Data on midship bending stresses from four ships

CH1EF

INTERNATIONAL SYO.SIUM ON THE DYNAMICS OF MARINE VEHICLES AND STRUCTURES IN WAVES

at

University College London, May l971

Paper number 30

DATA ON MIDSHIP BENDING STRESSES FROM FOUR SHIPS

by

G. Ward and M. Katory (with Appendix by P. Gedling)

Lab. y.

Schepsbouwkunde

Technische Hogeschool

Deth

1. INTRODUCTION & SUMMARY

Data loggers have been fitted by B.S.R.A. to four ships to

measure main hull and local strains together with other parameters used in

the general assessment of ship performance in service. This note presents

an analysis of some of the logger data on the main hull bending stresses

from three of these ships. A complementary project at B.S.R.A. is

the recording of main hull bending streeseS using statistical counting

gauges; these have been used on 38 ships over the last 19 years and data

from such gauges, fitted to the same ships as above, are also presented.

The main hull stresses, as measured by the loggers, have been analysed using a numerical filtering technique to separate the wave induced stresses from the springing stresses and the results have been presented in

cumulative probability forni. This form of presentation _{suggests the maximum}

stress likely to be experienced in say a ship's life-time. A similar

presentation of the statistical strain gauge data has been given using a

simple cumulative analysis of the number of stress reversals counted;

also a method has been applied, to the same data, that fits a theoretical

double exponential distribution to the maximum stress over a number of watches

chosen at random to give projections of hull bending stresses which are likely to be experienced over specified time-spans and with a known degree

of statistical confidence.

Analysis of the combined signals of wave induced and springing

stresses has shown that an equation originally proposed by Rice (Ref. i)

and recently used by Miles (Ref. 2) defines the short term behaviour of

-2-Calculations have been carried out for the wave induced stresses, using programs developed at B.S.R.A., and these have been developed in the same cumulative probability form as the analysed ship data for

comparison purposes at a probability corresponding to a ship's lifetime.

Further work is required to complete the analysis of the measured

d.ata and the calculations and in particular to consider the combined wave induced and springing stresses.

3

1. AUTOMATIC DATA LOGGING SYSTEMS

The objective in using data loggers was to record a large sample of the required data for a ship in normal service with no interference to

the ship's routine and a minimum of extra tasks for the crew. The first

system used by B.S.R.A. was a 25 channel automatic data logger developed

from a successful aircraft flight recorder. Ships A and B were fitted with

these (see Table 1 for ship particulars).

This logger automatically records information in digital form

every 12 hours, for a period of 20 minutes, with a scanning rate of 25

channels per second, that is each channel is sampled once per second. To

provide for a sufficient sampling rate to allow springing stresses to be deduced,, five channels are used for one strain gauge measuring main hull

bending stresses, making the scanning period for this gauge 0.2 secs. The

only operation required by the crew is to change tapes about once every

15 days, and periodically post these back to B.S.R.A. In addition to this

task the crew are asked to fill ii log-sheets which provide general data on the ship's condition and also visual estimates of the sea conditions prevailing during each watch.

The initial requirement for data loggers was essentially from the speed and power performance point of view, but a later requirement to

measure local strains led to the choice of a second system which was

fitted to ships C and D (see Table 1 for ship particulars). This has

many more channels than the first system and is used in a mode which logs

information on 90 channels with a scanning rate of 30 channels per second.

Data is again logged automatically every 12 hours for a period of 20

transducers use more than one channel and in particular the main hull bending stress uses 15 channels to provide a scanning period for this

gauge of 0.2 secs.

3.

STATISTICAL STRAIN GAUGES

The investigation using statistical strain gauges has been

ii operation at B.S.R.A. for the last 19 years and in that time 38 ships

have supplied service stress data covering a total of over 50 years of

recording time. The equipment used for measuring the main hull bending

stresses (Ref. 3) will only be briefly described here. It is a strain

gauge, with a 100 in gauge length, arranged to record the number of

excedences, at predetermined stress levels, on electro-mechanical counters. The gauge is mounted on the deck structure near amidships, either near the centre line or near the deck edge, and the recorder is usually located

on the bridge, for the deck officers' convenience in logging the counts

each watch. The gauge does not record changes in the mean level of the

stress but only records the out-to-out longitudinal stress excursions experienced in the deck structure owing to wave bending action or to main

hull vibration.

In this note only the statistical strain gauge data is given

for those ships also fitted with data loggers. The position of the gauges

in these ships is given in Table 2. The main hull stresses given for the

data logger have also been measured by a 100 in strain gauge, which was

5

).. DATA PROCESSING OF LOGGER STRESSES

Fig. i shows the scheme for processing the data recorded by the

loggers. When received at B.S.R.A. the magnetic tapes which in both

systems are in a non-standard digital format are read into the computer and

operated on by pre-analysis programs. These check for parity, scanning

and formatting errors and make corrections before transferring the logged

data to magnetic tapes in standard computer format. These in turn are

further processed by a preliminary analysis routine which contains calibration information, to provide a summary of the data, such as mean value and standard deviation of each parameter, and also to provide a copy

of the data for further analysis such as that decribed below. The stress

data are analysed to provide spectra together with the area under the

spectra m and their second rn2 and fourth m moments. The latter are used

-

2'

\!

