Assessment of motions and forces of lift operations with sheerlegs in an irregular sea + Appendices

(1)

jun ii 99

in

Assessment of the motions and forceS,

of lift operations with sheerlegs

in an irregular sea

Report no OvS, 99/06

EN. van Liere

APPEND

147;44

1,41.

TU Delft

Subfaculteit Ontwerpen Constructie en Productie

Vakgroep Maritieme techniek

Tëclinischc Universiteit Delft

Sectie Ontwerpen van Schepen

14,110c.I07'

CES

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ASSESSMENT OF THE MOTIONS AND FORCES OF LIFT OPERATIONS WITH SHEERLEGS IN AN IRREGULAR SEA

APPENDIX A

MOTION RESPONSE OF THE PENDULUM

In chapter 3.3 a number of different riggings is shown. Each of these riggings

combined with the module defines a pendulum with other motion response. However, for the simulations in Oscar only one model of the pendulum is used. Therefore we

have to investigate in what extend the dynamic behaviour of the model in Oscar corresponds to the dynamic behaviour of the pendulums in reality.

In this appendix the motion responses of three different models of the pendulum are investigated. The dynamic behaviour of most pendulums in practice can be simplified to these models.

In this appendix the mass of the load is defined as the total mass of the load, including

the mass of the rigging and the mass of the tackles.

The three models of the pendulum, which will be discussed in this appendix, are shown in figure Al.. Below a short description is given of each model.

1 The Oscar pendulum.

The Oscar pendulum consists of a wire and a load consisting of a mass without

inertia, in general called mathematical pendulum. This is the model that is used for the simulations in Oscar.

The Single pendulum.

The Single pendulum consists of a bar and a load, that has mass and inertia. The connection of the load to the bar is fixed, so the load will make the same rotations as the bar and its mass inertia will influences the motions of the pendulum.

The Double pendulum.

The pendulum is a combination of the Oscar and the Single pendulum. A wire models the upper part and the lower part is equal to the Single pendulum. The

upper and lower part can rotate relative to each other.

In the sections below the motions of the pendulum are defined in a two dimensional plane. In this plane the vertical axis is called the z axis and the horizontal axis is called the y axis.

For the models of the pendulums the next assumptions are used: The wires and the bars have a fixed length.

The elements have no mass, except the load.

The rotations of the elements of the pendulum are smaller then 0.1 rad (-5.73

degrees).

Harmonic forces excite the pendulum.

The vertical motions of the top and the bottom of the pendulum are equal. The vertical and horizontal motions of the pendulum are independent.

These assumptions are done to define the formulas for the motion responses of the

models of the pendulums. For comparison of the motion responses of the pendulums. occurring dimensions of the pendulums in reality are used. The following dimensions are used:

The length of the pendulum is between the 30 and 70 metres. The length of the

pendulum is defined as the distance between the top of the pendulum and the COG of the load.

The radii of gyration of the load are between the 4 and 12 metres (these radii concern square homogeneous loads with a length between the 10 and 30 metres).

TU DELFT SMIT ENGINEERING BV 66

2'.

(3)

Figure AA

Three models of the pendulum

Oscar pendulum Single pendulum Double pendulum

wow-tli

(4)

In this appendix the formulas for the motion responses of the pendulums are derived

by using the 'virtual energy balance' [Reynen, 1991].

Al..

THE OSCAR PENDULUM

In figure A.2 the model of the Oscar pendulum is given. The measures of the

pendulum are given by:

= length of the wire (m) = mass of the load (kg)

If only the horizontal motions of the top of the pendulum are considered, these

motions can be described by: )7t 7-- Ut )7t = Ut e-yo

(Al).

7-- Ut e0

at =8ut Uyo

In which:

xo;e-yo;-e-zo = unity vectors of the global coordinate system (-) In the me way the motions of the load can be described:

)7/ = = Ut '-6yo lw

)71 =

+0 -/w

6-2

= ijt

yo ±Ow 'iw 2 (Ow )2 .f -e1 -&-y0 +

(A.2)

53F1 =out --60

In which: x, _{= position vector of the load (m)}

= angle of the wire (rad)

E1;j2;E3 = unity vectors of the local coordinate system of the wire

As can be seen, there are two degrees of freedom: ut and f3,.

Besides the motions of the pendulum, the external forces actingon the pendulum

have to be defined. The external forces acting_{on the top of the pendulum are a}

vertical force, which is equal to the weight of the pendulum, and_{a horizontal harmonic}

force. The external force vector at the top can be described by:

In which:

= position vector of the top of the pendulum (m)

= first derivation to time of position vector )7 (m/s)

= second derivation to time of position vector iF (m/s2)

6)7 = infinite small motion of position vector )7 (m)

ut = horizontal motion of the top (m)

ft,yo

= external force vector in the top (N) = horizontal force in the top (N) = acceleration of gravity (m/s2)

(A.3) =

(5)

The only external force at the bottom of the pendulum is the gravitation, which can be

described by: 0

f.=

0 (AA),

rn, g

In which: =external force vector at the load (N)

With the definitions of the motions and the forces the virtual energy balance can be

constructed:

6TO.tn, =6X1 +- 6-itft (A.5)

The left part of the equation defines an infinite small change in the internal energy of the pendulum, which is in this case the mass forces of the load times an infinite small motion. The right section defines an infinite small change in the external energy acting

on the pendulum, which is in this case the external forces times an infinite small motion.

Substitution of the motions and forces in the virtual energy balance gives:

5ut - (6-y() .r771 _yo _{M " 13w} _{' w} _{f Ivo "- yo)+}

843w 1w

(j2

6-y0 M/ O'w ' 6'2

rnl g .

_.zo)=

The rotations of the pendulum are assumed to be small, so we can define the

products of the unity vectors: = sin( 3,) = f31/4,

6-zo cos(13w ) -1

yo =cos( [3w ) 1

ezo = sin( )

Equation (A.6) can be rewritten:

Sur .(ml .ur

mr 13'w

Iwi

ft,y0

.iw .(77/ m1 1w + 13w

rrit gr).= 0

11

11 Because lit and

OW are the two degrees of freedom of the system, they are

independent of each other, so the equation above can be written as two equations:

;

f

t ,yo

[it f3w

=0

it4/ /w Pw

g =0

The equations can be written in matrix formulation:

.[Kv

.1w

0

ut ut t,yo

13w /w_

mi

0

If we assume that the excitation of the pendulum is harmonic, we can define the horizontal force in the top and the motions of the pendulum as follows:

ft,yo = Ftyo cos(w t)

ut =Ut coop t)

(A.11)

=B, COS(Ct) t)

(A 6) (A 7) (A.8) (A.9) (A 10) = +

1+ 0

L

(6)

In which: Ft_.yo = amplitude of the horizontal force ft.yo (N)

Ut = amplitude of the horizontal motion ut (m)

Bw = amplitude of the radial motion (3w (rad)

Co = radial frequency (rad/s)

In this case the amplitudes can have a positive as well as a negative value. The derivations to the time of the force and the motions can be determined:

With matrix operations the motions can be described as function of the horizontal

force:

/w 1

[

ut ft,yo g 032 (A.15) MI

P. /,

g _

The motions of the top and the load can be described separately by:

f

(t,y0 /w 1 \ (A.16) ut m1 g CO2 ./w t,yo 1 ml

The ratio between the horizontal motions can be described using formula (A.16): Id/ = _{(A 17)}

g 032 -

/w Lit

=U Ut sin(w t)

(A.12) vv =

co B, -sin((.0

t)

In the same way the second derivation to the time can be determined: fit = 2

- Ut cos(w t)= co

2

(A.13)

13w =

2 Bw cos(w

2

Equation (A.10) can be rewritten:

_

2

CO2 _ut ₁

ft,yo-2 2 _rnt (A.14)

In which: P- = ratio between the horizontal motions of the load and the top

of the pendulum (-)

The natural frequency of the pendulum can be defined ifwe assume that the

horizontal motion of the load is larger than the horizontal motion of the top of the pendulum. With the equation given above we can calculate the natural frequency as

follows:

cc4=45( (J)2I w)--> 0

ut

So the natural frequency of the pendulum is:

2 g

CO, =

(7)

"

---Figure A.4

Model of the Single pendulum

Figure A.3

Motion response of the Oscar pendulum

o 0.3 0.6 0.9 1.2 I .8 2.1 2.4 2.7

Oscar pendulum (1w=30m)

---- Oscar pendulum (1w=50m) 0.) (rad/sec) Oscar pendulum (1w=70m)

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-ASSESSMENT OF THE MOTIONS AND FORCES OF LIFT OPERATIONS WITH SHEERLEGS IN AN IRREGULAR SEA

The ratio between the motion of the load and the top can now be described by:

2

Up _COP

2 2

Lit CO

In figure A.3 a few examples are given of the ratio between the motion of the load and the top as function of the radial frequency. As can be seen, the ratio has one peak at the natural frequency. For larger frequencies the ratio gets very small and has a negative value. This means that the load moves in the opposite direction of the top of the pendulum. The pendulum delivers a restoring force to the horizontal motions of the sheerlegs. The larger the motions of the pendulum are the smaller the motions of

the sheerlegs will be.

