LABORATORIUM VOOR
SCHEEPSCONSTRUCTIES
TECHNISCHE HOGESCHOOL - DELFT
RAPPORT Nr.
BETREFFENDE:
concerning the Structural Behaviour of bulkheads. - Unfairness and Distortions
of Stiffened Plates.
by Ir. P.A. van Katwijk.
July 1966.
*
Concerning the Structural Behaviour of Bulkheads.
and
Unfairness and Distortions of Stiffened Plates.
by
Ir. P.A. van Katwijk.
CONTflIBUTIONS TO THE REPORT OF I.S0S,C. COMMITTJL
3b ON "ORTHOGONALLY STIFFENED PLATING IN
3-DIMEN-SIONAL STRUCTUR".
--July 1966.
s
Concerning the Structural Behaviour of Bulkheads.
Introduc tion.
In general the behaviour of bulkheads under hydrostatic loads has been satisfactorily established as far as the central regions and magnitudes of the maximum stresses there are concerned and more
than one method of elastic analysis leads to reasonable results. Rigorous solutions have not yet been possible owing to
uncertain-ties regarding boundary conditions0 So many imponderabilia influ-ence the degree of fixation or the lack of it that in practically all theoretical approaches to the problem of' the strength of bulk-heads the boundary conditions are drastically simplified and either reduced to a condition of simple support or to one of full fixation. In many cases simple support is preferred as it provides a kind of safety factor in the magnitude of the stresses in the central re-gion of the bulkhead where flange-efficiency of beams and local o' overall distortions may have a detrimental effect upon the way the load is taken up. The boundary regions of bulkheads have been some-what neglected, perhaps out of necessity, because of the many ways in which the connections to adjoining structural parts can be rea-lized and because of the wide range of the number of parts invol-ved. In many instances structural details have been investigated 't by means of experiments and in this way factual knowledge has been gathered. In some eases theories were advanced for dealing with connections such as the bracketed or the bracketless, but laudable
as they are in themselves they are only applicable to individual details and are rather too cumbersome to be of practical use. An-other drawback is that much uncertainty exists regarding the actual type of loading to which these details and more generally the boun-dary regions are subjected.
Even though with the coming of age of the computer, sophisticated theories can now be numerically realized the above mentioned diffi-culties remain to a large extent. They must be solved by means of factual data gathered at sea and concerning the loads to which the
den-2
ved from experiments, preferably full scale ones.
Thus a better understanding of interaction mechanisms will be possi-ble. Once sufficient numbers of experimental facts are available they may lead to qualitative analysis of interaction phenomena. This may
result in the rejection o.f sorne structural remedies now applied to
boundary cornections that failed because of cracking and to the adop-tion of other soluadop-tions which follow logically from experimental evi-dence. Cuite often for instance a cracked bulkhead to double bottom connection is replaced by one more rigid (especially in case of cor-i' rugated bulkheads) where it should be made more flexible. There ought
not to be a large difference in rigidity between two connected
struc-tures as it will be the less rigid that will suffer most unless the connection is made wholly flexible.
The need for understanding interaction mechanisms is growing now that there is an increasing tendency to lihten structural scantlings part-ly out of the desire to save weight and partpart-ly because of improved techniques reventing corrosion. Local damage such as cracking then becomes a serious matter that must be prevented. Furthermore the in-fluence of low cycle fatigue effects will grow and they always become manifest at the boundary regions where high stress concentrations
ex-ist.
Considering all this it would be advisable if, in the course of
expe-rimente wether- elastic or iastic, special anid intensive attention is
paid to the strain distribution in the boundary regions. Even if the connections should not be "realistic" nor the loads "actual" the ex-periments may lead to improved structural thinking and these are the reasons why, in the Deift experiments described later, soecial
atten-tion is being paid to the bulkhead's bottom and top connecatten-tions as well as to the stringer connections. It is hoped to reoort on these matters in
1967.
Until now deflection have been important only when buckling or local failure through buckling constituted the design criteria. This how-ever may change as is evidenced by the attention now given to large deflection analysis. Experience has shown that deflection calculations are even more sensitive to errors in assumed boundary conditions. It will be clear from what has been stated before that here also the so_ lution lays to a large extent in the gathering of factual data.
