Proceedings of the Eleventh (2001) blternational Offshore and Polar Engineering Conference Stavanger, Norway, June 17-22, 2001 Copyright 2001 by Tile International Society of Offshore and Polar Engineers ISBN 1-880653-51-6 (SeO; ISBN 1-880653-52-4 (VoL I); ISSN 1098-6189 (SeO

Structural Design of the Truss Spar- An Overview

J. Wang, S. Berg, Y.H. Luo, A. Sablok and L. Finn CSO Aker Engineering, Inc.

Houston, TX, USA

ABSTRACT

This paper provides an overview of the Truss Spar structural design with emphasis on the design and analysis of the truss structure, based on firsthand design experiences. The structural design criteria and main loading conditions are outlined. Discussions are focused on the methodologies and procedures using random wind and wave time domain analyses. In particular, the paper covers the truss in-place strength analysis, truss wet tow transportation analysis, upending analysis, and truss fatigue analysis. Structural analyses of the truss critical connections and the heave plates are also discussed. Technical issues related to structural and hydrodynamic modeling, time domain motion and environmental load simulation, structural load mapping, as well as computer software requirements are addressed. Analysis results are presented to illustrate the various loading conditions and the structural behavior for a generic Truss Spar design.

KEYWORDS: Truss Spar, time domain, structural strength, fatigue

INTRODUCTION

The Spar platform has become one of the most attractive development concepts as the offshore industry moves towards deep and ultra-deep water frontiers for new oil & gas discovery and production. It can be designed for drilling/work-over, production and storage of oil, and is well suited for water depths from 500 to 3000 meters, and above. Since the first Spar platform was installed in 1996, the Spar technology has evolved from the first generation Classic Spar design to the second generation Truss Spar design. The first Truss Spar will be installed in the fall of 2001 in the Gulf of Mexico. The second and the third Truss Spars will be installed in later part of 2001 and the spring of 2002, respectively. It is expected that more Truss Spars will be built in the future as the Truss Spar gains greater recognition by the offshore industry. While the Truss Spar design offers significant weight and cost savings as well as added damping for the heave motion in comparison with the Classic Spar, it presents unique challenges in the structural analysis and design of the truss.

During the past several years, various technical papers have been published on spar motions and hydrodynamic analysis (Halkyard,

1996, Kim, Ran, et al, 1999, Magee, Sablok, et al, 2000), as well as on general spar design (Glanville, Halkyard, et al, 1997). However, very few papers exist in the literature related to structural design of the Truss Spar. The objective of this paper is to provide an overview of the various aspects involved in the structural design and analysis of the Truss Spar. The primary focus will be on the design methodologies and the time-domain based analysis procedures utilized for the structural design of the recent Truss Spars.

THE TRUSS CONCEPT

The Classic Spar is a deep-draft cylindrical floating vessel. The Truss Spar design replaces the cylindrical midsection of the Classic Spar with a truss type section, hence the name Truss Spar. An example Truss Spar design is shown in Figure 1. The truss is inherently more efficient than the cylindrical midsection of plated construction as a structural link between the hard tank, which provides the buoyancy, and the soft tank, which carries the fixed ballast. In particular, the truss section of the Truss Spar is a space frame structure similar to a jacket type structure. It usually consists of four non-battered main legs, horizontal braces, X-braces, and heave plates. The tubular members of the truss are generally designed to be buoyant for the entire service life of the Spar platform. The heave plates are integral parts of the truss design, normally consisting of a stiffened plate structure with girders supported by the truss horizontal braces. The main function of the heave plate is to increase the heave natural period of the Truss Spar, thus improving the heave motion performance. This is achieved as the heave plate entraps a large volume of water and increases the added mass for the heave motion. The edges of the heave plates extend past the perimeter of the truss on all the four sides, creating a shelf with edge effect, which helps to increase the drag-induced damping in the heave motion of the Truss Spar. The truss and heave plates also laterally support the top tensioned risers (TTR), steel catenary risers (SCR), and the pull tubes for the SCRs and umbilicals.

The truss structure is connected to the hard tank by overlapping the truss leg tubular members with the hard tank. The hard tank and the truss structure are generally fabricated separately, and then joined by welding the legs at the intersection between the hard tank and the

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truss. The truss is connected to the soft tank in a similar way. Due to the high criticality of these connections, considerable structural analysis and design efforts are required to ensure the adequacy of the connections in terms of structural strength and fatigue.

