ENVIRONMENTAL CONDITIONS AND ENVIRONMENTAL LOADS

MARCH 1991

CLASSIFICATION NOTES

NO. 30.5

Det nonke Verita• Cla..mc.tion AIS VERITASVEIEN I. 1322 H0VIK. NORWAY TEL.INT.: +47 2 47 99 00 TELEX: 76192

FOREWORD

Det norske Veritas is an independent Foundation with the objective of safeguarding life, property and the environment at sea and ashore.

Classification, certification and · quality assurance of ships, offshore installations and industrial plants, as well as testing and certification of materials and components, are main ac­tivities.

Det norske Veritas possesses technological capability in a wide range of fields, backed by extensive research and development efforts. The organization is represented world-wide in more than 100 countries.

©Del norske Veritas 1991

Classification Notes are publications which give practical in­formation on classification of ships, mobile offshore units, fixed offshore installations and other objects. Examples of de­sign solutions, calculation methods, specifications of test pro­cedures, quality assurance and quality control systems as wen as acceptable repair methods for some components are given as interpretations of the more general rule requirements. An updated list of Classification Notes available is given in the latest edition of the Introduction-booklets to the «Rules for Classification of Steel Ships», the «Rules for Classification of Mobile Offshore Units» and the «Rules for Classification of Fixed Offshore Installations».

Computer Typo;etting by Division Ship and Offshore, Det norske Veritas Classification A/$ Printed in Norway by Del nor-ske Veritas

3.91.2000

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..

CONTENTS

1. Introduction . • . . • • • • • • . . . . . . . . • . • . . . • . • . 4 5.3 The shape coefficient . . . . . . . . . . . . . . . . . . . . 12 I.I General ............................... 4 5.4 Wind effects on heJidecks . . . . . . . . . . . . . . . . . 15 1.2 Environmental conditions . . . . . . . . . . . . . . . . . . 4 5.5 Dynamic analysis of wind sensitive structures 15 1.3 Environmental loads ..................... 4 5.6 Model test$ . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2. Wind conditions . • . . . • . • • . . • . • . . . • . • • • • . • 4 6. Wave and current loads • . . • . • • . . • . • . • • . • • 15 2.1 Average wind .......................... 4 6.1 Wave and current loads on slender members . . . 15 2.2 Gust wind . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 6.2 Wave loads on large volume structures . . . . . . . 19

6.3 Second order wave loads on large volume 3. \Vave conditions • . • . . • • • . • • • • . • . • • • • • . • . • S structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 3.1 Wave theories . . . . . . . . . . . . . . . . . . . . . . . . . . 5 6.4 Slamming loads from waves . . . . . . . . . . . . . . . 20 3.2 Short term wave conditions . . . . . . . . . . . . . . . . 5 6.5 Shock pressure from breaking waves . . . . . . . . . 20 3.3 Long-term waye statistics . . . . . . . . . . . . . . . . . . 7

7. Vortex induced oscillations • . • • • • . • . . . . • . . . 22 4. Current and tide • . . . • • • • • . • . • • • . • . • . . • • • 10 7. l General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 4.1 Current . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 7 .2 Wind induced vortex shedding . . . . . . . . . . . . . 24 4.2 Tide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 7.3 Current induced vortex shedding . . . . . . . . . . . 24

7.4 Wave induced vortex shedding . . . . . . . . . . . . . 26 S. Wind loads • . . • • • • • . • • . . • • • . . • . • . • . • . • 11 7.5 Methods for reducing vortex-induced oscillations 27 5.1 Wind pressure . . . . . . . . . . . . . . . . . . . . . . . . . 11 5.2 Wind forces .... : . . . . . . . . . . . . . . . . . . . . . . 11 8. References . • • . • • . • . • • • • . . • . • . • . . . • • . . . 28

. <£.;

4

1. Introduction 1.1 General

1.1.1 This Classification Note gives guidance for description of important environmental conditions as well as giving guid­ance for arriving at environmental loads. EnvironmentaJ conditions are described in clauses 2-4 while environmental loads are described in clauses 5-7.

l.2 Environmental conditions

1.2.1 Environmental conditions cover natural phenomena which may contribute to structural damages, operation dis­turbances or navigation failures. Phenomena of general im­p~rtance are:

e Wind • Waves • Currents.

Phenomena which may be important in specific cases are:

• Ice • Earthquake • Soil conditions • Temperature • Fouling • Visibility • Tides.

1.2.2 T.he phenomena are usually described by physical var­iables of statistical nature. The statistical description should reveal the extreme conditions as well as the long- and short­term variations.

1.2.3 The environmental design data should be representative for the geographical areas where the structure will be situated, or where the operation w!ll take place. For ships and other mobile units which operate world-wide, environmentaJ data for particularly hostile areas, such as the North Atlantic Ocean, may be considered.

1.2.4 Empirical, statistical data used as a basis for evaluation of operation and design must cover a sufficiently long time period.

Table 2.1 Wind speed ratios.

z (metres)

Classification Notes - No. 30.5

For operations of limited duration, seasonal variations must be ta.ken into accovnt. For meteorological and oceanographi­cal data, 3-4 years is a minimum. Earthquakes must be based on long-term historical data.

1.3 Environmental loads

1.3.1 Environmental loads are loads caused by environmental phenomena.

EnvironmentaJ loads to be used for design are to be based on environmental data for the specific location and operation in question, and are to be determined by use of relevant methods applicable for the location/operation taking into account type of structure, size, shape and response characteristics.

2. Wind conditions

2.1 Average wind

2.1.1 Wind velocity changes both with time and with height above the sea surface. For this reason the averaging time and height must always be specified.

Common height level is z = 10 metres. Common averaging times are 1 minute, 10 minutes or I hour.

Wind velocity averaged over I minute is often referred to as sustained wind velocity.

2.1.2 The average wind speed and the wind height profile may be estimated by the formula

U (z, t) = U (zr. tr)( 1 + 0, 137 In :r - 0,047 In t: ) where

z z, t t, U (z, ti U (z,. t,)

= height above the still water sea surface level. = reference height = IOm. = averaging time. = reference time = I 0 minutes. = average wind speed by specified z and t. = reference wind speed.

The ratio U (z, t) / U (z,. t,) is given in Table 2.1 for:

Time

3 seconds 5 seconds 15 seconds 1 minute JO minutes 60 minutes

1,0 0,934 0.910 0,858

5,0 1,154 1,130 1,078

10,0 l,249 t,225 1,173

·20,0 1,344 1,320 l,268

30.0 1,399 1,375 1,324

40,0 1,439 L4!5 1,363

50,0 1,469 1,445 l,394

100,0 1,564 1,540 1,489

2.1.3 The statistical behavior of the average wind speed U (z, t) referred to a fixed height and averaging time may he described by the Weibull distribution given as:

Pr (U) u Uo c

0,793 0,685

1,013 0,905

1,108 1,000

1,203 1.095

1,259 1,151

1,298 1,190

1,329 1,220

1,424 l,315

= cumulative probability of U. U (z, t} = wind speed. Weibull scale parameter. Weibull slope parameter.

0,600

0,821

0.916

1,011

1,066

1,106

1,136

1,231

Pr (U) = I - ex{ - ( ~o ) ]

where

2.1.4 The most probable largest wind speed for an exposure time, T, may be obtained by:

aa~ification Notes - No. 30.5

Umn (z, t) = 0 0 ( ln J.. )

l/c

where

T exposure time. T. = average time period of constant wind speed, usually 3

hours.

2.2 Gust wind

2.2.1 In the short time range the wind may be considered as a random gust wind component with zero mean value, super­posed upon the constant, average wind component.

• Solitary wave theory:

J!..<Ol ,l - '

• Stokes' 5th order wave theory:

h 0,1 :::;; Ts o,3

• Linear wave theory (or Stokes' 5th order):

h 0,3sT

where

5

h 2.2.2 Gust wind cycles with period shorter than about l mi- A.

= water depth. = wave length.

nute, may be desribcd by the gust spectrum

-f-S(f) = 4 K u2

(z, t) ? (2 + )5/6

where

S = power spectral density (m2/Hz). f = frequency (Hz).

f = non-dimensional frequency, f = fL f U (z, t). L length scale dimension (m); may be chosen equal

to l800m. " surface drag coefficient; may be chosen equal to

0,0020 for rough sea and 0,0015 for moderate sea. U (z, t) · = average wind velocity.

2.2.l Gust wind velocity, defined for instance as the average wind velocity during an interval of 3 seconds, may normally be assumed to follow the Weibull distribution law, see 2. 1.3-2.1.4.

3. Wave conditions 3.1 Wave theories

3.1.1 Wave conditions which are to be considered for design purposes, may be described either by deterministic design wave methods or by stochastic methods applying wave spectra.

By deterministic methods the seas are described by regular, periodic wave cycles, characterized by wave length (period), wave height and possible shape parameters.

The deterministic wave parameters may, however, be predicted by statistical methods.

3.1.2 The kinematics of regular waves may be described by analytical or numerical wave theories. Among these may be mentioned;

• Linear wave theory, by which the wave profile is described as a sine function.

• Solitary wave theories for particularly shallow water.

• Cnoidal wave theories which cover the waves above as special cases.

• Stokes wave theo ries for particularly high waves.

• Stream:function waves which are based on numerical methods and accurately describe the wave kinematics over a broad r,mge of water depths.

By spectra! description of random sea~, the linear wave theory is almost aJways used.

