Stress and strain distribution in a vertically corrugated bulkhead

STUDIECENTRUM T.N.O. VOOR SCHEEPSBOUW EN NAVIGATIE

NETHERLANDS' RESEARCH CEÑTRE T.N.O; FOR SHIPBÚILDrNG AND NAVIGATION

SHIPBUILDING DEPARTMENT MEKELWEG 2, DELF

STRESS AND STRAIN DISTRIBUTION IN

A VERTICALLY CORRUGATED BULKHEAD

(MATERIAALSPANNING EN REKVERDELING IN EEN VOUWSCHOT MET VERTIKALE VOUWEN)

by.

PROF. IR. H. E. JAEGER

and

IR. P. A. VAN KATWIJK

(Ship Structures Laboratory, Technological University Deift)

Issued bj the Gouncil

This report is not to be públished

unless verbatim and unabridged

REPORt No. 73 s June 1965

The research reported in this publication originates from a careful investigation into the strength of corrugated bulkheads, carried out by the Ship

Structures Laboratöry of the Technológical Uni-vetsity Deift.

In order to avoid all irrelevant influences the experimental research has been performe on

full scale constructions in the laboratory.

Four test-bulkhçads assembled into a large

tank were granted by the shipbuilders' association

in the Netherlands, the "Centrale Bond van

Scheepsbouwmeesters in Nederland". This aid is gratefully acknowledged hçre

Part of the information available at that time

has been presented in a paper read at the ATMA 1965 session last april n Paris!

CONTENTS..

page Summary . . . ..

...5

i Introduction

..

. 5 2- The experiments .- . 6 2A

General considerations ...

6

.2.2 Loading; strain- and deflection readings 6

3 Theoretical considerations 10

4 Expérimental results. - . li

4.1 General remarks . . . li

4.2 Flexure of bulkhead 2. 13

4.3 Behaviour of a beam with a half corrugatiofi as cross-section 13 4.4 Behaviour of a transverse (corrugated)strii of.ünit height . 16 5

Cònchïsions ...

. 18

5.1 Conclusions from the pra&ical point ofview 18

5.2 ConclusiOns from the scieñtifi point of view . 19

Acknowledgements - . ... 20

References . . .. . - 20

LIST OF SYMBOLS

b width or breadth of bulkhead or platepanei V

unsupported span of "beam? or height of bulkheadpanel V

xÌ

y = coordinates zJ

u as subscript to symbol denotes outside plate surface

component-i as subscript- to symbol denotes inside plate surface component

M, beam bending moment -M local transverse bending moment

moment of inertia about Xaxis

-W lxxi, section modulus .about X-axis (moment of resistance) beam bending stress

total beam stress

-= transverse local bending stress = transverse normal stress

ot = total transverse stress

For further stress symbols see figure 10 A a constant (a ratio of lengths)

STRESS AND STRAIN DISTRIBUTION IN

A VERTICALLY CORRUGATED BULKHEAD

by

PROF. IR. H. E. JAEGER

and

IR. P. A. VAN KATWIJK

Summary

Under the sponsorship of the Netherlands Research Centre T N O for Shipbuilding and Navigation the authors carned oui a laboratory experiment on a full scale corrugated bulkhead with shallow vertical troughs, which forms a part of a

testing tank for watertight bulkheads.

An investigation was made into the stress and strain distribution in this structural part when charged with a hydrostatic load Deflection readings were also obtained for a charge by compressed air.

The results of this investigation show to all practical intents and purposes a satisfactory agreement with a theory proposed by the first author and two of his collaborators in a report published by the above mentionedsponsors [1].

ticulars and bulkhead code numbers. The stringers may be either.r4gid1y interconnected or released individually to deflect under loading; both situa-tions may be studied. The corners of the tankwere

constructed from heavy tubes in order to provide a fixation for the sides of the bulkheads.

¿09cm

IF

top panel bottom 225 16 t= 7.5mm 1= 2504cm4 we -300cm3 61cm L I t cxD Jr2Lu t 9mm I 7475 cm W= 1116cm3 61cm t 6mm h 45B3cmL we 384cm3 op pt bottom pond 5325 cm

i

Introduction

When vertically corrugated bulkheads came to be accepted as structural members in ships, the first author, in collaboration with BURGHGRAEF and

VAN DER HAM, proposed a simple and straight

forward method for the calculation of stresses in

these structures [l.].

Although model tests have been çarried out, for instance by CALDWELL [2] añd GETZ [3], ño

extensive full-scale laboratory experimenis have hitherto been realised. Some measuring has been

done aboard ships, but because of practical

reasons they had räther an irícidental nature.

In 1958, when the Ship Structures Laboratory

acquired a testing tank for watertight bulkheads a series of experiments was started with the

fol-lowiñg geñeral objectives in mind.

An investigation into the behaviour of bulk-heads under hydrostatic loading; first in the

elastic region and finally in the plastic region.

A verification of the simplified theoretical

methods of calculation.

C. A comparison between laboratory experiments

and measurements taken aboard ships.

d. An investigatiOn into the applicability of corn-pter-assisted methods of calculation.

The testing tank was described by the first author [4] and consists of two corrugated and two plane

bulkheads as can be seen in figure 1 where a

6 t=075 tO.75 28 -8325 70 t2 L25'9'1I I201 50 92 61 61 10 59258865 886 rBOE8 t=1.4

- T

Bheod 61

CROSS-OVER BEAMSWITH FLAN COUPLINGS

toe

(L dimen5ions fl cm)

lAVE IS PLACEO DIRECTLY ON BOTTOM OF CONCRETE BASIN

Fig. 2. Longitudinal section through bulkhead 2.;

arrange-ment of bottom longitudinals in way of bulkhead 2.

All bulkheads conform to the rules of the

Classi-fication Societies except for the plate thickness

which has been reduced because no allowance for corrosion has been considered necessary. Besides

it was considered advisable to realise

plastic

conditions with re1atie1y low loads.

Bulkhead 2. is the subject of this report which

treats objectives a.. and b.. A longitudinal (i.e.

vertical) section is shown in ligure 2 and the par-ticulars of bottom and deck connections are also

given.

2 The experiments

-2.1 General considèrations

When carrying out experiments with strain gauges of the resistance-wire type on a large object as the testing tank two kinds of temperature influences have to be considered.

The first one is common to all experiments

namely changes f the overall temperature during

the time when the actual test

is progressing.

These changes, which äre the same all over the test piece, can be compensated for by the use of

dummy gauges.

The second influence is inherent in large test pieces loaded by fluids not drawn from a

reser-vòir via a recirculation system. In the case of the

testing tank.with a capacity of 200 m3 (44,000 gallons) the following will happen.

At the start of a loading cycle the tank

tempera-ture will be roughly the same as that of its sur-rundings. When zero readings have been taken, loading conirnences by filling the tank with. water. This water, which will be considerably lower in temperature because it is supplied through a special

main, starts cooling down the lower portion of the tank. The latter results in considerable and coñ-tinuously changing thermal strains throughout the

whole structural system. It is evident that the

accuracy of the strain readings taken at successive stages of loading or unloading and the possibility of reproduction will be severely endangered.

In order to avoid this the tank has been equipped

with a spraying system so that the structure's

thermal behaviour resembles that of one. fully

filled, with water for the duration of a test period.

2.2 Loading, strain- and deflection readings

The general stress level at maximum load had

of course to be kept within the elastic region for

all structural parts of the tank until all four

bulk-heads and their attendant stringers have been

irvestigated. This condition is satisfied when the tank has been filled up to deck-level ; the

hydro-static pressure at the base of the bulkhead then

being 0.95 kg/cm2 (13.6 lbs/sq.in).

