RAL01806F-221-057-405 Deck Fittings and Supporting Structure R1.pdf

Structural Analysis for the Deck Fittings and Supporting Structure Buoy Barge

Prepared for:

St. Lawrence Seaways Development Corporation Massena, NY

Project 221-057 Revision 1 Document No. RAL01806F-221-057-405

Prepared by Robert Allan Ltd.

Naval Architects & Marine Engineers www.ral.ca

Project 221-057 Rev. 1 January 31, 2022

Deck Fittings and Supporting Structure Buoy Barge

Revision Control Sheet

Prepared by: Alireza Mirzajani Date Jan. 31/22

Engineer of Record: Norbert Schumacher, P.Eng.

Rev. Date Description By Checked Approved

1 Jan. 31/22 First Issue AM NS NS

Confidential

All information contained in or disclosed by this document is proprietary and the exclusive intellectual property of Robert Allan Ltd. This design information is reserved for the exclusive use of the client identified herein. All further use and sales rights attached thereto are exclusively reserved by Robert Allan Ltd., and any reproduction, communication or distribution of this information is prohibited without the prior written consent of Robert Allan Ltd. Absolutely no modifications or alterations to this document may be made by any persons or party without the prior written consent of Robert Allan Ltd.

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Executive Summary A finite element analysis (FEA) is conducted on the deck outfitting including single bitt post, bollard, chock, kevel, winch foundation and supporting structure that were added or modified as required for the buoy barge in order to ensure the designed structure is sufficient for the stated ratings.

Design loads and allowable stresses for the supporting structure are based on class requirements and supplier information.

The analysis shows that the stresses developed in the supporting structure under the design loading conditions are within allowable limits; therefore, the structure is sufficient for the stated rating and deemed fit for the required service.

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Contents Revision Control Sheet

Executive Summary

Abbreviations

1 References

2 Background

3 Assumptions

4 Geometry

5 Materials

6 Allowable Stress and Result Interpretations

7 Elements

8 Boundary Conditions and Results

8.1 Load Condition A: Pushing Condition - Line Tension Aft, and 0 Deg Up

8.1.1 Loads and Boundary Conditions

8.1.2 Results

8.2 Load Condition B: Pushing Condition - Line Tension Aft 30 Deg Inboard, and 0 Deg Up

8.2.1 Loads and Boundary Conditions

8.2.2 Results

8.3 Load Condition C: Pushing Condition - Line Tension Aft, and 30 Deg Up

8.3.1 Loads and Boundary Conditions

8.3.2 Results

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8.4 Load Condition D: Pushing Condition - Line Tension Aft 30 Deg Inboard, and 30 Deg Up

8.4.1 Loads and Boundary Conditions

8.4.2 Results

8.5 Load Condition E: Mooring Condition - 90 Deg Line Outboard

8.5.1 Loads and Boundary Conditions

8.5.2 Results

8.6 Load Condition F: Mooring Condition - Line Toward Forward

8.6.1 Loads and Boundary Conditions

8.6.2 Results

8.7 Load Condition G: Kevel - Load Toward Aft Horizontally

8.7.1 Loads and Boundary Conditions

8.7.2 Results

8.8 Load Condition H: Kevel - Load Toward Aft and 45 Deg Outboard

8.8.1 Loads and Boundary Conditions

8.8.2 Results

8.9 Load Condition I: Kevel - Load Toward Aft and 45 Deg Upward

8.9.1 Loads and Boundary Conditions

8.9.2 Results

8.10 Load Condition J: Kevel - Load Toward Aft, 45 Deg Outboard, and 45 Deg Upward

8.10.1 Loads and Boundary Conditions

8.10.2 Results

9 Capacity

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10 Conclusion

Appendix A: Contact Stress in Bitt Post Pipe with Liner from Pushing Tension Line

Appendix B: Contact Stress in Bollard Pipe with Liner from Mooring and Pushing Tension Line

Appendix C: Contact Stress in Fairlead Pipe with Liner from Pushing Tension Line

List of Figures 1 Aft Quarter Starboard Side Deck Fittings Model Geometry, Shell Thickness

Represented by Colour (Units: mm)

2 Aft Quarter Starboard Side Deck Fittings Model Geometry, Shell Thickness Represented by Colour (Units: mm)

3 Aft Center Kevel Fitting Model Geometry, Shell Thickness Represented by Colour (Units: mm)

4 Aft Center Kevel Fitting Model Geometry, Shell Thickness Represented by Colour (Units: mm)

5 Aft Quarter Starboard Side Deck Fittings - Material Usage in the Finite Element Model

6 Aft Quarter Starboard Side Deck Fittings - Material Usage in the Finite Element Model

7 Aft Center Kevel Fitting - Material Usage in the Finite Element Model

8 Aft Center Kevel Fitting - Material Usage in the Finite Element Model

9 Mesh for Finite Element Model

10 Mesh for Finite Element Model

11 Mesh for Finite Element Model

12 Mesh for Finite Element Model

13 Load Condition A: Applied Loading and Constraints

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14 Load Condition A: Applied Loading and Constraints

15 Load Condition A: Total Deformation (mm)

16 Load Condition A: Total Deformation (mm)

17 Load Condition A: Total Deformation (mm)

18 Load Condition A: von Mises Equivalent Stress (MPa)

19 Load Condition A: von Mises Equivalent Stress (MPa)

20 Load Condition A: von Mises Equivalent Stress (MPa)

21 Load Condition A: von Mises Equivalent Stress (MPa)

22 Load Condition A: von Mises Equivalent Stress (MPa)

23 Load Condition A: Areas of von Mises Stress in Grade A Steel Fittings and Supporting Structure ≥ 190 MPa

24 Load Condition A: Areas of von Mises Stress in Grade A Steel Fittings and Supporting Structure ≥ 190 MPa

25 Load Condition A: Areas of von Mises Stress in ASTM A53 Grade B Pipe Fittings Pipes ≥ 190 MPa

26 Load Condition B: Applied Loading and Constraints

27 Load Condition B: Applied Loading and Constraints

28 Load Condition B: Total Deformation (mm)

29 Load Condition B: Total Deformation (mm)

30 Load Condition B: Total Deformation (mm)

31 Load Condition B: von Mises Equivalent Stress (MPa)

32 Load Condition B: von Mises Equivalent Stress (MPa)

33 Load Condition B: von Mises Equivalent Stress (MPa)

34 Load Condition B: von Mises Equivalent Stress (MPa)

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35 Load Condition B: von Mises Equivalent Stress (MPa)

