887-B399-05_ABS MVR Finite Element Analysis_Rev(-)_signed.pdf

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NSF McMurdo Offload Infrastructure 9 June 2023 ABS MVR Finite Element Analysis i File No. 887-B399-05, Rev. -

Revision History

Section Rev Description Date Approved

ABS MVR Finite Element Analysis ii File No. 887-B399-05, Rev. -

Table of Contents

References ................................................................................................................. iv

Executive Summary

Section 1 .............................................................................................................. Global FEA

1.1 Summary

1.2 Structural Model

1.2.1 Modeling Principles

1.2.2 Model Geometry

1.2.3 Material Properties

1.3 Loads and Boundary Conditions

1.3.1 Loading Conditions

1.3.2 Boundary Conditions

1.3.3 Inertial Relief

1.4 Results

1.4.1 Deflections

1.4.2 Reactions

1.4.3 Calculated Stresses

1.4.4 Buckling and Ultimate Strength Assessments

1.5 Conclusions

Section 2 .................................................................... Ice Stringer and Access Hole FEA

2.1 Summary

2.1.1 Modeling Principles

2.1.2 Model Geometry

2.1.3 Material Properties

2.2 Loading and Boundary Conditions

2.2.1 Boundary Conditions

2.2.2 Loading Conditions

2.3 Allowable Criteria

2.4 Results

2.4.1 Typical Midship Results

2.5 Conclusions

ABS MVR Finite Element Analysis iii File No. 887-B399-05, Rev. -

Section 3 ............................................................... Permanent Mooring Foundation FEA

3.1 Summary

3.1.1 Modeling Principles

3.1.2 Model Geometry

3.1.3 Material Properties

3.2 Loading and Boundary Conditions

3.2.1 Boundary Conditions

3.2.2 Loading Conditions

3.3 Allowable Criteria

3.4 Results

3.5 Conclusions

ABS MVR Finite Element Analysis iv File No. 887-B399-05, Rev. -

References

1. ABS Steel Barge Rules, 2023.

2. ABS Marine Vessel Rules, 2023.

3. ABS ‘Safehull-Dynamic Loading Approach’ for Vessels, 2018.

4. Hughes, O., Ship Structural Analysis and Design, SNAME, 2010.

5. Optimum Structural Design Inc., MAESTRO, Version No. 2021.0.0.

6. Glosten, Midship Section, 887-B301-01.

7. Glosten, Transverse Structure, 887-B309-01.

8. Glosten, Deck & Bottom Structure, 887-B307-01.

9. Glosten, Side Plating, 887-B307-02.

10. Glosten, Longitudinal Structure, 887-B311-01.

11. Glosten, Barge Permanent Mooring Arrangement, 887-B412-01.

12. Glosten, Strut Detail, 887-B354-28.

13. Glosten, Local Scantling Calculations, 887-B399-01.

14. Glosten, ABS Design Methodology and Parameters, 887-B003-01.

15. Robert McNeel and Associates, Rhinoceros, Version No. 7.2.21012.11001.

16. Glosten, 887_18ft.3dm.

17. Glosten, 887-B399-05_Full Hull FEA_Rev(-).mdl.

18. Glosten, 887_ABS Structure Calcs_Rev(-).xlsm.

19. Glosten, 887_18ft.gf1.

20. Glosten, Weight Estimate, 887-B115-01.

21. Creative Systems Inc., General Hydrostatics (GHS), Version No. 18.50, 2023.

22. Glosten, 887-B399-05_Full Hull FEA_Rev(-).rlt.

23. IACS Structural Requirements for Polar Class Ships, 2019.

24. ABS Draft POLARIS-based Ice Class Selection Study and MDAT Analysis, 2022.

25. Siemens, FEMAP, Version 2301.

26. ABS, Overwintering a Barge at McMurdo Station, HETC-2022-4964362-2, Rev. 1, 2023.

27. Glosten, Hydrostatics, 887-B125-01.

28. Hughes, O. & Ma, M., Elastic Tripping Analysis of Asymmetric Stiffeners, Computers and

Structures, Vol. 60, No. 3, 1996.

29. Hughes, O. & Ma, M., Inelastic Stiffener Buckling and Panel Collapse, Computers and

Structures, Vol. 61, No. 1, 1997.

30. IACS Shipbuilding and Repair Quality Standard, Rev. 10, 2021.

ABS MVR Finite Element Analysis 1 File No. 887-B399-05, Rev. -

Executive Summary

Global and local Finite Element Analyses (FEA) were performed to demonstrate compliance with the ABS Steel Barge Rules (SBR) and ABS Marine Vessel Rules (MVR) Part 6 requirements for Polar Class vessels (Refs. 1 and 2), based on the framework and process identified in the ABS Design Methodology (Ref. 14). If no explicit guidance was given for a specific analysis, then the ABS MVR and ABS Dynamic Loading Approach (DLA) Guide were followed (Ref. 3).

Global FEA was performed using MAESTRO. The entire vessel was modeled at full breadth and length using net scantlings. The model was hydrostatically balanced, based on the loading condition, and constrained. Inertial relief was used to balance the model and minimize restraint forces. Additional accelerations were added to influence loading for some conditions. The intent of the global analysis was to evaluate the gross structural response due to the loading conditions described herein.

Five scenarios bounded the expected operational loading profile, consisting of the barge in worst-case hogging and sagging transit load cases under hogging and sagging waves, respectfully, per ABS SBR 3-2-1/13, the barge in a sagging transit load case with a ramming ice impact on the bow per ABS MVR 6-1-2/25, the barge in worst-case transverse sagging winter condition while beset in ice per the ABS Design Methodology, and the barge in worst-case transverse hogging summer condition per ABS SBR 3-2-1/15. These scenarios are intended to evaluate the longitudinal and transverse strength of the vessel, as well as bound acceptable longitudinal and transverse distribution of cargo weight. Two additional scenarios, consisting of the barge in worst-case hogging and sagging transit load cases in a stillwater condition, were analyzed per ABS SBR 3-2-1/7. All global load cases were analyzed to verify compliance with buckling adequacy per Reference 4 and that stress values were below those allowed by the ABS

SBR and ABS MVR Part 6.

Local FEA was performed using FEMAP/NASTRAN. One local FEA model was developed to evaluate the hull's linear response to the ice design load patch in way of a typical ice stringer and bulkhead. Design ice loads were developed in accordance with ABS MVR 6-1-2/5. The local

FEA model was evaluated in accordance with acceptance criteria indicated in the ABS MVR 6-

1-2/15.

The permanent mooring foundations for the strut connections were analyzed by local FEA.

Design loads for the strut connections were developed in alignment with ABS MVR 3-5-1/11.

The applied loading greatly exceeds maximum loads calculated in the mooring analysis. Results of the local FEA model were evaluated in accordance with the acceptance criteria in the ABS

MVR 3-5-1/11.

