magnified in Section 2, Figure 24.

The resultant stresses and stress ranges for three elements in Location 2 are shown in Section 2, Figure 24. All of them are with the criteria:

56921 2223 kg/cm2 < 3040 kg/cm2 for HT32

2451 kg/cm2 < 3840 kg/cm2 fatigue E curve, α = 1.00

56933 2893 kg/cm2 < 3040 kg/cm2 for HT32


56974 3589 kg/cm2 < 4500 kg/cm2 for HT32


The typical mesh size for these elements for the above model is about 80 mm. Second (2nd) zooming may be required in association with the faceplates of the deck longitudinal stiffeners replaced by plate elements, as shown in Section 2, Figure 25.

The stress values for the same three elements in the second zooming model are increased and may have exceeded the allowable stress.



FIGURE 24 Stress Distribution of Location 2

FIGURE 25 2nd Zooming



13 Hopper Knuckle Connection

Upper and lower hopper knuckle connections near the bilge corners of double hull tankers are a major concern for ship designers. There are three types of construction for knuckled parts, i.e., built-up, small bent and large bent types, as shown in Section 2, Figure 26. The “built-up type” is preferred by engineers in charge of strength analysis. However, bent types are equally preferred for various reasons.

FIGURE 26 Types of Bilge Corners

It is difficult to justify the FE results of the “Small Bent Type” because of the small radius and small offset, as shown in Section 2, Figure 25. The offset should be as small as is practical, while the radius should be as large as possible.

The small bent type is used for many bulk carriers with some success, while others have had various structural troubles. Caution should be used in applying the experiences with bulk carriers to the double hull tankers because of the heavy bending moments due to the double side structures.

There has been discussion as to which criteria should be applied to different model types with different mesh sizes. Based on the FE analysis for various types of vessels, the following guidelines have been established as the most comprehensive:

i) Tertiary stresses are included in the analysis.

ii) Yielding and fatigue strength are evaluated.

iii) Mesh size is generally 1/4 of stiffener spacing (about 200 mm). If small bent type hopper knuckle corners are used, smaller mesh sizes (about 1/16 stiffener spacing) are used to consider the effects due to the small radius and offset.

iv) Von-Mises stresses in the top and bottom surfaces of the elements are checked against the “Detail Stress” criteria in Subsection 2/3 (4100 kg/cm2 for Mild, 4500 kg/cm2 for HT32).

v) Membrane stresses are checked against the permissible stress ranges in the Rules.

Sample models in Section 2, Figure 27 show the different mesh size model for obtaining maximum stresses and associated stress ranges. For detailed fatigue strength analysis considering the concept of “Hot Spot Stress”, refer to the applicable sections of the Rules.



FIGURE 27 Varied Mesh Sizes



13.1 Hopper Knuckle Connection Model with Mesh Size 1/4Sp

FIGURE 28 Stress Calculation and Distribution



13.7 Yielding and Buckling It is not unusual to provide intermediate brackets between ordinary transverse webs, especially when larger transverse web spacing is used. These structures have occasionally been missed in FE analysis and have resulted in fractures in many locations. Resultant stresses must comply with the “Detail Stress” criteria in Subsection 2/3.

Evaluation of the buckling strength of the brackets with large, straight free edges is also important. Refer to 3-2-9/Table 1 “Thickness and Flanges of Brackets and Knees” in the Rules for Building and Classing Steel Vessels, where it is stated that brackets must be fitted with flanges where the depth of their longer arms exceeds 750 mm. Free edges exceeding 1000 mm in length may be required to be reinforced by stiffeners.

If the proposed structural details cannot be justified by the above consideration, the “Elastic Buckling Evaluation” should be discussed with the designers.

FIGURE 31 Yielding and Buckling Check



15 Double Bottom Floor Structures

Double bottom floors of oil carriers are not as critical as those of bulk carriers. However, floor spaces in oil carriers are usually larger than those of bulk carriers and reinforcements in the cutouts for longitudinal stiffeners are to be carefully designed.

Local 3D zooming analysis starts with replacing the rod elements of longitudinal stiffeners by plate elements. Section 2, Figure 32 shows the local 3D fine mesh model for double floor structural analysis.

