Wave loads on a T-2 tanker

Reprinted from «EUROPEAN SHIPBUILDINGD NO. 1, 1961, VOL. X. 1961

Norwegian Ship Model Experiment Tank Publication No. 62, February 1961

WAVE LOADS ON A T-2 TANKER

THE INFLUENCE OF VARIATION IN WEIGHT DISTRIBUTION WITH CONSTANT MASS MOMENT OF INERTIA ON SHEARING FORCES

AND BENDING MOMENTS IN REGULAR WAVES BY

-. At.

.

-THE TANKER MODEL RUNNING IN WAVES OF LENGTH EQUAL TO MODEL LENGTH AT A SPEED

EQUIVALENT TO 16 KNOTS SHIP SPEED.

4

WAVE LOADS ON A T-2 TANKER MODEL

Introduction

This is the first in a series of reports on model

tests in -regular waves of a T-2 tanker model

performed at the Norwegian Ship Model Experiment Tank, Trondheim. The investiga-tions are sponsored by Det norske Veritas and backed economically by Norges Teknisk-Na-turvitenskapelige Forskningsrad, and is being carried out in co-operation with the Davidson Laboratory, Stevens Institute of Technology in the U.S.A.

To cover the very rapid growth in ship size in the last decade, the ship classification societies have directed much of their interest and work towards the problem of longitudinal strength. The weak part of the practical solution of this problem at present is the determination of the

forces acting upon a ship hull in a seaway,

represented by longitudinal bending moments and shearing forces, as well as local slamming forces. Model tests in waves have proved to be

a very promising tool

for investigating the

wave-introduced forces and moments. Accord-ingly, Det norske Veritas proposed in 1958 a research programme at the Norwegian Ship Model Experiment Tank to investigate the in-fluence of the block coefficient and of the load

distribution

(i e. the longitudinal still water

bending moment and mass moment of inertia)

on the wave bending moment and shearing

forces. At that time, however, a rather similar test programme liad been planned at the David-son Laboratory, and a coordination of the two

programmes was agreed upon. The Davidson

Laboratory undertook the investigation on

block coefficient influence by testing three

Det norske Veritas, Research Department, Oslo (formerly the Norwegian Ship Model Experiment Tank, Trondheim)

Det norske Veritas, Research Department, Oslo The Norwegian Ship Model Experiment Tank, Trondheim

THE INFLUENCE OF VARIATION IN WEIGHT DISTRIBUTION WITH CONSTANT MASS MOMENT OF INERTIA ON SHEARING FORCES AND BENDING

-MOMENTS IN REGULAR WAVES By

M. Lotveit 1), Chr. Miirer 2), B; Vedeler 2) and

Hj. Christensen 3).

models with block coefficients 0.68, 0.74 and

0.80 (see ref. [1]), and the Norwegian Ship

Model Experiment Tank started test work on the influence of the load distribution, applying a model with similar lines as the middle of the Davidson models (a T-2 tanker model).

The Trondheim tests were extended to mea-sure not only the bending moments and shear-ing forces amidships, but also the moments and

shearing forces at the quarterlengths. The

methods of measuring moments and forces

were those developed at the Davidson Labora-tory during the preceding years (see Appendix

and ref. [2] and [3]).

A preliminary series of tests was

under-taken in

1958, mainly to test. the new

appa-ratus and instruments which had to be

devel-oped and worked into the test programme.

Some of the results of these preliminary tests were published in ref. [4]. Experience gained from the tests rendered it necessary to intro-duce some minor alterations and improvements

to the instrumentation employed in the

fol-lowing test series, the results of which will be published in the present and successive reports. Test programme

To separate the influence of the still water

bending moment and the longitudinal mass

moment of inertia, two main series of investi-gations have been conducted. One series

in-volved a variation of still

water bending

moment while keeping the mass moment of inertia constant, the other series covered a

va-riation in

mass moment of

inertia while

keeping the still water bending moment constant. A description of the former of the

main series, together with the results of the

bending moment and shearing force measure-ments, is given in the present report.