The FEA analyses performed indicate the vessel complies with global and local strength requirements indicated in ABS SBR, ABS MVR, and Basis of Design (Ref. 14).

ABS MVR Finite Element Analysis 1 File No. 887-B399-05, Rev. -

Section 1 Global FEA

1.1 Summary

The global model was used to bound acceptable transit, summer, and winter stillwater loading conditions by evaluating longitudinal and transverse strength in accordance with ABS SBR 3-2-

1/7, ABS SBR 3-2-1/13, ABS SBR 3-2-1/15, ABS MVR 6-1-2/25, and the ABS Design

Methodology.

1.2 Structural Model

1.2.1 Modeling Principles

The global model was made in MAESTRO version 2021.0.0 (Ref. 5) from References 6 through

10. Shell, bulkheads, girders, and frames were modeled with plate elements; stiffeners, along with some girder and frame flanges, were modeled with beam elements; and stanchions were modeled with rod elements.

Plate elements mainly consist of quad shell elements. A small number of tri shell elements were used to represent plate where necessary in areas of structural transition. Shell elements have stiffness in and out of plane. All beam elements are hybrid elements; the axial stiffness is based on the beam section only while the bending stiffness is calculated from the combined section of the beam and the effective width of plate. Rod elements have axial stiffness only.

The model is meshed with 16" elements, or one stiffener spacing, in compliance with ABS MVR

3-2-20/3.5 and Reference 14. Scantlings are taken net of deductions required by buckling specified in ABS MVR 3-2-A4/3.1.1 and ABS MVR 6-1-2/21.

Discontinuities caused by access holes on the longitudinal and transverse bulkheads were included in the model for stress analysis.

Several conservative deviations from the structural drawings in References 6 through 10 were undertaken to simplify modeling:

1. Moved furthest-inboard mesh element of deadrise shell knuckle with bottom shell 2” inboard to line up with longitudinal bulkhead and deck stiffeners so that thin elements in way of the bulkhead would not be necessary. See Figure 1 for detail, where blue shows the hull surface and bulkhead as per the structural drawings, and gray shows the hull surface and bulkhead as per the MAESTRO model.

2. Simplified side shell radiused corners by flattening bottom edge. Conservatively used

1/2" plate all around, rather than 7/8" plate around the corners. See Figure 2 for detail, where blue shows the hull surface as per the structural drawings, and gray shows the hull surface as per the MAESTRO model.

3. Simplified rakes and deadrise to match simplified side shell in corners. Conservatively used 1-1/4" plate all around, rather than 1-1/2" plate around the corners. See Figure 2 for detail.

4. Did not model 4" Schedule 160 pipe stanchion connecting deck and bottom transverse frames between spans on FR 1 and FR 61.

5. Simplified stiffening and framing scheme to reduce diversity of scantlings.

ABS MVR Finite Element Analysis 2 File No. 887-B399-05, Rev. -

a. Simplified side shell stiffeners by using only FB4-1/2x1" everywhere, rather than increasing depth in way of the corners and sides.

b. Simplified deadrise and rake ice frames by using only FB9-1/2x1" everywhere, rather than increasing depth in way of the corners and sides.

c. Simplified longitudinal bulkhead headers by using only FB5x1/2" everywhere, rather than using FB6x1/2" on the deck header.

6. Brackets, clips, rings, and other small structural details were only modeled where necessary for accuracy in the buckling panel recognition.

7. MAESTRO cannot evaluate buckling in way of a hole in the mesh. To address this, in way of access holes in longitudinal bulkheads, transverse bulkheads, and rake diaphragms, filler elements of 0.01" plate were used to approximate the effect of the hole.

Buckling and stress results for these filler elements were ignored for the purpose of the analysis.

Figure 1 Detail of deadrise and bottom shell knuckle

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Figure 2 Detail of corner surface

The scantlings used are shown in Table 1, Table 2, and Table 3.

Table 1 Plate scantlings

Scantling Location(s)

0.01" PL

Access hole in longitudinal bulkhead, access hole in transverse bulkhead, access hole in rake diaphragm

5/16" PL Collision bulkhead plate, transverse bulkhead plate

3/8" PL

Bottom transverse frame web, rake diaphragm plate, deadrise diaphragm plate

7/16" PL Longitudinal bulkhead plate

1/2" PL

Deck transverse frame web, deck longitudinal girder web, side shell, longitudinal bulkhead strake, transverse bulkhead insert plate

5/8" PL Bottom longitudinal girder web

3/4" PL

Deck plating, rake diaphragm strake, collision bulkhead strake, transverse rake bulkhead strake, deadrise watertight diaphragm strake, deadrise nontight diaphragm strake

1" PL Bottom shell, ice stringer web

1-1/4" PL Deadrise shell

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Table 2 Beam scantlings

Scantling Location(s)

FB4x5/16" Longitudinal bulkhead bottom strake bracket in way of ice frame

FB4x3/8" Bottom transverse frame flange

FB6x3/8" Rake diaphragm strake bracket in way of deck longitudinal girder

FB5x1/2" Rake diaphragm strake header, longitudinal bulkhead strake header

FB6x1/2"

Bottom longitudinal girder bracket in way of bottom transverse frame, deck longitudinal girder bracket in way of deck transverse frame, rake diaphragm soft bracket flange, rake diaphragm soft bracket header

FB7x1/2" Deck transverse frame flange

FB8x1/2" Bottom stiffener

FB4-1/2x1" Side shell stiffener

FB9x1" Deadrise longitudinal girder flange

FB12x1" Deck longitudinal girder flange, bottom longitudinal girder flange

FB15x1" Ice frame

FP8x2-1/2x7/16" Collision bulkhead outboard frame, deadrise diaphragm outboard frame

FP12x3x7/16" Rake diaphragm frame, longitudinal bulkhead frame

FP12x2-1/2x7/16" Collision bulkhead inboard frame, deadrise diaphragm outboard frame

FP16x3x1/2" Deck transverse frame in corner

FP18x6-1/2x1/2" Collision bulkhead midboard frame, deadrise diaphragm midboard frame

L4x3x5/16"

Deadrise watertight diaphragm outboard stiffener, deadrise nontight diaphragm outboard stiffener, longitudinal bulkhead stiffener, collision bulkhead deadrise outboard stiffener

L5x3-1/2x5/16"

Collision bulkhead stiffener, deadrise watertight diaphragm inboard stiffener, deadrise nontight diaphragm inboard stiffener, collision bulkhead deadrise inboard stiffener

L6x3-1/2x5/16" Transverse rake bulkhead stiffener, nontight bulkhead stiffener, watertight bulkhead stiffener

L6x4x5/16" Deadrise nontight diaphragm strake header

L4x3x3/8" Rake diaphragm stiffener

L6x4x3/8" Deck stiffener

L8x4x1/2" Collision bulkhead strake header, deadrise watertight diaphragm strake header

12x1/2" web w/ 12x1" flange center

Transverse watertight bulkhead frame, transverse nontight bulkhead frame

ABS MVR Finite Element Analysis 5 File No. 887-B399-05, Rev. -

Table 3 Rod scantlings

Scantling Location(s)

10" Sch 160 pipe Stanchion connecting deck and bottom longitudinal girder between transverse bulkheads

WT 12x65 Stanchion connecting deck and bottom longitudinal girder in way of rake diaphragm

Standard plate thickness deductions were made in accordance with ABS MVR 6-1-2/21 for ice belt shell and ABS MVR 3-2-A4/3.1.1 elsewhere to attain net scantlings for all plate, beam, and rod elements for evaluation of buckling strength. Per ABS MVR 3-2-20/9.1 and ABS DLA

Guide 15/5, stress results for gross scantlings may be determined by increasing the normal and shear stress components by the ratio of gross and net scantlings. Net thickness, after deductions, is shown for each scantling in Table 4.