FIGURE 32 Local 3D Zooming Analysis

15.1 Double Bottom Floor and Web Stiffeners Double bottom floors are to be reinforced by web stiffeners. Both ends of web stiffeners are usually welded to the faceplates of the bottom and inner-bottom longitudinal stiffeners. The size of these web stiffeners and their end details are to be evaluated, depending on the floor spacing.

The resultant stress of 5632 kg/cm2 of web stiffener near the inner-bottom longitudinal stiffeners is too high for the “Detail Stress” criteria in Subsection 2/3 (4100 kg/cm2, Mild). It may require backing brackets. A similar evaluation must be applied to find the location of the additional backing brackets.



FIGURE 33 Web Stiffeners on Double Bottom Floors



FIGURE 33 (continued) Web Stiffeners on Double Bottom Floors



FIGURE 34 Stress Distribution of Web Stiffener on the Double Bottom Floor

15.3 Cutouts Most of the cutouts are usually fitted with collar plates for oil carriers because of larger floor spacing. Evaluation of the cutouts without collar plates is to be referred to the applicable sections of bulk carriers, using the intermediate zoomed model in Section 2, Figure 33:

FIGURE 35 Cutouts

Configuration of the cutouts and design details at the ends of the web stiffeners are to be evaluated using finer mesh sizes, as suggested in the “Fine Stress” criteria in Subsection 2/3.



FIGURE 36 Finer Mesh Models (Cutout)



FIGURE 37 Stress Distribution (Cutout)



FIGURE 37 (continued) Stress Distribution (Cutout)

15.5 Opening on Double Bottom Floor Free edge stresses around any small openings should not exceed the following “Fine Stress” criteria from Subsection 2/3:

fi = (Yield_Strength) * Sm * 2.5 = 6000 kg/cm2 (Mild)

= 7600 kg/cm2 (HT32)

= 8170 kg/cm2 (HT36)

If the stress distribution in the floor plate is close to the allowable stress of 2400 kg/cm2 (Mild) and a small opening (R = 100 mm) is provided in the middle of floor plate, this small opening can be accepted only by inspection.



FIGURE 38 Stress Distribution in Floor Plate

17 Tripping Bracket No reduction should be allowed in determining the span length of longitudinal stiffeners unless small brackets are fitted on the opposite side. Adding tripping brackets usually results in higher stress on the opposite side. The stress value at these locations needs to be reviewed. Section 2, Figure 39 shows the lower part of the centerline longitudinal bulkhead connected to the vertical webs with tripping brackets. This figure also shows the stress distribution along the longitudinal stiffeners and vertical web at the tripping bracket locations. Section 2, Figure 40 shows the stress distribution of a finer mesh analysis of the indicated area of Section 2, Figure 39 for the tripping bracket connect area.



FIGURE 39 Tripping Bracket Stress



FIGURE 40 A Finer Mesh Analysis for the Indicated Area of Figure 39


S E C T I O N 3 Bulk Carrier

1 General

The local fine mesh models for analysis of bulk carriers serves the same purpose as the one for tanker. However, the critical areas for bulk carriers may be different from those for tankers, and these critical areas will be discussed here.

3 Global Model

The sample bulk carrier global model used for the “Local 3D Approach” discussion is taken from the ABS Guidance Notes on SafeHull Finite Element Analysis of Hull Structures, as shown in Section 3, Figure 1:

FIGURE 1 Sample Global Model

Section 3 Bulk Carrier


FIGURE 1 (continued) Sample Global Model

5 Local Fine Mesh Model for Lower Stool Structures

One of the typical structural configurations of bulk carriers is the transverse corrugated bulkhead and upper/lower stool structures. The structural details of the joints between the inner-bottom plates and the top plates of the lower wing tank or the lower transverse stool are highly critical. The detail local 3D fine mesh analysis is required since the structural detail may not be able to be modeled in the global model. Section 3, Figure 2 shows the local 3D model, which covers all the critical areas for such analysis.

Extremely high stress concentration is observed in the double bottom girders. Such stresses are occasionally far above the tensile strength of the material. This practice has been justified by comparing the structural details with those of old, good ones. FE analysis is just one of the parameters for such comparison.