STRUCTURAL DESIGN CRITERIA

The Spar hull/truss structure must meet the strength and fatigue criteria for various in-place and pre-service conditions. In design practice for the Gulf of Mexico, the truss tubular member design is based on API RP 2A, and the stiffened plate design for the hard tank, the soft tank and the heave plates is based on ABS and DNV rules. Design matrices are usually used to define the load case criteria for structural analysis. An example design matrix for the Truss Spar in- place conditions is shown in Table 1. Note that different topside and riser cases may govern the truss structural design for different functional and environmental conditions. Different factors of safety are usually applied depending on the design conditions and load combinations.

Design Condition

In-place Operating In-place Extreme

Environment Topside Case

x x

In-place Survival x x Damaged Condition x x

Table 1 Design Matrix for In-place Conditions

Riser Factor Case of

Safety x x

x x

x x

x x

Similarly, a design matrix can be used to define the load cases for the Truss Spar pre-service conditions, from fabrication to the topside installation, as shown in Table 2 below.

Design Condition Environment

Fabrication Load-out Dry Tow x Float-off x Wet Tow x Upending x Mooring/Riser Installation x Topside Installation x x

Table 2 Design Matrix for Pre-service Conditions

Topside Case

Factor of Safety

x

x

x

For structural fatigue, different factors of safety are normally applied to different parts of the hull structure depending on criticality of the member and ease of inspection/repair. A typical fatigue criteria matrix is shown in Table 3.

Importance

Non-critical

Critical

Non-critical

Critical

Inspection

Easy inspection

Easy inspection

Difficult or cannot be inspected

Repair

Can be field repaired Can be field repaired Difficult or non-repairable in field

Factor of Safety

Difficult or cannot be inspected

Difficult or non-repairable in field

10

Table 3 Fatigue Criteria Matrix

Since the truss is located at about 200 to 650 feet below the waterline, inspection and repair would be very difficult and costly. Therefore, the factor of safety is usually 10 for the primary truss members and critical connections, and 5 for the secondary members.

IN-PLACE STRENGTH

For the Spar in-place condition, the following loads should be considered for the hull/truss design:

Static loads: Gravity loads (topside weight, hard tank, soft tank and truss

weights, fixed and variable ballast weights, various outfitting weights, etc.),

Buoyancy loads and hydrostatic pressure.

Dynamic and environmental loads: Mooring loads, Riser loads, Wind loads, Wave loads, Current loads, Motion induced inertia loads.

The truss structure must have adequate strength to resist the loads from extreme events such as the lO0-year hurricane. Events for survival such as the lO00-year hurricane and one truss brace member damaged conditions may also need to be considered depending on specific project requirements.

Unlike the tension leg platform (TLP), the Spar platform is a true compliant system, whose natural periods for all the six degrees of motion are significantly greater than the predominant wave period. Hence, the low frequency wind load will have significant impact on the dynamic response of the Spar (Halkyard, 1996). In particular, for the Truss Spar, the time varying dynamic wind load contributes significantly to the pitch/roll motion, which in turn contributes the most to the global bending moment and shear in the truss. Currently, it is quite difficult to use existing software packages based on traditional frequency domain analysis for accurate prediction of the Truss Spar global motions and loads under the combined random wind and wave conditions. This is mainly due to the significant nonlinear effects in the nonlinear hydrodynamic loading (nonlinear drag, free surface effect, and second order wave loading), nonlinear mooring and riser restoring forces, and large displacement surge/sway and pitch/roll motions. Therefore, programs based on time domain analysis are generally required in order to obtain more accurate motions and loads for the truss design. CSO Aker's MULTISIM program is a full time-domain based computer program for Spar motion simulation and hydrodynamic load generation (Paulling, 1995). It has been calibrated extensively with model tests and field measurements (Prislin, et al, 2000), and has been used on recent Truss Spar design projects.

In practice, the global structural model of the truss can be developed using beam elements with a general-purpose structural analysis software package, such as SESAM, SACS or StruCAD. To facilitate one-to-one load mapping for structural design, the hydrodynamic model needs to be generated identically to the structural model. Modeling considerations should be carefully balanced between the details for the structural model and the hydrodynamic model to achieve optimal computational efficiency. An example computer model used for the truss analysis and design is

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2001-JSC-373 J. Wang Page 2 of 8

shown in Figure 2. Note that in this model the truss section is modeled in detail, including the member segmentation, offsets, and TTR stems and pull tubes for SCRs, etc. On the other hand, there is no need to model the topside, hard tank and soft tank in detail for the truss design. For the hard tank and soft tank design, shell elements are used to generate detailed finite element models for stress analysis. Detailed finite element models are also required for analyzing the truss critical connections and the heave plates.