For most practical purposes. the following wave theories are recommended:

3.2 Short term wave conditions

3.2.1 Short term stationary irregular sea states may be de­scribed by a wave spectrum; that is, the power spectral density function of the vertical sea surface displacement.

Wave spectra may be given on table form, as measured spec­tra, or on parametrized, analytic form.

3.2.2 The J onswap spectrum and the Pierson-Moskowitz spectrum are most frequently applied. The spectral density function is:

S(w) = (! g2 (2n)- 4 w- 5 exp

[ 5 ( )-4 I (OJ-top )

2 J - 4 ~ +e-2 ~ lny

where

w = angular wave frequency, ro= 2nf = ln(f. f = wave frequency, f = l/T. T = wave period, T = l/f. Wp = angular spectral peak frequency wp = 2nfp = 2n(f P· g = acceleration of gravity. a = generalised Phillips' constant. u = spectral width parameter.

= Q,t)7 if W.$ a>p· = 0,09 if w> CLJp.

y = peakedness parameter.

The Pierson-Moskowitz spectrum appears for y= i.

3.2.3 The Pierson-Moskowitz spectrum is generally applied for open, deep waters and fully developed seas. The Jonswap spectrum is normally used for fetch-limited, growing seas and without swell.

3.2.4 The peak period T P may be related to the average zero-crossing wave period T z by

T:i: = Tp( 151 "7,, ) 1/2

The parameter a is given by

' 4 5 H;- WP «= 16--2 - (1 - 0,287 In }')

. g

where

H, = significant wave height.

If no particular vaJues are given for the peakedness parameter y, the followio~ value may be applied:

6

where T p is in seconds and H, is in metres.

If the period is not given for a particular sea-state, a tentative estimate

Tz=6H~·3

where Tz is in seconds and Hs is in metres.

3.2.5 The spectral mome!:lts M 0 of general order n is defined as

where

n - I, 0, 1, 2, ...

The Jonswap spectrum above has approximately

M __ l_H2 -1 4,2 +y - I - 16 s lL>p 5 +y

1 2 Mo=}6Hs

M __ 1_H2 6,8 +y I - 16 s Wp 5 +y

M =-1-Hla} ll +y 2 16 s p 5 +y

Quantities that may be defined in terms of spectral moments are among others:

• Significant wave height:

H5 =4.JMo' • Average wave period:

Tz = 2n( ~: Y'2

• Significant wave slope:

• Spectral width:

3.2.6 If the power spectral density S(f) is given as a function of the frequency f rather than as the function S(w) of w, the relationship is

S(O = 211: S(w)

Similarly, if the moments of the circular frequency spectrum S(t) are denoted M0 (f), the relationship to Mn in 3.2.5 is

Cla~fication Notes - No. 30.5

M0 (t) = f 00 fl S(t) df = (211.F n Mn . 0

3.2.7 Directional short~rested wave spectra may be derived from the nondirectional wave spectra above as follows:

S(ro, ix) = S((!)) f(a)

where

o: = angle between direction of elementary wave trains and the main direction of the short-crested wave system.

S(co, a) = directional short-crested wave power density spectrum.

f(a) = directionality function.

Energy conservation requires that the directionality function fulfills the requirement

I «mu .

f(ix) da= I «min

The directional function f(a) may have the general form

f(a) = const.· cos5 o: where2:S:s:S:8

Due consideration is to be taken to reflect an accurate corre­lation between the actual seastate and the power constant, s.

The main wave direction may be set equal to the prevailing wind direction.

3.2.8 The statistical distribution of individual wave crests Z in an irregular stiort-tei::m stationary seastate may usually be described by the Rayleigh distribution. The cumulative proba­bility function P(Z), that is the probability that a crest shall be equal or lower than a value Z, is

P(Z) = 1 - e- ( fz) 2

where

The highest wave-crest Zm.u within a time t is

Zmax = }s HsFnl'f

where

N = t/Tz.

To the first approximation one may put

Zma;,i.::::Hs

3.2.9 The peak-to-trough wave height H of a wave cycle is the difference between the highest crest and the deepest trough between two successive zero·upcrossings.

The wave-heights are Rayleigh distributed with cumulative probability function

' P(H) = I - e - ( AHH r

where

= ~ ·2 (I - c2 ,,2p12 JS

c = a constant ::::: 1,0.

'.fhe highest crest-to-trough wave height Hmax within a time t IS

•

aas.sification Notes - No. 30.5

where

N = t/Tz.

l J 2 2 Hmax = J2 H5 (l - C 'I ) ln N

To the-first approximation one may put

'1= 0,43

c = 1,0

Hma.x~l,8 Zmax

3.2.10 In evaluation of the foundation's resistance against cyclic wave loading, the temporal evolution of the storm should be taken into account. This should cover a sufficient part of the growth and d~cay phases of the storm.

If data for the particular site is not available, the storm profile in Fig. 3.1 may be applied.

1.0 Hi!> (t)

>\.max 0.5

Fig. 3.1

0 6 12 18 24 30 36 42

TIME JN HOURS

Significant wave height relative to maximum value as a function of time during a stonn.

3.3 Long-term wave statistics

3.3.1 The long-term variation of the seas may conveniently be described by a set of seastates, each characterized by the wave spectrum para91eters, that is, (Hs, T2 ) or (a, Tp, y) de­fined in 3.2.5 and 3.2.4 respectively.

3.3.2 There are currently three ways to describe the marginal long-term probability distribution of the significant wave­height:

a) The three-parameter Weibull distribution with probability density:

( Hs-Ho )j-J -(~)i H H

e H 1 -H0 1- 0

j f(H~) = H1 - Ho

(HI)< H)

This distribution has evident advantages in connection with extreme seastate prediction.

b) The generalised gamma distribution with probability den­sity:

r(b) is a complete gamma function.

This distribution is most convenient for establishing long­term distribution for individual crest-heights.

c) The log-normal/Weibull distribution with probability den-sity function: ·

7

There are also constraints on the parameters of the two parts such as to give continuity in cumulative probability and in probability density at Hs = H2. This distribution is convenient for extreme seastates and in prediction of persistence of low and medium sea.states.

The two-parameter Weibull distribution is obtained by:

• Putting Ho = 0 in a).

• Putting b = l in b).

• Putting H2 = 0 inc).

• µ1nH and <TtnH are parameters fitted to the asymptotic parts of the empirical data.

3.3.3 To establish an extreme design storm in a time span t (order 20 years), it is convenient to agree upon a design stonn duration -r, usually 3, 6 or 12 hours, in advance. The number m of short-term intervals in tile time span t is then

t m=7

The significant wave height in the extreme-design storm is then

a) By the three-parameter Weibull distribution: I{

Hs.max =Ho+ (H1 - Ho) (In m) )

b) By the generalised gamma distribution (approximate for­mula):

l/j

Hs.max = H1( In r~) + (b - I) ln ln f~) )

c) By the log-nonnal/Weibull distribution:

If Hs.max = HI (lnm) J

The other spectral parameters of the extreme seastate may be chosen as advised in 3.2.

Design stonns with a preferred value for the storm duration are advised in 3.3.4 and 3.3.5 below.

3.3.4 If the time t covers a total of N wave cycles, a long­term marginal distribution of the individual wave crests are preferably obtained in terms of a general gamma distribution. The probability density is

dk - I ( z )k

f(Z) = l(~)D ( ~ ) e - o A two-parameter Weibull distribution is obtained for d = I. Two methods may be advised, viz.

• The optimised elementary method. • The saddle-point method.

3.3.5 The optimised. elementary method is based on two­parameter Weibull distributions.

The de:>ign storm duration adviSed is:

j -t=N2+jTz

where

8

T, = a relevant value for the average zero~rossing wave period.

The corresponding significant wave height is

(

2 )2;j Hs,max = H1 2 + j In N

The extreme long-term _wave crest is:

. 2 +j

Zm =_!!l._21/J.Jj(-1-1 N)T ax ..Jf J j+2 n

In the long-term wave crest distribution the parameter d = l.

The parameter k is found from Table 3.1.

The scale parameter D is

D = Zmax (In N)- l/k

3.3.6 The saddle-point procedure takes into account that there may be a relationship between average zero.crossing wave period and significant wave height of the form:

T2 = r H!

The long-term distribution of the wave crests then has the pa­rameters

s l d=b-y+2

k =--3!_ 2 +j

D = is- ( ~ Y'k ( ~ y6 An extreme design condition is established by the aiding vari­ables

fc = lnRN + (d - 1) lnlnRN

Classification Notes - No. 30.5

This gives the significant wave height of the extreme design storm

lf

lis,max= H 1( 2 !j fc)

1

The duration of the extreme design stonn:

_J_f. T= e2+j •Ti

where

Tz the average zero-crossing wave period representative for the storm.

The extreme individual crest height . l/k

Zn.ax= D fc

The peak-to-trough wave height may be estimated as in 3.2.8.

3.3.7 When specific wave data for a site are not available, the data in Fig. 3.2 and Table 3.2 may be used. In this source a two parameter Weibull distribution for the significant wave height is assumed, and numerical values for the parameters j and H1 are given for the most relevant oceanic regions in the world.

3.3.8 In some cases the design wave is defined as the wave with the crest Zs which has an exceedance probability of s (for instance s= 10-2).

With some approximation this value may be estimated as

where

N f(Zmax)

l I I z6 = Zuiax + N f <Zmaxl ln T

= the extreme wave crest in one year, calculated ac­cording to 3.3.5 or 3.3.6.