36 Load Condition B: Areas of von Mises Stress in Grade A Steel Fittings and Supporting Structure ≥ 190 MPa

37 Load Condition B: Areas of von Mises Stress in Grade A Steel Fittings and Supporting Structure ≥ 190 MPa

38 Load Condition B: Areas of von Mises Stress in ASTM A53 Grade B Pipe Fittings Pipes ≥ 190 MPa

39 Load Condition C: Applied Loading and Constraints

40 Load Condition C: Applied Loading and Constraints

41 Load Condition C: Applied Loading and Constraints

42 Load Condition C: Total Deformation (mm)

43 Load Condition C: Total Deformation (mm)

44 Load Condition C: Total Deformation (mm)

45 Load Condition C: von Mises Equivalent Stress (MPa)

46 Load Condition C: von Mises Equivalent Stress (MPa)

47 Load Condition C: von Mises Equivalent Stress (MPa)

48 Load Condition C: von Mises Equivalent Stress (MPa)

49 Load Condition C: von Mises Equivalent Stress (MPa)

50 Load Condition C: Areas of von Mises Stress in Grade A Steel Fittings and Supporting Structure ≥ 235 MPa

51 Load Condition C: Areas of von Mises Stress in Grade A Steel Fittings and Supporting Structure ≥ 235 MPa

52 Load Condition C: Areas of von Mises Stress in ASTM A53 Grade B Pipe Fittings Pipes ≥ 170 MPa

53 Load Condition D: Applied Loading and Constraints

54 Load Condition D: Applied Loading and Constraints

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55 Load Condition D: Applied Loading and Constraints

56 Load Condition D: Total Deformation (mm)

57 Load Condition D: Total Deformation (mm)

58 Load Condition D: Total Deformation (mm)

59 Load Condition D: von Mises Equivalent Stress (MPa)

60 Load Condition D: von Mises Equivalent Stress (MPa)

61 Load Condition D: von Mises Equivalent Stress (MPa)

62 Load Condition D: von Mises Equivalent Stress (MPa)

63 Load Condition D: von Mises Equivalent Stress (MPa)

64 Load Condition D: Areas of von Mises Stress in Grade A Steel Fittings and Supporting Structure ≥ 230 MPa

65 Load Condition D: Areas of von Mises Stress in Grade A Steel Fittings and Supporting Structure ≥ 230 MPa

66 Load Condition D: Areas of von Mises Stress in ASTM A53 Grade B Pipe Fittings Pipes ≥ 170 MPa

67 Load Condition E: Applied Loading and Constraints

68 Load Condition E: Applied Loading and Constraints

69 Load Condition E: Total Deformation (mm)

70 Load Condition E: Total Deformation (mm)

71 Load Condition E: Total Deformation (mm)

72 Load Condition E: von Mises Equivalent Stress (MPa)

73 Load Condition E: von Mises Equivalent Stress (MPa)

74 Load Condition E: von Mises Equivalent Stress (MPa)

75 Load Condition E: von Mises Equivalent Stress (MPa)

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76 Load Condition E: von Mises Equivalent Stress (MPa)

77 Load Condition E: Areas of von Mises Stress in Grade A Steel Fittings and Supporting Structure ≥ 190 MPa

78 Load Condition F: Applied Loading and Constraints

79 Load Condition F: Applied Loading and Constraints

80 Load Condition F: Total Deformation (mm)

81 Load Condition F: Total Deformation (mm)

82 Load Condition F: Total Deformation (mm)

83 Load Condition F: von Mises Equivalent Stress (MPa)

84 Load Condition F: von Mises Equivalent Stress (MPa)

85 Load Condition F: von Mises Equivalent Stress (MPa)

86 Load Condition F: von Mises Equivalent Stress (MPa)

87 Load Condition F: von Mises Equivalent Stress (MPa)

88 Load Condition F: Areas of von Mises Stress in Grade A Steel Fittings and Supporting Structure ≥ 235 MPa

89 Load Condition G: Applied Loading and Constraints

90 Load Condition G: Applied Loading and Constraints

91 Load Condition G: Total Deformation (mm)

92 Load Condition G: Total Deformation (mm)

93 Load Condition G: von Mises Equivalent Stress (MPa)

94 Load Condition G: von Mises Equivalent Stress (MPa)

95 Load Condition G: von Mises Equivalent Stress (MPa)

96 Load Condition G: Areas of von Mises Stress in Grade A Steel Fittings and Supporting Structure ≥ 235 MPa

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97 Load Condition H: Applied Loading and Constraints

98 Load Condition H: Applied Loading and Constraints

99 Load Condition H: Total Deformation (mm)

100 Load Condition H: Total Deformation (mm)

101 Load Condition H: von Mises Equivalent Stress (MPa)

102 Load Condition H: von Mises Equivalent Stress (MPa)

103 Load Condition H: von Mises Equivalent Stress (MPa)

104 Load Condition H: Areas of von Mises Stress in Grade A Steel Fittings and Supporting Structure ≥ 235 MPa

105 Load Condition I: Applied Loading and Constraints

106 Load Condition I: Applied Loading and Constraints

107 Load Condition I: Total Deformation (mm)

108 Load Condition I: Total Deformation (mm)

109 Load Condition I: von Mises Equivalent Stress (MPa)

110 Load Condition I: von Mises Equivalent Stress (MPa)

111 Load Condition I: von Mises Equivalent Stress (MPa)

112 Load Condition I: Areas of von Mises Stress in Grade A Steel Fittings and Supporting Structure ≥ 235 MPa

113 Load Condition J: Applied Loading and Constraints

114 Load Condition J: Applied Loading and Constraints

115 Load Condition J: Total Deformation (mm)

116 Load Condition J: Total Deformation (mm)

117 Load Condition J: von Mises Equivalent Stress (MPa)

118 Load Condition J: von Mises Equivalent Stress (MPa)

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119 Load Condition J: von Mises Equivalent Stress (MPa)

