REPORT No. 66 S February 1965
(S 1/46)
STUDIECENTRUM T.N.O. VOOR SCHEEPSBOUW EN NAVIGATIE
NETHERLANDS' RESEARCH CENTRE T.N.O. FOR SHIPBUILDING AND NAVIGATION)
SHIPBUILDING DEPARTMENT MEKELWEG 2, DELFT
*
INVESTIGATIONS INTO THE STRENGTH OF
SHIPS' DERRICKS. PART I.
(ONDERZOEK OMTRENT DE STERKTE VAN LAADBOMEN)
by
Ir. F. X. P. SOEJADI
Scientific Officer of the Ship Structures Laboratory University of Technology Deift
Issued by the Council This report is not to be published unless verbatim and unabridged
page Summary 5 I. Introduction 5 Preliminary investigations 5 General considerations 6 Theoretical considerations 7 4.1 Basic analysis 7
4.2 Ultimate strength considerations 9
4.3 The variable sectional dimensions 10
Experiments 10
5.1 Static tests 10
5.2 Dynamic tests 11
Discussion of experimental results 12
6.1 The influence of the asymmetrical loading condition 12
6.2 The influence of stepping a derrick according to present-day practice 14
6.3 The failure tests 16
6.4 Comparison of theory and experiment 16
Supplementary tests 17
Conclusions 20
Acknowledgenien t 22
References 22
LIST OF NOTATIONS
x,y rectangular coordinates L or i derrick-length
« angle indicating derrick-position with respect to the horizontal
h distance between heel of derrick and span-attachment at the mast
E modulus of elasticity
F area of cross-section
I moment of inertia
W section modulus
q uniform load per unit length
a initial deflection in way of '/2L normal stress
s strain (unit elongations)
P axial thrust
Mb external bending moment
M, internal bending moment in wa of x
k2 P/El u 1/kL
t tons (metric tons of 1000 kg)
INVESTIGATIONS INTO THE STRENGTH OF
SHIPS' DERRICKS. PART I.
by
Ir. F. X. P. SOEJADI
Sum rnaiy
An investigation is made into the strength of ships' derricks under static, as well as under dynamic loading conditions. This report presents the results of the static investigations. A study is made of the effectiveness of the stepped derrick
constructed according to present-day practice as compared to the corresponding derrick of cylindric form.
The conventional construction method of stepped derricks with long inserted parts in way of the transitions proved to
be objectionable rather than benificial other methods of interconnecting tubes of different diameters were therefore tested.
The results of the dynamic tests will be presented in Pari II.
i
Introduction
Cargo-handling equipment, though only a minor
part of the totality called "ship", will never cease to
draw attention, because non-functional equipment immediately lowers the earning profits; moreover, failure of masts, derricks or rigging may cause damage to cargo and, worse, also to human beings. The greater part of studies on cargo-handling equipment concerns the problems of masts: stayed
or unstayed, single or bipod, the problem of
water-tight transition through a deck, etc. A good body
without sound limbs, however, need not be worth-less, but in any case it is worth less; the same applies to the good mast without derricks of correct design. The investigation into the strength of derricks reported here, was made by the Ship Structures Laboratory of the Delft Technological University
under the sponsorship of the Netherlands' Research
Centre T.N.O. for Shipbuilding and Navigation. It was based on the attempts to comply with the wish of the Inspection of Factory and Dock Labour
at Rotterdam i.e. to have the disposal 0f a design method, scientifically justified, yet simple enough for quick application.
The matter cannot be classed as very urgent, because derrick casualties do not often occur and it
is even believed that the conventional method of construction leads to overdesign. Moreover, a der-rick is an object having such a simple form that there is a tendency among shipbuilders to make little fuss about the design-method in the sense that,
when loading-cases heavier than normal are to be expected, the derricks are simply made stronger,
for example by increasing the thickness of the tubes over the amount obtained by the design-method usually applied. It goes without saYing that the
path of economy and efficiency is purposely aban-cloned then.
The investigations of the Delft Ship Structures Laboratory comprise general and theoretical con-siderations, experimental investigations under
la-boratory conditions, and measurements on derricks in real rigging conditions.
As will be read theoretical considerations led to
the conclusion that it was desirable to make a com-parative study of the properties of a conventionally
stepped derrick as compared to the properties of the corresponding cylindrical boom. The conclu-sions of this investigation are not in favour of the stepped derrick, so that a further investigation on the subject of' "stepping" was made. It was found
that the cylindrical form is quite favourable;
conse-quently the need for a refined design-method for stepped derricks has come into another light.
The experiments on derricks in real rigging and
under actual working conditions were aimed at the elucidation of the influence of dynamic factors; the
results of these experiments will he presented in a
following publication.
2
Preliminary investigations
Sorne students in naval architecture at the Delft 'Technological University [1], [2], f3], made the-oretica studies of the strength problem of derricks
formulated as follows:
to be analysed: "the strength of stepped derricks; a
determination of the most favourable number and length of the (cylindrical) steps; a study into the most economical tube-diameter and
tube-thickness of the steps."
Even though the formulation is short, the solution of the problem is far from simple because of the
6 lo - 590.8 0.7 -0.6
great number of variables, the principal variables
being:
the variable section (variable in diameter and
tube-thickness);
the ratio of the length of the steps; the number of steps;
the eccentricity of loading c.q. initial deflection;
the own weight; the axial compression; the way of manufacturing.
This great number is an impediment for a purely
mathematical design-method, the more so if a
sim-ple method is aimed at.
HERFST [1] confined the loading of a derrick to axial thrust and its own weight, the latter being considered as a concentrated load at mid-length; end-moments were left out of consideration.
Sys-tematic calculations were made concerning a spe-cial (non-existing) type of derrick having a
contin-m
VALUES OF r,, FOR SEVERAL RATIOS OF MOMENTS OF INERTIA OF DERRICKS FORMED AS IN FOLLOWING FI SURE
Fig. 2. Diagram for stepped derricks under
axial compression
lig. I. Boom of continuous variable sectional dimensions
uous change of sectional dimensions (diameter and
material thickness) as shown in Fig. 1.
Based on suggestions in [2] VERTREGT [3] made
systematic calculations of stepped derricks,
man-ufactured of commercial steel tubes, with two steps,
as is usual in the Netherlands. The lengths of the steps were (for all derricks) confined to:
0.1OL for the two endsteps,
0.15 L for the two intermediate steps, 0.50 L for the middle tube.
Only the axial loading was considered; no end-moment nor the own weight was taken into account.
The method of successive approximations finally resulted in a diagram which is presented as Fig. 2.
Except for this diagram which may be useful for
practical application, the studies mentioned above are of academic value; however, they led to the decision to perform experiments either under labor-atory conditions or on derricks aboard ships, or both.
By courtesy of the shipowner, Messrs. Verenigde Nederlandse Scheepvaart Maatschappij, two 5-tons* derricks could be obtained for the preliminary tests. The principal test of these preparatory
exper-iments is reported in [4].
3
General considerations
No uniform, international design method for
der-ricks exists, each shipbuilding (i.e. derrick building)
country having its own regulations.