Loading and unloading take eight hours each, including the time needed to take the necessary strain readings. A test cycle, loadingunloading,

is completed in two consecutive days, while

cooling down is started twelve hours in advance, to be stopped only after the tank is fully charged

and to be resumed just before unloading is

actu-ally started.

-Strain readings are taken during two cycles for

each of the two conditions, that is for stringers fixed and stringers free.

The positions of the groups of strain measuring stations on bulkhead 2. are shown in figure 3

to-gether with their subdivision into "measuring

.sections". . Each group covers One bulkhead panel. The central measuring sections 3 are meant to

provide verification of the practical value, of the

theory proposed in [1], which is summarized in

the -following section. If there should be. notable

discrepancies between measured and calculated

stresses the central measuring sections couid pro vide clues to the improvement of the' theory. The

number of stations in the section most heavily

stressed (111.3) was therefore extended across the full width of the bulkhead in the form of .a basic

400

275

la SEC11ONt-3 15 i5a16 SECTIONIIE-4 27 SECTl0NE-5 .22 lo 1o22 2o 8a 9 17 18 28 u, - C.) o 34..34O_35. 2/. 19 29 .36 GRP. OF PANEL lOo u, D --u, D 2 SECTION lt 2 SECTION It 3 SECTION II - £ .SECTION]E -5 SECTION E -SECTIOMIIL 2 n

pattern (stations 51-62b and 65-76 in figures

.12a-13). Measuring sectións 1, 2, 4 and 5 should complete the picture of stress and strain

distribu-lion and facthtate the derivation of the curves of

bending moments.

A total of 15 series of experiments with an

aver-gç of 4 loading cycles per series were needed to

i top paneL

Fig. 3. Distribution of measuring points on bulkhead 2.

BOTTOM

u,

a)

gather strain readings from the gauge pattern

shown in. figure 3.

Some 1800 active gaugçs including replace-ments were involved, attached in pairs on both sides of the plate along the X and Y-directions.

The nominal gauge-length and -resistance being

4 min (5/32") and 120 ohms respectively.

2525o26 26o 27 _27a STR.I

4/.ä5 11 202122 30 3737a38 .55 12 23 31 38a 6 21. 32 13 6 25 390 26 ¿0 14 GRP. 0F PANEL lit la_D ID .10 la D g

STANDARD MEASURING SECTION

bottom paneL GRP.OF PANEL I STR. I 23 15 21. 11 16 22 12 18 5 ,13 1/. 19 .20 SECTION I-2 SECTION I -SECTION I - 4 ÌECTIONr 5 SECTION lE 1 16 20 8a 14 19 19 190 10 17 20o 7a 13 iBa 23

8 g 6 5 4 3 2 O

The accuracy of reproduction often equalled

that of the registerin apparatus. (+ 3 strain)

and seldom exceeded ± 10

strain, the latter

corresponding to a stress of ± 26 kg/cm2. An

example of a load-micro-strain curve for a highly strained spot is given in figure 4.

During the final stages of the present

investiga-tion the nature of a few of the plotted strain

distributions needed clarification and additional

strain readings were required..

To save time compressed air was used for

charg-ing up to a maximum pressure of 0.6 kg/cm2

(8.7 lbs/sq.in) as the .lifferènt type of load was thought not to influence the natuie of the strain distributiòn appreciably. At the same time

ex-60 80

is

80 140 180 £200220 240 260260 £300 32031.036038041.00420 ¿LO 1.60 480 ¿800520540560 580

20

¿0608010020406080200204060 B00U 2U

Fig. 4. Load-micro-strain curve

tensive defleciion measurements were made with dial gauges to obtain moré information about the

mode of deflection transversely across the bulk-head panels and also about local bending of the panels between the folds j.c. the corrugations proper. Figure 5 shows the system used for the deflection measurements.

When considering the experimental results it should be born in miñd that the testing tank has

béen manufactured according to normal shipyard practice. The bulkheads thereforé show the same

deviations from the draughtéd plans that

all

structures may be liable to. The initial unfairness

is shown in figure 6. - i

----.

I . I I BY STRAfr'1IMCATOR FOR V-6/5- -62 LUES

-

T

STARTOF LOCAL YIELDI4G .

-HEIGHT OF W8rERLEVEL _INASE

.. 2-7-62 qm=844kgIcm

-p..

Alud

- AiII

£2-8-63 i.2i-8-63

/

V

.

/

f

..

B HEAD 2 AS i i HOR OUTSIDE CROSS-OVERS FREE

.

FOR THE FIRST TIME ON 276!62 8

m

I

oIuTRDs mr mr mr m m mr m 10 Orm,, b2° i 20ITn

ifflljli Itiitit lilt liii

mm .10 20 30 LO 10 20 30 10 20 10 vn o lo o lo 10 1m O 10 10 lo nm

Fig. 6. Disalignment and: unfairness plotted on the basis of the unloaded, developed (strétched) bulkhead 2.

mm 9

1

V-123 4 I 'r 6789 111111'10 I

-I]I.I. [-III

I

---''

1'r10'

5T

- 3hOLiL2h3LLLhS 74249 - --.--. =

H

C

ii

r _ÇCJ . - . -\ 0 00 ________

iulil:i'Tr

I_I

i i

-

i

ro-p

i

I1E5 6 7 8

iiariiiiiiri

T 20 -

-U1_HIÌIÌTI

-2 22

ÌIIIIiIT1ÌIT1II

0 22 2 20 28 3' 3' 3'

fl. -.

jjIiiii

C--i 82 83 :

::

lì

n 234-678910 C, ¿L U410302L-.273C31-434..I37.P4OnL2L3 L ¿42

.'

-'

¿In.

LNWARDS m

'o

-h---I

I!

Fig. 5. System used for the deflection measurements

3

Theoretical considerations

The following is a short summary of Report no. 15 S, "Investigation of the stress distribution in

corrugated bulkheads with vertical throughs" [1].

In order to assess the stresses in a laterally

loaded, vertically corrugated bulkhead, the follow-ing assumptions are made:

The bulkhead consists of a number of similar and identically loaded bars having a constant

cross-section formed by half a corrugation profile.

The stringers are considered to act as rigid

supports for these bars.

Local transverse bending stresses may be cal-culated as for a corrugated strip of unit height and infinite length. This strip is to be

consid-ered simplysupported at the corrugations proper

and therefore equivalent to a continuous beam.

d. The corrugation angle remains a constant,

which also follows from c..

Figure 7 illustrates the concept of the bulkhead as an assembly of separate parts.

Y

Fig. 7

A consequence of a. and c. is that the deflection

of the "beams" has to be equal across the breadth of the bulkhead except very close to the side

con-nections, so that a cross-section deflects as a

corrugated beam with doubly hinged ends, the

latter

being realised by the

outermost

half-corrugation profile.

In the vertical or Y-direction the calculation of the curve of bending moments can be carried out simply, due to assumptions a. and b.. Since

the connections to deck and bottom will neither

act as simple support nor as full fixation,

calcula-tions are carried out for both condicalcula-tions and con-sequently the real curve of bending moments will

be located somewhere in between the two

com-puted ones.

Provided the "beam's" cross-section is of

effective and the stresses are derived from the

usual beam formula:

M. z

ay = 'xx

in the transverse (horizontal or X-)direction the

local bending stress oj is computed on the basis of assumptions c

and d, while the normal stress

tension or compression, is derived fr.om the

conditions of equilibrium for half a corrugation profile.