120 Load Condition J: Areas of von Mises Stress in Grade A Steel Fittings and Supporting Structure ≥ 235 MPa

List of Tables 1 Model Geometry Boundaries for the Aft Quarter Starboard Side Deck Fittings and

Supporting Structure

2 Model Geometry Boundaries for the Aft Center Kevel and Supporting Structure

3 Material Properties for Grade A Steel

4 Material Properties for ASTM A53 Grade B Pipe

5 Allowable Stress

6 Load Condition A: Summary of Results

7 Load Condition B: Summary of Results

8 Load Condition C: Summary of Results

9 Load Condition D: Summary of Results

10 Load Condition E: Summary of Results

11 Load Condition F: Summary of Results

12 Load Condition G: Summary of Results

13 Load Condition H: Summary of Results

14 Load Condition I: Summary of Results

15 Load Condition J: Summary of Results

16 Summary of Capacity

17 Dedicated SWL for Deck Fittings (Total Load from All Lines)

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Abbreviations ABS American Bureau of Shipping DL Design Load FEA Finite Element Analysis FR Frame RL Reference Load

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1 References The following references are used in this finite-element analysis:

Robert Allan Ltd. Calculations:

A: 221-057 Deck Fittings R1.wbpz

B: 221-057 Deck Fittings Line Contact R1.xlsx

C: 221-057 Seaways Guardian Line Tension Calculation R1.xlsx

Robert Allan Ltd. 3D Geometry:

D: 221-057 Deck Fittings FEA R1.3dm

Robert Allan Ltd. Drawings:

E: 41610, Pushing and Access Arrangements, Revision 1

F: 40500, Deck Equipment Arrangement and Structure, Revision 1

Supplier Information:

G: 063059, DF-356-UF-65-11R-GLV, 65 Ton Barge Winch, Revision 3

Class Rules:

H: ABS, Rules for Steel Vessels for Service on Rivers and Intracoastal Waterways (2021), Part 3, Chapter 2, Section 4/25

I: ABS, Rules for Building and Classing Marine Vessels (2021), Part 3, Chapter 2, Section 7/4

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2 Background The mooring equipment supporting structure must be suited for ratings and working ranges presented in the Deck Equipment Arrangement and Structure [F]. These loads are the worst-case loads described in the RAL drawing Pushing and Access Arrangements [E].

The finite element method is used to predict the stresses and deflections in the deck fittings and supporting structure. This report will demonstrate that the stress in all critical areas of the structure is at or below the allowable stress under the load conditions defined in Section 8. Additionally, the Capacity to Allowable Stress (CAS) is determined for reference.

3 Assumptions

a. Thin Shell Assumption (Plane Stress Assumption)

Where plate material used in a structural assembly is thin relative to its other dimensions and not subject to significant loads perpendicular to the plane of the plate, it can generally be treated as a thin shell. In the FEA model, two-dimensional shell type elements that support membrane and bending loads are applied. Thin shell elements are the primary element type in the analysis.

b. Minor Stiffeners and Brackets

Minor stiffeners and brackets only have a minor effect on the stress profile and are thus omitted. In critical areas of this model, the minor stiffeners and brackets have been included to ensure that the stress profile and load paths are correct.

c. Gravity

Forces resulting from the self-weight of the structure are negligible in comparison to the applied loads and are therefore neglected.

d. Loads

Design loads and geometry factor for the deck fittings supporting structure are based on the RAL drawing Deck Equipment Arrangement and Structure [F]. A safety factor of 2 is used for all all equipment when pushing. A factor of 1.25 is used for mooring equipment as per Class requirements.

e. Joint Connection

Unless otherwise specified, the strengths of the welded or bolted connections are not evaluated in this analysis. In the FEA model, each part in the assembly is bonded to adjacent parts using connections or node sharing to emulate connections that are assumed to be at least as strong as the weakest component

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Deck Fittings and Supporting Structure Buoy Barge in the connection.

f. Linear Elastic Analysis

The finite element analysis assumes linear-elastic material properties. No permanent deformation occurs to the modelled geometry even if yield or the ultimate strength of the material is exceeded. Because of the linear assumption, capacity of the structure to allowable stress limits can be determined by simple linear scaling of the results.

g. Small Displacements

The analysis assumes that the deformation is small and the deflection of the element has negligible impact on its stiffness.

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4 Geometry The finite element model geometry was developed in Rhino 7 as thin shells prior to import into ANSYS Mechanical 2020 R2, where the material properties and plate thicknesses were defined. The model includes all structural members critical to the load path, including bulkheads, deep webs, and girders.

Minor brackets and stiffeners are included in areas critical to the load path.

The following model boundaries are chosen for the purposes of determining the stress distribution in the areas of interest. The selected boundaries are sufficiently far away from the structure of interest to ensure the results of this analysis are relatively insensitive to the boundary constraint formulations.