An integrated time-domain based procedure for Truss Spar in- place strength and fatigue analysis is presented in Figure 3. In this procedure, the design starts with a Truss Spar configuration generated using CSO Aker's ISAP (Integrated Spar Analysis Program) software. The governing loads for the hard tank design are mostly the compression loads from the hydrostatic pressure and the wave induced dynamic pressure at the lower portion, and the wave loading at the upper portion of the hull. The global bending moment due to pitch/roll is relatively less significant for the hard tank due to its large structural section modulus. Structural design based on hydrodynamic pressure using a frequency domain approach is thus considered adequate for the hard tank.

For truss structural design, conventional frequency domain methods may not be adequate since the governing loads are mostly from the pitch/roll low frequency motions. With the time domain approach, snapshot load cases are generated post-processing the results of random load time histories from hydrodynamic motion analyses. The criteria for design load case selection are based on the maximum bending moment and shear force envelopes at the truss levels, as well as at time steps corresponding to the maximum pitch/roll and heave motions, which may induce maximum bending and heave plate loads. Example truss global bending moment and shear force envelopes for a 100-year hurricane from 10 realizations of 3-hour time domain simulation are presented in Figure 4.

For the critical truss connections at the hard tank and soft tank, detailed finite element models are generated independently. These models can be treated as sub-models of the global Truss Spar model, which consists of the truss space flame model and coarse mesh shell element models of the hard tank and the soft tank. The truss global deformations corresponding to the critical load cases can be mapped as boundary conditions for detailed finite element analysis and stress code checks.

TRANSPORTATION AND INSTALLATION

The transportation and installation of the Truss Spar typically include long ocean-crossing dry tow on a barge or a heavy lift vessel, float-off near shore in shallow water, a shorter horizontal wet tow to the platform offshore site, and on-site upending. Only the truss strength analyses under the wet tow and upending conditions are discussed here.

The global load levels for the hard tank and soft tank are generally much lower for wet tow than for in-place condition. On the other hand, for the truss members, the load level could be higher during wet tow depending on the sea state criteria. In general, the Truss Spar can be towed horizontally at a speed of 2-3 knots with significant wave height in a range from 2.5 to 3.5 meters. The key part of the wet tow analysis is to generate the wave induced structural loads on the hull/truss and heave plates during the wet tow condition. Once the loads are determined, the truss structure can be analyzed using linear stiffness method, and code checks can be performed. Similar to the in-place strength analysis, the total loads (both static and dynamic) on the truss can be calculated in the time domain, in

which the wave induced hydrodynamic forces on the truss members and the inertia loads due to the hull rigid body motions are included. Detailed structural loads can then be mapped from the wet tow hydrodynamic model to the structural model as quasi-static snapshot load cases at selected time steps corresponding to the maximum truss bending moment, shear force, and heave plate pressure based on the bending moment and shear force design envelopes. Example truss global bending moment and shear envelopes are presented in Figure 5 for the wet tow condition.

The structural model and the hydrodynamic model for wet tow can readily be extended to perform the hull upending analysis for the Truss Spar installation. To simulate the upending process and capture the maximum dynamic loads on the truss, a quasi-static staged flooding process is used to flood the soft tank in several stages. For each flooding stage, time domain upending simulation is conducted in calm water or with wave and current, and the total loads on the truss are obtained. Subsequently, snapshot load cases are generated for structural analysis. Example truss global bending moment and shear force envelopes are presented in Figure 6 for the upending condition with five flooding stages for the soft tank. It is observed that the direction of global bending moment and shear changes during the upending process indicating the hull/truss is changing from the initial sagging condition to the final hogging condition as the soft tank is completely filled with water.