The most elementary method to arrive at scant-lings of a derrick makes use of the basic Euler-formula o-2EI/L2, further applying a factor of safety
of 5; mathematically this can only result in
cylin-drical booms.
In the course of time refinements were applied to
this method such as the consideration of the lon-gitudinal distribution of the internal bending mo-ments which led to the process of diminishing the
sectional dimensions towards the ends like tapering
off (gradually) or stepwise (discontinuously). This can be seen as an indication of the consciousness that the cylindric form is not the most economical
form.
The strive after economy, however, was not extended to decreasing the factor of safety, because
* All tons in this publication are metric tons.
I,
IJOL J f115L 05L .._0.i5.L ...t1
while on the one hand few accidents occur on account of failure of derricks, on the other hand a safety factor, even as large as 5, was considered inadequate as an allowance for the effects of special circumstances such as:
end-moments,
union purchase work,
C. dynamic loading (accelerations, braking),
cl. corrosion,
e. impact forces (by faulty manipulations). It can be agreed that allowance is to be made for the factors a. up to d., but complete compensating
for faulty manipulations, as is sometimes demanded,
raises the magnitude of the safety factor to a level which makes the application of a refined design method ridiculous.
A few authors developed improved design meth-ods, of which may be mentioned the method of
BURTON DAVIES [5], that of the Union Metal
Man-ufacturing Co. [6] and the method published by MCNAUGHT [7]. Analyses of these methods were made, but it lies outside the scope of this
investiga-tion to present them in this report, the present in-vestigation developing along its own lines, as may be observed from the following chapters.
4
Theoretical considerations
4.1 Basic analysis
The basic problem of derrick-design concerns the
analysis of a single derrick, rigged in a certain
posi-tion, loaded by a weight in the hook and its own
Fig. 3. Conventional rigging outfit
weight, no guy-forces, no special guide-rollers or
such like. The problem seems to be simple enough,
but as is stated in Section 2 a great many variables
are involved.
Analysis of the rigging configuration (Fig. 3) will
lead to the conclusion that the actual loading con-sists of axial compression and own weight which are the certain loads, and that an end-moment at the top and initial deflection may be present.
The magnitude of the end-moment depends on the position of the derrick with regard to the hor-izontal indicated by a, the ratio h/I, the attachment of the upper cargo purchase block and the head span block to the derrick top (Fig. 4).
Fig. 4. Types of derrick-top
A certain configuration may result in a zero
end-moment of course. It is obvious that at the heel of a derrick no bending moment can be present,
be-cause the heel is free to pivot; there is a possibility of torsion by friction in the heel fitting or when the span-attachment to the mast is not located per-pendicularly above the heel fitting.
The factor of initial deflection is the most un-certain factor in derrick-design. Initial deflection may be present on account of manufacturing tol-erances. Own weight may cause an initial
deflec-Ç
THE CASE OF A LOADED PRISMATIC DERRICK SCHEMATIC)
SUBCASE I
UNIFORM WAD Q, PER UNIT LENGTH
M 1400 jTh 4_500 2700 1150 1750 450 '5 INITIAL DEFLECTION - I
AXIAL LOAD P * UNIFORM LOAD ASSUMPTION A UNIFORM WEIGHT
DISTRIBUTION
M5
SUBCASE it
AXIAL LOAD P* ONE ENO MOMENT Mb
SUBCASE
AIIIAL LDAO P*INITIAL DEFLECTION ASSUMPTION A SINUSOiDAL INITIAL
DEFLECTION
50.a SIr44.
tion of an initially straight beam, it may increase an initially present downward deflection, but it may also counteract an initially upward deflection. Moreover, it will oniy be merely coincidental when a derrick is manufactured and rigged in such a way
100
5900
that an initial deflection lies in the vertical plane through the longitudinal axis.
The correct loading-case having been assessed it will be understood that the case of a derrick of cylindrical form was taken as the starting point of a theoretical approach of the problem.
For a cylindrical boom the loading-case men-tioned above can be split up into an axial compress-ive load, a uniformly distributed load (own weight),
an end-moment and initial deflection, see Fig. 5. A necessary condition for superposition when
subdividing the total loading-case is: the same axial
compressive force in all sub-cases, as is illustrated in Figs. 6, 7 and 8.
In the Appendix an elaboration is given of the sub-cases and the final superposition; this super-position leads to the following expression for the total internal bending moment
q Fcos u(l - 2x/L)
k2L cosa
sinkx
P.a
+ M
.+
sin---sin kL
i - kL2/t2
LThe total stress in the extreme fibre can then be found as being the summation of the axial stress and the bending stress.
The process of transforming the basic cylindrical form into a certain stepped form (as is common practice)
is meant to obtain uniform strength.
Whether this is actually achieved by the applica-tion of the present-day method was the next p
rob-=
2700
i ETC. STRAIN GAUGE NUMBER ALL GAUGES ARE PLACED LONGITUDINALLY
.4
Fig. 9. The cylindrical and the corresponding stepped derrick
1750 1400 1750
+
1418 124i4_ -4-8 Fig. 5. Fig. 6. Fig. 7.lem to investigate. To this end two objects for experimental investigations were manufactured: - a cylindrical boom of a given length,
- a boom of the same length, but stepped and
con-structed according to present-day practice in the Netherlands, with a middle tube of the same sectional dimensions as the cylindrical boom. Fig. 9 shows the two booms and their dimensions.
A comparative study could then be made:
ofthe results of experiments with the cylindrical
boom and the results of the application of the above-mentioned expression for the stresses in the extreme fibre;
of the results of experiments with the stepped boom and the results of the study mentioned
under a. for the same loading conditions. It will be clear that the results of the experiments
comprise the influences of all variables (i.e. the in-fluences of all variables find expression of their own accord) ; in this way the differences between stress-values found experimentally and theoretically might be considered as standards for the influences of the
variables which have been left out of the theory. It
was found, however, that the way ofobtaining such
standards is hampered by the uncertain character
of the factor of initial deflection.
4.2 Ultimate strength considerations
As the thrust on a derrick forms the principal
loading it is only natural that the approach to the
design of derricks was usually sought along the path leading to "buckling" as the phenomenon of failure.
The phenomenon called "buckling" is mostly pictured as a sudden occurrence: a straight, slender
bar, centrically compressed, will at a certain
mag-nitude ofthe compressive load, pass from the straight
to the buckled state.
Failure of an eccentrically compressed bar or of
a centrically compressed bar with initial deflection, however, is also considered as a buckling
phenom-enon, although deflection of the bar is proceeding
from the beginning of the increase of the load. The
problem then is whether a stress criterion or a stability
criterion determines the moment of failure.
Advocates of the stress criterion treat this as a
stress problem of the second order (i.e. the effects of deformations on the loading-condition are taken into account then). The attainment of a certain value of the stress in an extreme fibre (e.g. the yield stress) is taken as determining the carrying capacity in this case.
The stability criterion starts from the equilibrium
between internal and external bending moments,
and the criterion for failure is defined as the
condi-tion at which this equilibrium is broken, because
the material is no longer able to afford the necessary
internal resistance (as BLEICH [8J called it: "the breakdown of internal resistance").