Longitudinal Boundaries

Aft Boundaries Forward Boundaries Vessel Stern Fr.13

Transverse Boundaries

Port Boundaries Starboard Boundaries

3657.6 mm of Starboard Side Vessel Side

Vertical Boundaries

Lower Boundaries Upper Boundaries Bottom Top of Deck Fittings

Table 1 – Model Geometry Boundaries for the Aft Quarter Starboard Side Deck Fittings and Supporting Structure

Longitudinal Boundaries

Aft Boundaries Forward Boundaries Vessel Stern Fr.13

Transverse Boundaries

Port Boundaries Starboard Boundaries 2743 mm of CL 2743 mm of CL

Vertical Boundaries

Lower Boundaries Upper Boundaries Bottom Top of Deck Fittings

Table 2 – Model Geometry Boundaries for the Aft Center Kevel and Supporting Structure

The model is developed using the old design drawings and modified parts. The geometry after import is shown in the figures below. Colours indicate thickness in millimeters according to the legend at the top left corner of each figure. Solid bodies are shown in grey since their thickness is inherent in the CAD geometry. Although this vessel is anticipated to operate in fresh water only, 2mm of corrosion allowance is considered in accordance with Class rules, which are used as guidance for design of the deck equipment supporting structure.

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Figure 1 – Aft Quarter Starboard Side Deck Fittings Model Geometry, Shell Thickness Represented by Colour (Units: mm)

Figure 2 – Aft Quarter Starboard Side Deck Fittings Model Geometry, Shell Thickness Represented by Colour (Units: mm)

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Figure 3 – Aft Center Kevel Fitting Model Geometry, Shell Thickness Represented by Colour (Units: mm)

Figure 4 – Aft Center Kevel Fitting Model Geometry, Shell Thickness Represented by Colour (Units: mm)

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5 Materials For the purposes of this analysis, the following materials are defined in ANSYS:

• Grade A Steel

• ASTM A53 Grade B Pipe

The material assignment for the description of material model finite element model is shown in Figures 5, 6, 7, and 8.

Figure 5 – Aft Quarter Starboard Side Deck Fittings - Material Usage in the Finite Element Model

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Figure 6 – Aft Quarter Starboard Side Deck Fittings - Material Usage in the Finite Element Model

Figure 7 – Aft Center Kevel Fitting - Material Usage in the Finite Element Model

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Figure 8 – Aft Center Kevel Fitting - Material Usage in the Finite Element Model

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These materials are defined in ANSYS using the materials properties shown in the tables below.

Density 7,850 kg/m3

Elastic Modulus 200 GPa Poisson’s Ratio 0.3 Yield Strength 235 MPa

Table 3 – Material Properties for Grade A Steel

Density 7,850 kg/m3

Elastic Modulus 200 GPa Poisson’s Ratio 0.3 Yield Strength 240 MPa

Table 4 – Material Properties for ASTM A53 Grade B Pipe

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6 Allowable Stress and Result Interpretations This analysis is completed using the Maximum-Distortion-Energy Criterion (von Mises Criterion) to assess the structure against failure. This criterion takes both shear and normal stresses into account to develop a combined, “equivalent” stress. Therefore, separate evaluation of shear and normal stress are not required. In the case of stress in a shell element, the equivalent stress reduces to the following simple formula:

σeq = σ2 x −σxσy +σ2 y +3τ2 xy (1) where:

σx is the axial stress in the elemental x direction σy is the axial stress in the elemental y direction τxy is the shear stress in the elemental xy plane

The allowable stress is calculated using Equation 2, below.

σallowable = D×σy (2) where:

D is the Class design factor, and σy is material’s yield strength

The Class allowable stress for each material and location shown in Table 5.

Material Class Allowable Material Structure Yield Design Equivalent

Strength Factor Stress Grade A Steel Fittings and Supporting Structure 235 MPa 1 235 MPa ASTM A53 Grade B Pipe Fittings Pipes 240 MPa 1 240 MPa

Table 5 – Allowable Stress

The analysis assumes that the Class allowable stress criteria listed in the table have been developed for classical approaches where the average stress is calculated. The finite element model will show peak stresses at discontinuities that are not captured in a classical approach. These discontinuities are ignored for the purposes of demonstrating compliance of the designed structure with Class requirements. This does not affect the safety of the structure since these peaks ignored in the results section of the finite

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Deck Fittings and Supporting Structure Buoy Barge element model are self-limiting (a small amount of yielding in the area of the peak stress results in a more even, but higher average stress distribution through the whole structural member).

In an area where a stiffness or geometric discontinuity or stress concentration exists, only one element that is near the discontinuity is permitted to exceed the reported maximum stress. The area around the localized peak will tend to engage and hold more of the load so for the purposes of this analysis, the maximum stress is determined as the average stress in the element(s) adjacent to the discontinuity. In areas where no stiffness or geometric discontinuities exist, the maximum stress is taken as the maximum nodal stress.

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7 Elements Several Element Types are used in the analysis. The shell geometry is represented by 1st order quadrilateral shell elements with triangular shell elements used only as a filler element. Full-integration is used with incompatible modes in order to ensure higher accuracy in bending dominated problems.

Element size is approximately 50 mm, decreasing to 15 mm in the area of force application. Contact between geometry is done through Contact and Target Elements. These contact elements are used to bond the geometry together without use of node-to-node alignment. Solid elements are generally, 1st order brick elements with tetrahedral elements used only as a filler element. See ANSYS model [A] for more details.

The mesh used for analysis of the description of mesh... is shown in Figures 9, 10, 11, and 12.

Figure 9 – Mesh for Finite Element Model

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Figure 10 – Mesh for Finite Element Model

Figure 11 – Mesh for Finite Element Model

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Figure 12 – Mesh for Finite Element Model

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8 Boundary Conditions and Results The design load conditions and results for the deck fittings and supporting structure are presented in the sections below.

In all load conditions, a high stress exists in the area of tow line or mooring line contact with the fittings.

This stress is a result of the method load application, which uses two descrete force vectors instead of a uniform pressure distribution. It is therefore considered an artificial stress and ignored in the assessment.

A separate analytic calculation is used to ensure that the pipe wall thickness is sufficient for the expected contact stress. This can be seen in reference [B], Appendix A, Appendix B, and Appendix C.

