Grillage&Seafastening_DesignExample

INDEX 1. Purpose 2. References 3. Barge Characteristics & Loading Condition 4. Modules Characteristics & Lay out on the Barge Deck 5. Environmental Conditions during Transit 6. Motions Analysis Results 7. Loads on Grillage and Seafastening 8. Grillage & Seafastening Structural Check. 9. Barge Local Structural Analysis. 10. Barge Longitudinal Strength Check. 11. Barge Stability Check.

Annexes: Annex A – Figures of FEM Analysis Analysis Annex B – Barge Longitudinal Longitudinal Strength Check Check Results Annex C – Letter from ABS Indicating Indicating the SWBM and Shear Shear

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1. PURPOSE.

The Modules M05 and M06 for the P-56 will be transported from Nuova Pignone yard located in Caju, Rio de Janeiro, RJ, to Angra dos Reis, RJ, on the barge BS-1.

The present document presents the structural check of the barge and the calculations pertaining the grillage and seafastening of the modules, and stability calculations for the tow.

2. REFERENCES.

[1] Noble Denton – 0030/ND Rev 3 – Guidelines for Marine Transportations. [2] Drawing 01.214- Seção Mestra Balsa de Serviço no.1, 23/03/73, Verolme Estaleiros Reunidos do Brasil, Petrobras. [3] I-RL-3010.71-1231-960-NOQ-001 I-RL-3010.71-1231-960-NOQ-001 Rev 0 – M06 Module Weight Control Report. [4] I-RL-3010.71-1231-960-NOQ-002 I-RL-3010.71-1231-960-NOQ-002 Rev 0 – M05 Module Weight Control Report. [5] ABS Rules for Testing and Certification of Materials. [6] ABS Rules for Building and Classing Mobile Offshore Drillings Units, 2006, Part 3 Hull Construction and Equipment; items 3.11 and 3-2-1 (ii). [7] 1156_BS-1 Generalidades e Especificações. [8] I-DE-3010.66-5130-960-MUZ-008 I-DE-3010.66-5130-960-MUZ-008 – P-53 Compression Modules, Grillage and S eafastening, Reformed Grillage (2/4) and New Grillage (3/4). [9] Letter (H)-799/93(S-1) of 04/10/93, from ABS to Petrobras indicating the SWBM and Shear (reproduced in the Annex C). [10] CSM010-TPN Rev A - Technical Report – Seakeeping – Numerical Evaluation (P-56 Platform M05 and M06 Modules Transportation), São Paulo 2009. [11] Document Review Comment Sheet – job no. 097210-011-P, Noble Denton, 25/09/2009. [12] Marine Operations DNV, Part 1, Chapter 3, Design Loads, J an 1996. [13] DNV Classification Notes 30.1 May 1992 – Buckling Strength Analysis. [14] DNV Rules for Classification of Ships.

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3. BARGE CHARACTERISTICS & LOADING CONDITION.

The barge BS-1 of Petrobras will be used. Principal particulars as follow: Length:

75.0 m

Breadth:

23.0 m

Depth:

5.0 m

Maximum draft:

4.02 m

Deadweight:

5347 tons

Lightweight:

1105 tons

LCG: 37.50 m from bow;

for displacement of 6452 tons

TCG: 0.00 m

VCG: 2.80 m

Classified by ABS American Bureau of Shipping Load on deck 3.5 t/m 2.

Sea transportation draft: 2.70 m (trim (trim astern) Ballast used: all tanks empty (only residual water) except peak tank AFS with 115.6 m 3.

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4. MODULES CHARACTERISTICS & LAY OUT ON THE BARGE DECK

The final positions of the modules on the barge are as follows (shown in figure below): Item

Weight (tons)

LCG (m)

TCG (m)

VCG (m)

Module M05 (ref[4])

1318

18.48

0.045

7.815

Module M06 (ref[3])

1385

-18.13

0.675

7.605

The datum references:

LCG from midship, positive forward; TCG from centerline, positive to

port side; VCG from deck

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5. ENVIRONMENTAL CONDITIONS DURING TRANSIT Distance from Guanabara Bay to Angra dos Reis Bay:

72 NM

Considering conservatively the convoy speed of 4 knots, the voyage duration will be 18 hours. Using a contingency time of 25% (item 6.6.1.d of ref.[1]), the time anticipated for the voyage or operational reference period will be 22,5 hours. The reference period T R of the marine operation will be less than 72 hours and so the operation could be defined as Weather Restricted, according to section 6.3 of ref.[1]. Therefore the design environmental conditions could be set independent of extreme statistical data. Wave Conditions:

Noble Denton requires a significant wave height of H S = 3,653 m as design criteria. This value was found using the cumulative probability function of Weibull with 10% of probability to be exceeded, with Ho and j for Brazilian East coast (zone 74) of ref.[12]. The corresponding H MAX required by Noble Denton is 1,86 x 3,653 = 6,795 m According to ref.[1] the peak period to be examined in motion analysis will be: 7,21s < TP < 10,95s. The Jonswap spectrum is recommended taking into consideration the navigation will be in shallow waters, so, the zero up-crossing period corresponding to that peak period is (item 7.3.3 of ref.[1]):

5,82s < TZ < 7,82s.

Wind Conditions:

A wind velocity of 35 knots (18 m/s) will be adopted for structural design criteria. For stability criteria Noble Denton requires 50 m/s.

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6. MOTIONS ANALYSIS RESULTS The motion analysis of the barge was carried out with the software WAMIT using the environmental data of item 5. According to ref.[10], de results for wave height of 1,86 Hs are (maximum values):

M05 Results

Unit

Value

Description

Ax

m/s2

0.605

Max. pitch & surge accelerations at module’s CoG

Ay

m/s2

1.968

Max. roll & sway accelerations at module’s CoG

Az

m/s2

2.711

Max. heave acceleration at module’s CoG

Acc.MaxRoll

rad/m2

0.145

Max. angular roll accelerations at module’s CoG

Acc.MaxPitch

rad/m2

0.091

Max. angular pitch accelerations at module’s CoG

Roll Max.

deg.

10.048

Max. roll angle

Pitch Max.

deg.

5.750

Max. pitch angle

M06 Results

Unit

Value

Description

ax

m/s2

0.623

Max. pitch & surge accelerations at module’s CoG

ay

m/s2

1.926

Max. roll & sway accelerations at module’s CoG

az

m/s2

2.741

Max. heave acceleration at module’s CoG

Acc.MaxRoll

rad/m2

0.145

Max. angular roll accelerations at module’s CoG

Acc.MaxPitch

rad/m2

0.091

Max. angular pitch accelerations at module’s CoG

Roll Max.

deg.

10.048

Max. roll angle

Pitch Max.

deg.

5.750

Max. pitch angle

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7. LOADS ON GRILLAGE AND SEAFASTENING

The figure below shows the feet numbering used in the calculation.

