Strain, stress and flexure of two corrugated and one plane bulk-Head subjected to a lateral distributed load, TNO Report 110 S, April 1968

REPORT No. i lo S

April 1968 (S 1/28)

NEDERLANDS SCHEEPSSTUDIECENTRUM TNO

NETHERLANDS SHIP RESEARCH CENTRE TNO

SHIPBUILDING DEPARTMENT LEEGHWATERSTRAAT 5, DELFF

STRAIN, STRESS AND FLEXURE OF TWO CORRUGATED

AND ONE PLANE BULKHEAD SUBJECTED TO A LATERAL,

r

DISTRIBUTED LOAD

(REK, SPANNING EN DOORBUIGING VAN TWEE VOUWSCHOTTEN EN EEN VLAK SCHOT ONDERWORPEN AAN EEN LATERAAL GELIJKMATIG VERDEELDE BELASTING.)

by

Prof. Ir. H. E. JAEGER

and

Ir. P. A. VAN KATWIJK

Issued b, the CoUncil

SSL'i31

Issued by the Council

REPORT No. 110 s

April 1968

(S 1/28)

NEDERLANDS SCHEEPSSTUDIECENTRUM TNO

NETHERLANDS SHIP RESEARCH CENTRE TNO

SHIPBUILDING DEPARTMENT LEEGHWATERSTRAAT 5, DELFT

*

STRAIN, STRESS AND FLEXURE OF TWO CORRUGATED

AND ONE PLANE BULKHEAD SUBJECTED TO A LATERAL,

DISTRIBUTED LOAD

(REK, SPANNING EN DOORBUIGING VAN TWEE VOUWSCHOTTEN EN EEN VLAK SCHOT ONDERWORPEN AAN EEN LATERAAL GELIJKMATIG VERDEELDE BELASTING.)

by

Prof. Ir. H. E. JAEGER

Professor in Naval Architecture, Delft Technological University and

Ir. P. A. VAN KATWIJK

© Netherlands Ship Research Centre TNO, 1968

In het kader van het schottenonderzoek, dat door het Labora-torium voor Scheepsconstructies van de Technische F-Iogeschool te Deift wordt verricht, zijn de eerste resultaten gegeven in een eerder verschenen rapport no. 73 S, gepubliceerd in 1965. Verder onderzoek resulteerde in de informatie die in deze publikatie is samengevat.

Het hoofddoel van het ondernomen onderzoek was bet op-stellen van een voldoende betrouwbare rekenmethode voor een prognose van het elastisch gedrag van schotconstructies. Daar-voor zijn bu het verder onderzoek spannings- en

doorbuigings-metingen verricht aan Lwee typen vouwschotten en een uitvoering

van een viak schot onder de gebruikelijke belasting. De meet-waarden en de afgeleiden daarvan zijn grondig geanalyseerd en vergeleken met de resùltaten van de opgestelde rekenmethode die is gebaseerd op een gemodificeerde balktheorie. in tegenstel-ling tot andere mogelijke methoden blijkt de voorgestelde reken-methode ook tijdens de bewerking een goed inzicht te geven in de fysische verschijnselen.

Veci inspanning is verricht voor een beter inzicht in het door-buigingsmechanisme van dergelijke constructies, de samenhang in verband met randvoorwaarden en de invloed van maat- en vormafwijkingen. De maat- en vormafwijkingen zijn voor dit onderzoek bepaald aan de betreffendeschotpanelen, die vervaar-digd zijn in de normale produktie op de werf.

Hoewel een aantal verschillen tussen reken- enmeetresuitaten nog niet verklaard kan worden is de voorgestelde rékenmethode voor praktische toepassingen voldoende bedrijfszeker voor een prognose van het elastisch gedrag van viakke- en vouwschotten. Verder blijkt de invioed van maat- en vormafwijkingen op de spannings- en doorbuigingsverdeling van die aard te zijn, dat het zeker gewenst is te overwegen in bet fabrikageproces standaard afwijkingsgrenzen in de vorm van toleranties te introduceren. In het licht van de toekomstige ontwikkeling naar grotere schepen en dus ook grotere constructies is het van belang te kun-nen beschikken over meer informatie van reed te verwachten be-lastingen door middel van metingen aan boord van schepen. Het onderzoek leverde tevens nog direkt toe te passen prak-tische informatie op, zoals de gunstige invloed van symmetrische stringers c.d., die in een schotontwerp kunnen worden verwerkt.

NEDERLANDS SCHEEPSSTUDIECENTRUM TNO AFDELING SCHEEPSBOUW

In thescope of the bulkhead structures research carried out in the Ship Structures Laboratory of the Deift Technological Univer-sity, the first results have been presented in an earlier report no. 73 S, published in 1965. Further investigations resulted in the

information reported in this publication.

The primary objective was to obtain a calculation method sufficiently reliable to give a realistic prediction of the elastic response of bulkhead structures.

For this reason strain- and deflection measurements have been taken on two types of a corrugated and one type of a plane

bulkhead subjected to the usual load. The measured valües and the derivatives thereof have been thoroughly analised and com-pared With calculated resuitsobtained with a computingmethod based on a modified beamtheory. Contrary to other possible computing methods this modified beam theory gives a better insight into the physical phenomena.

Much effort has been-spent on a more profound-understanding of the flexure mechanism, the incorporation of boundary con-ditions and the influence of unfairness and disalignment. For the subject investigations the values for disalignment and unfair-ness had to be taken from the test specimens, which have been constructed according to normal yard-practice.

Although some deviations between calculated and experimen-tal results could not yet be explained the proposed computing method produced sufficiently reliable results regarding the elastic behaviourof corrugated- and plain bulkhead structures.

Furthermore the influence of unfairness anddisaiignments on stress and deflections proved to be of such extent that it might be considered necessary to require standard limit deviations in the production process.

Regarding future developments such as larger ships and con-sequently larger structùres it may be of importance that more information on realistic toads by means of shipboard measure-ments should be madeavailabele.

The investigations also yielded quite some information to be directly used for practicar application such as the beneficial in-fluence of symmetric stringers, which could be taken account of in a new design.

NETHERLANDS SHIP RESEARCH CENTRE TNO SHIPBUiLDING DEPARTMENT

OUTLINE OF DISCUSSED SUBJECTS

page

General remarks 5

Objectives of the experiments modifications Reasons for the discontinuation of compressed air loading

Theoretical 'consideratIons 6

2.1' Extension of elementary beam theory with respect to boundary conditions. Practical advantages of the beam model compared to the grillage model.

2.2 Cylindrical fiexure'of'corrugated panels as a requiement.fortheuseof the

plate-strip 'modeL Flexùre mechanism:and' governing parameters., Analysis of available

experimental data. Discússion of initial unfairness influence on transverse

bending moments.

Experimental results and' their analysis IO

3.1 Longitudinaldeflections and bending moments, correspondence.with calculations

based on an extended beam model'. Possible sources of error

12' End connections.

Strain distributiòns near the bottom and the stringers of the corrugated bulk-heads Local deformation of originally plane sections Designing for equal bend ing. moments at three points of an unsupported beam - span inadvisable. Influence of stiffener brackets of the plane bulkhead and danger of excessive, rigidity in regard tothe bending moment distribution

3.3 Transverse déflections and bending moments, comparison with calculations

Analysis of errors. Errors caused by unfairness of test objects, upper and lower limitscalculated according tosection 22.

Influence of the variation in plate thickness and the radii of curvature of the folds

The necessity for full scale experiments 22

Objectiveof theoreticaland experimental research. Possibility of'crack initiation caused by local strain hardening. Lack ofinformation concerning:service loads,

including cyclic ones.

Comparison of corrugated.ànd plane bulkheads 23 In regard to stresses, material weight and.boundary. connections. Financial aspects

are nOt considered.

Conclusions 24

The most important cónclusions are

J. Very high priority, must be assigned to full scale experiments aboard ships at

sea

Knowledge concerning locally large strains is vital and cannot be gathered from modelexperimenis

For practical purposes the improved beam model is a very convenient tool. Excluding economic considerations, symmetric stringers are to be preferred on corrugated bulkheads.

5.' Corrugated bulkheads can be much less in weightthan a plane stiffened one. 6. In case.planestiffened bulkheadsare used, the end connections of its stiffeners

should either be bracketless or the brackets shouldbe as small as possible.