2(J-cz)

exj

where (z,n) = the probability density function of z

z = the height of the peak stress divided by the root-mean-square of the record

2

m2 m

o

erf error function

exp exponential

(1)

in the Miles equation (Ref.

vTi

2). 2

--z + [l + erf{z = . e 2(1-n) 2

The stress data are also filtered to separate the wave induced from the springing stresses before passing through the spectral analysis

routine. The requirement is for a band pass digital filter that will only

pass the wave encounter frequencies, using the 20 minute records with a

sampling period of 1 second. Also a band pass filter is required that will

only pass the data in the vicinity of the two node mode of vibration

slid, for this, any 5 minutes of a 20 minute record are used with a

sampling period 0.2 second. The selected 5 minute records are also

filtered by a band pass filter to obtain the wave induced stress in order to determine the corresponding amplitudes of combined, wave induced and

springing stresses. Filtering techniques have been described by Martin

(Ref. ) and the output of such a filter is defined by

N2

6

N1

where y1(t) is the input, T is the sampling time interval and the numerical filter is the (N2-N1l) weights Bk. The filtering of a set of data is

achieved by moving equation (2) along the data points (N2-N1)/2 times. This

gives a weighted value to each point in turn with a contribution from the N points before and after where 2NN2-N1. Ref. 4 provides information

the weights Bk to be used for various types of filter. Fig. 2 illustrates

diagramatically the combined and filtered signals and also defines the stress

peaks and reversals.

Numerical procedures are used to define the stress reversals from which histograms for the various records are computed and also their

root-mean-square (R.M.S.). Long-term probability trends are calculated

following the methods used by Lewis and Hoffman (Ref. 5). These assume

that the peak-to-trough distribution of stresses within a record are

Rayleigh distributed and the R.M.S. stress values are normally distributed

within any one weather group. The weather groupings used, for both the

logger data and the statistical gauge data, are given in Table 3.

Long-term probability trends are calculated based on the R.M.S. of thr stress

7

reversals in each record, the measured maximum stress reversal in each record and the predicted distribution of maxima of stress reversals assuming a double exponentional form for this distribution.

DATA PROCESSING OF STTISTICAL GAUGE STRESSES

The stress counts per watch together with other relevant information, such as Beaufort Number, wind direction, ship's heading,

sea area, ship's loading condition, are first checked for consistency before

the data is put into punched card form and then transferred onto magnetic

tape. A computer sorting routine is then used to group the data into

various categories such as Load or Ballast condition and Weather Groups. Detailed sortings are being carried out on the total data but for the

purposes of this note only Weather Groups and Load and Ballast conditions

are presented separately.

Figs. 3 to 6 show the data, for each of the four ships, presented

in histogram form for each Weather Group to allow the effect of weather to be seen, but for the probability distributions based on these data and

shown in Fig. 7 the combined data were used. The cumulative probability

values Q were derived from the formula

Q=l

nXCn+l

E n+l

where C = cumulative count up to the n th stress level and En = the total

n

Register

-8

Table 1 shows the results of a method. of analysis which

is described in detail in the Appendix. In this method the analysis is

carried out on the maximum stress logged in each watch. From these a

frequency distribution is formed using the gauge interval of i ton/in2

for the groups. _{That is, a maximum stress of less than 1 ton/in2 would}

be in the O-i group and a stress of 3 ton/in2 would be in the 3-1f group.

The maximum stress data is assumed to follow a double exponential form for which the parameters are derived in the manner described in the

Appendix. _{Goodness-of-fit tests on the derived equations did not generally}

show up well when the method was applied to the total data sample per ship or to the data divided into Weather Groups but a considerable improvement was achieved by applying the method to the maximum stress logged in ten

watches picked at random from the total data.

A particularly large sample of data, which is used in Table )4,

was obtained by grouping together the statistical strain gauge data for six

sister ships*, one of which is ship 'B' in Table 1. The data, which

is divided into two groups to correspond to the periods of operation

before and after major structural modifications, have been further anälysed

by treating the maximum stress in twenty watches and. the maximum in one

hundred watches all chosen at random. For this large sample, satisfactory

and consistent fits were obtained for each of these higher groupings.

6. THEORETICAL CALCULATIONS

To support the work on ship measurements, calculation

procedures have been programmed at B.S.R.A. to determine the wave induced

motions and loads. This work has provided a suite of programs that will

-9

calculate, for seas from various directions, the pitch, heave, roll,

sway and yaw motions (with a close fit method for calculating the

hydrodynamic coefficients), the vertical and transverse bending moments

and shear forces and the twisting moments. Short and long term

distributions can also be calculated using the Pierson-Moskowitz formulation

of sea states. In addition to these the springing bending moments can be

calculated using a program based on the theory by Goodman (Ref.

6).

The objective of this work is to provide designers with the capability of calculating the various loads on the hull structure for rational

structural design procedures.

In the various full scale measurements taken by B.S.R.A. on

ships in service the sea state is not directly recorded. There is no

suitable instrument for this and hence the weather is identified by the measurement of wind speed together with the deck officer's estimate of

the sea state and the Beaufort number which are used to corroborate the

measured data. However, this means that measured stresses cannot be used

directly to verify calculated stresses in the short term but it is anticipated that a satisfactory comparison of long term predictions, by methods based on measured and calculated stresses, should establish overall

confidence in a completely theoretical approach.

7. DISCUSSION OF MAIN HULL STRESSES MEASURED BY DATA LOGGER

Figs. 8 to 15 present examples for ships 'A' and 'D' of

the analysed information for peak stresses for both 20 min and 5 min

records. The peak stresses are non-dimensionalised with respect to the

variance of the record and are given in histogram form; also peak stresses

are given in spectral form for the filtered and unfiltered data, for both 20 min and 5 min records. The theoretical distributions superimposed on the histograms are those derived from the use of equ. (1) using the spectral

'I' 10 'I'

-properties as quoted on each spectral diagram. The data given in these

figures, and others like them, verify the filtering techniques used.