The properties ofthe material also play a role in
the buckling problem ; this may appear self-evident,
but expressing the material properties, other than the E-modulus in a method of solution makes the matter very complicated, especially in the case of eccentric loading and/or initial deflection.
The well-known buckling formula of Euler with the modulus of elasticity in the numerator is valid
for axial compression in the elastic region, whereas the same Íòrmula can be applied in the plastic region with the USC of the tangentmodulus or of the reduced modulus.
The problem of perlect elastic material, i.e.
un-limited validity of Hooke's law, loaded eccentrical-ly, can be tackled as a computation of a static
con-dition, but attention has to paid to the influence of deformations on the loading condition. The
well-known expressions for deflections, moments, stresses
etc. result from these manipulations, the so-called secant formula being an example.
It can be decided then, that the stress in the
extreme fibre is not to exceed a certain value and
that the load causing this stress may he considered as the critical stress (this is the stress theory). Only
the modulus of elasticity represents the properties of the material here.
The elastic-plastic properties of a material are
ex-pressed in the stress-strain diagram. By means of this diagram the equilibrium between the internal and external bending moments can be analysed; the load for which equilibrium is not possible any longer is defined as the failure-load according to the stability theory.
The instant that the yield point is reached need not necessarily mean the moment of failure; this depends to a high degree on the form of the
trans-verse sections, the slenderness degree, the
eccentric-ity of the point of application of the load (in mag-nitude and in location with respect to the principal
axes), as is also confirmed by the results of several experiments performed by CHWALLA [9].
According to TIM05HENK0 [IO] the difference between the load causing the commencement of yielding and the failure-load is small for small
ec-centricities and decreases for increasing slenderness degrees. It is supposed that this statement holds for
the case of derricks, as these objects have
slender-ness degrees (defined as the ratio of effective length to radius of gyration) over 100, and because of the
lo
fibre has only to extend over a small area before buckling occurs). As a matter of fact the experi-ments proved that the start of yielding is a good indication for the moment of failure.
4.3 The variable sectional dimensions
Consideration of the bending moment diagram of a bar under axial compression and bending loads
indicates that the bar of uniform cross-section must not be the most economical one. This led to the procedure of transforming the basic cylindrical form into a stepped form as is common practice in
derrick-design.
The search for the most economical and efficient form of structures may be considered to be a human
need. In his treatise "Sur la figure des Colonnes"
[11] LAGRANGE informs us that the simple
cylin-drical form of columns could not satisfy even our
anchestors:
,,On a coutume de donner aux colonnes la figure d'une
conoïde qui ait sa pius grande largeur vers le tier de sa hauteur, et qui aille de là en diminuant vers les
deux extrémités, d'ou résulte ce qu'on appelle
vulgaire-ment le renflevulgaire-ment et la diminution des colonnes."
According to LAGRANGE the choice of this form
seemed to be based on nothing else but the argu-ment to quote the shape of the human body.
The following may serve as an illustration of the
need for Caution when looking for the most econom-ical form of structures.
LAGRANGE analysed the buckling problem of
axially compressed columns of any kind formed by
a surface of revolution, his next step being the
an-alysis of the problem of the most efficient column.
He put the problem thus: to find the curve which by its revolution about an axis in its plane deter-mines the column of greatest efficiency relative to its mass, the column having a Certain length of course. Calculus of variation led him to the aston-ishing conclusion that one of the solutions is the right circular cylinder, e.g. the right cone is found to have its greatest efficiency when degenerated into a right circular cylinder!
The analysis of LAGRANGE, quoted above,
con-cerned continuously varied diameters; the analysis of the problem of the most efficient beam of dis-continuously varying sections would be still more
intricate the more so for a loading case of axial load,
own weight, end-moment and initial deflection. A more practical approach of the latter men-tioned problem lay in the comparative study meant in Section 4.1; this must result in indications
con-cerning the effectiveness of the method of stepping
as is applied nowadays. Of course this would only
give an answer to the question whether the objec-tive of stepping is attained by the method under consideration, but it might also serve as the basis for a further investigation.
5
Experiments
The experimental investigations made by the Ship Structures Laboratory of the Delft University of Technology were focussed upon the following items:
the influence of an asymmetrical loading
condi-tion (end-moment at one end only);
the effects of varying the sectional dimensions according to present-day practice;
the distribution of forces when working in union
purchase;
the influence of dynamic conditions;
general observations concerning the application of glassfibre reinforced plastic for derricks. Parts c., d. ande, will not be discussed in the present report, but in Part II.
5.1 Static tests
The experiments on the cylindrical and the stepped boom mentioned in Section 4.1 were performed under laboratory conditions, i.e. the derricks were not rigged as on board a ship, but suspended in the 500 tons testing machine (Fig. 10), the loads
ap-Fig. 10. Suspension of derrick in the 500 t testing machine
plied being as in practice viz, compression, one end-moment, own weight, initial deflection (if any). The loads thus exerted had a static character in that pulsating was not performed; the latter bears no importance in the case of derricks.
5.2 Dynamic tests
The influence of dynamic conditions as occurring in practice cannot be imitated in laboratories. In-vestigations in this field must be made on equip-ment in real rigging and it is only natural that one is thinking of ships' equipment then.
Measuring on board a ship, however, in many cases will be unwelcome, for it may hinder the proper exploitation of the ship. Therefore it may be considered a happy coincidence that measure-ments could be made on derricks as parts of the loading equipment of the Dockers' Training School at Rotterdam. This school has the disposal of a complete cargo handling equipment mounted on a replica of a part of a ship (Fig. il).
Fig. 11. The "training-ship" of the Dockers' Training
School, Rotterdam ad 5.1
5.1.1 Testset-up
As mentioned above the laboratory tests were per-formed in the 500 tons testing machine. No
descrip-tion of the testing machine is given here, suffice it to refer to [12].
The suspension of the derricks in the testing ma-chine was achieved by a ball-and-socket joint at either end. These joints allow a pure compressive force to be exerted on the derrick in question by the testing machine.
The end-moment could be set-up by a special device (Fig. 12) which made it possible to exert a
moment of a desired magnitude on the derrick-end in question, independently of the 500 tons machine. The moment apparatus exerted the moment in such a manner as was necessary to intensify the bending
Fig. 12. The moment apparatus
already set-up by the derrick's own weight. It goes
without saying that in the chosen horizontal suspen-sion the effect of own weight is greatest. Thus it has
been the aim to create the most unfavourable cir-cu rnstances.
0f course rigging-arrangements of derricks exist calling forth other external loads (e.g. when the cargo-runner is led over an extra guide roller at-tached to the underside of a derrick), but the prin-cipal external loads on a derrick in normal rigging conditions (single, used as a "swinging" derrick) are the axial thrust and the end-moment.
5.1.2 Strain measurements
The location of the wire resistance strain gauges is
shown in Fig. 9. Side gauges were fitted to record
possible side-way deflection.
The stations at the stepped derrick were chosen in correspondence with the stations at the cylin-drical derrick. Other considerations for the choice of certain stations at the stepped derrick are:
the transition of the strains from one tube to the
following tube of different diameter; the influence of the inserted parts;
the influence of welding.