= number of wave cycles in one year (14,400 · 365). the value of the long-term probability density function for the individual wave crests in 3.3.4 for argument Z = Zn>J<·

Classification Notes - No. 30.5 9

•

Fig. 3.2 Nautic zones for estimation of tong-term wave distribution parameters /I/.

Table 3.1 Table to obtain the parameter k of the long-term

Table 3.2 Weibull parameters j and H 1 for the long-term probability distribution of the significant wave height.

"ave crest distribution. The data refer to the zones io Fig. 3.2.

j k Area j H1 00 2,000 1 1.41 2.76

10,00 l ,780 2 1.53 2.60

8,00 . 1,7 12 3 1.72 3.75

6,00 1,614 4 1.64 3.38

4,00 - 1,444 5 1.81 2.41

3,33 1,354 6 1.63 3.37

2,86 l ,276 7 2.04 4.05

2,50 1,208 8 1.97 4.35

2,22 1,144 9 l.89 4.18

2,00 1,086 10 l.58 2.98

1,82 l,034 ll 1.53 2.93

1,67 0,988 12 1.79 3.95

1,54 0,944 13 1.95 3.86

1,43 0,904 14 1.68 3.19

1,33 0,868 15 1.72 3.68

1,25 0,834 16 l.82 4.02

l , 18 0,802 17 1.49 3.13

1, 11 0,774 18 1.58 2.56

1,05 0,746 19 1.43 2.91

1,00 0,722 20 1.78 3.88

0,67 0,538 21 1.79 . 3.41

0,50 0,428 22 1.90 2.89

0,40 0,356 23 1.57 2.75

10

24 1.67 3.48

.25 1.70 3.23

26 1.43 2.28

27 1.40 2.21

28 1.32 l.87

29 l.38 2.29

30 1.69 3.51

31 1.74 2.89

32 l.70 2.39

33 1.84 2.75

34 1.61 2.64

35 1.81 2.84

36 2.21 . 3.06

37 1.78 2.23

38 1.51 1.80

39 1.10 2.43

40 1.76 3.05

41 1.71 3.07

42 1.29 2.35

43 l.71 3.04

44 2.45 3.41

45 2.23 3.07

46 1.46 2.15

47 2.01 2.95

48 1.55 2.19

49 2.62 3.25

50 l.43 2.46

51 1.67 2.38

52 I.74 2.77

53 l.80 2.65

54 2.59 3.20

55 2.12 2.37

56 2.27 2.86

57 1.48 l.76

58 l.71 1.88

59 2.07 2.62

60 1.37 1.98

61 2.13 2.70

62 1.43 2.10

63 2.03 2.56

64 2.52 3.05

65 2.20 2.71

66 2.70 3.09

67 2.29 2.91

68 2.43 3.06

69 l.86 2.54

70 2.43 3.16

71 1.86 2.31

72 2.33 3.19

Classification Notes - No. 30.S

73 2.44 3.31 74 2.07 2.99

75 1.62 2.86

76 2.19 3.60

77 2.28 3.78

78 l.87 3.09

79 l.73 2.73

80 1.83 3.00

81 1.99 3.43

82 2.05 3.29

83 2.09 3.18

84 2.31 3.47

85 2.27 3.98

86 1.94 3.76

87 1.41 2.72

88 1.70 3.49

89 1.91 3.76

90 1.69 3.69

91 l.80 3.91

92 1.78 3.73

93 1.47 2.89

94 t.95 4.41

95 2.47 4.51

96 1.49 3.06

97 1.80 4.11 98 . l.85 3.99

99 2.06 4.40

IOO 2.12 4.67

101 1.83 3.84

102 l.60 3.28

103 1.74 4.02

104 1.72 3.49

4. Current and tide

4.1 Current

4.1.1 When detailed field measurements are not available the variation in current velocity with depth may be taken as:

v(z) = vtide(Z) + Vwiod(z.)

( h )1/7

Ytide(Z) = Vtide ~ z forz ~ 0

( ho+z) Vwind{z) = Vwind ~ for - h0 sz~O

vwind(z) = 0 for z <-ho

where

v(z) = total current velocity at level z. z = distance from still water level, positive upwards. Viidc = tidal current velocity at the still water level.

•

,,

a~fication Notes - No. 30.5 1 l

vw;nd.,. wind-generated current velocity at the still water level. 5. Wind loads b water depth to still water level (taken positive). ho reference depth for wind generated current ho = 50m. 5.1 Wind pressure

4.1.2 The variation in current profile with variation in water depth due to wave action is to be accounted for.

In such cases the current profile may be stretched or com­pressed vertically, but the current velocity at any proportion of the instantaneous depth is constant, see Fig. 4.1. By this method the surface current component shall remain ·constant.

CURREllT PROFllE: CURRENT PROFILE $TREtCHING

Wll!4 NO WAVE < Yeo • Vc1 VC?l

l Act > Ac~ > "a)

Fig. 4.1 Recommended method for current profile stretching with waves.

4.1.3 In open areas wind-generated current velocities at the still water level may, if statistical data are not available, be taken as follows:

vwind = 0,015 U(z, t) z = 10 metres, t = l hour

4.2 Tide

4.2.l The tidal range is defined as the range between the hi­ghest astronomical tide (HAT) and the lowest astronomical tide (LAT). see Fig. 4.2.

4.2.2 Mean water level (MWL) is defined as the mean level between the highest astronomical tide and the lowest astro­nomical tide, see Fig. 4.2.

4.2.3 The s.torm surge includes wind-induced and pressure­induced effects.

4.2.4 Still water level (SWL) is defined as the highest astro­nomical tide including storm surge. see Fig. 4.2.

STILL \o' A TEA LEVEL t $/lit I V -:;;::;­

Ii I GHE ST ASTR()NOHl(Al TIOf I #AT I

MEAN WATER LEVEl I lfWl. I

LOWEST ASTRONOMICAL TIDE 101" I

Fig. 4.2 Definition of water lenls.

AS'Tll()NfJK/('A{ T /Pitt 11ANQ£

5.1.1 The basic wind pressure (q) may be calculated from the following equation:

where

q = the basic wind pressure or suction. p .,. the mass density of air; to be taken as l .225 kg/m3 for

dry air. v,2 the wind velocity averaged over a time interval t at a

height z m above the mean water level.

5.1.2 Any external horizontal or vertical surfaces of closed structures, which are not· efficiently shielded, should be checked for local wind pressure or suction using the following equation:

where

p = wind pressure or suction. q = the basic wind pressure or suction, as defined in 5 .1.l. Cp = the pressure coefficient.

5.1.3 The pressure coefficient may be chosen equal to ).{) for horizontal and vertical surfaces.

5.2 Wind forces

5.2.l The wind force Fw on a structural member or surface acting nonnal to the member axis or surface may be calculated according to:

where

c q A

Fw = C q A sinix

the shape coefficient. the basic wind pressure or suction, as defined in 5.1.1. projected area of the member nonnal to the direction of the force. A is to be taken as the projected area of the member normal to the direction of the forces. angle between the direction of the wind and the axis of the exposed member or surface.

The most unfavourable wind direction in the horizontal plane should be used when calculating the stresses in a member due to wind. The spatial correlation of the wind may be taken into consideration for large surfaces.

5.2.2 If several members are located in a plane normal to the wind direction. as in the case of a plane truss or a serie of co­lumns. the solidification effect 1> must be taken into account. The wind force FwsoL may then be calculated as:

where

FwsOL = C., q At/> sinix

the effective shape coefficient. see 5.3.7. the basic wind pressure according to 5. l. l. as defined in 5.2. l. To be taken as the projected area enclosed by the boundaiies of the frame. · solidity ratio. defined as the projected exposed solid area of the frame normal to the direction of the force divided by the area enclosed by the boundary of the frame normal to the direction of the force.

lZ Classificatioo Notes - No. 30.5

a angle between the wind direction and the axis of the exposed member, as defined in 5.2.1.

5.2.3 If two or more parallel frames are located behind each other in the wind direction, the shielding effect may be taken into account. The wind force on the shielded frame FwsHI may be calculated as

FwSHI = Fw,, (a)

(if Eq. in 5.2.I is applicable)

or as

FwsH1 = FwsoL '1 (b)

(if Eq. in 5.2.2 is applicable)

where

,, = shielding factor.

The shielding factor 11 is dependent on the solidity ratio (4') of the windward frame, the type of member comprising the frame and ~he spacing ratio of the frames. The shielding factor may be chosen according to Table 5. l.

If more than two members or frames are located in line after each other in the wind direction, the wind load on the rest of the members or frames should be taken equal to the wind load on the second member or frame.

Table 5.1 The shielding factor IJ·

Spa- Value of ri for an aerodynamic solidity ratio </> of cing 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 ratio (%

Up 1.0 0.96 0.90 0.80 0.68 0.54 0.44 0.37 to 1.0

2.0 LO 0.97 0.91 0.82 0.71 0.58 0.49 0.43

3.0 LO 0.97 0.92 0.84 0.74 0.63 0.54 0.48

4.0 1.0 0.98 0.93 0.86 0.77 0.67 0.59 0.54

5.0 1.0 0.98 0.94 0.88 0.80 0.71 0.64 0.60

6.0 l.O 0.99 0.95 0.90 0.83 0.75 0.69 0.66

Spacing ratio tt: The distance, centre to centre, of the frames, beams or girders divided by the least overall dimension of the frame, beam or girder measured at right angles to the dire<:tion of the wind. For triangular or rectangular framed structures diagonal to !he wind, the spacing ratio should be calculated from the mean distance between the frames in the direction of the wind.

