A reduced method for the calculation of the shear stiffness of a ship hull

OEPORT No 148 S

Februari 1971

S3/-)

NEDERLANDS SCHEEPSSTUDIECENTRUM TNO

NETHERLANDS SHIP RESEARCH CENTRE TNO

SHIPBUILDING DEPARTMENT

LEEGHWATERSTRANF .5 DELFT

*

A REDUCED METHOD FOR THE CALCULATION OF THE

SHEAR STIFFNESS OF A SHIP HULL

(EEN VEREENVOUDIGDE METHODE VÓOR HET BEREKENEN VAN DE

AFSCHUIFSTUFHEID VAN EEN SCHEEPSRÖMP)

by

IR. W. VAN HORSSEN

(Laboratory of Applied Mechanics, Deift University of Technology)

De methoden voòr het berekenen van scheepstriilingóñ waarbij de romp wordt beschouwd ais een elastische balk met over de lengte varierende massa en stijtheid, zijn, hoewel er een aantäl beíwarn aan kteven, nog vrij algemeen in gebruik.

Bij deze betekeniñgen en speciaal bij die voor trillingen van hogeré orde, moet de invloed van de afschuiving in rekenin wôrden gebracht.

Soms wordt dit gedaan door gebruik te maken van correctie-factoren zoals die in de literatuur worden gegeven. In bet in 1965 gepubliceerde rapport no. 75S ,,Scheepstrillingen van het vracht-en passagiersschip s. ,Oränje Nassau" toonde Van Horssen reeds aan dät deze factoten aanieiding kunnen geven tot aan-zienlijke fouten.

Bij de huidige rekenmethoden, waarbij gebruik wordt ge-maakt van digitale rekenautomaten, kunnen zônder veci corn-plicaties de äfíchuifstijtheden zeif in de berekening worden opge-fornen.

Het bepalen van deze afschuifstijtheden voor een aantal door-sneden van cefi scheepsrómp voigens de elementarie balktheorie, vergt evenwel een vrij gecompliceerde berekening, zodat toe-passing van eón betrouwbare benaderingsmethode veci tijd en werk kan besparen.

Biózeno, Koch en Lekkerkerker pasten reeds in 1956 een be-naderingsmêthode toe, die in dit rapport wordt toegelicht, waar-bu tevens een groot aantal resultaten van ,exacte' berekeningen wordt gepresenteerd waarinede het schatten van een coöfficiënt voor de benaderde methode wordt vereenvoudigd.

HET NEDERLANDS SCHEEPSSTUDIECENTRUM TNO

The methods for the calcûlàtion of ship vibrations, considering the hull as an elastic beam with longitudinally varying mass and stiffness are, although they have a number of drawbacks, stili rather commonly in use.

In these calculations and especially in those for the higher modes of vibration the influence of the shear must be taken into account.

Sometimes this is allowed for by usingcorrection factors as given in the relevant literature In the report no 75S "Hull vibra tions of the cargo passenger motor ship Oranje Nassau published in 1965, Van Horssen already showed that these correction factors may lead to considerable errors.

For the present-day calculation methods, employing digital computers, the shear stiffnesses themselves can be used in the calculatinns without much complications.

The exact determination of the shearstiffness for a number of cross sections of a ship hull in accordance with the elementary beam theory, however, requires rather elaborate calculations. Application of an approximate method that can be used with conildence, therefore, can save time and labour.

Biezeno, Koch and Lekkerkerker already in 1956 applied such an approximation method which is explained in this report Also a large number of results of 'exact' calculations are presented to facilitate the choice of a coefficient for the approximate method.

THE NETHERLANDS SHIP RESEARCH CENTRE TN()

sum

ry

CONTENTS

page

7

1

Introduction

7

2

Shear stiffúess resisting a vertical shear force

7 2.1

Theoretical treatment

2.2

Suggestion for an approximate calculation of the shear stiffness

of cross sections of a ship hull.

9

2.3

Cross sections and corresponding C-factors

9 3

Shear stiffness resisting a horizontal shear force

9

3 1

Thin walled closed cross sections

9

3.2

Thin-walled open cross sections

10

4

Fiñal rem rks

Literature

Appendix A

C-factors for vertical shear stiffness

,. . . 12

Appendix B

CH-factors for horizontal shear stiffness

. 16

LIST OF SYMBOLS

a

height of an element

a

relative displacerñeñt (of section i)

b

width

c

constant

f

displacement by shear, per umt length

h

height

I

length

q

load per unit length

s

distance along centre line of thin wall

x

longitudinal coordinate

y

coordinate along centre line of thin wall element

z

vei'tiöal coordinate (ship)