Table 4 Net scantling thicknesses

Scantling Gross Thickness

(in)

Deduction

(in)

Net Thickness (in)

5/16" PL 0.313 0.020 0.293

3/8" PL 0.375 0.020 0.355

7/16" PL 0.438 0.022 0.416

WT12x65 (equivalent pipe) 0.473 0.024 0.449

1/2" PL 0.500 0.025 0.475

3/4" PL 0.750 0.038 0.713

1" PL (bottom shell only) 1.000 0.118 0.880

1" PL 1.000 0.040 0.960

10" Sch 160 pipe 1.125 0.040 1.085

1-1/4" PL (deadrise shell only) 1.250 0.197 1.053

1.2.2 Model Geometry

Aside from the geometry simplifications previously described in 1.2.1, all model surfaces and beam traces are directly from the vessel structural model in Rhino (Refs. 15 and 16). See Figure

3 and Figure 4 for an overview of the model (Ref. 17).

ABS MVR Finite Element Analysis 6 File No. 887-B399-05, Rev. -

Figure 3 MAESTRO model overview, Perspective

Figure 4 MAESTRO model overview, Perspective half-hull

1.2.3 Material Properties

The vessel is constructed of either H36 or 50 ksi steel. As 50 ksi steel has a lower yield strength than H36 steel, 50 ksi steel was used as a conservative steel property for the MAESTRO model.

Table 5 provides details of the material properties assigned in the model.

Table 5 Material properties of 50 ksi steel

Property Value Units

Yield Strength 50 ksi

Ultimate Strength 70 ksi

Elastic Modulus 29,700 ksi

Poisson's Ratio 0.28 ---

ABS MVR Finite Element Analysis 7 File No. 887-B399-05, Rev. -

Density 0.28 lbm/in3

1.3 Loads and Boundary Conditions

1.3.1 Loading Conditions

In this report, a “condition” describes a particular environmental scenario (e.g., stillwater or hogging wave), and a “load case” describes a load distribution (e.g., transit sagging or summer transverse hogging). A “loading condition” describes a combination of a load case and a particular condition (e.g., transit hogging – stillwater or winter transverse sagging – partial beset in ice upper).

The loading conditions considered reflect those required by ABS SBR 3-2-1 and ABS MVR 6-2.

These conditions include the transit hogging stillwater, transit sagging stillwater, transit hogging wave, transit sagging wave, transit ramming ice impact, winter Beset in Ice, and summer stillwater conditions. The stillwater, wave, and impact conditions are intended to evaluate the longitudinal strength of the vessel per ABS SBR 3-2-1/7, ABS SBR 3-2-1/13, and ABS MVR 6-

2-1/25. The winter and summer conditions are intended to evaluate transverse strength of the vessel per the ABS Design Methodology and ABS SBR 3-2-1/15. See Table 6 for a summary of the loading conditions and their respective originating rules.

Table 6 Summary of loading conditions

Loading Condition

Load Case Condition Originating Rule

0 Lightship Stillwater N/A

1 Transit Hogging Stillwater SBR 3-2-1/7

2 Transit Sagging Stillwater SBR 3-2-1/7

3 Transit Hogging Hogging Wave SBR 3-2-1/13

4 Transit Sagging Sagging Wave SBR 3-2-1/13

5 Transit Sagging Ice Impact MVR 6-1-2/25

6 Winter Transverse Sagging Full Beset in Ice Design Methodology

7 Winter Transverse Sagging Partial Beset in Ice Upper Design Methodology

8 Winter Transverse Sagging Partial Beset in Ice Lower Design Methodology

9 Summer Transverse Hogging Stillwater SBR 3-2-1/15

Although Reference 20 indicates variation in displacement between the transit, winter, and summer loading cases, the upper ice (maximum) waterline displacement was conservatively used to determine maximum deadweight capacity for all load cases in this analysis.

The worst-case hogging stillwater load case was used to analyze the hogging wave condition.

The worst-case sagging stillwater load case was used to analyze the sagging wave and ice impact conditions. These conditions were used to bound the range of acceptable stillwater bending moments. The beset conditions impose a transverse sagging effect on the vessel, so they were analyzed with a worst-case transverse sagging load case; likewise, the stillwater condition imposes a transverse hogging effect on the vessel, so it was analyzed with a worst-case transverse hogging load case.

A lightship load case was calculated to verify weight distribution only. In general, weight distributions, shear force curves, and bending moment curves are shown from MAESTRO output. Unless otherwise specified, deadweight is applied as a scaling of nodal mass.

ABS MVR Finite Element Analysis 8 File No. 887-B399-05, Rev. -

1.3.1.1 Lightship Case

The lightship weight distribution was developed according to Reference 20. The structural weight distribution of the model was calculated using the self-weight of elements from element properties. Remaining lightship weight includes a structural delta (due to changes indicated in

1.2.1, use of net scantlings, and steel allowances), outfitting, and margins. This remaining weight was added in a trapezoidal distribution at full breadth between 0 and 328 ft aft of FP, with the corners at the transition between the midbody and rakes, 35 ft from the vessel ends. Components of the lightship distribution are shown in Table 7.

Table 7 Lightship weight distribution components

Weight Component Distribution Weight

LT

Structure MAESTRO 2,233

Remaining Lightship Trapezoidal 784

Lightship Sum

(Structure + Additional Lightship) 3,017

The lightship weight distribution from MAESTRO is shown in Figure 5.

Figure 5 Lightship weight distribution, longitudinal

-50 0 50 100 150 200 250 300 350

W e ig h t D e n s it y

L T

/f t) x (ft aft of FP)

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Figure 6 Lightship weight distribution, transverse

The maximum hogging stillwater bending moment for the lightship stillwater condition is -

18,473 LT-ft at midships.

1.3.1.2 Transit Hogging Case

Per Reference 20, 1,047 LT of deadweight was placed in a split rectangular distribution at full breadth between 0 to 134 and 194 to 328 ft aft of FP to induce a hogging moment, in addition to the lightship distribution described above. The distribution was extended to establish an operational limit for hogging loading, corresponding with approximately 4 LT/ft at the ends.