8.1 Load Condition A: Pushing Condition - Line Tension Aft, and 0 Deg Up

This load condition simulates the line leading from a pushing tug which applied on the barge deck fittings toward aft horizontally. The design line tensions come from Deck Equipment Arrangement and Structure Drawing [E] and a geometry factor of 2 (if applicable) and as well as safety factor of 2 are used to confirm the supporting structure capacity.

8.1.1 Loads and Boundary Conditions

The model is constrained using “Simply Supported” constraints at the edges shown in the figure below.

The constrained edges coincide with relatively rigid structure, such as bulkheads or are structural continuations such as the hull shell. The constraints are sufficiently far from the area of applied loading as not to influence results in the area of interest.

The boundary constraints and line forces are applied using discrete force vectors applied to the equipment as shown in the figures below.

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Figure 13 – Load Condition A: Applied Loading and Constraints

Figure 14 – Load Condition A: Applied Loading and Constraints

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8.1.2 Results

The results presented in this section show the equivalent stresses and total deformation induced by the loading and constrains as described in Section 8.1.1. The maximum equivalent stress and maximum deflection induced by this loading are summarized in the table below. As discussed in Section 6, results disregard the stress peaks that would be blunted by small amounts of localized deformation. The deflection is unaffected by this phenomenon for the number of significant digits indicated.

Maximum Deflection 2.7 mm Peak Maximum Safety

Equivalent Allowable Factor over Stress Stress Allowable

Grade A Steel Fittings and Supporting Structure 190 MPa 235 MPa 1.24 ASTM A53 Grade B Pipe Fittings Pipes 190 MPa 240 MPa 1.26

Table 6 – Load Condition A: Summary of Results

The figure below shows the total deformation of the structure under the applied loads. Given the small scale of this deformation, it is not expected to affect the operation or capacity and is therefore considered acceptable.

Figure 15 – Load Condition A: Total Deformation (mm)

The equivalent stress in the various structures and materials is shown in the figures below.

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Figure 16 – Load Condition A: Total Deformation (mm)

Figure 17 – Load Condition A: Total Deformation (mm)

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Figure 18 – Load Condition A: von Mises Equivalent Stress (MPa)

Figure 19 – Load Condition A: von Mises Equivalent Stress (MPa)

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Figure 20 – Load Condition A: von Mises Equivalent Stress (MPa)

Figure 21 – Load Condition A: von Mises Equivalent Stress (MPa)

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Figure 22 – Load Condition A: von Mises Equivalent Stress (MPa)

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The figures below show the areas with stress levels in exceedance of that reported in Table 6. These areas of high stress do not affect the reported capacity, as they are deemed to be self-limiting localized stress concentrations that would yield under the first load cycle and engage more of the surrounding material without any visual change in geometry of the structure.

Figure 23 – Load Condition A: Areas of von Mises Stress in Grade A Steel Fittings and Supporting Structure ≥ 190 MPa

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Figure 24 – Load Condition A: Areas of von Mises Stress in Grade A Steel Fittings and Supporting Structure ≥ 190 MPa

Figure 25 – Load Condition A: Areas of von Mises Stress in ASTM A53 Grade B Pipe Fittings Pipes ≥ 190 MPa

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8.2 Load Condition B: Pushing Condition - Line Tension Aft 30 Deg Inboard, and 0 Deg Up

This load condition simulates the line leading from a pushing tug which applied on the barge deck fittings toward aft horizontally and 30 degree inboard. The design line tensions come from Deck Equipment Arrangement and Structure Drawing [F] and a geometry factor of 2 (if applicable) and as well as safety factor of 2 are used to confirm the supporting structure capacity.

8.2.1 Loads and Boundary Conditions

The model is constrained using “Simply Supported” constraints at the edges shown in the figure below.

The constrained edges coincide with relatively rigid structure, such as bulkheads or are structural continuations such as the hull shell. The constraints are sufficiently far from the area of applied loading as not to influence results in the area of interest.

The boundary constraints and line forces are applied using discrete force vectors applied to the

Figure 26 – Load Condition B: Applied Loading and Constraints

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Figure 27 – Load Condition B: Applied Loading and Constraints

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8.2.2 Results

The results presented in this section show the equivalent stresses and total deformation induced by the loading and constrains as described in Section 8.2.1. The maximum equivalent stress and maximum deflection induced by this loading are summarized in the table below. As discussed in Section 6, results disregard the stress peaks that would be blunted by small amounts of localized deformation. The deflection is unaffected by this phenomenon for the number of significant digits indicated.

Maximum Deflection 3 mm Peak Maximum Safety

Equivalent Allowable Factor over Stress Stress Allowable

Grade A Steel Fittings and Supporting Structure 190 MPa 235 MPa 1.24 ASTM A53 Grade B Pipe Fittings Pipes 190 MPa 240 MPa 1.26

Table 7 – Load Condition B: Summary of Results

The figure below shows the total deformation of the structure under the applied loads. Given the small scale of this deformation, it is not expected to affect the operation or capacity and is therefore considered acceptable.

Figure 28 – Load Condition B: Total Deformation (mm)

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Figure 29 – Load Condition B: Total Deformation (mm)

Figure 30 – Load Condition B: Total Deformation (mm)

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Figure 31 – Load Condition B: von Mises Equivalent Stress (MPa)

Figure 32 – Load Condition B: von Mises Equivalent Stress (MPa)

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Figure 33 – Load Condition B: von Mises Equivalent Stress (MPa)

Figure 34 – Load Condition B: von Mises Equivalent Stress (MPa)

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Figure 35 – Load Condition B: von Mises Equivalent Stress (MPa)

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The figures below show the areas with stress levels in exceedance of that reported in Table 7. These areas of high stress do not affect the reported capacity, as they are deemed to be self-limiting localized stress concentrations that would yield under the first load cycle and engage more of the surrounding material without any visual change in geometry of the structure.