Corrugted - and swed ed nlatin.
A review of pub)ished work since the
1964
I.S.S.C,Since the
1964
Congress several renorts have become generally available covering various kinds of loading and different types of corrugations. 1n the following paragraphs the reports will bediscussed briefly.
Corrugated bulkhead, hydrostatically loaded in the elastic region.
The experiments in the elastic range on a full-scale shallow-troughed corrugated bulkhead in the Ehip Structures Laboratory in
Deift culminated in a paper (i)* and a mort (2). The bulkhead is ? part of a testing tank for watertight bulkheads which has been
ful-ly described in the Proceedings of the I.S.S.CO
1961.
Briefly itmay be stated that the experiments are part of a series with the
following general objectives.
1) Investigating the behaviour of bulkheads under distributed loa-ding; first in the elastic regio, finally in the plastic
re-gion.
3
2)- Verificating simplified theoritical methods of calculation.
3)
Comparing whenever possible laboratory exer4.rents andmeasure-ments on board of ship(s).
.4)
Investigating the application of computer-assisted methods ofcalculation.
The publications (1) and (2) report on part of sub 1) and sub 2). Experiments on a deep-troughed bulkhead subject to the same part of sub 'i) and sub 2) have been carried out and in connection with sub 4) will be reported on early in 1967. For further details see
the section on future work and papers.
One of the methods mentioned under sub 2) has been published by Jaeger et al (3). The main conclusions in connection with the
ulation of maximum stresses, obtained so far are summarized be-low.
The bulkhead can be considered as a group of identical and identically loaded continuous beams on rigid supports.
The rigid supports mentioned above are realised by the
strin-gers.
As long as nothing more definite about the degree of fixation of the beam's ends is known these ends should be considered as simply supported
Transverse bending stresses can be assessed by considering a strip of unit height across the bulkhead as a continuous beam on rigid supports (the folds of the corrugation profile). Cohtratjon causes no additional transverse stresses.
The first of the conclusions is also supported by analysing experi-mental results obtained by Skjeggestad and Bakke (+).
As regards sub L) this subject will be dealt with in the section on
computer methods. Here it is sufficient to state that a method of
analysis as already used in the aeronautical sciences has been
a-dapted by Smith
(5)
and can be applied to corrugated bulkheads.Corrugated bulkhead, under distributed load, in the plastic region.
The test arrangement is shown in figure 1 which has been taken from
(Li). The end-connections of the corrugations have been supposed as
simply supported. The scale of the model was 1:3.7e the scantlings being in accordance with the rttles of Det Norske Ventas. The lat-ter does not allat-ter the fact that the stringers are so heaviiy dimen-sioned that the test piece may as well be considered as three test
pieces in one. Strain values were obtained by means of electric wire resistance strain gauges with a filament length of 1G mm.
The loads that were to produce plastic hinges in the corrugated
I
beams have been calculated for either bending only or shear only. From the two values thus obtained, limit loads were calculated for the case of combined bending and shear. The experimental results agreed better with the load value for the case of bending only
(this was the highest), a fact which the authors attribute to
After severe plastic deformation caused by buckling the first
cracks appeared at a load sorne 60% higher than the one at which
extensive yielding had taken place. After repairs had been effect-ed serious cracking occurreffect-ed at a somewhat higher load and the ex-periments were discontinued.
Cracking began in the tension flange of the corrugation profile in
way of the intersection with a frame, later on cracks appeared in the centerpanel near to a stringer. This is just what can be ex-pected.
During exneriments within the plastic region the model was at times completely unloaded and then reloaded. The load-deflection curves show a practically lineair behaviour of the structure.
Local buckling of the individual late panels did not occur in the elastic zone owing to the dimensions of these panels.
* It must be stated finally that the stress concentration values can
be but indicative, what with a scale factor of
3.7
and a gaugelength of 16 mm on the model.
Corru,ated and swedged platin, in deckhouse side walls.
Although already dealt with in the 1961+ report of I,S.S.C.
commit-tee 3c on superstructures the following is included because it deals iith experiments which should verify certain theories on
elastic analysis. The reference becoming generally available in
196k.
More work has been carried out in this field by Japanese scientists but no papers in English are as yet available.The Society of Naval Architects of Japan has published in
(6)
theresults of theoretical and experimental studies concerning the bending of ships' deckhouses and superstructures including those with corrugated or swedged plating s side walls.