In the following sections we will see in what extend the dynamic behaviour of the Oscar pendulum corresponds to the dynamic behaviour of the Single and Double

pendulum.

A.2. THE SINGLE PENDULUM

In figure A.4 the model of the Single pendulum is given. This pendulum seems to be

the same as the Oscar pendulum, however, there are some differences. The load of

the Single pendulum has mass inertia and the load is connected to a bar instead of at 'wire. A bar is used to ensure that the load will rotate.

The new measures of the pendulum are: lb = length of the bar (m)

= radius of gyration of the load in x direction (my

The motions of the Single pendulum are defined in the same way as the motions of the Oscar pendulum. The only difference is that a bar replaces the wire, so:

T(/ = 3-(t /b -64 = Lit yo

)71 =1:1( Ob .1b

=

+0b

(Ob )2 lb 6-4 t

6)71 =Z3ut +5(3b lb --E,5

In which: 13b _{= angle of the bar (rad)}

= unity vectors of the coordinate system of the bar

The external forces acting on the pendulum are equal to the forces acting on the Oscar pendulum. However the internal energy of the pendulum is changed, because the radii of gyration are added to the mass of the load. The virtual energy balance is

now defined by.

8-i1.m1 1+613,b- 6rn1-ri.x2 -0.1) 5)7/'

+5r(tit

(A.22)

In which the second term in the left part of the equation presents the internal energy due to the rotational acceleration of the load.

The products of the unity vectors of the bar and the global coordinate system are

defined in the same way as those of the wire:

(A.20) (A.21)

lb-(A.23) = Sin 03 b b .zo cos(pb )=-- 1 e-5 )/() = COS(r, b 1 ZO = Sin

(1 b)Pb

41b-iyor 0-5. Ti'yo y =

(9)

Figure A.5a

Motion response of the Single pendulum

Figure A.5b

Motion response of the Single pendulum

11 I I I I I I! ii 1 11 i ! 1 11 :_-_,.-.,...:.---_-:-=.:r.---z---.,---===-.7 , ----.7 ,,, --- ,=--, ,

7

' 1 1 i I I

--

- 2-10 0.3 0.6 0.9 1.2 l'.5 ii.8 2.'4 endulum (1b=50m r1=4m)

endulum (1b=5Orn r1=8m) CO 1( rad/seC)1 endulum (lb 50m r1=17m) 2.4 ±2'.,7 Single Single Single i 2 0 II 1 , , t

it

,

41 , 1 i

ii,

ul

._

_i__ il 'I 1 I 1 1 : i: ii , i

'Ii

pendulum (1b=30m r1-=8m), pendulum (1b=50m r1=8m) pendulum (lb=70m r1=8m) 1.5

'is

2.2 c), EracUsec) 2.4 2.7 Single

-- Single

Single

I

0 0.3 0.9

(10)

Substitution of the motions and forces in equation (A.22) gives:

In the same way as we did for the Oscar pendulum we can define two equations:

6136

With matrix operations the motions can be described as function of the horizontal force: 2 rl.x2 lb2 (1)2 )

°

Ut 2

g lb

(1)13 = 2 2 lb rl,x

=0

With this equation we can define the value of the natural frequency of the pendulum:

In figure A.5a and figure A.5b a few examples are given of the ratio between the

motion of the load and the top as function of the radial frequency. As can be seen, the

ratio has one peak at the natural frequency.

TU DELFT SMIT ENGINEERING By 71

(A.24) (A.30) /b2 1 ut ft,yo

g.11)-0)2

F.,1,x 2 co 2 (A.27)

g 'ib

(1)2

ri,x2

The motions of the top and the load can be described separately by:

t.yo lb2 1 Ut = Ig .15

2 0 2

w 2

f

1 (A.28) =ut +1313 -lb ml 0.)2

The ratio between the motion of the load and the top can be described as:

2 2 LI/ = =

g

CO '0,x

_(A.29) 2 2 2 2 LI( b 'I,x )_'b ft,yo

= 0

Ut +

lb

mi (A.25) 2 '/ x 4-I3b Ut+ 13.b

g= 0

So the following matrix formulation can be given:

2 2 g 2 CO -2 ri _x 1+

[U

13b 'lb ft.yo (A.26) mi 0 2

Sut (5-_{y -rn1 'Lit} _{yo +} _yo

_{rniO;b/b -65}

_{ft,yo 'eryo)+}

6-5 / 6y0 +e5 0.6'/b 65 -1-2

6-6'n71-0b. 1;x

6+&5MIg&z0

'b b

_

+

-'b

(11)

II

Figure A.6,

Model of the Double pendulum

Figure Ala

Motion response of the Double pendulum

1 2i 1 1 0 1 II 1 ...--I 1 ii ii . Ill

/

i 3' . - ----r , 7 1 1 I) 17 03 0.6 09 pendulum (1w=25m pendulum (1w=25m pendulum (1w=25m 1.2 lb=25m lb=25m 1b=25m 15 1 r1-6m) r1=8m) r1=10rn) 00 2.i/ '2'4 (0 (rad/sec) Double Double Double 2.7

(12)

For larger frequencies the ratio converges to a positive value. This value can be

retrieved from formula (A.29):

g '1b *ri.x2 0.,2 (A.31)

''b

'lb

(1)2'

x2 )lb

2 ' (1) 2 r1,x 2 + lb 2

We can see that this is a positive value, so the load moves in the same direction as the sheerlegs. In section A.4 we will discuss the influence of the motions of the

pendulum to the motions of the sheerlegs in more detail.

A.3. THE DOUBLE PENDULUM

In figure A.6 the model of the Double pendulum is given. The pendulum is a

combination of the Oscar pendulum and the Single pendulum. A wire models the upper part and the lower part is equal to the Single pendulum. The upper and lower part can rotate relative to each other. Besides the motions of the top and the load of the pendulum, also the motions of the connection point between the wire and the bar

should be defined.

The motions of the connection point are:

kc =Yet +1w = -dy0 +1w

Xc = e-yo ÷ Ow

61

eyo + IL

(IL )2 ./

Lit '6-yo +IL 'Iw

5. c

=Sur e

j2

In which: _x _{position vector of the connection point (m)} The motions of the load are now defined by:

)71 )71 out =

+16.6.4 =Lit

+lb

6-4 = .jto + Ow .1w e2 Pt) 'lb 6-2 (Ow )2 ' t yo w w

-e-yo +IL

b

UP

=51-it

e-yo +Ow iw

2+813b

The internal and external forces working at the double pendulum are the same as

those working at the single pendulum. Therefore also the definition of the virtual energy balance of the double pendulum equals to the one of the single pendulum. The substitution of the motions in the equation of the virtual energy balance gives:

mi

Eyo+iTyom,

+

'.1,/o ml 0.t) 'lb -65 -6yo ft,y

e2 rn1 -63/0 _rn/

-0

-lw

₂₊

ml Pb

m1 g

e5 +6.5 62 +e5

_{Ob lb55+}

2 .

r

i'x

.55 +55 'rn1 g5zo

lb

-/b e-5 (13b)2 ./5 .e4

(A.33)

(A 32) (A.34)

=0

o13w 1w 613b .1b ' = +

(13)

El

1

11

Figure A.7b

Motion response of the Double pendulurn

Figure A.7c

Motioniresponse of the Double pendulum

2 , , q i 11 11 4 1 1 I , p t a II _i 11 III 1.

if

t,

i

. _ 101 m 1 i 7 I 1 1 , 1 t I i i . __

Ii

Fl --", F I P ii ! 1 ro 0.3 0.6 0.9 1.2 1.5 9,8 2.1 2.7 Double pendulum 01w=25m lb =15m r1=8m)

--- Double pendulum (1w=25m 1b=25m r1=8mr) in) (rad/sec) Double pendulum (1v.-25m lb=35m r1=8m) .3 11 In --$ 1 A , , , 1 1 'I 1 1, I II I ill in

--

_..