A

cross-sectional area

A

"vertical" area

AH

"horizontal" area

C

factor for calculation of vertical shear stiffness

C,,

factor for calculation of horizontal shear stiffness

D

shear force

E

Young's modulus

E

elastic shéar energy per unit length

G

shear modulus

I

moment of inertia of cross section

M

bending moment

S

first moment of an area

S,

vertical shear stiffness

S,,,

horizontal shear stiffness

angle relative to the vertical

5

wall thickness

o

bending stress

i

Introduction

In the numerical calculation of natural frequencies and

vibration modes of a ship hull one is faced with the

difficulty that one deals with a very complicated

three-dimensional construction. In a first attempt one is

al-most intuitively led to replace the ship by a beam

model.

In the present report we. shall describe a method

according to which the shear stiffness of this beam both

in vertical and horizontal direction is determined In

the following we shall for the sake of convenience

refer- to

"vertical shear stiffness" and "horizontal

shear stiffness" respectively.

A cross section of a ship is thin-walled, either of the

open or closed type depending on whether the section

is made over a hatch way or between hatches where

the main deck is "full". The double bottom part Of

the cross section, however, is always Of the closed

type.

In dealing with vertical vibrations a simplifying fact

is that inertia forces act along an axis of

symmetry.-In a horizontal direction, however, there is no axis of

symmetry. We are even faced with the difficulty that

the horizontal inertia forces do not coincide, in general,

with the centre of shear. This- causes a coupling

be-tween horizontal and torsional vibrations.

Chapter 2 of the present report deals with the

deter-mination of vertical shear-stiffnesses and in Chapter 3

the horizontal shear stiffnesses are treated. The

well-knowñ method, valid for prismatic beams is applied,

based on a stress distribution according to elementary

beam theory. Since the calculation of ship-hull

vibra-A REDUCED METHOD FOR THE Cvibra-ALCULvibra-ATION OF THE

SHEAR STIFFNESS OF A SHIP HULL

by

Ir. W. VAN HORSSEN

Summary

-It is explained how the shear stiffness of a thin-walled cross section is calculated in accordance with the elementary beam theory and the concepts "vertical area" and ,,horizontal areá" are introduced.

It is shown that it is possible to express the shear- stiffness in this vertical-or horizontal area by adding a cOefficient C that depends on the geometry of the cross section. This coefficient C, for ship-like cross sections only varies within rather restricted limits and can also be estimated rather well by comparing the cross.section under consideration with a cross section of à similar shape for which the shear stiffness has. been obtained in the exact way.

Thus by thiding the coefficient and calculating the verticäl- or horizontal area, the shear stiffness of a cross section can often be / obtained in a sufficiently accurate way.

A collection of cross sections for which the C-values fòr vertical and ¡or horizontal sheàr stiffness have been calculated is -added to the report to facilitate the choice of a coefficient.

For calculating the horizontal shear stiffness of open cross sections a different approach is needed. For this type too, an approx-imate calculation method is presented.

Yet it will be nessary sometimes to calculate the shear stiffness of a cross section by the "exact" method. It is recommended that the C-factors derived by such calculations be published iñ some way.

tions requires the treatment of a great number of cross

sections, the numerical work to .be done is quite

cumber-some. For this reason it seems worthwhile to derive a

simple method by which a rough-and-ready rule may

be applied to certain types of cross sections.

Follow-ing this rule that Biezeno, Koch and Lekkerkerker

applied for the first time in 1956, the shear rigidity is

written as the product of the .shear modulus, the

"vertical area" of the cross section (to be defined in the

sequel) and a constant. The magnitude of this constant

depends on the shape of the cross section. This will

be illustrated with a few examples, which may at the

same time serve as a gùide in estimating the magnitude

of this constant for a cross section under investigation.

2

Shear stiffness resisthig a vertical shear force

2.1

Theoretical treatment

Figure 1 shows an elementary part of a beam with a

length dx loaded by shear fOrces and bending moments.

qdx dD

+-dx

M(I

1 dx Fig. i dM

+--dx

7

8

This load introduces bending stresses o and shear

stresses

t.

The distribution of shear stresses over the

cross section is assumed to be in accordance with

elementary beam tbeory The strain energy

acdumu-lated in the beam element may be calcuacdumu-lated. It is the

volume integral of a square function of the stresses.

The energy may be separated into a part originating

from the bending stresses and a part originating from

the shear stresses. The latter part will be called E8.

