hcalc

miscellaneous calculationsby chyetanya kunte

Abstract

This document serves as a technical commentaryand user manual (where applicable) for calculationscripts in this repository.

1 sea transport forces on cargo

Due to logistics, quality control and prohibitive costs, off-shore structures (viz., jackets, topsides, modules, piles)and even vendor equipment are typically fabricated on-shore, and then typically towed on a cargo barge to theirintended service locations, usually offshore. The cargo istypically transported on an unpropelled (dummy) barge,usually towed by pairs of tug boats. Transportation andarising stresses out of it therefore become important as-pects in ensuring pre-service compliance for an offshorestructure or the equipment transported.

1.1 Importance of tow analysis

• To assess and design the structure for transportstresses.

• To provide additional temporary members (sea-fastenings) for support during transport.

• To strengthen structure to suit transport analysis,orient member spanning to be beneficial and eco-nomical during transport.

1.2 Factors affecting tow

• Sea-state.

• Barge size (larger barge—more stable, lowerstresses; smaller barge—higher stresses).

• Weight of the cargo (structure, equipment, piles,etc).

• Overall COG (center of gravity) of the structure.

• Overall COR (center of rotation) of the transportbarge.

1.3 Forces during tow

Forces during tow transportation consist of the following:

• Self weight of the cargo (structure, equipment,piles, etc).

• Any non-modeled pre-installed item loads.

• Equipment dry weights.

• Inertia forces.

Sea transportation induces inertial forces on the cargodue to barge’s motion characteristics, draft, and Meto-cean design conditions. This guideline and the associ-ated script aid in determining these sea-transport forcesusing simple calculations—without having to rely on so-phisticated and often expensive software, such that [a]the cargo and its structural framing can be designed towithstand them, and / or [b] if economics favor it, choosea barge with benign motion characteristics, which usuallymeans a larger barge.

1.4 Barge motion characteristics

Barge motion characteristics are usually determined bya barge motion analysis, taking the tow route in to ac-count. In the absence of such a detailed analysis, GL No-ble Denton recommends default motion criteria, whichcorrespond to the nature of transportation and barge di-mensions. Since such a generic criteria does not explicitlyillustrate Metocean characteristics (viz., wave steepness,significant wave height and period, et al.) considered ineither deriving or implicitly, these may be deemed some-what conservative.

For unrestricted (open sea) transportation, the follow-ing (commonly used) characteristics have been extractedand reproduced below from GL Noble Denton’s Guide-lines for Marine Transportations.

case loa, b t α β h1 > 140m and >30m 10s 20° 10° 0.2g2 > 76m and > 23m 10s 20° 12.5° 0.2g4 ≤ 76m or ≤ 23m 10s 25° 15° 0.2g

where,loa – Barge length overall (m).b – Barge width (m).t – Full cycle period (in seconds).α – Roll single amplitude angular acceleration (typi-

cally given in degrees).β – Pitch single amplitude angular acceleration (typi-

cally given in degrees).h – Heave single amplitude of linear acceleration (typi-

cally given in terms of g, or in meters). To convert a heaveof 0.2g in to meters, for example, it can be calculated ash = 0.2g · (Th

2π )2 (m).

g – Acceleration due to gravity, typically 9.81m/s2.

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The other angular acceleration parameter is Yaw; andother linear acceleration parameters are Surge, Sway. Tonote, a heave of 0.2g corresponds to an approximate valueof 5m.

1.5 Accelerations

1.5.1 Roll

θr = (2π

Tr)2 · α (1)

The roll angle, α, is taken in radians in the equationabove. Correspondingly, θr is in rad

s2 .

1.5.2 Pitch

θp = (2π

Tp)2 · β (2)

The pitch angle, β, is taken in radians in the equationabove. Correspondingly, θp is in rad

s2 .

1.5.3 Heave

gh = (2π

Th)2 · h (3)

In the equation above, h is in meters, and correspondinggh is in m

s2 .

1.5.4 Surge and Sway

Surge and Sway single amplitudes each can be calculatedusing Pitch and Roll parameters respectively, and there-fore, they are often not furnished.

Surge (in terms of g) can be calculated as follows:

Surge = 1.0 · g · sinβ (4)

and Sway (in terms of g) can be calculated as follows:

Sway = 1.0 · g · sinα (5)

Further, Surge and Sway can both be calculated bymultiplying with the term,

(T2·π

)2 to obtain them in me-ters.

1.6 Transport forces on cargo

In the following, W is the design weight of the cargo. Lx,Ly, and Lz are lever-arm distances between center of grav-ity (cog) of the cargo and barge center of rotation (cor).