,/11

7

-a= Fj IL 11 11 1 it .1 III r ) --, II / t , i i c,;, IF HI 1 II li 1 ,,.' I 1 IC 03 0.6 CO 1.2 1.5 pendulum (1w=l5m lb=25m r1=8m) pendulum (1w=25m 1b=25m r1=8m> pendulum (1w=35m 1b=25m r1=8m) Double 9113 2Y1 2.4 (,),(Ead/se0 2'.7 Double

-- Double

2,4

(14)

The following products of unity vectors can be used:

e1 .64 = cos(pw

e1 .e5

= Sin(i3w [b),

NJ, _13 b 5.4 = sin( Pb

i3w)i3b

Rw

-65 = COS(I3w --p0),1

Equation (A.34) _{can be described as three separate equations:}

ft

at +Ow ./. +0:b

b

=0

Lit MI +Ow -lw +11.bIb +13w -g = 0 2 Ut

+IL

'1w Bb

Ib+13b-

;

+Pw

'b

Rewritten in matrix notation:

The motions of the pendulum can now be described by:

g lb °)2 ri,x2

The motions of the top, the connection point and the load_{can be described separately}

by: ft _w /1)2 1 Ut = 2 g

g

co 2

ri,x2 o)

-g =0

ft.yo r 1 2 'b 1

tic =Ut + L ' lw =

2 2 2 MI .g

lb

'0,x 0.) ft,y0 1 Ut = Ut +

_{+13b.ib =}

2 MI

The ratio between the motion of the load and the top can be described as:

g '(g -0)2-ri,x2

= =

ut _-CU

/w g

'Ib

'

g

2 2 2 2 2

2 -co

-

co2 CO2 -CO2 -g--- CO2 lw _6)2

1_0)2

lb -CO2 2

2"

1+ ri,x Ut Pw 136 -ft,y0 (A.37) 0 0 lb2 Ut 13w .1w 13blb ft.yo /w g 2 lb 1 (A.38)

g 'ib 0)2

rt,x2 /w CO2 rT71 (A 39) (A.40) 13b) e2

)

/b IF r n

(15)

11

Figure A.8

Motion, response of four pendulums

Figure A.9

Motion response of lour pendulums!

II 3 II I i il II IIIII I II I

-1

I L -- -2, I II I I I, II II 4 I I 1 o 0.3 0.6 0.9 14.24 1.5 pendulum (1w=50m) pendulum (1b=50m r1=4m) pendulum (Iw-20m lb=30m r1=4m) pendulum (1w=30m lb-20m r1=4m) Double Double 146 2.1 2.44 to (radisec) _ 24.14 Oscar

T.' Single

i I' i 1 -I: -1 I p i 4 1 I 1 , i

I/---.. 4 KO 6.3 0.6 0.9 11.2 145 pendulum (1w=50m) pendulum (16-50m r1=8m)i pendulum (1w=20m lb=30mi r1-8m) pendulum (1w=30m lb=20m r1=8m) Single Double Double 11.8 2.1.41 2.4 Co (rd/sec) 2.7 Oscar

(16)

With this formula we can define the value of the natural frequency of the pendulum:

ui 2 fw I 2 2 )_ b2 co 2 u t 2 (.L) = ^ 2 . rt.x 2

In figures A.7a, A.7b and A.7c a few examples are given of the ratio between the

motion of the load and the top as function of the radial frequency. As can be seen, the ratio has two peaks, one at each natural frequency.

MASS FORCES OF THE PENDULUM

The mass forces are the forces that are caused by the accelerations of the mass of the pendulum. Because the mass forces are the product of the mass and its

accelerations, we first have to define the accelerations of the mass. The accelerations of the load of the pendulum can be defined using the motions of the top of the fly-jib and the ratios as defined for the model of the pendulum.

In the sections Al,. A.2 and A.3 the ratios between the horizontal motions of the top

and the bottom of the pendulums are given. These equations yield for the motions in y direction as well as for the motions in x direction.

The ratios of the three pendulums are given below. Motion ratio of the Oscar pendulum:

1-1-0 =

g 0)2 1w

Motion ratio of the Single pendulum:

g 'lb 6)2 ri,x2

s =

\Y '1,x

,

2)

/ b 2

u2

Motion ratio of the Double pendulum:

g

6-ib(02.0,x2)

= 2

.1)-(g

w

lb (1)2 *ri,x2

g /

2 ())2

In the introduction of this appendix it is mentioned that the vertical motions of the load and the top are the same. So using one of the ratios as given in formulas (A.42), (A.43) and (A.44) the motions of the load can be defined by given motions of the top of the pendulum: Ut.x 1711 = Lii.y Ut,z LI 0 0

In which: 1.71 = translation vector of the load of the pendulum (m)

Fit = translation vector of the top of the pendulum (m)

Using the equations as given above, we can also define the mass forces of the pendulum. The accelerations of the load of the pendulum are:

2 ui 2

17t

(A 45) (A 46) g (1-0(2

+164w

+162)-±likx2

+lb lw +lb2

4 . r1.x2 (A.41) g i(A.42) (A.43) .(A.44)I

= 0

(17)

LI

---0.3 0.6 0.9 1.2 1.5 Oscar pendulum (1w50m) ---- Single pendulum (1b=50m r1=12m) Double pendulum (1w-20m lb=30m r1=12m) Double pendulum (1w=30m lb=20m r1=12m)

Figure A.10

Motion response of four pendulums

LI

1.8 2.1 2.4 2.7

co (rad/sec)

(18)

The mass forces of the pendulum are:

p 0 0

= m1 .E71 = mi p _{0 '17t} (A 47)

001

-In which: = vector of the mass forces of the pendulum (ND'

This vector is defined in the global coordinate system, while we are interested in the forces relative to the lift structure of the sheerlegs, so the force vector has to be

defined in the sheerlegs coordinate system. In appendix D the accelerations ofmass

points of the lift structure are determined, but these definitions can also be used for

the pendulum.

(19)

APPENDIX B

MASSES AND DIMENSIONS OF THE LIFT STRUCTURE

The masses and dimensions of the sheerlegs are retrieved from a number of documents of Smit International [Blom, 1992] and [C.B., 1994]. For the calculations done in this project the model of the lift structure of the Taklift 4 and of the Taklift 6/7

is simplified. The masses of the various wires in the lift structure_{are added to the}

masses of the frames, because the masses of the wires are small compared to the masses of the frames. A part of the mass of the preventer (proportional to the position

of its COG) is added to the mass of the A-frame, because the preventer_{isn't loaded}

by forces coming from the rest of the lift structure and the pendulum.

The calculation of the new concentrated masses and positions of theCOG's of the

frames is determined in this appendix. For the Taklift 4 the masses of the elements

are concentrated in four frames, namely the A-frame, the fly-jib frame, the fly-jib brace

and the luffing frame. For the Taklift 6/7 only three frames_{are taken into account,}

because the luffing frame of the Taklift 6/7 is a part of the barge. The radii of_gyration

of the masses of the model have to be estimated. because they_{are not given in the}

documents.

For this project a number of simplification are used for the model ofthe lift structure.

These simplifications are:

The dimensions as given below are typical dimensions. For_{example, the length of}

the A-frame is the distance between the pivot points of the bottomand the top of

the frame, thus not the total length.

The wires are modelled as one line, while in reality the wires_{consist of two}

bundles.