'1he reasoning in [1] is that contraction in Y direction will be prevented, thus additional stresses will ensue. These stresses will be Of a local bending nature mostly, since o is predominantly a bending

Table I. Experimental verification of assumptions

Except panel I, see section 4.2.

+ Signifies affirmation. 2 L 6 8 10 12 11. 16 mr,, ins 2 I. m 0.25 05 TYPE OF LOAD:

{mP.01

stress. In X-direction contraction will have its

way because of the low transverse rigidity of the bulkhead. The total stresses therefore vill be:

ayt =

and

xt -. oxb±axn

where o' = Poisson's ratio = 0.28.

A more gçneral review of the theory on

cor-rugated bulkheads may be found in [5].

4

Experimental results

4.1 General remarks

'T'lite stresses are derived from the experimental

750m ABOVE BASE MIDSRN PANEL, I

4I2Sm ABOVE BASE MIDSPAN PANEL IL

1375rn ABOVE BASE MIDSPAN PANEL

-Fig. 8. Mea.sured deflection across half breadth of bulkhead relative to the bóundaries, stringers free, ündera compressed

air loading (q = 0.6 kg/cm2) and a hydrostatic loading

.11 Assumption -Measured --. . deflections Measured ax Measured

-Relevant figs. Conclusion

a ± * . + + 8, l2a, 12b +

b

-

₊ . + Il,, l2a, 12b forstress +

e + * _{+ + 8, l2b, 13 for max. stress +}

d _{No evidence, subjectof detection not yet}

12

14 12 8

I., I i I I it I t

05

CENTRAL C(JGATION R&IL

(bottom paneL) ins0.75 0.5 025 I '

i.t

'i:1i 'i

mm2O 18 16. 14 12 10 8 6 1. 2 TYPE OF LOAD: of Bhead COMPRESSED AIR S..

- average of Left- and

right- hand corrugations -.----.- of ahead

HYDROSTATIC (MAXJ _{average of Left- and}

¼ _{right- hand corrugations}

+ additionaL- gau9è stotions

DECK STRI

-1

o mmL . 2 0 I. I i.

'l

Fig. 9. Measured longitud.inal deflection ¿f bullthea.d relative to the boundaries, strihgei free, under a cpmpressed air loading (q = 0.6 kg/cm2) and a hydrostatic loading

5.50 18-523

-5

I 16 -&90

-4.73 14-4.24. 4.12 12 350 330 -10'_ 3

-:-{:

2.75

8-f ZIO

-2

6

-181

I.--1

0.82

2-

\

0.37 rtl BTOM

ft0Om

mm4 o ft - m 9 28

8

2624 --..- 7 22-m

20_

POSITION OF - _{DEFLETIÖN OF}

GAUGE STATIONS _{RELATIVE TO R.H.C. &}

for for L. Ñ.C.

air wäter

C

-

- far compressed air

- for

hydrostatic Load 858

7.61

strain readings by means of the. well known for-mulae:

E E

=

lv

2 (Sy+VCx), ax

=

lv

2

(e+ve)

Table I summarizes the results of the experiments

as far as the verification of the assumptions ad

from section 3 is concerned.

4.2 Flexure of bulkhead 2.

The transverse deflections at - or near - mid-span

of the bulkhead panels and relative to the four

boundaries are given in figure 8. The panels II and

III show clearly that the corrugatiòn profiles

behave as a groúp of similar beams. This is

con-sistent with CALDWELL'S observations on his

models {2J, which are in the same range of char-acteristic dimensions, viz, the width-height ratio

b/I and the specific flexibility l/EI. However,

panel I having, a lower ratio b/Al (A> 1) and

consequently a higher specific flexibility Al/EI,

shows a different mode of deflection although the

central part of the deflection cürve in figure 8 is still rather flat.

The longitudinal deflection of the bulkhead's

centre line and

tITle average deflection of the corrugations proper (i.c. the folds) to the right añd

left of said centre line are shown in figure 9

to-gether with the relative displacement of the centre

line.

=

0YC./2 =

The overall longitudinal deformation of the

bulkhead and its stringers is of a, normal pattefn,

even though the large displacement of the stringers is somewhat surprising. The stringer deflection, however, hardly influences the strain and stress

distributions in the central parts of the bulkhead.

panels; this will be discussed more fully in the following section.

4.3 Behaviour of a beam with half a corrugation as

cross-section

The subscripts to the stress symbol a, to be used

in the. following sections are clarified in figure 10.

The curve of experimentally derived beam

bending moments 'as shown in figure 11 generally

compares best with the theoretical values' obtained by assuming fúll fixation at the 'bottom and simple

support at the deck (see appendix, part 1).

How-ever, the highest mid-span' 'bending moment

occurs close to measuring section III-3 where 'the

experimental value exceeds the calctÏated one

by 33%. As the degree of fixation depends on the

relative rotational stiffesses of the bottom

struc-ture and the-: bulkhead beams, no method of

calculation that is both simple and sufficiently ac-curate can as yet.be given.

T'he stress' distributions across the beam sections

that are also given in figure 11 show that the

com-pression flanges are not wholly effective; they de-flect towards the neutral axis of the beam because

longitudinal normal stress

13

measured longitudinal stress, external plate

sur-face

measured 'longitudinal stress, internal plate sur-face

cy.0+ o,.i 2

longitudinal heart-of-plate beam bending stress

= longitudinal local plate bending

stress, external plate surface

0b.i =

= longitudinal local plate bending

stiess, internal plate surface

C?i.t/2'lIC.t/2

= measured transverse stress, external plate surface = measured transverse stress, internal plate surface

YX.0 +Ûx.,

X.f2 - 2

.14 te,ft. -m io -io ô BULKHEAD (13 A stringérs free

D. fixed (foi- panel only)

+ fulLy fixed at deck and bottom }calculated according to [i]

X simply supp at deck and bottom

simply supp. at deck and fully fixed at bottom

Gy4

?

yb.0 .10 +

+H-29 SECTION']It- 2 SECTION 3 X' X SECTION 4 24 + ± BULKHEAD®

( O stringers free _{! measured}

fixed)

+ ends 5irnpy supp. _caicuutèd X ends fully, fixed _J

f D stringers free _'

measured

U fixed)

yb.0 _{A ends simply supp.}

kips. kgrr? 400 200 o - 200 10 -10

L ends fully fixed j) calculated

see fig: 10 for expldnaion of stress symbols

1000 900 600 400 200 O - 400 - 600. - sop -1000 kips kg/cm2 1000 800 600 400 200 o - 200 - LOO - sop - 800 kips kg/cm2

Fig. 11. Comparison of measured beam bending moment and transverse distribution of longitudinal stress with calculated

values cm

Ir Ir

-io5 .

II

, li .F io

.'1»l_

2.10e I --STR.I e MSI e -M.S.2 M.S.5 1- - DECK GRP. OF PANEL I STR. M S3 RP. OFNELI X GRP. OF PANEL M.S.5 tift -10 I . -B -6 - -' -4 -2 -r 2 i ¿ r BOTTOMT ¿ 6 8 10 tmft __ ,' I F 'I -9 -6 0 2 1. 6 8 10 taft 10. 2.10 3i0 kgcm

Table II. Loads on the central cross-bver beams in metric tons

of the hydrostatic load imposed on them. The

flaiiges under tension are more effective, being

reinforced by the hrdrostatic load. The webs show a stress distribution that is reasonably linear.