Aerodynamic solidity ratio P=¢·a

where

if! = solidity ratio, see 5.2.2. a =constant.

= 1.6 for flat-sided members. = 1.2 for circular sections in subcritical range and for flat-sided

members in ·conjunction with such circular sections. = 0.6 for circular sections in the supercritical range and for

flat-sided members in conjunction with such circular sec· tions.

5.3 The shape coefficient

5.3.1 The shape coefficient Coo for circular cylinders of in­finite length may be chosen according to Fig. 6.2. Reynold's number Re is then defined as:

where

D Vtz Re=-v-· (a)

D = diameter of member. Viz = wind speed. v = kinematic viscosity of air, may be taken as

1.46·!0-s m2/sec. at 15°C and standard atmospheric pressure.

S.3.2 The shape coefficient Coo for other shape than circular cylinders may be found in Table 5.2.

•

Oassificatioo Notes - No. 30.5 J3

Table 5.2 Shape coefficients c_ for various members of infinite length.

Ft 1 . FY Ft 1 Ft f • Ft I -r~·, --I I--~

~vJJ-L' d-~ er-~~ ~-I~~ o~rJ_:: o- -

·W F~ -J ~ I--.......j.t--Q1j -1 045j 0.43j

a 4.o Cn Cra Cn Cr,. Cn Crn Cn Cra Cn Cm Cn oo + 1.9 +0.95 + 1.8 + 1.8 + 1.75 +O.l + 1.6 0 +2.0 0 +2.05 0

45° + l.8 +0.8 +2.1 + 1.8 +0.85 + 0.85 + 1.5 -0.1 + 1.2 +0.9 + 1.85 . +0.6 90° +2.0 + 1.7 - 1.9 -1.0 +0.1 +1.75 --0.95 +0.7 -1.6 +2.15 0 +0.6 135° -1.8 +0.1 - 2.0 +0.3 --0.75 +0.15 --0.5 + 1.05 -1.l +2.4 -1.6 +0.4 1so· -2.0 ;-Q.l -1.4 -1.4 -1.75 --0. l - l.5 0 -1.7 ±2.l -l.8 0

Ft t .. t t Ft r Ft t Ft t Ft 1

T~ll- F"n cr-1!~ ~-II--2_ d-1~ 2- o"~r~~ d-1~~ O'-i- i 1.6j -~- i.....;.;::

b. ~ -ll-o.1i --1 i.:... ~ --1 ~ o ... sJ 0.5j

a Crn Cn Cm Cn Crn Cn Crn Cn Cr .. Cn Cra Cn

o· + 1.4 0 +2.05 0 + 1.6 0 +2.0 0 +2.l 0 +2.0 0 45° + 1.2 + 1.6 + 1.95 +0.6 + 1.5 + 1.5 +1.8 +0.1 + l.4 +0.7 +l.55 +l.55 90° 0 +2.2 0 +0.9 0 + 1.9 0 +0.1 0 +0.75 0 +2.0

Note: Jn this table the force coefficient Cr is given in relation to the dimension j and not io relation to the effective frontal area ft.e.

5.3.3 The shape coefficient C for individual members of finite length may be obtained as:

C=JCCoo (b)

where

" the reduction factor as a function of the ratio l/d (may be taken from Table 5.3, where d = the cross-sectional dimension of a member norm.al to the wind direction and I = the length of the member).

Table 5.3 Values of reduction factor 'K for member of finite length and slenderness. (Ref. Fig. 7.1)

l/d 2 5 JO 20 40 50 JOO 00

Orcu1ar 0.58 0.62 0.68 0.74 0.82 0.87 0.98 LO cylinder, subcritical flow

Circular 0.80 0.80 0.82 0 .90 0.98 0.99 1.0 LO cylinder; supercrit· ical flow

Flat plate 0.62 0.66 0.69 0.81 0.87 0.90 0.95 1.0 perpen· dicular to wind

5.3.4 For members with one end abuting on to another member or a waJI in such a way that free flow around that end of the member is prevented, the ratio l/d should be doubled for the purpose of determining "· When both ends are abuted as mentioned, tile shape coefficient C should be taken equal to that for an infinite Jong member.

S.3.5 For spherical and parabolical structures like radar domes and antennas, the shape coefficient C may be taken from Table 5.4.

Table 5.4 Sb ape coeff1Cients· C for sphere-shaped structum;.

Structures Shape coeffi· cient

D Hollow hemisphere, concavity 1.4 - to wind

~ Hollow hemisphere 0.35 -

a Hollow or solid hemisphere, 0.4 - concJ1vity to leeward

-D I Solid hemisphere and circular 1.2 disc

-0 Hemisphere on horizontal 0.5 plane ,

-0 Sphere Re .s 4.2·105 0,5

·4.2-105 <Re< 106 0.15

Re;:::; 106 0.20

For hollow spherical cupolas with a «rise» less than the radius, one can interpolate linearly for the ratio f/r between the values for a cir-cular disc and a hemisphere.

5.3.6 For three-dimensional bodies such as deck houses and similar structures placed on a horizontal surface, the shape coefficients may be taken from Table 5.5.

14 Classificstioo Notes - No. 30.5

. Table S.S Shape coefficient C for three-dimensional bodies placed on a horizontal surface •

EXAMPLE A {K0 EXAMPLE B

;:~ /'*' i~~ \k(

~ Plan shape I b Cr for height/breadth ratio ~ w d .

Up to 1 I 2 4 6

4i-~4 1.2 1.3 1.4 1.5 l.6

w~o:r :::::: 4

-~~b ~ 1/4 0.7 0.7 0.75 0.75 0.75

4+. 3 1.1 1.2 l.25 l.35 1.4 -0} 3

- ~} 1/3 0.7 0.75 0.75 0.75 0.8

.r-!;-

-0} 2 1.0 1.05 1.1 1.15 1.2

2 - Q~ 0.5 0.75 0.75 0.8 0.85 0.9

r" -,

•I d • •

-0} 1.5 0.95 1.0 1.05 I.I 1.15

1.5

-9~J 2/3 0.8 0.85 0.9 0.95 1.0

Plan shape I b Crfor height/breadth ratio ~ -w d

Up 10 0.5 1 2 4 6 JO 20

~

0} I I 0.9 0.95 1.0 1.05 I. J l.2 1.4 -b = the dimension of the member normal to the wind. d == the dimension of the member measured in the direction of the wind. . l = the greater horizontal dimension. w = the lesser horizontal dfillension of a member.

Example A: l = b, w = d. Example B: w = b, I = d.

Oauification Notes - No. 30.5

5.3.7 The effective shape coefficient Ce for single frames is given in Table 5.6.

Table S.6 Effective sbape coefficient C0 for single frames.

SoIUliry ratio Effective shape coefficient Ce

"' Flar-si<h Circular sections members ~< 4.2·105 ~;;::: 4.2-105

O.l 1.9 1.2 0.7 0.2 1.8 1.2 0.8

0.3 1.7 1.2 0.8

0.4 1.7 1.1 0.8

0.5 1.6 u 0.8 0.75 Ui 1.5 1.4

1.0 2.0 2.0 2.0

5.3.8 All shape coefficients given in 5 .3.1 through 5.3. 7 in­clude the effect ·of suction on the leeward side of the member.

5.4 Wind effects on belidecls

S.4.1 The wind presi.-ure acting on the surface or helidecks may be calculated using a pressure coefficient <;. = 2.0 at the leading- edge of the belideck, linearly reducing to Cp = 0 at the trailing edge, taken in the direction of the wind. The pressure may act both upward and downward.

5.5 Dynamic analysis of wind sensitive structures

5.5.1 A detailed dynamic wind analysis considering the time variation of wind forces should be performed for wind exposed equipment and objects sensitive to varying wind loads. Typi­cally, high towers, flare booms, compliant platforms like ten­sion leg platforms and catenary anchored platforms etc. should be considered for such analysis.

S.S.2 The gust variation of the wind field can be described as the sum of a sustained wind component and a gust compo· nent. The fluctuating gust velocity can be described by a gust spectrum as given in 2.2.

S.5.3 The spatial correlation (or distribution) of the gust in a plane normal to the sustained wind direction can be de­scribed by a coherence function using a horizontal decay fac­tor, normal to the sustained wind direction, and a vertical decay factor.

5.5.4 The instantaneous wind force on a wind exposed structure can be calculated by summation of the instantaneous force on each wind exposed member. The instantaneous wind pressure q can be calculated by utilizing:

where

u

Vz x

q =+pl vl + u - x I (v,. + u - i)

the instantaneous speed and direction variation from the sustained wind. the instantaneous wind speed and direction. the instantaneous velocity of the structural member.

5.S.S For time domain calculations. time histories of wind velocities corresponding to spectra as given in clause 2 can be used in combination with the force calculations given in 5.5.4 to establish time histories of the wind forces.

15

5.5.6 When using a frequency domain calculation, the in­stantaneous wind spectrum can normaliy be linearized to

l 2 q = 2 p V7- +p V:z. U

for structures where the structural velocity (x) is negligible compared to the wind velocity.

S~.7 In direct frequency domain analysis, the solution can be obtained by multiplication of the cross spectral density for the dynamic wind load with the transfer function of response.