The theoretical distributions generally compare well with the histograms for both the filtered and unfiltered data as was found by Miles

ÇRef. 2). The spectral width parameter a was found to be quite close to

unity, that is the peaks are Rayleigh distributed, for all the filtered springing records but was generally between

0.6

and 0.7 for the filtered

wave induced stress records. This is a result of negative peaks in the

latter as illustrated in Fig. 2. The corresponding histograms show the

negative peaks in the filtered wave induced stresses but not in the

filtered springing stresses. By using stress reversals and not peak

stresses in the long term probability trends of wave induced stresses, the assumption of a narrow band Rayleigh distribution will be more nearly

satisfied.

The other assumption made in the long term probability trends is that the R.M.S. of the reversals is normally distributed within each Weather

Group. An example of the R.M.S. data is shown plotted on a normal base in

Fig. ₁₆ and the straight line distribution of the data justifies the

assumption.

An examination of the combined wave induced and springing stresses and the filtered stresses supports the conclusion given by Lewis in Ref. I that the combined stress is less than the sum of the corresponding wave

induced and springing stress amplitudes.

Equ. (i), in its cumulative probability form, has been used to predict the maximum peak stress in a record and Table 5 shows the results

of these calculations against the analysed maximum in the corresponding

records. The records were chosen at random and it seems that the spectral

data in Miles' equation predicts the maximum well enough for further applications. A suitable method for combining individually calculated wave induced and springing stresses still needs to be tried and proved for the long term probability trends.

The spectral analysis for ships 'A' and 'C' showed that there

was some springing in nearly every record. For ship 'D' there were

many records which showed the presence of 2 node mode vibration stress

in moderate weathers, in the same way as was observed for ships 'A'

and 'C'; the level of this stress, in terms of R.M.S. of the filtered

record for the higher frequency stress, was similar over various 5 minute portions of the records, in those cases where this was checked.

Also for ship 'D' there were several records where the R.M.S. of the filtered high frequency stress was considerably larger than that of

the rest of the records and it is taken that these were caused by impulsive loading.

Figs.

r(, 18

and 19 show the long term trends of wave induced

stress reversals. The base is in terms of cumulative probability, that

is a probability of exceeding a particular stress once, but this can alternatively be considered in terms of number of cylces which on average

will experience that particular stress once. It is generally assumed

8

that a ship s lifetime of 20 years is covered by about 10 cycles, which

is equivalent to a probability of 10

The trend curves shown in Figs. 11, 18 and 19 have been calculated

12

-considered in Ref. _5. These methods are based

on:-the R.M.S. of on:-the stress reversals in each record

the measured maximum stress reversal in each record and the predicted distribution of maxima of stress reversals assuming a double exponential form for this distribution

The data have also been analysed by Weather Groups (W.G.'s) but only for

method (a) above is a full set of these shown. For methods (b) and (c)

only the combined W.G. Curve is shown. It should be noted that the trend

lines have been presented on a conunon base for methods (a) and (b)

determined by the number of cyôles and this accounts for the separation of log (300) at the origin as the analysis in method (b) is based on

records with an assumed 300 cycles per record. Method (c) is also based

this

on number of records and in / case the presentation shows a separation tending to log (300) at the low probability levels. Method (b) does not seem to be consistent with the other two and this is presumably due to the assumption of a normal distribution of the maximum stress within each

Weather Group.

Also shown in these Figs. is the maximum stress reversal

recorded and this has been plotted at the point corresponding to the number

of cycles over which this maximum stress applies. This point should lie

on the trend line based on methods (a) and (b) for combined W.G.ts and in fact in the three cases given it lies just below the trend line for

method (a) but above that for method (b). This is further evidence that

13

-Also shown in Figs. 1, 18 and 19 is the statistical gauge projections in a ship's lifetime and in Figs. 18 and 19 the corresponding

theoretical values. Figs. li and 19 show reasonable consistency at

the lifetime point but the logger data in Fig. 18 is much different

from the other two. This is considered to be due to lack of data for

ship 'A' in the higher W.G.'s; in fact most of the data recorded was

for W.G.2.

8. DISCUSSION OF STATISTICAL STRAIN GAUGE DATA

Figs. 3 to 6 show histograms of stress reversals collected

over about two years of operation by each ship. The data have been

presented in this form for possible use in building up loading informatifor

fatique calculations; that is the loading on similar ships in various

combinations of the Weather Groups can be constructed to represent the

ship's life. The sanie data have also been presented in Fig. 7 in a

cumulative proportion form, that is in terms of probability. For the

lower probability values, ships 'A' and 'C', show the lowest stresses, with ship 'B' somewhat higher, and ship 'D' well above the rest. The

figure shows data for ship 'A' in the Load and the Ballast conditions.

The number of high stress counts was not considered large enough to justify other than a mean line through the data but there seems to be a tendency for the Load condition to be the more highly stressed, and

this is supported by the projections given in Table 1.

