REPORT No.
NOV. 1969
SSL 146
SHIP STRUCTURES LABORATORY
DELFT UNIVERSITY OF TECHNOLOGY
INTERNATIONAL SHIP STRUCTURES
CONGRESS 1970
REPORT OF COMMITTEE 5:
"STIFFENED PANELS IN 3-DIMENSIONAL STRUCTURES"
REPORT Ño.
SSL 146
NOV. 1969
SHIP STRUCTURES LABORATORY
DELFT UNIVERSITY OF TECHNOLOGY
INTERNATIONAL SHIIP STRUCTURES
CONGRESS 1970
REPORT 0F COMMITTEE 5:
"STIFFENED PANELS IN 3-DIMENSIONAL STRUCTURES"
4th INTERNATIONAL SHIP STRUCTURES CONGRESS. September 1970,
Tokyo.
Report of Committee 5
uStiffened Panels in 3-Dimensional Structures".
Committee Members: Ir. P.A. van Katwijk (chairman) Dr. N. Ando Mr. P. Campus Mr. P.F. Lindemaim Mr. J.I. Mathewson Mr. J. Saethre Mr. G.O. Thomas Prof.Dr. M. Yaînakoshi
Issued by the Ship Structures Laboratory, Mekeiweg 2, Deift 8,
Contents.
I Introduction.
II Finite Element and Finite Difference Methods (F.E.M. and F.D.M.).
III Review of Theoretical and Experimental Work.
IV Transverse Strength.
V Methods of Analysis and Optimization for Use in Design. VI Service Loads on Ship and Marine Structure.
VII Conclusions and Recommendations. Reference List.
Introduction.
In March 1968 the committee suffered a serious loss when its chairman Mr. J. Ciarkson passed away in a regrettable accident. The work had to start without the capable leadership of this amiable scientist. His conviction that it is the scientist's duty to extract as much as possible practical information frOm his findings and to present this in an uncomplicated manner will continue to be reflected in the.work of this committee.
The committee met in Delft in September 1968 (all members from Europe attending) to discus.s the business at hand, subsequent work has been carried out by correspondence. This report is the result of a common effort, all members having contributed within the limits of the time at their disposal.
Since the previous committee reported to the 1967 International Ship Structures Congress in Oslo, there have been issued so many papers and
reports daling in one way or another with stiffened panels that it is
impossible to discuss or review them all, consequently the material used in the present committee report is that which was readily avail-able to the members. Papers and reports not mentioned in this report but known to one or more of its members are listed separately.
It has been considered useful to include a number of references (/1,1/ - /1.20/) having an introductory nature in the sense that they provide. general or elementary information concerning subjects related in one way or another to those discussed further on. These references reflect as it were how the subjects divided amongst the International Ship Structures çongress' technical committees are inter-connected and at the same time they may explain why in this report these subjects had to be discussed albeit briefly and only from the point of view of this committee.
On a limited scale the subjects of marine structures (drilling plat-forms etc.) has been introduced in some sections of the report, notably in the one discussing service loads. It is recommended that these sea-going structures be considered as a special type of ship and that they be treated as such by the technical committees of the International Ship Structures Congress. Alternatively a committee on Marine Struc-tures might be appointed.
Apart from the introduction the following sections are presented:
Finite Element and Finite Difference Methods (F.E.M. and F.D.M.). Review of Theoretical and Experimental Work.
Transverse Strength.
Methods for Use in Design and Optimization. Service Loads on Ship and Marine Structures. Conclusions and Recommendations.
In the section on F.E..M. and F.D.M. attention is paid to thé problems of finding suitable models to represent the actual structures..
Section III includes a discussion of work carried out in the elasto-plastic and elasto-plastic regions of steel, but it must be realized that generally the use of purely plastic design methods in obtaining the scantlings of ship structures should, be avoided because. these methöds can not be applied to dynamically loaded structurés. At the most
meth-ods based on a.limited amount of allowable pastic strain could be
used as has been siggested by I+ibbering /1.6/ (p. 861). Strictly speak-ing transverse strength should not be regarded as an independent corner
2
of the entire field of ship structural strength problems. There are however reasons to discuss the transverse strength problem separately
andthe most important one is that sincethesecond International
Ship Structures Congress in 1964, considerable efforts have been spent on the development of satisfactory methods of analysis.
In generalit must be stated that the develOpment of methods of
anal-( ysis, automated or otherwise, has progressed enormously and this has
led to the formulation of the part of this committee's mandate reading "To recommend methods of analysis for use in design".
As a direct consequence section V came into being and it is in connecT. tion with this section that the committee had to venture across its
own work boundaries into the fields of other committees.
Closely related to sections IV and V is number VI and.much effort has
been devoted to gathering and reviewing the available infcrmation con-cerning the actual service loads on ship and marine structures.
It stands to reason that the application of the presently available sophisticated methods of stress and displacement analysis will be fully effective only if the correct loading conditions are known, particular-ly where detail anaparticular-lyses are concerned. It will become clear that the factual knowledge regarding the service loads is very limited still, despite the significant progress that has been made in this field. Virtually nothing is known for instance concerning the phase relation-ship between longitudinal bending moments (vertical and horizontal), the torsional moments, the transverse hydrodynamic loads and the vari-ous acceleration-induced inertia forces. The last mentioned may be of
considerable local signIficance. Admittedly the problem is complex to the extreme, nevertheless even the gathering of limited factual data as for instance Hagiwara /VI.6/ has done is highly important quite apart from serving the purpose of making designers realise how little is ac-tually known and how approximate are the static loads now commonly used in strength calculations. In this context it should be noted that a capacity for carrying high nominal static stress levels has no relation with the possible danger of fatigue cracking that may result from lower nominal dynamic stress levels..
It was to be expected that the work of this committee in connection with its report should lead to some conclusions and disclose the need for new and continued research work, matters which are discussed in the last section.
Finally it must be noted that while the International Ship Structures Congress is the result of the desire (and need) to provide experts in the field of ship structural strength of various countries with an
op-portunity to meet and to discuss their problems, the committee is of the opinion that the reports to the Congress should be informative to both the specialist and the interested shipbuilder or naval architect.
II. Finite Element and Finite Difference Methods (F.E.M. and F.D.M.).
Finite Element Methods (F.E.M.).
Since the latest International Ship Structures Congress report consider-able advance has been made in the application of F.E.M. to the invest-igation of ship structures composed of stiffened panels.. Although most published work to date has been largely concerned with elastic static analysis it has been demonstrated that the F.E.M. may also be extended to non-linear and dynamic (vibration) problems. The present state of the art with particular application to ship structural components is adequately covered by the papers presented at the Symposium on Finite Element Techniques held at Stuttgart University in June 1969 /11.1/ -/11.11/.