FIGURE 2 Critical Structure Details



7 Local Stress for Transverse Lower Stools

Mesh size is fixed at 1/4 stiffener spacing and maximum surface stresses (top and bottom) of the plate elements are checked against the “Local Stress (WT)” criteria in Subsection 2/3.

FIGURE 3 Mesh Size and Surface Stress Distribution



FIGURE 3 (continued) Mesh Size and Surface Stress Distribution

Maximum Surface Stress (cargo hold side)

CG0 SG1 SG2 SG3 S1 4416 (3) 4214 (3) 4134 (3) 3549 (3) S2 2515 (1) 2542 (1) 2564 (1) 2408 (1)



9 Fatigue Evaluation for Transverse Lower Stools

Simplified fatigue strength can be applied to the fine-mesh model with its mesh size equal to 1/16 stiffener spacing in addition to the “Local Stress” check in Subsection 2/3.

FIGURE 4 Fine Mesh Model for Simplified Fatigue Strength

Surface stresses (top and bottom) become both tensile and beyond elastic limit as the mesh size gets finer (about 50 mm). Accordingly, stress fluctuation can be estimated using the average of the top and bottom stresses.



FIGURE 5 Stress Fluctuations

11 Connection of Lower Wing Tank and Inner Bottom

In general, the intersections of the inner bottom and the sloping bulkhead of the lower wing tanks are less critical compared with the connection of inner bottom and transverse stools. Section 3, Figure 6 shows the connection of lower wing tank and inner bottom structure and the stress distribution for a fine mesh analysis.



FIGURE 6 Built-Up Type Connection Structure

of Inner-Bottom and Sloping Bulkhead



Section 3, Figure 7 shows the dynamic stress range using the finer mesh model.

FIGURE 7 Maximum Stress Range

It is difficult to justify the small bent-type bilge corners unless the bottom girder is located just at the middle of the curved plate, resulting in a 0 offset, as illustrated in Section 3, Figure 8. A large radius of R = 500 mm could significantly reduce the stresses.

Adding stiffeners on the curved part could be an alternative solution.

FIGURE 8 Small Bent Type Connection



FIGURE 9 Mesh Size 1/4Sp



FIGURE 10 Mesh Size 1/8 Sp



FIGURE 11 Mesh Size 1/16Sp



13 Double Bottom Floors

Scantlings of double bottom floor structures were determined by global FE analysis. The local scantlings for local detail structures should be evaluated by local 3D fine mesh model.

Large access openings in double bottom floors are to be checked using the “Detail Stress” criteria in Subsection 2/3 and fatigue permissible stress ranges. Mesh size is determined by cutting one quadrant into eight (8) divisions.

FIGURE 12 Stress and Large Access Openings

Some of the cutouts for the bottom and inner-bottom longitudinal stiffeners are designed without collar plates. To justify these cutouts, resultant stresses in the adjacent elements are to comply with the “Local Stress (NT)” criteria in Subsection 2/3 (3000 kg/cm2 for Mild steel).

The local stress analysis shows that three cutouts in Section 3, Figure 13 are to be reinforced by collar plates for this model since their stress levels are higher than the local stress criteria.



FIGURE 13 Floor Plate with Openings and Cutouts

In addition to shear stress consideration, collar plates are to be fitted depending on the structural details at the ends of the web stiffeners.

FIGURE 14 Details at Ends of Web Stiffeners

If the maximum stresses at the ends of the web stiffeners can not comply with the “Detail Stress” criteria in Subsection 2/3, the associated cutouts are to be reinforced by collar plates, as shown in Section 3, Figure 15.



FIGURE 15 Associated Cutouts Reinforced by Collar Plates



FIGURE 15 (continued) Associated Cutouts Reinforced by Collar Plates

Buckling strength of double bottom floor panels has been evaluated in the global model analysis. However, for panels with access openings, the Eigen value buckling approach may be appropriate. Section 3, Figure 16 shows the buckling result by the Eigen value buckling approach. Local buckling may happen close to the opening.