To use Fig. to predict the maximum stress in say a ship's

life one needs to know the number of stress counts over some unit of

time. For ship 'D' an average stress reversal period was found to be

12 secs which gives for a ship's life of 20 years about 1 x 101 cycles

or, in probability terms, 0.25 x 10 This figure could also apply

l4

-'A' and 'C', however, the average stress reversal period was about twice

that for ship 'D' and this gives for a life of 15 years about lO7 cycles or a

probability of 10 A comparison of the projected lifetime stress maxima

at these probability levels with those calculated using the method described

in the Appendix and listed in Table 4 shows that the projection lines

of Fig. ₇ give results about 10% lower than those in Table 1. The results

given in Table 1 are considered the more accurate for reasons referred to

below and also for the fact that the projected lifetimes used in Table 1 are precise in terms of number of watches rather than of estimates of the

variable time period for stress reversals.

In addition to the projected maximum in a lifetime. Table 1

shows a 95% control interval for this value as well as the maximum value to

be expected in one hundred ship-lives. The 95% control interval is a range

within which the lifetime maximum will occur with a probability of 95%. An

increase from one life to 100 ship-lives increases the projected maximum

stress by about 35%.

It should be noticed that in Table 1 the data for ship 'B'

has been increased by including similar data from five sister ships. This

has allowed the method. the results of which are summarised in Table 14, to

be thoroughly tested. Generally the use of the maximum stress from every

watch was not satisfactory but by treating the watches, chosen at random, in groups of 10, 20, 100 and 200 the samples,from whìch the maximum stress was taken,became more homogeneous and the stress projections became

acceptable. It would seem that groups of at least 10 are probably necessary

and such groupings are probably sufficient, as even groups of 200, which were possible with the large sample under ship 'B', did not change the

-

15-The data for ship 'B' and its sisters have been entered in two groups, one for the ships as originally built and one for the ships after

a substantial modification which increased the midship sectional modulus.

The ratio of the original section modulus, at the Upper Deck, to the

modified modulus is

0.773.

This relates to a mean projected stress for a

lifetime of 255 NN/m2 before rnodification and 195 /m2 after modification,

which gives a corresponding ratio of 0.765.

Table does not contain maximum stress projections for ship

'D because the data for this ship has obviously suffered from truncation at the high stress end as can be seen in Fig. 6b and such truncation would

seem to distort the double exponential fit to the data.

CON CLUS IONS

Although all the data in hand have hot been analysed and not all the theoretical predictions of the stress likely to be experienced in a ship's lifetime have been completed, the comparisons which have been made support the use of completely theoretical methods for the calculation of

wave induced stresses for new ship designs.

The use of statistical strain gauges together with the use of a double exponentional distribution applied to the maximum stress in 10 watch-periods provides a relatively cheap and efficient means of deriving

data on maximum likely design loads. The gauge also provides histograms

i6

-The Miles eq.u. (i) has been shown to fit a conibine _{signal of}

wave induced end springing stresses quite well. Further work is required to assess the use of this equation in long term predictions.

REFERENCES

Rice, S.O., Mathematical Analysis of Random Noise. Selected

Papers on Noise and Stochastic Processes, Dover Publications Inc., 1951t.

2. Miles, M.D., On the Short-Teim Distribution of the Peaks of

Combined Low Frequency and Springing Stresses. Soc. Nay. Arch.

& Mar. Engrs., Symposium in Ottawa, 1971.

Johnson, A.J. and Taylor, K.V., Wave Induced Stresses in Ships

in Service. Proceedings of Conference on Stresses in Service,

Inst. of Civil Engrs., 1966.

Martin, M.A., Freqiency Domain Applications in Data Processing. Technical Information series No. 5ÎSD 31t0, General Electric Co., Missile & Ordnance Systems Dept. Phil, U.S.A. 1957.

5 Hoffman, D., van Hooff, R. and Lewis, E.V., Evaluation of Methods

for Extrapolation of Ship Bending Stress Data. Ship structure

Committee, SSC-231t, 1972.

Goodman, R.A., Wave Excited Main Hull Vibration in Large Tankers

and Bulk Carriers, R.I.N.A. 1970.

Lewis, E.V. and Wheaton, J.W., Study of Combined Wave and

Springing Stress of the 'tEdward L. Ryerson". Soc. Nay. Arch.

8. Gumble, E.J., Statistics of Ectremes, Columbia University

THOD OF ANALYSIS OF MAXIMUM STRESSES PER SHIP-WATCH PERIOD USING STATISTICAL GAUGE DATA

Reduced Variate

The Double Exponential distribution is

-c(x-u)

P(x) = e e , for all real x.

The distribution has two parameters, a and u, and by setting a = i and u = O, we obtain a standard form with no parameters, termed

the reduced form:

P.(x)

ee,

for all real

Suppose we have the general form and particular values of

a and u have been chosen. Then for any value of x with cumulative

probability P(x), a value can be found for the reduced form variate y,

say, which has the same cumulative probability. Thus,

P(x) = P(y),

ee

y =

and y is termed the reduced variate and can be obtained from x by a

change of origin nd scale.

Plotting a sample

The general form is -a (x-u) -e

P(x) = e

and taking natural logarithms twice gives - log {- log P(x)} = a(x-u).

If we have a sample of observations x,...xn, the cuinulat5,..

probabilities P(x) can be estimated from the ranks of the sample in

ascending order. For example, P(x5) is estimated by 5/(n+l), P(xl

by lO/(n+l) and so on (it can be shown that these are better estimat,,3 than 5/n, 10/n, etc.).

A plot of - log

I-

log {m/(n+i)}7 against xm should therefore be linear except for sampling fluctuations if the underlyinì

distribution is, in fact, Double Exponential. An example of such a

is shown in Fig. Al.