7 The influence of initial distortion on the transverse stresses in stiffened panels

STRAIN, STRESS AND FLEXURE OF TWO CORRUGATED AND ONE PLANE

BULKHEAD SUBJECTED TO A LATERAL, DISTRIBUTED LOAD *)

by

Prof. Ir. H. E. JAEGER and

Ir. P. A. VAN KATWIJK

Summary

Two corrugated and one plane bulkhead subject to a distributed lateral load were tested and most of the results are given and dis-cussed An extension of the beam model as briefly dealt with earlier [I) is introduced generally and verified for certain cases The assumption underlying the method of calculat,ng the transverse bending moments and stresses in corrugated panels is verified with the aid of experimental data gathered both in the Laboratory itself andfrom previous papers by other authors As a result a suggestion is made regarding the limitations imposed on the validity of this hypothesis by the aspect ratios and 'flexural rigidity ratios of corrugated panels Transverse bending moment curves obtained both experimentally and theoretically are compared and tor cor rugated panels the possible influence of initial unfairness is discussed.

The end connections of bulkhead panels are examined in more detail Attention is paid to the importance of tests on full scale struc tures subject to static loads which restrict the nominalstresses totheelastic range

The corrugated bulkheads arecompared with the plane one and finally a number of conclusions is presented.

i

General remarks

In an earlier paper by the same authors [2] the testing tank for watertight bulkheads has been discussed and the results of experiments on the corrugated bulkhead 2 (see fig. I) were presented.

t 75mm t= 9mm

I 2504cm' 1= 6781cm"

W 300cm3 W1=1079cm W2= 364cm3

Fig. 1. General arrangement of the testing tank in way of the lower stringer.

*) Report no. 131 Ship Structures Laboratory Technological

University, Delft.

As objectives of an envisaged series of experiments were listed:

Investigation of the bulkheads' repónses to hy-drostatic loads, first below the limit of prQpor-tionality and secondly beyond it.

Verification of the theoretical method of calcu-lation based on the elementary beam and strip model.

'Comparison of laboratory experiments with data obtained aboard ships in service.

Investigation of the applicability of computer-assisted methods of strength analysis.

The following modifications have been introduced: to a. A uniform, distributed load as an additional

way of charging the test structures. (compressed air).

furthermore:

A comparison of corrugated and plane bulk-heads

Investigation into' the distribution, the magni-tude and the possible influence of initial dis-tirtionÑ.

Some remarks concerning the' first modification are necessary here. The type of loading has been realized by using compressed air. The main reason for its in-troduction has been the desire to 'speed up the experi-ments and to dispose of most of the extensive treat-ment necessary for waterproofing the hundreds of strain gauges used. Regarding this satisfactory results were achieved, but experience has shown that due to this load either the upper bulkhead panels were very highly strained or the lower panels insufficiently, so

consequently the use of compressed air was discontin- models are available, as for instance the grillage. The

ued. merits of the grillage model can not be denied, but

there are disadvantages too:

2 Theoretical considerations

2.1 The mod/ied single beam model

For practical purposes the calculated values of the beam bending moments, forces and deflections of stiffened plates and particularly of bulkheads have been based until now, on the elementary beam model. As has been stated in the conclusion presented in [2] section 5.2, this model with ends either fully fixed or simply supported or a combination of these two, does not provide satisfactory answers The rigorous sim-plification of the actual boundary conditions generally results in serious divergencies of the actual conditions. An extension of the model, such that other beams joining the original one at its ends are partly but ap-propriate!y included, is the obvious answer. 'The dis-advantage of such an improved model', namely the increased amount of manual computatiOns can be eliminated by using a digital computer. An example of such an extended model was discussed by the second author of this paper in part 2 of [3] from which figure 2 has been taken. From this figure it becomes obvious

iiii i

eqwvalent strutu 1

L4

_L

bulkhead and adjoining st ucturea

Fig. 2. Example of an improved beam model.

that heavy supporting members or some plane of sym-metry provide nearly correct, clamped endings for the extended model. lt is equally clear that any error in the newly assumed end conditions will be quickly reduced in size at each intermediate support. Consequently the end - or boundary conditions of the original beam are implicitly, but nearly correctly defined. An improved elementary 'beam model has been used to calculate the beam bending moments and the deflections of bulk-heads 1, 2 and 4 of the testing tank.(Seefigs. 7, 8,9 and

10).

The first results, together with some experimental data were given in a paper presented' to the ,,Associa-tion Techni4ue Maritime et Aéronautique" at the yearly session in April 1967 [1]. An extensive discussion is given in section 3.1 below.

It may be argued that the 'beam model and its im-proved version are obsòlete5 since more advanced

improved beam modet

of the blkheod

The boundary problems are the same as those men-tioned in connection with the single beam.

The calculations are directed at solving the un-knowns at the ñodes, thus providing the possibility of determining the moment -, force- and displace-ment distribution along the single eledisplace-ments of the grillage.

The accuracy of the calculations just mentioned

depends to a large extent on the error introduced by the assumption of certain boundary conditions. im-provements may be obtained by applying the principle as discussed earlier in connection with the single beam. The consequences will be a considerable extension of the computer program involved, ari increase in re-quired input data and an increase in computer time. Consideringthiscombined with thefact that in practice, where structures as shown in figure 3 are most com-mon, the necessary information is limited to the maxi-mum values of the generalized forces concerned, it is thought'that theimproved' beam model is avery. attrac tive' arid useful one.

Finally, attention also must be paid to the determi nation of the 'local (or tránsverse) forces in stiffened plates and particularly to those in corrugated bulk-heads. gnUage modeL of the stiffened pLate ""PL If ica beam modeL of the stiffened plate

orthogonaLLy stiffened pLate

of the type'èonvnon to most merchant shipe

Fig.. 3. Orthogonally stiffened plate most common in merchant

ships.

2.2 The plate-strip model

The magnitude of löcal, that is transverse '(see fig. 4a), stresses or forces in laterally loaded, stiffened plates is calculated with the aid of the plate-strip'model, subject to the condition that the structure deflects cylindrically for the greater part of its width. It is generally accepted that this requirement is met when

supported rectangular plate this value is 5. For corru-gated panels it is not the only parameter invölved and upon examining, qualitatively, the flexure mechanism of these structures other parameters may be found. To the aûthors' knowledge this subject has not yet been investigated, but it is considered desirable to do so now, regarding the present evolution in naval con-struction.

In what follows all displacements are supposed to be

section shown partly n

figs. 4b,c.d

be considered, so that the distributed load q may be replaced by one acting on the folds only (see fig. 4a). Part of a corrugated panel, with its top connection removed is shown in figure 4a, including a model re-presentation of the structure. The model consists of discrete elementsf, w and e, the former are thin, slender plates and the latter are slender rods which replace the corrugations. The angle of corrugation is kept at a constant value by the rods that also transfer the load

S = width of o corrugated cross - section

Z (load direction)

X (transverse direction)

FIG.

(width of f1 arid w1 remains constant)

FIG. La

2 _Ç

FIG. Ld.

Fig 4. Structural model and transverse.deflection mechanism of a corrugaíed panel.

to the -elements-w;-The- plates-f-and iv-have a fiexural-rigidity in their own plane that is high compared with both their rigidity in the working direction of the load and their torsional rigidity relative to the sense of the y-axis.

Whereas the top and bottomedges of the corrugated panel are supported and restrained, the sides will be allowed at first to slide along fictitious walls parallel to the y-z plane.

Considering the foregoing the corrugated panel will deflect .cyliÌdrically and the cross-section indicated in figure 4a is partly shown relative to its zero load posi-tion in figure 4b.

Now a force r will be applied in order to eliminate the displacement of the. sides and in figure 4e the resultant deformation of the cross-section is presented. The elementf1 is subject to torsional bending and since there is no reason to suppose that its width should in-crease, the rod c1 will be forced towards the left and be slightly twisted in the process. The distance between the elements c1 and e2 has been increased somewhat and this increase is met, mainly by a twisting of the element w1 and for the rest by a displacement of c2 contrary to the direction of the load, a sideways dis-placement of e2 is prevented by the elementf2. Thusthe influence òf the restoring forces r does not extend beyond the element f2. The local deflections between

2-o

1 signifies non-cylindrical bending

Roman numbers appLy to individuaL paneLs

+ - . + values corn for J

.

test piece 1,2,1. ref (Getz [6])

test pieces(steeL)i- ref. (CatdweLL [5]

test pieces( al) i-4 ref. ( CaIdweLL [s]

centre panât ref. (Skjeggestad [i])

end panel ref. (Skjeggestad [i])

DaFT buLkheads G1,2,4 CS1-4 e CAl-4 SK

{

+ {®]II

CS2 64-]I

13

cD' Cs1 CVUNDRICAL BENDING CA2 CA-SK 1,111 CAl 62-11E +

-the-corrugations- which- have beennele'ctedwillThòt alter, this situation.