5.S.8 In a frequency domain al$lysis a modal fonnulation may be applied.

The modal responses Ulll.Y be combined with the Square­Root-of-Sum-of-Squares (SRSS) method if the modes are not too closely related. In case of modes. having periods close to each other, the Complete-Quadratic-Combination (CQC) method can be applied. ·

5.5.9 All relevant effects as structural damping, aerodynamic damping and hydrodynamic damping should normally be considered in the analysis.

S.5.10 For the structural design, the extreme load effect due to static and dynamic wind can be assessed by:

Fe = F5 + g a(f)

where

f 5 the static response due to the design average wind speed.

u(f) the standard deviation of the dynamic structural re­sponses.

g == wind response peak factor.

S.6 Model tests

S.6.1 Data obtained from reliable and adequate model tests are recommended for the determination of pressures and re­sulting loads on structures of complex shape.

6. Wave and current loads 6.1 Wave and current loads on slender membe~

6.1.1 Wave loads on slender members having cross-sectional dimensions sufficiently small to allow the gradients of liquid particle accelerations and velocities in the direction normal to the member · to be neglected, may be calculated using Morison's equation. Normally, Morison' s equation is applica­ble when the following condition is satisfied:

.2.> 5 D

where

A. the wave length. D diameter or other projected cross-sectional dimension

of a structural member.

6.1.2 In cases where Morison's equation is applicable, the inertia force may be calculated by the formula:

Fm =p v a +pcm v Raf

where

Fm == inertia force acting normal to the axis of the member. If sectional hydrodynamic added mass coefficient and volume per unit length are used Fm is a force per unit

16

v

length. If three-dimensional hydrodynamic added mass coefficient and complete volume of member are used Fm is the total force on the member.

= mass density of fluid. · = two- or three-dimensional added mass coefficient. In

general Cm is a function of cross-sectional shape and orientation of body, Reynold's number, Keulegan­Carpenter number and roughness. Cm values as func­tion of the former two factors are usually ac:x:epted.

= particle acceleration normal to member axis. = relative acceleration between liquid particle and mem­

ber normal to the member axis. volume or sectional volume (volume per unit length) of the liquid displaced by the member. a reference volume (total or sectional) to which the hydrodynamic added mass coefficient may be related.

Qas&ificatioo Notes - No. 30.5

6.1.3 Recommended values of Cm for different smooth cross-sectional shapes. are given in Table 6.1 and 6.2 for two­and three-dimensional bodies respectively. Values of added mass coefficients for a smooth circular cylinder close to a wall are given Table 6. l. These values are based on potential the­ory and are thus only accounting for cross-sectional shapes and orientation. Other values for Cm may be used provided that the chosen values can be justified.

The values of Cm for circular cylinders with in-service marine roughness should normally not be less than 0.8. The effect of marine growth and appurtenances as anodes etc. should be considered when selecting effective diameters (and volumes} and added mass coefficients.

CJa~ificatioo Notes - No. 30.5 17

Table 6.1 Added mass coefficients for two-dimensional bodies, i.e. infinitely long cylinders.

Section through body Direction of motion Cu. Va

I 0 ... J. 2a ~

Vertical l.O it a2

I .Q. Vertical 1.0 1t a2

I 0 ~

Vertical 1.0 it a2

i &=:::II Vertical 1.0 7t a2 ~

a/b = oo LO

0} a/b = lO 1.14

l afb = 5 l.21 afb = 2 Vertical l.36

it a2 a/b = 1 1.51

~ a/b = 0.5 l.70 a/b = 0.2 1.98 a/b = 0.1 2.23

!Jj d/a = 0.05 l.61 . } d/a = o.ro Vertical l.72 1t a2

d/a = 0.25 2.19

~

t ~1·

a/b = 2 0.85 a/b = l Vertical 0.76 n a2 afb = 0.5 0.67 afb = 0.2 0.61

FUJI~ Horizontal 2.29 it a2

J J WALL

-{~ - Horizontal I+ ( .JL_ 2a y n: a2

2 0 2a b

18 Classification Notes - No. 30.5

Table 6.2 Added mass coefficient for three-dimensional bodies.

Body shape Direction . Cm VR of motion

CircuJar disc

' I. c:Y,2' Vertical 0.64 ..ina3

3

Elliptical disc b/a c,,, 00 1.0

12.75 0.99 lo~ Vertical 7.0 0.97 ~ a2 b 6

~b ,./ 3.0 0.90 1.5 0.76

Flat plates LO 0.64

Rectangular plates b/a Cm 1.0 0.58-

i / 7-;! Vertical 1.5 0.69 ~ a2 b 4 2.0 0.76

~ ~.,,, 3.0 0.83 00 l.00

Triangular plates

i ,edflQ. Vertical ! ( tan '1 )3/2 al

3 ~ !! ~

Spheres

' O~· Any direction 0,5 4 -na3

3

Bodies of a/b Cm revolution Ellipsoids Axial Lateral

1.5 2.0 0.30 0.62

ro.l~ Lateral or axial 2.51 0.21 0.70 .!. n a2 b 3.99 0.16 0.76 3 .,Ao '9 6.97 0.08 0.86 7 9.97 0.04 0.93

0.02 0.96

b/a Cm I 0.68 2 0.36 3 0.24

Square prisms ~CDJ Vertical 4 0.19 a2 b

6.1.4 In the cases where Morison's equation is applicable the drag force may be calculated by the formula:

where

I Fo=TpCov, Iv,! A

Fo = drag force nonnal to the axis of the member. Co = drag coefficient for the flow normal to the member

axis. p mass density of liquid. v, liquid particle velocity relative to the member normal

to the member axis. I Vr I = absolute value of v, introduced to obtain proper sign

ofFo.

5 0.15 6 0.13 7 0.11 10 0.08

A area of member taken as the projection on a plane nonnal to the force direction.

6. 1.5 The current induced drag forces are to be determined in combination with the wave forces. This may be done by vector addition of wave and current induced particle velocities. If available, computations of the total particle velocities and accelerations based on more exact theories of wave/current interaction will be preferred.

6.1.6 When using Morison's equation to calculate the hy­drodynamic loads on a structure one should preferably take into account the variation of Co as function of Reynold's number. the Keulegan-Carpenter number and the roughness

Oassification Notes - No. 30.5

number in addition to the variation of cross-sectional geom­etry.

• Reynold's number (Re= U D/v}. • Keulegan-Carpenter number (Kc = Um T/D).

• Roughness (k/D).

• Distance between the cylinder and a fixed boundary (H/D).

where

D = diameter. H = clearance between the cylinder and a fixed boundary. T = wave period. k = roughness height. U = flow velocity. Um = maximum orbital particle velocity. v = kinematic viscosity of the water.

As a guidance for the surface roughness used for determination of the drag coefficient, the following values may be used:

k (metres)

Steel, new uncoated 5·10- 5

Steel, painted 5·10- 6

Steel, highly rusted H0- 3

Concrete no- 3

Marine growth S·I0- 3 - 5·10- 2

The effect of marine growth and appurtenances as anodes etc. should be considered when selecting effective diameters and drag coefficients.

6.1.7 Two-dimensional drag coefficients for smooth circular cylinders and cylinders of various roughnesses in steady uni· form flow as a function of Reynold's number are given in Fig. 3.2.

6.1.8 Values for the hydrodynamic drag coefficient Co for other smooth cross-sectional shapes in steady flow may be chosen equal to the corresponding wind shape coefficients given in Tables 5.2-:5.6.

6.1.9 Hydrodynamic drag coefficient for circular cylinder in oscillatory flow with in-service marine roughness should nor­mally not be less than 1.1. The drag coefficient for a smooth circular cylinder in osciUatory flow should not be less than 0.7.

6.1.10 Tentative values of the drag coefficient as function of the Keulegan/Carpenter number for smooth and· marine growth covered circular cylinders for supercritical Reynold's numbers are given in Fig. 6.3. The figure is valid for free flow field with.out any influence of a fixed boundary.

6.1.11 The drag coefficient for steady current is equal to the asymptotic value for Kc equal to infinity. For combined wave and current action, the increase of Kc due to the current may be taken into account.

6.1.12 To detennine the drag coefficients for circular cylin· ders close to a fixed boundary, the drag ccefficlents given in 6.1.1 O may be multiplied by a correction factor obtained from Fig. 6.4.

6.J.13 For several cylinders close together. group effects may be taken in to account. Jf no adequate documentation of group effects for the specific case is available, the drag coefficients for the individual cylinder may be used.

6.1.14 An increase in the drag coefiicient due to cross flow vortex shedding should be accounted, see 7.3.3.

19

6.1.15 Tentative values of drag (Co) and drag interference coefficients (Io) (or composite cylindrical shapes are given in Fig. 6.6 and 6. 7. The coefficients are based on a series of model tests with shapes as defined in Fig. 6.5 and given as a function of length solidity St in constant and oscillatory flow. The Reynold's number and Keulegan/Carpenter number are re­ferred to pitch diameter, Dp.

The solidity. ratio SL is defined a.s:

The interference drag coefficient is definea as:

CoDp ID= (b)

Ici!/o;

where

= diameter of individual cylinder, see Fig. 6.5. = pitch diameter, see Fig. 6.5. = drag coefficients for the individual cylinders without

any interaction. length solidity ratio. Interference drag coefficient.

6.1.16 If a deterministic wave ana·iysis is used to calculate globaJ loads, a reduction in the drag coefficients given in 6.1.7-6.1.14 may be appropriate. In such cases the drag coef­ficient for circular cylinders is, however, not to be taken less than

C0 =0,6

where no, or moderate marine growth is considered.