Since

-loa

i-log P(x)} = a(x-u) = y (the reduced variate)

the expression -log

_L

-log {rn/(n+l)} / can be regarded as an estimate

of the reduced variate corresponding to x.

Estimating ci and u

For the linear regression equation x = a + by, it can be shown that the least squares estimates of a and b can be expressed as: b = ro

_xy

¡G and

ax-by

where and and 2

r correlation coefficient of x and y = standard deviation of x

= standard deviation of y x = mean of x

y = mean of y

For r close to unity, the estimate of b becomes

approximately

We have seen that theplotted data should be close to the

line y = cx(x-u), where y = -log

_L

-log {m/(n+l)}

I,

and we can w-rite this

line as x = u+ y/a..

Applying the approximate least square formulae we obtain estimates of a and u as follows:

1/ci = o ¡o

_xy

or a = o ¡o

_yx

u = =

Grouped Data

A complication arises when the sample members are not

individually but only in groups. In this case, to derive the plott

positions, the procedure is to plot each group as one point, the

appropriate rank being the geometric mean of the highest and lowest

in the group. For example, if a group consisted of observation; ".

ranks 3, 4, 5 ... 12, the_plotting position of the group on log (i"

linear paper would be /x 12/(n+1) against a group average, or c'i;

and

3

In the estimation of a and u, grouping does not affect the

computation of y and o since these quantities only depend on the sample

size. y

Thus,

= E

[_ioS

C -log

(

J I

.th

x. = central value of i group

i

th

f. = frequency in i group

i

Estimation of Group Central Values

Since the best central values can only be found after the theoretical distribution is known, an iterative method is used which can

be shown as

follows:-Set initial estimates of central values

4.

Obtain theoretical distribution

++

Find new estimates of central values

4.

Leave loop after three iterations

In all cases considered so far, the method has converged with

sufficient accuracy in three iterations.

The revised estimate of xj. the central value of the th group

L''-- _{is taken to beexpected value of the variate within the group. This}

can be written:-2 L

ml

[_loS

[ -log ( a..)]

_2

in

2

However, for the evaluation of x and a ith. grouped data, central values must be assigned to the groups to gve the following:

1k

=nL Lx.

ii

i=l

1k

2-

2 -a

nL

f.x.

-x

X.

₁₌₁

ii

where and

x. = E{xi-i<x<l}

_{=fP(x)dx fP(x)dx}

where p(x) is the Double Exponential probability density function. Goodness -o f- fit

The components of the Chi-squared goodness-of-fit criterion are evaluated, one for each group. These are summed to give a single

value which can be compared with a suitable x2 percentage point from tables, with degrees of freedom three less than the number of groups involved (number of groups less number of parameters estimated less one). Groups with small expected frequencies (less than about five) are not used but are pooled to

give fewer, larger groups.

Projected Maximum Stress

In a ship's life of N watches the stress x which is expected to occur once is given by

l-F(x) = 1/N A(l)

where F(x) is the cumulative distribution of x, this result being

independent of the form of F(x). If F(x) is the double exponential

distribution it can be shown that the x in equation A(i) is also the modal maximum, i.e. the most likely maximum in N watches. In this

particular case A(l) becomes:

log N

xu+

A(2)

a

To obtain an upper limit for the lifetime maximum, the method described

in reference (8), p.2)4, is used, in which N in equation A(2) is divided

by a small risk of exceedance,

u,

giving

= log(N/a) A(3)

For example, for = 0.05 equation (3) becomes

x _u log (20N) A( 14)

and this gives the stress which has a i in 20 chance of being exceeded

in N watches. By comparing equations A(2) and A(14) it is obvious that

this stress can also be interpreted as the stress expected to occur

exactly once in twenty ships' lives.

To find a lower limit for the lifetime maximum, the following

x

u+Jo

N i log L..

1w

A( 5)

where w takes values near unity. This equation is also valid for upper limits, i.e. for small values of w, but in these cases it reduces to equation A(3), which is easier to compute.

Control intervals for the lifetime maximum can be

constructed using equations A(3) and A(5). For example a 95% control

interval is found by setting w =

0.915

in A(5) for the lower limit and

w

0.025

in A(3) for the upper lirait. These control limits have been

TABLE i SHIP PABTICULARS L B D T C C I I/ B W 'Y pp m m m Tonnes 2 2 m

cm m

Upper Deck 2 cm m Ship "B" Loaded 213.36

3oJ8

i6.1t6 9.1k 36,500 .600 -1.69x106 193,000 (Containership) *1. 38x106

*l19 000 H.T. Steel in D'k Mild Steel in B'tm

Ship "C" Loaded 281.98 26 23.39

i8.18

199,300 .8L6 .909 7.069x106 75,130 (0.B.0.)

H.T. Steel in D'k Mild Steel in B'tm

Ship "G" Ballast 281.98 114.26 23.39 12.8 135,000 .826 .869 1.069x106 75,130

H.T. Steel in D'k Mild Steel in B'tm

Ship "D" Loaded 218.0 30.L8 18.6 9.558

39,00

.727 1.2x106 117,830 (Containership)

H.T. Steel in D'k Mild Steel in B'tm

*

As originally built After structural modifications

Ship "A" Loaded

330.71 51.82 25.603 19.577 284,700 .828 .906 10.09xl06 177 200 (Tanker)

H.T. Steel in Deck and Bottom

Ship "A" Ballast

330.71 51.81 25.603 6.02 76,100 .765 .817 lO.09xl06 717 ,200

TABLE 2

POSITIONS OF 100 INS. LONG BASE STRAIN GAUGES

(The statistical and logger gauges on each ship are adjacent to each other).