Strain measUrements on the central cross-over beams when attached to the stringers yielded loads

which show a satisfactory agreement with values

derived from the calculated beam reactions on

the stringers. Table II givs these values.

Releasing the stringers from the cross-over

160 80 60 200 180 160 140 - 40 -60 -80 f100 -140 kga ON PA!LS 0b1 uoi7sk9Tl2 f lx-1207G0 -xb nn MI--M 0xb ON c Bb 25

beams hardly influences the stress and, strain

distribution in the bulkhead panels For bulkhead

panel III this is evidentin the figures 11, 12a, b and f13, for the panels II and I the differences are even less and the observed values for the condition stringers fixed have been omitted to avoid con-fusion,

Consequently it may be stated that the cross-over

'beams only support the stringers and that the

stringers support the-bulkhead.

Fig. l2a. Stress 'distribution across breadth of bulkhead 137.5 cm above base

596061 596768 747675

stringers _{} for mcx. md}

x M0 c1cuLated with shecrstress correction

s M0 without correction

B'cd ©

Fig. 1 2b. Distribution of measured transverse bending moments (Mi) compared with calculated values 60

-80

-140

65 57 62à62b15

975rrw

EXTENDED kEASURING SECTION lIt -3; DISPOSI11ON OF POINTS. POINTS 16-26 STANDARD MS. -tbins' kgfl 200 180 15 Central cross-over

beam of: Measured load

Calculated for fixed bottom

fixed deck

Calculated for simply supp. bottom

-- simply supp. deck

Calculated for fixed bottom

- simply supp. deck

Upper stringer Lower stringer 12.9 20.5 12.8 ' 19.8 13.1 22.9 139 19.4

16

C

515253

transverse heart of pLate stress

EEXt : trverse heart of pthtè Strain

15

16 18x19

0

.6

62a _6b 15 22 63 61.

EXTENDED MEASURING SECTION ]IE-3; DISPOSI11ON OF POINTS

POINTS 16-26 STANDARD MS.

DSTRIBVI)ON OF' and EEXt

as measured on section I-3

O stringers free 1 2 _S , for max.load Ee0i

fr.

2k A fixed bottom panel 66 67 68 70 71 top panet 73 71. 7576 -6 C C

CC

C C

fc

C C C

MEASJRJN S CTIÓN ]!L-3; DISALIGNMENT AND UNFAIRNESS OF PANELS PLOTTED ON THE BASIS OF THE

DEVELOPED (stretched) BULKHEAD' IN UNLOADED CONDFI1ON

see fig,1O for exptanation of -stress- symboLs Fig. 13. Initiâl unfairness and the distribution of stress and strain for measuring section III-3

4.4 Behaviour of a transverse (corrugated) strip of unit

height

In figure 1 2b the experimentally established curve of transverse bending moments is shown and it may be compared with two sets of theoretical

values. One set has been calculated in the manner summarized in section 3, the other set includes a cotrection for the transyerse normal forces acting on, and, in the plane of, the flanges (see appendix,

parts 2, 3 and 4). A similar cOrrection has been

used by GETZ [3].

Generally the theoretical

values correspond weiF with those obtained by experiment, and the discrepancies which occur cn mostly be traced directly to the initial

unfair-ness of the strip as shown in figure 13. It may be argued that the influence of the above mentioned

correction is too small to justifr the laborious

computations involved. However, the magnitude

of the normal forces is determined by the

geo-metrical properties of tlie corrugation profile and by the magnitude, of th4 hydrostatic load, so that

application of the correction must be left tO the

kg/cm2 - 200 mm 6 mm 150

individual.,designer (see also table III, section 5). For purposes of analysis the corrugations proper

have been treated as curved beams in order to arrive at the correct values for the heart-of-plate

stresses there. In figure 13 gauge station 19 gives

a correc.t value ax.t/2 = 10 kg/cm2 while the.

value obtained frOm the average of the out an4 inside surface stresses would be

x.t/2

=

2

clz.0 +az j

= 120 kg/cm2

against a theoretically calculated value of

ax.t/2 = 42 kg/cm2 (appendix part 5). The distributiOn of these stresses as shown in figure 13 lacks the regularity that marks the curves of figures l2a and l2b. The actual stress values are rather low so that there is a relatively large

influence of observational errors (see section 2.2) and. initial unfairness.

Now that the experimental results in their

separate direçtioús. Y and X have been discussed,

attention should be paid to contraction effects.

Considering a cross-section of the Thhead the

influence of the transverse deformation r on the longitudinal strains or stressçs will be discussed

first. Where is almost wholly a bending strain

nó harm will be done if the small normal strain

is neglected and only the bending strain exb is considered.

The contraction effects of r will appear either

as a component ve or as a component va acting locally, that is. over thé plate thickness, since Cxb is acting in this way (see figure 14).

The longitudinal strain readings obtained along

a cthss section of the corrugation profile yield a

very small plate bending strain o (see figure 14),

which is practically a constant across the width of

a flange, varies linearly across - the web with a change of sign halfway and is again a constant

across the .other flange. In fact the measured

longitudinal plate bending strain shôws exactly the type of distribution and order of magiitude

in-Fig. .14. Local bending-strain relations (No drawn to scale)

hèrént in an independent single beam subject to

bending by a hydrostatic load.

Ïf ve existed it would completely dominate, even blot out e and the resulting longitudinal plate bending strain distribution would be para-blic across flange .and web, with two changes of

sign across the flanges, which indicates

anti-clastic bending in longitudinal direction. But, as

has been Ñtated before, this type of strain

distri-bution was not observed at all;

therefore the

occurence of -

Vzb has been prevented.

Conse-quently v must have been acting, instead, so

that rather a large longitudinal plate bending

streSs dybmust be found, the distribution of which

has to be very closely related to that of8xb.

Instead of the distribution of zb that of 0xb may be taken because the factor ypb can be

neg-lected.

In figure l2a the distribution of the outside

surface component of o viz. is shown and

18

it may be compared to figure 1 2b showing the

dis-tribution of M which is proportional to zb.0

The close relätionsbip between and b is ev-ident.

The first hypothesis of sectión 3, viz, that

con-tractional distortion

ifi the Y-direction is

pre-vented, is therefore correct.

Similar reasòning with regard to VEy.t/2 leads

to the cònclusion that the second hypothesis of section 3 regarding cóntraction is also correct. A comparison between. figure 12a and figure 13 illustrates this clearly.

In figure 13 the measured 6.t/2 has been drawn

to the scale of E. Et/2 in order to facilitate the comparison with the ay.g/2 curve of figure 12a,

and to show that obviously no relation exists

be-tween the horizontal heàrt-of-plate stress and strain.

The direction of the principal stresses was

examined

at the flanges of the beams at the sections II-3

and III-3,

at the geometrical neutral axis of the half

corrugation profile of seçtion II-3.

As was to be expected: the principal stress direc-tions coincided with th Y- and X-axes.

5 Conclusions

The experimental results discussed in the

pre-ceding section have been obtained from one type

of corrugated bulkhead, but general conclusions

can already be: formulated as far as the practical

and the scientific point of view are considéred. Meanwhile exeriments in the elastic range have

already started on the deep-troughed bulkhead 1.

in order to obtain more general data on the be-haviour under load of structures represçnted by

the bulkheads 1. and 2..

5.1 Conclusions from the practical point of view

The practical conclusions may be given in the

form of a manual for the calculation of stresses in vertically corrugated bulkheads subject to hydro-static loading.