It is evident from the papers and the discussions of this symposium that the F.E.M. are now firmly established in the shipbuilding industry as a necessary prerequisite to the satisfactory design and development of .ship structures, particularly those of large tankers bulk carriers, open ships etc. The type of problems which have been treated by the F.E.M. may be summarized as follows:
2-Dimensional Problems
3-Dimensional Problems
Plane Stress Problems
Plane Grillages Deckst Bulkheads,
1Side & Bottom Shells
Plane Frames Heavy Transverses
Tanker s
- Bulk Carriers - Open Ships - Warships
Drilling Rigs and similar structures
Bracket Connections Deep Web Girders Stress Concentrations
The general conclusions arising from this work are summarized below:
a) Until now the bulk of the successful ship structural analysis work has been achieved by utilising only three basic elements:
Uniform beam element.
Constant stress triangular plane stress element. Linear stress quadrilateral plane stress element.
b) There are in existence a number of programs available to the
design-er which will handle such elements in the elastic range, whilst a limited number only are available which extend to the non-linear field and include dynamic response..
c) The more rapid acceptance by the designer of the F.E.M. as a design tool is inhibited principally by two factors:
1) The physical size and complexity of certain ship structural
components in relation to the computer facility available. Such a case may arise in the 3-dimensional analysis of ship structures extending over a considerable length of the ship. In such a case Smith /11.2/ recommends physical partitioning by means of substructures.
L
-2) The considerable time and effort inherent in the preparation of input data in most finite element programs and in the
interpretation of their output.
Some remarks must be made regarding these conclusions:
ad a) The choice of elements having simple stress functions is a very attractive one since it results in a limited demand for storage space in the computer when dealing with a structural model containing many nodes. For a nominal stress analysis the application of these elements will give satisfactory results as long as plate bending stresses do not occur or may be dis-regarded. In some cases however the plate bending stresses must be known as for instance in the case of oil tight bulkheads where transverse plate bending stresses may be much higher than the longitudinal beam bending stresses (the plate acting as
flange to the stiffening member).
When analysing dynamically loaded structural details, local plate bending effects should not be disregarded since they may
cause very high plate surface stresses and if these occur in fatigue sensitive spots conditions for the initiation of cracks may be favourable.
As yet there is no known information concerning the analysis of ship structural details by the application of F.E,M. using elements with more advanced stress functions.
ad b) When using a ready-made program the designer should thoroughly familiarize himself with the type of mathematical model used to represent the structure and with the assumptions underlying the choice of this model in order to arrive at a correct interpre-tation of the compuinterpre-tational results. The userts manual should contain all the necessary information.
ad c-l) Some problems connected with the selection of a suitable. model will be discussed below.
ad c-2) The expenditure of considerable time and effort in order to prepare the input data is an oft mentioned disadvantage of the F.E.M. To a large extent it may be neutralized by the develop-ment of data generating routines. Some as discussed by R$ren /II.L/, /11.12/ involve routines requiring a minimum input and they are tailored to specific recurring structural analysis prob-lems such as for instance transverse tanker frames. Another
more general approach utilizes a family of standard mesh ideal-isations in which the super nodes at the connecting boundaries need only be specified.
Another time consuming effort is involved when the printed out-put has to be analysed by the user who, after getting rid of all the information serving the purpose of checking in one way or another items like input data, the process of calculation
and so on, is facing large amounts of figures denoting coor-dinates, stress-values etc. that have to b.e evaluated. It will undoubtedly increase the attraction of the F.E.M. programs if
the output can also be presented in the form of graphs, show-ing the distribution of the relevant parameters. It is true that plotting programs although basically simple, require much storage space in the computer but the resultant saving in out-put analysis time will certainly justify the sacrifices in-volved.
Structural Models.
The problems associatéd with the selection of a suitable model to
rep; -rt the actual structure have been discussed amongst others
by Smith /11.2/, /11.13/, Gallagher /11.3/, R$ren /11.1-î,, /11.12/ and Moe /11.5/.
Generally the selection of the model is governed by the type of the
loads acting on the structure and by the required information on the structural response. to these loads as well as by the capacity of the computer employed. As a rule it can be stated that simple models suf-fice whenever the required information is limited to overall response. and that the more detailed the required information, the more accurate the model must be.
This can be illustrated by considering the manner in which a trans-verse strength calculation for a large tanker may be carried out., First the entire length of the cargo tank section (or a sufficiently large part of it) is analysed in order to obtain correct boundary conditions for a stress analysis of the transverse frames and - wash bulkheads. The model in this case is a spatial framework wherein the principal longitudinal and transverse strength members are represented by beams.. The required information is restricted to the generalized
forces and displacements at the nodes, which together with the local
loads are needed in the next step - the analysis of the transverse mem-bers. It is tempting to use a beam model for the heavy transverse web
frames but considering the large brackets and the short, deep plate girders out of which these frames are fashioned, one can hardly expeét
a beam model to. be. satisfactory.
RØren /11.12/ remarks that many deep transverses show more resemblance to plate panels with large cut-outs than to beams and he goes on to discuss the problems connected with the beam model in this case, notably with regard to system lines, joint regions, effective shear area, effect-ive flange and stress distributions. He comes to the. conclusion that a finite element model using plate and beam elements is to be preferred. Moe ./11.5/ discusses comparative analyses concerning the bending moment distribution in a transverse web. Three models were involved, one finite element model and two beam models, the latter differing individually in the selection of the system lines, one having the nodes placed at the intersection of the plate flanges and the other having the nodes at the intersections of the neutral axes. For both beam models the joint
re-gions were considered rigid.
The agreement in bending moment distribution between calculations based on the finite element model and on the. beam model with the flange-based system lines appears to be good for practical purposes. No mention is made of the shear force distribution.
Another comparison between calculations based on different models in-volved one beam model based on Yamaguchi's span point method /11.14/, one variable section beam model and one finite element model, the work being carried out by Nagamoto et al. /11.16/, The study concerns the displacements and rotations at the end of a girder structure subject to
end loads and also the stress distributions resulting from the loads. The large brackets are analysed with the curved beam theory, a wedge theory and a finite element method utilizing triangular plate elements, From figure 11.1 it becomes dlear that in order to obtain the same.
generalized displacements for the finite element model and the span point beam model the latter requires two .different span points for
bending and shear loads and that neither coincide with the theoretical
span point. In the case of the variable section model three different c-values are needed to accomplish agreement with the. finite element model results. Although it.is possible to use a single value for S/Som
and S/S and also one for c that will give reasonable agreement
o
M 5 ¿ 3 2 06 08 10 12 14 SI l5omSam Span point for bending.
b(F.e.m.)
-Ø3 t
0.6 0.8 1 12 1.4
S/
I S0
Span point for shearing.
60 50 40 30 20 10 E E V C a, o 4-C V E a, u o 120 110 100 go 80 70
Comparison between beam theory analysis with span
point and finite eLement technique.
-6
(F.e.m.) Finite element method.
FIG. . 1, COMPARATIVE STUDY BY NAGAMOTO ET AL.