Components of the transit hogging distribution are shown in Table 8.

Table 8 Transit hogging weight distribution components

Weight Component Distribution Weight

LT

Lightship Sum 3,017

Deadweight Split rectangular 1,047

Transit Total Sum 4,064

The transit hogging weight distribution is shown in Figure 7, and the transit hogging stillwater bending moment and shear force curves are shown in Figure 8 and Figure 9.

-60 -40 -20 0 20 40 60

W e ig h t D e n s it y

L T

/f x (ft stbd of CL)

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Figure 7 Transit hogging weight distribution

Figure 8 Transit hogging stillwater shear force

-50 0 50 100 150 200 250 300 350

W e ig h t D e n s it y

L T

/f t) x (ft aft of FP)

-400.000

-300.000

-200.000

-100.000

0.000

100.000

200.000

300.000

400.000

-50 0 50 100 150 200 250 300 350

S h e a r F o rc e

L T

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Figure 9 Transit hogging stillwater bending moment

The maximum stillwater bending moment for the transit hogging stillwater condition is -30,946

LT-ft at midships. The maximum shear force is 279 LT at 32.8 ft aft of FP.

1.3.1.3 Transit Sagging Case

Per Reference 20, 1,047 LT of deadweight was placed in a rectangular distribution at full breadth between 124 and 204 ft aft of FP centered at midships to induce a sagging moment, in addition to the lightship distribution described above. The distribution was extended to establish an operational limit for sagging loading, corresponding with approximately 13 LT/ft at midships.

Components of the transit sagging distribution are shown in Table 9.

Table 9 Transit sagging weight distribution components

Weight Component Distribution Weight

LT

Lightship Sum 3,017

Deadweight Rectangular 1,047

Transit Total Sum 4,064

The transit sagging weight distribution is shown below in Figure 10, and the transit sagging stillwater bending moment and shear force curves are shown in Figure 11 and Figure 12.

-35000

-30000

-25000

-20000

-15000

-10000

-5000

-50 0 50 100 150 200 250 300 350

B e n d in g

M o m e n t (L

T -f

ABS MVR Finite Element Analysis 12 File No. 887-B399-05, Rev. -

Figure 10 Transit sagging weight distribution

Figure 11 Transit sagging stillwater shear force

-50 0 50 100 150 200 250 300 350

W e ig h t D e n s it y

L T

/f t) x (ft aft of FP)

-300.000

-200.000

-100.000

0.000

100.000

200.000

300.000

-50 0 50 100 150 200 250 300 350

S h e a r F o rc e

L T

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Figure 12 Transit sagging stillwater bending moment

The maximum sagging stillwater bending moment for the transit sagging stillwater condition is

9,425 LT-ft at midships. The maximum shear force is 272 LT at 114.8 ft aft of FP.

1.3.1.4 Wave Conditions

Hogging and sagging waves were developed to match an amidships wave bending moment per

ABS SBR 3-2-1/13. This bending moment is equivalent to 𝑆𝑊𝑆𝑀𝑏, where 𝑆𝑊 and 𝑆𝑀𝑏 are defined as follows:

𝑆𝑊 = 7.123 𝐿𝑇/𝑖𝑛2

𝑆𝑀𝑏 = 𝐶1𝐶2𝐿2𝐵(𝐶𝑏 + 0.7)

𝐶1 = 10.75 − ( 984 − 𝐿

1.5

𝐶2 = 1.44 × 10−4

The required wave-induced bending moment is equivalent to +/-99,657 LT-ft. To apply this bending moment, a hogging wave was imposed on the transit hogging load case while a sagging wave was imposed on the transit sagging load case. Total required bending moments are the direct sum of the wave-induced and stillwater bending moments per ABS SBR 3-2-1/13. In other words, the wave-induced bending moment is equivalent to the total bending moment minus the stillwater bending moment.

To develop the hogging and sagging waves in MAESTRO, the wavelength was set to the length of the vessel and the wave height was scaled to match the required wave-induced bending moment. A full-length wave was used because MAESTRO measures wave phase angle from the forward perpendicular.

In the hogging wave condition, the wave height required to meet the desired wave-induced bending moment would surpass that of a breaking wave. A breaking wave is the maximum theoretical wave height for a given wavelength, limited to a minimum ratio of 7. Thus, for the

-8000

-6000

-4000

-2000

10000

12000

-50 0 50 100 150 200 250 300 350

B e n d in g

M o m e n t (L

T -f

ABS MVR Finite Element Analysis 14 File No. 887-B399-05, Rev. -hogging wave condition, wave height was limited to that of a breaking wave and heave acceleration was added so that the wave-induced bending moment matched that which is required. In the sagging wave case, no heave acceleration was required to meet the desired wave-induced bending moment. See Table 10 for details on the hogging and sagging waves compared to the wave required by ABS.

Table 10 Comparison of ABS design wave to MAESTRO waves

Design Wave

(ABS)

Hogging Wave Sagging Wave

Wavelength (ft) N/A 328 328

Wave Amplitude (ft) N/A 23.4 10.2

Wave Steepness N/A 7.0 16.1

Heave Acceleration (ft/s2) N/A 3.3 0.0

Heave Acceleration (g) N/A 0.37 0.00

Wave Phase (deg) N/A 180 0

Wave-induced Bending

Moment (LT-ft) +/-99,657 -100,624 +99,877

Plots of the shear force and bending moment along with hull immersion for the Transit Hogging

– Hogging Wave and Transit Sagging – Sagging Wave conditions are shown in Figure 15 through Figure 16.

Figure 13 Transit hogging – hogging wave immersion, Profile

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Figure 14 Transit hogging – hogging wave shear force

Figure 15 Transit hogging – hogging wave bending moment

-2000.000

-1500.000

-1000.000

-500.000

0.000

500.000

1000.000

1500.000

2000.000

-50 0 50 100 150 200 250 300 350

S h e a r F o rc e

L T x (ft aft of FP)

-140000

-120000

-100000

-80000

-60000

-40000

-20000

-50 0 50 100 150 200 250 300 350

B e n d in g

M o m e n t (L

T -f

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Figure 16 Transit sagging – sagging wave immersion, Profile

Figure 17 Transit sagging – sagging wave shear force

-1500.000

-1000.000

-500.000

0.000

500.000

1000.000

1500.000

-50 0 50 100 150 200 250 300 350

S h e a r F o rc e

L T

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Figure 18 Transit sagging – sagging wave bending moment

Table 11 summarizes the wave loading conditions and their maximum bending moments (all at midships).