B Midships Port & Stbd 0.8 in Inboard

On longitudinal on Upper Dk. (Logger gauge on Port side only)

TABLE 3 WEATHER GROUPINGS

Weather Group Beaufort No. Wind Velocity, Knots

I

Oto3

itolO

II

_4to5

_llto2l

III

_6to7

_22to33

IV

8to9

31to17

V

lOtol2

48toT1

A i1 m aft of Midships 1.01 in to port off

On Upper Dk. Plating above a long'l

C

3.65

in aft of Midships Portside, 1.0 in Inboard

On Upper Dk. Plating above a long'l

D Midships Portside, 1.2 in Inboard

On Longitudinal on Upper Dk.

Data Processing Scheme for Data Logger

Ilagnetic tape from Ship's Data Logger

Check tapes and re-write in computer compatible form

Probability distribution for all Weather Groups using ship weather distributions

FiG.

i

Apply calibrations, perform preliminary analysis and write to tape for further analysis

Filter data:

(a) 20 min. records for wave frequencies (b) Any 5 min. of a 20 min. record for

vibration frequencies

Plot filtered data on time base,

Spectral Analysis

Calculation of moments for 20 min.

or ₅ min. records.

Histograms of peaks and their R.M.S. Probability density distribution of peaks

using Miles1 equationlbn each record

t

Y

Histograms of stress reversals and their R.M.S.

1

Probability distribution for ₅ min. and 20 min. filtered data assuming Rayleigh distribution of reversals and normal distribution of R.M.S.;

for each Weather

Group-V

Probability distribution accoiìting for all Weather Groups using ship weather distributions

Probability distribution for 5 min. and 20 min. filtered data based on

measured maxima & ptedlcted extreme stress reversal for each RJ-LS.

assuming a double exponential distribution of extremes; for each Weather Group,

(

peaks

potie)

Pci±cie

&!k

iVe.. ¡ve pek

R

('o5ìVPid

(y

peaks)

flG.2

ILLUSTRATION or COMßIND & flLTERD STRESS 3IGNALS

COMB/I\1E20 S14t'iÌL

Ò1c 57

Es

FLyERED /fßRMYIoN

5r,zEs3

FI-TEe?ED w,qv,

5Tfl?55

G No DRAWN BY

Tos/ ti4

TONS/

FIG.3

3 2

5NiP 'P

LLOD

-t-A1..LAST)

HLSTOGRAM5 OF 5TRSS CYCLES

Y WEATH

GQUP5

SrATLSTtCAL GAUGE

W.G. i N HZS

72Z2

RESEARCH ITEM I

w.c. 3

NC H'Q3; 1043

j

4 o LØ OF NUVt6E

OF CYC.LS

(..5

w.c. 2

Ñ k'S

2804

W.Ca. 5

ERSr 6

2 3 _{- 50} so too

-BRITISH SHIP RESEARCH ASSOCIATION

REPORT No

DRO. No DRAWN BY,.

s1.ss

_{7o S/lu'}

Src s

* ON S/IN

FIG.4

3 -1 o I 2. 3

W.C. 3

RESEARCH ITEM REPORT No

W

34i-(s9

Ñ° HS Io1(.

I

'1-4

0 LO NL)Mf3E.f b

2

BRITISH SHIP RESEARCH ASSOCIATIO

WALLSEND RESEARCH STATION

NtHS

4.4

1 7 s 4 3 2 3

w.. 2

Ñ HS 3160

I

w,c, S

?"J

H'S 4

- ici

MN'

loo

MW/ loo a

SHIP

'

(ST6D C*AL))

HiSTOC,R.AM5 OF 5TR.SS CL

6Y JEA1kE.Z GÇWL)PS

5TATISflCAL

AU

DRGNo DRAWN 8V £TR.ta ss TONS/IN2 7 S-rR..sc -ThÑ5/IN& 1 3

FIG.

5-i

I

SNIP

(LQAD +.57)

ISTOcR.AM

OF STRESS C..YCLES ¿Y WE.ATHE

C,POU15 (w.cm.); FROM

STATISTICAL

GIALJGE W.CA.

i

N t-S

3

57

w.. 3

N' k'RS

647

H

7 4 3 2 1 o i z 3 4

LOC OF NUMP.

F CYCL

2

N HS

I'5O

I 2 1

4

.5-- LOO

'Q

RESEARCH ITEM

BRITISH SHIP RESEARCH ASSOCIATION

REPORT No

WALLSEND RESEARCH STATION

M

DRG No DRAWN BY

To

N 4 3 2 'o

FIG. 6

3 2 o

RESEARCH ITEM REPORT No

,1 I

w.c. 3

NJ

HS

t?(0 o

j

LOG 0F NUMßE.f. OF

CYcL-BRITISH SHIP RESEARCH ASSOCIATIO

WALLSEND RESEARCH STATION

SHIP L

tSTORM5 OF TE55 C1CLS ß

VATHR GOUP5

o

STATISTICAL

GAL1E

Wc,

j

wc,. 2

ÑH'IH5

N l-RS

1800

WG,. 4

H'S

77'

ls-o

2

4

-s-ísr

- loo

-6 4 4

rtc. 6b

¡0 g ¿

SHt'