(fig. 6 &7 from [.16)
these values are dependent on the structural configurationand they
will differ from case to case so that a finite element model is to be preferred. The advantages of the latter become even more evident if
the stress analysis of structures like those of figure 11.1 is con-sidered, for then the complete analysis from loads to stresses can be carried out in one continuous operation on one type of model, whereas the other methods require a sequence of models with the possibility of n accUmUlation of errors. Tlìe use of a fiñite element model may be limited because of the available storage space in the computer;
so to avoid excessive storage demands Nagainoto et ai.,
/11.16/
devel-oped a method of analysis based on the hybrid model shown in figure 11.2, which appeárs to give satisfactory results although the system lines coincide with the neutral axes of the girders.Finally these authors presnt, a number of conclusions, many of them practical and useful for designers. From the.point of view of struc-turai model presentation they state that it is necessary to take
ac-8
Comparison between beam theory anotysis with
variabLe section and finite element technique. 60 50 40 30 20 10 E E
Structural pattern
JE
'
4
-S
of new rigid frame caLcu'ation
F
/
Member force and deformation.
o
oy
combined with finite element technique.
FIG. 11.2, HYBRID MODEL ( after
ref. [iL.16],fig.25)
MEMBER () IS FINITE ELEMENT PART.count of the secondary (i.e. transverse) stresses in the relatively wide flanges of curved brackets or of the curved parts of brackets. This implies the use of plate bending elements in the flange repre-sentation3 or separate corrections to flange stresses in case beam elements are used.
It must be remarked that in frame work models the connections between the beams are assumed to be rigid and while this is generally true, the designer should be aware of the fact that non-rigid joints may be encountered; non-rigid in the sense that the plane of the connection does not maintain its shape when subjected to forces. This can occur generally in joints of stiffened plating (plane or tubular) where in-sufficient attention has been paid to ensuring the continuity of the stiffening, for instance in marine structures Where two or more tubular plate beams are interconnected.
The occurrence of a non-rigid joint has been observed by Jaeger c.s. /111.3.5/ during experiments with a corrugated bulkhead, where the reduc-tion in the (beam-) bending moment value at the joint was of the order of magnitude of 30%,
Flexible joints in themselves are not object,ionable but they may cause inadmissable rotations and displacements, furthermore they also may produce highly localized bending stresses which may be of consider-able magnitude. If nominäl compressive stresses, acting in the same direction as the bending stresses are present local buckling may oc-cur. In case of dynamic loads being imposed on the connection the bend-ing stresses occurrbend-ing as they do very close to welds, are definitely undesirable. it is commendable. therefore in case of doubt to carry out an analysis of the joint in question by means of the finite, element
8
method, using elements suited to plate bending and if necessary to in-plane loading.
To the knowledge of this committee such elements have not yet been applied to detail anai.ysis of ship and marine structures. It is
re-commended that this application be investigated, especially as the use of special steèls may introduce thinner plates which will be more sensitive to local bending. Plate bending elements require far more storage space than the constant or linear stress elements and for this reason their application will have to be limited to struc-tural detail analyses.
In general the efficacy of a finite element model of a plate struc-ture depends not only on the configuration of the strucstruc-ture and its loads, but also on the shape of plate element used, on the stress or displacement function assigned to it, on the representation of the
loads and on the fineness of the mesh employed. Very iteresting
in-formation concerning this subject can be found in the results of com-parative studies (based on convergence and error percentage) by
Gallagher /11.3/ in connection with instability analysis and by Clough c.s. /11.17/ regarding plate bending analysis.
An application of the F.E.M. that has not yet been discussed is the analysis of heat flow in a structure. Considering the increasing num-.
ber of ships being built to transport liquefied gases or heated liquid cargos, methods of analyzing the heat flow and the ensuring thermal deformations and stresses may be required. Visser /11.18/ has devel-oped a finite element method, based ön the displacement technique to establish the magnitude of the time dependent temperatures in a set of distinct points of the structure. If the division in elements is maintained the determination of the thermal deformation is a natural sequel to the previous calculation. The thesis contains a section in
which amongst other subjects are discussed the reduction of input data and the checking on the accuracy of the solution. A number of examples is given. The application of the method is limited to linear systems and structures that may be divided into plane elements.
Finite Difference Methods (F.D.M.).
Although a major portion of the efforts to develop satisfactory methods of analysis is being directed towards the F.E.M. attention is also be-ing paid to the possibilities offered by the finite difference methods (F.D.M.). The range of application of the F.D.M. has been discussed in the report of committee 3b ("Stiffened Parels in 3-Dimensional Struc-tures") to the International Ship Structures Congress 1967 /1.4, pp.. 143, 144/ and need not be repeated here.
A recent work involving non-linear effects has been presented by Weiss
/11.19/ who has solved the differential equations of non-linear plate theory with the assistance of an improved difference method, the multi-point method, after its extension by the use of a rectangular lattice. The calculations were carried out on the TR.4 computer of the Hamburg University and for each load condition 6 to 8 iterative steps were nec-essary. The solution is given for a continuous plate on simple supports having infinite shear stiffeners along the edges. Rectangular and square loaded areas of diffe'ent sizes in the pánel centre and aspect ratios
of 1, 2 and 3 are considered. Maximum deflections and stresses are pre-sented in non-dimensional graph form suitable for design purposes. The analysis was corroborated by experiments on both aluminium and steel
y
a. RectanguLar pLate with built-in edges
uniform pressure.
FIG. ,3. ( ref.
Setoguchi c.s. /11.20/ point out the analogy between the basic differential equations for the analysis of:
i) bending stresses in a rectangular plate with all edges clamped and subjected to a uniform lateral
load.-(Figure II.3a).
2) thermal stresses in a rectangular plate without edge loads and subjected to a parabolic temperature distribu-tion. (Figure II.3b).
The authors demonstrate that both equations have the generalized
form:
I4f
3Lf
tff
a+2b
1-cg(x,y).
Xt'
x2y2
aYLfAfter transforming this expression into a finite difference equation, they discuss the latter 's solution by the alternating direct implicit method. Convergence seems to be very rapid and the accuracy of the
solution good.
Concerning the diagonal v.s. orthogonal stiffening against local buck-ling of plate panels subjected along all edges to distributed in-plane and shear loads, the Division of Ship Design, Chalmers University of Technology, Gothenburg., Sweden, is developing a finite difference ap-proach and a program for the calculation of the buckling factors (eigen-value problems). The method is approximate but by calculating three
values of the critical stress for different fineness of the mesh an extrapolation formula may be solved which in the case of convergence gives the asymptotic value Which is much closer to the correct
crit-ical stress value than only one calculation may give.
It is expected that the development of F.D.M. will continue although its application to stress analysis of stiffened panels will probably be limited to local problems.
X
T=02x2+b2y2+c2xy a1x +b1y+c
b. Rectan9utar plate with free edges under
temperature distribution.
10
-III. Theoretical and Experimental Work.
This section has been sub-divided into four pa'ts: Theoretical work in the elastic region.
Theoretical work in the elasto-plastic and plastic region. Experimental work in the elastic region.
L)
Experimental work in the elasto-piastic and plastic region.In the reference list this division is copied and consequently óne reference may appear two or more times in which case a cross-reference is provided.
This system has been chosen in order to present a bit more information than can
generally be obtained from the title of the reference alone. Every effort has been made to apply this system of cross-referring consistently hut com-pleteness cannot be guaranteed.