1.6.1 Roll and Heave

Vertical force from roll:

Fvr = W ·(cosα+ θr ·

Ly

g

)(6)

Vertical force from heave corresponding to roll:

Fvhr =

(W

g

)· gh · cosα (7)

Horizontal force from roll:

Fhr = W ·(sinα+ θr ·

Lz

g

)(8)

Horizontal force from heave corresponding to roll:

Fhhr =

(W

g

)· gh · sinα (9)

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1.6.2 Pitch and Heave

Vertical force from pitch:

Fvp = W ·(cosβ + θp ·

Lx

g

)(10)

Vertical force from heave corresponding to pitch:

Fvhp =

(W

g

)· gh · cosβ (11)

Horizontal force from pitch:

Fhp = W ·(sinβ + θp ·

Lz

g

)(12)

Horizontal force from heave corresponding to pitch:

Fhhp =

(W

g

)· gh · sinβ (13)

1.7 Load combinations

Phasing is assumed to combine, as separate load cases, themost severe combinations of the following:

• Simulating Beam seas: 100% Roll ± 100% Heave

• Simulating Head seas: 100% Pitch ± 100% Heave

• Simulating Quartering seas: 50% Pitch + 50% Roll± 100% Heave

In addition, effective horizontal shear force due to bargeinclinations, corresponding to the max. pitch/roll angle,may be included in the cases above. Typically, wind forcesis not considered in the above combinations.pitch and Heave:

V erticalforce = Fvp ± Fvhp (14)

Horizontalforce = Fhp ± Fhhp (15)

roll and Heave:

V erticalforce = Fvr ± Fvhr (16)

Horizontalforce = Fhr ± Fhhr (17)

1.7.1 Generating inertia forces using sacs

There are at least two ways of generating inertia forcesfrom barge motions in sacs software, as illustrated below:

Using motion cards:

* AS PER NOBLE DENTON CRITERIA* PITCH ANGLE = 12.5d; PERIOD = 10s; SURGE = SIN(12.5) = 0.216* ROLL ANGLE = 20d ; PERIOD = 10s; SWAY = SIN(20) = 0.34TOWOPT MNECLD WP -12.389 0.000 -8.500 XYZPOSITION* HEAD SEA CONDITION (100% PITCH AND 100% HEAVE)MOTION 21 +12.5 10. +.216 +0.2MOTION 22 -12.5 10. -.216 +0.2MOTION 23 +12.5 10. +.216 -0.2MOTION 24 -12.5 10. -.216 -0.2* BEAM SEA CONDITION (100% ROLL AND 100% HEAVE)MOTION 25 +20. 10. +0.34 +0.2MOTION 26 -20. 10. -0.34 +0.2MOTION 27 +20. 10. +0.34 -0.2MOTION 28 -20. 10. -0.34 -0.2* SIMULATING QUARTERING SEAS (50% ROLL, 50% PITCH AND* 100% HEAVE)MOTION 29 +10. 10.+6.25 10. +.108+.17 +0.2MOTION 30 -10. 10.+6.25 10. +.108-.17 +0.2MOTION 31 -10. 10.-6.25 10. -.108-.17 +0.2MOTION 32 -10. 10.-6.25 10. -.108-.17 -0.2MOTION 33 -10. 10.+6.25 10. +.108-.17 -0.2MOTION 34 +10. 10.+6.25 10. +.108+.17 -0.2MOTION 35 +10. 10.-6.25 10. -.108+.17 -0.2MOTION 36 +10. 10.-6.25 10. -.108+.17 +0.2END

This above method, not only generated inertia forces, butalso combines them as per instructions in the input.

Using acceleration cards:

* AS PER NOBLE DENTON CRITERIA* PITCH ANGLE = 12.5d; PERIOD = 10s; SURGE = SIN(12.5)= 0.216* ROLL ANGLE = 20d ; PERIOD = 10s; SWAY = SIN(20) = 0.34TOWOPT MN CG -12.389 -8.500 XYZLCFAC 1.10 2ACCL 0.00 0.00 0.00 1.00 0.00 0.00ACCL 0.00 0.00 0.00 0.00 1.00 0.00ACCL 0.00 0.00 0.00 0.00 0.00 1.00ACCL 1.00 0.00 0.00 0.00 0.00 0.00ACCL 0.00 1.00 0.00 0.00 0.00 0.00ACCL 0.00 0.00 1.00 0.00 0.00 0.00END

The accelerations thus generated need to be further suit-ably factored and combined with the weight of the cargoto get total inertia loads.

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1.7.2 Generating inertia forces by hand

Transport forces in terms of W and L for commonly used GL Noble Denton motion criteria:case Description Vertical force Horizontal force

1 roll ± heave W · ( 0.9397 + 0.1378 ·Lyg ± 0.1891 ) W · ( 0.3420 + 0.1378 ·Lz

g ± 0.0688 )1 pitch ± heave W · ( 0.9848 + 0.0689 ·Lx

g ± 0.1982 ) W · ( 0.1736 + 0.0689 ·Lzg ± 0.0349 )


g ± 0.0688 )2 pitch ± heave W · ( 0.9763 + 0.0861 ·Lx

g ± 0.1964 ) W · ( 0.2164 + 0.0861 ·Lzg ± 0.0436 )


g ± 0.0850 )4 pitch ± heave W · ( 0.9659 + 0.1034 ·Lx

g ± 0.1944 ) W · ( 0.2588 + 0.1034 ·Lzg ± 0.0521 )

Last updated: August 24, 2012. Type set in XƎTEX.

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