Figure 36 – Load Condition B: Areas of von Mises Stress in Grade A Steel Fittings and

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Figure 37 – Load Condition B: Areas of von Mises Stress in Grade A Steel Fittings and Supporting Structure ≥ 190 MPa

Figure 38 – Load Condition B: Areas of von Mises Stress in ASTM A53 Grade B Pipe Fittings Pipes ≥ 190 MPa

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Deck Fittings and Supporting Structure Buoy Barge

8.3 Load Condition C: Pushing Condition - Line Tension Aft, and 30 Deg Up

This load condition simulates the line leading from a pushing tug which applied on the barge deck fittings toward aft and 30 degree upward. The design line tensions come from Deck Equipment Arrangement and Structure [F] and a geometry factor of 2 (if applicable) and as well as safety factor of 2 are used to confirm the supporting structure capacity.

8.3.1 Loads and Boundary Conditions

The model is constrained using “Simply Supported” constraints at the edges shown in the figure below.

The constrained edges coincide with relatively rigid structure, such as bulkheads or are structural continuations such as the hull shell. The constraints are sufficiently far from the area of applied loading as not to influence results in the area of interest.

The boundary constraints and line forces are applied using discrete force vectors applied to the

Figure 39 – Load Condition C: Applied Loading and Constraints

January 31, 2022

Deck Fittings and Supporting Structure Buoy Barge

Figure 40 – Load Condition C: Applied Loading and Constraints

Figure 41 – Load Condition C: Applied Loading and Constraints

January 31, 2022

Deck Fittings and Supporting Structure Buoy Barge

8.3.2 Results

The results presented in this section show the equivalent stresses and total deformation induced by the loading and constrains as described in Section 8.3.1. The maximum equivalent stress and maximum deflection induced by this loading are summarized in the table below. As discussed in Section 6, results disregard the stress peaks that would be blunted by small amounts of localized deformation. The deflection is unaffected by this phenomenon for the number of significant digits indicated.

Maximum Deflection 4.7 mm Peak Maximum Safety

Equivalent Allowable Factor over Stress Stress Allowable

Grade A Steel Fittings and Supporting Structure 235 MPa 235 MPa 1.00 ASTM A53 Grade B Pipe Fittings Pipes 170 MPa 240 MPa 1.41

Table 8 – Load Condition C: Summary of Results

The figure below shows the total deformation of the structure under the applied loads. Given the small scale of this deformation, it is not expected to affect the operation or capacity and is therefore considered acceptable.

Figure 42 – Load Condition C: Total Deformation (mm)

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Deck Fittings and Supporting Structure Buoy Barge

Figure 43 – Load Condition C: Total Deformation (mm)

Figure 44 – Load Condition C: Total Deformation (mm)

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Deck Fittings and Supporting Structure Buoy Barge

Figure 45 – Load Condition C: von Mises Equivalent Stress (MPa)

Figure 46 – Load Condition C: von Mises Equivalent Stress (MPa)

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Deck Fittings and Supporting Structure Buoy Barge

Figure 47 – Load Condition C: von Mises Equivalent Stress (MPa)

Figure 48 – Load Condition C: von Mises Equivalent Stress (MPa)

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Deck Fittings and Supporting Structure Buoy Barge

Figure 49 – Load Condition C: von Mises Equivalent Stress (MPa)

January 31, 2022

Deck Fittings and Supporting Structure Buoy Barge

The figures below show the areas with stress levels in exceedance of that reported in Table 8. These areas of high stress do not affect the reported capacity, as they are deemed to be self-limiting localized stress concentrations that would yield under the first load cycle and engage more of the surrounding material without any visual change in geometry of the structure.

Figure 50 – Load Condition C: Areas of von Mises Stress in Grade A Steel Fittings and Supporting Structure ≥ 235 MPa

January 31, 2022

Deck Fittings and Supporting Structure Buoy Barge

Figure 51 – Load Condition C: Areas of von Mises Stress in Grade A Steel Fittings and Supporting Structure ≥ 235 MPa

Figure 52 – Load Condition C: Areas of von Mises Stress in ASTM A53 Grade B Pipe Fittings Pipes ≥ 170 MPa

January 31, 2022

Deck Fittings and Supporting Structure Buoy Barge

8.4 Load Condition D: Pushing Condition - Line Tension Aft 30 Deg Inboard, and 30 Deg Up

This load condition simulates the line leading from a pushing tug which applied on the barge deck fittings toward aft, 30 degree inboard and 30 degree upward. The design line tensions come from Deck Equipment Arrangement and Structure Drawing [F] and a geometry factor of 2 (if applicable) and as well as safety factor of 2 are used to confirm the supporting structure capacity.

8.4.1 Loads and Boundary Conditions

The model is constrained using “Simply Supported” constraints at the edges shown in the figure below.

The constrained edges coincide with relatively rigid structure, such as bulkheads or are structural continuations such as the hull shell. The constraints are sufficiently far from the area of applied loading as not to influence results in the area of interest.

The boundary constraints and line forces are applied using discrete force vectors applied to the

Figure 53 – Load Condition D: Applied Loading and Constraints

January 31, 2022

Deck Fittings and Supporting Structure Buoy Barge

Figure 54 – Load Condition D: Applied Loading and Constraints

Figure 55 – Load Condition D: Applied Loading and Constraints

January 31, 2022

Deck Fittings and Supporting Structure Buoy Barge

8.4.2 Results

The results presented in this section show the equivalent stresses and total deformation induced by the loading and constrains as described in Section 8.4.1. The maximum equivalent stress and maximum deflection induced by this loading are summarized in the table below. As discussed in Section 6, results disregard the stress peaks that would be blunted by small amounts of localized deformation. The deflection is unaffected by this phenomenon for the number of significant digits indicated.