1. Theoretical work in the elastic region.
The development of the F.E.M. does not mean that other methods of analysis have become outdated or surpassed. In very many cases where only a limited
amount of information is required other methods than the F.E.tI. will be more efficient and less time-consuming. This is particularly true for the local analyses of stiffened panels in case a response to some local lodd is needed.
Some relevant work is reviewed below.
Chang /111.1.1/ considered grillages under normal and axial loads, basing
his analysis on variational calculus and Laplace transforms,. This work was
extended to obtain the elastic stability loads of initially straight orthogonal
gridworks where beam properties, arrangements and boundary conditions are
fair-ly arbitrary /111.1.2/. Furthermore he developed a simple method for the elastic analysisof laterally loaded grillages /111.1.3/ by treating a plane
orthogonal-ly stiffened plate panel as a series of beams on an elastic foundation. He found that by using certain matrix transformations the deflection equations could be uncoupled, resulting in very low computation times rendering the
meth-od suitable for ready application in design. The accuracy of the analysis has
been checked against published results of other approaches and comparison
re-vealed very close agreement. A different method of analysis applicable to
simple piane orthogonal grillages has been developed by Efleby /III.l.L/ and concerns a solution by computer making use of Clapyron's three moment equation.
Approaching the analysis of uni-directionally stiffened panels from another point of view Shimizu /111.1.5/, /111.1.6/ formulated a matrix method based
on a combination of the plate bending and plane stress theory which may be applied to laterally loaded panels with web frames among the stiffeners. The underlying assumptions are:
The plate is stiffened in one direction and the edges perpendicular, to the stiffeners are simply supported.
The ends of the stiffeners are restrained from torsional rotation, but they are free to warp.
Elastic deformation on the cross section of the stiffener is ne-glected.
The originaL theory /111.1.5/ has been /111.1.6/ and experiments were carried good agreement was observed. Analogous oped one to analyse the dynamic stress panel, a subject which is discussed in and Brittle Fracture".
-reworked into a non-dimensional form
out to obtain confirmation. Fairly to this method Shimizu /111.1.7/ devel-distribution in a vibratìng stiffened the report of committee 11 "Fatigue
Mansour ¡III.. 18/ extended Schade's work with an investigation of ship bottom plating under uniform lateral and inpiane loads within the scope of the "linearized (secönd order) orthotropic plate theory". Ignoring shear
deflections, a series solution is found with whichdesign curves have been
calculated. The boundary conditions are taken as simply supported, as clamped
or as a cmbination of these two.
Orthotropic plate theory was also used by Jan /111.1.9/ in order to establish the response -to line shear loads of a box girder with orthotropic enveiope plating. The line shear loads imposed by longitudinal bulkheads (and deck-houses) on the deck and bottom of the ship's hull are represented by a func-. tion based on Dirac's S-distribut±on. One conclusion of this study is that the influence of the longitudinal bulkheads on the longitudinal stress dis-tribution in the flange plating of tfr ship's hull is of a secondary order. for conventional cases. Consequently it can be stated that these effects
can be disregarded when strçsses in stiffened hull panels are analysed.
No information is available regarding the analysis of stresses in large in-dividual hull panels subject to torsional shear. The difficulty lies with the establishment of correct conditions of loading and displacement at the bound-aries of such panels. In order to define these conditions analysis of the en-tire hull would be required and once this had been done a more detailed anal-ysis of the se-1ected panel would follow as a natural sequel. The subject of torsion which is especially important for ships with wide openings in deck and side shell is outside the scope of this committee's mandate arid the. reader is referred to the report of committee "Stress distribution in Hull Struc-ture' and to the list of additional literature.
The analysi.s of stress and deformation in structural details has been carried out successfully by F.E.M. and it is to be expected that these methods will supersede the analytical ones in the near future. For the present however anal-ytical methods are still being developed and often compared with the finite element approach. The work of Nagamoto et al. has been partially discusseä al-ready in the previous section. (Ref. /11.15/ and /11.16/) and it will be dealt with more extensively in part 3 of this section "Experimental work in the elas-tic regioni'. Svanholm c.s. /111.1.10/ have investigated the stress distribution in the plating around a crossing of two orthogonal stiffeners. Both theoretical and experimental analyses were carried out. The plate with the two stiffeners (placed along the lines of symmetry Of the square plate) was simply suppórted at the stiffener's ends and subjected to a concentrated load at the cross-point. For this case the authors found that the stress field is composed of two
orthogonal fields, each one related to asingle stiffener-with-plating
subject-ed to a concentratsubject-ed load. Thus it would be justifisubject-ed to use the full spacing between two stiffeners as nominal flange breadth in spite of the fact that the plating will then be used twice in the same calculation. The authors investigated other loading cases but-. here agreement with the experiments was not entirely
satisfactory. Caution must be exercised in applying the method to stiffened
plates with slender panels between the stiffeners.
2. Theoretical work in the elasto-plastic and plastic region.
The development o.f methods of analysis applicable to structures loaded beyond their material limit of proportionality is a logical and necessary sequel to the investigation of elastic structural response.. A situation where only the latter has been thoroughly explored and where there is uncertainty concerning the elasto-plastic and plastic response leads to the adoption of unnecessarily high factors of safety, the more so if uncertainty also exists as to the know-ledge of the correct manner and magnitude of loading which is generally the case with ship structures. Post-elastic analysis of stiffened panels in ships
is complicated because of the possible occurrence of membrane effects, their influence having been discussed in the previous committee report /111.2.1/. It is to be expected that t.he use of methods of collapse analysis for the de-sign of stiffened panels in ships will be limited to cases where the dede-sign load is clearly defined and can be conside±ed as static. Since the majority
12
-of ship structures are subject to cyclic loading, the development -of meth-ods for elasto-plastic analysis will open up a wider range of application and considerable effort should be spent on the subject. In this connection it must be realized that the analysis should be concerned with strains rather
than with stresses because the amount of straining is important for
cyclic-ally loaded structures.
Radomsky c.:s. /III.2.2/ have stated that: tilt is important to realize that large strains in a structure are not necessarily caused only by Large defiec-tions. Once local yieiLding occurs, it is possible for sirains to becöme con-centrated in that particular region even though the deflection corresponding to initial yield is not greatly exceeded." The authors enlarge upon this
state-ment by discussing the elasto-piastic response of simplebeams (rectangular
cross-section) subject to a number of bending loads. Theoretical relations between maximum deflection and the corresponding maximum strains are estab-lished and they show that in elastic-perfectly plastic material short plastic zones may develop causing large strains in the beam although the deflectjon connected with first yield is not greatly excèeded. Strain hardening however elongates the plastic zones producing a more favourable strain distribution than would occur without it and the more pronounced the strain hardening char-acteristics the less concentrated will be the strain. The influence of the shape of the bending moment distribution on the. strain concentration has also been investigated and it has been found that this influence is considerable in that the higher the gradient of the bending mOment curvê in the region of its maximum value, the more concentrated will be the local strain.