In the analysis of thin walled beams it appears that

the

t

may be assumed to be distributed uniformly over

the wall thickness and directed along the centre line

of the wall. The equilibrium equation of a wall element

yields the well-known formula

in which

D = shear force

ö = wall thickness (local)

I = moment of inertia of the entire cross section

with respect to the horizontal mediañ

S = first moment of area with respect to the

horizontal median of cross sectional area

between free edge and plane through point

being investigated

The energy E8 per unit length of the beam is given by

D2

E

Ids=

Ids

J2G

2G12J .c

where

dr

denotes a line element along the centre line

of the wall and G denotes the shear modulus.

The energy E8 is written in the form

(2)

This expression suggests to consider f as the shear

displacement per unit length. In investigating ship hull

vibrations the combination of the shear displacement

f and the bending displacement should be identified

With the displacement of the local mass.

We next introduce the shear stiffñess S, of the

ideal-ized beam model by the formal expression

which in combination with equation (3) yields

D2

E8 =

2S

Finally the following expression of the shear: stiffness SV

in terms of the geometry of the cross section! is obtained

by equating the right-hand sides of equations (2) and

(5)

G12

SV

- j'-ds

For two simple examples the determination of the

shear stiffness is carried out:

Example 1

A rectangular cross section (see figure 2). The shear

stress

t

follows from (1)

DyS(fa+y)

₌

_{(ay_y2)}

5i/53

_ôa3

Equation (2) gives

36D2 a

36D2 E5

f(ayy)dy=

25a6Go

23OôaG

With equation (5) this expression leads to

=

aG = *AG

where A is cross-sectional area.

Example 2 (see figure 3)

For cross sections having an inclined position it ap

pears that for calculating the shear stiffness the

"vertical area" must be taken. This vertical area is

a

cos2. And it can be derived that

= 5aGcoso

Fig. 3 y (6)

t =

DS

(1)

Df

(3) Fig. 2 D

2.2

Suggestion for an approximate calculation of the

shear stiffness of cross sections of a ship hull

In a vibrating ship the deformation of the hull,

con-sidered as a beam model, may be split up, as we have

seen, into bending deformation .and shear

deforma-tion. Especially for the higher frequencies the latter

deformation is very important, but already in the

in-vestigation of the lowest frequency neglecting the shear

deformation leads to considerable errors in the results.

In order to take the shear deformation into account

it is necessary to know the magnitude of the shear

stiffñess of a large number of cross sections of the ship.

The determination of these magnitudes according to

the method described in the previous paragraph

re-quires calculations that are tedious and cumbersome.

In order to avoid these calculations we may make use

of a more simple formula by which the shear stiffness

is determined with a sufficient degree of accuraçy.

The two simple examples given in the previous para

graph suggest the introduction of a so-called "vertical

area"

4V

given by

A = Jcos2dA

(7)

Here

represents the angle between the centre line of

a wall element and a vertical line. This implies that if

a wall element is situated horizontally it does not

contribute to the vertical area and therefore it does not

contribute to the vertical shear stiffness.

The vertical shear stiffness, is now written in the

form

S = CÁVG

(8)

and.it appears that for the simple cross sections dealt

with in the previoùs paragraph C is a constant, -, and

does not depend on .

There is some doubt, however, whether for all cross

sections the shear stiffness is given correctly by

equa-tion (8) using a value * of the coefficient C.

Calcu-lations carried out for several cross sections show

in-deed that equalling the "exact" value according to

equation (6) to the value given by equation (8) yields

a value of C that depends on the geometry of the cross

sectién. But it appears, due to the fact that equation (8)

expresses the shear stiffness in terms of the vertical

area A instead of the whole area A itself, that C differs

only slightly for different kinds of cross sections.

Moreover it seems possible, after some experience, to

estimate the magnitude of C, as cross sections may be

divided into certain types. In order to illustrate this

and in order to acquire some experience we give in

Appendix A a few results of "exact" calculations, that

have been carried out bearing on different types of

cross sections.

In dealing with vertical vibrations one can generally

assume that the shear force is acting along a line of

symmetry of the cross section. Hence one may easily

indicate, for reasons of symmetry, points of the

cross-section where the shear stress is zero (viz, the

inter-sections of the cross section with the line of symmetry).

Applying formula (1) one may then determine the

shear stresses in a straight-forward line. The final step

consists of calculating SV according to equation (6).

On the other hand the vertical area A may be

deter-mined. Identifying the value of SV obtained in the

"exact" way with formula (8) yields the pertaining

value of C.

2.3

Cross sections and corresponding C-factors

In Appendix A a number of cross sections frequently

used and the corresponding values of C are given.