5.1.3. Apparatus
The apparatus used are shown in Fig. 13. Visualiza-tion of the strains, of course, was effectuated by strain-indicators (readings); when recordings had
to be made this was done by means of the Siemens
Oscillofil fed by the strain indicators. Variplotters (XY-recorders) were used to plot defiections
12
Fig. 13. Measuring apparatus
5.1.4 Test procedure
The first thing to be done before the proper tests was the determination of the position of rotational
equilibrium. This was achieved by turning the
der-rick around in the ball-and-socket joints; deviation
from the straight form (e.g. initialdeflection) would
result in a preference of having a certain position (the rotational equilibrium), with the deflection downwards. This position was taken as the test position.
The strains caused by bending by own weight were measured by turning the derrick in question
around in the ball-and-socket joints over 1800; nat-urally this will give the double effect. The deflected position is taken as the datum position for the proper measurements, in other words the initial strains caused by own weight are not included in the
strain-values caused by the proper experiments; conse-quently the diagrams are exclusive of these initial
values, except where the contrary is stated explic-itely.
The proper experiments concern the following
loading-cases:
only external bending moment Mb, only axial force P,
- combinations of Mb and P,
failure test.
The magnitude of P: the largest P-value exerted during the static tests was limited to 40 tons.
The magnitude of Mb: the magnitude of end-moments Mb possibly occurring in practice is a sub-ject of controversy in shipbuilding circles, some
considering Mb to be negligible, others having the
opinion that Mb might be considerable.
As was stated before, in any case the magnitude
of the end-moment depends on the rigging
arrange-ment. Because it was intended to investigate the
special effect of a single end-moment as one of the
principal loadings, the magnitude of this moment was not limited to a value too low to be of
impor-tance, nor too high to give an exaggerated image
of the effect of this special kind of loading.
These considerations led to the conclusion that
a value of Mb = 11/2 tm would be a realistic choice, the actual value becoming 1.38 tm because of man-ufacturing reasons.
Experiments were also carried out with 1/4>< 1.38 tm, 1/2>< 1.38 tm and /4>< 1.38 tm, but the results being equivalent only the results of the experiments with 1.38 tm and /2>< 1.38 tm are presented in this report.
The failure tests were performed for the loading-condition Mb = 1.38 tm and P increasing from zero to failure-load.
5.1.5 Test objects
The two test objects for the comparative
investiga-tions were manufactured by N.y. de Keijzer, man-ufacturer of steel masts and derricks.
The choice of the dimensions was based upon the maximum span-length of the 500 tons testing machine. This resulted in a cylindrical and a cor-respondingly stepped derrick of 11.70 m length, both stated for "a maximum thrust of 131/2 tons",
the middle tube of the stepped derrick being of the same cross-sectional dimensions as those of the cylin-drical derrick (see Fig. 9).
The interconnection of two tubes of different diameter was established as in common practice: the smaller tube is inserted in the larger one over approx. 0.50 m, the difference between the outer diameter of the inner tube and the inner diameter of the larger tube being bridged by longitudinal strips. The end of the larger tube is then swage-jointed to the smaller one.
6
Discussion of experimental results
6. 1 The influence of the asymmetrical loading condition
It can be felt intuitively that the effect of one
enti-moment cannot be the same as the effect of a
sym-metrical loading with two equal moments at either
end of a derrick. It may be mentioned that DAVIES
{5J applies the secant ratio for his design-method; this implies the loading condition with two equal end-moments which is not quite comparable with the actual loading case.
The most important consequence of the asym-metrical loading condition is that the position of the maximum internal bending moment depends on the magnitude of the compressive load; in the Appendix it is expounded that a simply supported
prismatic bar, loaded by a certain end-moment at
one end, and axial loads Pof successive magnitudes,
will show a shift in the position of the maximum internal bending moment from the moment-loaded end (x = O) for P = O to x = '/.2L for P = it2EI/L.
The other loadings, (P + own weight) and (P + ini-tial deflection), will effect a maximum bending moment at 1/2L; this circumstance will force the
position of the total internal bending moment closer
to midlength.
Cylindrical derrick
Fig. 14 shows the shift of the location of the max-imum stress for the cylindrical derrick. Failure of
1000 hg/e 1000 0 t rn Ms 069 ti rown wyht
this derrick was displayed as a buckle at a distance of 3 cm from midlength on the side of the end-moment.
Stepped derrick
The situation for the stepped derrick is more in-tricate because of the discontinuously varying sec-tional dimensions; the discontinuous transitions from one tube-diameter to a different one form "thresholds" for the stresses.
For the relatively long middle tube it can be observed (Fig. 15) that a shift of the relative
max-imum is also present, approaching 1/2L for the fail-ure condition. This relative maximum is not the
S 40
PS Ot
ltg. 14. Test results for the cylindrical derrick (exclusive of initial values by own weight)
loco
1000
1000
1000
V
N., t Voloes trflOfl,efl1 of first yletdin9VV
V
toes for p, tN
reticot volves T M1 1 38 t rn 3000 2000 1000 sto l014 1000
d
1000 = O Im__I
P 30 t M1 059 t,, weig.fljFig. 15. Test results for the stepped derrick (exclusive of initial values by own weight)
highest value for the whoic derrick, consequently failure did not occur at or in the neighbourhood of
'/2L; this is one of the consequences of the discon-tinuous variation of the sectional dimensions.
6.2 The influence of stepping a derrick according to present-day practice
The process of stepping a derrick, with insertions of approx. 0.5 m length, and strips to bridge the difference in tube diameters, has far more conse-quences than is possibly realized.
It is logica] that stress-variations should occur in way of the transitions and it was expected that these variations would manifest themselves as
stress-con-centrations at the weld-joints.
1000
1000
10
The measured values of the strains at the stations indicated in Fig. 9 tempted to draw the stress-distribution lines as in Fig. 16 (upper figure), i.e. an increase from the value at the ends to a peak-value at the first weld-joint, then a fall down to a value proportional to the sudden increase in
sec-tional dimensions followed by an increase to a
peak-value at the second weld-joint, then again a fall on account of the larger sectional dimensions of the
middle tube, the latter having a regular distribution of stresses. From observations later on, however, it had to be concluded that the stress-distribution round about the steps is not so simple.
The most important conclusion to be drawn from
a comparison of the diagrams for the cylindrical
3000 200o 1000
IlL
151 loi 50t.
PuI
II
£ vOtos ot mo ont of first vieldmmig.-0 voLtes for P
-if for P1.t___________
1380,5, i w2000 1000 01 kg/ 2000 1000 P 0 20 40 to,,,
Fig. 16. Comparison of stress values of the cylindrical and of the stepped derrick
and for the stepped derrick will be that the object of obtaining a more economical structural form by the procedure of "stepping" is not attained. The greater part of the stresses on the stepped derrick are smaller than the corresponding stresses on the cylindrical one, for equal loading conditions, but a more uniform stress-distribution is not realized.
Whereas it can be stated that for the smaller loadings the stepped derrick is stiffer than the
cylin-drical one it was found that the failure-load of the former was smaller than the failure-load of the latter; in general it had to be concluded that the influence of the discontinuities is farther reaching than may be assumed.