An extension of this theory to rolled sections attached to plates would con-stitute a we]come addition to the means of analysis already availabj.e to the designer. Such an extension need only concern the extreme fibres of the
stiff-ener because the nutral axis of the stiffstiff-ener-plate combination is located close to the plate and it would require unacceptably large plastic strains in
the stiffener's outer fibre before the plate would reach the stage of yield initiation. This has been borne out by experiments on laterally loaded plates stiffened in one direction conducted by Wah /111.2.3/, /III.2,ti-/, /111.2.5/. On the basis of these tests he proposed an analytical procedure describing the behaviour of these structures as far as banding moments and deflections are concerned. Wah defines the collapse pressure as the one where the struc-ture suffers relatively large deflections because the stiffener sections lose
much of their stiffness, which occurs when the stiffeners become plastic at
the centreline i.e. at mid span. An expression for this collapse pressure is presented and discussed.
Wah has also developed a method for the elasto-plastic analysis of uniform
grillages under lateral loads /111.2.6/.. The analysis is carried out by F.D..M. with two discontinuity functions representing the rotation at the
plastic hinges, permitting a complete description of the structure from
initial loading to collapse. The tOrsional stiffness of the beams is neglect-ed and the material is supposneglect-ed to be elastic perfectly-plastic.
Viner ,'III.2.7/ has developed the basic plastic theory for application to the design of ship structural members i.e.. beams, plates and grillages. 1-Je considered these structures under axial load, pure bending and combined
axial and bending loads. Plastic moduli and shape factors for a range of
ship sections in association with an effective width of plating are derived and presented in the form of graphs or tables.
The influence on collapse of strain hardeniñg, shear, torsion and buckling
are all treated. It is concluded that strain hardening effects and torsion
may be neglected in the treatment of most ship structural members whilst the
influence of shear may be accounted for by a correction to the web area when
deriving the plastic modulus of the section. Although the influence of
buck-ling may be aqcounted for in the calculation of the collapse load it is con-sidered preferable for design purposes to require that buckling should not
occur until the strain hardening range is reached. The theory thus presented is then developed to a convènient formulation fOr the design of two basic
13
-Bulkheads with allowance for variable boundary support conditions. Decks supported by cantilevers.
The. design formula for plates has been verified against experimental work by Ciarkson /111.2.8/ whilst the prediction of bulkhead failure is n good
agreement with the experiments carded out by Skjeggestad c.s. /111.2.9/.
With regard to the collapse prediction of cantilever supported decks
reason-ably good agreement has been reached with small scale steel model tests
car-ried out by Lloydts Register of Shipping Crawley Laboratöries.
Another approach to the calculation of collapse loads for cross-stiffened panels has teen presented by Nagasawa c.s. /111.2.10/ who made use of the upper bound theorem. The method was compared with a series of experiments
and it was found that the calculated values for the collapse load were 10 " 50% in excess of the experimental values. The angles of the hinge lines were also computed theoretically and in this case the agreement with the experiment was satisfactory.
It is clear that collapse analysis can be used locally too, in the sense that a single structural member or its details may be subjected to it. A single member for instance can be the stiffener of a watertight bulkhead and an
ex-ample of the application of collapse, analysis is presented by Ross /111.2.11/. The collapse mechanism of brackets has been studied by Campus /111.2.12/ who verified his theory by experiment.
The ultimate strength of deep plate. girders is a subject demanding attention as a result of the increase in the size of ships. Akita c,s. /111.2.13/ have developed an approach to establishing the ultimate strength of girders in
L -the post buckling range.. The structures concerned are subjected to shear loads,
to bending loads or to both. It is assumed that the lateral buckling of the girder is prevented and that local buckling of the flanges will not. occur. The accuracy of the theory is verified with the aid of experimental results published earlier in the U.S.A. and in Japan and it appears to be good. On the basis of their theoretical study the authors conclude that the presently used design criterion of elastic buckling of the web can reasonably be re-placed by one based on the ultimate strength of the girder because the past-buckling strength of the web is very large. They state furthermore that once the relation between the structural dimensions and the ultimate load of the plate girder is established., it will be possible to use this relation for a minimum weight design, adding however that the dynamic .strength of the struc-tures thus obtained must be studied further.
Mori et al. /III.2.1LII studied the shear buckling of web plates and double bottom floor plates mainly experimentally, their theoretical methods being based on adapted existing methods. The investigations were directed primarily to plates having circular or elliptic holes,, in some cases together with slots.
Concerning the theory basedon Stowell's method the authors conclude that it
is possible to estimate to 'some extent the s'crength of plates with openings.
3. Experimental work in the elastic region.
An increasing amount of experiments is being carried out aboard ships instead of in the laboratories and this is as it should be since the available
ad-vanced theoretical methods of analysis require experimental verification under
actually occurring conditions which can best be realized in situ, that is, on board. In the 'laboratories the work will be directed more and more towards comparative experiments concerning the influence of changes in configuration or of systematic changes in .parametrs. Of course the basic research in struc-turai response will be continued and just as fatigue experiments, will remain' inside the laboratories.Generalìy elastic experimental analysis will become a
preliminary to elasto-plastic and collapse analysis or to fatigue tests' because the F.E.M. is expected to replace the independent elastic experiments in most
An example of the complexities inherent inshipboard measurements can be
found in a paper by Schwager c.s. /111.3.1/ concerning a problem-oriented investigation of the stress-distribution in a corrugated transverse
bulk-headaboard a bulkcarrier. The bulkhead was loaded by flooding the hold and
apart from the direct load the ensuring stresses were influenced by the longitudinal bending of the ship, the increase in transverse load (hydro-static pressure on the ship sides) and the forces exerted on the bulkhead by the inner bottom.
The direct load causes the primary beam bending stresses and the local trans-verse bend3ng stresses. In order to 3nsure that a minimum of zero drift should occur special measures had been taken and these were generally successful. The authors commend that in forthcoming cases the full loading be applied a number of -cimes before the data reading actually starts, because in newly
built ships permanent deformations occur locally and these may give the
im-pression that large zero drifts are present.
The experiméntal stresses were cOmpared with the results of simplified cal-culations, the agreement being reasonable as far as tendency and order of magnitude were concerned. It is doubtful if any other theoretical approach
(F.E.M. excepted) would have been more successful because the connections
of the bulkhead todeck and inner bottom (tanktop) were very complicated
struc-turally. Of course steps coul'l have been aken to reduce the magnitude of
stresses cauced by other than the direct, load.. Additional ballasting might
have reducedthe bending moment to its pre-load value, the increased draught,
of the vessel would have reduced the ther loads as well. Temperature influ-ences w2re avoided by the use ofdummy gauges and by carrying outthe.
ex-periments under constant ambient temperature whenever possible. It must be
realized that temperature influences can be a very disturbing factor, thermal
strains may be high and they are difficult tc. compensate or to correct for
afterwards. This is true for full scale laboratory tests as well, butthere
the investigator has a better control over them or he can take steps to ac-quire this control as has been done for instance by Jaeger c.s. /111.3.2/, /111.3.3/ in connection with their experiments on one corrugated bulkhead.
