Wave Scatter Diagram

Yllae scatcr di4ram: I I a

'I

i$f{i

5

{E i4?

ll t: 6

Er

;8.

Hs 90 80 70 60 50 40 30 20 IO

Wave height excedance diqram.

1d

tg q,

Btd

(o 3

atd

C) € E'

$

ro'

x ul 10

5.5

5.5 7.080 8.5

9'oro. rO.5U.5

T m

Vllave spestrum {one per sea statel:

Probebilistic currsi for eac*r 3e:t

sbe

and hot spot:

P{s)

s

_n

o CD tr t! 0 6 o, +, 6 q \a r00 50 2A 10 5 2

Cumulatiw

strs

history: Cumulatiw stres history

{usingft

h

S-N

curs:

1f

los ',16

1d

td

_ld

_tolo Number of cycles l

Fiowe

9-10

continue.d

Wavcs and wavc loading 331

t-dynomic response Spectrol rondom worae onclysis generolly required wove theory occeptoble lineorisotion of wove thoery Drog looding 2

(

possibly in deeper intermediote woter ) smoll or lineorised non lineority importont

Time domoin onolysis

lncreqsing onqlJois comPlexity

Figure

6.68

Procedure

Frequency domoin dynomic onolleis in lineor rondom

woves

eg. fixed structures sub.iect to fotigue

wove looding Regulor wove stotic

onolysis, possiblY with o smoll

dynomic

omplificotion foctor

eg. most fixed

structures subject to extreme looding

ond shollow woter

structures subject to fotigue looding Time domoin dynomic onolysis in lineor rondom woves eg. deep woter jockets Time domoin dynomic onolysis in non lineor rondom wo\res Qr opproximote onolysis ldeolly required for intermediote woter depth jock-ups

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

Ectrum

5

(see

Statlstlcal and spcctial dcscrlptlon

of

random loadtng and reeponsc 91

Figure

3.4

Overview

of

Sections

3.9

and 3.10 shoving

relevance

to

fatigue

and

strength

analYsis

It is

also

necessary

to

ealculate

the

statistics over

much

longer

periods

of

months

or

years.

In

these cases

different

statistical

distributions

are

used

to fit

the

non-stationary

parent

or

extreme

distributions.

These

long

term

statistics

are

discussed

in

Seciion 3.1O.

This

section

is

relevant

to

wave,

wind

and

earthquake

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

time

is

caUea

a

stochastic process. Many experimental

measurements

of

random

processes

are

caried

out

digitally

'

with

sample-s

taken

at a

series

of

regularly

ili"a

-

ti."",

(Figure

3.5).

If itru

sampling

interval

is A

(constant)

then

the

set

of

discrete valuis

of

y"(t) at

time

t

₌

rA

is

called

a

discrete time

series.

i

1.

i

I

L

.

stattstlcal and spectral dcscrlptlon

of

random loadlng and response 79

statistics.

of

the

extremes

of

wind

speed,

significant wave

height and

earthquake

magnitude.

Section 3.1

is

concerned

with

the

properties

of

a

single

time

history

that

are

not

dependent

on

sequence

or

cyclic

frequency'

irj

inaicot." 'frequencY domoin'

Exoerirnents o.1d onbllses usuollY oerf6rmed tP orepqre 66b'e-i/bIon aor'd s' et c' I

--+*

t I t !

Figure

3.2

Overviev

of

sections 3.1

to

3.4

shosing

relevance

to

spectral

dynamic

analysls

of a

structure

subJect

to

wave loading

Sections3.zto3.4considerseguence_andfrequencyeffects.associatedwitha

random load which

is

definabre

in

teims

of

the

staiistics

of a

single variabre-

These

seetions

are

directly

applicable

to

l^'"u"

rotaing and

the

structural

response

to

waves

where

the

single

v#iauie

would be

waier

surface

elevation

(see

Figure 3'2)'

Section

3.3.8

brings

together

th;

ideas

of

_"p".i""

and

aynamics

to

explain

the

theoretical

background

to

the

_{"p..irt--aitysis}

metioa which

is

widery used

for

the

Jynamic

fatigue

analysis

of

structures

in

waves'

_rd

_whir.'.

_can

_onl

sections

3.5

to

3.8

extend

tt"-iou"" to

loading

which

c€rn

only

be

defined

by

several

variables.

-This

section

is

mainly relevant

to

ttre

response

of a

structure

to

wind

turbulence

(see

Figure

3.3).

Th;

important

results

iot

the

wind

are

also

summarised,

using

a

more

complicaied

notation,

in

Chapter

8'

The relationship

between

the ctrapter

g

ani

a;;;

I

notations

is

explained

in

Section 3.6.4.

coG)

-S)y

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 ,oled into .iqsaber €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

'tlpical

,r.lzontal -$stent +€dure ,ition is al'axes, f, q4 can .,Qis is ckee in "raI axes

rtrs

of

e

small iirc 6.1.,

Figure 6.I. Typical idealization of a jacket structure

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

-nsht-hano screw ruIe axis would point to generaie the

'.,,

'i',

6'm)

1:

ats Ueing ,:!*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* -j a..t: :::::

rEure

rJ.

Typical offsbore oj'-tting

_lio

production pladorm. Key: _{a -jacket;} b

_-

module

sup'port frame; c. - piles; d - ddling derrick; e

_-

heliiopter pad; _{f_} ariUine

;i

productioo equipment;

_g:.fl"*

stack; h

_-

survival craft; i _{-,r"oti,iog'.*ri*;}

_i:

_pffig.-al;

_t

_{_ pA"} sleeves; I _- drilling irad production risers; m _- exporrpipelne; o _{-'d"-il"oitioo'}

',jj