Some practical conclusions from strength research in shipbuilding

ARCHEF

LABORATORIUM VOOR

SÇH EEPSCQNSTRUCTI ES

TECHNISCHE HOGESCHOOL - DELFT

RAPPORT Nr.

SOME PRACTICAL CONCLUSIONS FROM STRENGTH RESEARCH IN SHIPBUILDING

by

Ii-J-.-J-i'W.-NIBBER ING

Some Practical Conclusions from Strength

Research in

Shipbuilding*)

Shpbu11ding is sometimes blamed for being conservative. There

might be some truth in this, but I for one believe that what is called conservatism in fact is a dislike of taking unnecessary risks. It is a fact that ships nowadays are virtually never lost

as a result of a deficiency in strength. This, in my view, is a very favourable situation and prooi of a healthy respect for

human safety. This may be underestimating the economic aspect,

but it should be remembered that a similar unequalled high

standard of personal safety exists In, for instance, passenger

vessels. And there, safety is obtained at a very high price indeed.

Where the strength of ships is concerned, the existing safety is largely due to a type of strength research which in shipbuilding has almost been brought to perfection. Before embarking on this subject, it may be useful to discuss what Is covered by the

vague term "strength research". It is mostly associated with

theoretical and experimental investigations concerning the

load-bearing capacity of structures. A, at least equally important, problem in shipbuilding, however, is the estimation of the loads themselves. To what forces must a ship be able to stand up? There has for a long time been much uncertainty in this field and this is still reflected in actual shipbuilding practice.

How-ever, In little more than ten years, much progress has been made, as will be shown in the second part of this paper.

Until recently the problem was that only limited knowledge of the magnitude of loads was available. A natural consequence of this would have been the introduction of a large safety factor

or, rather: Ignorance factor , in order to compensate for

that deficiency. In shipbuilding, however, this uneconomical policy could be avoided by what can be called empirical re-search. In probably no other field of engineering has a situation

been created in which practical experience is so efficiently used as in shipbuilding. It is well-known that this is largely due to the existence and the activities of the ëlasslfication societies.

An important factor, however, was the relatively slow

develop-ment in the dimensions and types of ships, owing to which the design of newbuildings could be based on experience gained in existing ones. This situation changed drastically in a relatively

short time and this called for strength research in a less

em-pirical form, with the final intention to be able to calculate the required section modulus of ships independently of the general

practical experience. For a long time to come, however, the primary function of strength research will be to provide the

tools and background necessary for the proper selection, analysis bnd1Ïiterprctatlon-of-practical-information--It--is--refreshlng- to

see that the classification societies fully realise that this is

necessary.

The virtually ideal empirical or semi-empirical approach to the strength problem in shipbuilding, of course, also has certain disadvantages in that a compromise must be -made between safety, economy and practical feasibility. From the above it

might be deduced that all ships are constructed optimally, but this would be too optimistic a view. Appreciable differences in technical skill and workmanship exist in different sh1pyar6 This factor has become highly important with the introduction of welding in shipbuilding. Accurate dimensions of plates and

sections favour the quality of welds, unfairness of plating

induced by welding reduces the efficiency of plate structures and the welding Itself depends more on human skill than

riveting.

Another influence causing differences In the margin between the required and necessary strength In ships Is due to the fact that classification rules cannot take into account all kinds of variables existing in ships. Route, speed and cargo distribution can play an important part.

With the growing Insight in such factors, it might become

desirable for shipbuilders to carry out Investigations and special

calculations for each ship to be built 1f they are to take full

advantage of modern scientific achievements. Proposed im-provements, of course, should be approved by the classification societies.

In accordance with the principles of the orthodox method, the longitudinal bending moment in a ship can be divided into the

) 'Paper read at Thtrd Europort Exhibujon. Rotterdam. 1964

BY IR. J. J. W. NIBBERING

Fig. 1.

Fig. 2.

The relative position of ship and wave then does not change and a static calculation can easily be effectuated. This is nor-mally done for the conditions wave crest amidships (fig. 1) () and wave trough amidships (fig. 2). It was soon realized by

Smith that this situation 'is not so static as was supposed. The

water particles of the wave are constantly accelerated and

retarded depending on their position. Due to this pressure of the water in a wave crest Is lower and in a wave trough higher

than indicated by the hydrostatic -height. The correstion involved can be up to 20o/OP

The so-called standard-wave calculation is still in use for the estimation of the wave bending moment although everybody realizes that It is a rough approximation. But this is not so

important when its results are only used as a means of corn-parison between different ships of rather corresponding types

and dimensions.

In the course of time attempts have been made to improve the

method in order to obtain a better estimation of the real bending

moment. For instance Robb and Alexander have presented

methods in which heaving and pitching is taken into account. Heaving ispimarllyaconsequence of the fact that a ship with wave crest amidships is In a higher position then with wave-trough amidships. This Is due to the relatively smaller amount

of displaced water at the ends of a ship as compared.with amidships.