In order to obtain actual boundary conditions it is necessary-to introdUce moments- M-and forces R at the

sides, in this case -the above- reasoning is also valid as will be clear after examining figure 4d.

Now, it is evident that the-first corrUgated cross-section at the- side acts as a. double jointed, spring restrained hinge mainly because, of the mere presence of the element w1 with its low torsional rigidity. Should -the deflections- become too large then the

second'cross-section will join the first in the hinge act.

Since the order in which loads are applied to a structure -does not influence the final deformation (in the elastic region!), the deduced flexure mechanism is also that of a corrugated panel with all sides initially restrained.

In conclusion it can be stated that cylindrical de-flection of a corrugated panel depends not only on its width-height ratio but also on the torsional rigidity of the elements w and on the flexural rigidity of the corrugated cross section. The relation between the làtter two is discussed- 'in the appendix.

-The authors have analysed experimental data ob-tained in the Ship Structures- Laborator-y at -DeIft and elsewhere[5, 6, 7'] in an effort to define for which values of the width height (b/I)- and the rigidity ratio (It/J)

y b l-oç CS 4 + - + 61

rity ratio

Fig. 5. Range-of cylindrical deflection as a function of.the width-height ratio b/land rigidity ratio It3/I.

NON - CYLINDRICAL BENDING 6 7 e

ck1t

A4

1

sI

cylindrical deflection will occur. Figure 5 presents the results of this analysis and the regions of cylindrical and non-cylindrical deflection are separated by a tran-sition zone as indicated. Since the potran-sition and shape of the zone are only partly provided by the analysed data, the missing parts can bèfound by reasoning as follóws. 1f ll is more and more reduced relative to I, so that the rigidity ratio becomes progressively less, the flexibility of the hinges will increase.

Ultimately cylindrical deflection will occur indepen-dent of the width-heigt ratió. On the other hand, an increasing rigidity ratio signifies a growing Stiffness of the hinges finally leading to single plate flexural beha-viour which depends only on the width-height ratio. In the analysis three horizontally corrugated bulk-headS have been included, namely CAl, CSI and GI (fig. 5).

CALDWELL states [5] that deflection was linearly proportional to local depth of water, therefore, cylin-drical deflection should occur in cäse of constant load transverse to corrugations. GETZ [6] gives a deflection curve that shows definitely non-linearity as regards local load and therefore no cylindrical deflection would occur in case of constant transverse load. Testpieçes CA4 and CS4 have a zig-zag pattern and the position of CS4 suggests that this panel may have been very near to non-cylindrical bending.

Thus, the conditions governing the use of the strip model have been established. The calculations based on this model have already been extensively discussed in the appendix of [2] sections 3 and 4. A slight cor-rection concerni ng these calculations must be mention-ed here, namely that the flexural rigidity of the Strip should be taken as that of the plate and not as that of a beam.

The strip model yields satisfactory results for corru-gated bulkheads, provided that model and .actual structure correspond mathematically as regards the initial distortions, the radii of curvature of the folds and the plate thickness. In practice these cnditions can not be realized and the consequences will be dis-cussed briefly as far as the initial distortions are con-cerned, because these are considered to be of great im-portance. The matter of the radii and the plate thick-ness will be dealt with in section 3.3'.

The distortions may occur as disalignments of the folds relative to each other or to the sides of the bulk-head or as unfairnesses of the individual panels relative to the folds.

Assuming that the application of the load to the bulkhead does not alter the original deviations it must follow that they shall influence the bending moment distribution since the normal fòrces P in figure 6a are no longer in lineé

This inflUence will be approximated on the basis of the following hypotheses.

The principle of superposition is valid. Both ends of a single span are fixed.

The additional end bending moments, are not car-ned over to the next support outside the spän con-sidered.

The discussion will be limited to two case related to the flange representation in the strip model.

Initial deflection ät midspan of one beam element. Disalignment of one single support of the contin-uous beam.

In figure 6b these cases are presented and theadditional bending moments Mxdd are giveñ.

So the magnitudes of the originally calculated bending moments could be corrected if the actual values of disalignment and unfairness were known, but this would hardly be a practical solution.

In practice attention centres mainly around extreme bending moment and stress values so that it will be better to try and establish limits inside of which most of the corrections will occur. This can be done by statistical means assuming that the disalignments and distortions caused by the manufacturing processes are distributed according tostatistical rules. However as soon as the panel has been positioned in a larger assembly deformations caused by an improper fit may disturb or even obscure the regular pattern of the orig-inal unfairness. A more extensive discussion of this subject was submitted by the second author as a contribution to a committee report for the I.S.S.C. 1967 in Oslo [8]. The discussion here will be limited to the initial unfairness of the panels li and III of the bulkheads 1 and 2 because the panels I, which are separately fabricated units, had to be excluded owing to very large deformations, caused by forceful fitting during assembly. For the sake of providing infor-mation the overall 'initial unfairnesses of all the bulk-heads are presented in the appendix (figs. A-3, A-4, A-5, A-6, A-7 and A-8).

Figure 6c gives the distribution of initial unfairness relative to transverse base lines passing through the sides of the panels. The standard deviation with the mean value provide the means to establish the upper-and lower limit of scatter based on the calculated maximum bending moments, so that the majority of actual maximum bending moment values will occUr in the range _dd In figure 6b the limit 'values of the distortions are given.

Whetherthe additional moments dobecome manifest as sizeable differences between actual - and calculated bending moments depends on the relative magnitude

- 10

_i

ci

1:

N

\

N

A

\

of lt has been found that P depends largely' on the geometry of the corrugated section and also on the local load. About the parameters governing jt (the statistical mean value) and so (the standard deviation) nothing is known but proposals concerning means of obtaining information have been put forward in [81. 3 Experimental results and their analysis

3.1 Deflection and bending moments in the longitu-dinal direction

311 General remarks

In the figures 7,8 and 9 the experimental and calculated curves of deflections and bending moments are present-ed 'for the corrugatpresent-ed bulkheads. For the plane bulk-head only the bending moments are given in figure lo, because the deflection readings have proved to be unreliable, although the mode of deflection was clear. The theoretical values for alt bulkheads have been obtained by using the improved beam model.and the computations have been carried out on the University's computer TR4 using programs developed by the

MQdd.

Mx odd d

p' _{M add.}

P-1

Madd.

FIG6b ADDITIONAL BENDING MOMENTS DUE TO UNFAIRNESS 6

second author. The influence ofshear on the deflections has been taken into account, and the. stringers are no longer considered as rigid supports.

For the sake of information the deflection curves for compressed air loading have been provided, des-pite the large flexure of the panels I the load-strain relation of all gauges was linear within the whole range of charging.

3.1.2 The corrugated bulkheads

As Stated earlier the. theoretical calculations of the beam bending moments and the deflections include the influence of the stringer deflectións. In this case the measured 'deflections have been used, but calculated values may be' used in practice.

The theoretical results agree very well with the experimental curves, except for the panels III of both bulkheads, where differences are in evidence along the. full height of the panel for bulkhead 1 and 2 (see figs. 7 and 8). The experimental bending moment values are less than the calculated ones, while for the deflections the opposite is true. These two

correspond-24 22 20 18 16 14 12 10 8 BULKHEAD (D PANELS ]t.311 BULKHEAD ® NELS 131E

987654321 0-1-2-3-4-5-6-7

765.3 2

UJ1 ': i1ij

--

P M2 M1 _ixl

FIG.6a. STRUCTURAI 'MODEL FOR THE CALCULATION OF THE TRANSVERSE BENDING MOMENTS.

»Stotisticct mean.

Standard deviation.

unfairness in mm OutwoT-dS (4)' - nwords(-)

FIG. 6c'. DISTRIBUTION OF INITIAL UNFAIRNESS.