The writers make use of the following definitions.
i) A vertically corrugated plate is one where the corrugated pro-file is placed vertically. This is contrary to common practice
where this type of plate is called horizontally corrup;ated
be-cause the corrugations proper or fold lines are positioned
ho-ri zontall.
-6-description of a horizontally corrugated plate.
2) No distinction is made between corrugated and swedged plating.
In order to avoid confusion the more common definitions will be used in what follows.
The use of corrugated or swedged plating as sides of deckhouses or superstructures has some very attractive aspects because of the or-thotropic characteristics of these structural elements (see figure 2) and because of their relatively light weight.
In the case of figure 2-A the theory is not developed oh the basis
' of the orthotropic plate but on that of the flat plate element
con-sidered as a beam loaded in its own plane and imposing only shear forces on the adjoining elements.
From the theory it can be deduced that longitudinal stresses from the hull are not transmitted to the deck forming the top of the
deckhouse.
It may be necessary to support these side walls with vertical stlf-fen-; if so, care must be taken that the advantage mentioned abo-ve il1, not be wholly lost. This is realised by not connecting the
lo'est corrugation trough (or swedge + part panel) to the
stiffe-ner.
The case of figure 2-B is divided into two elementary problems
viz.:
The deckhouse is subject to tension only. The deckhouse is subject to bending only.
As regards a) tension in this case means shear and although the
ef-fect of shear lag is not considered it appears to be taken care of in the use of an effective width.
Concerning sub b) this type of plating does not have very much re-sistance against the bending moments shown in the figure and neither has the deck, so that the tOt&lstructural resistance against bending is taken as nile
In all cases expressions for the effective area and moment of ine-tia of the deckhouse are given. (These relate of course to bending of hull and deckhouse).
Experiments with models,
Although in the theoretical part deckhouses are mentioned practi-cally to the exclusion of superstructures, the experiments deal solely with superstructures. However the latter may be considered as a special case of the former, to wit a deckhouse extending from side to side is a superstructure.
Three testpieces had suerstructures with horizontally corrugated
side walls, one where the walls were no-t stiffened, one with
ver-tical stiffeners without a connection to the lowest corrugation trough and one where the stiffeners were attached over their whole length. For all models the superstructures were 1000 mm long, 400 mm wide and 110 mm high. The corrugation angle was 90° and all
pa-nels were 10 mm in breadth. Plate thickness was mm while the stifferiers were
.8
mm thick.Correspondence between model experimental results and theoretical calculation was very good and as long as the stiffeners (if any) are not attached over their whole length the stresses in the super-structure deck are effectively reduced.
One model was tested with vertically corrugated plating, the dimen-sions of the superstructure being 1000 x 400 x 205 mm with a plate
thickness of 1.6 mrn The load was one of pure bending applied to
the hull.
The originally calculated values heavily overestimated the stresses in the superstructure deck. In the theory the magnitude of these stresses is mainly governed by one parameter which in turn is de-'pendent for the most part on the type of end connection assumed for
the corrugated beams or their plate panels. A recalculation of the
t
parameter based on a more realistic assumption of the end connecti-ons resulted in much improved values which were however somewhat lower than the observed ones.
A final adjustment of the relevant parameter led to satisfactory agreement. It would be interesting to know if the end connections which resulted in the correct parameter values will be correct in
other Cases.
Shipboard measurements.
After the model experiments discussed above measurements were car-ried out on the deckhouse of a submarine chaser subjected to a sagging moment when drydocked. The sidewalls in this case were
ver-tically swedged, the swedges being of a traDezodal shape.
The calculated stress values in the deckhouse top did not agree very well with the measured values because the deckhouse was not situated symmetrically about 5 L and because part of the wall
con-,sisted of flat plates. lso the deckhouse wEis less effective than
was assumed.
An analysis of stresses measured In the swedged plating confirmed the basic assumptions of the theory namely shear loading at top ard deck and behaviour as a group of columns. (see figure 2-B). If a proper effective shear modulus could be established the theo-retical method will give satisfactory results.