Table 11 Bending moment comparison

Loading Condition

Loading Condition Name

Stillwater

Bending

Moment

Wave-induced

Bending

Moment

Total

Bending

Moment

(LT-ft) (LT-ft) (LT-ft)

Transit Hogging –

Stillwater -30,946 0 -30,946

Transit Sagging –

Stillwater +9,425 0 +9,425

Transit Hogging –

Hogging Wave -30,946 -100,624 -131,570

Transit Sagging –

Sagging Wave +9,425 +99,877 +109,302

Figure 19 and Figure 20 show the bending moment required by ABS SBR 3-2-1/13 and its envelope curve required by ABS MVR 3-2-1/3.5.2 compared with the bending moment curves generated by the waves in MAESTRO.

20000

40000

60000

80000

100000

120000

-50 0 50 100 150 200 250 300 350

B e n d in g

M o m e n t (L

T -f

ABS MVR Finite Element Analysis 18 File No. 887-B399-05, Rev. -

Figure 19 Comparison of hogging wave bending moment between MAESTRO and ABS

Figure 20 Comparison of sagging wave bending moment between MAESTRO and ABS

The large wave height and consequently short waterline in the hogging wave condition results in a steep bending moment curve. However, since vessel structure parallel midbody extends from

35 to 293 ft aft of FP, the waves at midships in both hogging and sagging wave conditions adequately reflect the bending moment curve required by ABS MVR 3-2-1/3.5.2.

1.3.1.5 Transit Ice Impact

A ramming Ice Impact condition was modeled to match the bending moment and shear force curves from ABS MVR 6-1-2/25. Per the MVR, the Ice Impact condition was imposed on the

Transit Sagging load case. Similar to the wave-induced bending moment calculation, total required bending moments are the direct sum of the impact-induced and stillwater bending moments per ABS MVR 6-1-2/25.1. In other words, the impact-induced bending moment is equivalent to the total bending moment minus the stillwater bending moment.

-120000

-100000

-80000

-60000

-40000

-20000

-50 0 50 100 150 200 250 300 350

W a v e

B e n d in g

M o m e n t (L

T -f t) x (ft aft of FP)

ABS

MAESTRO

-20000

20000

40000

60000

80000

100000

120000

-50 0 50 100 150 200 250 300 350

W a v e

B e n d in g

M o m e n t (L

T -f t) x (ft aft of FP)

ABS

MAESTRO

ABS MVR Finite Element Analysis 19 File No. 887-B399-05, Rev. -

The design vertical ice force at the bow, 𝐹𝐼𝐵, is defined as the minimum of 𝐹𝐼𝐵,1 and 𝐹𝐼𝐵,2 in ABS

MVR 6-1-2/25.3. Because only the minimum force is to be considered, either may be used. In this analysis, 𝐹𝐼𝐵,2, as defined below, is taken as the minimum.

𝐹𝐼𝐵,2 = 1.20𝐶𝐹𝐹

When 𝐶𝐹𝐹 is taken from MVR 6-1-2/5.3 Table 1 for Ice Class PC6, the minimum vertical force is 661 LT. This force was applied as a pressure to a roughly 22'×100' section of the rake and deadrise shell to model a beaching Ice Impact scenario. To account for the 25° rake angle, the force was increased by 1 cos (25°)⁄ ≈ 110%, corresponding to a uniform pressure of ~5.5 psi.

Figure 21 illustrates the ice pressure area.

Figure 21 Transit Ice Impact pressure distribution, Perspective

To adjust the shear force curve to match that which is required by ABS and to counteract aft pitching acceleration induced by the ice pressure area, a forward pitching acceleration of 0.18 rad/s2 was applied. To counteract aft surge induced by the ice pressure area, a forward surge acceleration of 2.1 ft/s2 (0.23g) was applied. Shear force and bending moment curves for the

Transit Ice Impact condition are shown in Figure 22 and Figure 23.

ABS MVR Finite Element Analysis 20 File No. 887-B399-05, Rev. -

Figure 22 Transit ice impact shear force

Figure 23 Transit ice impact bending moment

See Table 10 for details on the impact compared to the impact required by ABS.

Table 12 Comparison of ABS design impact to MAESTRO impact

Design Impact

(ABS)

Impact

Vertical Force (LT) 661 705

Pitch Acceleration (rad/s2) N/A 0.19

-1000.000

-800.000

-600.000

-400.000

-200.000

0.000

200.000

400.000

600.000

800.000

1000.000

-50 0 50 100 150 200 250 300 350

S h e a r F o rc e

L T x (ft aft of FP)

-10000

10000

20000

30000

40000

50000

60000

70000

80000

-50 0 50 100 150 200 250 300 350

B e n d in g

M o m e n t (L

T -f

ABS MVR Finite Element Analysis 21 File No. 887-B399-05, Rev. -

Surge Acceleration (ft/s2) N/A 2.1

Surge Acceleration (g) N/A 0.23

Impact-induced Bending

Moment (LT-ft) +23,785 +60,561

Impact-induced Shear Force at 35 ft aft of FP (LT) +661 +881

ABS MVR 6-1-2/25.5 and 25.7 specify envelope curves for impact-induced shear force and bending moment. Figure 24 and Figure 25 present plots of the impact-induced bending moment and shear force curves given by MAESTRO (labeled “MAESTRO”), compared to those required by ABS MVR 6-1-2/25 (labeled “ABS”). Beam theory dictates that the bending moment curve is equivalent to the antiderivative of the shear force curve. For reference only, the “ABS” shear force curve from Figure 24 was integrated to produce the “ABS (Derived)” bending moment curve in Figure 25.

Figure 24 Impact-induced shear force comparison to ABS

-800

-600

-400

-200

0 50 100 150 200 250 300 350

S h e a r (L

T x (ft aft of FP)

MAESTRO

ABS MVR Finite Element Analysis 22 File No. 887-B399-05, Rev. -

Figure 25 Impact-induced bending moment comparison to ABS

As shown, the shear force and bending moment curves from MAESTRO exceed those required by ABS MVR 6-1-2/25. The “MAESTRO” shear force curve is quite similar to the “ABS” shear force curve (Figure 24), but the “MAESTRO” and the “ABS (Derived)” bending moment curves greatly exceed the “ABS” bending moment curve (Figure 25).

Since the Ice Impact loading condition in MAESTRO was tailored to match the required impact-induced shear force curve, and MAESTRO develops the bending moment by integration of shear force within the software, one would expect that the “ABS (Derived)” bending moment curve would nearly match the observed “MAESTRO” bending moment curve. The discrepancy between required and derived bending moments is because the ABS required bending moment includes a factor of 𝑠𝑖𝑛−0.2(𝛾𝑠𝑡𝑒𝑚), where 𝛾𝑠𝑡𝑒𝑚 is the rake stem angle measured from the horizontal. The required bending moment does approach the “ABS (Derived)” bending moment curve for very shallow stem angles. As this analysis considers the “MAESTRO” bending moment curve, which resembles the “ABS (Derived)” curve, it is conservative.

Table 13 summarizes the Ice Impact loading condition along with its maximum bending moment and shear force.