The stringrs can be considered

as rigid

supports.

The bulkhead can be considered as a group of

identical aiid identically loaded continuous

beams on rigid supports, while the connections

to deck ad bottom or tank top may be: taken as simply stpported, or as fixed, or as a com

bination of the two, depending on the relative

Table III. Maximum experimental and calculated stresses at the measuring setion III-3 (stress values in kg/cm2)

Note: The experimental values given in the table above have been obtained fror the standard measuring section. A more general impression of the total stresses may be obtained by taking the average stress values for corresponding points of the extended section.

66.u+ 1i. 62.0 + y. 63.66+ j. 71. U

For example (figure 12a)

-4 bottom panel li 2.0 q = _{O.825 kg/cm2} 1.0

2.u\

W1 =

_{W21 = = W.. 300 cm3} toppanel 3.i 1.i W1, = W2Ç = W3 W = 330 cm' i -3.0 ¿u

Calculated for Calculated for Calculated för Total _{Experimental simply supp. deck fixed deck simply supp. deck}

simply supp. bottom fixed bottom - fixed bottom

-1.172 - 266

1109

- 388

- 8a

- 118 - 91.7 - 213 0,.2.j °y.2.0 -- 558 - 985 - 453

1065

- l77

795 - 281 - 890 1iU ± 783 . + 551 +1023 + 507 + 753 + 211 + 848 + 315 ± 406 + 1078 + 423 +1074 + 153 ± 778 + 249 + 882 - -

-Calculated without CaIu1ated with .

-Total surface .

stress Experimental

corrug. as curved beams and without

corrug. as curved beams and with

correction orrection Total value

of a,, calculated 1361 +1156

1179

+1017

1247

+1085 with corrected a.2.66 +1006

1246

+1056

1140

+l027

1332

ai-value ax.a.i - -i-- 832 656 +1140

1056

+118,4 904 879 +1067

1017

+1179 958 +1120

only of the reaction forces of these beams. This

conclusion may be 'taken to apply also to flat

bulkheads with vertical stiffeners and horizontal stringers, because the shape of the "beams" is not

relevant. The theoretical methods of calculation

for these bulkheads which are based on the afore

mentioned type of stringer loading as, for instance,

the one proposed by MUCKLE [6] are therefore correct in this respect.

As regards the points b. and c., further

in-vestigations are necessary. The calçulation of the beam bending moment distribution needs a more

exact definition of the end conditions than, the two extremes of fully fixed or simply supported

or the half-way compromise between these two.

Figurç 11 shows clearly the too large 'range of possible st,ress values as a result of the application of two extreme types of end conditions.

While in the case of bulkhead 2. it is possible to assess the total niaximum stress in a satisfactory

way by assuming simple support at bottom and

deck (Table III), this should not be taken as a

general rule. It merely proves that in some cases it will be possible to obtain good 'results although

the component parts of the calculation are in error. In other words the sum of errors in the calcula-tion will not be practically zero for other cases.

The efficiency of the beam flanges must be

in-vestigated further because of the interaction be-tween hydrostatic loading and the contraction effects.

In this respect attention should also be paid to

the influence of unfairness resulting from' the

butt-welds located in the flanges (see figure 6). When-ever possible the butts should be welded in such

a way that the resulting distortion reinforces the resistance

against bending of the corrugation

profile.

Point d. is substantially correct and once the

above-mentioned need for improvement of points

b. and c. is realised the numerical values of the

load on the stringers will offer no problem. As to points e,. and f., 'the margin between cal-culated 'and measured transverse stresses as given

in Table III is very small when the influence of

normal stresses on the bending moments is taken

into account. This in itself is highly gratifying,

but some safety factor may have to be introduced

into the calculations as long as nothing definite

is known about both the amount and the influence

of "normal" initial unfairness and disalignment.

In connection with point e. it must also be stated

that the objections raised by WAH [7] to one of the methods of determining the transverse bending

19

specific flexibilities of the end connections

'The width-height ratio of the bulkhead panels

is assumed to be in excess of unity (see sec-tion 4.2).

With a. and b., the maximum bending stress

located approximately at mid-span of the

highest loaded bulkhead panel can be

cal-culated. The sum of this stress and the

con-traction component of the local transverse

stress can be considered as the maximum

longitudinal stress to be expected in the struc-ture with the possible exception of local stress concentrations. If conditions of simple support

are assumed at deck and bottom, a margin of

safety is provided for' irregularities which can

not be accounted for otherwise, such 'as for

instance the influence of initial unfairnèss.

Table III gives the maximum experimental and calculated stresses at the standard

meas-uring section III-3.

The load on the stringers composed of beam reaction forces, can be calculated with a., b. and c..

The transverse local, bending stress can be

assessed by considering a strip of unit height across the bulkhead, as a continuous beam on

rigid supports provided by the corrugation folds. If necessary the correction for the in-fluence of the normal forces may be introduced

(see appendix part 2, 3 and 4).

The transverse normal stresses, which may be rather small., can be obtained by considering

the conditions of equilibrium of half a

corruga-tion profile of unit height. The total stresses are:

yt = ayb±'axt

and

Og = axb+axn

where y = Poisson's ratio.

At the

sections where the beam bending

moment is highest the stresses og and are

the principal stresses.

5.2 Conclusions from the scient jjic point of view

Now more attention will 'be paid to the points a. to f. of the preceding section 5.1.

As far as the stresses are concerned point a. is

correct and it is expected, that the problem of the

stringer deflections will be cleared up at a later date after the 'stringers have been investigated thoroughly.

As already stated at the end of section 4.3 it is

evident tliat the stringers support the bulkhead

20

moments given in {l] are not valid in case of

bulk-head panels having a width-height ratio equal to or in excess of that of the panels Ii and III. This is

immediately evident frpm the transverse deflection cutves for these panels as shown in figure 8. Acknowledgements

The authors express their gratitude towards the shipbuilders' association in the Netherlands the

"Ceiitrale Bond vati

Scheepsboiiwmeesters in

Nederland" which provided the Ship Structures

Laboratory with the testing tank and particularly

towards the shipbúildiig yard "N.y. Koninklijke Maatschappij 'De Schélde'" the actual

construc-tors of the tank.

They are also indebted to Mr. J. VERSCHOOR, Mr. G. G. 'DEN iooÑ and Mr. 'C. 'DE Kpiy for their valuable assistailce 'in

carrying Óut the

extensive work of applying the strain, gauges and

obtaining the experimnta1 dátã, aíid to Mr. J:

HARREWIJN who produced all the drawings.

References

JAEGER, H. E. B. BURGHCìRAEF and I. vAÑ DER HAM,

Investigatioñ of the stress distribution in corrugated

bulkheads with vertical troughs. Netherl. Res. Centre

T.NO. for Shipb. End Nay., report no. 15 S,

Sep-tember 1954. Interñ. Shipb. Progr. 2 (1955), pp. 3-29.

CALD WELL, j. B., The strength of corrugated plating for

ships' bulkheads. Trans. I.N.A. 1955.

GETZ, J. R., N. TORGERSEN and K. MOEN, Korrugerte

skott II. Skiptekn. Forskn. Inst., nr. 16 (1956) (in

Norwegian)

JAEGER, H. E. Investigation of the stress distribution in corrugated bulkheads with vertical troughs and in flat bulkheads with stiffeners inside and outside the tank-space. Report of the Ship Structures Laboratory, Deift,

issued at theLS.S.C. 1961 in Glasgow.

Proceedings LSS.C. 1964. Report of Committee 3b

-Orthogonally stiffened plating.