The calculations of Robb and Alexander only take into account

the influence of the virtual weight-increases and -reductions corresponding to inertia forces, on the position of the ship in the standard wave. The Influences which were neglected are:

() &. nd of

1 The disturbance of the wave caused by the presence of a

moving body.

2 The damping of the heaving and pitching motions by forces corresponding to the wave-making-resistance of the ship in

vertical direction.

3 The virtual amount of water brought into movement during

heaving and pitching, called added massi

4 Different headings of the ship rèlative to the waves.

5 The irregularity of sea-waves. -6 The influence of slamming.

Slamming is a ¡eparate phenomenon and will not be Included

In this discussion.

The other factors have extensively been Investigated In recent years both theoretically and empirically.

We now make a big step and assume that all these factors can

be Included in calculations. Then the crucial point remains that we ought to know the states of the sea a ship will meet

through-out her life. This particularly applies to polnt: the

irregular-ity of the sea, for though we can imagine any sea-state we like,

we should know If it is realistic and how often It occurs. This leads us to the question if it Is possible to bring the apparent

SSL 99

so-called still water bending moment and the wave bending moment. The former can easily be calculated and will not be discussed. The simplest estimate of a wave bending moment is obtained by assuming that the ship speed is equal to the speed cf a wave whose length Is equal to that of the ship.

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disorder of the sea in one or ahother form on the basis of which the bending moments in a ship can be estimated. The answer

is yes. There exists very convenient and attractive methods

which have not so long ago been introduced in shipbuilding by St. Denis, and Pierson. The sea and associated phenomena

occurring with ships like movement and bending can be described

in a statistical way

It is important to realize that these methods are not a kind of substitute or approximation for one or another perfect method,

but that they are the only true and possible methods;

sea-induced phenomena a.re statistical phenomena.

For instance speaking about the maximum toad a ship will meet

in practice has no sense, we only can speak about the chance

that more or less extreme loads occur and how accurate this

statement can be made. The official, terms used in this respect

are probability and confidence 4imits

-

W

Fig. 3.

We now will show how the apparent 'disorder of seaways can be represented in mathematical and statistical forms.

The confused picture which the sea presents us can be con-ceived as the sum of a large number of regular sine-formed

Waves. Each sine-wave is characterized by three variables viz

length,. height and phase (fig. 3). In stead of length(2) is mostly

used the frequency w =

:

It will be clear that nothing is won In this representation, when

w2 w3

Fig. 4. Unrealistic wave spectrum.

all sine waves would be completely independent of each other

for instance as shown in fIg. 4 where for waves with frequencies

w 1, w 2, w 3... various imaginary wave heights are Indicated. This picture is in conflict with theory and also with analysis of

obsdrvations.

Fig. 5 shóws a realistic possibility. As can be seen a smooth curve can 'be drawn through the various points. In this figure

the ordinates are not equál to the wave height, but to the

wave height, squared divided by the value W.,Wn.j = 4w for

convenience. The reason is, that in this way the area below the

W1 + W2 + W3

curve is equal t'o the energy of the wave system per unit length,

which is a very valuable item for further manipulations. The energy is constant at every point of the sea within a restricted

area.

Fig. 5 is called energy spectrum; it shows the contribution to the total energy of eaeh individual sine wave.

Fig. 5. Energy spectrum.

Neumann and others have succeeded in calculating energy

spectra for fully-developed seas in idealized wind conditions. Such spectra contain a lot of information about the sea but not everything for the _{phase differences between thè various} elementary sine waves are not given. This cannot be else as the

phase differences are, - and must be - completely arbitrary.

Otherwise any wave system built up by a number of sine waves

would repeat a certain configuration periodically.'

With random phase differencfes wave configuration can never be repeated. It is probably known that for phenomena purely determined by chance. like waves certain statistical laws apply. For instance when the ordinate of the sea surface at a certain

point is measured at small intervals of time we can get a

distribution as given in fIg. 6. The mean value of course must

be zero. The figure shows that about 20 0/0 of all measurements

are approximately equal to zero, viz, fall in the interval

O,S<<0,5

Larger values for f.i. l,5<o(2,5 are less frequent. When for

each interval of h the corresponding frequency is plotted, We obtain a curve called frequency' distribution ,or histogram. It looks like a church-bell, although it can be a very slender one or a very broad one.

These church-bell c,urves all conform o a' function

P(x) =

V xR

probabiLity p

20%

'1

-..wave

ordinate X

Fig. 6. Histogram or frequency distribution. Gaussian shaped.

which has been found by Gauss and others.

This knowledge greatly reduces the number of observations necessary for the estimation of the frequency distribution of

wave-ordinates.

Several hundreds of observations are sufficient for a satis-.

factory calculation of the value R. This R-value is characteristic

for the state of the sea during which the measurements were taken; it is the only parameter in the Gauss function. As long as this state of sea does not change the R-value applies. Con-sequently any number of observations sufficient for a reliable calculation of the R-value, viz, a few hundred observations,

gives us the frequency distribution belonging to many thousands

of wave ordinates. The R-value can easily be calculated by

taking the double mean of the square of all observed values. With respect to the longitudinal bending of ships the frequency distribution of the vertical distances between the top and foot of adjacent waves is more important than the frequency

dis-tribution

of the wave ordinates. It does not conform to a

.-wve ampLitude H

FIg. 7. Rayleigh-shaped.