-70000

-60000

-50000

-40000

-30000

-20000

-10000

0 50 100 150 200 250 300 350

B e n d in g

M o m e n t (L

T -f t) x (ft aft of FP)

MAESTRO

ABS (Derived)

ABS MVR Finite Element Analysis 23 File No. 887-B399-05, Rev. -

Table 13 Summary of Ice Impact loading condition

Loading Condition

Loading Condition

Name

Stillwater

Bending

Moment

Stillwater

Shear

Force at

35 ft aft of

FP

Impact-induced

Bending

Moment

Impact-induced

Shear

Force at 35 ft aft of

FP

Total

Bending

Moment

Total

Shear

Force at 35 ft aft of

FP

(LT-ft) (LT-ft) (LT-ft) (LT) (LT-ft) (LT)

Transit

Sagging –

Stillwater

+9,425 -150 0 0 +9,425 -150

Transit

Sagging –

Ice Impact

+9,425 -150 +60,561 +881 +69,986 +731

1.3.1.6 Winter Beset in Ice Conditions

A winter beset in ice condition was assumed to bound the transverse sagging bending moment and was used to evaluate transverse strength per ABS SBR 3-2-1/15. Per Reference 14, the sea ice height is expected to be 8 ft. Additional transverse sagging bending moment was imposed by a rectangular distribution of deadweight along centerline at approximately the rated uniform deck load of 2500 psf. This distribution was applied as a scaling of nodal group mass over full length.

The nodal group used is shown in Figure 26.

Figure 26 Winter beset deadweight nodal group, Perspective

Ballast, bridge, and strut loads are not included, thus the transverse bending moment is conservative. The winter beset transverse weight distribution is shown in Figure 27.

ABS MVR Finite Element Analysis 24 File No. 887-B399-05, Rev. -

Figure 27 Winter beset weight distribution, transverse

Three separate Beset in Ice conditions were considered to bound the worst-case transverse bending moment. The first condition assumes the 8 ft of sea ice may support nearly the entire weight of the vessel, roughly 4000 LT. Some buoyancy was allowed so that the vessel could reach force and moment equilibrium; the applied pressure lifted the vessel such that ~50 LT was supported by buoyancy. The second and third conditions derive a displaced mass from the vertical displacement due to thermal ice expansion from Reference 26. A vertical displacement of 0.3 m corresponds to 659 LT displaced mass, measured down from the upper ice waterline, per Reference 27. For conservatism, 700 LT is used as the displaced mass. The second condition assumes a 3 ft band of ice supports 700 LT from the upper ice waterline, while the third condition assumes a 3 ft band of ice supports 700 LT from the baseline. See Table 14 for a summary of the Beset in Ice conditions.

Table 14 Summary of Beset in Ice conditions

Loading Condition

Loading Condition Name

Displacement

Due to Ice

Ice Belt

Height

Ice Belt

Upper

Bound

Transverse

Bending

Moment

(LT) (ft) (LT-ft)

Winter Transverse

Sagging – Full

Beset in Ice

4000 8 UIWL +12,609

Winter Transverse

Sagging – Partial

Beset in Ice Upper

700 3 UIWL -7,871

Winter Transverse

Sagging – Partial

Beset in Ice Lower

700 3 BL -11,345

See Figure 28 through Figure 30 for images of the ice pressure area for each beset condition.

-60 -40 -20 0 20 40 60

W e ig h t D e n s it y

L T

/f

ABS MVR Finite Element Analysis 25 File No. 887-B399-05, Rev. -

Figure 28 Winter beset pressure distribution, full lift, Perspective

Figure 29 Winter beset pressure distribution, partial lift, Perspective

ABS MVR Finite Element Analysis 26 File No. 887-B399-05, Rev. -

Figure 30 Winter beset pressure distribution, partial lift, Perspective

Plots of the transverse shear force and bending moment curves for each of the Beset in Ice conditions are shown in Figure 31 through Figure 36.

Figure 31 Winter full beset transverse shear force

Figure 32 Winter full beset transverse bending moment

-1000

-800

-600

-400

-200

-60 -40 -20 0 20 40 60

S h e a r F o rc e

L T x (ft stbd of CL)

-4000

-2000

10000

12000

14000

-60 -40 -20 0 20 40 60

B e n d in g

M o m e n t (L

T -f

ABS MVR Finite Element Analysis 27 File No. 887-B399-05, Rev. -

Figure 33 Winter partial beset upper transverse shear force

Figure 34 Winter partial beset upper transverse bending moment

-400

-300

-200

-100

-60 -40 -20 0 20 40 60

S h e a r F o rc e

L T x (ft stbd of CL)

-9000

-8000

-7000

-6000

-5000

-4000

-3000

-2000

-1000

-60 -40 -20 0 20 40 60

B e n d in g

M o m e n t (L

T -f

ABS MVR Finite Element Analysis 28 File No. 887-B399-05, Rev. -

Figure 35 Winter partial beset lower transverse shear force

Figure 36 Winter partial beset lower transverse bending moment

1.3.1.7 Summer Stillwater

A summer stillwater condition was assumed to bound the transverse hogging bending moment and was used to evaluate transverse strength per ABS SBR 3-2-1/15. Additional transverse hogging bending moment was imposed by a rectangular distribution of deadweight along the port and starboard edges at approximately the rated uniform deck load of 2500 psf. This distribution was applied as a scaling of nodal group mass over the full length. The nodal groups used are shown in Figure 37 and Figure 38.

-600

-400

-200

-60 -40 -20 0 20 40 60

S h e a r F o rc e

L T x (ft stbd of CL)

-12000

-10000

-8000

-6000

-4000

-2000

-60 -40 -20 0 20 40 60

B e n d in g

M o m e n t (L

T -f

ABS MVR Finite Element Analysis 29 File No. 887-B399-05, Rev. -

Figure 37 Summer stillwater deadweight starboard nodal group, Perspective

Figure 38 Summer stillwater deadweight port nodal group, Perspective

Ballast, bridge, and strut loads, of roughly 400 LT split between port and starboard edges (Ref.

20), are not included in this distribution. The distribution is assumed to be conservative because the loads are higher and further outboard than the ballast, bridge, and strut loads. The summer stillwater transverse weight distribution is shown in Figure 39.

ABS MVR Finite Element Analysis 30 File No. 887-B399-05, Rev. -

Figure 39 Summer stillwater weight distribution, transverse

Plots of the transverse shear force and bending moment curves are shown in Figure 40 and

Figure 41.

Figure 40 Summer stillwater transverse shear force

-60 -40 -20 0 20 40 60

W e ig h t D e n s it y

L T

/f t) x (ft stbd of CL)

-1500

-1000

-500

-60 -40 -20 0 20 40 60

S h e a r F o rc e

L T

ABS MVR Finite Element Analysis 31 File No. 887-B399-05, Rev. -

Figure 41 Summer stillwater transverse bending moment

The maximum stillwater transverse bending moment for the summer stillwater condition is -

34,489 LT-ft at CL. The maximum transverse shear force is 937 LT at 30 ft stbd of CL.