MUcKLE, W., Bulkheads with vertical stiffeners and

horizontal girders. Trans. N.E.C.I. of Eng. arid Shipb., 1962-6,3.

THEIN WAH, Special problems' in the design of bulk-heads, bottom structures 'and deck, plating. Chapter 7

of Guide fôr the analysis of ship structures, p. 346,

1

A cakulation of the cUrè of bending

moments M for a beam with half a

corrugation as cros-section

In figure A.l the beam is shown with its load and relevant reactions. In this case thedeck connection

is considered as a simple support while at the

bottom a full fixation, is presumed.

Bhéad panel I 2 R2 Bhead paneL ]t - R1. i I B'heod panel M 1 M R ,_=-.-M8 B

Fig. A.l. The loads acting on a "beam"

The unknown bending moments can be deter-mined by means of the equations of three moments

and this leads to:

2MB-j-Ml 8q8±7q1

at the bottom

MB+4M1+M2 7qB±l6ql+7q2 12

at the upper stringer.

'Denoting the right hand side of the equations byfn, fi and /2 respectively, the unknown mo-mentshave the solution:

MB

Ï2+l4

{(l+82)fB(2+2À)fi+f2}

M1

i2+14A

(2+22)fB+(4+4)fi2f2}

M2 = 11,4{fB-2fi+7f2}

After substitution of the numerical values:

MB = 3.5173 tm M1 = 2.4416 tm M2 .= 2.2862 tm

Now the four unknown support reactions can

be found from simple statics and the curve of

bending moments can be established for each span of the' beam.

For the span between the bottom and the lower stringer the curve is given by:

¡l.6775\

M =

\ 16.5

)3+2.897S2-7.59O+3.5l73

(eq. 1)

for: O <y

2.75m

2

_{Calculating the trai,sverse, or local,}

bending moments M according to the

method described in [1]

Figure A;2 states the problem, which is a simple

one as the internal bending moments at the

supports are all equal.

w w w

II((4

w

M

FLANGE WEB FLANGE

'b'' b ¿5.06 cni 33= 0.5

Fig. A.2. _{Stretched corrugated 'strip of unit height}

One equation of the three-moment type will

suffice for the determination of the moments

M2,.b

+

+

M.ßb

+

M.ßb

6E1 3E1 3E1

6E1

-q.b3

±

qß31)3

- 24E1

'24E1 z q8 = 0.61 5 t/m = 5.7950 t/m q1 61 =675t/m = 4.1175 t/m q2 0.61 = 4.00 t/m 2.4400 t/m 1= 275m )l= 400m

at the lower stringer or

'21

APPENDIX

22

Ç

(lß+ß2)

qb2 In this case ß = 0.5 so that:

₌

---The curve of benling moments across

the

flanges (top- and bottom panels) is given by:

M = ! (8x2 _8bx+b2)

O < x < b

and across the webs by:

M =

(8x2 _8ßbx-j-b2) O < x < ßb

3 Transverse normal forces in a corrugated

strip of unit heigth

In figure A.3 the geometrical properties of half a

coi-rugation profile are given, while figure A.4

q b X t Fig., A.3 (1 -4-8 cos a') Sz -, 3/ibq, (3ß+ß2) sina

(l+ß cosa)

Fig. A.4

shOws the manner of loading for a strip of unit

height together with the forces necessary to main-tain equilibrium.. Reference [1] gives:

R = S-f-'/2$ cos a + '/2ßbqy sin a (eq. 2)

'where

S=bqy

_{sin a}

while M.b/2 follows frm part 2: Mb/2 b2q

16

4 Influence of normal forces on the

trans-verse bendig moment M

The distribution of the normal forces across the corrugation section is

qualitatively shown in

figure A.5. Aong the flanges the curye of the

resulting nornal force follows a parabolical law,

along the web the curve is a third degree parabola

passing from compression to tension via zero value

at the geometrical centre of gravity of the section,. It is clear thatthe normal forces are largest in the two flanges and their influence on the transverse

bending momnts M will be investigated. Tn

order not to complicate matters, the parabolic

distributioñ asshown 'in figure A.5 is replaced by

an equivalent rectangular one, that encloses the

same area. Consequently the distribution along the web is sirip1ified to a 'linearly varying one

The problem is shown in figure A.6 and in order

to find the unknown moments M1 and M2 the

deflected shapes of the three bars must be found;

iiui

A A b ttø'n panel

u...,

Arn

A A A £ b top panel Fig. A.6 P

CROSS SECTION OF BARS

The condition of continuity at the supports

pro-vides the equations with which

M1

and M2 can be solved. A slight problem arises here because bar 2. is evidently in an unstable condition, as

M1

will not be equal to M2. This is remedied by assuming very small compensating bending mo-ménts along the bar in such a way that they do not

influence the deflection line of the bar (This

matter will be more fully discussed later).

The elastic line of bar 1. may be obtained from TIM0sHENKO's "Theòry of elastic stability", or it may be derived from the differential equation:

EIziIV+P.zi" = q

which yields the solution:

[ b4q, b2Mzil [cos {u(l 2x/b)} _]

zl=I

II

11+

L16E1u4 4EIu2j L cos u J

b2q

+

_8EIu2 (x2_bx) where and Z3 =

u =

1=

bliP

2

' EI

.l.t

₁₂ (

Disregard.ing the linearly varying force P the deflection of bar 2. is given by:

i [q,x4

(MiM2)x3 ßb.qx3

M2.x2 Z2

- EIL24

+

6ßb 12 2

±1

(ßb)3q

ßb.Mi

ßb.M2

24 6 3

The curvature of bar 3. may be derived from that of bar 1. by substituting - P for P so that u

becomes iu where i = Vi. Development of

cosine u into a power series ofu shows that cos(iu) = cosh u and thus:

r b'q, b2M1 Icosh {u(1 2x/b)}

L16EIu

+

4EIu2i I cosh u

b2qi

8EIu2 (x2_bx)

The conditions of continuity are: Z'1(o) Z'2(ßb) and Z'2(0) Z'

which leads to:

Ml(3t

₊

_2ß)

_{+M2.ß =}

=

b2q (3 tg u-3u+u3ß3 \ 4u3 = plate thickness (eq.3)

]-(eq. 4) (eq. 5)

M1.ß±M(3t±2ß)

= b2q (u3ß3+3u-3 tgh u' 4u3 (eq.6)

After introducing the relevant numerical values

the equations may be solved for M1 and M2. The small bending moments supposedly acting along bar 2., i.c. the web, do in fact exist and their magnitude is P . z2

where in P is the normal

force at the point x and Z2x is the deflection at this point. The error resulting from neglecting the influence of PXz2

on the bending moment

distribution along the web is' small and not worth the labour of a more rigorous solution.

5 Numerical example

(see Table III, section 5.1)

An example of the numerical calculation of the

stress components and of the total stresses will be

given for Some points of section III-3.

In the longitudinal direction the beam bending

moment at this cross-section is obtained from

equation 1.

Fory = 1/2 =1.375 mis found that Mu.m =

= 1.7059 tm.