S N I I I 1 2 3 Ç

LO

OF NU1EvZ OF CYCLES

I*STOCP..AM OF STRS5 CYCLES 6Y WaPTL-4EYZ G ROUP

(w G); FÇ2OM

5TAT1STIeAL GAUGE

!50

-50

BRITISH SHIP RESEARCH ASSOCIATION

WALLSEND RESEARCH STATION

UK(j NO ,SC)CMrÇLfl I

I JI

DRAWN BY

jREPORT No

CUMULATIVE PROPORTION DISTRI8UTON FOR STATISTICAL GAUGE STRESS CYCLES

o

,1

FIG. 7

NtP St-i P 'b T

Io-',

I- -3 Io

CL)MULATIVE

PRO8AL3ILITIES

ThP

Lot' CCNTNTION

S HIP ,A', 6ALLAST

4' SI-412 'L3PCRTGAUGE

SHIP '6'SThb

o

SHIP 'C

+ St-liP

8'

STE.SS

go_4 I - So

4-

2

loo -

_lLT)

O

c

_°'854

,Zì45

722

OF gECOIZ)

'0

₂₀

2o

t'T,Ñ5

LCO/D

flG.8

SPECTRA or STRESSES

UÑ/.LYRQ

0609

3t3

OF RECOO

Io

2o

30

'8

/6

'4-

2

Io

WPVE ÌNbUCD

t-Fo

EQu()

-2

o

2

3

4

O 2. 3

2otmvs. ,CCO(?O

5/-//P A

FK. 9

bISTRL&TIONS

OF PEAK

ST?ESSES

Peak 57±res5

/-'eak 5L1ve5s

57re.s

Var ¡c

3tYe5s Vr/ance

u,vrlL-,-E ÇI D

ç7L-T-I

(ED

100

¡00

'Q

L t

SJ1Jfv5 icoRO

Ç/fVfLTI/

D

7(

Q.Q227

M5 3-36

CF ?ECOß b

p. ¡q.

FO

SPEC1RP O

SRESSES

II

I t t I

F /LTiiU

0.93

&.JG. O RECO!Zb o

₅₀

_lOo so

vi

32

FgOM QOE(I)

3re5s Vr,dM

o

¡ Peak. .5tre.5$ .S PR NG t N G

5tes

V'ariafrlce

¿J NF/L7&ic'&L

FL-TRED

5î'mv RLECOD

51-I/p A

FiGli

1$TRIEUTIONS O

PEAk STI?ESSS

o

2

3

Peak 5ve.5

I

Io

/0000

/000

loo

=

f

ILYO

lo

o

FK. 2

5lP D

cO.69

íM5= 2187

OF ECoRb

Io

o r»7/'.

4cO

2o

J

o

c_ p. î'.'?.

Io

SPECTRA OF STESSE5

UNF(I-TZER2D

oÇO 432

N15

224-8

OF

2o

/4

/2

2oî'i/Ìv'S. /LCQRD

'D'

flG.

3

DSTRUTIONS OF PEAK STRESSES

2

3

Q

z

3

4

Peek SLV-e55

Pedk 5tve5s

5Lvej.ç

/ay/.r7ce

5t'ess V-,ice

F,LTE,'ED

¿J,VF/ LTERED

10000 Iø O

'co

'ô

q-F1k.To

51'4/N5. ICoiO

I

C. P. t-i.

FICi. 14

SPECTRA 0F STRESSES

2o

-1ç3 16 ¡2

-

(o

-SPING ING

C) 2

3

4

2

o

PeQk ..5L,-e,s

PeÁ j&eç

iireSj

5yes Veri,ìce

FILTERED

UNF/L-TLF?ED

5 ¡'-'1/NS. RECOR D

51-1/P D

RIG. IS

F1G. 16

_I I

-5H/P iO

(J.ave £ncDLJfl L:

r-$? ve$55}

,C

i'IO,t-lÑh.,/Ty

0F

¿3î15 57,E55 y-1fT/u/N

7/i'1.R

cRoUP iii

I I I i

UNUL,PF(VE PRo5F1/L/7ES

J I 98 99

90

95

2o

3o

4o 50

6 70 2

0.5

5 so 70

50

ft'15

40

30

2o

l0

0-J 0 0f

FIG. 17

139

MP4/2

roLL W.G BASED ON MEASuRE

MAX. STiESS PER RECORD

WEATHER

J

CROUP I AL.L WC.s

W63

's'

F'OR ALL W.(i e}AE:D ou CLCuLATEb

-MAX, STRESS DITRiß.UTIOÑ

lo_%

I0'

I0'

k,-'

IO

to.'

L0'

IO

CUMI)LATIVE POAIL%TY

_____L..o4(300)

UP

BALLAST STRESS REVERSAL TREÑDS BA E

ON LOGGER DATA

140 120

_loo

STRESS

M

40 2Q 's' 5.' s'

'o

.5'

STAT C.AuE

'orEcTl Or.«fZoM

TALE 4)i2Oi$

pzorE.c.TIoN rROM

.MS. ALL w.G.

s..' s... s..' .5' 5% '.5.. .5' MAX. MEA5ORED STWSS

-

5% . 5' 5%. 5. .5-BAUD ON R.M.S Or STRS REVERSALS

FOR ALL W.G. BASEb ON

J

MEASURED MAX. STRESS

PER RECORD.

WEATHL GRoup I

7

s-' w.c ALL W.Cs w.4.2 s' -S-.5». '5 S--MPX. MEASURED STRE.$S 5' -s--Ss

N

BA5Eb QN Ç.M.S. or STRESS REVERSALS

'

I0 IO tO so 10

CUMULATIVE

PRO6AiLITY

L

LO(3oo

FIG. IS

SHIP

BALLAST.