C0 =0,7

where ma~e growth is considered.

For individual member design, the drag coefficients are to be selected according to 6.1.7-6.1.14.

6.1.17 In some cases it may be necessary to ini;lude higher orders terms in Morison's equation. This may be the case if the higher order terms are important for the excitation of struc· tural dynamic response.

6.2 Wave loads on large "Volume structures

6.l.1 The transfer function for linear wave loads on large bodies should.be determined by diffraction theory. The theo· ries may be based on sink source methods or finite fh1id ele­ments. For simple geometical shapes analytical solutions may be used. The results from sink-source methods should be carefully checked for surface piercing bodies such that irreg· ular frequences are avoided. If a new structural concept is in­troduced and the loads can not adequately be described by state of the art methods, model experiments are recommended.

6.2.2 The wave loads on structures composed of large voJume parts and slender members may be computed by a combination of wave diffration theory and Morison's equation. The mod­ifications of velocities and acceleration due to the large volume parts should however be accounted for when using Morison's equation.

6.2.3 In the vicinity of large bodies the free surface elevations (i.e. wave height) may be increased. This should be accounted for .in the wave load calculations as well as for estimates of deck clearances.

20

6.2.4 Hydrodynamic interaction between large volume parts should be accounted for.

6.3 Second order wave lOads on large volume structures

6.3.l Second order hydrodynamic load effects may in many cases be important for the design of large volume structures in waves. Such load effects should be investigated. The different effects are explained in 6.3.2-6.3.6.

6.3.2 When a linear .regular first order wave is interacting with itself and an ocean platform, forces of different characters are created. In addition to first order linear exciting forces, mean nonlinear second order forces (drift forces) and non-li­near forces varying in time with twice the first order wave frequency act on the structure. In the present state of the art effects of higher order than two are usually neglected.

6.3.3 Irregular waves are assumed to be composed of an in­finite number of fundamental frequencies and amplitudes (a wave spectrum). In irregular sea the resulting second order exciting forces contain three components. These arc the mean forces (drift forces), forces varying in time with the difference frequencies (often called slow drift forces) and with the sum frequencies of the wave spectrum (high frequency forces).

6.3.4 The difference frequency forces may in particular be important for design of mooring and dynamic positioning of offshore structures as well as for offshore loading systems. For large volume structures with a small waterplane area the slow drift forces.may create large vertical motions.

6.3.5 The sum frequency forces may become an important excitation source in considering wave load effects on certain offshore platforms as for instance the tension leg concept and deep water gravity platforms.

6.3.6 The second order forces should be determined by a consistent second order theory or by model tests.

6.4 Slamming loads from waves

6.4.1 Horizontal members in the splash zone are susceptible to forces caused by wave slamming when the member is being submerged. The dynamic response of the member should be accounted for.

6.4.2 For a horizontal member the slamming force per unit leDgth may be calculated as:

where

Fs slamming force per unit length in the direction of the velocity.

p = mass density of fluid. Cs = slamming coefficient. D = member diameter. v velocity of water surface normal to the surface of the

member.

6.4.3 The slamming coefficient C, may be determined using theoretical and/or experimental methods. For smooth, circular cylinders the value of C8 should not be taken less than 3.0.

6.4.4 As the slamming force is impulsive, dynamic amplifi­cation must be considered when calculating the response.

For a horizontal member fixed at both ends, dynamic arnplifi· cation factors of l .5 and 2.0 are recommended for the end moments and the midspan moment, respectively.

O~ficatioo Notes - No. 30.S

6.4.5 The fatigue damage due to wave slamming may be de­termined according to. the following procedure:

• Determine minimum wave height, Hmm, which can cause slamming.

• Divide the long term distribution of wave heights, in excess of Hmi11, into a reasonable number of blocks.

• For each block tbe stress range may be taken as:

A CTj = 2 [a <1sJam - (ub + crw>J

where

<Tsiam = stress in the element due to the slam load given in 6.4.2.

CT1> = stress due to the net buoyancy force on the element. u.., = stress due to vertical wave forces on the element. a = factor accounting for dynamic amplification, see

6.4.4.

• Each slam is associated with. 20 approximate linear decay­ing stress ranges.

• The contribution to fatigue from each wave block is given as:

n· i=20 . K

y·=R-J ~ (-1 ) J N· L. 20

J i=20 - n1

where

ni = nwnber of waves within block j. N; = critical number of stress cycles (from relevant S-N

curve). associated with !J. a;. n; = number of stress ranges in excess of the limiting

stress range associated with the cut off level of the S-N curve.

R reduction factor on number of waves. For a given element only waves within a sector of IO degrees to each side of the perpendicular to the member have to be accounted for. In case of an undirec­tional wave distribution, R equals 0.11.

K slope of the S-N curve (in log-log scale).

6.4.6 The calculated contribution to fatigue due to slamming has to be added to the fatigue contribution from other variable loads.

6.5 Shock pressure from breaking waves

6.S.1 Breaking waves causing shock pressures on vertical surfaces should be considered.

6.5.2 In absence of more reliable methods the procedure de· scribed in 6.4.2 may be used to calculate the shock pressure.

6.5.3 The coefficient Cl depends on the configuration of the area exposed to shock pressure. A lower limit of c. for circular cylinders is 3.0.

6.S.4 The area exposed to shock pressure may be taken as a sector of 45 degrees with a heigh of 0.25 Hn8 • where Has is the most probable largest breaking wave heigh in n years, Fig. 3.8. The region from SWL to the top of the wave crest should be investigated for the effects of shock pressure.

6.S.5 The impact velocity (v) should be taken as that corre· sponding to the most probable largest breaking wave height in n years. The most probable largest breaking wave height may be taken as 1.4 times the most probable largest significant wave height in n years.

aassification Notes - No. 30.5

JO

I ~ I 2.29

2.0

\ ----1.0

I I i

I OS 10 10 )0 u

" ....

Fig. 6.1 Recommended value of the added mass coefficient, Cm for a circular cylinder. Inflµence of a fixed boundary on the added mass coeffi­cient, Cm, of a circular cylinder.

c ... ~ '.

'" \\ .• v'I' .,;. • ..,

' \\ ~" I ---1.0

' \Y . ~ ....-,,,o·l

' ,, .x 1.10·~

Hi / ~ /.$ ·~ 1 ~/ '/ ~ '~ A/

.... , "'~OOTI~

~~ " . o.s

' Rt

Fig. 6;2 Drag coefficient for circular cylinders for steady flow.

1120

11100 ------,,,

111000---~ '', ', '

to k,.,..-.......,......,........, '',,,,~~, -----------------------

0.5

-----------------------

DIAGRAM BA.SEO ON lOGARITHIC INTE.A­POtATION BETWEEM k/0•'120 AND k/0·1110000

o~~~~~-+-~~~~~. ~~~~-+--~~~--t

0 10 io 30 40

Fig. 6.3 Drag coefficient Cd as function of K< for cylinders in waves. Re> 5·105•

2.0 ~ ~

"-...._

1.5

1.0

Q.O 0.2 Q4 0.6 0.8 1.0 H.IO

Fig. 6.4 Influence of a fixed boundary on the drag coefficient of a circular cylinder in oscillatory supercritical flow. Kc> 20, Re= 105 - 2· J06.

Oi

owlll· 0 -· ·--0 0 0

P· - 0 I 0 0

Fig. 6.5 Parameters of typical composite cylindrical shapes.

22

0.8 Kc:20

O O.S 1.0 1.S 2.0 SL LENC5TH SOL I 01 TY

Fig. 6.6 Drag coefficient as function of length solidity ratio for smooth composite cylinder shapes. (~ = 6·105)

10 1.0

0 0.S 1.0 1.S 2.0 SL LENGTH SOL.IOlTY

Fig. 6.7. Interference drag coefficient as function of length solidy ratio. (~ = 6·105}

Fig. 6.8 Area to be considered in evaluating the loads due to shock pressure on circular cylinders.

Classification Notes - No. 30.5

7. Vortex induced oscillations 7.1 General

7.1.1 Wind or any fluid flow past a member may cause un­steady flow patterns due to vortex shedding. This may lead to vibrations of the member normal to its longitudinal axis. Such vibrations should be investigated.

7.1.l At certain critical flow velocities, the vortex shedding frequency may coincide with or be a multiple of the natural frequency of motion of the member, resulting in harmonic or subhannonic excitations. The following provides guidance on both methods for determining the motion amplitude and/or the forces on the member.

7.1.3 In the following the necessary criteria for presence of vortex shedding is listed. The vortex shedding frequency may be calculated as follows:

where

f= St.:!.... ·D

f = vortex shedding frequency (Hz). St = Strouhal's number. v = flow velocity normal to the member lixis. D = diameter of the member.

Vortex shedding is related to the drag coefficient of the mem­ber considered. H.igb drag coefficients usually accompany strong regular vortex shedding or vice versa. This means that the Strouhal's number (St) is a function of Reynold's number (Re) for smooth rounded members. The relationship between St and ~ for a circular cylinder is given in Fig. 7. I. For other cross sectional shapes St may be taken from Table 7.1-3.

0.1 1.0 10 1<>2 10J 10• 10s 106 107

lie

Fig. 7.l Strouhal's number for a circular cylinder as a function of Reynold's number.

Clamfication Notes - No. 30.S

T•ble 7.1.