The centrelines of the wires and frames_{are crossing in the junctions, while in}

reality the centrelines lay out of the connection points. For example, the _main

tackles and the fly-jib of the Taklift 4 are not connected at the_{same point of the}

A-frame.

The length of the wires as given below is defined as the distance between two

junctions of the lift structure, thus not as the distance between the _connection

points (sheaves, etc.) in reality.

The frames have a small thickness compared to their_{length and breadth and can}

therefore be aped are two dimensional elements, so they have no thickness.

The sets of tackles are put together to single tackles, _{so there is only one top}

tackle and one main tackle.

The masses of the frames are including masses of sheaves, upper blocks of

tackles and other appendages.

For the masses of the wires that have no constant length a mean value is estimated.

In this appendix the masses and dimensions of the model of the lift structure are discussed. First the original dimensions are given and after that the definitions of the masses and radii of gyration of model are discussed.

TU DELFT SMIT ENGINEERING By ₇₆

(20)

Al

Mt

NAF

Mt

Tt

Figure B.2

Model of the lift structure of the Taklift 6/7

(21)

ORIGINAL MASSES AND DIMENSIONS OF THE LIFT STRUCTURE

In figure B.1 and B.2 the models of the lift structures of the Taklift 4 and the Taklift 6/7

are shown. In which: A = A-frame = fly-jib frame = fly-jib brace = luffing frame Mt = main tackles pr = preventer Tt = top tackles wA = main stays wF = upper stays wJ = lower stays wL = luffing wires

These models are used for the calculations of the dynamic forces. The dimensions of the frames are defined as shown in figure B.3.

In which: .=breadth of the bottom of the frame (m)

b2 = breadth of the top of the frame (m)

Cf,or = original longitudinal position of the COG of the frame (m)

If = length of the frame (m)

The subscript"? stands for a frame, e.g. the A-frame, the fly-jib frame, etc.

The origin of the coordinate system of the barge is positioned at the intersection of the baseline, the APP (aft perpendicular) and the centreline (see figures BA and B.2). Below the masses and dimensions of the lift structures of the Taklift 4 and the Taklift

6/7 are given. TAKLIFT 4

Table B.1 Connection points of the lift structure at the barge of the Taklift 4 in local system of axis

x coordinate (m)

Z coordinate (m)

Barge extremity

83.1 7

Pivot of A-frame

77.5 8.7

Connection of lower stays

76.25 8.22

Pivot of preventer

- 74.3

Connection of main tackles

62.7 8.95

Connection of top tackles

55.8 8.6

Pivot of luffing frame

52.5 7.43

Connection of lower stays

49 7.88

Connection of luffing wires

9.38 7.73

(22)

Figure 33

Model of a frame

Figure BA

Extra measures

(23)

Table B.3 Masses and dimensions of the wires of the Taklift 4

*) = estimated mass and length for mean values of the outreach and the offset

In which: I = length of &wire (m)

= mass of a wire (ton)

In which: r _{= reefing factor of the tackle (-)}

The reefing factor stands for the number of wires connected to the lower block of a

tackle divided by the number of winches connected to the tackle.

Extra dimensions (see figure BA):

Angle between fly-jib frame and brace aFJ =100 deg Connection of preventer at A-frame: dpr=20.62 m

Mf,or (ton) If (M) Cf.or (m)

bl (m)

b2 (m)

A-frame

329 54.4 33.63 19.6 6.6

Fly-jib frame

124.2 30 18.432 8.1 3.8

Fly-jib brace

71.8 23 16.827 8.1 7.8

Luffing frame

48 23 18.5 14.7 14.7

Preventer

70 25.6 16.1 14.7 10 (ton)

I, (m)

Main stays

14.4 61.59

Upper stays and top tackle wire

15.6 40.7

Lower stays and top tackle wire *)

18.4 75

Luffing wires dry 15.9 50

m (ton)

r(-)

Main tackle

20 12

Top tackle

60 9

Table B.2 Original masses and dimensions of the frames of the Taklift 4

In which: _Mf,or = original mass of a frame (ton)

Table BA Masses and reefinqs of the lower blocks of the Taklift 4 I

(24)

TAKLIFT 6/7

Table B.7 Masses and dimensions of the wires of the Taklift 6/7

*) = estimated mass and length for mean values of the outreach and the offset

Extra dimensions:

Angle between fly-jib frame and brace aF = 114.5 deg

Connection of preventer at A-frame dpr=18 m

8.2. _{CALCULATION OF THE MASSES AND RADII OF GYRATION OF THE MODEL}

For the calculations of the dynamic forces, the mass of the lift structure is assumed to

be concentrated in four frames. In this section the fourmasses and the radii of

gyration are determined.

TU DELFT SMIT ENGINEERING BY 79

x coordinate (m)

z

coordinate

(m)

Barge extremity

72.2 5.5

Pivot of A-frame and connection of lower

stays

68 7.1

Pivot of preventer

_- 5.5

Connection of main tackles

33.5 15.1

Connection of top tackles

27.7 14.3

Connection of main stays

₂₇ _28.5

mf.or (ton) If (m) Cf.or (m) ID, (m) b2 (m)

A-frame

272 50 29.35 21 6

Fly-jib frame

58 20.5 14 9 4

Fly-jib brace

34.3 15 9.8 9 7.1

Preventer

15 23.71 12.5 12.4 12.4 mw (ton)

I, (m)

Main stays *)

19.2 75

Upper stays and top tackle wire

6.4 30

Lower stays and top tackle wire

5.9

45.8 m (ton)

r (-)

Main tackle

89 16

Top tackle

44 10

Table 8.6 Original masses and dimensions of the frames of the Taklift 6/7

Table BM _{Masses and reefinqs of the lower blocks of the Taklift 6/7}

Table B.5 Connection points of the lift structure at the barqe of the Taklift 6/7 in

local system of axis

I

(25)

iBar plus mass in top of bar

m,

(26)

DETERMINATION OF THE FOUR MASSES

The masses of the wires and the mass of the preventer will be added to the masses of

the frames for the model of the dynamic forces calculation. The masses of the frames for the model are:

M wA pr pr M A = M A'°r 2 _pr MF = MF,or 2 M wJ M wF = MJ,or 2 2 M wL M wA M L = M L.or 2 2

In which: mf = new defined mass of a frame (ton)

Besides the new mass that is calculated, also the position of the COG is adjusted for each frame. This is done as follows:

M wA Cpr

M A,or C0

IA + MI pr pr 2 _/pr M wF CA = CF = Cj CL lf,x M A M wF M F ,or ' C F ,,or 2 "F J m01. _Jar M wJ M wF 1 2

j

2 117J M wL ' L M wA L M L,or C L,or 2 2 mL

In which: Ct. = new defined position of the COG of a frame en)

RADIUS OF GYRATION WITH RESPECT TO THE X AXIS

The radius of gyration with respect to the x axis of the frame depends on the mass

distribution in y direction. The major part of the mass of a frame is concentrated in the two vertical main legs, so the radius of gyration with respect to the x axis is equal to the mean distance between the main legs and the centreline of the frame:

1 bi + b2 rf ' 2 2 ( 1 b1+ b2 2 (B 3) 2 2

In which: _11,x =moment of inertia with respect to the x axis of the frame (ton

m2)

rf = radius of gyration with respect to the x axis of the frame (m) (B 1)

M F _{(B 2)}

+ +

+

(27)

RADIUS OF GYRATION WITH RESPECT TO THEY AXIS

The radius of gyration with respect to the y axis will be calculated by using the formula for the moment of inertia of a bar (perpendicular to the longitudinal direction of the

bar): 1 1b,yc = 162 12 1 bye = mt:,

In which: _/b,yc = moment of inertia with respect to the y axis relative to the centre of the bar (ton m2)

'bye = moment of inertia with respect to the y axis relative to the

end of the bar (ton m2)

I b = length of the bar (m)

mb =mass of the bar (ton)

This formula is valid only when the mass of the beam is homogeneous distributed. However, the mass of the frames of the sheerlegs is not homogeneous distributed,

because the COG's are not positioned in the centre of the frames. Two methods are

used to estimate the mass inertia with respect to the y axis.