It can be concluded that the calculation of stresses in corrugated and swedged plating subject to one sided shear loads can be carried out satisfactorily. Comparison with Norwegian work on the same or related subjects is not possible owing to the confidential nature of the relevant reports.
Future work and papers.
Corrugated plating.
As mentioned before the work on corrugated p1atin Delft has
been continued. The experiments have been augmented by a series where a constant and equally distributed load was imposed on the
corrugated bulkhead. Special attention has been paid to the regions near the stringers and the deck- and bottom connections. Reports will be published in 1967.
The stringers themselves will be extensively experimented iipon In
the future.
weed piìting.
In the Engineering Structures Laboratories of the Imperial College
in London tests have been carried out on Standard. Mansard Al-alloy
sheets to study the applicability of ort'hotropic plate theories on
small and large deflections. Experiments with a uniformly distri-buted load applied to the concave side of the test pieces, which were simply sunported along their boundaries, have shown close ag-reement with the theory. The effect of loading the convex side of
th testpioces is being investigated.
IO
-L1T OF TFERENCES.
(i) Jaeger, N.E. and Van Katwijk, P.A.
"Vrificatíon Exp6rimena1e d'une Mêthode de Calcul de Cloi-sons en Thies Ondulées à Plis Verticaux".
Association Techn. et Mar. et Aéro. Cession
1965.
Jaeger, H.E, and Van Katwijk, P.A,
"Stress and Strain Diatribution in a Vertically Corrugated
Bulkhead".
Netherlands' Research Centre T,N,O. for Shipbuilding and
Navi-gation, Shipbuilding Department. Report No.
73S.
(Intern. Shipb.
Progr.-133 (1965) pp 353
and following).Jaeger, H.E., ]3urghgraef, B. and Van der Ham, I.
"Investigation of the Stress Distribution in Corrugated Bulk-heads with Vertical Troughs".
Netherlands' Research Centre T.N.00 for Shipbuilding and
Navi-gation. Report No.
15S.
(Intern. Shipb. Progr. 2
(1955)
pp3-29).
(k)
Skjeggestad, B. and Bakke, E."Corrugated Bulkhead Laterally Loc1ed to Ultimate Failure".
S.F.I. rapport nr.
R57.
Jan.1965.
Smith, C.S
"Elastic Analysis of Stiffened Plating under Lateral Loading". PreprintR.I,N.A.
Wi8 (1965).
60th Anniversary series. Vol. 9.
Published by the Society of Naval Architects of Japan.
o 'D 1:
o o
In in Li
I 'I, TESTING TAMKI
PL 3mm u.- A 160x8I'
D/
I 1111 lI IJI
.'238 220BULKHEAD MODEL AND TESTING TAI<
6. 5
J. 80'c80x9
160,t6-.-L 20x200
A A
SECTION THROUGH BULKHEAD
UNITS IN mm ) AT A CORNER (UNITS IN mm)
MODEL SCALE :1:3.7
FIG. i
Copy taken from S.F. I. Rapport nr. R 57. Jan. 1965
"Corrugated bulkhead laterally load.i to ultimat, failure
SKJEGGESTAD, B. and BAKKE, E.
p DÌ 'D 'I Q PL1O 3S 1280
-r---
is 940 1100 940 10 BULKHEAD MODEL 10 D O D BULKHEAD MODEL D0-HORIZONTALLY SWEDGED OR
CORRUGATED NFIG.2
VERTICALLY SWEDGED OR
CORRUGATED.11
-Unfairness and Distortions of Stiffened Plates.
In previous proceedingst this committee paid attention to initial unfairness and distortion of stiffened plates and made it clear how the problem of obtaining useful practical knowledge about the order of magnitude of these deviations is comr)licat.ed by the large number of variables involved and the enormous amount of data that is required before any statistical study can be made.
So it may be sorne time before oxrresslons with which to calculate
the probable unfairness or distortions of a given structure will be a reality. The Shipyards themselves can assist in dealing with this ìroblem if they were to gather as much data as possible from their own structures. In this way such, imponderables as production methods, workmanship, welding techniques etc. might be neglected so that the problems regarding the relevant parameters could be some-what clarified.
As it is not possible to eliminato the deviations altogether it is only sensible to learn how to minimise them so that they may be neglected and/or how tó work with thi.