Wind Profile dimensions in mm Value of St

..... o 0.120

Ibf=r i 0.137

~ 50 .1 '.o.s

~H 0.120

¥+ h1.0

1 {H 0.144

~ 50 ·I

t. t . 5

i '~·¢1 I 0.145

~

! ~I .. ,. I 0.140

1 i- !O ~ 0.153

l t•f. 0 0.145

. 12.¢• i

1 w 0.168

0.156 t .,.&

! ~ 50 ~ 0.145

CTUNOElt

~ 11. 800 <It•< 19 tOO 0.200

7.1-4 For rounded hydrodynamic smooth members, the vor­tex shedding phenomenon is strongly dependent on Reynold 's number for the flow, as given below:

23

Wind Nofile d;;,,ensions in mm Value o/St

t • t.O

! 1a:s~I

·~ 12.41 0.147

I ~ 50 ~

t• 1.0

i .. ~. l=:p 12.!t 0.150 1B I 1

I- !IO ~

- 0.145

JL 1 0.142

/ ~ 50 ·I 0.147

- 0.131

l t• t.o

H!=L 0.134

/ w 0.137

{::ti_ 0.121

! ~ 25 1-23~ 25 ~ 0.143

t::fL 0.135

~ 254J·2' j.

~CL: 0.180

L 100 ~ 0.114

ti: 1 2

~ 50 ~ 0.145

101 :s; Re< 0.6·!0" Periodic shedding

0,6·!06 :s; Re< 3'106 Wide-band random shedding

3-106 ~ R. < 6·106 Narrow-band random shedding

R. ;:::, 6-106 Quasi-periodic shedding

For· rough members the vortex shedding shall be considered strongly periodic in the entire Reynold's number range.

24

7.1.5 For deterorination of the velocity ranges where vortex shedding induced oscillations may occur, a parameter V.., called the reduced velocity, is used. V, is defined as

v

Classification Notes - No. 30.5

7.2.3 In-line excitations are not likely to occur unless there are large concentrate4 masses excited.

7.2.4 Cross-flow excitations may occur when:

Vr = f· D 4,7 < v, < 8,0. 1

where

v = flow velocity normal to the pipe axis. fi = natural frequency of the pipe. D = pipe diameter.

7.1.6 Another parameter controlling the motions is the sta­bility parameter, k5, defmed as

where

2·m,, 'J ks7--2-

pD

p = mass density of surrounding medium (air or fluid). D = element diameter. IDc = generalised mass per unit length of the element defined

as

L L m [y(x.)]2 dx + L M; [y(ll.j)J2

Ille= d L [y(x)]2

dx

-;s = generalised logaritltmlc decrement (27f·~) of damping defined by

f>= f>s + f>wil + <Sb

f>1 = logarithmic decrement of structural damping. f>soi1s = logarithmic decrement of soils damping. t5b = generalised logarithmic decrement of hydrodynamic

damp1ng. m mass per unit length, including structural mass, added

mass and the mass of any containment within the ele­ment.

Mj = concentrated point mass. y(x) = normalized mode shape. L = length of the element. d = submerged length of the element.

7.2 Wind induced vortex shedding

7.2.l Wind induced cyclic excitations of pipes may occur in two planes, in-line with or perpendicular to the wind direction.

The amplitudes of the vortex shedding induced motions due to wind may be derived according to the simplified approach for vortex shedding in steady current given in 7.3, substituting the mass density of the water with the mass density of the air (pa;, = 1,225 kg/ml for dry air).

7.l.l In-line excitations may occur when:

1,7 < Vr < 3,2

7.2.5 The upper limit of the stability parameter k$ for cross­flow excitations may be taken as 25 unless more accurate data exist.

7.2.6 The amplitude for fully developed cross-flow oscil-lations may be found from Fig. 7 .2.

7.2.7 For strongly turbulent wind flow, the given figures for amplitudes are conservative. A more accurate calculation may be performed in accordance with the principles outlined in 7.4.

l.30

1.20

l.10

t .00

0.90

o.ao

0.?0

I lS 0 .6')

~

t O.'l()

0.40

O.S>

o.ao

0 .10

c.o

Fig. 7.2

c l • 6 8 lO 1-2 l 4 U5 18 20 2? 24 2626 Xt

.,,.. ""2"''' ti ..

Amplitude of crossflow motions as function of k,.

7.3 Current induced vortex shedding

7.3.1 Vortex shedding resonance or locking-on may occur as follows:

In-line (flow parallel) excitations when;

1.0 ~ v, ~ 3.5

Ks~ 1.8

Depending on the flow velocity the vortices will either be shed symmetricaliy or alternatively from either side of the cylinder.

For 1.0 < v, < 2.2 (first instability region), the shedding will be symmetrical and the maximum amplitude of the oscillations is determined as a function of the stability parameter, Ki, see Fig. 7.2. For a given reduced velocity the motions will be suppressed if the stability parameter is above a certain thresh­old value.

I

Classification Notes - No. 30.S

ANPL. DIAM.

Fig. 7.3

D O.!>

IH·LIHe MOTION

\.0 l.S

Amplitude of in-line motion as a function of k,-

2 ()

The criteria for onset of the motion in the first instability re­gion is given in Fig. 7.4.

For v, > 2.2 the shedding will be unsymmetric, and the motion will take place in the second instability region (2.2 < v, < 3.5) for K .. < 1.8. The maximum amplitude of the oscillation as function of Ks is given in Fig. 7.3.

If the current is fluctuating due to turbulence moving in and out of the vortex shedding region the phenomenon will behave as waves.

MOTION

0.8 1.0 1.$ 2.0

Fig. 7.4 Criteria for: onset of the motion in the first in-Jioe instabil­ity region. (1.0 «V, < 2.2).

The locking-on range for cross-tlow oscillation is 4.8 5: v, 5: 12.0 for all Reynold's numbers.

The maximum amplitude of the cross-flow oscillations may be determined from Fig. 7.2.

The mode shape parameter.}' (see Table 7.2 for typical values). used in this figure is defined as

}'= Ymax

where

L'-[y2(xl] dx

L 1 [y4(xl] dx

1(2

y(x) = mode shape. Yrnax = maximum. value of the mode shape. L = length of the pipe.

25

Table 7.2 The mode shape parameter of some typical struc-tural elements.

Szructural element y

Rigid cylinder 1.00

Pivoted rod 1.29

String and cable 1.16

Simply supported beam 1.16

Cantilever, 1st mode 1.31

Cantilever, 2nd mode 1.50

Cantilever, 3rd mode l.56

Clamped~lamped, 1st mode 1.17

Clamped.clamped, 2nd mode l.16

Clamped-pinned, I st mode l.16

Clamped-pinned, 2nd mode l.19

7.3.2 The combination of waves and current should be by vectorial addition of current and wave induced velocities. Further, the lock-in regions and amplitudes are found by using the criteria given for oscillations due to waves.

7.3.3 In connection with strong transverse locking-on, an increase in the {in-line) drag coefficient of the member takes place

where

Co= Coo 1+ 0·9 Y [y(x.)] D(x)

Y amplitude of displacement. y(x) = mode shape. Coo= the drag coefficient for the stationary cylinder. D(x)= member diameter.

7.3.4 The vortex shedding is shed in cells. A statistical mea­sure for the length of the cells is the correlation between forces for sections at different length apart. This is formulated by the correlation length

l - 3 D + 50 D· y (y{x)) for Y y(x) < 02 c 0.5 D - Y {y(x))

D le ~oo for Y y(x) ~ T

The lack of correlation over the length of the cylinder influ­ences the transverse forces.

In a vortex cell the transverse force can be determined by

F cell = + p Cr v2

D sin{2nft)

where Cr~0.9.

For a long pipe (( << L) the lack of correlation modifies the force to be

~- I ., Feel! - .JLc/L Cr.

2 p v- D sin(2nft) .

For le> L. JLc/L ~ 1 (as approximation).

7.3.5 Vortex shedding in combination with composite pipe bundles.

26

Vortex shedding takes place on combination o.f pipes or on pipe bundles as global vortex shedding (on the total enclosed volume) or as local vortex shedding on individual members.

Pipes spaced so densely that the drag coefficient for the total enclosed volume exceeds 0. 7 can be exposed to global vortex shedding.

The global . vortex shedding represented by a transverse lift coefficient will depend on the total drag coefficient roughly so that

Co-0.7 Cr~Cro Coo-0.7 (C0 > 0.7)

in which Cw is the transverse flow coefficient for the enclosed body if it is solid. In addition there may be local vortex shed­ding on individual members.

Pipes spaced so, that the drlrg coefficient for the total enclosed volume is below 0.7 will only be exposed to local vortex shed­ding on members.

7.4 Wave induced vortex shedding

7..4.1 Waves and/or current flow past a member may cause unsteady flow patterns due to vortex shedding. This may lead to vibrations of the member normal to its longitudinal axis. Such vibrations should be investigated.

7.4.l At certain critical flow velocities, the vortex shedding frequency may coincide with or be a multiple of the natural frequency of motion of the member, resulting in harmonic or subharmonic excitations. The following provides guidance on both methods for determining the motion amplitude and/or the forces on the member.

7.4.3 The vortex shedding in waves falls into two categories:

1) Vortex shedding of the same type as in steady current. This type exists for Kc> 30.