M06

M05

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Trim = tetaroll = fipitch =

0,35 10,05 5,75

degree degree degree

trim angle roll angle pitch angle

Wm = Lm = Bm = Hm =

1318 30,00 18,75 12,80

t m m m

module weight module length module breadth module height

a= b= ag = bg =

18,750 17,160 9,420 7,230

m m m m

distance between module feet in transverse direction (m) distance between module feet in longitudinal direction (m) distance from aft starboard module foot to COG in transverse direction (m) distance from aft starboard module foot to COG in longitudinal direction (m)

Distribution factors module foot no.1 r1 = module foot no.2 r2 = module foot no.3 r3 = module foot no.4 r4 =

0,2879 0,2907 0,2097 0,2117

Static vertical forces - roll angle =

10,048

module foot no.1 r1xWm module foot no.2 r2xWm module foot no.3 r3xWm module foot no.4 r4xWm az0= az90= ax = ay = hg = tetarollacc = fipitchacc = Fevt hs= Fevt bs= Feht+ = Feht- = Fehl+ = Fehl- = rxx2 = It = Met = ryy2 = Il = Met = hwt = hwl = Fwt = Fwl =

= = = =

374 377 272 275

MÓDULO M05


0,00

module foot no.1 r1xWm = module foot no.2 r2xWm = module foot no.3 r3xWm = module foot no.4 r4xWm =

379 383 276 279

graus

Static vertical forces - pitch angle+trim =

t t t t


6,103 377 381 275 277

t t t t graus t t t t

2,71 2,71 0,61 1,97 6,590 0,145 0,091

m/s2 m/s2 m/s2 m/s2 m rad/s2 rad/s2

heave acceleration in head seas acting on COG of module (m/s2) heave acceleration in beam seas acting on COG of module (m/s2) pitch and surge acceleration in head seas acting on COG of module (m/s2) roll and sway acceleration in beam seas acting on COG of module (m/s2) distance from top of grillage to COG of module (m) angular roll acceleration in beam seas (rad/s2) angular pitch acceleration in head seas (rad/s2)

364 364 554 427 260 182 54 70747 10258 111 146029 13347 7,76 6,41 288 180

t t t t t t 2 m 2 t.m kN.m 2 m 2 t.m kN.m m m kN kN

vertical load due to heave - hs = head seas vertical load due to heave - bs = beam seas transverse parallel to deck load due to weight&roll&sway&heave+ transverse paralel to deck load due to weight&roll&sway&heavelongitudinal parallel to deck load due to weight&pitch&surge&heave+ longitudinal parallel to deck load due to weight&pitch&surge&heavetransverse gyration radius of module transverse inertia of module moment due to roll longitudinal gyration radius of module longitudinal inertia of module moment due to pitch distance from top of grillage to COW of module for transverse wind (m) distance from top of grillage to COW of module for longitudinal wind (m) transverse wind load longitudinal wind load

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Dynamic vertical forces (heave, roll & sway): Component of heave+ for beam seas (Fevt bs) perpendicular to deck : module foot no.1 r1xFevt= 103 t module foot no.2 r2xFevt= 104 t module foot no.3 r3xFevt= 75 t module foot no.4 r4xFevt= 76 t 359 t Moment of horizontal load due to roll&sway&heave+ hgxFeht = Moment of horizontal load due to roll&sway&heave- hgxFeht = Moment due to roll Met = Moment due to transverse wind hwt x Fwt = Resultant dynamic vertical forces due to moments: module foot no.1 = 152 t (heave+) module foot no.2 = 152 t (heave+) module foot no.3 = 111 t (heave+) module foot no.4 = 111 t (heave+)

126 126 92 92

3649 2812 1046 228

t.m t.m t.m t.m

(Heave up) (Heave down)

1711 1201 1361 117

t.m t.m t.m t.m


t (heave-) t (heave-) t (heave-) t (heave-)

Dynamic vertical forces (heave, pitch & surge): Component of heave for head seas (Fevt hs) perpendicular to deck: module foot no.1 r1xFevt= 104 t module foot no.2 r2xFevt= 105 t module foot no.3 r3xFevt= 76 t module foot no.4 r4xFevt= 77 t 362 t Moment of horizontal load due to pitch&surge&heave+ hgxFehl = Moment of horizontal load due to pitch&surge&heave- hgxFehl = Moment due to pitch Mel = Moment due to longitudinal wind hwl x Fwl = Resultant dynamic vertical forces due to moments: module foot no.1 = 92 t (heave+) module foot no.2 = 93 t (heave+) module foot no.3 = 93 t (heave+) module foot no.4 = 92 t (heave+)

r1 = r2 = r3 = r4 =

78 93 93 92


starboard aft foot (crossing of axis 3 and A) port aft foot (crossing of axis 3 and H) starboard fore foot (crossing of axis 6 and A) port fore foot (crossing of axis 6 and H)

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FOR ROLL:

Total vertical reaction at module foot no.1:


F1+ = F1- =

F2+ = F2- =

629 144

t t

633 147

t t



F3+ = F3- =

F4+ = F4- =

458 105

t t

461 107

t t

FOR PITCH:



F1+ = F1- =

F2+ = F2- =

574 181

t t

580 182

t t



F3+ = F3- =

F4+ = F4- =

444 105

t t

446 108

t t

Dynamic transverse forces (Feht+Fwt)

583

t

Dynamic longitudinal forces (Fehl + Fwl) =

278

t

module foot no.1 = module foot no.2 = module foot no.3 = module foot no.4 =

337 337 246 246

t t t t

module foot module foot module foot module foot

138 140 138 140

t t t t

foot 1 = foot 2 = foot 3 = foot 4 =

no.1 = no.2 = no.3 = no.4 =

starboard aft foot (crossing of axis 3 and A) port aft foot (crossing of axis 3 and H) starboard fore foot (crossing of axis 6 and A) port fore foot (crossing of axis 6 and H)

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Trim = tetaroll = fipitch =

0,35 10,05 5,75

degree degree degree

trim angle roll angle pitch angle

Wm = Lm = Bm = Hm =

1385 30,00 18,75 12,80

t m m m

module weight module length module breadth module height

a= b= ag = bg =

18,750 17,160 10,050 10,280

m m m m

distance between module feet in transverse direction (m) distance between module feet in longitudinal direction (m) distance from aft starboard module foot to COG in transverse direction (m) distance from aft starboard module foot to COG in longitudinal direction (m)

Distribution factors module foot no.1 r1 = module foot no.2 r2 = module foot no.3 r3 = module foot no.4 r4 =

0,1860 0,2149 0,2780 0,3211


10,048

module foot no.1 r1xWm = module foot no.2 r2xWm = module foot no.3 r3xWm = module foot no.4 r4xWm = az0= az90= ax = ay = hg = tetarollacc = fipitchacc = Fevt hs= Fevt bs= Feht+ = Feht- = Fehl+ = Fehl- = rxx2 = It = Met = ryy2 = Il = Met = hwt = hwl = Fwt = Fwl =

254 293 379 438

graus t t t t

MÓDULO M06


0,00

module foot no.1 r1xWm module foot no.2 r2xWm module foot no.3 r3xWm module foot no.4 r4xWm

258 298 385 445

t t t t

Static vertical forces - pitch angle+trim =

6,103

graus


256 296 383 442

t t t t

= = = =

2,74 2,74 0,62 1,93 6,380 0,145 0,091

m/s2 m/s2 m/s2 m/s2 m rad/s2 rad/s2

heave acceleration in head seas acting on COG of module (m/s2) heave acceleration in beam seas acting on COG of module (m/s2) pitch and surge acceleration in head seas acting on COG of module (m/s2) roll and sway acceleration in beam seas acting on COG of module (m/s2) distance from top of grillage to COG of module (m) angular roll acceleration in beam seas (rad/s2) angular pitch acceleration in head seas (rad/s2)

387 387 577 442 276 194 54 74355 10781 111 153476 14028 7,76 6,41 288 180

t t t t t t 2 m 2 t.m kN.m 2 m 2 t.m kN.m m m kN kN

vertical load due to heave - hs = head seas vertical load due to heave - bs = beam seas transverse parallel to deck load due to weight&roll&sway&heave+ transverse paralel to deck load due to weight&roll&sway&heavelongitudinal parallel to deck load due to weight&pitch&surge&heave+ longitudinal parallel to deck load due to weight&pitch&surge&heavetransverse gyration radius of module transverse inertia of module moment due to roll longitudinal gyration radius of module longitudinal inertia of module moment due to pitch distance from top of grillage to COW of module for transverse wind (m) distance from top of grillage to COW of module for longitudinal wind (m) transverse wind load longitudinal wind load