FIGURE 16 Buckling Evaluation by Eigen Value Approach



15 Corrugated Bulkhead

In general, the critical areas for transverse corrugated bulkheads are located at the connections to the top structure of the lower stool. The global model analysis should be used to evaluate the entire transverse corrugated bulkhead and predict the critical areas. The maximum element stress (surface) at the bottom end of the corrugation must comply with the “Local Stress (WT)” criteria in Subsection 2/3, in addition to the SafeHull global model yielding check. Section 3, Figure 17 shows a fine mesh model analysis model and stress distributions.

FIGURE 17 Fine Mesh Model Yielding Check



Although SafeHull load case 9 is applicable only to deep tank bulkheads, the same criteria can be applied to ordinary bulkheads to detect critical areas in flooding conditions. Maximum stresses are allowed up to 100% of the yield strength of the material.

FIGURE 18 Yielding Check From SafeHull Load Case 9



Buckling strength can be evaluated by Steel Vessel Rules corrugated bulkhead local plate panel buckling criteria. The alternative is using the Eigen value approach for the corrugated bulkhead buckling check. To be more conservative, mesh size must be based on (8 × 8) zooming, as shown in Section 3, Figure 19.

FIGURE 19 Buckling Check



FIGURE 19 (continued) Buckling Check

17 Hold Frames

For single skin bulk carriers, the hold frames act to extend the depth of the shell structure and hence to increase the local structural lateral bending rigidity. The loads, external pressures and cargo pressures are transmitted through hold frames to the upper and lower wing tank structures, and therefore, the connections of hold frames to wing tanks are subject to large local bending moments.

The scantlings of the hold frame structures can be verified based on the results of the global model yielding evaluation. Section 3, Figure 20 shows the stress distribution of the hold frame structure from the global analysis, which indicates possible high stress at the lower bracket of the hold frame.

Buckling Check – Eigen Value Approach (8 × 8)



FIGURE 20 Hold Frame Analysis from Global Model

Such high stress areas need to be evaluated by the local 3D fine mesh model. Also, the fatigue strength consideration should be applied to the structural details at the ends of the hold frames, in addition to the yielding check, which will require a finer mesh analysis. Section 3, Figure 21 shows the fine mesh model and the corresponding stress distribution from such fine mesh model analysis.



FIGURE 21 Fatigue Strength

19 Hatch Opening Structures

Bulk carrier hatch opening structures are subject to not only the hull girder bending moment, but also to the hull girder torsion moment. Such loads result in distortion of openings and “warping” stress, which may cause hatch opening structural problems.

19.1 Hatch Side Coaming – End Brackets Hatch coaming end brackets are designed to reinforce the hatch coaming structures. Section 3, Figure 22 shows the end bracket drawing and the corresponding FE model. To evaluate such a detail structure, the detail FE model has to be modeled. Section 3, Figure 22 also shows the stress distribution of end bracket structures.

Free edge stresses of the end bracket must comply with the “Detail Stress” criteria in Subsection 2/3 as well as the permissible dynamic stress ranges based on the fatigue S-N curve “B” or “C” requirements. Weld beads are located where edge stresses are not critical.

Stresses in edge stiffeners must comply with the “Local Stress (NT)” criteria in Subsection 2/3.



FIGURE 22 Edge Stresses



FIGURE 22 (continued) Edge Stresses



19.3 Hatch Side Coaming – Drain Hole Small openings, such as drain and air holes, can be located anywhere, provided that they are free from structural discontinuity and weld beads. The “Fine Stress” criteria in Subsection 2/3 are applicable to the free edge stresses of the hole. However, where there is a structural discontinuity, such as in Section 3, Figure 23, fatigue strength consideration must be applied according to permissible stress ranges based on the “E” curve.

FIGURE 23 Drain Hole



FIGURE 23 (continued) Drain Hole

19.5 Hatch Opening Corners Free edges of hatch opening corners must comply with the “Local Stress (NT)” criteria in Subsection 2/3 as well as with permissible stress ranges based on the fatigue S-N curve “C” requirement.

Section 3, Figure 24 shows the FE model for hatch corner analysis and the maximum stress and dynamic stress distribution for local stress and fatigue life evaluation.



FIGURE 24 Hatch Opening Corners



FIGURE 24 (continued) Hatch Opening Corners

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