1.3.1.8 Hydrostatics Validation

Weight distributions and model integrity were further confirmed by evaluating the hydrostatics of lightship and upper ice waterline displacements in GHS (Ref. 21) and MAESTRO. This confirms the hull shape was modeled in MAESTRO with similar fidelity to the model used in

Reference 19. See Table 15 and Table 16 for a summary of hydrostatics comparisons in both stillwater conditions.

Table 15 Comparison of hydrostatics data at lightship displacement

GHS Value MAESTRO Value Difference

Heel 0.00 deg 0.00 deg 0.0%

Trim 0.00 deg 0.00 deg 0.0%

LCF 164.0 ft 164.0 ft 0.0%

LCF Draft 6.38 ft 6.50 ft 1.9%

Table 16 Comparison of hydrostatics data at upper ice waterline displacement

GHS Value MAESTRO Value Difference

Heel 0.00 deg 0.00 deg 0.0%

Trim 0.00 deg 0.00 deg 0.0%

LCF 164.0 ft 164.0 ft 0.0%

LCF Draft 8.00 ft 8.13 ft 1.6%

Most of the differences exhibited in the hydrostatics are due to slight differences in the shape of the deadrise/rake shell around the corners, explained in 1.2.1.

-40000

-35000

-30000

-25000

-20000

-15000

-10000

-5000

-60 -40 -20 0 20 40 60 B e n d in g M o m e n t (L

T -f

ABS MVR Finite Element Analysis 32 File No. 887-B399-05, Rev. -

1.3.2 Boundary Conditions

The model was restrained with a single 6 degree of freedom restraint at its center of gravity. The restraint is connected to nearby deck plating in way of deck transverse frames using four weightless soft springs. The springs have a spring constant of 2.55 LTf/in, which was automatically selected by the “Add CG Constraint” feature in MAESTRO. The restraint is shown in Figure 42.

Figure 42 Restraint detail, Perspective half-hull

1.3.3 Inertial Relief

Inertial relief, in the form of added accelerations, was used to achieve low reaction forces.

Inertial relief accelerations were chosen automatically by MAESTRO. For the transit hogging – hogging wave and transit sagging – sagging impact loading conditions, the added heave, surge, and pitch accelerations superseded the accelerations required for inertial relief, so some restraint reactions were expected. See Table 17 for a summary of inertial relief accelerations. Restraint reactions are documented in the Results section.

Table 17 Additional accelerations

Loading Condition

Loading Condition Name

Surge Heave Sway Roll Yaw Pitch

(in/s2) (in/s2) (in/s2) (rad/s2) (rad/s2) (rad/s2)

Transit Hogging

– Stillwater

-2E-10 -9E-10 -4E-10 -2E-10 -9E-10 -4E-10

ABS MVR Finite Element Analysis 33 File No. 887-B399-05, Rev. -

Transit Sagging –

Stillwater -3E-14 -3E-02 -4E-05 -4E-05 7E-09 -9E-09

Transit Hogging –

Hogging Wave

6E-06 40 * 3E-04 -5E-10 -2E-14 -2E-12

Transit Sagging –

Sagging Wave 4E-07 -6E-02 9E-05 -3E-05 2E-09 -1E-11

Transit Sagging –

Ice Impact 28 * 6E-01 -8E-04 3E-07 -1E-06 0.19 *

Winter Transverse

Sagging – Full

Beset in Ice

-2E-03 2E-05 1E-01 -1E-08 4E-06 -2E-09

Winter Transverse

Sagging – Partial

Beset in Ice Upper

1E-07 6E-02 -9E-05 3E-07 3E-13 -8E-12

Winter Transverse

Sagging – Partial

Beset in Ice Lower

-6E-03 6E-02 2E-01 -1E-05 1E-04 -7E-08

Summer Transverse

Hogging –

Stillwater

-4E-09 -5E-02 8E-07 3E-06 4E-12 -2E-11

* Additional acceleration applied rather than inertial relief acceleration

1.4 Results

All results are read from Reference 22. Results pertaining to bulkhead access hole filler of 0.01" plate thickness are not shown, as they were only included in the model to allow MAESTRO to adequately evaluate panel-level buckling.

1.4.1 Deflections

The maximum observed deflection occurred in the transit sagging, ice impact condition with

8.46" at the forward end of the vessel, shown in Figure 43.

ABS MVR Finite Element Analysis 34 File No. 887-B399-05, Rev. -

Figure 43 Scaled deflection in transit sagging, ice impact condition, Profile

The second largest observed deflection occurred in the transit sagging, sagging wave condition with 7.00" at the ends of the vessel, shown in Figure 44.

Figure 44 Scaled deflection in transit sagging, sagging wave condition, Profile

Deflections for each load condition are shown below in Table 18.

Table 18 Deflections summary

ABS MVR Finite Element Analysis 35 File No. 887-B399-05, Rev. -

Loading Condition

Loading Condition Name Maximum

Deflection

(in)

1 Transit Hogging – Stillwater 1.82

2 Transit Sagging – Stillwater 0.367

Transit Hogging –

Hogging Wave 7.00

Transit Sagging –

Sagging Wave 6.17

Transit Sagging –

Ice Impact 8.46

Winter Transverse Sagging – Full

Beset in Ice 0.442

Winter Transverse Sagging –

Partial Beset in Ice Upper 0.990

Winter Transverse Sagging –

Partial Beset in Ice Lower 1.35

Summer Transverse Hogging –

Stillwater 1.26

1.4.2 Reactions

Restraint reactions, listed in relative magnitudes for simplicity, for each load condition are shown below in Table 19. Note that x, y, and z axes in MAESTRO correspond to longitudinal, vertical, and transverse directions with respect to the vessel.

Table 19 Restraint reactions summary

Loading Condition Loading Condition Name Fx Fy Fz

(LT) (LT) (LT)

Transit Hogging

– Stillwater

-5E-11 -6E-10 -3E-10

Transit Sagging –

Stillwater

-2E-10 -2E-10 -8E-11

Transit Hogging –

Hogging Wave

1E-06 3E-05 -9E-04

Transit Sagging –

Sagging Wave

2E-11 4E-09 4E-09

Transit Sagging –

Ice Impact

-2E+00 -1E-01 3E-03

Winter Transverse

Sagging – Full Beset in

Ice

-5E-09 -3E-05 2E-06

Winter Transverse

Sagging – Partial Beset in

Ice Upper

-2E-10 -8E-10 -2E-10

ABS MVR Finite Element Analysis 36 File No. 887-B399-05, Rev. -

Winter Transverse

Sagging – Partial Beset in

Ice Lower

1E-10 -6E-10 -3E-11

Summer Transverse

Hogging –

Stillwater

-2E-10 -8E-10 -1E-11

The largest reaction force of 2 LT occurred in the ice impact condition due to the combination of the applied pressure patch and surge acceleration. The soft springs used to connect the center of gravity restraint to surrounding geometry could only carry axial forces, so the restraint had no moment reactions in any loading condition.