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Dynamic vertical forces (heave, roll & sway): Component of heave+ for beam seas (Fevt bs) perpendicular to deck : module foot no.1 r1xFevt= 71 t module foot no.2 r2xFevt= 82 t module foot no.3 r3xFevt= 106 t module foot no.4 r4xFevt= 122 t 381 t Moment of horizontal load due to roll&sway&heave+ hgxFeht = Moment of horizontal load due to roll&sway&heave- hgxFeht = Moment due to roll Met = Moment due to transverse wind hwt x Fwt = Resultant dynamic vertical forces due to moments: module foot no.1 = 107 t (heave+) module foot no.2 = 107 t (heave+) module foot no.3 = 160 t (heave+) module foot no.4 = 160 t (heave+)

89 89 132 132

3681 2819 1099 228

t.m t.m t.m t.m


1760 1235 1430 117

t.m t.m t.m t.m



Dynamic vertical forces (heave, pitch & surge): Component of heave for head seas (Fevt hs) perpendicular to deck: module foot no.1 r1xFevt= 72 t module foot no.2 r2xFevt= 83 t module foot no.3 r3xFevt= 107 t module foot no.4 r4xFevt= 124 t Moment of horizontal load due to pitch&surge&heave+ hgxFehl = Moment of horizontal load due to pitch&surge&heave- hgxFehl = Moment due to pitch Mel = Moment due to longitudinal wind hwl x Fwl = Resultant dynamic vertical forces due to moments: module foot no.1 = 89 t (heave+) module foot no.2 = 103 t (heave+) module foot no.3 = 103 t (heave+) module foot no.4 = 89 t (heave+) r1 = r2 = r3 = r4 =

75 103 103 89


starboard aft foot (crossing of axis 6 and H) port aft foot (crossing of axis 6 and A) starboard fore foot (crossing of axis 3 and H) port fore foot (crossing of axis 3 and A)

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FOR ROLL: Total vertical reaction at module foot no.1:


F1+ = F1- =

F2+ = F2- =

432 94

t t

482 123

t t



F3+ = F3- =

F4+ = F4- =

645 141

t t

720 183

t t

FOR PITCH: Total vertical reaction at module foot no.1:


F1+ = F1- =

F2+ = F2- =

417 95

t t

482 110

t t



F3+ = F3- =

F4+ = F4- =

593 173

t t

655 229

t t

Dynamic transverse forces (Feht+Fwt)

606

t

Dynamic longitudinal forces (Fehl + Fwl) =

294

t

module module module module

243 243 363 363

t t t t

module module module module

136 158 136 158

t t t t

foot foot foot foot

no.1 = no.2 = no.3 = no.4 =

foot 1 = foot 2 = foot 3 = foot 4 =

foot no.1 = foot no.2 = foot no.3 = foot no.4 =

starboard aft foot (crossing of axis 6 and H) port aft foot (crossing of axis 6 and A) starboard fore foot (crossing of axis 3 and H) port fore foot (crossing of axis 3 and A)

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8. GRILLAGE & SEAFASTENING STRUCTURAL CHECK. 8.1. Grillage Design. 8.1.1. Grillage under axis 3. The figure below shows a top view of the grillage located under axis 3. Color key: Seafastening is in blue. Grillage is in black (existing beam) and red (new elements). Part of module that contacts grillage is in magenta.

All beams will be verified using formulations for simply supported beams in both ends. Only the components more loaded will be checked because all beams have the same cross section (including those less loaded).

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Grillage more loaded under axis 3: A. Existing beam (in black) (data from ref.[8]) Total Height ( cm ) Web Height ( cm ) Web Thickness ( cm ) Flange Width ( cm ) Flange Thickness ( cm ) Web Area ( cm2 ) Section modulus ( cm3 )

120,00 115,00 3,80 65,50 2,50 874,00 53738,92

Beam length ( cm ) Vertical force ( t ) Distance from support near side ( cm )

500,00 720,00 159,00

Reaction_side shell ( t ) Reaction_bulkhead ( t )

491,04 228,96

Maximum bending moment ( t*cm ) Maximum bending stress ( t/cm2 ) Utilization ratio Maximum shear force ( t ) Maximum shear stress ( t/cm2 ) Utilization ratio

78075,36 1,45 0,90 491,04 0,56 0,56

B. Support beam near side shell (in red) Total Height ( cm ) Web Height ( cm ) Web Thickness ( cm ) Flange Width ( cm ) Flange Thickness ( cm ) Web Area ( cm2 ) Section modulus ( cm3 )

120,00 115,00 2,50 50,00 2,50 287,50 19664,50

Beam length ( cm ) Vertical force ( t ) Distance from support aft ( cm )

250,00 491,04 125,00

Reaction_support_aft ( t ) Reaction_support_fwd ( t )

245,52 245,52


21974,04 1,12 0,77 245,52 0,85 0,85

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C. Support beam near longitudinal bulkhead (in red) Total Height ( cm ) Web Height ( cm ) Web Thickness ( cm ) Flange Width ( cm ) Flange Thickness ( cm ) Web Area ( cm2 ) Section modulus ( cm3 )

120,00 115,00 1,50 50,00 2,50 172,50 17552,17


250,00 228,96 125,00


114,48 114,48


10245,96 0,58 0,40 114,48 0,66 0,66

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8.1.2. Grillage under axis 6. The figure below shows a top view of the grillage located under axis 6. Color key: Seafastening is in blue. Grillage is in black (existing beam) and red (new elements). Part of module that contacts grillage is in magenta.

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Grillage more loaded under axis 6 A. Existing beam (in black) (data from ref.[8]) Total Height ( cm ) Web Height ( cm ) Web Thickness ( cm ) Flange Width ( cm ) Flange Thickness ( cm ) Web Area ( cm2 ) Section modulus ( cm3 )

120,00 115,00 3,80 65,50 2,50 874,00 53738,92

Beam length ( cm ) Vertical force ( t ) Distance from support near costado ( cm )

500,00 482,00 159,00

Reaction_side shell ( t ) Reaction_bulkhead ( t )

328,72 153,28


52267,12 0,97 0,67 328,72 0,38 0,38

B. Support beam near side shell Total Height ( cm ) Web Height ( cm ) Web Thickness ( cm ) Flange Width ( cm ) Flange Thickness ( cm ) Web Area ( cm2 ) Section modulus ( cm3 )

120,00 115,00 2,50 50,00 2,50 287,50 19664,50


250,00 328,72 91,00


209,07 119,66


19025,23 0,97 0,67 209,07 0,73 0,73

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C. Support beam near longitudinal bulkhead Total Height ( cm ) Web Height ( cm ) Web Thickness ( cm ) Flange Width ( cm ) Flange Thickness ( cm ) Web Area ( cm2 ) Section modulus ( cm3 ) Beam length ( cm ) Vertical force ( t ) Distance from support aft ( cm ) Reaction_support_aft ( t ) Reaction_support_fwd ( t ) Maximum bending moment ( t*cm ) Maximum bending stress ( t/cm2 ) Utilization ratio Maximum shear force ( t ) Maximum shear stress ( t/cm2 ) Utilization ratio

120,00 115,00 1,50 50,00 2,50 172,50 17552,17 250,00 153,28 91,00 97,48 55,79 8871,00 0,51 0,35 97,48 0,57 0,57

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8.2. Seafastening Design A. Plate welded on top of grillage to restrain transversally the module Maximum transversal force ( t )

363,00

Thickness of stoppers ( cm ) Width of stoppers ( cm ) Length of stoppers ( cm ) Size of weld ( cm )

2,50 100,00 90,00 1,90

Contact pressure ( t/cm2 ) Utilization ratio Shear stress in the weld ( t/cm2 ) Utilization ratio

1,45 0,67 0,97 0,97

B. Plates welded on top of grillage to restrain longitudinally the module Maximum longitudinal force ( t ) Thickness of stoppers ( cm ) Width of stoppers ( cm ) Length of stoppers ( cm ) Size of weld ( cm ) Contact pressure ( t/cm2 ) Utilization ratio Shear stress in the weld ( t/cm2 ) Utilization ratio

