Final towing Analysis Report

July 23, 2015 [CIMC RAFFLES]

Leg Towing Analysis reportPrepared - Hamish Forsythe

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Contents1. Executive Summary..............................................................................................................3

2. Method of Analysis...............................................................................................................3

2.1 Criteria................................................................................................................................3

2.2 Models Description.............................................................................................................4

2.3 Boundary Conditions..........................................................................................................6

2.4 Loading...............................................................................................................................6

2.5 Allowable Stresses............................................................................................................11

2.6 Result................................................................................................................................11

References..............................................................................................................................12

APPENDIX A............................................................................................................................13

OUTPUT DATA....................................................................................................................14

Model Plot:.........................................................................................................................15

Appendix B - Output Plot........................................................................................................17

Appendix C - Chord Properties................................................................................................20

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1. Executive SummaryThis particular JU is a jack-up rig with a triangular shaped hull with three triangular layout truss legs positioned within it.

The purpose of this report is to provide evidence via FE analysis that the legs provide adequate strength to support the structure during towing in both of the following conditions:

1. field tow (125.3m leg length)

2. ocean tow (112.86m leg length)

The results gained here are sufficient to confirm that the leg strength will support the hull structure and also that the rack chock rated capacity is not exceeded during any of the towing conditions.

We can say that the maximum stress compared to the permissible stress never exceeds a ratio of 0.77 for any towing condition, which is essential as it must stay below 1 at all times.

2. Method of AnalysisThe Analysis for this project was completed using the commercial FEA (Finite Element Analysis) Software SACS Executive 5.3. This software is very efficient at defining truss sections. Within this software a three dimensional beam-element model was defined via a general leg arrangement and calculated loads (via NI534_Jackup Rules SI) applied to the design. This analysis was developed to let us analyse the leg elements under varying towing conditions. We had to be very careful when defining the loading location as the length of the leg would vary for the ocean Vs the field towing condition. We only apply the loading over the section of the leg that lies above the spud can, this would not however make a difference to the overall result as, all loads i.e. structural weight and inertial force, were applied as distributed forces along the length of the chord which that towing condition applies I.e. for field towing, up to 125.3m and for ocean towing, up to 112.86m. (Also model is designed of weightless members).

The found stresses were then compared against the rule required and allowable values. This was completed via the SACS 5.3 Analysis system, where, upon ensuring completion of an accurate model, we can generate a postvue model and determine the maximum UC ratios within each member group.

Each condition (ocean and field) were analysed for a number of loading conditions, this was done for the fore leg of the model as well as one of the aft legs.

2.1 CriteriaThe analysis for the leg strength has been carried out in accordance with the ABS (American Bureau of Shipping) MODU (Mobile Offshore Drilling Unit) Rules as well as allowable stress design criteria.

In order to know what the required stresses are, we need to use the NI534_Jackup Rules SI and use the equations and the process presented in these rules to calculate our applied loads. We then use these values to determine if our model is within the ABS MODU Rules.

ABS MODU rules specifies the following criteria for transits in field and ocean conditions:

Field Tow - Leg strength is to be developed to withstand a bending moment caused by a 6°single amplitude roll and pitch at the natural period of the unit (11 second) plus 120% of the gravity moment cause by the angle of inclination of the legs.

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Ocean Tow - Leg strength is to be developed to withstand a bending moment caused by a 15°single amplitude roll and pitch at a 10 second period plus 120% of the gravity moment caused by the angle of inclination of the legs.

2.2 Models DescriptionThe model consists entirely of beam elements with the appropriate material and section properties applied. These section properties include:

The dimensions Axial area (only for tubular sections) Moment of inertia around Y and Z axis Torsional moment of inertia (Y + Z)

Cross section types supported in sacs are:

Tubular

Wide flange

Compact wide flange

Box

Tee

General Prismatic

Channel

Plate Girder

Angle

Cone

Stiffened Box

Stiffened Cylinder

The main side chords are modelled as prismatic sections as they are constructed as a split pipe with the rack separating it along its local longitudinal axis. According to the leg general arrangement, at a height of 40704mm above BL the chord changes it's axial area and hence we insert a different prismatic section here.