According tO the sign convention given in

figure A. 1, the stresses must be determined with:

M - z °yb =

'xx

The position of the points at which the stresses will

be calculated are shown in figure A.3. The extreme fibre stresses are:

aybl.i = t7yb2.i =

1.7059.10

300

kg/cm2 = 568 kg/cm2 and = ayb4.0 =

1.7059. 10

300 kg/cm2 = +568 kg/cm2

The stresses at the complimentary points are:

yb1.0 = yb2.0 = 1.7059. 105 330

kg/cm2 = 517kg/cm2

Oyb3 i = ayb4.i =

1 7059.105

330 kg/cm2 = +517 kg/cm2

24

The transvCrse normal stresses for these points are derived from equatiön 2 after substitution of the numerical values given in figure A.3 and with qy = 0.8125 kg/cm2. R

61

On1.i = Oznl.0

=

H 0.75

= 81 kg/cm2

R--S

31

xn2.i = axn2.0

=

= 42 kg/cm2

=

fl3.0 = +42 kg/cm2 On4. i = Ovn4 = + 81 kg/cm2

The transverse curves of bending moments are

obtained by first solving the eqúation 5 and 6 for

M1 and M, then substituting these values into the equations 3 and 4 and differentiating them

twice with respect to (see alsó figure A.6).

This results in:

M.1= +109.65kg cm

M2 = + 97.Ô7 kg cm

forx = b/2 = 22.53 cm:

M.i.b/2 = lO9.2 kg cm

M.3.b/z = - 97.45 kg cm

in order to arrive at the correct values of the

extreme fibre stresses ih way of the corrugations

proper (i.ç. the folds) these must be treated as curved beams as shown, in figure A. 7.

Fig A.7

The average radii of! curvature of the

corruga-tion were established by observacorruga-tion to be

r1 - 2.30cm and consequently T = ri+t =

= 3.05 cm

In ccstrength f materials, Part I" TÎMOSÊNKO

gives, the following formulae for the extreme fibre stresses: M. h2 r. u .4. e Mii1

r.i =

A - e where: t

e = r

ln

-Ti

A=lxt=t

hi=t/2e

/Z2 = t/2+e

-In the case under consideration:.

r.0 = .75l6M

= -11.7720M

For the stations 1 and 4:

crb=F

' -'/12 i

Mt/2

lhus

zb.1.i = 1166kg/cm2 =

xb.1.0 Oxb.2.i .= + 1069 ka/cm2 Ovb.2.0 =, 1290 kg/cm2 xb.3.i +1142 kg/cm2 axb.3.0 = - 946 kg/cm azb.4.i =, 'l039kg/cm2= xb .4 .0

The total stresses follow främ:

17xt = 'Yxb +On

and L

=

where r - 0.28

Thus for og.1.i and yt.1.i for example, is fOund:

= l166-8l= 1247 kg/cm2

= ._68+0.28Hi247) =

_9llkg/cm2

The complete set of stress values has already

been given in the last column of Table III section

5l.

2

t

₂

PUBLICATIONS OF THE NETHERLANDS' RESEARCH CENTRE T.N.O. FOR SHIPBUILDING AND NAVIGATION

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No. i S The determinaion of the natural frequencies. of ship vibrations (Dutch).

. Byprof. ir H. E. Jaeger. May 1950.

No 3 S Practical possibilities of constructional applications of aluminium alloys to ship construction By prof. ir H. E. Jaeger March 195 1.

No 4 S Corrugation of bottom shell plating in ships with all welded or partially welded bottoms (Dutch)

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No. 5 S Standai-d-recommendüonS for measured mile and endurance trials of sea-going ships (Dutch).

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No. 6 S Some tests on stayed and unstayed masts and a comparison of experimental results and calculated stresses (Dutch).

By ir A. Verduin arz4 ir B. Burghgraef. June 1952. No. 7 M Cylixider wear in marine diesel engines (Dutch).

By ir H. Visser. December 1 952.

No. 8 M Analysis and testing of lubricating oils (Dutçh) .

. By ir R. N. M. A. Malotaux and irj. G. Smii.July 1953.

No. 9 5 Stability experiments ön models of Dutçh and French standardized 1ifboats.

By prof. ir H. E. Jaeger, prof. ir J. W. Bonebakker and J. Pereboom, in collaboration with A. Audigé. October 1952.

No. 10 S On collecting ship. service performance data and their analysis.

B, prof. ir J. W. Bonebaicker. January 1953.

No. i 1 M The ùs of three-phase current for auxiliary purposes(Dutch) .

Byirj.C.G.van Wjk. May 1953.

No. 12 M Noise and noise abatement in marine engine rooms (Dutch).

By " Technisch-Physische Dienst T.N.O.- T.H." April 1953.

No. I 3 M Investigtion of cylinder war in diesel engines by means of laboratory machines (Dutch).

By ir H. Visser. December 1954.

No. 14 M The purification of heavy fuel oil for diesel engines(Dutch) . By A. &emçr. August 1953.

No. 15 S Investigation of the stress distribution in corrugated bulkheads with vertical troughs.

By prof. ir H. E. Jaeger, ir B. Burhgraefand I. van der Ham. September 1954.

No. i 6 M Analysis and testing of lubricating oiLs II (Dutch) .

By ir R. N. M. A. Malotaux and drs J. B. Zabel. March 1956.

No. 17 M The applicador ofnew physicalmethods in theexamination oflubricating oils.

By ir R. N. M. A. Malotaux and dr F. van Zeggeren. March 1957.

No. 18 M Considerations ón the application of three phase current on board ships for auxiliary purposes especially with regard to fault protection, with a survey of winch drives recently applied on board of these ships and their

in-fluence on the gierating capacity (Duthh).

By ir J. C. G. van Wjk. February 1957. No. 19 M Crankcase explosions (Dutch) .

By ir J. H.; MinkhorsL April 1957.

No. 20 5 An analysis of the application of aluminium alloys in ships' structuresJ

Suggestións about the riveting between steel and aluminium alloy ships' structures. By prof. ir H. E. Jaeger. January 1955.

No. 2 1 S On stress câ1cultions in helicoidal shells and propeller blades.

By dr ir J. W. Cohen. July 1 955.

No. 22 S Some notes on the calculation ofpitching and heaving inlongitudinal waves.

By ir J. Gerritsrña. December 1955.

No. 23 S Second series of;stability experiments on models oflifeboats.

By ir B. Brghgraef. September 1 956. !

No. 24 M Outside corrosion of añd slagformation on tuibes in oil-firedboilers (Dütch). By dr W. J. Taat. April 1957.

No. 25 S Experimental determination of damping, added mass and added mss moment of inertia of a shipmodel.

By ir J. Gerritsma. October 1957.

No. 26 M Noise measurements and noise reduction in ships.

By ir G. J. van Os and B. van Steenbrug.ge. May 1957.

No. 27 S Initial metacentric height of small seagoing ships and the inaccuracy and unreliability of calculated curves of righting levers.,

By /rof ir J. W. Bonebakker. December 1957.

No. 28 M Influence of piston temperature on pisixm fouling and piston-ring wear in diesel engines using residual fuels.

By ir H. Visser. June 1959.

No. 29 M The influence of hysteresis on the 'alue of the modulusof rigidity of steel. By ir A. Hoppe and ir A. M. Hens. December 1959.

No. 30 S An experimental analysis of shipmotions in longitudinalregular waves.

By ir J. Gerritsma. December 1958.

No. 31 M Model tests concerning damping coefficients and the increase in the moments of inertia due to entrained water

of ship's propellers.

By N.J. Visser. October 1959.

No. 32 S The effect of a keel on the rolling characteristiçs of a ship.

By ir J. Gerriisma. July 1959.

No. 33 M The application of new physical methods in the examination of lubricating oils.

(ContinUation of report No. 17 M.)

By ir R. N. M. A. Malotaux and dr F. van Zeggeren. November1 959

No.34 S Acoustical principles in ship design. By ir J. H. Janssen. October 1959.