158,00 2,50 90,00 40,00 1,90 0,70 0,33 0,69 0,69

C. Plate welded on deck to restrain transversally the grillage Seafastening design ( stopers welded on deck to restrain the grillage ) Maximum transversal force ( t )

363,00

Thickness of stoppers ( cm ) Width of stoppers ( cm ) Length of stoppers ( cm ) Size of weld ( cm )

5,00 75,00 100,00 1,90

Contact pressure ( t/cm2 ) Utilization ratio Shear stress in the weld ( t/cm2 ) Utilization ratio

Two plates 2,5 cm fillet welded

1,29 0,60 0,98 0,98

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D. Tube 10” SCH 60 to restrain longitudinally the grillage Maximum axial force ( t )

165,89

Outer pipe diameter ( cm ) Inner pipe diameter ( cm ) Pipe length ( cm ) Pipe radius of gyration ( cm ) Area (cm2 ) Tension/compression stress ( t/cm2 ) Lambda ( kl/r ) Allowable compression stress ( ksi ) Allowable compression stress ( t/cm2 ) Utilization ratio

27,30 24,76 394,00 9,22 103,32 1,61 42,73 27,80 1,95 0,82

Weld design (connections tube x plates ) Maximum axial force ( t )

165,89

Length of each weld ( cm ) 50 Size of weld ( cm ) 1,20 Shear stress in the weld ( t/cm2 ) 0,98 Utilization ratio 0,98 Weld design (connection longitudinal plate x deck plate) Maximum longitudinal force ( t ) Length of each weld ( cm ) Size of weld ( cm ) Shear stress in the weld ( t/cm2 ) Utilization ratio

158 100 1,20 0,93 0,93

Weld design (connection transversal plate x deck plate ) Maximum vertical force ( t ) Length of each weld ( cm ) Size of weld ( cm ) Shear stress in the weld ( t/cm2 ) Utilization ratio

50,56 50 1,20 0,60 0,60

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8.3. Deck frame contact pressure check

Near side shell Length of effective contact: 1130 – 50 – 100 – 50 = 930 mm

Near side shell: Reaction_support ( t ) Thickness of beam under deck ( cm ) Length of bracket lower side ( cm ) Length of effective contact ( cm ) Thickness of longitudinal under deck ( cm ) Length of contact ( cm ) Pressure of contact ( t/cm2 ) Utilization ratio

Near long. bulkhead Length of effective contact: 800 – 75 – 100 = 625 mm

245,52 1,90 113,00 93,00 1,50 20,00 1,19 0,55

Near longitudinal bulkhead: Reaction_support ( t ) Thickness of beam under deck ( cm ) Length of bracket lower side ( cm ) Length of effective contact ( cm ) Thickness of longitudinal under deck ( cm ) Length of contact ( cm ) Pressure of contact ( t/cm2 ) Utilization ratio

114,48 1,00 80,00 62,50 1,50 20,00 1,24 0,57

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9. BARGE LOCAL STRUCTURAL ANALYSIS. 9.1. FEM Analysis. LOADS ON THE GRILLAGE SUPPORT The applied loads to grillage support are to be taken as the calculated forces in sea transport indicated in item 8.1.1 A. Loads used in the FEM analysis: Load on grillage support near the side shell

= 491 t

Load on grillage support near the longitudinal bulkhead

= 229 t

Total

= 720 t

Each grillage support (side shell and longitudinal bulkhead) will have two brackets, one in each both side, therefore the loads on each bracket will be:

Load on grillage support bracket near the side shell

= 245.5 t = 2408.36 kN

Load on grillage support bracket near the longitudinal bulkhead

= 114.5 t = 1123.25 kN

Those loads will be the loads applied on one barge frame. A Finite Element Model (FEM) was developed to analyze the barge structure comprising three frames spaces in the most loaded grillage, considering only the region between the longitudinal bulkhead and the side shell. To analyze the model it was used the software GIFTS V6.9.1a. MODEL DESCRIPTION The barge structure was represented by a finite element model composed of beam and plate elements. The model encompasses four frames, deck plate, side shell, bottom plate and longitudinal bulkhead. The figure 1 of Annex A shows an isometric overall view of the element subdivision used in the model. Model main dimensions: Width (X) = 601 cm;

Height (Y) = 500 cm;

Length (Z) = 750 cm

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The figure 2 of Annex A shows the model of one transverse frame. The origin of the coordinate axis was taken in the bottom level (Y=0), at the cross point of the longitudinal bulkhead bulkhead with the first frame (X=0 and Z=0). The drawing of ref.[2] shows the dimensions of t he barge midship section. The program GIFTS classify the various types of structural components in dimension group, calling then “thickness”. The following "thicknesses" were used in the GIFTS model to represent the barge scantlings (see Table II of Annex A):

a) Plate "thickness":

a.1) thk 1

7.0mm

Longitudinal bulkhead;

a.2) thk 2

10.0mm

Deck and bottom frame webs;

a.3) thk 3

12mm

Side shell frame & longitudinal bhd. webs;

a.4) thk 4

12.7mm

Side shell;

a.5) thk 5

19mm

Deck plate;

a.6) thk 15 15mm

Deck frame web reinforcement near side shell (not used);

a.7) thk 16 19mm

Reinforcement in upper part of side shell frame;

b) "thickness" of beam elements:

b.1) thk 6

Bar 200x16mm (ZA=-0.8;YA=0)

Deck and bottom frame flanges;

b.2) thk 7

Bar 250x16mm (ZA=-0.8;YA=0)

Side shell frame & long. bhd. flanges;

b.3) thk 8

Angle L bar 101x101x12.7mm 101x101x12.7mm

Inclined angles (ZA=-0.635;YA=10.1) (ZA=-0.635;YA=10.1)

b.4) thk 9

Angle L bar 203x203x12mm

Vertical angle (ZA=-0.6;YA=20.3)

b.5) thk 10 Bar 200x15mm (ZA=0;YA=-10)

Bottom longitudinals & Side shell (two lower long.);

b.6) thk 11 Bar 150x16mm (ZA=0;YA=-7.5)

Long. bhd. (two lower long.);

b.7) thk 12 Bar 160x15mm (ZA=0;YA=-8)

Side shell (five upper long.);

b.8) thk 13 Bar 130x15mm (ZA=0;YA=-6.5)

Deck longitudinals;

b.9) thk 14 Bar 120x15mm (ZA=0;YA=-6)

Long. bhd. (five upper long.);

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MATERIAL

The barge material was assumed to be common steel with yielding stress ( y) = 235 N/mm 2 (GIFTS identification number = 1) according to ref.[5]. See Table II in Annex A. DESIGN CRITERIA

According to ref.[6], for stress based on Von Mises criteria calculated by FEM using combined loads, von Mises stress is not to exceed ( y/1.11) = 0.90( y); conservatively it is used: σVON MISES ≤ 0.80 ( y) GIFTS gives von Mises results in terms of % of the material

y.



BOUNDARY CONDITIONS

To transfer the shear forces through the longitudinal bulkhead and the side shell, the nodes at the border of the model, in X=0 and X=601cm, Y from 0 to 500cm, Z=0 and Z=750cm, all have vertical displacement = 0 (displacement Y = 0).

To represent the bottom and deck stiffness, the displacement in X and Z direction of the nodes at the deck and at bottom borders were made = 0 (in Z = 0 and Z = 750 cm, X from 0 to 601 cm, Y = 0 and Y = 500 cm).