These experiments which were extended to include another corrugated bulkhead
and a plane stiffened one have been discussed in references /III.3.-l-/ and /111.3.. 5/. These experiments, apart from providing extensive information con-cerning the stress and strain distributions in the three bulkheads, showed
clearly the advantages of cross-sectiónally symmetric plate structures and
the penalties for violating this symmetry. In the corrugated bulkheads the beam bending stresses are regularly distributed and consequently the struc-turai material is used far more efficiently than it is in plane stiffened pan-els. The penalties incurred when violating the symmetry of the structures are weil known, witness the unpleasant experience with the one-sided stringers, now happily a thing of the past. Already. brieflymentioned earlier was the non-rigidity of the bottom connection of the two corrugated bulkheads,
re-sulting in a noticeable reduction of the magnitude of the carrying-over
bend-ing moments. This loss of rigidity occurred within the join. itself in that the originally fiat piane of contact became arched under load, mainly because the 20 mm thick bottompiate deflected under the influence of the 7,5 and 6 mm
thick compression flanges of the corrugated beam, while in way of the tension
flanges the bottom plating was restrained because of the structural arrange-ments. The reduction in end bending moment magnitude carried with it an
in-crease in the mid-span moment of the corrugated beam. The amount of in-joint deformation can not be calculated, except perhaps by means of the F.E.M.. Consequently it is necessary to secure the integrity of the joint itself..
This has also been recognized by the classification societies as can be seen from figure 111.3.1 where. the relevant directivesof Germanischen Lloyd are
illustrated for relatively small tank bulkheads, while for the heavier bulk-heads a box girder on the tanktop is recommended /111.3.6/.
The experimentally derived m3ximum equivalent stresses. (according to the
hypo-thesis of Tuber-Hencky) in the corrugated bulkheads were decidedly lower than
in the plane stiffened bulkhead, while the former had 48% and 57'%.of the steel
bulk 15 bulk
-FIG.
.3.1. (from ref.
[iir.3.6j)
heads used by Skjeggestad c.s. /111.2.9/ had a ieight ratio of ito .55 in
favour of the corrugated bulkhead, while the reserve strength after forma-tian of the plastic hinges was approximately 3.25 and 2 times the plastic hinge load for the plane bulkheads and the corrugated one respectively. Finally a remark must be made relevant the strain measuring technìque.
In many cases it is unavoidable that butt welds are present within the loca-tion of the pattern of gauge staloca-tions on plates. These welds can appreciable.
disturb the regularity of the local stress and strain distribution as has been experienced 'by Schwager c.s. /111.3.1/ and Jaeger c.s. /111.3.5/. If this influence is unwanted the welds should be ground down to the plate thickness over a length extending well beyond the limits of the gauge pattern. In his experiments with small scale grillages Ciarkson /111.3.7/ investigated the influence of butt-welds in plate panels subject to concentrated, lateral loads but he found no difference in local panel behaviour. Considering the fact that the welds had been ground flush with the plate surface and that the weld material little overmatched the parent panel material it is not
surpii-ing that no influence could be detected. These tests also showed that very small effective breadths may occur around the centrally loaded panel, the range being given as 10 to '25% of the stiffener spacing. A similar but less
extreme experience has been reported by Chneau et al.. /111.3.8/ who estimate the reduction in effective breadth.t'obe 50% at lid span in casé. of a grill-age beam segment being subjected to a concentrated load in that location. The model in this case was that of a ship's deck supported by six pillars, four at the corners and two at mid span of the longest sides and the theoretic-al approach was based on a matrix method. Nagasawa c.s.. /111.3.9/ applied
Ando's method of analysis/III.3.10/ to their test pieces in order to
calcul-ate the stresses and deflections. The experiments involved 16 specimens. divided into four groups, each group consisting of four geometrically equal structures fabricated out of different steels. All experiments were carried out under the condition of simple support along the' four sides', while the edges were restrain-ed from sliding inwards. In general there was good agreement between theory and experiment where the defiections and extreme fibre stresses of the stiffeners were concerned.
Stress analysis of structural details, carried out analytically and experiment-ally on sometimes refined models may be required when, the design of a special ship is being developed. Mo'i et al. report on such an investigation where,
additional stiffening.
beside other problems, the strength of structures in the region of the bilge have been studied. The structural arrangement of the original design of the bilge section is shown in figure 111.3.2 and the objects of the study
were: A -A
- - Limit
of model. ig,s Ld&Oo
Qo
uQ120
r
16 -1I
2260 12.0 R =600 R=1800 las 6400FIG. .3.2. Structural arrangement actual ship.
C fror
f. 13
I Applied Load A 117 R200 600 2133 1533 4 J 'D 'DFIG.
.3.3. MODEL R. (from ref [.3.11)
Verification of the calculated effective breadth of the curved
inner hull plating. Comparison of experim-ental stress
distribu-tion in the web plates with values based on a
curved beam analysis. Establishitig the in-fluénce of a local ad-ditional web.
Thé effective breadth of the
-urved inner hull plating ..aiculated according to the
method of Anderson /111.3.12/ was found to be very small, the calculations were con-firmed by the experimental findings. This can be seen in figures 111.3.3 and
111.3.14 which also show the
models used for the
exper-imental investigation. Effective breadth by calcuLation 57mm FLoor Load P=4t O - 5kg/mm2 FLoor
Stress measuring point.
(Compression)
Bending strass distribution in inner hull plate
at- biLge corner. -
-LiJ uI
tíRend
iI.
b12S 825
I412.5206 A -A 206
-Hatched part the shape of added floor. Girder½
/
o
e
J,, 125x30x5 shows 117R20d'
10 - 1530 213317
-Applied LoadA;L
FIG. t.3.4. MODEL I (from
Ordinary floor:
Added floor.
LongitudinaL member
con-necting added floor with
ordinary floor.
Fixed at bilge.
FIG. 1.3.5. SimpLá model to calcuLate the efficiency of on odded fLoor. (from ref.
r
125x30x5 C,, CT, D Effective breadth by calcuLation 57 mm. FLoorBending stress distribution
at bilge corner.
ref. [1.3.11])
Added floorLoad P=4t
O kg/mme FLoorStress measuring point
in inner hull plate
The experimentally established stress distribution in the central curved part of the web is reasonably approached by the calculated values, while at the end of the curved section in the double bottom the straight beam theory appears to give a better fit than the curved beam theory.
There existed some doübt as to the manner in which the added web with its hm-ited length would share the loads with the adjacent webs and the matter was studied partly theoretically and partly experimentally. The assumptions on which the structural model for the calculation was based have been stated asfóllows:
The structure can be re-presented by a cantilever group fixed at the bilge. As the efficiency effect
is mainly determined by the (lower rigidity) side shell part, the calcula-tians are carried out for that part (figure 111.3.5). The added web ('floor" in the figures) is connected to the adjacent webs by a longitudinal end member
(
Q
in figure 111.3.5).The load is transmitted to the added web by the bendT Ing rigidity, shear rigid ity and torsional rigidity of the connecting longitu-dinah.