Maximum Deflection 4.4 mm Peak Maximum Safety

Equivalent Allowable Factor over Stress Stress Allowable

Grade A Steel Fittings and Supporting Structure 230 MPa 235 MPa 1.02 ASTM A53 Grade B Pipe Fittings Pipes 170 MPa 240 MPa 1.41

Table 9 – Load Condition D: Summary of Results

The figure below shows the total deformation of the structure under the applied loads. Given the small scale of this deformation, it is not expected to affect the operation or capacity and is therefore considered acceptable.

Figure 56 – Load Condition D: Total Deformation (mm)

January 31, 2022

Deck Fittings and Supporting Structure Buoy Barge

Figure 57 – Load Condition D: Total Deformation (mm)

Figure 58 – Load Condition D: Total Deformation (mm)

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Deck Fittings and Supporting Structure Buoy Barge

Figure 59 – Load Condition D: von Mises Equivalent Stress (MPa)

Figure 60 – Load Condition D: von Mises Equivalent Stress (MPa)

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Deck Fittings and Supporting Structure Buoy Barge

Figure 61 – Load Condition D: von Mises Equivalent Stress (MPa)

Figure 62 – Load Condition D: von Mises Equivalent Stress (MPa)

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Deck Fittings and Supporting Structure Buoy Barge

Figure 63 – Load Condition D: von Mises Equivalent Stress (MPa)

January 31, 2022

Deck Fittings and Supporting Structure Buoy Barge

The figures below show the areas with stress levels in exceedance of that reported in Table 9. These areas of high stress do not affect the reported capacity, as they are deemed to be self-limiting localized stress concentrations that would yield under the first load cycle and engage more of the surrounding material without any visual change in geometry of the structure.

Figure 64 – Load Condition D: Areas of von Mises Stress in Grade A Steel Fittings and Supporting Structure ≥ 230 MPa

January 31, 2022

Deck Fittings and Supporting Structure Buoy Barge

Figure 65 – Load Condition D: Areas of von Mises Stress in Grade A Steel Fittings and Supporting Structure ≥ 230 MPa

Figure 66 – Load Condition D: Areas of von Mises Stress in ASTM A53 Grade B Pipe Fittings Pipes ≥ 170 MPa

January 31, 2022

Deck Fittings and Supporting Structure Buoy Barge

8.5 Load Condition E: Mooring Condition - 90 Deg Line Outboard This load condition simulates the line leading from mooring that applied horizontally to outboard of the barge deck fittings. The design line tensions comes from Deck Equipment Arrangement and Structure Drawing [F]. The geometric factor is simulated with the force vectors shown. A factor of 1.25 on the SWL is used in accordance with Class rules for mooring fittings.

8.5.1 Loads and Boundary Conditions

The model is constrained using “Simply Supported” constraints at the edges shown in the figure below.

The constrained edges coincide with relatively rigid structure, such as bulkheads or are structural continuations such as the hull shell. The constraints are sufficiently far from the area of applied loading as not to influence results in the area of interest.

The boundary constraints and line forces are applied using discrete force vectors applied to the

Figure 67 – Load Condition E: Applied Loading and Constraints

January 31, 2022

Deck Fittings and Supporting Structure Buoy Barge

Figure 68 – Load Condition E: Applied Loading and Constraints

January 31, 2022

Deck Fittings and Supporting Structure Buoy Barge

8.5.2 Results

The results presented in this section show the equivalent stresses and total deformation induced by the loading and constrains as described in Section 8.5.1. The maximum equivalent stress and maximum deflection induced by this loading are summarized in the table below. As discussed in Section 6, results disregard the stress peaks that would be blunted by small amounts of localized deformation. The deflection is unaffected by this phenomenon for the number of significant digits indicated.

Maximum Deflection 2.4 mm Peak Maximum Safety

Equivalent Allowable Factor over Stress Stress Allowable

Grade A Steel Fittings and Supporting Structure 190 MPa 235 MPa 1.24 ASTM A53 Grade B Pipe Fittings Pipes 190 MPa 240 MPa 1.26

Table 10 – Load Condition E: Summary of Results

The figure below shows the total deformation of the structure under the applied loads. Given the small scale of this deformation, it is not expected to affect the operation or capacity and is therefore considered acceptable.

Figure 69 – Load Condition E: Total Deformation (mm)

January 31, 2022

Deck Fittings and Supporting Structure Buoy Barge

Figure 70 – Load Condition E: Total Deformation (mm)

Figure 71 – Load Condition E: Total Deformation (mm)

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Deck Fittings and Supporting Structure Buoy Barge

Figure 72 – Load Condition E: von Mises Equivalent Stress (MPa)

Figure 73 – Load Condition E: von Mises Equivalent Stress (MPa)

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Deck Fittings and Supporting Structure Buoy Barge

Figure 74 – Load Condition E: von Mises Equivalent Stress (MPa)

Figure 75 – Load Condition E: von Mises Equivalent Stress (MPa)

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Deck Fittings and Supporting Structure Buoy Barge

Figure 76 – Load Condition E: von Mises Equivalent Stress (MPa)

January 31, 2022

Deck Fittings and Supporting Structure Buoy Barge

The figures below show the areas with stress levels in exceedance of that reported in Table 10. These areas of high stress do not affect the reported capacity, as they are deemed to be self-limiting localized stress concentrations that would yield under the first load cycle and engage more of the surrounding material without any visual change in geometry of the structure.

Figure 77 – Load Condition E: Areas of von Mises Stress in Grade A Steel Fittings and

January 31, 2022

Deck Fittings and Supporting Structure Buoy Barge

8.6 Load Condition F: Mooring Condition - Line Toward Forward This load condition simulates the line leading from mooring that applied horizontally to forward of the barge deck fittings. The design line tensions comes from Deck Equipment Arrangement and Structure Drawing [F]. The geometric factor is simulated with the force vectors shown. A factor of 1.25 on the SWL is used in accordance with Class rules for mooring fittings.