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LOADING THE MODEL

Hydrostatic loads:

The barge draft during the transport will be 2,70m. Therefore the hydrostatic pressure in the bottom will be 2.715 N/cm 2 ((1.025 x 2.70 / 10) x 9.81), uniformly distributed on the full area. Each bottom node had its hydrostatic load in function of its adjacent area. To represent the contribution of the hydrostatic pressure acting in the central tank bottom frames, the following forces were applied to the nodes correspondents to the bottom frame, at the longitudinal bulkhead: 250 x (549 – (61/2)) x 2.715 = 351932 kg = 3452.452 kN The hydrostatic pressure acting on the side shell is 2.715 N/cm 2 and zero at level 270 cm, varying linearly between them. The nodes were loaded accordingly.

Grillage loads:

Figures 3 of Annex A show the loads acting on the nodes near the side shell of the frames at Z =250 cm and Z =500 cm, respectively. These nodes are the most loaded ones (2408.36 kN spread on 113 cm = 21.3129 kN/cm). The nodes near the longitudinal bulkhead were also loaded with their correspondent loads, totaling 114.5 t (1123.25 kN spread on 90 cm = 12.4806 kN/cm).

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The load values of Figure 3 of Annex A (nodes near side shell) are shown in t he following table: Node No.

Load (N)

731 (and 1231)

138540

3028 (and 3128)

277070

3012 (and 3112)

277070

3025 (and 3125)

277070

730 (and 1230)

301000

3023 (and 3123)

325030

3002 (and 3102)

325030

3021 (and 3121)

325030

729 (and 1229)

162520

TOTAL =

2408360 (245.5 t)

The load values for the nodes near the longitudinal bulkhead are: Node No.

Load (N)

721 (and 1221)

380580

722 (and 1222)

561460

732 (and 1232)

181030

TOTAL =

1123070 (114.5 t)

Figure 4 of Annex A shows the elements numbering near the side shell, under the grillage bracket support.

The element close to the node 731 (or 1231), near the side shell, was removed to represent more accurately the reality (there is an empty space of 100mm near this area, see ref.[2]).

To obtain von Mises stress under 80% in all model elements it was necessary to provide the following reinforcements under the deck, near the side shell, as shown in Figure 5 of Annex A:

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- To install vertical bars of 200 x 16 mm (Thick. No. 6) in X = 549 cm and X = 575 cm, the first going from the deck down to Y = 375 cm and the second going down to Y = 470 cm; - To increase to 19mm (Thick. No.15) the thickness of the frame web plate under the grillage bracket support near the side shell; - To extend the flange of the deck frame until the side shell (Thick. No.6). To extend the flange of the side shell frame until the deck (Thick. No.7).

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RESULTS

The results are for the reinforced structure, as shown in Figures 2 and 5 of Annex A. The reinforcements are two vertical bars welded to the web frame in the indicated positions, the increase of web plate thickness and the extension of the flanges of deck and side shell frames.

The extremes values obtained from the FEM analysis is shown below:

JOB:p56_17

7-OCT- 9

LOADING CASE 1

17:42:33

PAGE 1

MAXIMUM RESULTANT DEFLECTION(S) FOR MODEL. MAXIMUM TRANSLATIONAL DEFLECTION = 6.3508E-01 AT POINT 1257 MAXIMUM ROTATIONAL DEFLECTION = 1.2051E-02 AT POINT 1170 EXTREMUM FOR PLOT: VON MISES MINIMUM STRESS = 8.3379E+00% AT ELEMENT 1775 MAXIMUM STRESS = 7.4573E+01% AT ELEMENT 1783

The element 1783 (= to the no. 1786) is the lower part of the bar stiffener added to extend the flange of the side shell frame up to the deck, as can be seen in Figure 4 of Annex A. The von Mises stress in this element is 74.57% of y (<0.80y).

The results for other elements in the upper part of the frame, near the side shell, are shown in Figures 6 and in the list of Table I of Annex A.

Figure 7 of Annex A shows the von Mises stresses distribution throughout a transverse frame, it can be seen that the values are low outside the upper corner area near the side shell.

REINFORCEMENTS

Remove the plate of 10mm and 12mm between level Y = 4375mm and Y = 5000mm, and between X = 4880mm and x = 6010mm, and install a plate of 19mm. The plate change must be made in all frames under grillage supports near the side shell.

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Vertical bar of 100 x 16mm welded both sides of deck frame web near the side shell, just under the first deck longitudinal, going down to the level 3750mm (from base line). The reinforcements must be placed in all frames under grillage supports near the side shell.

Vertical bar of 100 x 16mm welded both sides of deck frame web near the side shell, located 260mm from the side shell, going from the deck down to the level 4700mm (from base line). The reinforcements must be placed in all frames under grillage supports near the side shell.

To improve the connection between deck frames and side shell frames, and additional reinforcement is indicated: To extend the flange of the deck frames up to the side shell and also up to the longitudinal bulkhead; to extend the vertical frames flange up to the deck (both near the side shell and the longitudinal bulkhead).

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9.2. Local Buckling Check of Bulkhead and Deck Frame Web. The procedure of ref.[13] will be used to verify the buckling resistance of bulkhead and deck frame panels. The usage factor of ref.[14] will be used. 9.2.1. Axis 06 of Modules 05 and 06 P = 482 t

load on the grillage due to module foot.

Load on grillage support near side shell: 482 x 3.41/5.0 = 329 t Load on transverse bulkhead (FR4 or FR28): Load on frame (FR5 or FR27):

329 x 0.91/2.5 = 120 t 329 x 1.59/2.5 = 209 t

Load on grillage support near longitudinal bulkhead: 482 x 1.59/5.0 = 153 t Load on transverse bulkhead (FR4 or FR28): Load on frame (FR5 or FR27):

153 x 0.91/2.5 = 56 t 153 x 1.59/2.5 = 97 t

Bulkheads FR4 and FR28: Near side shell: 1st row: Compression stress:

σCOMP = 120 / (113 x 0.75) = 1.416 t/cm 2

The shear stress can be evaluated supposing the entire shear passing to side shell through the bulkhead full height: Shear stress:

τ = 120 / (500 x 0.75) = 0.320 t/cm 2

Panels dimensions:

1st panel 2nd panel

Plate Thickness 0.75 cm 0.75 cm

Width (cm) 52 61

Height (cm) 62.5 62.5

Vertical stiffeners 200 x 15mm 1st panel:

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According to ref.[13] the usage factor is η =1.146 > 0.85 and so the plate thickness of the panel must be increased. 2nd panel: According to ref.[13] the usage factor is η =1.488 > 0.85 and so the plate thickness of the panel must be increased. Increasing the thickness of both panels to 10mm: Compression stress: Conservatively using the same shear stress

σCOMP = 120 / (113 x 1.0) = 1.062 t/cm 2 τ = 0.320 t/cm 2

1st panel: The usage factor according to ref.[13] is now:

η = 0.648 < 0.85.

OK

η = 0.768 < 0.85.

OK

2nd panel: The usage factor according to ref.[13] is now: 2nd row: Considering load spreading in 30 degrees: Compression stress:

σCOMP = 120 / ((113+2 x 36.1) x 0.75) = 0.864 t/cm 2

Note: 2 x 36.1 to take into consideration the load spreading in the side shell. Shear stress:

τ = 120 / (500 x 0.75) = 0.320 t/cm 2 (conservatively)

Same panels dimensions. 1st panel: According to ref.[13] the usage factor is η = 0.742 < 0.85 2nd panel: According to ref.[13] the usage factor is η = 0.962 > 0.85. Increasing the thickness of both panels to 10mm: Compression stress:

σCOMP = 120 / ((113+2 x 36.1) x 1.0) = 0.648 t/cm 2

Conservatively using the same shear stress

τ = 0.320 t/cm 2

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The usage factor according to ref.[13] is now:

η = 0.518 < 0.85.

OK

All 2nd row will be 10mm thick plate. 3rd row: σCOMP = 120 / ((113+ 2 x 36.1+2 x 36.1) x 0.75) = 0.620 t/cm 2 Conservatively using the same shear stress τ = 0.320 t/cm 2 1st panel: According to ref.[13] the usage factor is η = 0.572 < 0.85

OK

2nd panel: According to ref.[13] the usage factor is η = 0.738 < 0.85

OK.