In the first method it is assumed that the mass inertia if the frames equal to the mass

inertia of a bar with the same length and mass:

1/ 2

'

/1

I f

' 12

In which:

ify

= moment of inertia with respect to the y axis of the frame (ton

m2)

rfy

= radius of the inertia with respect to the y axis of the frame On)

In the second method it is assumed that a part of the mass of the frame is

concentrated in the top of the frame. This can be explained by the fact that the top of a frame is constructed for the largest loads and in the top extra mass are connected, e.g. sheaves, upper blocks of tackles and wires. The frame can be modelled as homogeneous bar with the length of the frame and a mass at the top of the bar, such that the COG of the frame remains located in the original location, See figure B.5. The sum of the two masses is the mass of the frame. The masses are calculated as follows:

If cf

mb =

Mr

0.5.4

(B.6)

Mt = MI

Mb

In which: _Mt = extra mass in the top of the frame (ton)

(B 4)

(B 5) =

(28)

The moment of inertia of the two parts is calculated relative to the COG of the frame

and summed:

r1

If y

mf

The two methods to determine the mass inertia with respect to the y axis as described

above give for each frame of the sheerlegs almost the same values. The average

value of the calculated radii of gyration is given below for each frame. The calculated masses and radii of gyration of the frames are:

TAKLiFT 4

TAklift 6/7

B.3 SIMPLIFICATIONS OF THE LIFT STRUCTURE OF THE TAKLIFT 4

The frames of the lift structure of the Taklift 4 are constructed in a different way than the frames of the lift structure of the Taklift 6/7. One of the differences concerns the top of the A-frame and the top of the fly-jib frame.

In the top of the A-frame of the Taklift 6/7, the main stays, the main tackles and the fly-jib are connected to one bar and have therefore the centrelines of the connection points at the same (axis in y direction). The same yields in the top of the fly-jib frame of the Taklift 6/7, where the upper stays and the top tackles are connected to one bar. See figure Be..

In the top of the A-frame of the Taklift 4, the main stays, the main tackles and the

fly-jib are not connected at one axis and in the top of the fly-fly-jib frame the upper stays and

the top tackles are not connected at one axis. See figure B.7.

rrif (ton) If (m) cf (my rx (m) ry (m)

A-frame

380.2 54.4 32.52 6.6 16.7

Fly-jib frame

132 30 19.12 3 9.3

Fly-jib brace

88.8 23 18.01 4 6.9

Luffing frame

63.15 23 19.58 7.3 6.5 mf (ton) If (m) cf (m) rx (m) ry (m)

A-frame

289.5 50 29.73 6.7 15.4

Fly-jib frame

61.2 20.5 14.3 3.2 6.4 Fly-jib brace

40.5

15 10.6 4 4.6

/f.y 'Mt

-cf

+Mb

If2

-+

12

cf

if ]2

-2 (B.7)

Table B.9 Calculated masses and dimensions of the frames of the Taklift 4

Table B.10 Calculated masses and dimensions of the frames of the Taklift 6/7

(29)

Since the elements of the lift structure of the Taklift 6/7 are connected to one bar in

certain junctions (top of the A-frame and top of the fly-jib frame), the definition of the

bar model is simple and the outreach of the top tackles is equal to the horizontal

distance between the bow and the top of the fly-jib frame. Since the lift structure of the Taklift 4 is not as simple as the lift structure of the Taklift 6/7 the following problems

had to be solved.

The main stays and the fly-jib are not connected at the same point at the top of the A-frame. The connection point of the fly-jib is positioned at the longitudinal

centreline of the A-frame and therefore considered to be the junction of the bar model. The length of the main stays should be adjusted to this point. The original length of the main stays is 58.47 metres and the distance between the connection

points of the fly-jib and the main stays is 3.12 metres. Since these two lengths are almost in one line for normally used outreaches, these lengths can be added, so

the length of the main stays becomes 61.59 metres. This length is already given in table B.3.

The main tackles and the fly-jib are not connected at the same point at the top of the A-frame. In this project the main tackles are considered connected at the same

location as the fly-jib. This estimation can be done, because the mass of the load in the main tackles is zero in this project and most times the main tackles are hanging right under the connection point of the fly-jib.

The top tackles and the upper stays are not connected in one point. The top

tackles are connected 1.4 metres below the longitudinal centreline of the fly-jib frame at a distance of 30 metres from the lower pivot of the frame. For a small

outreach and a small offset the difference in outreach of the top of the fly-jib frame

at the centreline and the top tackles is about 1.4 metres.

(30)

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yr

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int.!

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(31)

APPENDIX C

DESCRIPTION OF OSCAR

In this appendix a short description is given of the simulation program Oscar. The

description is a standard appendix for documents of Smit !Engineering.

(32)

1. _{OSCAR ILMOULLING ASPECTS}

1.1. STRUCTURE OF PROGRAM

OSCAR II

is an integrated simulation and analysis program for analysing the

_ocean

performance of (a system of) bodies.

OSCAR

_{II uses either the strip theory or the 2-0}

or 3-D diffraction theory to determine the hydrodynamic properties of these bodies. Several bodies can be combined into one system for analysis by means of connectors. Connectors can be of different types; with a 'fixed connector the user can specify the

degrees of freedom,

'tension-only' or _{'compression-only' connectors,}

_'spring',

'dampers' and 'flexible' connectors (e.g. anchor lines).

The pre-described system of bodies is called a project within

OSCAR

_{II. For each}

project, a data file has to be set up, in which the bodies and their initial positions in the global system of coordinates are defined. The data file may 'insert' other data files, e.g. the data files in which the body is defined. This allows the use of the same body data

file for different

OSCAR

II projects.

In addition to the data file, a command file is required. This command file allows the user to define and modify the connectors between bodies and to specify the contents of the compartments. This file also contains the instructions for the type of analysis to be performed, as well as instructions to produce reports of the results.

The system of bodies has to be in equilibrium prior to start the dynamic analysis. This equilibrium can also be determined (search for) by the program. The following report facilities are available to check the equilibrium: the geometry of the bodies; buoyancy,

weight and connector forces per body, the forces acting on these bodies, etc. After the dynamic analysis, a postprocessing menu is activated to extract the results

from the database. Output facilities comprises: the

RAO's

of connector forces and

motions of any point on each body, the most probable extreme values in an irregular seastate, velocities and accelerations, etc.

1.2. LOCAL AND GLOBAL COORDINATE SYSTEMS

Each body has been defined within its own local (body) coordinate system. All

coordinate systems are right-handed. For the vessels the origin

is

at keel level,

centerline, sternside. The positive X is directed forward, positive Y directed portside and positive Z directed upwards.

All the bodies used in a Project can be possitioned in a global coordinate system. The directions for the environmental influences (waves, wind and current) are defined in this global system of axis.

(33)

1.3. _STATISTIC

The dynamic analysis will be performed for a range of regular waves as well as for the irregular waves specified. The results in irregular waves, however, will be obtained by statistical post-processing on the basis of the regular wave analysis. A summary of the theory behind this statistical manipulation will be discussed in this section.

This theory is based on the assumption that an irregular signal can be reproduced by the summation of a limited number of independent sinusoidal functions, each having its own frequency, amplitude and phase.

Mechanical and physical systems may be interpreted as a transducer transmitting

energy from the input x(t) towards the output or response y(t). Suppose the output is uniquely determined in terms of the input: y(t) =L[x(t)], then the system is completely defined if the nature of the operator L is known. The spectral density representation of a stochastic variable allows an output density function to the input density function by

means of a frequency response function (also referred to as Response Amplitude

Operator), provided the observed system is linear:

Syx

) =S(w) Xyx() 1 2

in which:

s(6))

= Spectral density function of input x(t)

S(o)

= Spectral density function of output y(t)

(co)

= Response function operator

yx

co =

Frequency

The following quantities can now be calculated with the use of the spectral density

function:

= fo S

(CO)

condo

xn

When S is an even, real function and x has a narrow spectrum and zero mean value, the standard deviation and the average period of the irregural phenomena x(t) can be obtained from: = \Ira

x

xo

Mx°

= -

_Mx1

(n E

_N+)

(34)

When x follows a Rayleigh distribution, then it can be calculated that the significant

double amplitude of x(t) equals:

2xa//3

=

40x

The most probable extreem value for N oscillations, can be expressed in the derived standard deviation as follows:

xmax = a

*

* In (N)

For N =1000, the most probable extreem (single amplitude) can be derived from:

Xrnax

3.72 * ox

In OSCAR II this factor 3.72 is the default value for determining the most probable

extreme value. The 1000 oscillations taken into account, corresponds to one hour

exposure time for the wave periods of about 3.6 seconds, or three hours for wave

periods of about 10.8 seconds, etc..