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Figure 1 - SACS beam-element model

Figure 2 - Typical chord arrangement

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2.3 Boundary ConditionsBoundary conditions were applied at the locations on the chords where the legs were connected to the lower and upper jack-case guide as well as the rack-chock. To simulate the boundary conditions and appropriate constraints on the leg for towing conditions, the members connecting to the location of the rack-chock, lower and upper guides were modelled as a stiff link where the end joint on them was fixed in all directions. This fixidity is defined in SACS as (111111) where it is constrained in all directions and all rotational axis. The fixidity at the end of these members connects to the hull. Furthermore the pre-mentioned joints had proper end releases to simulate load transfer between the leg and the jack cases. This transfer varies depending on the equipment and the difference is shown below.

The lower/upper guides do not provide any moment restraint, however, the rack chock is more complex and is able to constrain in both the vertical and lateral directions. The releases which are applied at the ends connected to the chords are:

Local axis Dx Dy Dz Rx Ry RzLower Guide and Upper Guide 1 0 1 1 1 1

Rack Chock 1 0 0 1 1 1*Note: '1' is a release in the mode and direction as shown in the member's local axis. These releases are used for both the towing and storm conditions.

Also, D= direction and R = rotation in the above table.

Figure 3 - Fixidity, 111111, at end of connecting chords

2.4 LoadingLoad are applied to the model through specific combinations of basic load cases. Each basic load case is derived from a specific force applied to the structure and these are as follows:

1. Leg dead weight; uniformly distributed load in the vertical direction on each chord. [kN/m]

2. Inclined weight; uniformly distributed load in the lateral direction on each chord [kN/m]. The two basic load-cases separate the longitudinal (x) and transverse (y) load vectors.

3. Lateral inertial load; Uniformly increasing load in the lateral direction on each chord. The load is derived by setting the starting distribution amplitude to 0[kN/m] at the base of the model and to a maximum value at the top of the leg. Two basic load cases separate the longitudinal (x) and transverse (y) load vectors. [kN/m]

4. Vertical inertial load; uniformly distributed load in the vertical direction on each chord. This simulates the unequal downward from the differing vertical acceleration at each chord.

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We apply each of the above loads to both a fore and aft leg, thus giving us a total of eight basic load cases.

The derivation of load amplitude and position, and their method of application are explained in the following sections.

The weight of the leg, the depth of the spud can, the full length of the leg and the applied weight per/m is incredibly important to determining the overall vertical stresses on the structure as this directly has an effect on all the stresses.

Leg Weight excluding can 5637.48 kNFull leg length 125.3 m

Spud can height 4.572 mLeg Weight 46.70 kN/m

Leg weight, as vertical load on each chord 15.57 kN/mdraft 4.572 m

Also the calculation of the basic load cases are shown in the figure below:

Load case direction description1 (all chords) x Longitudinal load due to the pitch2 (all chords) y Transversal load due to roll3 (chord 1) -z Vertical load due to pitch or roll4 (chord 2) -z Vertical load due to pitch or roll5 (chord 3) -z Vertical load due to pitch or roll6 (all chords) x Longitudinal load due to inclined weight7 (all chords) y Transversal load due to inclined weight8 (all chords) -z Vertical load due to deadweight

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The combined load cases are separate for two conditions: field towing and ocean towing. Each condition as mentioned before has different requirements in terms of inertial acceleration and natural roll/pitch period. The accelerations are based upon Figures 4 and 5:

Figure 5 - NI534_Jackup Rules parameters for calculation of inertial accelerations and towing loadings

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Figure 4 - Vertical loading, applied on all chordsFigure 4.1 - Combined inertial and inclined lateral loads - applied on all chords

Figure 4.2 - Total combined loads applied to entire leg


Figure 6 - Jack-up general arrangement, shows yi and xi for the jack-up

The acceleration is calculated at the top of the leg and is applied to each appropriate inertial load case as the load factor. The vertical loads per chord are also calculated and each chord's basic load case is appropriately factored.

The method for calculation of all vertical and inertial induced loads are shown below.

Given that we know the ABS requirements for transit towing conditions, we must be able to apply these in order to calculate the overall loading forces.

We must know the following parameters:

1. angular acceleration for the pitch αp and the roll αr. these are obtained from the following formula:

α R=AR(2πT R

)2

α P=A P(2 πT P

)2

Where A is the roll single amplitude of the unit as defined in the ABS MODU Rules (6 degrees for field tow, 15 degrees for ocean tow). when we apply these values in the above equation we should convert these values to radians. Also, T is the natural period of the motion, which we know to be 11s for field tow and 10s for ocean tow for either pitch or roll.