MEASURED } hydrostatic (max.) CALCULATED MEASURED } compressed air CALCULATED -mm 20 18 16 14 12 10 8 6 4 2 BULKHEAD DECK

II,I,l,IuIII,IuIILI

I i 95m

2018161412108 642 0I3.5

_flIIfl I kgcm 23 I. 5 6 7 cm.NL L1 i

with displacement of the supports X without dispLacement of the supports

extended or improved eLementary beam kgcm - 310 -210 -1O I i I I I -210 . -10e O I I O kgcm 210 3.15 4iO I I I

Fig. 7. Longitudinal deflection and bendingniomentcurves; bulkhead2.

I I

10 210 31D 410

kgcm

12

CALCULATED } hydrostatic (max)

9 MEASURED 't

I CALCULATED j compressed air

mm 12 10 8 6 1. 2 0 I I i I' i I

Ii' L'

I 12 10 8' 6 L 2 0 mm BULKHEAD ® DECK kgcm 310 210 I' i 'I upper stringer lower stringer BOTTOM 95 m 310e .kgcm 1 23 I. cm &ili 1955

/'

:I cm

3 with displaòement of the supports

X without dispLàcement of the suppots

Fig. & LongitudinaUdeflectiòn and bending moment curves; bulkhead 1.

MEASURED kgcm io5 210 31b5 ¿1O5

I'

I i J 2iO 3i0 kgcm l'iII 210g

i

o

ing facts can be caused only by a relaxation of the bottom connection of the bulkheads. It will be shown in the next section that this is the case indeed and: the direct cause is a local deformation within - and very near to - the connections. The greatest differences occur in bulkhead 2, its flexural rigidity being55% of that of bulkhead 1.

It will be clear that the local deformation of the bottom connections must either be kept strictly within limits or, better still, be prevented altogether, as an unknown decrease of the bending moment at the bot-tom causes unpredictable increases of the moments at mid-span and in way of the stringer.

Provided that the local deformations are prevented then the actual bending moments Will be accurately predicted by the set of values calculated for non-rigid supports. In practice rigid supports may have to be used in the calculations and the values for this case are also presented in figures 7 and 8. Supposing now that an actual set of bending moment values is represented by the values corresponding to non-rigid supports then comparison with the set for rigid supports will provide an impression of the errors involved.

It must be recalled here, that such a comparison based on experiments has beendiscussed in section 4.3 of [2] concerning bulkhead 2 and that for its panel Ill the beam bending moment curves for constrained and for released stringers were presented in figure II of the same reference. It was stated there that little difference was found in stress values between the cases of rigid - and non-rigid supports. In the table below the differences in bending moment values between the two support conditions are presented for three posi-tions along the span of panel III of bulkhead 2, first for the theoretical calculations and second for the experimental values.

BULKHEAD 2

The smallest difference values occur at mid-span where the highest beam moment should be situated and Where the nominal stress distribution corresponds best with the actual one It is clear that in this case rigid supports may indeed be assumed for the purpose of calculation. It is also evident that the accuracy of the prediction depends more on the correct local

rigidity of the boundary connections than on the assumption that the supports are rigid.

Comparison of the two sets of theoretical values for bulkhead 1 leads to the same conclusions as were

arrived at for bulkhead 2 above, as far as the midspan bending moments are concerned. At the stringer and the bottom rather large errors result from the rigid support hypothesis. In this respect figure 9 shows, for

the sake of comparison, a number of calculated

bending moment values, obtained with various structural models. At the upper stringer both pairs of theoretical values show little difference, however had the deck connection been more rigid they would have been more pronounced.

Finally there are two more ways in which the as-built structUre can differ from the model.

The nominal moment of inertia may not equal the effective one.

Initial disalignrnents of the supports relative to each other and to the end may be present.

a. Effective moment of inertia

Comparative calculatións have shown that the bending moment values are insensitive to variations in the moments of inertia where the order of mag-nitude is concerned that is usually associated with effectiveness of this parameter; This is not too sur-prising really, considering the differences in the cal-culated bending moments between bulkheads ¡ and 2. (The latter having a.55 flexural rigidity as com-pared to 1.00 of the former).

Stress distributions of course are sensitive to the changes mentioned above. For bulkhead i the effective moment of inertia equalled the nominal one, because of the relatively small width of thé flanges of the corrugated cross-section. For bulk-head 2 the effective breadth of the flanges was analysed on the basis of the experimental beam bending stress distributiOn atmidspanof all three panels. The results of this analysis are, presented in the table below.

The differences in effectiveness are possibly due to local initial distortions and to the local transverse deflection of the flanges caused by the local hydro-static load.

Bending Moment difference values. Rigid supports minus non-rigid ones

Stringer; ton m. Midspan; ton m. Bottom; ton rn. by theory

.40

+.lO +.60 by experiment

.22

.03

_+.45

Effective breadth, bulkhead 2. (1.00 = b)

Midspan Tension flange Compression flange

panel I .85 .71

panel II .81 .81

14

I

TI

panel 321 actual structure ¿h deck MEASURED + upper stnnger Lower stringer bottom :( Experimental curve) CALCULATED -extended or improved elementary beam 23 elementary beam without displacement with displacement ¿h

41O 31O 21O O 1O 21O 31O 61O ,51O

kgcm kgcm

...BUaKHEÁD ®

Fig.'9. Calculated !ongitudinal bending moment values, based on various beam models. (Panels JI and Ill).

cn N L! 275 600 cfi

without displacement 'of the supports with displacement of the supports panel i panel ii kgcm _21105 I o _2lO5 31O kgcm upper stringer lower stringer BOTTOM

b. Initial disalignments of the supports

This fact will not have any influence so long as the bulkheads are only laterally loaded, but in case of buckling loads, the stresses in the structure will be influenced.

3.1.3 The plane bulkhead

Most noticeable in figure lO is the influence on the experimental bending moment curve of the bracket at the bottom end of the stiffener. The extreme rigidity is accentuated by an unknown downward deflection of the bottom of the testing tank. For this reason no attempt has been made to determine empirically the effective span of the stiffener on panel III. In the struc-tural model which is also shown in figure 10 the span has been taken as the length of the stiffener less the

height of the bottom bracket. In the case of the

stiffener on panel I the effective length equalled the total length, because the deck beam is not directly

kgcm

- 2ifl -1O O 1O 210e 31O

I L I - i__J

DECK CMCVMED

strig

connected to the stiffener, so that in effect the existing bracketed connection has been replaced by a bracket-less one.

The lack of reliable information concerning flexure combined with the unknown degree of tank bottom deflection prevent an investigation of the accuracy of the calculations. The curves for panel I, which is the least influenced, appear to be very promising.

3.2. The end connections

3.2.1 The corrugated bulkheads

Longitudinal direction (Direction Y, from the bottom towards the deck.)

Although the connections to the stringers are not exact-ly end connections, they will be considered as such. In figure 1 1 the longitudinal strain distributions are

presented for the straightened cross sections very near the bottom and both stringers. Those near the deck have been left out because of the very low observed strain values. Although there are three different types of stringers, the measured strain distributions all show the same character. In the tensión flange the inside surface strain is constant along the width of the flange while the outside surface strain is reduced to a mini-mum value at midflange. For the compression flange this pattern is reversed and along the webs a very clear and plain pattern is evident near the symmetric (i.e. the upper) stringer of bulkhead 2 (top, right of fig. li) and to a lesser degree for the upper stringer of bulkhead 1 (top, left), elsewhere the distributions

clearly show the influence of hard spots inherent in asymmetric stringers with fill-in plates. These hard spots can be easily detected in the transverse strain distributions of the same straightened cross sections presented in figure 13.

In case of the bottom connection the distribution is seriously influenced by the. presence of bottom longi-tudinals and the heavy transverse bottom frame (see also structural details in fig 11).

1f the bottom longitudinals are thought to have been removed altogether, the strain peaks between corru-gations C1 and C2 and at C4 would not occur and a strain distribution would be left showing the same

pattern as those at the stringers. One important

difference would show up in the heart of plate strain distribution (not shown), namely that in the central regions ofbothflanges the heart of plate strain will be negligible. Consequently the beam bending moments at the ends would be very small.