In this appendix the

gures Al through A9 give

values of C for soiíie simplified cross sections. The

figures AlO through Al7 give values of C for real

cross sections of a number of ships. In these last

figures those parts of the cross sections are also

indi-cated which are supposed to contribute to the vertical

area. Parts not contributing to the vertical area are

drawn with a dotted line. In these parts the shear

stresses are small in comparison with the shear stresses

in the other parts and therefore they may be neglected

in the energy E3 in equation (2).

Now in actual practice one proceeds in the

follow-ing way:

Look for that cross section with a known value of

C that resembles the cross section of which the

shear stiffness has tobe calculated.

Calculate the so-called 'vertical area' AV for the

cross section under investigation.

Multiply A

by the value of C and the shear

modulus G.

3

Shear stiffness resistilig a horizontal shear force

3.1 Thin-walled closed cross sections

The determination of the horizontal shear stiffness is

much more complicated than that of the vertical one.

This is caused by the fact that the horizontal shear

force does not act along a line of symmetry of the cross

section. In the previous chapter the shear force was,

as mentioned, acting along the line of symmetry and

in such a case it is easy to indicate a point (or points)

where the shear stress has to be zero (viz, the

inter-sections of the cross section with the line of symmetry).

When there is a horizontal shear force it is not possible

to determine the shear stresses in a simple way. This is

only

possible for the case of a simply-connected cross

lo

section. The presence of the double bottoth makes the

cross sectión multiple-connected and now we have

to calculate the statically undeterminate shear stresses.

If the cross section is built up of n cells then the

shear stress distribution is n-fold undeterminate. The

unknown shear stresses can be found from the

condi-tion that the cross seccondi-tion has to transmit only a shear

force (acting in the shear centre) and a bending moment

but no torsional moment. Absence of torsion, i.e. the

specific torsion is zero, leads to the well-known formula

which has to hold for each cell

;--ds

O (9)

Applying this formula for each cell gives n equations

for the n statically unknown shear stresses. If the

n equations are solved the shear stress distribution in

the entire cross section can be calculated.

The shear stresses found in.this way represent the

total shear force. The working line of the shear force

is fixed by equating the moment of the shear force to

the moment of the shear-stresses around an arbitrarily

chosen point. When the working line is known also

the so-called shear centre can be found as the

inter-section of the working line and the line of symmetry of

the cross section.

It has to be remarked that for all calculations the

elementary beam theory is the starting point. With the

known shear stress distribution the elastic energy per

unit length of the beam may be calculated in the same

manner .as described in chapter 2. The shear stiffness

follows now in the same way as described in 2.1, for

mula (2) through (6). Only for the moment of inertia

of the entire cross section with respect.to the horizontal

median the moment of inertia with respect to the

vertical median shoUld be read.

In order to avoid the above-mentióned complicated

calculations we may make use also of a much more

simple formula. In the same manner as defined in the

previous chapter we now define the horizontal shear

stiffness as

SH = C11AØG (10)

where

C11

a constant depending on the geometry of the

cross section,

AH = the so-called horizontal area.

This horizontal area is defined in the same way as the

vertical area, only cos2 in equation (7) has to be

re-placed by cos2(ir/2 - cc).

The constant CH differs slightly for different kinds

of cross sections, due to the fact that equation (10)

ex-presses. the shear stiffness in terms of the horizontal

area AH instead of the whole area A itself.

In Appendix B, figure Bl, CH-factors are given for a

simplified cross section. The figures B2 through B6 give

C11-factors for some real cross sections of ships. In these

figures are also indicated those parts of the cross

sec-tions which are supposed to contribute to the 'hori

zontal area'.

3.2

Thin-walled open cross sect ions

There are several parts of a ship where the decks are

not continuous in transverse direction athwartship, for

instañce in way of the engine room casing and in way

of the cargo hatchways. The cross section of the ship

may in this case be of the type as given in figure 4. For

the calculation of the horizontal shear stiffness of

such an open part of the ship we follow quite a

dif-ferent procedure. In figure 5 a topview of a part of a

ship is shown weakened by openings in the decks. We

consider this part with length ¡ and calculate the

relatIve shear deformation between the cross sections

AA and BB. In this shear deformation we also have

to take bending effects of the deckplates into account,

as these contribute a not negligible part Of the shear

stiffness.

The problem is solved approximately by making a

A Fig 4 Fig. 5 1

1'

I

I

I

/

/

I

/

/

_II I L I

i

/

I

_i

I

i

2 3 4 5

rough assumption for the relative displacements of the

deckplates between the sections AA and RB. The

distance between a deck and the keel is called z. The

part of the ship between AA and BB is horizontally

divided, for instance, into five sections (see figure 4),

from which the side shell of section 5 is added to the

double bottom and the shell "strakes" i through 4 are

added to a deck. If we now make the assumption that

the underfòrmable cross sections AA and BB as rigid

cross sections displace and rotate parallel to each

other, then the relative displacement of each section

can be written in the form

a =

a5+cz

(11)

where

a

relative displacement of section i,

a5

= relative displacement of double bottom,

C

= constant.