8.6.1 Loads and Boundary Conditions

The model is constrained using “Simply Supported” constraints at the edges shown in the figure below.

The constrained edges coincide with relatively rigid structure, such as bulkheads or are structural continuations such as the hull shell. The constraints are sufficiently far from the area of applied loading as not to influence results in the area of interest.

The boundary constraints and line forces are applied using discrete force vectors applied to the

Figure 78 – Load Condition F: Applied Loading and Constraints

January 31, 2022

Deck Fittings and Supporting Structure Buoy Barge

Figure 79 – Load Condition F: Applied Loading and Constraints

January 31, 2022

Deck Fittings and Supporting Structure Buoy Barge

8.6.2 Results

The results presented in this section show the equivalent stresses and total deformation induced by the loading and constrains as described in Section 8.6.1. The maximum equivalent stress and maximum deflection induced by this loading are summarized in the table below. As discussed in Section 6, results disregard the stress peaks that would be blunted by small amounts of localized deformation. The deflection is unaffected by this phenomenon for the number of significant digits indicated.

Maximum Deflection 2 mm Peak Maximum Safety

Equivalent Allowable Factor over Stress Stress Allowable

Grade A Steel Fittings and Supporting Structure 235 MPa 235 MPa 1.00 ASTM A53 Grade B Pipe Fittings Pipes 235 MPa 240 MPa 1.02

Table 11 – Load Condition F: Summary of Results

The figure below shows the total deformation of the structure under the applied loads. Given the small scale of this deformation, it is not expected to affect the operation or capacity and is therefore considered acceptable.

Figure 80 – Load Condition F: Total Deformation (mm)

January 31, 2022

Deck Fittings and Supporting Structure Buoy Barge

Figure 81 – Load Condition F: Total Deformation (mm)

Figure 82 – Load Condition F: Total Deformation (mm)

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Deck Fittings and Supporting Structure Buoy Barge

Figure 83 – Load Condition F: von Mises Equivalent Stress (MPa)

Figure 84 – Load Condition F: von Mises Equivalent Stress (MPa)

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Deck Fittings and Supporting Structure Buoy Barge

Figure 85 – Load Condition F: von Mises Equivalent Stress (MPa)

Figure 86 – Load Condition F: von Mises Equivalent Stress (MPa)

January 31, 2022

Deck Fittings and Supporting Structure Buoy Barge

Figure 87 – Load Condition F: von Mises Equivalent Stress (MPa)

January 31, 2022

Deck Fittings and Supporting Structure Buoy Barge

The figures below show the areas with stress levels in exceedance of that reported in Table 11. These areas of high stress do not affect the reported capacity, as they are deemed to be self-limiting localized stress concentrations that would yield under the first load cycle and engage more of the surrounding material without any visual change in geometry of the structure.

Figure 88 – Load Condition F: Areas of von Mises Stress in Grade A Steel Fittings and

January 31, 2022

Deck Fittings and Supporting Structure Buoy Barge

8.7 Load Condition G: Kevel - Load Toward Aft Horizontally

This load condition simulates the line leading from a pushing tug which applied on deck kevel toward aft in the horizontal plane. The design line tensions comes from Deck Equipment Arrangement and Structure Drawing [E], and a safety factor of 2 is used to confirm the supporting structure capacity.

8.7.1 Loads and Boundary Conditions

The model is constrained using “Simply Supported” constraints at the edges shown in the figure below.

The constrained edges coincide with relatively rigid structure, such as bulkheads or are structural continuations such as the hull shell. The constraints are sufficiently far from the area of applied loading as not to influence results in the area of interest.

The boundary constraints and line forces are applied using discrete force vectors applied to the

Figure 89 – Load Condition G: Applied Loading and Constraints

January 31, 2022

Deck Fittings and Supporting Structure Buoy Barge

Figure 90 – Load Condition G: Applied Loading and Constraints

January 31, 2022

Deck Fittings and Supporting Structure Buoy Barge

8.7.2 Results

The results presented in this section show the equivalent stresses and total deformation induced by the loading and constrains as described in Section 8.7.1. The maximum equivalent stress and maximum deflection induced by this loading are summarized in the table below. As discussed in Section 6, results disregard the stress peaks that would be blunted by small amounts of localized deformation. The deflection is unaffected by this phenomenon for the number of significant digits indicated.

Maximum Deflection 1.8 mm Peak Maximum Safety

Equivalent Allowable Factor over Stress Stress Allowable

Grade A Steel Fittings and Supporting Structure 235 MPa 235 MPa 1.00

Table 12 – Load Condition G: Summary of Results

The figure below shows the total deformation of the structure under the applied loads. Given the small scale of this deformation, it is not expected to affect the operation or capacity and is therefore considered acceptable.

Figure 91 – Load Condition G: Total Deformation (mm)

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Deck Fittings and Supporting Structure Buoy Barge

Figure 92 – Load Condition G: Total Deformation (mm)

Figure 93 – Load Condition G: von Mises Equivalent Stress (MPa)

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Deck Fittings and Supporting Structure Buoy Barge

Figure 94 – Load Condition G: von Mises Equivalent Stress (MPa)

Figure 95 – Load Condition G: von Mises Equivalent Stress (MPa)

January 31, 2022

Deck Fittings and Supporting Structure Buoy Barge

The figures below show the areas with stress levels in exceedance of that reported in Table 12. These areas of high stress do not affect the reported capacity, as they are deemed to be self-limiting localized stress concentrations that would yield under the first load cycle and engage more of the surrounding material without any visual change in geometry of the structure.

Figure 96 – Load Condition G: Areas of von Mises Stress in Grade A Steel Fittings and

January 31, 2022

Deck Fittings and Supporting Structure Buoy Barge

8.8 Load Condition H: Kevel - Load Toward Aft and 45 Deg

Outboard

This load condition simulates the line leading from a pushing tug which applied on deck kevel toward…