The actual distribution already shows a heart of plate strain that is negligible across the greater part of the width of what should be the compression flange. This is most evident for bulkhead I and somewhat less

2-1O -1 O 135 2O 3)35 5-1O

k 'cm2g1 BULKHEAD -100 0- -1000-kg/cm2 1000- -1000-kg/cm2 100 0--lODO-' kg/cm2 C4 kg/cm2 1000-O. -1000-kg/cm2 kg/cn £000 3000- 2000- 1000- O-- 1000O-- 1000- -2000-kg/cm2 y

fr4*

/

\c3fr

11.99 1476 0 206 S

.... a local hydrostòtic toad 0.670/cm2+

1.68 j

2125 0 372 0

12281

young 's mod. s strain

at a

1-LONGITUDIÑÁL STRAIN DISTRIBUTION

cl 0 1279 : 458 'C -at b42 9----C4 C3 I I I I.4. -: i I

/

I weLd Left r- undisturbed LocaL LOOdO.395k%m2 upper stringer, 55OE above: bottom

\Local hydrastatic Load

for detaiLs of stringers

see f ig.1 q 275 above bottom Lower stringer

i \ Local hydrostatic load 0.680 k%m2 \

- inside (Loaded side

outside (unLoaded side

aLL dimensions in' cm

magnitude of tong. BM. in tm 01.05 2388 0 1042 BULKHEAD ©-01851 S 877

a-f-C2 0 1705 1497 12.201 01853' S 910 12.34

IEEyi

---EEyu °

-Fig. l'i. Longitudinal strain distributions at endsofcorrugatedpanels.

<J= 4096

weLd' ground down

to plate thickness

12.18 I

C3

Eyi plate surface strain;Loaded side.

Eyu = plate surface strain; unLoaded side. kg/cm2

-

1000 O - -1000 kg/cm2 - 1000 - 1(300 kg/cm2 - 2000 - 1000' C' o -1000 kg/cñ kg/cm2

-

1000 o - - 1000 lg/cm2 kg/cm2 - '4000 - 3000 - 2000

-

1000 O -'-1000 --2000 kg/cm2 11.721

>

£076 4e

Local hydrostatic Load 098k%m2 Il' '

for bulkhead 2, where the distribution near fold C4

(fig. Il, bottom right.) is already influenced by the bottom longitudinal around the corner.

Little or no heart of plate compressive strain in the flange means that the bottom plating gives way, resulting in the noticeable reduction in the end bending moment already discussed in the previous section. In order to obtain confirmation of the deduced down-ward deflection of the bottom plating in way of the relieved compression flange, additional deflection measurements were carried out on the surface of the bottom plating outside bulkhead 2. This bulkhead was chosen for reasons of accessibility. In figure 12 the relevant deflections have, been plotted relative to the bottom longitudinals and transverses and they leave no doubts as to the correctness of the above deduction. In conclusion it must be stated that this kind of struc-tural arrangement in way of the end connection of a corrugated bulkhead is very undesirable. It causes high strain concentrations (far above nominal yield strain values) but it also allows part of the structure to shirk its load.

It is doubtful if an arrangement whereby bottom longitudinals cross the bulkhead at every midflange

ml 0.30 deflection scale.

ml

ml 02 0 03 0 Y SECI)DN A-A 920

oms

point could be considered an improvement. It certainly would increase the load bearing of the compression flanges, but as certain woüld be the introduction of yet another strain concentration, this time compressive, constituting a real danger of local instability through buckling.

Arranging the longitudinals in such a way that they cross the bulkhead at midpoint of the webs, would eliminate the strain concentrations. However the joint would, as a consequence, become. very flexible, leading to a further decrease of the bending moments near the bottom and increasing those at midspan of the corru-gated beam and at its ends near the stringers. Especial-ly at the stringers this would be undesirable because of the accompanying increase of the, presently already high, strain values and gradients at the folds C1 and C2 (fig. 11)'. To prevent this from happening addi-tional stiffening of the bottom plating in line with the flanges of the bulkhead is necessary and this would result in a strain distribution resembling those in way of the symmetric stringer of bulkhead 2, except may be in the central part of the web, which is the least vulnerable anyway. BU»EAD®

_IF

t.__r41

j

II

I

F-

T

UI

a..

I

..-

____u,

Ii

I

I____

..

____It

i.

r ir

ii-i 020 (d.h dìne,s i, ml

Fig. 12. Distribution of downward deflections of the bottomplating outside the testing tank.

0.3,-o 0,4 02 ml 030 0.4 0 0.4 0 deflection scale. o 02 -0 03 o 0.3 o 0.3

O-kg/cm2 _BULKHEAD 1000-o kg/cm' 1000-_-4 I o

,'"

'lti I C4 C3 _,i.6 I

ti

-1000-

'4

kg/cm2 kg/cm2 1000-o 2000-

100

0--1000- C4 kg/cm2 11.681 2:281 C3 / " /

i'

ILL)-C2 I C1 1018 y r2 at 'a L.. /4-'r t 't \1ocaL 4 U at b-I-i8 el

t

weLd Left undisturbed ''C4 88.8. 889 i Ec,«

---G----young's mod. e strain

.1 EExu O

BULKHEAD ©

Local. 'hydrostatic load 0.395 k%,

- f;'

,,

q "«ö C3 C4 C 2 1.871 upper sfrrnger 550 above bottom Io 3808 J,

local, hydrostatic Load 0.670 k91cm2

for details of strnger

see fig. i 275 above bottom hydrostatic q (I Lower stringer load 0680_k%m2/21

inside (Loaded side)

outside (unloaded 9de)

-Local hydrostatic load 0.948kg1

C1! , i' i

at a

-at b.

0 29411 le -5l Io 2471!

À:

Fig. 'I-3. Traüsversestrain-distribütions at endsof corrugated panels.

kg/cm2 s- -x - 1000

4__-+

O 12.20 I 3 1

x

C4 12181 C4 i r. ' /_L88.8 . 88.8

= plate sürfoce strain;,Loaded side. plate surface strcin;'unloaded side.

-- 1000 kg/cm2 - 2000 - 1000 o - -1000 --2000 kg/cm2 -1000 - 1000 kg/cm2 2000 1000 o - .1000 kg/cm2 18

TRANSVERSE STRAIN DISTRiBUTION

C4 Ç3

-1000- 201j

kg/cm2

1000--'--st b'.-l. -8671 12.341

L.. weLd ground down

I to pl.cite thicknèss l-1250,1 at a 256801 at b -1000- ₁₇₂₁ kg/cm2 kg/cm2 alL dimensions in cm magnitude of Long. B.M in tm 2.01 kg/cn -1000 o - 1000

0--1000- 19g I \tocai hydrostatic load

kg/2 C3

11.791

Transverse direction (Direction X.)

The transverse strain distributions- are presented in figure 13.

A comparison of the distributions near the upper stringers with those near the lower makes it clear why the one-sided stringer (i.e. the lower) with fill-in plates (see fig. 1.) is definitely undesirable from a

structural point of view. Even the difference in the stringer load per corrugated cross section can not explain away either the high strain concentrations that occur in the section situated 5 cm above the fill-in plate of the lower stringer of bulkhead 2, nor the un-balanced distribution along the cross-section. Moving from this section and its. fellow Section of bulkhead I towards the stringer, the peak stresses at C1 and C2 increase very rapidly as can be deduced from the se-parately indicated values which apply to a.cröss section 2 cm above the fill-in plate. It is remarkable that only the outside surface strain shows this increase. lt is

hoped that an explanation for

this phenomenon together with an answer to the question of effectiveness of the bulkhead as a stringer flange can be found after - the stringers themselves have been investigated.

In conclusion it must be stated that symmetric stringers or those like the upper one of bulkhead I are to be preferred above the one- sided stringers With fill-in plates, because the high strain concentrations in-herent in the latter constitute real danger sports. 3.2.2 The plane bulkhead

Regarding the bottom and deck connections of the stiffeners on the plane bulkhead it must be stated that as far as the bending moments are concerned both brackets (see fig. IO) need not have been present at all. The stiffener - deck beam connection can be realized just as well by a bracketless one and the stiff-ener - bottom longitudinal connection would defiñitely be better Without the brackets. In case unacceptably large deformations are feared at the actual point where the bulkhead - and bottom plate stiffener combinations are welded together, small curved brackets ([9] "ideal" type) could be used. An investigation towards experi-mental verification of this statement is envisaged because of the excellent opportunities offered by the present test pieces.