The deformation of the deckstrips of deck i (i = i to 4)

is shown in figure 5. Assumilig that the two deckstrips

of deck i have to transmit a shear force D. and also

assuming that the strips are búilt-in both in cross

section AA and in cross sectión BB, it is easily to

re-cognize that

Dl

Dl3

a =

+

24E11

where

S1 = shear stiffness of one deckstrip of deëk i

= moment of inertia of one deckstrip of deck i

for bending in a horizontal plane,

E

Young's modulus.

The shear stiffness S. of one deckstrip can be written

in the form

S = CGA

(13)

in which

the area of one deckstrip,

G = shear modulus,.

C ,

the usual factor for rectangular cross

sections.

Expression (12) is now written in the form

a5 + CZ1

fi

12

+

24EI

There is good reason to believe that the shear force

D5

of section 5 is acting in the heavy keelpiate. The shear

stiffness S5 of this section may be equalled to the easily

(12)

(14)

calculated shear stiffness of the closed cell formed by.

the double bottom construction The quantities

a5

and c, unknown up to now, can be found from the

conditions that the shear forces

D1

are identical with

the totäl horizontal shear force

D

acting in the centre

of gravity (z = z.z) of the cross-section

When a5 and c are found from equations (15), the

horizontal displaceffient

a

of the centre of gravity is

also known

a = a5+cz

(16)

For the horizontal displacement theexpression can also

be written

a =

Dl

(17)

'JI'

where Sff represents the average horizontal shear

stiff-ness of an open cross section. Thus it is found that

Dl

=

a5+cz,

(18)

4

Final remarks

the given factors both for the vertical shear stiffness

and for the horizontal shear stiffñess of cross sections

of a ship hull are calculated only for a few types of

crosssections. This number of cross sections may be

iñcreased every time the shear stiffness of a ship hull

is to be calculated. Iñ such a case for one or twò cross

sections the shear stiffness is to be calculated with the

method described in chapter 2, while for the other

cross sections the shear stiffness has. to be roughly

calculated with the .aid of the C or CH factors given in

this report; For the "exact" calculated shear

stiff-nesses C or Cff factors can now be determined and in

this way the number of known C and CH factors is

increased. lt is recommended that the. factors, fòund

after completion of this

report,

will regularly be

published;

Literature

I. OHTAKA, K, F. HIETNO, M. Ou, A study of vertical vibratiön of ships (ist report) Journal of Zosen Kiokai The Soc of Naval Arch. of Japan, Vol. 116, 1964.

2. Kuri, T., Vibration of ships with special reference to

shearing vibration. I.S.P., Vol. 4, No. 32, April 1957.

11

D =

Dz =

i=i

5 1= i D Dz1 (15)

12

Appendit A

C-fáctors for veÉtical shear stiffness.

(Parts not contributing to the vettical area are drawn with a dotted line)

0.80 0.75 0.70 L 0.95 0.90 0.85 0.80 0.75 0.7Q r> 0.6J 1> 0.90 0.85 0.80 0.75 0.70 0.65 0.60 x 2 Fig. AI O 05 1 15 x/b Fig. A3 0 0.25 05 0.75 1 1.25 1.5 1.75 2 0° 100 20° 30° 40° 50° - bh

Fig. A2 Fig. A4 (angels above 300 rarely occur)

o 05 1 15 0.90 t 0.85 0.90 t 0.85 0.80 0.75 0.70

O.75cS 2c5 2

Fig A7 C = 0.73

O25 Fig. A5 C = 0.81 2h Fig. A6 C 0.65 2b 13

I 5

6b 5.5b Fig. A8 C = 0.72 25

cl

25 25 1 7b 6h

Fig. A9 C 70

25 25 2b 2b

14

L1.

L L 1. L L J J J J J

o

1

nay. br. deck

I-- - =--

--Fig. All C = 0.83 without stfperstîuctùre C = 0.84 with upersthicture

Fig. A13 C = 0.75

main deck

Fig.A15 C=0.84

L,

-I-

J-4

L.t 3-J main deck

Fig. A17 C =0.76

-I-main decki

-

-,

-¿j

¿j

r[

15 i-- L- I-o u L-V-

r

TJ

i

rï1

I i--r

r

_r

T

u r i r

16

Appendix B

CÑ-factors for horizontal shear stiffness.