L)
in calculating the rigidityof this member, the
effect-125x30x5 D O wi : i ol o ü: 1IRerid 1237 o (Compression)
18
-ive breadth was determined so as to coincide with the experimental result. The value thus obtained equalled 3 longitudinal frame spaces. This value is considered almost adequate in view of the shape of the structure. The efficiency of the added web in the actual desigñ was then calculated to be 85% using the experimental result that the stress in the inner shell plate in way of the added web was 88% of the stress value in way of the adjacent con-tinuous webs.. On comparing the stress distributions shown in figures 111.3.3 and III.3.Li it can be seen that the prçsence of the added web ieduces the stress
peaks to approximately 55%of their originalvalue so that this manner of local
stiffening appears to be very effective. The need for the above mentioned study became clear after longitudinal and transverse strength calculations for the entire initial design had been carried out.
As a direct result of the growth in size of thé large tankers and the accompany-ing development of methods of trànsverse strength analyses, experimental stréss analyses under static loads have been carried out on board of these ships.
These experiments dealt with ovral1 response and with locl response, the
former in their manifestation as deflections and the latter in the form of stress distributions in transverse rings or deep girder connections. Takaki et al. /111.3.13/ reported on experiments concerning a ship with long tanks and a horizontal girder system in the wing tanks, the results being compared with a theoretical approaóh based on the slope-deflection method and Yamakoshi's method concerning the relative, deflection of wing tanks /111.3.114/. The fol-lowing conclusions are presented:
Considerable streses were observed in the transverse web rings, depending
mainly 'on the shearing deformation of the wing tank.
The wash bulkhead in the wing tank appears to be not too effective as far as shear rigidity 'is concerned.
The horizontal girder system is undesirable in wing tanks of large tank-ers having long tanks as this leads to reduced scantlings of the trans-verse frame rings (see 1) above).
14) Wash bulkheads in long tanks should be designed carefully becausé large
stresses may occur in them.
The wing tank wash bulkhead as illustrated in reference /111.3.13/ looked' more like a heavy transverse web frame ring with a heightened perforated web in way of the bottom, than like a perforated stiffened panel. The cut-out percentage is someihere in the neighbourhood of 35%, this is slighly higher than the''max-imum values occurring in Augestad's experiments /111.3.15/ which showed that
for a large cut-out area (30%) the bulkhead beame more and more.like a frame
where the effective moment of inertia was concerned.
Further full scale experiments aboard two ships having the same structural con-figuration(horizontal side stringers in, the hing tanks) have been undertakenr by Nagamoto et al. /111.3.16/. The ships had a deadweight capacity of 118.500 and 180.00.0 ton, for the smaller of the two vessels several conditions of load-ing were investigated, namely one at full ul1age draught with all centre tanks
and two wingtanks aft completely full and two forward wingtanks about 60% full, the other conditions being those of tank testing.
The theoretical strength calculations were developed from the three dimensional strength calculation in collaboration with Mori. (See section on Transverse
Strength).' The relative defiections of -the longitudinal members showed a- general-ly good agreement between experimental and calculated values, the same can be said about the stress values in the transverse rings.
The authors conclude that:
The method of calculation is sufficiently accurate for practical purposes. The centre.tank test load appears to be severe for the bottom and deck transverses in the centre tank and for the vertical web fitted to the longitudinal bulkhead. For other members the wing tank test condition
19
-appears severe. Stresses in the bottom and deck transverses of the trans-verse ring without cross ties in the wing tanks would be fairly high. Experiments on three extensively instrumented oil tankers have resulted in
a number of papers by Okabe etal. /111.3.17/ and Nagamoto et al. /111.3.18/,
/111.3.19/ and /111.3.20/. The ships A, B and C involved had a.deadweight capacity of 122.000, 157.000 and 202.000 ton respectively. The investigations were directed towards establishing the deflections of the side shell through-out the tankpart, the relative deflections of watertight- and wash bulkheads
and transverserings and.the stress distributions in these rings. The
experim-ents were carried out during the hydraulic testing of the tanks. Okabe et al. /111.3.17/ report on these tests and compare the results with thöse of a three
dimensional strength analysis. In general the calculated and observed
deflec-tion values agree rather well, the thdoretical deflecdeflec-tions mostly exceeding the experimental ones by a reasonably small amount. The calculated stress dis-tributijon in the transverse ring agreed very well with the experimentally
es-tablished distributions. In ships A and B a large error seems to occur between theory and experiment in way of the curved flange of the bracket of the bottom transverse in the wing tank located near the longitudinal bulkhead. This ap-parent error proved to be caused by incomplete instrumentation as only uni-directional strain gauges had been used. In ship C this fault was remedied and in this case the differences between theory and experiment were greatly
re-duced and became acceptable. High stress and strain values were observed in the flanges of the brackets connecting the bottom transverss to the longitu-dinal bulkheads, the magnitudes ranging from 26 - 30 kgf/mm for ships A and B (both or stress and for Young's modulus times strain) and not exceeding 23 kgf/mm for the stresses in ship C. These figures support the conclusions given above concerning the severity of the tank testing condition.
Nagamoto et al. analysed the structural detaiis of ship A (figure 111.3.6) and com-pared the experimental observations with those obtained by means of model experim-ents and theoretical calculations. The an-alysed details contained curved flanged brackets which Were theoretically analysed by F.E.M. and in some cases also by the wedge theory and the curved beam theory.
In general the results of the F.E.M.
cal-Analysed
culation were the most satisfactory
especial-details.
-ly when compared with the model tests, which is natural considering that for the model experiments the loads were clearly defined.
The authors state that for curvedflanges
of brackets thè effective breadth of the flange should be introduced into the F.E.M. model and they applied Anderson's theory to obtain the proper values. If it seems
strange thatthis was necessary then it
must be realized that if no plate bending elements were used (reference /111.3.20/ provides no relevant information) the trans-verse bending of the flanges has been dis-regarded in the F.E.M. model. The agreement between full scale experiments and the F.E.M. based analyses was initially unsatisfactory for the curved flange of the bracket in. the bottom T-connection although the effective breadth values had been Worked into the theoretical model but in this case the above discussed incomplete instrumentation with strain gauges was the source of the errors which after a theoretical correction of the experimental values were reduced to an
acceptable order of magnitude. Some of the calculated stress distributons in
the web plate and bracket of the bottom transverse in the wing tank showed con-siderable difference between theory and full scale experiment, the cause is not
discussed in reference /111.3.20/ but it might be attributed to the gauge instrumentation which, if the illustrations in reference /111.3.17/ have been interpreted correctly, was limited to one side of the plating so that local bending could not be recognized.
The above discussed full scale experiments have provided a wealth of informa-tion the study of which is regrettably hampered by a Janguage barrier al-though the paper by Okabe et al. /111.3.17/ contains many illustrative figures which are in roost cases well provided with English texts. This applies also
to a paper by Nagamotoc.s. /111.3.21/ which treats a subject that has been
discussed too by Haaland /111.3.22/ and Abrahamsen /111.3.23/. The investiga-tion is concerned with the manner in which longitudinal stiffeners can be carried through the web of a deep transverse and jt was initiated because of fatigue cracks occurring in practice. (See f igute 111.3.7). The mechanism of force transmission and the stress distribution around the slot were analysed theoretically and experimentally with models and at full scale. The theoretical analysis was carried out by F.E.M. and proved to be reliable.
