Wave Scatter Diagram

Yllae scatcr di4ram:

Hs 90 80 I

70 60 I

50

40 a

30 5

20 6

'I

i$f{i

{E i4? Er ;8.

ll t:

IO

5.5

Wave height excedance

1d tg q,

diqram.

5.5 7.080 8.5

9'oro. rO.5U.5 Tm

Vllave spestrum {one per sea

statel:

sn

Btd (o

3

atd C)

€

E'

ro' $ x

ul

10

Probebilistic currsi for eac*r 3e:t sbe and hot spot: P{s)

Figure 9.10 Fatigue analysis

Cumulatiw

S-N

strs

Cumulatiw stres history

history:

{usingft h

curs:

r00 o CD tr

50

t! 0 6

o,

+, 6

2A

q

\a

10 5

2

1d

',16

los

1f

td

ld

tolo

Number of cycles l

Fiowe 9-10

continue.d

Wavcs and wavc

loading

dynomic response

tSpectrol rondom worae onclysis

generolly required

wove theory occeptoble

lineorisotion

(

possibly

of wove thoery in

deeper intermediote

woter )

Drog

non lineority importont

looding

smoll or

2

lineorised

Time domoin onolysis

Regulor wove stotic onolysis, possiblY with o smoll dynomic

omplificotion foctor

Frequency domoin dynomic onolleis

in lineor

rondom

Time domoin dynomic onolysis

in lineor

rondom

woves

woves

eg. fixed structures

eg. deep woter jockets

opproximote onolysis

eg. most fixed structures subject to extreme looding ond shollow woter structures subject

Time domoin dynomic onolysis in non lineor rondom wo\res Qr

sub.iect to fotigue wove looding

ldeolly required

for intermediote woter depth

jock-ups

to fotigue looding

lncreqsing onqlJois comPlexity

Figure 6.68 Procedure for the selectlon of ltave loadlng analysis nethodology

331

Statlstlcal and spcctial dcscrlptlon of random loadtng and reeponsc

91

From figure 3.2 ( woves ) or figure 3.3 ( wind )

-l

{^A."

see figures P.2

e

3.4)

'."lrL Probobilitv

density of omplitude

o

Distribution of extreme stresses

inol-3hour

ind or seo-stote

Distribution of extremes of meon hourlv wind soeed

oi

si6nificont' wove-heioht over

mony ye6rs

517

Figure 3.4 Overview of Sections 3.9 and 3.10 shoving relevance to fatigue

and

strength analYsis

Ectrum

5

(see

periods of It is also necessary to ealculate the statistics over much longer to fit used are months or years. In these cases different statistical distributions are statistics term long the non-stationary parent or extreme distributions. These earthquake wind and discussed in Seciion 3.1O. This section is relevant to wave, calculations. ' A random process may be either continuous, BB. water surfaee elevation, or discrete, eg. *"o" heights. A continuous process (Figure 3.5) which is random with random time is caUea a stochastic process. Many experimental measurements ofregularly series of processes are caried out digitally ' with sample-s taken at a (constant) then the A is interval (Figure sampling itru If 3.5). ti."", ili"a set of discrete valuis of y"(t) at time t = rA is called a discrete time series.

stattstlcal and spectral dcscrlptlon of random loadlng and response

.

statistics.

of the extremes of wind speed, significant

magnitude.

Section 3.1 is concerned with the properties dependent on sequence or cyclic frequency'

79

wave height and earthquake

of a single time history that are not

i 1.

i

I L

irj inaicot."

'frequencY domoin'

coG)

(f)

-S)y

Exoerirnents

o.1d

onbllses usuollY oerf6rmed tP orepqre 66b'e-i/bIon aor'd s' et c'

I

--+*t

Figure

3.2

to spectral dynamic Overviev of sections 3.1 to 3.4 shosing relevance loading analysls of a structure subJect to wave

Sections3.zto3.4considerseguence_andfrequencyeffects.associatedwitha These of the staiistics of a single variabrerandom load which is definabre in teims waves to response structural are directly applicable to l^'"u" rotaing and the

I t !

seetions surface elevation (see Figure 3'2)' where the single v#iauie would be waier and aynamics to explain the Section 3.3.8 brings together th; ideas of "p".i"" metioa which is widery used for the theoretical background to the "p..irt--aitysis waves' rd whir.'. can only Jynamic fatigue analysis of structures in which c€rn onl be defined by 3.8 extend tt"-iou"" to loading ttre sections 3.5 to -This response of a structure to section is mainly relevant to several variables. important results iot the wind are also wind turbulence (see Figure 3.3). Th; notation, in Chapter 8' The relationship between summarised, using a more complicaied I notations is explained in Section 3.6.4. the ctrapter g ani a;;;

Quasistatic loading and

response

217

a framed ,,r*,hereas

elgments

l*ents of "fue finite ...

:

:er prop:.,is then -sements .e$rre. :+s using ::: trans-

e;global into .iqsaber

,oled

€rt,:loads

'tiiat the

;e nodal *rder to €-Sat is,

that

a

*rmed.

: natrix is

at the

:

*ination q*s and :

*.,hlow

*cofa

rre con,:ubular 'is first i9 nodes

6.I.

'tlpical

Figure

-$stent +€dure ,ition is al'axes,

for example) will be co^nstrained or given a prescribed displacement to account for the effect of the foundation. The next step in the analysis is to determine the stiffnesses of eactr member in the frame work -- tlis peing_done in terms of principal mem'ber axes O--r,nymzm ?s defined in -Figure 6-2. T\e sinele Udm element in this diagram has 12 degrees of freedom, three trinslations and three rotations along and about member axes' directions at each end of the members. These are shown in Figure 6.2 with the rotational degrees of freedom denoted by double headed arrows showing the direc.tion that the screw ruIe axis would point to generaie the -nsht-hano rotation. These degrees of freedom are systemaiically nimbered by

Typical idealization of a jacket structure

,r.lzontal

f, q4

can

.,Qis is ckee in "raI

axes

rtrs e

of

small

iirc

6.1.,

'.,,

'i',

6'm)

ats Ueing 1: ,:!*1e structure

,:les

to failure

i35,oceur when

*4s

used in

** fatigue

Afe

Fe cumulative

'.*eterministic

*'diagram of gifieant wave :e

{*e

Figure

e*lher condi:lrousand) in .ber of waves g,',Priod and

x

.{converted

*e,number of .,5{gure 6.12. pliod range

: asd period ge, analyses **ge against Er?sx 3. It is €,:my wave i*qice of an e+qservative

**d for each qilsntration ** with rhe

t*'yield the

r:ics of the eed spectral *siag period

"el response i* box 6) at *cress peaks

qryrence of *.ed.and the

qage zero

fe.relt from a3$dated in .*4r- eentration

urcertainity 'Fetroleum

t4

,lg-

l*

U"j ',jj

-j a..t:

:::::

rEure

rJ.

Typical offsbore oj'-tting lio production pladorm. Key: a -jacket; b - module c. - piles; d - ddling derrick; e productioo - heliiopter pad; f_ ariUine equipment; g:.fl"* stack; h - survival craft; i pffig.-al; t _ pA" -,r"oti,iog'.*ri*; sleeves; I - drilling irad production risers; m exporrpipelne; o sup'port frame;

i:

;i

-'d"-il"oitioo'