After we have found the above values, we can use the below equations to find:

a) the horizontal load distribution under roll and pitch motion

b) the global forces in upright (only loads induced by pitch motion) and inclined position (only loads induced by roll motion) for the vertical force induced by the leg to the unit structure under roll/pitch motion at upper guide level.

a i) Horizontal Load distribution under roll motion:

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F ir=pi(1.2 gsin ( A R )+α R z i)

Where;

pi : weight, in tonnes, of an elementary length of leg li. (We can find this via dividing the full weight of the leg, by the length of the leg).

zi : Distance, in m, measured as shown in Fig. 4.

b i) And, the total vertical force FVP, in kN, induced by the leg under roll is obtained via:

FVR=Pleg ¿

Where;

Pleg : Total weight of the leg, in tonnes

yi : Distance, in m, as shown in Fig. 4.

Similarly for the pitch motion:

a ii) Horizontal Load distribution under pitch motion:

F ip=p i(1.2 gsin ( AP )+α P z i)

b ii) The vertical force FVP can be found from:

FVP=Pleg ¿

Where:

xi : Distance, in m, measured as shown in Fig. 4.

The combined load cases are grouped into two part:

1. Field Transit

2. Ocean transit

There are reversals of lateral loading in the longitudinal direction only since the legs are symmetrical in the transverse direction. The combined load cases are shown in figure 7.

It should also be mentioned that if we apply the full horizontal forces for the whole structure to each leg, we can set the load condition factor equal to 1/3 seeing as there is three chords.

Figure 7 - Load case names and direction

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Figure 8 - Calculation of leg loadings for all conditions

2.5 Allowable StressesAllowable stresses are as per the AISC manual of Steel construction ASD codes. Because the applied loads are instantaneous maximums and are cyclic in nature we can use the 1.3333 factor for the allow stress modifier (AMOD). The chord and racks are 690MPa, the internal braces are 240MPA. The following general rules for permissible (i.e. UC</=1.0) stresses are followed: F=Fy/F.S.

where:

Fy = specified minimum yield point or yield strength.

F.S. = factor of safety

For combined loadings F.S. = 1.25 for axial or bending stresses, F.S. = 1.88 for shear stress.

Yield stress Allowable shear stress

Allowable axial/bending stress

Chord 690.0 367.0 552.0Internal bracing 240.0 127.7 192.0Horizontal/diagonal bracing

360.0 191.5 288.0

SACS unit checks for AISC also account for other stress limiters such as unbraced length and allowable compression loads.

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2.6 ResultId Max UC

Horizontal braces H01/H03/H02 0.58/0.07/0.06K-brace K01/K03 0.79/0.71Chord C01/C02 0.37/0.64

Therefore, the legs satisfy code requirements.

ReferencesABS Rules for building and classing Mobile Offshore Drilling Units, 2012

NI534_Jackup Rules SI

ANSAISC 360_10

SACS Executive 5.3

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APPENDIX AINPUT FILE AND OUTPUT DATA

OUTPUT DATA

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Model Plot:

Figure A1 - Member Group - Vertical (below 40704 ABL)

Figure A2 - Member group - Horizontal (Below 40704 ABL)

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Figure A3 - Member Group - Vertical (above 40704 ABL)

Figure A4 - Member group - Horizontal (above 40704 ABL)

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Figure A5 - Joint Fixities and member releases

Appendix B - Output Plot

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Figure B1 - Max UC Ratios

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0.07 (H03)

0.37 (C01)

0.71 (K03)

0.19 (PL1)

0.64 (C02)

0.79 (K01)

0.06 (H02)

0.58 (H01)


Figure B2 - Worst Load cases for each member group

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OPF (PL1)

ORF (H02)

OPF (C01)

OPF (H03)

ORA (K03)

ORA (K01)

OPA (H01)

ORA (C02)


Appendix C - Chord Properties

Y-Shear area

843.24 cm^2

Z-Shear area

175.43 cm^2

Area 1002.21897 cm^2

Ip 285794.9612 cm^4

I-y 130080.0393 cm^4

I-z 155714.9219 cm^4

Y-Shear area 731.9405338

cm^2

Z-Shear area 175.4265338

cm^2

Area 907.230006 cm^2

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Ip 267885.4311

cm^4

I-y 125039.8784

cm^4

I-z 142845.5527

cm^4

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Final towing Analysis Report

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