STRESS REVERSAL TRENDS ,ASED ON LOGGER DATA

STRESS M

40

30

20

'o

TgES -i2

MÑ/

70

G0

VOR ALL WATH

P1.SED ON

CALCUL.ATE. MAX STRESS DTRIB.UTiO4

.50

STAr. GAU

PROTECT I(.*.1 (FoM

TAtL

4) =I3

MN/

¶-4EogETicRL CL(.

FOR VETJCAL 6E'JbIÑ(.

MiI/

"S

P«OCTION FROM RMS,ALL W.Gs.

b

(O

STAI Au6E

_{pOTEC TIûN(FìOM}

F

WEATHE4

32o MÑ/i1 N

pPOrEcTIoÑ rZoM

M.SJ ALL '.'f(5

FOc ALL WC YASED ON

MEAUcCb MAX. TßESS PER

W.61. 3

RECORD

W,G, £

W.s

Foc ALL WGs ,P5E..tb ON

4 ALL W. CALCULATED MPX. SISSDSTRI6LifloN

-'f

N MAX 'S..-5. N

MAWED

's '5S 5.

-STESS

N 'S.

+

.5... 's

\

Io_' Io_e

CUMULATIVE pgoeABILIyY

N N

'

\

N

\

"S.'

\

N

\

\

TgENDS _{BASED ON I.M.S OF}

_{'TRESS REvEALS}

k

LOG.C300) 32o 280

240

200 S TR E P...'i 2 160 120 pO

SHP,

STRE:SS REVERSA TREÑDSBASEDONLOGGER

DATA

flc

Al

015o

s

s

ÎÖNS/1Ñ2

100

MÑ,/2

4-- SO 2

SHIP

tO

NO. OrwATcS 550

t I I I 04 0.6 0.8 0.9 0.95 C.UMULATIVE

Pcor3LrTy

EXAMPLE ooUaLE

.XPONENTtPL. RIT TO STRESS iv1AXIMA RROrvi S1/,Ti5TIC?1L. GAUGE

+ I I I

O9

0.999

0.9999

TABLE 4

LoNC TERM POZTECTEDST.ESSVALU1ES BYF(TTNG DOL)&LE EXP0NNTLDST SLJTJOÇ'S To

SY?E.SS MAXIM/A MEASoRE

s'y' THE STATsTKAL STZA(N CUGES

NOrE: T X2VLUE SHOULD ÇE.P'JEALLy &E LESS TI-IAN TI-tE SX StC.ÑIFICANT Poir-..'T VALuE Fòi

A P4EAt'JINcrUL POTE-CTI0N OF STRESS T0LO%W Ö6AßILrÍY VALUES.

t

NOT SIG NIiCANT AT T'-tE j0/LEVEL,YHEREFORE A STRESS POECflON HAS ße-.N MADE

SHiPS LiFEflME Th<EN AS 30000 WATCHES(15 000 IN GALLASTI0o0 ¡N LoDCcTIors)

ro.sNIpsA

*

APPEARS Toe>E AGOob FT Of'd PL0TTING(ACruIL FIT SHN N FKJ¼).AS -r-t

IS HI(,I-LY I(*NWCANT I)UE To A L.AQE CONT6UTI0N FROM ONLY ONE STrESS

A MAXIMtJM 5TES Po.TIoN I4'.5 ßEJ'4 tvlADE.

Se

bA-rA Tyç'

5piPtC

Ssz 2 bÇ.IZ

FJ,oM

5%

Sui.

po,j-p'OCÍEr) MAXIIt.IL)M STsS P.EVERSALS

'osit-uzwi' V#.c-' IN Lo,./EZ 2-SZ COMTOL tx'c'- 2-6 CONTROL MOST LIKELY VAL'. IN

S,jic' Li Poit'.rr _{POINT too}S.eL'

Ç WPÇTCI-t

1N-48-tt5

109

i-' 2

(.o

I 3

122

186

198

Lobb

3

HS

I 46

I ¡ 3 7-8

I 39

I 2 2 1 8 3

1 99

'A

48s

us

18

₂ te-0

136

120

179

190

MLLAST

36is

¡SS

72

3

78

i 35

(20

179

190

C ALLW#TCI1E 92S ,4-.5

4

9-5 LoADED J ipj (0 92

3'9

I

38

131

I (8

¡69

(79

'C ALL4JATCHES S0 (G-2 2

0

i2o

106 1S9 168

6,LLAST I IN (0 55 NOT EÑOU(,I-i PTP

è; ALLWATCHIS S5l

L;2

8 5SIST I

to

Ç95 -o 7 ¡'-,.i

126

337

369

St*I95. I

j2O

29

S-3

267

2.29

342

I ,.jSó

It

41

4 9-5

2I

23

366

MobIFtc-ATIOÑ I J LOO

59

l- 2 6-0

254

2. 24 3 34- 3 s_4. ¡ i,,j2oo

t;

38

2'

L12

32.2. '34-o

255

'S'

ALL WA-rcI4es i 6 2.82 IÇ2.'

Z3-2

19-2

6

I5 12-G SHIP5 t -J 20 7(,4 IS_-s S t . I 202 1 80

264

279

AFTCR 1N50 3oS_ 5-L1. 4

S5

¡.94

i 74

250

265

Mo)icP,TLoÑ

i

p loo I 2 76 I -6 2-6 3 2 7-5

60

191 192

72

(72

2 56, 14-7

259

261

MAÑ (95