Near longitudinal BHD: 1st row: Compression stress:

σCOMP = 56 / (80 x 0.75) = 0.933 t/cm 2

The shear stress can be evaluated supposing the entire shear passing to side shell through the bulkhead full height: Shear stress:

τ = 56 / (500 x 0.75) = 0.149 t/cm 2

Panels dimensions:

1st panel 2nd panel


Width (cm) 61 61

Height (cm) 62.5 62.5

1st and 2nd panels: According to ref.[13] the usage factor is η =0.954 (> 0.85) and so the plate thickness of the panels must be increased. Increasing the thickness of both panels to 10mm: Compression stress: Conservatively using the same shear stress

σCOMP = 56 / (80 x 1.0) = 0.700 t/cm 2 τ = 0.149 t/cm 2

The usage factor for both panels according to ref.[13] is now: η = 0.485 < 0.85.

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2nd row: Considering load spreading in 30 degrees: Compression stress:

σCOMP = 56 / ((80+36.1) x 0.75) = 0.643 t/cm 2

Shear stress:

τ = 0.149 t/cm2 (conservatively)

Same panels dimensions. 1st and 2nd panels: According to ref.[13] the usage factor is η = 0.675 < 0.85

OK.

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9.2.2. Axis 03 of Modules 05 and 06 P = 720 t

load on the grillage due to module foot.

Load on grillage support near side shell: 720 x 3.41/5.0 = 491 t Load on frame:

491 x 0.5 = 245.5 t

Load on grillage support near longitudinal bulkhead: 720 x 1.59/5.0 = 229 t Load on frame:

229 x 0.5 = 114.5 t

Frames: Near side shell: 1st row: Compression stress:

σCOMP = 245.5 / ((113-5-10-5) x 1.9 + 20 x 1.5) = 1.188 t/cm 2

The shear stress can be evaluated supposing the entire shear passing to side shell through the side shell web frame full height: Shear stress:

τ = 245.5 / (500 x 1.2) = 0.409 t/cm 2

It will be examined the web panel of the deck frame limited by the two last deck longitudinal near the side shell and the extended flange of deck frame (using the GIFTS coordinates, the panel is limited by X = 488cm and X = 549cm , and by Y = 437.5cm and Y = 500cm). According to Table I of Annex A, the maximum shear stress of this panel occurs in element 1708 and is 3537 N/mm 2 = 0.361 t/cm2. Conservatively, the buckling check will use shear stress of 0.409 t/cm 2. Panel dimensions:

1st panel

Plate Thickness 1.9 cm

Width (cm) 61

Height (cm) 62.5

According to ref.[13] the usage factor is η = 0.605 < 0.85.

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2nd row: The 2nd row is composed of several elements as can be seen in Figure 4 of Annex A (elements from 1734 to 1739 of Z = 250). The stresses in the elements are shown in Table III of Annex A. Conservatively, taking the compressive stress and the shear stress of the most loaded elements to represent the load stress status of the panel: 1st panel (away from the side shell – elements 1736, 1737 & 1739): σCOMP (1736) = 7817 N/cm 2 = 0.797 t/cm2 τ (1737)= 1046 N/cm 2 = 0.107 t/cm2 2nd panel (near side shell – elements 1734, 1735 & 1738): σCOMP (1735) = 7374 N/cm 2 = 0.752 t/cm2 τ (1734)= 4470 N/cm 2 = 0.456 t/cm2 Panels dimensions:

1st panel 2nd panel


Width (cm) 61 52

Height (cm) 62.5 62.5

1st panel: According to ref.[13] the usage factor is η = 0.441 < 0.85

OK.

2nd panel: According to ref.[13] the usage factor is η = 0.500 < 0.85

OK.

3rd row: The 3rd row is composed of elements nos. 201 and 197 (see Figure 4 of Annex A). From Table III of Annex A, the stresses in these elements are: σCOMP (201) = 6971 N/cm2 and σCOMP (197) = 4683 N/cm 2 τ (201)= 559.7 N/cm 2 and τ (197)= 2785 N/cm 2 Conservatively taking the greatest values to represent the stresses in the panel of 1130 x 625mm: σCOMP = 6971 N/cm2 = 0.710 t/cm2 τ = 2785 N/cm2 = 0.284 t/cm2

Panel dimensions:

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1st panel


Width (cm) 113

According to ref.[13] the usage factor is η = 0.706 < 0.85

Height (cm) 62.5 OK.

Near longitudinal BHD: 1st row: Compression stress:

σCOMP = 114.5 / ((80-10-7.5) x 1.0+1.5 x 20) = 1.238 t/cm 2

The shear stress can be evaluated supposing the entire shear passing to longitudinal bulkhead through the frame full height: Shear stress: τ = 114.5 / (500 x 1.2) = 0.190 t/cm 2 (the web of the longitudinal bulkhead frame has 12mm thickness) Panel dimensions: Plate Width Thickness (cm) st 1 panel 1.0 cm/1.2cm 62.5 Note: usage factor calculated with thickness of 10mm.

Height (cm) 90.0

According to ref.[13] the usage factor is η = 1.291 > 0.85. It will be placed a vertical bar of 15mm thickness under de last deck longitudinal to reduce the panel dimension from 90.0mm to 61mm. Panel dimensions: Plate Width Thickness (cm) st 1 panel 1.0 cm/1.2cm 61.0 Note: usage factor calculated with thickness of 10mm.

Height (cm) 62.5

According to ref.[13] the usage factor is η = 0.836 < 0.85. 2nd row: Compression stress:

σCOMP = 114.5 / ((80-10-7.5) x 1.0+1.5 x 20 + 36.1) = 0.890 t/cm 2

Shear stress: τ = 0.190 t/cm2 (conservatively) Plate thickness = 1.2 cm and panel dimensions = 90 x 62.5cm According to ref.[13] the usage factor is η = 0.708 < 0.85 Side Shell:

OK.

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The side shell panel with the dimensions indicated below will be checked to buckling. The stresses acting on the panel will be the primary stresses due to the barge bending moment (4918 t.m) and shear force (484t) calculated in item 10 and the compressive and shear stresses determined by the FEM of item 9.1. Conservatively it will be used both values acting in the same barge cross section (actually the maximum values of moment and shear force does not occur in the same section). Primary stresses: Inertia moment of barge cross section (conservatively only plates are considered): 2 x [(1,27x5003)/12) + (0,7x5003)/12] + (2300/12) x (1,93 + 1,273) + 2300 x 2502 x (1.9 + 1.27) = 41041668 + 1707 + 455687500 = 496730875 cm4

Section modulus :

496730875 / 250 = 1986924 cm3

Deck compression stress deck: (4918 x 100) / 1986924 = 0.248 t/cm2

Compression stress on the 1º side shell longitudinal stiffener : (2500-625)x0.248/2500=0.186 t/cm2 Panel shear stress = 484 / (2 x 500 x 1.27 + 2 x 500 x 0.7) = 484 / 1970 = 0.246 t/cm 2 Secondary stresses on panel: The secondary stresses on upper side shell panel will be taken from FEM of item 9.1. The upper panel model near Z=250 is composed of several elements as shown in Figure 10 of Annex A (elements from 1631 to 1636 and 644, 648, 550, 572. The stresses in the elements are shown in Table III of Annex A. Conservatively, taking the compressive stress and the shear stress of the most loaded elements to represent the load stress status of the panel: σCOMP (1634) = 4934 N/cm 2 = 0.503 t/cm2 τ (1633)= 5542 N/cm 2 = 0.565 t/cm2 Combination of primary & secondary stresses: Compression stress (longitudinal to panel) = 0,248 t/cm 2 (deck level) 0,186 t/cm2 (1st long. level) Compression stress (transverse to panel) = 0.503 t/cm 2 Shear stress = 0.246 + 0.565 = 0.811 t/cm 2

1st panel


Width (cm) 250

According to ref.[13] the usage factor is η = 0.709 < 0.85

Height (cm) 62.5 OK.