HEAVE PLATE LOAD

For in-place conditions, the main structural loading on the heave plates is the hydrodynamic pressure induced by the wave and heave motion of the Spar. The truss global deformation due to bending and shear also has significant impact on the heave plate design. The effects of heave plates on the Truss Spar heave motion, and evaluations of the heave plate overall drag and added mass coefficients for global motions can be found in Prislin, et al (1998) and Magee, et al (2000). The pressure distribution on the heave plate is not uniform, nor is the center of pressure at the center of the plate. This is due to the heave plate size, Spar global pitch/roll motion, and combined wave and current loads. In order to capture the pressure distribution for structural design, the heave plate is divided into small sub-panels. In the time domain analysis, it is assumed that these sub- panels can be modeled using Morison equation elements with equivalent drag and inertia coefficients corresponding to each sub- panel. For practical design purpose, this approach works quite well giving maximum pressure similar to that of model tests (Prislin, et al, 2000). Snapshots of the pressure distribution can be taken at selected time steps for structural design. An example 3-D contour plot of the heave plate maximum pressure is shown in Figure 7 for a 100-year hurricane with the wave coming from the negative Y direction. As can be seen, the center of the pressure is skewed towards the negative Y direction. Once the pressure load cases are obtained, they can be mapped to the heave plate finite element model for structural analysis with boundary conditions mapped from the truss global deformation.

In addition to in-place pressure, the heave plate should also be designed for the hydrodynamic pressure during the wet tow. In fact, it is an important aspect of the wet tow analysis to obtain the maximum pressure loading for heave plate design. Depending on wet tow criteria, the pressure on the submerged portion of the heave plate for the wet tow condition may be significantly greater than that for the in- place condition, thus governing the heave plate design. Heave plate pressure distributions for wet tow are obtained using equivalent Morison equation elements for the heave plate sub-panels similar to in-place analysis. An example 3-D contour plot of the heave plate

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2001-JSC-373 J. Wang Page 3 of 8

maximum pressure is shown in Figure 8 for the wet tow condition with a 2.75-meter significant wave.

IN-PLACE FATIGUE

For the Truss Spar, the low frequency pitch/roll motion induced by the combined dynamic loading of random wind and wave is a very significant part of the total motion. In-place fatigue analysis of the truss structure requires consideration of the stress components at both the wave frequency and low frequency in the total stress spectrum. However, traditional frequency domain spectral analysis cannot fully capture the low frequency and nonlinear effects on fatigue damage. It is generally recognized that accurate results are best obtained by using a full time domain approach, which includes various nonlinear effects, as well as the random wind and wave loading. SEASTAR (a general- purpose nonlinear time-domain structural analysis program) has been used to perform time domain fatigue analysis of the truss structure in recent Truss Spar designs.

The stress concentration factors (SCF) for the tubular joints of the truss structure can be calculated based on Efthymiou's equations (1985) with the joints classified according to geometry, or based on the formulas recommended in API RP2A with joint classified according to the load path. For tubular joints, fatigue damages are calculated based on the S-N curves per API RP2A. For the truss critical connections to the hard tank and the soft tank, and other non- tubular joints, very detailed finite element analysis is used to derive the proper SCFs, and fatigue damages are calculated using proper S-N curves according to DNV RP-C203 (2000). Due to space limitations, only a few fatigue analysis results are presented here for illustration purposes. The results are based on hotspot stress time histories obtained using time-domain structural dynamic analyses, in which the fatigue analysis model is calibrated to give the same global motions as the hydrodynamic model. The fatigue damage accumulation is computed using rainflow cycle counting. Note that both the hull global rigid body motion and the truss structural dynamic responses are included in the hot spot stress time history calculation. Typical natural periods of the first two modes of structural dynamic response for the truss are usually between 1.5 to 1.9 seconds, corresponding to the truss bending with respect to the two principal axes. Therefore, the truss itself can be viewed as an inverted fixed jacket structure with little dynamic amplification from the wave excitation as the structural natural periods are far below the wave peak energy period.

Example power spectral density (PSD) functions of selected truss member end forces are shown in Figures 9 and 10. As can be seen, significant low frequency components exist in the axial forces of the truss main members, where most of the member internal force is axial force from the truss global frame action. The low frequency contribution is less significant (see Figure 10) for the bending moment in the heave plate horizontal girders. Here the bending moment is the dominant internal force component as most of the heave plate pressure is caused by the waves. Example truss member damage accumulations for different sea state bins are presented in Figures 11 and 12. The damage results indicate most of the fatigue damage is caused by the high sea states. More detailed discussions on the truss critical connection fatigue analysis can be found in a companion paper by Luo, et al (2001).

SUMMARY

Truss Spar structural design methodologies and procedures based on random wind and wave time domain analyses have been discussed with a focus to the truss structure. Example results of truss in-place strength and fatigue analyses, truss wet tow transportation analysis

and upending analysis have been presented to provide an overall view of the load conditions and structural behavior of the Truss Spar.