(Parts not contributing to the horizontal area are dtäwn with a dOtted line)

0.85 O.8Ö Fig. Bi 0.5 15 F1g. B2 Cif = 0.88 Fig. B3 CH = 0.90 0.95

I

0.90

topdèck

F---nay, br. deck

Fig. B4 CH =Ò.90 without sÎiprstrictúre Fig. B6 CH = 0.86

CH= 0.91 with súpórstrùctüre Fig.B5 Cif =0.88

L.,

D 17 D boier deck

upperbrjdge deck boat deck

bridge dek _{poop deck:}

main deck

L L . L

main deck

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57 M Determination of the dynaruic properties and propeller excited vibrations of a special ship stern arranethent. R. Wereldsma,

I 964.

58 S Numerical calculation of vertical hull vibrations of ships by discretizing the vibration system, J. de Vries, 1964.

59 M Controllable pitch propellers, their suitability and economy for large sea-going ships propelled by conventional, directly coupled engines. C. Kapsenberg, 1964.

60 S Natural frequencies of free vertical ship vibrations. C. B.

Vreug-denhil, 1964.

61 S The distribution of the hydrodynamic forces on a heaving and pitching shipmodel in still water. J. Gerritsma and W.

Beukel-man, 1964.

62 C The mode of action of anti-fouling paints : Interaction between anti-fouling paints and sea water. A. M. van Londen, 1964. 63 M Corrosion in exhaust driven turbochargers on marine diesel

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64 C Barnacle fouling on aged anti-fouling paints; a survey of pertinent literature and some recent observations. P. de Wolf, 1964. 65 S The lateral damping and added mass of a horizontally oscillating

shipmodel. G. van Leeuwen, 1964.

66 S Investigations into the strength of ships' derricks. Part I. F. X. P. Soejadi, 1965.

67 S Heat-transfer in cargotanks of a 50,000 DWT tanker. D. J. van der Heeden and L. L. Mulder, 1965.

68 M Guide to the application of method for calculation of cylinder liner temperatures in diesel engines. H. W. van Tijen, 1965. 69 M Stress measurements on a propeller model for a 42,000 DWT

tanker. R. Werelclsma, 1965.

70 M Experiments on vibrating propeller models. R. Wereldsma, 1965. 71 S Research on bulbous bow ships. Part H. A. Still water perfor-mance of a 24,000 DWT bulkcarrier with a large bulbous bow. W. P. A. van Lamrneren and J. J. Muntjewerf, 1965.

72 5 Research on bulbous bow. ships 'Part II. B. Behaviour of a 24,000 DWT bulkcarrier with a large bulbOus bow in a seaway. W. P. A. van Larrimeren and F. V. A. Pangalila, 1965.

73 S Stress and strain distribution in a vertically corrugated bulkhead. H. E. Jaeger and P. A. van Katwijk, 1965.

74S Research on bulbous bow ships. Part I. A. Still water investiga-tions into bulbous bow forms for a fast cargo liner. W. P. A. van Lammeren and R. Wahab, 1965.

75 S Hull vibrations of the cargo-passenger motor ship "Oranje Nassau", W. van Horssen, 1965.

76 S Research on bulbous bow ships. Part I. B. The behaviour of a fast cargo liner with a conventional and with a bulbous bow in a sea-way. R. Wahab, 1965.

77 M Comparative shipboard measurements of surface temperatures and surface corrosion in air cooled and water cooled turbine outlet casings of exhaust driven marine diesel engine turbo-chargers. R. W. Stuart Mitchell and V. A. Ogale, 1965. 78 M Sterñ tube vibration measurements of a cargo ship with special

afterbody. R. Wereldsma, 1965.

79 C The poe-treatment of ship plates: A comparative investigation

on some pre-treatment methods in use in the shipbùilding

industry. A. M. van Londen, 1965.

80 C The pre-treatment of ship plates: A practical investigation into the influence of different working procedures in over-coating zinc rich epoxy-resin based pre-construction primers. A. M. van Londen and W. Mulder, 1965.

81 S The performance of U-tanks as a passive anti-rolling device. C. Stigter, 1966.

82 5 Low-cycle fatigue of steel structures. J. J. W. Nibbering and J. van Lint, 1966.,

83 S Roll damping by free surface tanks. J. J. van den Bosch and J. H. Vugts, 1966.

84 S Behaviour of a ship in a seaway. J. Gerritsma 1966.

85 S Brittle fracture of full scale structures damaged by fatigue. J. J. W. Nibbering, J. van Lint and R. T.. van Leeuwen, 1966. 86 M Theoretical evaluation of heat transfer in dry cargo ship's tanks

using thermal oil as a heat transfer medium. D. J. van der

Heeden, 1966.