The stress distribution in the regions of the dis-continuities are influenced by the factors:
the sudden change of sectional dimensions; the inserted parts;
the welds, joining the larger tube to the smaller one;
the strips applied to bridge the difference be-tween the inner diameter of the larger tube and the outer diameter of the smaller tube.
As for the strips it can be noted that (sec Fig. 17) the resistance against bending in the plane A-A is not the same as that against bending in the plane
B-B. The manufacturer of the derricks supplied the information that inserting the smaller tube, with the strips welded on it, into the larger tube is not so simple, because the connection must be
tight-fitting; an axial thrust of 10 to 20 tons is sometimes
necessary to achieve this. In this procedure pres-training of the material is quite conçeivable.
Contemplations led to the supposition that the
interaction of above-mentioned 4 factors might re-sult in a more complicated stress-distribution at the discontinuities than was assumed. Therefore an
ad-Fig. 17. Cross-section a a step of a stepped derrick 2000 000 2000 000
-
Ai
Acyandr,cet
stepped-í
_P=2.t
-M1 1.3BtmAI____
-_____
ste.. ed_j
I,---
P= 't____
u..
p.. 13$ tu16
ditional strain gauge was fixed near one of the weld-joints on the smaller tube (no. 27 on Fig. 9).
Meas-urements gave the most astonishing result that the stresses at this place were smaller than in way of strain gauge no. 19; consequently the assumption that the stresses are increasing to a concentration-value at the weld-joints was not correct. The
ex-planation of this phenomenon is hard to find; stress-relieving of the place in question by yielding at places in the neighbourhood could have occurred only once, but the phenomenon showed up every-time, under all loading conditions.
The neighbourhood of a weld seemed to be the determining factor, for the same phenomenon was also found in the vicinity of butt-welds (without laps) in other test objects.
For the stepped derrick under consideration it had to be concluded that the peak-stress must occur in the surroundings of strain gauge no. 19 or in way of it. This was confirmed by the failure test, the buckle appearing exactly in way of strain gauge no. 19.
Strain gauges nos 25 and 26 (Fig. 15) are also additional gauges, no. 25 lying outside and no. 26
inside the region of the inserted part in question.
The interaction between insertions and welding upon the stress-distribution in the region of the discontinuities may be worth a seperate investiga-tion if the present manufacturing method is to be maintained.
Based on the observation that the stepped
der-rick does not fulfil the expectation of a better stress distribution than the corresponding cylindrical one, it was decided to focus the attention on other ways
of interconnecting such as stepping without inser-tions.
6.3 The failure tests
The failure tests were performed under the loading
Fig. 18. Buckling spot of stepped derrick
conditions Mb = 1.38 tm and P increasing from zero to maximum. The failure diagrams are given as diagrams oft-values (strain) and not of a-values
( stress), because at the moment offailure the mod-ulus of elasticity is not constant over the length, the
heaviest loaded places being in the plastic region. For the stepped derrick the place of buckling happened to coincide with a measuring station, the cylindrical derrick buckled at a 3 cm distance from the strain gauge at midlength (this proved to be within the region failure). The moments of first yielding could, therefore, be traced on the oscillofil-recordings; these moments were chosen as the mo-ments of failure.
The ultimate P-value for the cylindrical derrick
was 56.3 tons, and 53.5 tons for the stepped derrick.
6.4 Comparison of theory and experiment
Theoretically the results of theory and experiment for the simple case of a cylindrical tube must con-cur. Imperfections in the test-specimens, however, may cause deviations. In our case the principal imperfections which might have been present are:
deviations in material-thickness,
- unroundncss of the cross-sections of the tubes, - deviations from the straight form.
The formula derived for the internal bending mo-ment in cylindrical tubes consists of separate parts for axial thrust combined with own weight, end-moment and initial deflection respectively. The combinations axial thrust + own weight, and axial thrust + end-moment are readily to be calculated,
because they concern certain values. The figure for
initial deflection, however, is most uncertain.
Several design methods assume values for initial
deflection, down-wards, in the vertical plane (e.g.
Lteet/8O, another assumption being LIflh/4OO), but as a matter of fact, initial deflection need not be in the vertical plane through the longitudinal axis of the derrick, nor need it be downwards if occur-ring in the vertical plane, and it may experience alterations during the derrick's lifetime. In prac-tice, of course, it is advisable to reckon with the most critical condition.
Considering the uncertain character of the factor of initial deflection a special way was followed (see
Appendix) to check the concurrence of theory and experiment. Only the cases Mb = 1.38 tm and
P = lOt, Mb = 1.38 tm and P = 30 t were sub-jected to this check; the results are plotted in Fig. 14. As can be seen in this figure the theoretical values are in good agreement with the measured values except for the stations near the moment-loaded end; these deviations must be ascribed to
the disturbing influences of the provisions for
exert-ing the external bendexert-ing moment.
The question whether a stress criterion for failure might be valid for derricks has been considered under the heading "theoretical considerations". It was stated there that, for derricks, the same mag-nitude may be expected for the load causing the commencement of yielding (stress criterion theory)
or for the ultimate load according to stability con-siderations (stability theory). The failure-test on the cylindrical derrick proved that at the moment of failure the yield stress of the material (+ 3500 kg/cm2) was reached (Mb = 1.38 tm, Puitimate =
= 56.3 tons). Assuming zero initial deflection and a constant E-value a thrust-value of 56.3 tons and Mb = 1.38 tm, according to the derived formula,
cause a stress of 3460 kg/cm2 at midlength.
Failure of the conventionally stepped derrick also happened to occur at a place where a strain gauge was stationed. The strain-value at the
mo-ment of yielding was a little lower in this case than for the cylindrical derrick (see Fig. 14 and 15) although the material was identical; this may be due to the complex influence of the sudden
transi-tions, the long inserted parts and the welding
process.
In any case it was a happy coincidence that for
both derricks failure could be traced on the
record-ings; the magnitude of the strain at the beginning
1904
Fig. 19. Variations of stepped derrick
of yielding in both casesjustiflcs the conclusion that,
for derricks, the yield-point may be considered as determining the moment of failure.
7 Supplementary tests
Based on the findings reported in the preceding chapters it was decided to extend the static inves-tigations in order to determine the influences of
d(fferent ways of interconnecting.
It was stated that the present manner of inter-connecting, with long inserted parts and strips,
can-not be classed as very successful. Therefore it was considered worth trying the behaviour of stepped derricks of which the interconnections were made
without long insertions, under similar loading condi-tions as for the former test-objects.
From the remaining intact parts of the first two
test specimens Variation I was manufactured (Fig.
19 and 20). As is shown two different transition
rings were applied to bridge the differences between
the outer diameter of a smaller tube and the inner diameter of the larger i.e. a common ring at the
transition places nearest to the ends of the derrick
and a ring with breasts at the other two transitions.
The latter was considered to be a better means of
transition.