ACKNOWLEDGEMENT

The authors gratefully acknowledge CSO Aker Engineering, for support and permission to publish the paper. The authors also acknowledge the contributions of their colleagues, particularly, Drs. B. Zhang, R. Lu and S. Srinivasan.

REFERENCES

Det Norske Veritas (DNV, 2000), "Fatigue Strength Analysis of Offshore Steel Structures", RP-C203.

Efthymiou, M. and Durkin, S. (1985), "Stress Concentrations in T/Y and Gap/Overlap K-Joints", BOSS, Delft, The Netherlands.

Glanville, R.S., Halkyard, J.E., Davies, R.L., Steen, A. and Frimm, F. (1997), "Neptune Project Spar History and Design Considerations", Proc. of Offshore Technology Conference, Houston.

Halkyard, J.E. (1996), "Status of Spar Platforms for Deepwater Production Systems", Proc. of 6 th Int Offshore and Polar Eng Conf, Los Angeles.

Kim, M.H., Ran, R., Zheng, W., Bhat, S. and Beynet, P. (1999), "Hull/Mooring Coupled Dynamic Analysis of a Truss Spar in Time- Domain", Proc. of 9 th Int Offshore and Polar Eng Conf, Brest, France.

Luo, M.H., Lu, R., Wang, J. and Berg, S. (2001), "Time Domain Analysis for Critical Connections of Truss Spar", (submitted) Proc. of 1 lth Int Offshore and Polar Eng Conf, Stavanger, Norway.

Magee, A., Sablok, A., Maher, J., Halkyard, J.E., Finn, L. and Datta, I. (2000), "Heave Plate Effectiveness In the Performance of Truss Spars", Proc. of OMAE Conference, New Orleans.

Paulling, J.R., (1995), "MULTISIM: Time Domain Platform Motion Simulation- Theory and User Guide", 3 rd Edition.

Prislin, I., Blevins, R.D., and Halkyard, J.E. (1998), "Viscous Damping and Added Mass of Solid Square Plates", Proc. of OMAE Conference, Lisbon, Portugal.

Prislin, I., Gupta, H., Steen, A. Halkyard, J.E. and Finn, L. (2000), "Analytical Prediction of Motions vs Full Scale Measurements for Oryx Spar Neptune", Proc. of OMAE Conference, New Orleans.

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2001-JSC-373 J. Wang Page 4 of 8

t i! w __ t . . . . . . . . . I

.,11

_b~,

Fig. 1 Truss Spar Concept

Hard Tank

Truss

Heave Plate

Soft Tank

Fig. 2 Motion & Structural Analysis Model

ISAP (Integrated Spar Analysis Program) (Configuration/Sizing/Weight/Preliminary Analysis)

Detail Truss Space Frame Model (Truss In-place Strength Analysis)

Detail Truss Space Frame Model (Truss Time Domain Fatigue Analysis)

Detailed Hull Hydrodynamic Model (Time Domain, Random Wind & Wave)

Spar CG Motion Time History Output Time Domain Global Loads and Local Loads on Truss

Truss Strength Analysis Design Envelopes Snapshot Loads Code Checks

Truss & Connection Fatigue Truss SCF Calculation

Hotspot Stress Time History Rainflow Analysis & Fatigue Life

Preliminary Hull Configuration Scanting Design & Member Sizes

. . . . .

Detailed Hull Global FE Model (incl. detailed truss to hull connection)

Detailed Hull Hydrodynamic Model ....... (Frequency domain wave, hull pressure)

Combined TD & FD Loads Map Loads Hull Design

Map Loads for Connection Design

Connection SCFs Hull Strength Analysis Connection Strength

Buckling Checks

Fig. 3 Truss Spar In-place Strength & Fatigue Analysis

358

2001-JSC-373 J. Wang Page 5 of 8

600

500

'-' 400

0 .1

>

_.e 300 LLI

200

100

0

-5.E+05

. . . . I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

I i , Average, 10 records

700

. . . . Top of Truss

\

/ I I i I I I

0.E+00 5.E+05 1 .E+06 2.E+06

700

600

500

400 C 0 , l

>

,3i 300

200

100

0

- 10000

I- b-

; I I . I I ~ i I Im IE I lib

Average, 10 records

. . . . Top of Truss

-5000 0 5000 10000

Moment ( f t -k ips ) Shear (k ips )

Fig. 4 In-place Bending and Shear Envelopes for 100-yr Hurricane

700 I I Moment Z ~ I IOI I ~~nt Y

600 ~ . . . . Top of Truss 4.J ' () ,

500

A 400

300 m

200

100

700

i ()

_ ('1

()

: ('1

i . . . . . . . . . . ! : . . . . .