87 S Model experiments on sound transmission from engineroo accommodation in motorships. J. H. Janssen. 1966. 88 S Pitch and heave with fixed and controlled bow fins. J. H. V

1966.

89 S Estimation of the natural frequencies of a ship's double be by means of a sandwich theory. S. Hylarides, 1967. 90 S Computation of pitch and heave motions for arbitrary ship fc

W. E. Smith, 1967.

91 M Corrosion in exhaust driven turbochargers on marine engihes using heavy fuels. R. W. Stuart Mitchell, A. J. M. S Montfoort and V. A. Ogale, 1967.

92 M Residual fuel treatment on board ship. Part H. Compai cylinder wear measurements on a laboratory diesel engine filtered or centrifuged residual fuel. A. de Mooy, M. Ven and G. G. van der Meulen, 1967.

93 C Cost relations of the treatments of ship hulls and the fuel sumption of ships. H. J. Lageveen-van Kuijk, 1967. 94 C Optimum conditions for blast cleaning of steel plate. J.]

melts, 1967.

95 M Residual fuel treatment on board ship. Part L The effect of trifugiuig, filteringand homogenizing on the unsolubles in re fuel. M Verwoest and F. J. Colon, 1967.

96 S Analysis of the modified strip theory for the calculation of motions and wave bending moments. J. Gerritsma and WJ kelman, 1967.

97 S On the efficacy of two different roll-damping tanks. J. Bot and J. J. van den Bosch, 1967.

98 5 EquatiOn of motion coefficients for a pitching and heavini trOyer model. W. E. Smith, 1967.

99 S The manoeuvrability of ships on a straight course. J. P. E 1967.

100 5 Amidships forces and moments on a CB = 0.80 "Serie model in waves from various directions. R. Wahab, 1967. 101 C Optimum conditions for blast cleaning of steel plate. Conch

J. Remmelts, 1967.

I

102 M The axial stiffness of marine diesel engine crankshafts. P1 Comparison between the results of full scale measurement those of calculations according to published formulae.

Visser, 1967.

103 M The axial stiffness of marine diesel engine crankshafts. Pa Theory and results of scale model measurements and compd with published formulae. C. A. M. van der Linden, 1967. 104 M Marine diesel engine exhaust noise. Part I. A mathematical rr

J. H. Janssen, 1967.

I

105 M Marine diesel engine exhaust noise. Part II. Scale modi exhaust systems. J. Buiten and J. H. Janssen, 1968. 106 M Marine diesel engine exhaust noise. Part III. Exhaust s

criteria for bridge wings. J. H. Janssen en J. Buiten, 1967. 107 S Ship vibration analysis by finite element technique. Pi

General review and application to simple structures, stai loaded. S. Hylarides, 1967.

108 M Marine refrigeration engineering. Part I. Testing of a dece ised refrigerating installation.

J. A. Knobbout and R.

Kouffeld, 1967.

109 S A comparative study on fOur different passive roll damping t Part I. J. H. Vugts, 1968.

110 S Strain, stress and flexure of two corrugated and one pläne head subjected to a lateral, distributed load. H. E. Jaege P. A. van Katwijk, 1968.

Ill M Experimental evaluation of heat transfer in a dry-cargo tank, using thermal oil as a heat transfer medium. D. J. va

Heeden, 1968.

112 S The hydrodynathic coefficients for swaying, heaving and a cylinders in a free surface. J. H. Vugts, 1968.

113 M Marine refrigeration engineering. Part U. Some results of t a decentralised marine refrigerating unit with R 502. J. A. bout and C. & Colenbrander, 1968.

114 S The steering of a ship during the stopping manoeuvre. Hooft, 1969.

M Torsional-axial vibrations of a ship's propulsion system. Part I. Comparative investigation of calculated and measured

torsional-axial vjbpatjbñs in the shafting of a dry cargo motorship.

C. A. M. van der Linden, H. H. 't Hart and E R. Dôlfin, 1968. S A comparative stùdy on four different passive roll damping

tanks. Part IL J. H. Vugts, 1969.

M Stern gear arrangement and electric power generation in ships propelled by controllable pitch propellers. C. Kapsenberg, 1968. M Marine diesel engine exhaust noise. Part IV. Transferdamping data of 40 modelvariants of a compound resonator silencer. J. Buiten, M. J. A. M. de Regt and W. P. H. Hanen, 1968. C Durability tests with prefabrication primers in use of steel plates.