AVAILABLE MODELS (BODIES)

When creating a project with OSCAR II, use can be made of existing models of (SMIT

owned) equipment. Models are available for sheerlegs, transport barges, tugs and

suppliers. When a model is not available, it can be added to this collection.

The models do include descriptions of ballast tanks, light ship weight, COG position,

radii of inertia, etc. For the motion analysis, the hulls are described by a 3-D panel

model. The files which contain these data have been thoroughly checked and stored on the hard disk of the computer.

When using one of the existing models in a project composition, the required body data files of the involved equipment are included into the project data file. Additional data

which is project related, such as extra deckloads, nodes for the connection of slings, anchor wires, etc., is added in the project data file. With this setup, it is ensured that the validated data of the bodies remains unchanged.

(35)

Ul

_{marine, Inc.}

Engineers and Analysts

OSCAR II

OCEAN STRUCTURES

_{SIMULATION AND ANALYSIS}

for IBM P0-386 or compatible_{and larger computers}

OSCAR II is an integrated

ocean simulation and analysis program for analyzing the ocean performance of systems of bodies. These systems may be modeled or the program accepts existing models _{from the programs ISAAC and SAUL...}

and MOSES. In addition, other

existing models are accepted, such as SACS models or many STRUDL models.

Several bodies may be combined _{into one system for analysis. Connor.tors in the system may be defined interactively}

without redefining the model. When a system has been defined, the _{user may simulate the static and dynamic}

proc-esses with simple commands.

The engineer may find the ecuilibrium _{configuration due to the current ballast and weights. If suitable for initiation of a}

process, simulation may be initiated. If_{not suitable, the engineer may interactively redefine the ballast}

and/or weights

for a new equilibrium Configuration. _{OSCAR II will automatically alter the inertia matrices}

of the bodies to account for

the defined changes. With a few simple commands, the engineer may automatically perform _{a stress analysis of the}

system. The data is saved in the internal database by process name for later use. The engineer may change the name

of the process and have a large number of processes available for further consideration.

2. _{SOFTWARE DESCRIPTION OSCAR II}

a

(36)

MAJOR FUNCTIONS

HYDRODYNAMIC AND STRESS MODEL DIFFERENCES _{ARE EASILY RESOLVED}

HYDROSTATIC STABILITY MAY BE ASSESSED _{INTERACTIVELY FOR INTACT OR DAMAGED CONDITION}

HYDRODYNAMIC INERTIA, DAMPING AND LOADS MAY _{BE OPTIONALLY COMPUTED WITH MORISON'S}

EQUATION, STRIP THEORY OR 3D DIFFRACTION THEORY

TANKS MAY BE BALLASTED INTERACTIVELY AND THE STRUCTURE'S INERTIA AND WEIGHT AUTOMATICALLY CORRECTED

VESSELS MAY BE COMPOSED OF NUMEROUS HULLS _{TO HANDLE SEMI-SUBMERSIBLES}

MOORING LINES MAY BE COMPOSED OF UP TO FOUR SEGMENTS SEPARATED BY UP TO 3 CLUMP WEIGHTS

OR

ANCHOR LOCATION AND PRETENSION PERFORMED AUTOMATICALLY ANALYSIS PERFORMED IN EITHER TIME OR FREQUENCY DOMAINS

3D DIFFRACTION THEORY ALLOWS THE USER TO SPECIFY HULLS WHICH DO NOT INTERACT, RESULTING IN REDUCED COST ANALYSIS

FREQUENCY DOMAIN ANALYSIS ALLOWS CALCULATION OF VESSEL RESPONSE TO A SET OF WAVES OF

GIVEN DIRECTION AND PERIOD WITH OUTPUT REPORTS OF CONSTRAINT FORCE AND TOTAL

HYDRODYNAMIC FORCES AND MOMENTS

STATISTICS MAY BE GENERATED ON PIERSON-MOSKOWITZ. ISSC, JONSWAP, OR _{A USER-DEFINED}

SPECTRUM, PRODUCING RMS RESPONSES AND AVERAGE 1/10 AND MAXIMUM RESPONSES HYDRODYNAMIC MODEL LOADS ARE AUTOMATICALLY TRANSFERRED TO THE STRESS MODEL

INTERNAL LIBRARY OF STRUCTURAL ELEMENTS ALLOWS ANY ASSEMBLY OF BEAM AND PLATE _ELEMENTS

NON PRISMATIC MEMBERS, ALLOWING_BEAMS UP TO 10 SEGMENTS OF _{DIFFERENT SECTIONS}

BEAM SECTIONS MAY BE UP TO 14 DIFFERENT TYPES, TUBULAR TO AISC SHAPES, FROM THE INTERNAL LIBRARY OF SHAPES

PLATES MAY HAVE 3 OR 4 NODES

RIGID OFFSETS FROM INCIDENT NODES ARE ALLOWED FOR ALL ELEMENTS BEAMS AND PLATES MAY HAVE SOME LOAD-CARRYING CAPABILITY REMOVED

MODEL GENERATION OPTIONS ALLOW HULLS OF SYMMETRICAL OR RECTANGULAR SHAPE ENVIRONMENTAL LOADS ARE COMPUTED AND APPLIED AUTOMATICALLY,

APPLIED LOADS MAY BE EMITTED TO PERFORM A STRESS ANALYSIS

EASE-OF-USE

)SCAR II was conceived for the engineer as an integrated, easy-use program, allowing either batch or interactive lodes to be used, with powerful modelling and command language, and extensive error checking. The user may set up, use, and save command macros of complex sequences of commands, allowing the engineer to process the

(37)

up, use. and save command macros of complex

sequences of commands. allowing the engineer to process the workload much faster.

The internal database allows all information to be recorded and available_{when the program is restarted for subsequent}

runs and revisions to the configuration and data. This

feature saves much of the engineer's time and allows

concentra-tion on the task at hand. All reports are easy to read and understand and _{may be printed and saved.}

MAJOR FEATURES

DATABASE OF ALL DATA AND RESULTS

POWERFUL COMMAND AND MODELING _LANGUAGE

MACROS OF COMMANDS MAY BE CREATED

*INTERACTIVE GENERATION OF X-Y GRAPHS _{OF RESULTS}

INTERACTIVE GENERATION OF 3D VIEWS OF MODELS AND RESULTS

INTERACTIVE POSY PROCESSING OF _RESULTS

REPORTS EASY TO UNDERSTAND EXTENSIVE ERROR CHECKING

FOREGROUND OR BACKGROUND EXECUTION SI, ENGLISH OR METRIC UNITS

EXISTING MODELS MAY BE REUSED SEVERAL MODELS EASILY COMBINED

EFFICIENT, STATE-OF-THE-ART NUMERICAL ALGORITHMS

FUNCTION ORIENTED PROGRAM

OSCAR II's command driven form _{allows the user the option of selecting only those functions needed, without}

acquir-ing the complete program, thus providacquir-ing a more economical approach to attainacquir-ing the finished project. The key

commands are the BASIC ones, which will run independently. Each of the other commands requires the BASIC _{ones to} function.

BASIC COMMANDS

Model Generation _{- a structure may be treated as one or more hulls and a set of tubular and/or plate elements which}

are assembled into a single structure. Generation options and interactive graphics allow easy modeling of unusual

shapes.

Curves of Form may be generated for a set of draft and trim angles, and include displacement, waterplane_area,

locations of buoyancy center and center of flotation, transverse and longitudinal KM, load to change draft, and

_

rnoment to Change. trim:

*

(38)

- Intact and Damage Stability - righting arm

_{curves may be generated for a range of draft and trim angles. Results}

include value of righting arm, energy under the righting arm curve, and minimum location of _{down-flooding points.}

- Automatic Ballasting computes the ballast necessary to maintain equilibrium,_{given vessel configuration (draft.}

trim and heel) and loads.