3.3 The transverse deflections and bending moments

The deflections of the corrugated bulkheads have been measured only in the direction of the load, that is the Z-direction indicated in figure 14, as it was impossible to obtain readings of transverse displacements as well. Even so, the deflection curves as given in figure 14 pro-vide-sufficient information to verify the theory

discussed-in section 2;2 concerndiscussed-ing the flexure mechanism. The experimental curves at midspan of panel I of bulkhead I provide in fact a very satisfactory confirmation. The deflectiöns caused by the hydrostatic load illustrate the case for small displacements as actually discussed and those caused by the compressed air load represent the case where a second hinge is needed because of the larger displacements. In case of bulkhead 2, secondary hinge actions occur elsewhere in the cross-section and their presence can be explained as follows.

Considering the as drawn cross-section of this bulk-head it can be seen that the webs exert a compressive force on the upper flanges and a tensile one on the lower. Both flanges are also laterally loaded so that the compressed flange will deflect far more than the tensed one Consequently the reductions in flange span will not be the same, causing an increase in the distance between the folds of the compressed and of the tensed flange that can not be met by an elongation of the web Therefore the web will tWist, thereby reducing its pro-' jected height and increasing its projected width, so that in the direction of the load the two sides ofthe web do not show the same amount of displacement. The observations showed quite clearly that, for instance in the deflection curve for panel H the tensed flange 6-7 in the cross-section was moved bodily against the direction of the load. With bulkhead 1 the secondary hinge actions cañ not be detected as they are too small. This is reasonable because the normal flange forces and the flange span are less than for bulkhead 2.

The transverse bending moment distributions at midspan of the panels HI of all three bulkheads are presented in figure 15. The experimental moments hàve been derived from the observed stresses by cal-culation, so that for each bulkhead only one pair of

curves had to be analysed.

-In the corrugated bulkheads there are also trans verse heart of plate stresses, however they are neither very high nor very -accurate. The latter on account of the fact that they are calculated from the difference of two, large numbers, both containing observational errors

Starting with the curves for the corrugated bulk-heads, it can be seen that the differences between the theoretical and experimental values show a pattern. The differences may be -caused by two error

compo-nents, a systematic one and a random one.

a. Systematic error component

This can be traced to an approximation in thetheoret-ical calculation [2], sectiOns 3 and 4 of the appendix),

resulting in an over-estimation at the folds and an un-der-estimation at midspan of the flanges.

20'

mm

i fôr tIii same reasons mentioned above in relation to the secondary hinge ati'on.

'b. Randöm error component

This component may be 'stib-dividedi into three parts. b.l Local initial unfairness (relative to edges of whole

panel)

b.2 Local 'Variations in the plate thickness

b.3 Local variations in ,the radius of curvature of the folds.

Ad b.l.

The local unfairñess may differ appreciably from the 'values established on the basis' of the' statistical mean and its standard deviations. An example is seen in the experimental bending moment curve of bulkhead 2 in

f I.

hydrostatic TYE 'OF LOAD

W comØresséd ir

r hydrostatic

TYPE OF LOAD

compressed oir

Fig., 14. Midpanel transverse deflection curves.

/ 7.50 ro ABOVE BASE MIDSPAN PANEL I 4.125m ABOVE BASE MSPAN PANEL lt 2 3 5 ' 6 ,7 8 9 10 R' R MD 10 11 Q 2 L 6 a 10 mm m ABOVE BASE AN PANEL I

140 120 100 80 60 40 40 - 60 - 80 - 100 - 120 - 140 kgcm Fig. 15. Midpanel transverse bending moment distributions. 240 220 200 180 160 140 120 100 80 60 40 - 40 -60 -80 -100 -120 11.0 160 kgcm II : L i 200 180 r 160 kgcm 21.0 -60 - 80 -160 1/.0 120 100 80 60 40 - 40 - 60 - 80 -100 120 -140 kgcm MEASURED CALCULATED Range of possible bending moments due to initial unfairness.

22

the tensed flange containing a butt weld B and situated

to the left of the bulkhead's centre line. The flange dis-tortion is such that the butt weld is 6.5 mm out of line with the flange edges, in the direction of the load. The

resultant errors in bending moments are approximately

33% of the calculated ones, corresponding to a plate

surface stress error of 400 kg/cm2.

The correction for initial distortion, as discussed in section 2.2 previously, does not apply in this case. As can be seen from figure 6b this, correction may result in an increase of the theoretical bending moment or a decrease and it is clear that the highest correction

values should be used. Since interest is mainly centred

around the maximum bending moment values, only

these have been corrected. The resultant range of

possi-ble values has been indicated in figure 15, and apart from the exceptions mentioned earlier only the

experi-mental midflange values for bulkhead 2 are in excess of the possible spread.

Bearing in mind that the theoretical values at these positions have been underestimated for reasons ex-plained above in suba, the results of the applied initial

distortion correction are very promising. The "stan-dard spread" of the theoretical bending moments at

the folds is 14% for bulkhead 2 and 17% för bulkhead

1, at midflange these values are 1l% and 22%

respectiv-ely.

Ad b.2.

About the local variations in plate thickness no

infor-mation is available; If these were known the theoretical

bending stresses would have to be corrected as they

have to be derived from the moments with the

ex-pression a = M/W where W t2, and t is the plate

thickness. Putting the total thickness variation at

A %, the stresses will show an er.ror of 2A, %.

Ad b.3.

Concerning the variations in the radii of curvature of

the folds, it has been found that for the two test

bulkheads the standard deviation was high. Subsequent

calculations have indicated that the error in the exper-imental bending momentsat the folds due to Variations in the radius of curvature is small for the range of radii

concerned.

From the foregoing it must bè concluded that the total

error :in calculated bending stresses as a result of accu-mulation may be large, say 30%. Of course the average

error will be less, but even so it will be substantial, considering the figures for, the "standard spread" in

calculated bending moment values on the basis of the distortions.

Therefore it must be stated that as far as possible the

theoretical calculations concerning the transverse bending moments and stresses should include as much

as possible the initial distortion correction. (as

dis-cussed in section 2.2).

This applies especially to bulkheads where the

trans-verse bending stresses are equal to or in excess of the longitudinal beam bending stresses.

The experimental curves for bulkhead 4 have been

drawn according to a parabolic distribution and they

have been extended beyond the measured values near

the connection of the stiffener to the plating. The

calculated values were obtained for a strip of unit

width that has been considered fully fixed at the toe of

the weld connecting the stiffener to the plating This position of the point of fixation is not entirely correct but it is more realistic than one at the heart of the

stiffener.

The scatter is not inconsiderable for most of the

experimental peak values and the curves are not

sym-metric relative to the lines midway between the

stiff-eners. These phenomena occur because the stiffeners

do not deflect by the same amount. No specific

verification has been possible on account of the

ab-sence of reliable deflection readings.

4 The necessity for full' scale experiments

Theoretical and experimental research concerning

ship's structures is carried out in order tt develop

both improved methods of structural design and more efficient structures. The latter means, amongst other things less structural weight, that is: lighter scantlings. Consequently more detailed information is required regarding the stress - and strain distributions in way of

the connections of structures under static - and .dynam-icloads. Extension of the present knowledge concerning

actual service loads in ships and on their structural parts is urgently needed. The necessary information

has to be obtained fromexperiments carried out aboard ships in service as well as in laboratories on full scale

structures. Model experiments are usefull when it comes to providing informatiOn on overall response

of a structure to static loads, but no more.

It is known that local strain hardening in an

other-wise elastically strained structure may give rise to cracks

when a low-cycling load is applied, dependent on the number of cycles, the strain concentration factor and the nominal peak-to-peak values of the load. This local strain hardening which occurs at discontinuities in the

structure and notably at its end connections, can be detected by detailed instrumentation requiring for

instance veryumall gauge-lengths, the required loading in this case being within the elastic range.

Therefore full scale static experiments in the elastic rangemay provide;information asto if, when and where low cycle fatigue cracks will occur in a given structure, subjected to cyclic loads.

At first it seems questionable whether low cycle fatique should be considered in connection with bulk-heads, however the following facts Will provide food for thought:

Tank - or cargobulkheads must not exceed the elastically strained condition (nominally).

Where theoretical calculations are concerned, the loads on these bulkheads are nominal.