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10. BARGE LONGITUDINAL STRENGTH CHECK. Loads were applied as described below: Barge light weight plus grillage distributed linearly along barge length. Ballast in tank distributed linearly along tank length. Buoyancy distributed in a trapezoidal shape along wet length Concentrated reactions of embarked modules in t he supporting points. Reactions of module 05 on the deck of the barge R1 = 381.35 t

at X = 47.5 m from stern

R2 = 381.35 t


R3 = 353.17 t


R4 = 202.13 t


Reactions of module 06 on the deck of the barge R5 = 400.73 t


R6 = 400.73 t


R7 = 371.13 t


R8 = 222.41 t


Load calculations

At X1 (t/m)

At X2 (t/m)

Barge weight&grillage Buoyancy Ballast peak aft Ballast tanks 4 Ballast tanks 3 Ballast tanks 2 Ballast tanks 1 Ballast peak forward

-16,33 0 -21,14 -2,41 -2,41 -2,41 -2,41 -0,98

-16,33 69,10 -21,14 -2,41 -2,41 -2,41 -2,41 -0,98

At X3 (t/m)

58,20

At X4 (t/m)

0

X1 (m)

X2 (m)

0,00 1,38 1,70 7,50 22,50 37,50 52,50 67,50

75,00 7,00 7,50 22,50 37,50 52,50 67,50 73,30

X3 (m)

X4 (m)

68,00

72,61

Note: X is measured from barge stern

Resulting maximum shear force = 484.86 t at 10.0 m from stern Resulting maximum bending moment = -4918.05 t.m at 37.20 m from stern Complete analysis results are listed in Annex B. Ref.[9] indicates SWBM at sea of 14000 t.m and minimum shear of 770 t.

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SHEAR FORCE DIAGRAMM

BENDING MOMENT DIAGRAMM

Reactions at Supports

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11. BARGE STABILITY CHECK.

11.1. Intact Stability Barge tanks:

Tanks Capacity (m3)

Volume Used (m3)

% full

144,2 144,2 263,7 462 462 843 462 462 843 462 462 843 462 462 843 144,2 144,2 263,7

1,4 1,4 2,6 9,2 9,2 16,9 9,2 9,2 16,9 9,2 9,2 16,9 9,2 9,2 16,9 115,6 1,4 2,6 266,5

1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 80,133 1 1

Weight (t)

VCG (m)

Moment (t.m)

Barge LW Grillage & seafast. Ballast Total barge

1105 120 273 1498

2,80 5,63 1,24 2,74

3094 675 339 4108

Module 05 Module 06 Displacement

1318 1386 4202

12,79 12,58 9,14

16857 17436 38401

KG (m) Corrected KG (m) KM (m) GM (m) Draft (m)

9,14 9,18 18,14 8,96 2,70

Peak FW S Peak FW P Peak FW C 1S 1P 1C 2S 2P 2C 3S 3P 3C 4S 4P 4C Peak AF S Peak AF P Peak AF C Total ballast

VCG

FSC

(m)

Vertical moment (m,t)

0,05 0,05 0,05 0,05 0,05 0,05 0,05 0,05 0,05 0,05 0,05 0,05 0,05 0,05 0,05 2,8 0,05 0,05 1,242323

0,07 0,07 0,13 0,46 0,46 0,84 0,46 0,46 0,84 0,46 0,46 0,84 0,46 0,46 0,84 323,55 0,07 0,13 331,09

0,000 0,000 0,000 0,001 0,001 0,001 0,001 0,001 0,001 0,001 0,001 0,001 0,001 0,001 0,001 0,031 0,000 0,000 0,042

(m)

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Stability range (degrees) Maximum GZ (m) Wind heeling arm (m) Angle of static wind heel (degrees) Angle at 2nd interception (degrees) Area under GZ curve (m*radian) Area under wind arm curve (m*radian)

41,1 2,57 0,34 1,20 39,30 1,11 0,21

( from intact stability curve )

( from intact stability curve ) ( from intact stability curve ) >>>>> 1,4 x 0,21 ( from intact stability curve )

OK

From Cross Curves of Stability Θ (graus)

KZ (m)

KGsen(Θ) (m)

GZ (m)

10 20 30 45 60

3,50 5,70 6,17 5,89 5,13

1,60 3,14 4,60 6,50 7,96

1,90 2,56 1,57 -0,62 -2,83

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11.2. Damaged Stability Barge tanks:

Tanks Capacity (m3)

Volume Used (m3)

% full

144,2 144,2 263,7 462 462 843 462 462 843 462 462 843 462 462 843 144,2 144,2 263,7

1,4 1,4 2,6 452,8 9,2 16,9 9,2 9,2 16,9 9,2 9,2 16,9 9,2 9,2 16,9 115,6 1,4 2,6 710,0

1 1 1 98 2 2 2 2 2 2 2 2 2 2 2 80,133 1 1

Weight (t)

VCG (m)

Moment (t.m)

Barge LW Grillage & seafast. Ballast Total barge

1105 120 728 1953

2,80 5,63 1,24 2,10

3094 675 339 4108

Module 05 Module 06 Displacement

1318 1386 4657

12,79 12,58 8,25

16857 17436 38401

KG (m) Corrected KG (m) KM (m) GM (m) Draft (m)

8,25 8,29 16,85 8,57 2,97

Peak FW S Peak FW P Peak FW C 1S (Damaged tank) 1P 1C 2S 2P 2C 3S 3P 3C 4S 4P 4C Peak AF S Peak AF P Peak AF C Total ballast

VCG

FSC

(m)

Vertical moment (m,t)

0,05 0,05 0,05 2,5 0,05 0,05 0,05 0,05 0,05 0,05 0,05 0,05 0,05 0,05 0,05 2,8 0,05 0,05 2,10

0,07 0,07 0,13 1160,20 0,46 0,84 0,46 0,46 0,84 0,46 0,46 0,84 0,46 0,46 0,84 323,55 0,07 0,13 1490,83

0,000 0,000 0,000 0,001 0,001 0,001 0,001 0,001 0,001 0,001 0,001 0,001 0,001 0,001 0,001 0,031 0,000 0,000 0,042

(m)

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Heeling moment due to flooded tank (t.m) Heeling arm due to flooded tank (m) Wind heeling arm (m) Equilibrium angle after damage (degrees) Angle at 2nd interception (degre es) Area under GZ curve (m*radian) Area under wind arm curve (m*radian)

3944,67 0,85 0,08 5,03 ( from stability curve with damage ) 32,87 ( from stability curve with damage ) 0,46 >>>>>>> 1,4 x 0,05 OK 0,05

From Cross Curves of Stability

After damage

Θ (graus)

KZ (m)

Gsen(Θ (m)

GZ (m)

10 20 30 45 60

3,12 5,21 5,59 5,40 4,76

1,49 2,93 4,28 6,06 7,42

1,63 2,28 1,31 -0,66 -2,66

GZ (m) 5,03 10 20 30 32,87

0,79 1,43 0,46 0,08

Area under GZ (m*rad) 0,03 0,19 0,17 0,07

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11.3. Wind Forces Barge Data Barge length (m) Barge depth (m) Barge width (m) Barge draft (m)

77 5 22,4 2,64

Modules data Mod 05 VCOW (m) Area_T (m2) Area_L (m2)

9,99 240 384

Air density (kg/m3)

1,29

Mod 06 9,99 240 384

(Center of wind pressure above sea level) (Transversal area exposed to wind) (Longitudinal area exposed to wind)

For intact stability: Wind speed at 10 m (m/s) Item Module 05 Module 06 Barge Barge Displacement (t) Transversal moment (t.m) Heeling arm (m)