Gauss-distribution but another one, called Rayleigh distribution

which has the character of fig. 7 2H _H21

e ¡

R

The value R once again appears. For measurements of pheno-mena, for which Rayleigh distributions àply, the R-value can

Hi2

easily be calculated by R - _N

Here again we can estimate the frequency distribution for

thousands of peak-to-peak values occurring in one sea-state by

measuring only a few hundred ones. The R-value calculated out

of them determines the distribution of the whole.

Up to now nothing has been said about the connection between

the frequency distribution of peak to peak values and the

energy spectrum applying to the particular sea condition. There is an important connection, for the R-value of the frequency

distribution is equal to the area of the energy-spectrum. As stated before, this area Is equal to the energy of the wave

system per unit length.

It will be clear that many different energy-spectra can be formed, all having the same area. This of course means a

complication, particularly for theoretical research, but it will

be seen that for practice this difficulty can rather well be overcome.

We now come to our particular problem viz, the wave bending moment. There exist two hypotheses, rather well verified, -which enormously simplify the determination of bending mo-ments for ships in Irregular waves:

i The wave bending moment in an elementary regular sine wave of given frequency is proportional to the wave-height

M

=A

(co) (co)

A is called the response amplitude operator which

simply is the bending moment per unit wave height. 2 The total bending moment due to combinations of waves of

different frequencies Is equal to the sum of the bending

moments caused by the individual waves.

These two hypotheses give us the possibility to calculate the

64 Holland ShIpbuilding

bending moments of a ship for all kinds of wave spectra and

consequently for any R-value we like if we only dispose of

results of a limited number of model tests in regular sine waves

of different frequencies.

The procedure is simple: For each desired wave frequency the response amplitude operator is obtained with the aid of a model

test (Aj) - measured bending moment per unit wave height). Next, each ordinate of the wave-height-spectrum is multiplied

by the amplitude operator for the same frequency. The new

ordinates form altogether the bending moment spectrum.

Of course the bending-moment-energy-spectrum can in a similar

way be obtained out of the wave-energy-spectrum by multi-plying each ordinate by A 2.

The area of the obtained bending-moment-energy-spectrum is

equal to the parameter R of the frequency-distribution of

bending moments. (This is a similar relation as between the wave energy spectrum and the wave frequency-distribution.) We have started from a certain wave spectrum and finally have

obtained the corresponding frequency distribution of the bending

moments. It ¡s important to realize that if we should have

started from another wave spectrum of equal energy, a. different

R-value for the bending moments would have been obtained and consequently a different frequency-distribution of bending moments.

This is an unwelcome complication whlch necessitates disposing

of realistic wave spectra for all energy-conditions of the sea. When these spectra are available and also their relative quency of occurrence, a more realistic bending moment

fre-quency distribution can be obtained for each

wave-energy-condition than In the before-described procedure.

When we now dispose of a frequency-distribution of R-values

of the sea for the whole-lifetime of a ship (long-term distribution)

we can calculate the corresponding frequency-distribution of R-values of wave-bending moments and out of this the long-term distribution of the bending moments themselves.

The picture given here is a little too optimistic and too

sim-plified, but in principle it can be done. In a more or less

standardized form it will at least constitute a fine substitute for the standard wave calculations still in use.

I hope it is agreed that this is a very practical conclusion, particularly in view of the rapid developments In shipbuilding nowadays.

The restricted length of this paper does not allow an Illustration of the various achievements and methods for the most reliable estimation of longterm distributions of R-values or predictions of extreme values of bending moments. For those who like to

know more about this a list of literature is given, of which the last one Is particularly recommended. As a final observation it should be underlined that not only extreme values of bending moments are of interest for shipbuilding. The whole long-term-distribution is important because it is a very good measure for the fatigue loading of a ship during her life.

With the ever increasing safety of ships with regard to brittle fracture - and compressive instability fatigue might become a dominating factor in ship structural design.

LITERATURE

St. Dennis & W. Pierson: On the motions of ships in

con-fused seas.

Trans. S.N.A.M.E. Vol. 61-1953.

R. Bennett: Stress and motion measurements on ships at sea.

Rep. No. 13 of the Swedish Shipbuilding Research Association

1958.

E. V. Lewis: A study of midship bending moments in irregular

head seas. T2-SE-Ai tanker model. i

Journal of Ship Research. Vol. 1-1957 Nr. 1.

H. Jasper & J. W. Church: Structural seaworthiness studies. Trans. S.N.A.M.E. 1963.

G. Vossers: Fundamentals of the behaviour of ships in waves.

I.S.P. 1959.

(In Dutch: Grondslagen van het gedrag van schepen in

golven: Schip en Werf 1959 e.v.)

R. Bennet: Determination of wave bending moments for ship design.