1.4.3 Calculated Stresses

Standard plate thickness deductions were made in accordance with ABS MVR 6-1-2/21 for ice belt shell and ABS MVR 3-2-A4/3.1.1 elsewhere to attain net scantlings for all plate, beam, and rod elements for evaluation of buckling strength. Per ABS MVR 3-2-20/9.1 and ABS DLA

Guide 15/5, stress results for gross scantlings may be determined by increasing the normal and shear stress components by the ratio of gross and net scantlings. As the observed stresses for each loading condition are well below their respective limits, and each scantling has a different gross/net thickness ratio, the stress conversion was not performed in this analysis. Stress results are listed for net scantlings, and additional calculation must be performed to determine stress results for gross scantlings.

Allowable von Mises stresses for plate elements and axial stresses for beam elements were determined in accordance with the ABS DLA Guide. Allowable bending and shear stresses were determined in accordance with the ABS SBR and ABS MVR.

1.4.3.1 Von Mises Stress

Allowable von Mises stress levels were determined in accordance with the ABS DLA Guide

15/3.7 and 15/3.9. Allowable stress is determined by the formula 𝑐𝑙𝑐𝑓𝑆𝑚𝑓𝑦, where 𝑐𝑓 = 0.95.

The 𝑐𝑙 of 0.80 for watertight structure was used for both watertight and non-watertight structure, for conservatism. The strength reduction factor 𝑆𝑚 was determined to be 0.92 through linear interpolation between ABS H32 and HT36 steel, given the minimum specified yield stress 𝑓𝑦 for

50 ksi steel. Thus, the allowable von Mises stress is 34.8 ksi (Ref. 20).

For each loading condition, the nominal maximum von Mises stresses were recorded and can be seen below in Table 20. The nominal hull girder stresses are less than the allowable stress for all loading conditions.

Table 20 Maximum von Mises stress for each loading condition

Loading Condition Loading Condition

Name

Maximum von

Mises Stress

Allowable von

Mises Stress Usage

(ksi) (ksi) (%)

Transit Hogging

– Stillwater

7.60 34.8 22%

Transit Sagging –

Stillwater

8.93 34.8 26%

Transit Hogging –

Hogging Wave

29.3 34.8 84%

ABS MVR Finite Element Analysis 37 File No. 887-B399-05, Rev. -

Transit Sagging –

Sagging Wave

21.8 34.8 63%

Transit Sagging –

Ice Impact

15.1 34.8 43%

Winter Transverse

Sagging – Full Beset in

Ice

7.06 34.8 20%

Winter Transverse

Sagging – Partial Beset in Ice Upper

5.23 34.8 15%

Winter Transverse

Sagging – Partial Beset in Ice Lower

5.25 34.8 15%

Summer Transverse

Hogging –

Stillwater

8.71 34.8 25%

The maximum calculated von Mises stress in the hull girder is 29.3 ksi compared to an allowable stress of 34.8 ksi, exclusive to the plating surrounding access holes on the longitudinal bulkhead in the transit hogging wave condition. See Figure 45 for detail of the stresses surrounding longitudinal bulkhead access holes in the transit hogging wave condition.

Figure 45 Peak von Mises stress surrounding longitudinal bulkhead access holes in transit hogging wave condition, Perspective

1.4.3.2 Axial Stress

Allowable beam axial stress levels were determined in accordance with the ABS DLA Guide.

For all conditions, the ABS DLA Guide 15/3.7 and 15/3.9 define a maximum axial stress for beam and rod members of 34.8 ksi.

29.3 ksi

ABS MVR Finite Element Analysis 38 File No. 887-B399-05, Rev. -

For each loading condition, the nominal maximum axial stresses were recorded and can be seen below in Table 21. The nominal hull girder stresses are less than the allowable stress for all loading condition.

Table 21 Maximum axial stress for each loading condition

Loading Condition

Loading Condition Name

Maximum axial Stress Allowable axial Stress Usage

(ksi) (ksi) (%)

Transit Hogging

– Stillwater

11.3 34.8 32

Transit Sagging –

Stillwater

12.5 34.8 36

Transit Hogging –

Hogging Wave

33.4 34.8 96

Transit Sagging –

Sagging Wave

26.1 34.8 75

Transit Sagging –

Ice Impact

19.1 34.8 55

Winter Transverse

Sagging – Full

Beset in Ice

7.21 34.8 21

Winter Transverse

Sagging – Partial

Beset in Ice Upper

8.94 34.8 26

Winter Transverse

Sagging – Partial

Beset in Ice Lower

8.77 34.8 25

Summer Transverse

Hogging –

Stillwater

12.2 34.8 35

The maximum calculated axial stress in the hull girder is 33.4 ksi compared to an allowable stress of 34.8 ksi, exclusive to the flange of bottom transverse frames in way of the longitudinal bulkheads in the transit hogging wave condition. See Figure 46 for detail of the stresses surrounding the bottom transverse frames in the transit hogging wave condition.

ABS MVR Finite Element Analysis 39 File No. 887-B399-05, Rev. -

Figure 46 Peak axial stress surrounding bottom transverse frames in transit hogging wave condition, Perspective

1.4.3.3 Bending Stress

Allowable bending stress levels were determined in accordance with the ABS SBR and ABS

MVR Part 6. For stillwater conditions, ABS SBR 3-2-1/15.3 defines a maximum bending stress for transverse members of 30.7 ksi. For the ice impact condition, ABS MVR 6-1-2/25.9 defines a maximum bending stress for all members of 39.4 ksi. For the purposes of this analysis, the Beset in Ice condition is considered as a stillwater condition. The ABS SBR do not define a maximum bending stress for wave conditions, so the ABS MVR is optionally used. The ABS MVR 3-2-

1/7.3.1 defines a maximum bending stress for all members of 33.4 ksi in wave conditions.

For each loading condition, the nominal maximum axial stresses were recorded and can be seen below in Table 22. The nominal hull girder stresses are less than the allowable stress for all loading condition.

Table 22 Maximum bending stress for each loading condition

Loading Condition

Loading Condition Name

Maximum

Bending

Stress

Governing

Rule

Allowable

Bending Stress Usage

(ksi) (ksi) (%)

Transit Hogging

– Stillwater 4.91

SBR 3-2-

1/15.3 *

30.7 16%

Transit Sagging –

Stillwater 4.94

SBR 3-2-

1/15.3 *

30.7 16%

Transit Hogging –

Hogging Wave 15.9

MVR 3-2-

1/7.3.1 **

33.4 48%

Transit Sagging –

Sagging Wave 23.0

MVR 3-2-

1/7.3.1 **

33.4 69%

Transit Sagging –

Ice Impact 15.3

MVR 6-1-

2/25.9

39.4 39%

33.4 ksi

ABS MVR Finite Element Analysis 40 File No. 887-B399-05, Rev. -

Sagging…