(2)
20
-G, 11t.3.7.
from ref. [.3.21]
Of experiments how in progress and concerning large tankers., the following may be mentioned:
1.) N.C.R.E. Dunfermline.
A steel model of a section of a 250.000 ton d.w. tanker extending over three tank spaces has been constructed at a scale of 1:8. The model will
be extensively strain gauged andthe experimental results compared with
similar measurements on the actual ship and with the results of a 3-dimen-sional finite element analysis.
Dukes, Imperial College London.
A plastic model has been constructed extending over the full cargo tank length f the above mentioned ship and it also will be extensively strain
gauged.
3) Chevron tañker "John A. McCone" /III..3.2L/.
As part of the "Arizona Pioject" the vessel has been fitted with 5'.l-O strain gauges, some 100 of which are to be used also for dynamic
meas-uring. Data output must serve to verify the accuracy of a strength
pro-gram called DAISY (Displacement Automated Integral System).
4. Experimental work in the e1asto-lastic and
plastic region.
Most stiffened panels in ships are subjected to more than one type of load
and there are as yet no adequate theoretical methods to analyse the post-.eiastic behaviour of these structures, therefore the required relevant in-formation must come from experiments. A series of tests have been carried
out by Bureau Ventas at the University of Liege on plates stiffened either
transversely or longitudinally and subjected simultaneously to lateral and inplane loads. The models were assumed to be part of a single bottom of a
65.- m long ship located between two longitudinal girders and were
repro-duced at a scale of 1:2. The stiffener spacing was the same for both models,
flat bars (100 x 8 mm) with sniped ends having been used for the transverse-ly stiffened panels and angle bars (70 x 50 x 6 mm) for the longitudinally
stiffened ones to which the proper number of transverses had been fitteL
Six models of each type have been tested until collapse, occurred, the
com-pressive loads having been applied until the deformations of the model reach-ed the maximum value allowreach-ed for by the testing machine. This value corres-ponded to ten times the plate thickness for the transversely stiffened models,
that is 50 mm. The lateral prssure was kept constant during each test and
varied from 0,1 to 0,9 kgf/cm orresponding to 'elastic stresses in flexion
varying from 1,5 to 13,5 kgf/mm . Strain gauges were used to establish the
stress magnitudes in the elastic range while, a gréat nUmber of dial gauges provided information concerning the deflections under increasing load. The models were manufactured in a shipyard according to current practice and
in-itial deformations were measured in 48 points for each model. The topOgraphic
charts differed individually, the maximum deflections varied from 2 to 5 mm
while the r.m..s. varied from 0,8 to 1,5 mm.
The transversely stiffened models collapsed under a load of 100 ton, except nr. 1 test piece which collapsed prematurely due to a defect of mounting. The models all buckled in the same way with alternate waves between stiffen-ers.. The diagrams for axial force - axial deformaticn were quasi identical for each model and they were characterized by a long level line corresponding to large deformations under constant loads.. It may be stated (though actually impossible to verify theoretically) that for the transversely stiffened models, within the limits of the experiments,
1) The collapse
.2) The collapse
deformations
3) The collapse
21
-load is independent of the lateral pressure1
load remains constant for relatively large values of the load is not influenced by initial deformations.
Concerning the longitudinally stiffened models no definite results are
avail-able however in hese cases the lateral loads have an influence on the
col-lapse load smc9 it varies from 240 ton (with zero lateral load) to 200 tons
(with .9 k.gfïcm lateral load). After the collapse load has been reached it decreases abruptly at first and then slowly as the deformations increase. Stiffened panels in bulkheads are predominantly subjected to lateral loads, such panels have been investigated experimentally by Nagasawa c.s. /111.4.1/ under lateral loads only. Four types of stiffened panels were examined and each type was represented by four specimens manufactured from steels 'ha"ing
22
-involved. Simple support was provided along all four plate edges which were prevented from sliding inwards.
Thé experiments have shown that the deflections of the panels inçreased linearly with the load in the elastic range, the rate of increase of the deflection changed rapidly at the load causing full plastic moment of the
sections after which a new linear relation between deflection axid load was established. The point of intersection of the two linear branches of the load-deflection curves was used to define the collapse load., which was com-pared with a theoretical value obtained from the upper bound theorem.
(See section III.2).
Plate girders have been the subject of extensive experiments by Mori et al. /III.Ll.2/ who tested plate panels of double bottom floors under pure shear and web plates, of transverse rings of large oil tankers under pure shear and combined shear and bending conditions.
The floor panel. tests were conducted in order to obtain information concerning the influence on the buòkling strength of openings, aspect ratio, stiffeners and welded joints. These experiments showed the buckling .stresses to be 80
-90% of the ultimate stresses regardless of the opening ratio. .The maximum in-itial deformation of the specimens varied fron 0,20 to 1,00 mm but no relation between initial deformation and buckling stress could be detected although it was observed tha- the buckling stress was lowered when the initial deformation was similar to the buckling mode. The effect of various ways of stiffening can be found in figure 111.4.1 which illustrates the conclusion that the best
man-ner of stiffening is with stiffeman-ners on both,sides of the hole in the plate. Other conclusions reached were:
1) The buckling strength of a rectangular plate (a/b < 1,5 and a ) b) with
an oval hole is almost equal to that of a rectangular plate having a cir-cular hole with a diameter equalling the length of the oval hole.
The buckling strength of a plate which is butt welded diagonally is 30%
lower than for a plate without a weld. On the other hand the diagonal lap
joint does influence the buckling strength dependent of the relative di-rection of the shearing force, that is, if the compressive stresses occur parallel with the joint line the strength is nearly equal to that of an ordinary panel, but if the compressive stresses occur at a right angle
to the joint the strength is about 30% lower.
The experiments on the shear loaded web plates of transverse rings involved a number of structural configurations., namely without openings, with slots. (crossing of longitudinal stiffener) and with slots and a circular hole.
Each of the models existed in three plate thicknesses, while some additional
models were manufactured with än increased stiffener spacing and slots and
cir-cular hole and one where the slots had been fitted with collar plates. Buckling strength was reduced by 10 20% if only slots were present and by 20
-30% in case of slots and circular holes. The reduction due to the slots was
eliminated when collar plates where fitted, The relation between buckling load and ultimate load appeared to be constant for ail specimens, the ratio between
the two loads being 0,8.
The influence of a bending moment on the shear buckling strength was examined with the aid of specimens having no opening, slots only or slots and a circular hole while only one plate thickness was used and one ratio of bending moment
to shear force. The reduction f shea'buckling .strength due to bending. was
calculated by applying Bieichts formulae and the agreement with the experiment
was good.
1.25
F4
Lap weLded joint
f
t t
Butt weLded joint
Discrepancy at welded joint.
-z
0.05- 0.1St23
-0.0128 0.0170 Ring SOxL.5 FB Ring 25 x 45 FBo
FIG. .4.1. Effect of wetding and ctrengthening. (from ret.
[ 1.4.2.]
EB 50x4.5
FB 50 x45
I I L
0.2 0.3 0.4 0.5
Opening ratio DIS
o
0.25
0.1