50,00 Area_T Area_L (m2) (m2) 240 384 240 384 53,0 182

VCOW (m) 9,99 9,99 1,18

Speed (m/s) 50,00 50,00 41,26

Pressure (kg/m2) 156,08 156,08 106,29

Shape Coef. 1 1 1

Force_T Mom._T (t) (t.m) 59,9 678 59,9 678 19,4 48

VCOW (m) 9,99 9,99 1,18

Speed (m/s) 25,00 25,00 20,63

Pressure (kg/m2) 39,02 39,02 26,57

Shape Coef. 1 1 1

Force_T Mom._T (t) (t.m) 15,0 169 15,0 169 4,8 12

4131 1404 0,34

For damage stability: Wind speed at 10 m (m/s) Item Module 05 Module 06 Barge Barge Displacement (t) Transversal moment (t.m) Heeling arm (m)

25,00 Area_T Area_L (m2) (m2) 240 384 240 384 53,0 182 4131 351 0,08

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ANNEX A

FEM ANALYSIS FIGURES and TABLES

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Figure 1 – FEM of three f rame spaces, between longitudinal bulkhead and side shell

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Figure 2 – FEM of one frame (X = 0 is at the long. BHD; X = 601 cm is at the side shell); (Y = 0 is at the bottom; Y = 500 cm is at the deck).

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Figure 3 – Loads on the nodes of the transverse frame, near the side shell (Z = 250 cm and Z = 500 cm).

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Figure 4 - Elements numbering at Z = 250 cm and at Z = 500 cm, near the side shell and close to the deck

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Figure 5 – Reinforcements installed under the deck, near the side shell, in Z =250 cm and Z = 500 cm.

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Figure 6 - Von Mises stress resultant from the FEM analysis.

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Figure 7 – Distribution of von Mises stresses throughout the transverse frame

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Figure 8 - Elements material and thickness at Z = 250 cm and at Z = 500 cm, near the side shell and close to the deck

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Figure 9 - Elements material and thickness in the side shell near frame

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Figure 10 – Nodes and elements numbering in the side shell near frame Z = 250

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TABLE I FEM Results for Elements in the Upper Part of Frames, Near the Side Shell

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Note: T12 shear stress

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TABLE II Material and Thickness identification

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TABLE III FEM Results for Elements in the Middle Part of Side Shell Frame and in Upper Part of Side Shell Plating

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ANNEX B

BARGE LONGITUDINAL STRENGTH CHECK RESULTS

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Station cm 0 57,692 115,385 173,077 230,769 288,462 346,154 403,846 461,538 519,231 576,923 634,615 692,308 750 750 800 850 900 950 1000 1000 1060 1120 1180 1240 1300 1360 1420 1480 1540 1600 1660 1720 1780 1840 1900 1960 2020 2080 2140 2200 2260 2320 2380 2440 2500

V2 Ton 0,2726 9,691 19,1094 28,4009 45,4497 58,4098 67,2811 72,0636 72,7574 69,3625 61,8787 50,3063 34,645 16,4529 238,8629 213,7476 188,6769 163,6509 138,6696 113,7329 484,8629 454,9979 425,1972 395,4609 365,7888 336,1811 306,6378 277,1587 247,744 218,3936 189,1075 159,8858 130,7284 101,6353 72,6066 43,6421 14,742 -14,0937 -42,8652 -71,5723 -100,2151 -128,7935 -157,3077 -185,7575 -214,1429 -242,4641

M3 Ton-cm -5,36E-10 -287,41 -1118,193 -2484,128 -4634,093 -7649,698 -11295,055 -15334,272 -19531,461 -23650,731 -27456,193 -30711,956 -33182,132 -34656,794 -34656,794 -45971,869 -56032,295 -64840,304 -72398,13 -78708,007 -78708,007 -106903,511 -133309,044 -157928,465 -180765,634 -201824,412 -221108,657 -238622,229 -254368,988 -268352,794 -280577,506 -291046,984 -299765,088 -306735,677 -311962,611 -315449,75 -317200,953 -317220,08 -315510,991 -312077,545 -306923,602 -300053,022 -291469,664 -281177,388 -269180,054 -255481,521

Station cm 2500 2550 2600 2650 2700 2750 2750 2810,606 2871,212 2931,818 2992,424 3053,03 3113,636 3174,242 3234,848 3295,455 3356,061 3416,667 3477,273 3537,879 3598,485 3659,091 3719,697 3780,303 3840,909 3901,515 3962,121 4022,727 4083,333 4143,939 4204,545 4265,152 4325,758 4386,364 4446,97 4507,576 4568,182 4628,788 4689,394 4750 4750 4800 4850 4900 4950 5000

V2 Ton 158,2659 134,7141 111,2069 87,7445 64,3267 40,9535 441,6835 413,4124 385,2068 357,0669 328,9927 300,984 273,041 245,1637 217,3519 189,6058 161,9254 134,3105 106,7613 79,2778 51,8598 24,5075 -2,7791 -30,0002 -57,1556 -84,2453 -111,2694 -138,2279 -165,1208 -191,948 -218,7096 -245,4056 -272,0359 -298,6006 -325,0996 -351,5331 -377,9008 -404,203 -430,4395 -456,6104 -75,2604 -96,802 -118,2989 -139,7511 -161,1587 -182,5215

M3 Ton-cm -255481,5 -262805,8 -268953,7 -273927,3 -277728,9 -280360,7 -280360,7 -306272,4 -330472,6 -352965,4 -373754,8 -392844,6 -410239 -425941,8 -439957,1 -452288,9 -462941 -471917,5 -479222,4 -484859,6 -488833,1 -491147 -491805,1 -490811,4 -488170 -483884,8 -477959,8 -470398,9 -461206,2 -450385,6 -437941,1 -423876,7 -408196,3 -390904 -372003,6 -351499,3 -329394,9 -305694,4 -280401,9 -253521,3 -253521,3 -249219,5 -243841,8 -237390,4 -229867,4 -221275,3

Station cm 5000 5060 5120 5180 5240 5300 5360 5420 5480 5540 5600 5660 5720 5780 5840 5900 5960 6020 6080 6140 6200 6260 6320 6380 6440 6500 6500 6550 6600 6650 6700 6750 6750 6807,692 6865,385 6923,077 6980,769 7038,462 7096,154 7153,846 7211,538 7269,231 7326,923 7384,615 7442,308 7500

V2 Ton 198,8285 173,252 147,7398 122,292 96,9085 71,5893 46,3344 21,1439 -3,9823 -29,0441 -54,0417 -78,9749 -103,8438 -128,6483 -153,3886 -178,0645 -202,676 -227,2233 -251,7062 -276,1248 -300,4791 -324,769 -348,9946 -373,1559 -397,2528 -421,2854 -68,1154 -88,0935 -108,0269 -127,9156 -147,7596 -167,5589 34,5711 10,993 -9,9377 -26,6645 -39,1875 -47,5066 -51,6219 -51,5334 -47,241 -38,7896 -28,8058 -19,3572 -9,9388 -0,5203

M3 Ton-cm -221275,3 -232437,3 -242066,8 -250167,4 -256743,1 -261797,7 -265335,1 -267359,1 -267873,7 -266882,5 -264389,6 -260398,8 -254913,9 -247938,9 -239477,4 -229533,5 -218111 -205213,7 -190845,5 -175010,2 -157711,8 -138954 -118740,8 -97075,96 -73963,38 -49406,91 -49406,91 -45501,5 -40598,31 -34699,56 -27807,49 -19924,34 -19924,34 -21237,44 -21247,67 -20171,63 -18251,84 -15730,84 -12851,15 -9855,307 -6985,836 -4485,142 -2535,274 -1146,78 -301,704 -3,66E-08

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ANNEX C

LETTER FROM ABS INDICATING THE SWBM AND SHEAR

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Grillage&Seafastening_DesignExample

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