Ships are being built or are already in service with very long cargo tanks or with holds alternatively full in loaded condition. In the latter case the bulk-heads are loaded on one side only.

In addition:

Little information is available concerning the addi-tional loads, static and cyclic, caused by the bulk-head's participation in the overall response of the whole ship structure to service loads.

No information is available concerning the cyclic loads imposed by the cargo's mass forces resulting from the ship's movements in a seaway.

The influence of slamming on the strain levels of bulkheads in the fore-part of the ship is unknown. It is therefore logical to state that normally in service conditions cyclic loads will be superimposed on the static one and that as a result fatigue cracks may 'be initiated. Although they will not cause damage that endangers the structural safety of the ship, they are a nuisance, because they have to be repaired.

In the light of the above discussion, the transverse strain distributions presented in the figures 11 and 13 take on a new significance.

From figure 13 it is clear that if under cyclic loading cracks do occur, they will do so near the lower stringer in way of the folds C1 and C2 on the unloaded side of the plating of bulkhead 2

In figure Il in the cross section near the bottom, another possible location for crack initiation is indi-cated by -a strain peak. Propagation will lead in this case to detachment of the tension flange from the bottomplate.

It is unknown to the authors whether in practice the discussed type of damage has occured as no in-formation on this subject is available HoWever, they are convinced that lighter scantlings combined with the present practice of structural detail design will suffer from this type of damages

5 Comparison between corrugated and plane bulk-heads

It must be stated here that the comparison will be based on the relative structural merits of the- bulk-heads concerned and that the cost aspect is ignored.

The structures have been designed for the same

purpose and according to

the same regulations, namely to serve as watertight bulkheads The work-ing load and the sub-division of the total span are iden-tical for all, but the moment of resistance against bending of bulkhead 2 is less than that of the others. The corrugated bulkheads have a relatively flexible connection to the bottom structure (see details of fig. 10 or 11) and a very flexible connection to the deck whereas bulkhead 4 has a very rigid connection to the bottom structure and a relatively flexible one, to the deck. The connections at the sides are the same for all three structures.

In order to compare bulkhead 4 with the corrugated ones the expression of von Mises-'Huber-Hencky for the equivalent stress will be used.. Furthçrmore the specific Weight, characterized by the sectional -areas of a half corrugation-profile and pläte and rolled section combination, must be taken into account.

The equivalent -stresses and sectional areasare given in Table I below. Included is .a bulkhead 4c which is fictitious and corrugated, but has the same section modulus,.. plate thickness and beam (stiffener) spacing as bulkhead 4. The fictitious bulkhead is one of a series, all satisfying the same requirements, generated by a program developed .by the second author. This particular bulkhead is the one with the least weight of that series and it has the same corrugated shape as bulkhead 2.

Table I. Comparison of corrugated and plane bulkheads.

Even if allowance is made for the influence of the bot-tom deflection on its bending moments, bulkhead 4 can not be considered as an efficient structure. Re-ducing the rigidity 6f its bottom connection would lower the equivalent stress value, but even so it would still be the heaviest bulkhead of the, lot. The distinct advantage of the corrugated bulkheads lies in their bi-axially antisymmetric crosssection so that the struc-tural material is efficiently used.

-Bulkhead

eq. max. exp.

kg/cm2 eq. max. theory kg/cm2 section area cm2 section area in %.of bulkhead 4 I 1500 1580 429 ' 48 2 1370 - 1240 50.7 - 57 4 - 2100 1570 -89.7 100 -4e

-

670, 60.6 68

6 Conclusions

As far as the general experiments with corrugated bulkheads are concerned this report is final, although investigations will continue in regard to structural details and the plane bulkheads.

The currently available information allows the following conclusions to be drawn.

In view oíthe observed strains at the boundaries of the corrugated bulkheads and the tendency in practice to increase tank lengths in ships, very high priority should be assigned to experimental inves-tigations of actual loads occuring aboard ships. Simultaneously special attention must be paid to strain distributions close to the boundaries of stiffened panels in particular and to structural details in general.

For practical purposes the improved beam model provides very satisfactory answers. It cati also be used for beams with a corrugated cross sectiOn, provided that the end connections do not show internal local flexure.

Economic considerations excepted, symmetric stringers are to be preferred as supporting mem-bers for corrugated buIkheads Besides allowing changes in panel thickness to be effected, they are more in accordance with the symmetry inherent in the bulkheads' cross sections.

Considering the weight of material involved, cor-rugated bulkheads are decidedly more efficient than plane stiffened ones. This will be accentuated if the character of symmetry and flexibility of the former is recognized in the design of its structural details; If practicable, the end connections Of plane stiff-ened bulkheads should be bracketless. If brackets have to be introduced in order to prevent excessive local deformation of the joint, they should be as small as possible.

The available evidence indicates that it is undesir-able to design stiffeners or corrugated beams on the basis of equal bending moment magnitudes at the ends and at midspan.

Valuable information has been obtained from the discussed series of experiments owing to the use of full scale specimens.

Knowledge concerning initial distortions, variations in plate thickness and other deviations from the

mathematically correct design concept is needed in order to study their influence on local stresses. in this respect it must be realized that the effect of initial distortion depends on its orientation relative to the direction of the load.

Acknowledgements

The authors are indebted to their staff and to the lab-oratory technicians for their efforts in processing and gathering the enormous amount of data involved.

The assistance rendered by the University's Com-puter Centre, in particular by the punching typists and, the operators is deeply appreciated.

Finally thanks are due to the Netherlands Ship Research Centre T.N.O. for its encouraging and finan-cial support.

References

JAEGER, H. E. and VAN KATWIJK, P. A.: Analyse Théorique

d'Expériences Exécutées pour Déterminer la Résistance de Cloisons en Tôles Ondülées à Plis Verticaux et en Tôles Planes Renforcées. Bull. A.T.M.A., Paris,

Décem-bre 1967, pp. 643-664.

JAEGER, H. E. and VAN KATWIJK, P.A.: Stress and Strain Distribution ma Vertically Corrugated Bulkhead. Report no. 73 S, Netherlands' Research CentreT.N.O. for Ship-building and Navigation, ShipShip-building Department. June

1965.

VAN KATWIJK, P. A.: Modern'çomputation and some

Appli-cations in Shipbuilding. Schip & Werf vol. 35 nr 10, 11, (InDutch). 1968.

JAEGER, H. E., BURGHGRAEE, B; and VAN DER HAM, I.: In

vestigation of the stress distribution in corrugated bulk-heads withverticäl troughs. Report no. 15S, Netherlands' Research Centre T.N.O. for Shipbuilding and Navigation ShipbuildingDepartment. Sept. 1954.

CALDWELL, J. B: The strength of corrugated plating for ships' bulkheads. T.I.N.A., London, 1955.

GETZ, J. R.: Korrugerte Skott - I. Report S.F.I. no. 15. July 1956. ([n Norwegian).

SKJEGGESTAD, B. and BAKKE, E.: Corrugated bulkhead laterally loaded to ultimate failure. Report S.F.I. no. R

57. Jan. 1965.

& Proceedings of the Third International Ship Structures Congress Report of committee 3b. Vol. I, pp. 141-143.

Oslo, Sept. 1967.

9. JAEGER, H. E. and NIBBERING, J. J. W.: Beam knees and other bracketed connections. Report no. 38 S, Nether-lands' Research Centre T.N.O. for Shpbui1ding and Navigation, Shipbuilding Department. Jan. 1961.

It must be borne in mind that in the following a dis tinction must be made between beam bending in the central part of a corrugated panel and the hinge action at the sides parallel to the folds.

As has been stated in section 2.2. deformations are supposed to be elastic and relatively small, further-more pure torsion is assumed for the element w1 and pure bending for the corrugated beams. (Fig. A-l). The1atter assumption means that the influence of. shear on the deflection is initially neglected. It will become clear later on that this will make no difference in the final relation between the relevant rigidities.

It is reasonable to suppose that the hinge mecha-nism is activated as soon as the panels' overall deflec-tion is initiated, so that a certain transverse secdeflec-tion of the panelthe angleoftorsion of w1is linearly coupled to

the angle of curvature of the corrugated beams. The relevant basic equations are, see figure A-2:

dci d(p

= C (C = constant)

dy dy dço Mb

dy - Ei,,

dciM,

dy - GI,

it follows then that M, = CMb.