600

500

A 400

300

200

100

0 I ! ! i 0

........................... i ~ Shear in Y

Shear in Z

Fop of Truss

-2.E+06 - 1 .E+06 0.E+00 1 .E+06 2.E+06 - 10000 -5000 0 5000 10000 Moment (k ip - f t ) Shear (k ips )

Fig. 5 Bending and Shear Envelopes for Wet Tow

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J. Wang Page 6 of 8

700

600

500

~ 400 c- o

300 w

200

100

-2.E+06

I o Stage 1 [] Stage 2 ,II,-- Stage 3 Stage 4

Stage 5 TopofTruss : I

I i

i

- . . . . . . 1; - ! . . . . . . .

il

- 1 .E+06 0. E+00 1 .E+06 2. E+06

Moment (ft-kips)

700

600

500

A

400 c o . - - .

>

in 30o

200

100

o Stage 1 [] Stage 2

- - A - - Stage 3 Stage Stage 4 /-'-i_

. . . . Top of T russ /~ J I

0

-10000 -5000 0 5000 Shear (kips)

10000

Fig. 6 Bending and Shear Envelopes for Upending

600 -. 600 .-

400 --

co ~- 300 -. ,.,._., e)

o 200 0o "- o

13_

100 -.

0-,, ~o

-50 -50 Plate Y (it) Plate X 0)

400 -

~ 200

4- a

-200 -.

- 4 0 ~ 0

Plate Y (if) -50 Plate X (~)

Fig. 7 Heave Plate Pressure for In-place 100-yr Hurricane Fig. 8 Heave Plate Pressure for Wet Tow

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2001-JSC-373 J. Wang Page 7 of 8

Truss Leg Axial Forc~

3.5E+07 t " " ~

3.0E+07 . . . . . . .

2.5E+07 X b

~2.0E+07

o'~1.5E+07

~ 1.0 E+07

5.0E+06

0.0E+00 ,

004 FOe~~Hz) 012

2.0E+04

bin 06 (Tp = 8.5 s)

bin 09 (Tp = 10.5 s)

bin 12 (Tp = 11.5 s)

bin 15 (Tp = 12.5 s)

bin 17 (Tp = 14.2 s)

Force PSD Heave Plate Girder Bending Moment PSD 2.5E04

o)

~1.5E+04

E 1.0E+04

5.0E+03

0.0E+00

. . . . bin 06 (Tp = 8.5 s)

. . . . . . . bin 09 (Tp = 10.5 s)

-- bin 12 (Tp = 11.5 s)

x bin 15 (Tp = 12.5 s)

~ b i n 17 (Tp = 14.2 s)

t

. . . . . . r . -~- ~ . . . . . . 5_ _ l _

0.04 0.08 0.12 0.16 0.2

Freq (Hz)

Fig. 9 PSD of Truss Leg Axial Force Fig. 10 PSD of Heave Plate Girder Bending Moment

1.0E-03

9.0E-04

8.0E-04

7.0E-04

6.0E-04

g 5.0E-04

g~ 4.0E-04

3.0E-04

2.0E-04

1.0E-04

0.0E+00

Damage Accumulation in X-brace Member

[] API-X Curve

[] API-X Curve

. . . . . . . . .

1 2 3 4 5 6 7 8 9 10 11 12 13 14

Sea State bins

i

5 16 17 18

Damage in Heave Plate Girder Connection

1.60E-03

1.40E--03

1.20E-03

~ 1.00E-03

~ 8.00E-04 13

'~ 6.00E-04 i i

4.00E-04

2.00E-04

O.OOE+O0

B DNV E Curve- FD

m DNV E Curve - TD

[] DNV F Curve- FD

El DNV E Curve - TD

BIN BIN BIN BIN BIN BIN BIN BIN BIN BIN BIN 1 2 3 4 5 6 7 8 9 10 11

Condensed Bin Number

Fig. 11 Fatigue Damage at Truss X-brace Joint Fig. 12 Fatigue Damage at Heave Plate Girder

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