No. 35 S Shipmotions in longitudinal waves.

By ir J. Gerritsma. February 1960.

No. 36 S Experimental determination of bending moments for threemodels of different fulhiess in regular waves.

By ir J. Ch. De Does. April 1960.

No. 37 M Propeller excited vibratory forces in theshaft, of a single sçrew tanker. By dr ir J. D. van Manen and ir R. Wereldsma. June 1960.

No. 38 S Beamknees and other bracketed connections. I

By prof. ir H. E. Jaeger and ir J. J. W. Ni bberi ng. January1961.

No. 39 M Crankshaft coupled free torsional-axial vibratipns of a ship's propulsion system. By ir D. van Dort and N. J. Visser. September 1963.

No 40 S On the longitudinal reduction factor for the added mass of vibrating ships with rectangular cross-section

By ir W. P. A. Joosen and dr J. A. Sparenberg. April 1961.

No. 41 S Stresses in flat propeller blade models determined bythe moiré-method. By ir F. K. Ligtenberg. June 1962.

No. 42 S 'Applicationof modern digital computers in naval-architecture.

No. 43 C Raft tha1sand ships' trials with some underwater paint systems. By drs P. de Wolfcizd A. M. van Londen July 1962.

No. 44 S Some acoustical properties of ships with respect to noise-control. Part I.

By ir J. H. Jasen. August 1962.

No. 45 S Some acoûstical properties ofships with rOEpect to noise-control. Part II. By irJ. H.. Janscen. August 1962.

No. 46 C An investigation into the influence ofthe method ofapplication on the behaviour ofanti-corrosive paint systems in seawater.

By A. M. van Londen. August 1962.

No. 47 C Restilts of an inqtiiry into the condition ofthips' hulls in relation to fouling and corrosion.

By ir H. C. Ekama, A. M. van Londen and drs P. de Wolf. December 1962.

No. 48 C Investigations into the use of the wheel-abrator for removing rust and millscale from shipbuilding steel (Dutch)

Interim report.

By ir J. Remmelis and L. D. B. van den Burg. December 1962.

No. 49 S Distributiòn of damping and added mass along the length of a shipmodel.

By prof. ir J. Çerritsma and W. Beukelman. March 1963.

No. 50 5 The iñfliÌence of a bulbous bow on the motions and the propulsion in longitudinal waves.

By prof. ir J. Gerriisma and I41. Beukelman. April 1963.

No. 51 M Stress measurements on a propeller blade of a 42,000 ton tanker on full scale.

By ir R. Wereldsma. January 1964.

No. 52 C Comparative investigations on the surface preparation of shipbuilding steel by using wheel-abrators and the

application of shop-coats.

-By ir H. C. E/cama, A. M. van Londen and ir J. Remmelts. July 1963.

No. 53 S The braking of large vessels.

By prof. ir H. E. Jaeger August 1963.

No. 54 C A study of ship bottom paints in particular pertaining to the behaviour and action of anti-fouling paints.

By A. M. van Londen. September 1963.

No. 55 S Fatigue of ship structures.

By ir J. J. W. Nibbering. September 1 963.

No. 56 C The possibilities of exposure of anti-fouling paints in Curaçao, Dutch Lesser Antilles.

By drs P. de Wolf and Mrs M. Meuter-Sc/zriel. November 1963.

No. 57 M Determination of the dynamic properties and propeller exdted vibrations of a special ship stern arrangement.

By ir R. Werel&ma. March 1964.

No. 58 S Numerical calculation of vertical hull vibrations of ships by discretizing the vibration system.

By J. de Vries. April 1 964.

No 59 M Controllable pitch propellers, their suitability and economy for large sea gomg ships propelled by conventional, directly-coupled engines.

By ir C. Kapseñberg. June 1964.

No. 60 S Natural frequencies of free verticál ship. vibrations.

- By ir C. B. Vreugden/zil. August 1964.

No 61 S The distribution of the hydrodynamic forces on a heavmg and pitching shipmodel in still water

By prof. ir J. Gerritsma and W. Beukelman. September 1964.

No. 62 C The mode of action of anti-fouling paints : Interaction between anti-fouling paints and sea water.

By A. M. van Londen. October 1964.

No. 63 M Corrosion in exhaust driven turbochargers on marine diesel engines using heavy fuels.

By prof. R. W. Stuart Mitchell and V. A. Ogale. March 1965.

No. 64 C Barnacle fouling on aged anti-fouling paints; a survey of pertinent literature and some recent observations.

By drs P. de Wolf. November 1964.

No. 65 S The lateral-damping and added mass of a horizontally oscillating shipmodel.

Bv G. van Leeuwen. December 1964.

No. 66 S Investigatións into the strength of ships' derricks. Part I. By ir F. X. P. Soejadi. February 1965.

No. 67 S Heat=transfer in cargotanks of a 50,000 DWT tanker.

By D. j. van der Heeden and ir L. L. Mulder. March 1965.

No 68 M Guide to the application of method for calculation of cylinder liner temperatures in diesel engines By dr ir H. W. van Tjen. February 1965.

No. 69 M Stress measurements on a propeller model for a 42,000 DWT tanker.

By ir R. Wereldsma. March 1965.

No. 70 M Experiments on vibrating propeller models.

By ir R. Wereldsma. March 1965.

No. 71 S Research on bulbous bow ships. Part II.A.

Bi prof. dr ir W. P. A. van Lammeren and irj. J. Munsfewerf. May 1965.

No. 72 S Research on bulbous bow ships. Part II.B.

By prof. dr ir W. P. A. van Lammeren and ir F. V. A. Pangalila. June 1965.

No. 73 S Stress and strain distribution in a vertically corrugated bulkhead. By prof. ir H.E. Jaeger and ir P. A. van Katwijk. June1965.

Communications

No. i M Report on the use of heavy fuel oil in the tanker- "Auricula" of the Anglo-Saxon Petroleum Company (Dutch)

August 1950.

No. 2 S Ship speeds over the measured mile (Dutch).

By ir W. H. C. E. Rösingh. February 1951.

No. 3 S On voyage logs of sea-going ships and their analysis (Dutch).

By prof. ir J. W. Bonebaicker and ir J. Gerritema. November 1952.

No. 4 S Analysis of model experiments, trial and service performance data of-a single-screw tanker. By prof. ir J. W Bonebakker. October 1954.

No. 5 S Determination of the dimensions of panels subjected to water pressure only or to a combination of water pressure and edge compression (Dutch).

By prof. ir H. E. Jaeger. November 1954.

No. 6 S Approximative calculation of the effect of free surfaces on transverse stability (Dutch). By ir L. P. Herfst. April 1956.

No. 7 S On the calculation of stresses in a stayed mast.

By ir B. Burghgraef. August 1956.

No. 8 S Simply supported rectangular plates subjected to the combined action of a uniformly distributed lateral load and

compressive forces in the middle plane. By ir B. Burghgraef. February 1958.

No. 9 C Review of the investigations into the prevention of corrosion and fouling of ships' hulls (Dutch). By ir H. C. Ekama. October 1962.

No. 10 S/M Condensed report of a design study for a 53,000 dwt-class nuclear powered tanker

By the Dutch International Team (D.I. T.) directed by ir A. M. Fabery de Jonge. October 1963.

No. Il C Investigations into the use of some shipbôttom paints, based on scarcely saponifiable vehicles (Dutch).

By A M. van Landen and drs P. de Wolf. October 1964.