- Equilibrium Finding - given the load and ballast of the vessel. OSCAR II _{computes the equilibrium position.}

Minimum Ballast Movement

_{required to achieve a new vessel configuration is calculated.}

Longitudinal Strength

_{- the longitudinal bending moments and deflections of a loaded, ballasted}

vessel computed.

Jacketioadout Calculations

are made using the above computations. Mooring systems may be designed.

Slings may be designed.

3D Graphic Views of the several attributes of the model _{may be generated and displayed interactively or saved for}

later off-line processing,

- X-Y Graphs may be produced for any computed results.

Command Macros may be created by the _{user and saved for further use later.}

FREQUENCY DOMAIN

- _{Morison's Equation may be used for a combination of plates and tubes with}_{hulls, to form a structure or simulate a}

semi-submersible or self-floater.

- Frequency-Domain Analysis may be used for structure response to a set of waves of given period and direction

Reports include structure added mass and damping, pressures on the hulls and resultant total forces and moments

- Response Amplitude Operators (RAO's) may be calculated for motions of any point on the structure and motions of and inertial forces on bodies attached to the structure.

Statistics may be generated, using RAO's, based on

a variety of spectra, including Pierson-Moskowitz, ISSC,

JONSWAP, or user defined spectrum.

Results are the R MS and significant responses, and the average of 1/10 and maximum responses.

The 3D Diffraction allows the user to specify hulls which do not interact, thereby reducing the cost of analysis.

TIME DOMAIN

- Time-Domain determines time-history response of the system.

- Ocean conditions may consist of current, irregular waves and wind.

- Vessel Hydrodynamics frequency-domain results are transformed into time-domain loads. - Results are saved for later continuation or post processing.

- Database capability allows for restart at any time.

- Statistics can be computed from the time domain sample.

_

-are

(39)

-41'.<

-ce

JACKET LAUNCH

-Time-Domain simulation treats both the launch barges and the structure _{as bodies with 6 degrees of freedom.}

- Environmental Conditions may consist of current, wind_{or irregular waves.}

- Automatic Ballasting determines desired draft and trim _{prior to launch.,}

SAMPLE OF SIMPLE _SACHET INSTALLATICN TRANSPORTATION ANALYSIS

PERIOD (SEC)

SURGE-AMP:MEd-90.d S WAY-A MR: HE0-90. 0 4 _{HEAVE-PMP:HEO-90.0} ROLL-AMP:HEO-90.0 X PITCH-AMP:HUI-90.0 YAW-AMP:NE0-90.0

UPENDING

- Upending or lifting of a structure can be simulated via user defined installation sequence..

- Lifting or Flooding, or a combination of both, may be simulated for upending the_structure.

- Hook may be held at constant elevation or load while flooding _{or pumping.}

- Slings may be used for lifting purposes. - Environment may be current and wind loads.

- _{Database capability allows restart at}_{any event within an Installation sequence.}

(40)

LOAD

EMITTING

Loads which act on nodes and elements during a simulation may be emitted for_{user with a stress analysis program_}

TECHNICAL SUPPORT, MAINTENANCE

AND 'UPDATES,

The development engineers at ULTRAMARINE _{provide complete technical support and maintenance. This}

service is available via FAX, TELEX, TELEPHONE or AIRMAIL and normal 'response time is minimal, The program is _constantly

being 'enhanced, with updates available periodically.

COMPUTER RECOMMENDATIONS'

The program will run on many mainframe, _{mini and workstation computers, and the IBM PC-386 or compatible.} The minimum configuration for an IBM' PC-386 or compatible is MS-DOS VERSION' 4 or later with 640k RAM 'and 2M bytes

extended memory, math coprocessor,- 40M bytes hard disk, and 5-1/4"

r 34/2" floppy drive. The program will

support monochrome,, CGA, EGA or VGA monitors.

est

aiSSc

\

L

kid marine, inc.

Engineers and Analysts

3657 BRIARPARK, SUITE 105

-HOUSTON',, TEXAS 77042, U.S.A.

(41)

3

$04449364wWWw&OnewWWWW:80880wwwww440400:08480:764646047038/00023WW0644448

:I'L7MOT.COM:

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&DIMEN -SAVE -DIMEN METERS 84,-TONS

&PARAMET -SPOwATER 1.025 \

-M_DISTANCE 4

&TITLE ANALYSIS TAKLIFT 7

&SUBTITLE LIFTING WITH TOPTACKLES

0640000600:880808000008840008808,0045640wwww044800,74430400:WOKIWwwWWW

$ INITIALISATION MACRO.

0.884814,76®®03:60K06008668WWWWWWWWWW580407868346®®6861a0690,5303,8608407)

&MACRO LOAD INIT INMODEL

I Z-COORDINATE FOR LE11.20 8,

1 MEDIT

-TAG TENSELM 150 -LEN 20. \

-EMODULUS 103000, 'CONNECT TOPTAC -TAD .TOP 'CENL IND_MEDIT

&COMP -PERC TL7_WID 95 TL7_F3 87 TL7100 voo N,

TL7_2@ 90 \

TL7_1cm o \

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TL7_44 100

&EQUI _{-MAXIT 300 -MAXMOVE 0.05 0.2}

&ENDMACRO

&M_ACT LOADINIT MEI=

WOMOWWWWWWW@COOK0044600880687F0:04833z9wwww@WW940088WZOBB81847,90

DETERMINE THE HYDRODYNAMIC COEFFICIENTS

7 HEADINGS, 0.4

., 2.4 rad/sec (15.71

.. 2.61 sic);

(23 freq. 7s)

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&MACRO MOTA

&DESCRIBE BODY TL7

HYDRODYNAMIC

". 'PRESSURE TL7 LIETTOK -HEAD 0 301 60 90 120 150 180 \

7 °

.INSTATE 7L7 -L7DC

-o 'o t

OUTREACH (METRES)

6 &INSTATE TLOAD -LOG 92.0 0.0 48.3 0 0 0 $ 20

8 &INSTATE TLOAD -LOC 102.0 0.0 43.0 0 0 0 $ 30'

&INSTATE TLOAD -LOC 112.0 0.0 36.0 0 0 0 $ 40

&INSTATE TLOAD -LOG _{72.0 0.0 48.3} _{0 0 0} $

0 all

&INSTATE TLOAD -LOC _{82.0 0.0 43.0} 0 0' 0

$ 10 alt

&INSTATE TLOAD -LOC 92.0 0.0 36.0 0: 0 0 20; alt

-PERIOD 1.96 2.24 2.62 2.86 3.1w 3.49 \ 3.93 4.19 4.49 4.83 5.24 5.71 \ 6.28 6.98 7.85 8.98 9.47 10.47 \

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(42)

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D_HYD

&ENDMACRO

&M_ACT MOTA HYDRODYN

&MACRO MOT1 &DESCRIBE BODY TL7 HYDRODYNAMIC

END_HYD &ENDMACRO

&M _ACT MOT1 HYDRODYN

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&M _ACT MOT2 FREQ_RESP

&MACRO MOT] &DESCRIBE BODY TL7 FREQ_RESP . -SPEED 0 FR POINT .TOP REPORT END END

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(43)

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(44)

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$ ESCRIPTION OF TAKLIFT 70. FOR 'OSCAR

717.DAT $ENZENENANKOZNE.NNOWIDONNZWINNEOBWONDENONONNO@CENOW$INNENEEENC$20:001ar $ ADMINISTRATION; $$WWW04420NOWBOZ4140020,604NAWEBBRO4Ned0.9404000$14...WEBBNI.0.44 SEGE CONVENTIONS:' ORIGIN FRAME D' KEEL LEVEL CENTERLINE X. POS. FORWARD Y POS. PORTSIDE. Z POS. UPWARDS

$ HULL, DESCRIPTION COMMANDS': PORT STBD-PART OF STATION

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&DINER -SAVE -EIMER METERS M-TONS,