By now th importance of initial distortions is
generally
recogni-sed but in most papers on experimental work and its results they are not mentioned unless it is to explain discrepancies with the theory that can nct be accounted for otherwise and again in most cases they have not been measured beforehand.
As long as no definite facts or figures can be given concerning
ac-tuai initial unfairness or distortion of orthogonally stiffened plates and yet if more is to be known about their influence on strength characteristics all laboratory experiments should start with establishing the distortions of the testpieces. Once they are known it may be possible to assess their influence in order to avoid unpleasant surprises especially when loading beyond the elas-tic limit. If no qualitative estimate is possible then danger spots may be put under obsrvatiori either intermittently or continually for the duration of the experiments. This way the behaviour under
I
* See
especially the Proceedings of the 2nd I.S.S.C. 1964, pp
12
-increasing load of the particular spot becomes known. and Can be
studied, while at the same time warning is given in case of a deve-lopment which may endanger the whole experiment such as a premature local collapse that may trigger an overall co1lapse. Papers on ex-perimental work abound with remarks concerning unsatisfactory re-sults due to initial deformation, but quite often no more pirtinent
information is given.
Furthermore the inclusion of measuring t1* initial unfairness when-ever practicable and possible will provide factual experience Con-cerning questions as to if and when distortion may be disregarded or may be used to advantage or nuct be reckoned with. This may seem a bit far-fetched but it is well known for instance that in case of a laterally loaded orthogonally stiffened plate the overall elastic bending moment and shearforce distribution is not noticeably influ-enced by the normally existing unfairness or distortions. (Here
dif-ficulties are almost always caused by insufficient knowledge about the correct boundary conditions).
However as soon as stresses must be derived from these moments and forces, that is when the structural dimensions become comparable with those of their deviations, the influence of distortion or
un-fairness will become manifest.
Quite another type of :-1tial deformation is caused by the
assem-bling of urefabric-'ted eletients, either because of simply welding
te sub-assemblies toether or because of making them fit together. the latter cause may lead to distortion of whole sub-structures, especially if these consist of stiffened plates or corrugated
pla-tes (see figure '1). In most cases this results in a built-in
pre-disposition towards a certain mode of collapse because these
ini-tial deformations can be of considerable magnitude.
In practice one will have to deal with the finished structural
as-sembly and therefore with a combirotion of the two kinds of devi-ations discussed above. As std before the best that can be hoped for is that in tirie it will become possible to minimise a1' types
of size or shape deviations so that tier mf' hence may be neglect-ed. Until such a time a solution may be ound in establishing a
a
13
-practical upper limit value or an average value for the distortion
based on data. made available by the Shipyards (and) or
Classifica-tion Societies. If the number of data obtained per Shipyard is suf-ficiently large for a statistical analysis then it might be possi-ble to establish separate limit or norm-average values, otherwise
this may be tFied for a group of yards in the individual countries as it is thought that workmanship, production methods etc. (see above) will not differ much among the large yards in one country. As to the number of relevant parameters methods must be found by which they can be grouped together to form new ones, for instance an area number might be defined as A
hs
and athick-t (sect. area)
ness number as T = s; the meaning of the symbols is given in
fi-t
p
gure 2. Separate studies could be devoted to structures with
sym-metric or a-symsym-metric stiffeners, alternatively the type of weld-ing current could be used to distweld-inguish groups.
It is not intended to propose complete prOgrammes, the above are
merely suggestions that may contribute to solving the problem of
unfairness and distortion in ot±ffened plates. The assistance of
the shipyards in this natter is essential, in the first place
be-cause ultimately they will profit the most when the problem is
sol-ved and secondly because no structural research institution can
affordto empIióya team of technicians for the sole purpose of
gat-hering the enOrmous number of data that is needed. Measurements can
be carried out with the help of relatively simple instruments and '
the accuracy need not be better than 0,5 mmj,
Finally it should be realised that the refinements of stress cal-culation theories need not go beyond the accuracy of the combined production and strain measuring techniques, since the latter
t s
r
s = frame spacmg.
hheight of stiffener
tp = plate thickness.
tsthickness of web
FIG.1.
DISTORTION OF A CORRUGATEDBULKHEAD CAUSED BY MAKING lT FIT BETWEEN THE COLUMNS.
y
I
tp