The total length of this test object was about the same as that of the first test specimens; to achieve
76
5995
'coo
BZ7353
I ETC . STRAIN GAUGE NUMBER
ALL GAUGES ARE PLACED LONGITUDINALLY
535 21 23 U25 26 1249 / 7371 E 17 1747 1107 1749 7121 857 \
jS
\ 629 SX 64318 3000 2000 1000 1000
Q-Fig. 20. Stepped derrick Variation T
this it was necessary to form the middle tube from two parts of unequal lengths butt-welded to ea.ch other without an overlap. This provided another opportunity to try the behaviour of a pure butt-weld in a derrick-tube (in the preliminary test, reported in [4, similar butt-welds proved not to cause trouble, nor did failure occur at these places). As in the case of the conventionally stepped derrick an extra strain gauge was fixed near the corre-sponding weld joint (gauge no. il in Fig. 19).
Analysis of the stress distribution diagram (Fig.
21) leads to the following observations:
the stress-distribution per step is of a flatter char-acter than in the case of a conventionally stepped
derrick;
the transitions remain to be disturbing factors, but the absence of long inserted parts has a
soft-ening effect;
the presence of the mentioned butt-weld has a reinforcing effect, for the stresses in the proximity of the weld are always lower than may be ex-pected if the weld were not present;
- in general the influence of ring-welds in tubes on the surroundings seems to be of a reinforcing kind, for, here also, the strains shown by the gauge at 50 mm from the weld joint are lower than the strains at 250 mm from the weld at the same tube.
The failure test again was performed under the loading condition Mb = 1.38 tm, P increasing from
zero to maximum; the maximum axial thrust
amounted to 52.1 tons.
The buckle appeared at the weld joint, thus
not away from the weld joint as in the case of the
conventionally stepped derrick. This difference must be due to the influence of long inserted parts being
applied or not.
It is evident that the transfer of loading from a smaller to a larger tube and vice versa is different
P 40
Fig. 21. Test results of stepped derrick - Variation I exclusive of initial values by own weight)
1000 oLue t nornent f first e14j5
-I
/
--k- N-II,
II,
Il'
-r.
p.
-. - - -
.. .-t
-'I.-I
1ues P 30t M-069tn, -r I 0 va1es P lot M.0.69 tm 500 1000 s03000
2000
1000
1000
M1 = 138 tn,
Fig. 22. Test results of stepped derrick - Variation II (exclusive of initial values by own weight)
for the construction with direct connections (Varia-tion I may be considered to have direct connec-tions) or for the conventional stepped derrick with long insertions and strips. The direct connection has the character of a stiff (rusted) hinge - when the friction is overcome rotation in the hinge
fol-lows - whereas the latter mentioned connection method constitutes elastic fixations.
Both cases, meant above, are governed by the circumstance that the transition from one tube-diameter to a different one is abrupt. Therefore it was decided to eliminate this factor by making gradual (tapered) transitions.
A new test object was manufactured with tapered transitions between the steps (Variation II). The dimensions of this derrick and the location of the strain gauges are shown in Fig. 19 lower figure; for these supplementary tests the scanning of the most important parts of the derrick was necessary
oniy. This may explain the distribution of the strain gauges.
All interconnections were made by butt-welding
without laps. Fig. 22 shows the stress distribution
for similar loading conditions as for the former tests.
It must be concluded that, in general, this varia-tion too displays a much better stress distribuvaria-tion than the conventional stepped derrick; therefore it
2000
1000
1000
must be the long inserted parts that effect the
un-economical stress distribution.
The disadvantage of this Variation lilies in the
fact that the behaviour of the tapered parts in
bending is not quite controllable and it was to be
expected that the stresses at these parts would show complexities with relatively large peak-values.
The failure test under the loading conditions Mb = 1.38 tm and P increasing from zero to max-imum resulted in an ultimate axial thrust value of 47.6 tons, failure occurring at the transition be-tween gauges nos 8 and 13 (Fig. 19, lower figure). The tapered form of this transition effectuated a very elastic behaviour, so that an examination of this region after failure did not show any fracture, neither in the welds nor in the rest of the material
(metal-check-flaw-finder was used for this).
It was stated above that the long inserted parts introduce elastic fixation effects, whereas the ab-sence of them causes the straining right in way of
the abrupt transition places. In both cases the main cause of mentioned effects is the same viz, the mid-dle tube is too stiff relatively, so that part of the bending of this tube is shuffled off to the weaker intermediate tube. The greater the loading the greater is this part, and when a transition is located
in a region where the internal bending moment is
T P=40t P=301 IV P lot P = 30 t ¿:=rZ=_ P-20t / I FIL -=----II
t'
i
P-lot - J-__ifl_0i_____
M0t1
lì =120
Fig. 23. 'lapered transition ring of Variation 11, intact
4. Failure spot of Variation Il
considerable this will finally lead to overstraining of the smaller tube.
According to present-day design methods a 2-steps derrick has a middle tube of approx. 1/9L length. The transition from middle tube to inter-mediate tube then is located at approx. t/4L from midlcngth; this is inside the region of the higher
loadings.
It may be remembered (see also Appendix) that, for the case of a bar loaded with an axial thrust and an end-moment on one end only, the half of the bar on the side of the end-moment experiences a heavier loading than the other half, whereas the location of the maximum loading depends on the magnitude of the axial thrust. Consequently the transition from middle tube to intermediate tube
on the side of the end-moment is loaded more
heav-ily than its counterpart.
The test reported in [4] gives a strong indication
that a derrick with one short step at either end as tested at that time is a better construction in this respect; the length of the middle tube of this
test-object was 2/3L, the two end tubes being '/6L each. Shuffling-off of bending as meant above is
occur-ring in the regions of the smaller internal loadings, consequently this effect is smaller and the strength of this type of derrick is determined mainly by the
resistance of the middle tube. This explains the fact
that this test object (under similar loading condi-tions as for the test objects described above) did not fail by buckling in the end tube on the side of
the end-moment, but in the middle tube. The
length of 2/3L for the middle tube must be con-sidered the minimum length to avoid failure of the
smaller tube because of the shuffling-off effect.
'lable I. Ultimate thrust values
8 Conclusions
a. The objective of obtaining a more efficient der-rick (i.e. adaptation of the section modulus to the loading) by stepping a derrick according to present-day practice is not attained; the stress
distribution over the length of a stepped derrick
is far from flat and especially the smaller tubes
show a steepy stress gradient.
h. From the supplementary tests it can be con-cluded that the steepness of the stress gradient is determined by the long inserted parts being applied or not; the test objects without inser-tions showed a stress distribution with a flat character.
In general, the cylindrical derrick showed higher stresses than the corresponding, conventionally stepped derrick. Nevertheless the ultimate
strength of the cylindrical derrick is larger than
of the stepped derrick; thus, also in the respect of ultimate strength nothing is gained.
The transition places of stepped derricks, with or without insertion, effect complexities; this cannot be subdued by the applications of short gradual transitions as e.g. tapered rings. Welding as a means of interconnection seems to play an important role in summoning these
complexities. The behaviour of the surroundings
of ringwelds in tubes require a separate inves-tigation to elucidate the reinforcing effect of such interconnections. This concerns the regions
Cylindrical derrick
- according to the Euler formula 71.3 tons no
end-- according to diagram fig. 2 65.8 tonsj moment
- test result 56,3 tons
Conventionally stepped derrick.
end-tested 53.5 tons moment
Variation I, tested 52.1 tons 1.38 tm
P40t
-1 138 tn
P=lOt
2000
more pronounced.