&DESCRIBE BODY TL7

PORN -PERM 0.993 -DIETER IDDIF

-END POEM

$245.10/44.1710OC.4101WEENONONNONSOMONNBENNOZZOONS404...244.M.MS440

$ DEFINITION OF BARGE WEIGHT

$MINANDO*NW@OW40$*NWOOft0006924464..488N000041000~0014244EWB4.E

$ Light ship weight of barge

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*WEIGHT 2931 10 20 22 'CEN 36.19' 10.15, 5.15

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$ TANK DEFINITIONS

"..N.14HONEBOZONINCEONNANENNOINZWZOBONNWNENONIONNENINAINKN/NONNtd

&DESCRIBE COMPARTMENT 717_10P -CONTENTS 1.025 -MINIMUM 1)5/ RGEN -PERM -0.972 -STBD -LOCATION 000 0.75 0.0

VERSION DESCRIPTION Oscar DATE BY REV 0.0 DRAFT VERSION for 13.024 12-11-92 NvD CO $ 220 DRAFT VERSION for 13.320 11-03-93 AN CD $ 2,0 VERSION for 5.01 15-05-95 AN NEU

1.1 Minor update -5,01 11-01-95 HEN AW

$ EVL PLANE 0.00 5.805 -RECT 1.80 5.50 30.00, PLANE 11.90 66.10 -SECT 0.00 5.50 30.00' PLANE 72.00 -RECT 2.75 5.50 30.00 $ $ $

(45)

PLANE 0.00 5.805 -RECT 1.80 5.50 10.50 PLANE 9.00 -RECT 0.857 5.50 10.50.

END PGEN

&DESCRIBE COMPARTMENT TL7_105 -CONTENTS 1.025 -MINIMUM ij5 POEM -PERM -0.998 -PORT -LOCATION 0.0 -9.75 0.0

PLANE 0.00 5.805 -RECT 1.80 5.50 10.50

PLANE 9.00 -RECT 0.857 5.50 10.50 END POEM

&DESCRIBE COMPARTMENT TLT 1CP -CONTENTS 1.025 -MINIMUM 1/5 POEM -PERM -0.875 -STBD -LOCATION 0.0 1.50 0.0

PLANE 0.00 5.805 -RECT 1.80 5.50 9.00.

PLANE 9.00 -RECT 0.857 5.50 9:00

END" POEM

&DESCRIBE COMPARTMENT 11.7_1CS, -CONTENTS. 1.025 -MINIMUM511S

POEM -PERM -0.875 -PORT -LOCATION 0.0 -1.50 0.0

PLANE 0.00 5.805 -RECT 1.80 5.50 9.00

PLANE 9.001 -RECT 0.857 5.50, 9.00,

END POEM

ESCRIBE COMPARTMENT TL7_20 -CONTENTS 1.025 -MINIMUM _1.5 POEM -PERM -0.874 -STBD -LOCATION 0.0 7.50 0.0

PLANE 9.00 -RECT 0.857 5.50 15.00

PLANE 11.90 18.001 -RECT 0 00 5.50 15.00

END POEM

&DESCRIBE COMPARTMENT TL7_25 -CONTENTS 1.025 ,MINIMUM[ 1:5 POEM -PERM -0.954 -PORT -LOCATION 4.0 -7.50 0.0,

PLANE 9.00 -RECT 0.857 5.50 15.00

PLANE 11.90 18.00 -PROT 0.00 5.50 15.00 END POEM

&DESCRIBE COMPARTMENT TL7_3P -CONTENTS! 1.025 -MINIMUM POEM -PERM -0.967 -STBD -LOCATION 0.0 7.50 0.0

PLANE 18.00 27.00 -RECT 0.00 5.50, 15.40 END PGEN

%DESCRIBE COMPARTMENT TL7_35 -CONTENTS 1.025 -MINIMUM POEM -PERM -0.967 -PORT -LOCATION 0.0 -7.50 0.0

PLANE 18.00 27.00 -RECT 0.00 5.50 15.00

END POEM

&DESCRIBE COMPARTMENT TL7_4P -CONTENTS 1.025 -MINIMUM 1.6,.

POEM -PERM -0.951 -STBD -LOCATION 0.0 7.50 0.0 PLANE 66.00 66.10 -RECT 0.00 5.50 15.00

PLANE 72.00 -RECT 2.75 5.50 15.00

END POEM

&DESCRIBE( COMPARTMENT TL7_45 -CONTENTS 1.025 -MINIMUM 1.5 POEM -PERM -0.951 -PORT -LOCATION 0.0 -7.50 0.0

PLANE 66.00 66.10' -RECT 0.00 5.50 15.00

PLANE 72.00 -RECT 2.75 5.50 15.00 END PGEN

&DESCRIBE COMPARTMENT TL7_Fl -CONTENTS 0.860 -MINIMUM 1,15 POEM -PERM -0.963t -STBD -LOCATION 0.0 10-50 0.0

PLANE 27.00 39.001 -RECT 0.40 5.50 9.00

'END 'POEM

&DESCRIBE COMPARTMENT TI,? F2 .-CONTENTS, 0%860 -MINIMUM( 1.5

POEM -PERM -0.993 -ST213 -LOCATION 0.0 7.50 0.0

'PLANE 27.00 39.00 -RECT 0.00 5.50' 6.00

1.5

(46)

END POEM

&DESCRIBE COMPARTMENT TL7_Wl -CONTENTS 1.000 -MINIMUM 1.5 EN -PERM -3.955 -PORT -LOCATION 0.0 -10.50 1.1

PLANE 27.00 39.00 -RECT 0.00 4.40 9.00 END POEM

&DESCRIBE COMPARTMENT TL7_W2 -CONTENTS 1.000 -MINIMUM 1.5 PGEN -PERM -0.991 -PORT -LOCATION 0.0 -7.50 1.1

PLANE 27.00 39.00 -RECT 0.00 4.40 6.00 END POEM

SWiNtiri,wwwww040P@Woo@opwww®@wwwwriowaixia@wl,mq@@@@0%womm

&DIMEN -REMEMBER

(47)

APPENDIX D

CALCULATION OF MASS FORCES

In this appendix the definition of the mass forces will be discussed. The mass forces that will be considered in this project are due to the masses of the lift structure and of

the pendulum.

The mass forces are the products of the masses and the corresponding accelerations. In this appendix the masses and the accelerations are discussed separately. In the first section we will discuss the mass distribution of the lift structure and in the second

section the accelerations are discussed.

D.1. THE MASS DISTRIBUTION

In this section we will discuss a method to define the mass distribution of the lift structure of the sheerlegs. Because the mass forces of the pendulum are discussed in appendix A, only the masses of the lift structure will be discussed.

The masses of the wires and of the preventer are added to the masses of the frames, so the only remaining masses are three frames for the Taklift 6/7 (A-frame, fly-jib frame and fly-jib brace) and four frames for the Taklift 4 (three frames and luffing frame). In this section we will discuss the mass distribution of one frame; the mass distribution of the other frames is defined in the same way.

In general the mass forces of an object due to rotations are calculated using the

moments of inertia or radii of gyration. However, this method requires a lot of calculations, as will be described first. After that a method is described which makes

the calculations easier.

0.1.1. Definition of the mass inertia in general

In general there are two kinds of accelerations that cause mass forces, namely the

accelerations of translations and the accelerations of rotations. For each of these accelerations the mass forces can be calculated [Reynen, 1991]:

THE SECOND LAW OF NEWTON FOR ACCELERATIONS OF TRANSLATIONS:

M

= F

(0.1)

TO DELFT SMIT ENGINEERING BV 85

In which: a =acceleration vector of the mass (m)

=mass (kg) =force vector (N)

THE EQUATION OF EULER FOR ROTATIONAL ACCELERATIONS:

i") =

M

(D.2)

In which:

F

= relative impulse moment vector at the COG (kg m2/s)

= moment vector (N m)

The relative impulse moment vector ri can be described by the next formula:

Ixx Ixy Ixz

=

J dp

= xy

IYY I.Yz

ixz /yz /22.

(48)

e,

frame

ez

Figure D.1

Main inertia directions of a frame

Figure D.2

Positions of the mass points of a frame

e,1