Including the influenceofshear in the basic bending equation leads to:

=

(Mb+(r))

or:

= giving M1 = CM;,

APPENDIX

The rigidity ratio or the relation between beam flexural Wether M,, is used or M makes no difference in what rigidity and web torsional rigidity. _...follows.

At some distance l from the end of the panel the de-flection 5 of its central part is characterized by

o Mb1

Ei,,

and the angle of twist of the element w1 by

CM .1

ci V Y

GI,

Fig. A-2.

The displacement of c, relative to c2 (fig. A-I) is re-presented by

CM,,;lb

GI,

This is representative for the hinge action that allows cylindrical bending of the corrugated panel. Conse-quently it can be stated that in this case the unit hinge action haallows a deflection characterized by

ha

26

Now i, can be expressed as a fraction of the corrugated beam span I and rewriting ha leads to:

) GI I

ha = - x -i--- x

The factor l/EIb may be considered as a specific flexural rigidity, correspondingly GJ1/b as the inverse of a spe-cific torsional rigidity and hence their product as a

specific rigidity ratio. For the element w1 the torsional moment of inertia I can beexpressed as. cbt3 where C, is a constant; introducing this in ha leads to:

W,G lt3

ha

_CE x_i;:

As the first factor on the right hand side is a constant, it has been left out in figure 5 of section 2.2 leaving

as the parameter for the rigidity ratio.

The following figures A-3, A-4, A-5, A-6, A-7 and A-8 concerning the initial unfairnesses of the bulk-heads have been included as information.

2 3 mr 2 3 mr m ni 2 mr mi mi

mm 100 mmlO0 mm10O mm2O O mm2O O mmlOO

IlIiI!t, I!IIIflI1, il Ill!! ululi luuiijiu uuIiiiIiIili luiuii

S C C2 C3 C4 V C5 C5 C7 C5 i a U i, l3 l4 0

24e e r 1214 20 20 2 4 r r r 34 59 5920,2222 ¿5 ¡.550 5254 55 5952 52 64505170 72 74 75 75 80

5 I 20 2014 II 59202224202059323259 3940424245455052545e 555062

¿5 ¿4 .L5 e ¿, ¿ ¿59 0 32

Fig. A-3. Initial distortions; bulkhead 1.

59 59 10 72 74 75 7e 50 ¿54 32 ¿j 10 10 20 30 10 20 30 m o 10 20 m 10 20 m 10 20 im 10 20 o 10 20 10 20 o IO 20 m 10 IO 20 10 m 10 1 nroIsuluslnulousIT,unu2lunuau2luruI,132u3213,iOsu4liL3uASu22iASi5lulal20uSlu59iSlieiEuSileulllllulOr7liliiOl r n

:

F O

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I1IÌII11UII111ìITIM1F

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---.

iÌiiiÌ.I.IuIiIi

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-r

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r

iiÌiiiiiIìIÌiìiiiliìÏflI

:'iiiÌiiriiíiiÌiïiÌiiiiii

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r IO

iÌiiiÌiïiìiIiIIti1i1'

uni...,..

iii

rlusulununusuISulSuzluo3usutTrau3lu,135u70uau4ut3u4Su4lu4suslusIrssu 50ISeuslIeielueSulluflulSutlu'Im flIWARDS 2

\

_J...! otnARDs mr 0 l0-20-j 30-nm _ni

28 Bhecd © - - - - _BULKIAD.® C3C _Y5?6 C9C10 1112131I. 232422627 T7.1020 -!L C1 C2 20 0 ryn IuIitIiiijiiij] 20: Ç IIUiIìiiIIIiiIiIll'1

Fig. A-4. Initialdistortions; bulkhead 2.

CThC12 _TCt3C% CbC15 3S3637389I 7 bottnpanet _tcçpanet 1Q 0 mm 13W<HEAb ® Bhead mm o 10 20 30 mm 0 10 20 D 10 10 o 0 U o 10 o 10 o 10 rtm o 10 mm D 10 rim o 23 4

'6

7

._

___i__I__

._

-

_.

-o m0

lili

'uiiiIi.

iiiIIiiiiIii

i_I_

I

iiIi'

oI

1 m

rus. i uIa.-'.I----..

'liii

1.11

I I m1 :

.

---____iIW.I

I.

iii

m I im

FiiiiiIIIÏilIiIiTiiiii

I I m m m2 m

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iiiiiiÏiiiiiiÏiÌI

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I I I I

iIl.ITIÌ

m

O___________

FITIri 123 I 4 67891O11Q1314E IS ¿:. P19U202fl ,- ¿ç ¿ç 24-. 29 .3O3132

. mr

31. 2937: ¿012 ¿I. S H. INWARDS

r'

:1 '

j

WTWADS o o 10 o 10 mm o 10 20 30 ¿o

BULKHEAD INWARDS m

ri

_',lj

OUTWARDS 10 lo BULKHEAD @) f

i

T

i

i

T 1 2 3 4 5 6 7 8 9 10 11 12 13 1/. 15 16 17 18 19 20 21 22 23 24 25 U IV lU U bFfl

Fig. A-5 Initial distortions; bulkhead 3.

IV U ¡U U IUU UN lU U IUU lu U IO U lu J) U

BULKIADcD iini] Ïiiiijiij 1 2 3 4 [iiiJij _iiiiiTii 5 6 7 8 iiiiiii 9 iO 11 iiiIiiiIi 12 13 iiiiiii ii'iiiijij 14 15 16 1111141 1111111 17 18 19 20 21 lIJIlI] 114111]_ 22 23 24 25

RIEUNI

:uirni

ii

ii_iJ

I

Ir 11111

'.IlIiI_I_j-iiju'

iuuuiui

urn_ui_I

i

IURiJ_JI

1111

uuivauuui

1IL:=Iu

i IflhiIilI

Ì-'iiÌIÌiiii

IUI UUUiUI

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 im uifl 11111111 i"Ii" 1114111 11t'11 1Ri11 iiiIii] f11

o lo o 10 u, o t. o 10 o 10 10 o lo' 10 o lo o io 0 o '4 10 o g 10 o 10

o-10

0T

_s

o o Io _4

30 O lo o lo lo o INWARDS 10 OUTWARDS O lo o lo o lo o 10

23

RUIkMcAfl (Th

---...-J

010 "i'!" 25 - 4. 5 6 7 8 9 10 11 12 !' P!l1 pill] pipi 100 100' 1OO 100 100 13 14 15, 16' .17 19 19 20 21 22 23 21. 26

pill fll]il ']lll9ll [lupi

IphIl]' piilpi pimp

'010 100 10101 100 . 010 '010 'O'lo

'Fig. A-6. Initial distortions; bulkhead 4.

mm

lui

10 0 T

10

-.0 lo -s - o, e u, e. o, 10 lo 10 e u, lo

o

e e w lo 10 10

o

lo o' -10 mm-e 0 '6 7 8 10 11. 12 '14 15. 16 18 19 20 22 23 24 17 2l 100 101O' 100 100 010 100 -.1010 lo O O 10 0 10

biiij :j 'l'ululi ulind uui 5 6 '8 10 11 13 11. 15 16 17 18 19 20 21 22 23 21. mm 100 100

Ull

1; 2 3 T Io o 0, lo

o D u u o o

t

w D o-w u C D u u o e

I

3 2 o Statieticat mean. S Standard deviation.

ijfairness In mm inwards (-) - ( + ) outwards

p o 6.7

F i i i i I i i I -1 i ¡ I i i I i

2 1. 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 mm

DISTRIBUTION BULKHEAD ® PANEL I

i i I 2 6 6 8 10 12 PANELS , 3K 9.9 ii. ib ib 2mm 17 16 15 14 13 12 il 10 9 7 6 S 4 3 e o

[JJL

Fig. A-7. Distribution of initial unfairness of corrugated bulkheads.

po33 S&= 2.6

ç'

i i L1

I i"1

i -6 -4 -2 0 6 8 10 12 14 mm BULKHEAD ® PANELS rn ,

32 12 lo :

5

p= Statistical mean. S Standard deviotiòn. 4 6 8 10 12 iL

BULKHEADS © AÑD₍₄₎ COMBINED

Fig A-8. Distribution of initial unfairness of plane bulkheads.

BULKHEAD () PANELS i. il, i. BULKHEAD ® PANELLS 111ff.

unhairness ¡n mm