Therefore preference must be given to the
cylin-drical derrick as being
- the one with the most reliable character, - the strongest type ultimately,
- the one computable in a simple manner.
The formula derived can be adequately applied to compute the stresses in a cylindrical derrick. A statistical mean value of initial deflection must be reckoned with. The yield stress of the material can be considered to be the ultimate stress.
If one wants to hold to the manufacturing of stepped derricks it is the author's opinion that - the application of long inserted parts cannot
be recommended;
- the length of the middle tube, as determined by the present-day method, is not conform-able to the loading; the middle tube resist bending at the expense of the weaker inter-mediate tube.
In view of the findings of the present
experi-mental investigations and the conclusions which had to be made, the necessity of a better design
method for stepped derricks has obtained quite another meaning. A reflection of the following
questions is advisable
does one want to hold to the conception of stepped derricks with abrupt transitions (this includes the transitions with short tapered rings) notwithstanding the fact that these very transitions are unsuitable for a
satisfac-tory load-transfer?
does one want to hold to the manufacturing method with long inserted parts, even if the effectiveness and economy of this method is
disputable? of the transition from one tube to another of
different diameter as well as the regions of butt-welds connecting two tubes of equal dimensions. f. The investigations proved that there is no
ob-jection against butt-welding without laps in der-ricks' manufacture, provided correct welding is
applied; failure will not occur at the butt-weld
because of this weld, if occurring at this place.
Comparing the corresponding stress diagrams for the cylindrical and the conventionally step-ped derrick (Figs. 16 and 25) it can be stated that there is not any reason to reject the
cylin-drical derrick, J.
- neither on account of a "better" stress dis-tribution in the stepped derrick,
- nor because of a possible saving in weight to be gained with the stepped derrick, not to mention the more complex manufac-turing procedure and the correspondingly higher costs for stepped derricks.
The manufacturer informed that the
fabrica-tion of the cylindrical and of the corresponding k.
conventionally stepped derrick, of the length under discussion in this report, and fitted out
with all provisions for direct use on board would be in favour of the cylindrical derrick. This would imply a saving of D.fl. 130 in costs, 35kg
in weight and 10 manhours in time.
h. As regards the stepped derricks without
inser-tions as compared to the cylindrical derrick the following conclusions can be made:
for the lower loadings e.g. Mb = 1.38 tm and P = 10 tons again the cylindrical derrick must be preferred because of the absence of complexities in way of the transitions; for a higher loading, e.g. Mb = 1.38 tm and
P = 40 tons, mentioned complexities are even
cy1ndrL
t.ngth f -. -. tor
- conventlonLty stepped
22
Acknowledgements
The author wishes to acknowledge the assistance
and the benevolence he has received in accomplish-ing the investigations.
He should like to thank Messrs "Vcrenigde Ne-derlandse Scheepvaart Maatschappij" and Messrs "Koninklij ke Paketvaart Maatschappij" for the donation of the first test specimens He is also in-debted to "M. A. de Keijzer N.y." for the con-tribution in the costs and the manufacture of the
proper test pieces.
REFERENCES
The Board of the Dockers' Training School at Rotterdam granted permission and cooperation for measurements on the derricks of the School's cargo-handling equipment.
The help of the technicians and the staifmembers
of the Ship Structures Laboratory was invaluable; the author wishes to thank them all, naming Mr. H.J. DE RUITER and Mr.J. VERSCHOOR.
Mr. K.J. C. DE WERK and Mr. R. VAN LEEU WEN
arc thanked for elaborating the results of the
meas-urements and for preparing the illustrations.
1. L. P. HERFST, Studie betreffende de berekenirig van
Laadbomen. Unpublished report - Department of
7. D. F. MCNAUGHT, Cargo Handling Arrangements,
Chapter VIII of Design and Construction of Steel
Naval Architecture, Technological University, Deift Merchant Ships, 1955.
2. F. X. P. SOEJADI, \'oortzetting van de studie over dc
berekening van laadbomen. Unpublished report
8. H. BLEICH, Buckling Strength of Metal Structures.
McGraw-Hill, New York 1952. Department of Naval Architecture, Technological
University, Delft. 9. E. CHWALLA, Über die Experimentelle Untersuchungdes Tragverhaltens gedrückter Stäbe aus Baustahl. 3. M. VERTREGT, Systematische knikberekeningen van
laadbomen. Unpublished report - Department of Der Stahlbau, vol. 7, 1934.
Naval Architecture, I'echnological University, Deift. 10. 5. TIMOSHENKO, Theory of Elastic Stability. McGraw-Hill, New York 1936.
-1. F. X. P. S0EJADI, Experimental Investigations into the
Strength of Ships' Derricks - Preliminary Draft. 11. LAGRANGE, Sur la Figure des Colonnes. See: J.
Too-Report no. 85 of the Ship Structures Laboratory of HUNTER and K. PEARSON, History of Elasticity, vol. I. the Technological University, DeIft, July 1961. 12. J. CH. DE DOES, Description of the New Laboratories of 5. .1. B. DAvIEs, The Strength of Ships' Derricks. Trans.
Inst. of Naval Architects 1951.
the Department of Naval Architecture,
Technolog-ical Univessity. Deift. Part I. The Ship Structures
Appendix
A.1 The total loading case can be subdivided
into 3 subcases
(Figures 5, 6, 7, 8) Subcase I (Fig. 6)
Analysis along well-known lines leads to the
fol-lowing expression:
iii which
u=h/9l1andk2=Í'
Bij differentiating two times
I 2x
cos u
1 q '. i+1
P cosu Thus M= -
Ely" k2 cosuql
\. 1 I cos u Il --r/
2x 11Mmax acts in way of1/21
ql2 2(1 cosu)
Mmax
8 u2cosu
* **
* effect of the uniform load;
effect of the axial thrust P
this factor is small for small values of P and 2EJ
q
Pk2 L cos u
2x
1
will be infinite for P
=
Pcriticai=
12
Subcase Il (Fig. 7) For this case
Isin kx x
I.
P LSlflkl 1 Mb [sin kx=-
Pk2.
LS1fl ki M=
Eli'
=
M, :To find the place of the maximum bending moment
the procedure is
dM Mb
=k
coskxdx sin kl
This is zero when cos kx
=
O, provided sin ¡cl O¡cx
=
2
X
=
2k which ¡c2this means that the place of the maximum bending moment depends upon the magnitude of P. a. if Mmax is to be acting in the region O <x < i
then
so this is a cosec relation, not a secans relation
as in the case of an Mb on either end of the bar.
Suhcase III
Assuming a sinusoidal initial deflection we may
derive the following relation a Y =Yo+yi
=
sin k212 1-M=
Ely1"
=
I _}212It may be observed that P
=
Pcrjcai=
22EI/i2 isa critical value mathematically, for in this case the denominator will be zero; whether the bar has
failed before Perit was reached is not a mathemat-ical but a strength problem.
I
x>O--
>OorP>O
EI
<1 orP>
2!
EI
2 412 2EJif P <
4f2 there is not a real Mmax, but the bending moment in way of x=
i is largest.for x=1/il-kl=tinthiscase sinkl=O;
sin ¡cl
=
O - if ¡cl=
O, this means k=
O orP
=
O (no axial thrust),- if ¡cl
=
t, 2 etc.kl
= '
would mean P=
n2EI/12;this is the Euler buckling load for
a simply supported bar.