A. M. van Londen and W. Mulder, 1970.

S Proposal for the testing of weld metal from the vierpoint of brittle fracture initiatioñ. W. P. van den Blink and J. L W.

Nib-bering, 1968.

M The corrosion behaviour of cunifer 10 alloys in seawaterpiping-systems on board ship. Part I. W. J. J. Goetzeeand F. J. Kievits

1968.

M Màrine refrigeratiOn engineering; Part 1H. Proposal for a specifi-cation of a marine refrigerating unit and test procedures J A Knobboùt añd R. W. J. Kouffeld 1968.

S The design of U-tanks for roll damping of ships, J. D. van den Bunt, 1969.

S A proposal on noise criteria for sea-going ships. J. Buiten, 1969. S A proposal for standárdized measurements and annoyance rating of simultañeous noise and vibration in ships. J. H. Janssen, 1969. S The braking of large vessels JI. H. E. Jaeger in collaboration with

M. Jourdain, 1969.

M Guide for the calculation of heating capacity and heating coils for double bottomfuel oil tanks in dry cargo ships. D. J. van der Heeden, 1969.

M Residual fuel treatment on board ship. Part HI. A. de Mooy, P. J. Brandenburg and G; G. van der Meulen. 1969.

M Marine diesel engine exhaust noise. Part V. Investigation of a double resonatorsilencer. J. Buiten, 1969.

S Model and full scale motions of a twin-hull vessel. M. F. van

Sluijs, 1969.

M Torsional-axial vibrations of a ship's propulsion system. Part IL W. van Gent and S. Hylarides, 1969.

S A model study on the nôise reduction effect of damping layers aboard ships. F. H. van Tal, 1970..

M The corrOsion behaviour of cLûlifer-lO alloys in seawaterpiping-systems on board ship. Part II. P. J. Berg and R. G. de Lange,

1969.

S Boundary layer control on a ship's rudder. J. H.. G. Verhagen, 1970.

,M Torsional-axial vibrations of a ship's propulsion system. Part III. C. A. M. van der Linden, 1969.

S The manoeuvrabüity of ships at low speed. J. P. Hooft and

M W. C. Oosterveld, 1970.

S Resistance and propúlsión of a high-speed single-screw cargo liner design. J. J. Muntjewerf, 1970.

S Optimal meteorological ship routemg C de Wit 1970

S Hull vibrations of the càrgo-liner "Koudekerk". H. H. 't Hart,

1970.,.

S Critical consideration of present hull vibration analysis. S.

Hyla-rides. 1970.

M Marine refrigeration engineering. Part 1V. A Comparative study on single and two stage compression. A. H. vafi der Tak, 1970. M Fire detection in machinery spaces. P. J. Brandenburg, 1971. S A reduced method for the caiculation of the shear stiffness of a

ship hull. W. van Horssen, 1971.

Communications

11 C Investigations ¡tito the use of sorne shipbottom paints, based on scarcely Saponifiable vehicles (Dutch). A. M. ván Londen and P. de Wolf, 1964.

12 C The pre treatment of ship plates The treatment of welded joints prior to painting (Dutch). A. M. van Londen and W. Mulder,

1.965.

13 C Corrosion, ship bottom paints (Dutch). H. C. Ekania, 1966. 14 S Human reaction to shipboard vibration, a study of existing

literature (Dútch). W. ten Cate, 1966.

15 M Refrigerated containerized transport (Dutch). J. A. Knobbout, 1967:

16 S Measures to prevent sound and vibration annoyance aboard a seagoing passenger and carferry fitted out with dieselengmes (Dutch). J. Buiten, J. H. Janssen, H. F., Steenhoek and L A. S. Hageman. 1968.

l7S Guide for the specification, testing arid inspection of glass

reinforced polyester structures 1h shipbuilding (Dutàh). G. Hamm, 1968.

18 S An.experimental simulator fòr the manoeuvring of surface ships. LB. van den Brug and W. A. Wagenaar, 1969.

19 S The computer programmes system and the NALS language for numerical control for shipbuilding. H. le Grand, 1969.

20 S A case study on networkplanning in shipbtiilding (Dutch). J. S. Folkers, H. J.. de Ruiter, A. W. Ruys, 1970;

21 S The effect of a contracted time-scale on the learning ability for manoeuvring of large ships (Dutch); C. L. Trúijens, W. A. Wage-naar, W. R. van Wijk, 1970.

22 M An improved stern gear arrangement., C. Kapsenberg, 1970. 23 M Marine refrigeration engineering. Part V (Dutch). A. H. van der

Talc, 1970.

24 M Marine refrigeration engineering. Part VI (Dutch). P; J. G. Goris and A. H. van der Tak, 1970.