2) Vortex shedding with the shedding frequency as multi):>Je of the wave frequency. This type exists for 6 < Kc< 30 in which

is the Keulegan-Carpenter number where

Vm "" maximum orbital velocity due to wave motion. T = wave period. Ile = steady 1;tate current.

7.4.4 Vortex shedding for Kc> 30 only exists when the or­bital velocity component perpendicular changes Jess than 110% in a vortex shedding cycle. In mathematical terms

u D -

2 -8

< 1. 1 · Kc > 30 u t

where

u = the instantaneous orbital velocity. u = the instantaneous orbital acceleration.

For a sine wave motion this criterion corresponds to

( v:u )2

> ~.7 St kc co{ Arc sin( u~ .. ) J

Classification Notes - No. 30.5

Fig. 7.S

'STOP VORTEX 5'<EOOIN~

Criterion for presence of vortex shedding in waves.

7.4.5 Vortex shedding for I<.,> 30 follows the rules for steady current.

7.4.6 Resonance vibrations due to vortex shedding (lock-ing-on) may occur as follows for Kc > 30:

In-line excitations:

Cross-flow excitations:

l<vr<3.S

k5 < 1.8

7.4.7 The maximum expected response can be found from Figs. 7.2 and 7.3. 'Normally this response will be far higher than seen in natural sea. The vortex shedding has to satisfy both 7.4.4 and 7.4.6 which means that the member exposed to locking-on will be alternatively amplified and damped in the wave motion, see Fig. 7.6.

VORTEX SH£001_, FOR<:£

Fig. 7.6

TfN€

Vortex shedding and vortex shedding response cross-Dow (locking-on) in wave motion.

Normally the exact response must be calculated by available mathematical models which reflect the above features. As an approximate expression for very small cross-flow motion, however, the development of response in a locking-on period can be calculated by

J lc;(Ymax> -Y max= Yo L (I - exp ( - n 0 b)}

( le; le ) If L > I then use L = l

where

n11 the number of load cycles in the locking-on region. Yo the maximum value from one of the graphs in Fig. 7.2

or Fig. 7.3. fl = defined in 7 .1.6.

Between locking-on periods the amplitudes are reduced to

Classification Notes - No. 30.5

where

nd = the number of cycles in the damped region.

The formulae shall be used with caution because the variation in the velocity profiJe wm shift position of the damping and locking-on regions during the wave cycle.

7.4.8 Locking-on for Kc< 30. For this particular region a kind of resonance with waves vortex shedding take place. The vortex shedding frequency will be a multiple of the wave frequency.

In-line:

Vr >I

Cross-flow (with associated in-line motion):

3 < Vr < 9

The maximum amplitude response of the cross-flow compo­nent is around 1.5 diameter. The associated in-line amplitude component is less than 0.6 diameter.

7.5 Methods for reducing vortex-induced oscillations

7.5.l There exist two ways for reducing the severity of flow-induced oscillations due to vortex shedding, either a change in the structural properties, or change of shape by ad­dition of aerodynamic devices such as strakes, shrouds or spoiling devices which partly prevent resonant vortex shedding from occurring and partly reduces the strength of the vortex­induced forces.

7.5.2 Change of structural properties means changing of na­tural frequency, mass or damping.

7.5.3 An increase in natural frequency will cause an increase in the critical flow speed

n;D v=--

St

Thus v may become greater than the maximum design wind speed, or Vr may come outside the range for onset of resonant vortex shedding.

7.5.4 An increase in non-structural mass can be used to in­crease ks and hence the amplitude of oscillations. Due atten­tion has however to be paid to the decrease of natural frequency which will follow from an increase of mass.

7.5.5 Spoiling devices are often used to suppress vortex shedding locking-on. The principle in the spoiling is either a drag reduction by streamlined fins and splitter plates (which break the'rythmic pattern) or by making the member irregular such that vortices over different length becomes uneven and irregular. Examples of this may be ropes wrapped around the member, perforated cans or twisted fins.

In order for the spoiling devices to work they shall be placed closer than the correlation length for the vortex shedding.

The efficiency of the spoiling device should be determined by testing. The graphs for in-line and cross-flow motion can be

27

directly applied for the spoiling system by multiplying with the efficiency factor. ,

7.5.6 Use of pretensioned guy wires has proven effective to eliminate resonant vortex shedding.

The guy wires should be attached close to the midpoint of the member and pretensioned perpendicular to prevent cross-flow oscillations. The effect can then be summarized as follows:

• Increase member stiffness and hence natural frequency (small effect).

• Hysteresis damping of wires (large effect).

• Geometrical stiffness and damping of wires (large effect) (due to transverse vibrations of wire).

• Nonlinear stiffness is introduced which again restrains res-onance conditions to occur.

The wires have to be strapped and prc:tensioned in such a way as to fully benefit from both hysteresis and geometrical damping as well as the non.Jinear stiffness. The pretension for each guy wire should be chosen within the area indicated on Fig. 7.7.

Total pretension and number of wires bas to be chosen with due consideration to member strength.

An example is shown in Fig. 7.7 where a 3/4 inch wire is used to pretension a member with 30 m between the member and the support point. A tension (force) of 2.5 kN will -in this case give maximum non-linear stiffness.

Instead of monitoring the tension, the wire sagging may be used to visually estimate the tension. In the example shown, a sag of around 0.45 corresponds to the wanted tension of 2.5 kN.

.., v ct 0 ...

10

5

0.0

Fig. 7.7

LINE CHARACTER! STIC 3/ 4 INCH WIRE

FORCE- [)ISP~ACEMENT

FORCE ·SAG

0.1

MEM8::2G

~~"7g-•

0.2 QJ 0.4 0.45 0.5 SAG (Ml. 01 SP~ACEMENT (M)

0.6

Force-deflection curve for 3/4 inch stranded guy-wire with geometrical configuration as shown.

28

8. References This Classification Note has primarily been based on the fol­lowing references in alphabetic order:

• Blevins, R.D.: «Flow-induced», Van Nostrand Reinhold Company, New York 1977.

• BSI Code of Practice No. 3, Chapter 5, Part 2: «Wind Loads», September 1972.

• CIRIA Underwater Engineering Group, Report URS: «Dynamics of Marine Structures», London, June 1977.

• Fredse, J.. Sumer, B.M., Andersen, J., Hansen, E.A.: «Transverse Vibrations of a Cylinder very close to a Plane Wall», Proc. Offshore Mechanics and Arctic Engineering Symposium~ 1985.

• Gran, S.: «A course in Ocean Engineering», A/S Veritas Research, Report No. 88·2001.

• Heidemann, Olsen and Johansen: «Local Wave Force Coefficients», ASCE Civil Engineering in the Ocean IV, September 1978.

• Jacobsen, V., Bcyndum, M.B., Nielsen, R., Fines, S.: «Vibration of Offshore Pipelines exposed to Current and Wave Action», Proc. Third International Offshore Me­chanics and Arctic Engineering Symposium, 1984.

• King, R., Prosser, M.J.: «On Vortex Excitation of Model Piles in Water», Journal of Sound and Vibrations, Vol. 29, No. 2, pp. 169-180, 1973.

• Laken, A.E., Torset, O.P., Mathiassen, S. and Arnesen, T: «AspeC!S of Hydrodynamic Loading in Design of Pro­duction Risers», OTC paper No. 3538, May 1979.

• UiJken, A.E. and Faltinsen, O.M.: «Three dimensional S~ond order Hydrodynamic effects on Ocean Structures in Waves», Paper to be published in Applied Ocean Re­search.

Classification Notes - No. 30.5

• Ottesen Hansen, N.E., Jacobsen, V. and Lundgren, H.: «Hydrodynamic Forces on Composite Risers and Individ­ual Cylinders», OtC-paper 3541, May 1979.

• Ottesen Hansen, N.E.: «Vortex Shedding in Marine Risers and Conductors in Directional Seas», Symposium of Di· rectional Seas in the Oceans, Copenhagen 1984.

• Sumer, B.M., Freds0, J.: «Transverse Vibrations of a Pipe· line exposed to Waves», Proc. 5th International Symposium on Offshore Mechanics and Arctic Engineering (OMAE 86), Tokyo, Japan 1986.

• Sarpkaya, T.: «Vortex Shedding and Resistance in Har­monic Flow about Rough Circular Cylinders», BOSS 76-conference, Trondheim, Norway, August 1976.

• Sarpkaya, T.: «ln·line and Transverse Force on Cylinders near a Wall in OsciUatocy Flow at High Reynold's Numbers», OTC Paper No. OTC 2980, May 1977.

• Sarpkaya, T.: «Hydrodynamic Drag on Bottom mounted Smooth and Rough Cylinc!er in Periodical Flow», OTC Paper No. OTC 3761, May 1979.

• Sarpkaya, T. and Isaacson, M.: «Mechanics of Wave Forces on Offshore Structures», Van Nostrand, Reinhold Company, New York, 1981.

• Tsahalis, O.T.: «Vortex-induced Vibrations of a Flexible Cylinder near a Plane Boundary exposed to Steady and Wave-include Currents», Proc. Third International Off­shore Mechanics and Arctic Engineering Symposium, 1984.

• Tsahalis, D.T.: «The Effect of Sea bottom Proximity on the Vortex-induced Vibrations and Fatigue Life of Offshore Pipelines», Proc. Second International Offshore Mechanics and Arctic Engineering Symposium, 1983.

• Tsahalis, D.T.: «Vortex-induced Vibrations due to Steady and Wave-induced Currents of a Flexible Cylinder near a Plane Boundary».