Hence sin ¡cl
=
O may be disregarded.the magnitude of Mmax, for
41'
<
122EJ 2EI
24
a
Mmax =
k12 way of x = 1/21.
i
Superposition of the three subcases gives:
2x'
[cos.i
¡)
Mxtotai = Isjn kxlP.a
+
Mb [sin ku+
k2l21-The total stress in the extreme fiber is
+
W
F = area of cross section, W = section modulus.
A.2 The comparison of theory and
experiment
It was noted that a certain manner was followed to check theory and experiment for a certain
load-ing case. The total stress at a certain point can be
measured and it can be calculated according to the
expression
''tota1
eltotal =
+
in which M101
=
account of own weight) +
account of end bending moment) + account of initial deflection).
For 2 loading cases viz.
Mb = 1.38 tm Mb = 1.38 tm
P =
10 tonsP =
30 tonsatotaj at x = was measured
M1
atotai at x = 11.21 minus was calculated (2)
The difference between (1) and (2) may be con-sidered as the value forM111IW. Working reversely
the magnitude of the initial deflection a can then
be found.
This value of a then was used for the calculation
of crtota at the other stations and the results were
compared with the measured values at the cor-responding stations.
For the cases investigated good agreement was found between theory and experiment (Fig. 15).
(1)
M (on
+
M11 (onReports
No. i S The determination of the natural frequencies of ship vibrations (Dutch).
By prof. ir H. E. Jaeger. May I 950.
No. 3 S Practical possibilities of constructional applications of aluminium alloys to ship construction. B prof. ir H. E. Jaeger. March 1951.
No. 4 S Corrugation of bottom shell plating in ships with all-welded or partially welded bottoms (Dutch).
By prof. ir H. E. Jaeger and ir H. A. Verbeek. November 1951.
No. 5 S Standard-recommendations for measured mile and endurance trials of sea-going ships (Dutch).
By prof. ir J. W. Bonebakker, dr ir W. J. Muller and ir E. J. Diehi. February 1952.
No. 6 S Some tests on stayed and unstayed masts and a comparison of experimental results and calculated stresses (Dutch).
By ir A. Verduin and ir B. Burghgraef. June 1952. No. 7 M Cylinder wear in marine diesel engines (Dutch).
By ir H. Visser. December 1952.
No. 8 M Analysis and testing of lubricating oi]s (Dutch).
By ir R. N. M. A. Malotaux and ir J. G. Smit. July 1953.
No. 9 S Stability experiments on models of Dutch and French standardized lifeboats.
By prof. ir H. E. Jaeger, prof. ir J. W. Bonebakker and J. Pereboom, in collaboration with A. Audigé. October 1952.
No. 10 S On collecting ship service performance data and their analysis.
By prof irJ. W. Bonebakker. January 1953.
No. 1 1 M The use of three-phase current for auxiliary purposes (Dutch).
Bv irJ. C. G. van Wijk. May 1953.
No. 12 M Noise and noise abatement in marine engine rooms (Dutch).
By "Technisch-Physische Dienst T.N.O.-T.H." April 1953.
No. 13 M Investigation ofcylinder wear in diesel engines by means oflaboratory machines (Dutch).
By ir H. Visser. December 1954.
No. 14 M The purification of heavy fuel oil for diesel engines (Dutch).
By A. Bremer. August 1953.
No. 15 5 Investigation of the stress distribution in corrugated bulkheads with vertical troughs.
By prof. ir H. E. Jaeger, ir B. Burghgraef and I. van der Ham. September 1954.
No. 16 M Analysis and testing of lubricating oils II (Dutch).
By ir R. N. M. A. Ma/otaux anddrs J. B. Zabel. March 1956.
No. 1 7 M The application of new physical methods in the examination of lubricating oils.
By ir R. N. M. A. Malotaux and dr F. van Zeggeren. March 1957.
No. 18 M Considerations on the application of three phase current on board ships for auxiliary purposes especially with
regard to fault protection, with a survey of winch drives recently applied on board of these ships and their
in-fluence on the generating capacity (Dutch).
By ir J. C. G. van Wok. February 1957.
No. 19 M Crankcase explosions (Dutch).
By ir J. H. Minkliorst. April 1957.
No. 20 S An analysis of the application of aluminium alloys in ships' structures.
Suggestions about the riveting between steel and aluminium alloy ships' structures. By Prof ir H. E. Jaeger. January 1955.
No. 21 S On Stress calculations in helicoidal shells and propeller blades. By dr ir J. W. Cohen.July 1955.
No. 22 5 Some flotes on the calculation of pitching and heaving in longitudinal waves.
By ir J. Gerritsrna. December 1955.
No. 23 S Second series of stability experiments on models of lifeboats. By ir B. Burghgraef. September 1956.
No. 24 M Outside corrosion of and slagformation on tubes in oil-fired boilers (Dutch). By dr W. J. Taat. April 1957.
No. 25 S Experimental determination of damping, added mass and added mass moment of inertia of a shipmodel.
By ir J. Gerritsma. October 1957.
No. 26 M Noise measurements and noise reduction in ships.
By ir G. J. van Os and B. van Steenbrugge. May 1957.
No. 27 S Initial metacentric height of small seagoing ships and the inaccuracy and unreliability of calculated curves ol
righting levers.
By fro.f. irJ. E1 Bonebakker. December 1957.
No. 28 M Influence of piston temperature on piston fouling and piston-ring wear in diesel engines usmg residual fuels.
By ir H. Visser. June 1959.
No. 29 M The influence of hysteresis on the value of the modulus of rigidity of steel.
By ir A. Hoppe and ir A. M. Hens. December 1959.
No. 30 S An experimental analysis of shipmotions in longitudinal regular waves.
By ir J. Gerritsma. December 1958.
No. 31 M Model tests concerning damping coefficients and the increase in the moments of inertia due to entrained water
of ship's propellers.
By N. J. Visser. October 1959.
No. 32 5 The effect of a keel on the rolling characteristics of a ship. By ir J. Gerritsma. July 1959.
No. 33 M The application of new physical methods in the examination of lubricating oils. (Continuation of report No. 17 M.)
By ir R. N. M. A. Malotaux and dr F. van Zeggeren. November 1959.
No. 34 5 Acoustical principles in ship design.
B)' ir J. H. Janssen. October 1959.
No. 35 5 Shipmotions in longitudinal waves.
By ir J. Gerritsrna. February 1960.
No. 36 S Experimental determination of bending moments for three models of different fullness in regular waves.
By ir J. Ch. De Does. April 1960.
No. 37 M Propeller excited vibratory forces in the shaft of a single screw tanker.
By dr ir J. D. van Afanen and ir R. Wereldsma. June 1960.
No. 38 S Beamknees and other bracketed connections.
By prof. ir H. E. Jaeger and irJ. J. W. Nibbering. January 1961.
No. 39 M Crankshaft coupled free torsional-axial vibrations of a ship's propulsion system. By ir D. van Dort and N. J. Visser. September 1963.