The basic load distribution of the model

0 cv 20 _J CC LI 15 a_ 10 r cr

o5

Li LU 1) ₀

loaded tanker and was very similar to the di-stribution applied at the Davidson Laboratory tests. The still water bending moment corres-ponding to this basic condition was a small sagging one, whilst the other two distributions (II and III) were arranged to give hogging and sagging still water moments respectively. The weight distributions for Conditions I, II and III are shown in Fig. 1. Further details concerning the weight distributions are given in

Appen-dix A.

The model was made to scale 1 : 50 and cut at the midship and the two quarterlength sec-, tions, and the four parts were joined by steel flexure beams acting as dynamometers record-ing the bendrecord-ing moments and shearrecord-ing forces at the three sections. A detailed description of

the instrumentation for recording bending

moments and shearing forces is given in

Ap-pendix B.

The towing arrangement is constructed to allow the model full freedom in pitch, heave

and surge and continuous records of these

EP

M. 482. WEIGHT DISTRIBUTIONS CONSTANT MASS MOMENT OF INERTIA

motions were obtained simultaneously with the forces and moments. The results of these

measurements of

the model motions

will, however, appear in a later report. The regular waves were generated by a special type

gene-rator which is described in ref.

[4]. Wave

height and wave profile were recorded con-tinuously during all the tests.

The tests were for all three loading

condi-tions made in regular waves having wave

lengths of X = 0.60 L, 0.75 L, 1.00 L, 1.25 L,

1.75 L and 2.25 L, where L is the length be-tween perpendiculars of the model.

The wave height was kept approximately constant at abt. 75 mm (3 inches), i. e. the wave

height-model length ratio h/L 1/40. The

speed range covered for all wave lengths was :

Model speed: v = 0 1.65 m/sek

Corresp. ship speed: V = 0 22.5 knots

Froude number: FR = 0 0.30

In each series of runs in a certain wave

length several reruns were carried out in order to have a check on the recorded values. In

Ap-5 30

Fr 1

LIGHT MODEL CONDITION I CONDITION -CONDITIONDI 25 - - - SECTION AREAS

pendix C is given a description of the calibra-tion procedure of the instrumentacalibra-tion for mea-suring bending moments and shearing forces. Presentation of test results

The aim has been to present all the test re-sults in a dimensionless form which is

conve-nient when comparing tests

carried out at

different model scales or in full scale. The

bending moments have been presented as the dimensionless bending moment coefficient:

CM= M

C

L2Bh

and the shearing forces have been presented as the dimensionless shearing force coefficient:

cQ =

y LBh

If the variation

of bending moments and

shearing forces with wave heights is assumed to be linear, these coefficients are independent of scale and wave height.

As usual in longitudinal strength calcula-tions, a sagging moment is taken as positive and as a consequence of this sign convention a shearing force has been called positive when the sum of upward directed forces are in excess of the downward directed forces for the part of the hull situated aft of the section in ques-tion.

As there was practically no zero drift in the

instrumentation

for recording bending

mo-ments and shearing forces, no difficulty was

involved in splitting up the range of wave

bending moment or wave shearing force into sagging and hogging moments or positive and

negative shearing forces. From the practical

point of view it is of great importance to have

the ranges of wave bending moments and

shearing forces divided into positive and

nega-tive parts. A splitting-up of the ranges has

therefore been carried out throughout. The

zero position refers to the condition when the

Model is floating at rest in calm water. The

test results are not corrected for the bending moments and shearing forces introduced by the wave system of the ship at constant forward speed in calm water.

This report is concentrated mainly on the

results from the bending moment and shearing force measurements, but to give an impression of the motions recorded, Fig. 2, which gives the results of the recorded pitching, is included in the report. However, the complete results of 6

the motion measurements and the phase angles, together with some further analysis of the test

results, will appear in a later report. The

pitching angle is independent of model scale,

but to correct for small differences in wave

height and to follow the same scheme as for the presentation of results from the bending mo7 ment and shearing force measurements, the recorded pitch angles have been presented as

2 4// L

where sfr = pitch amplitude in radians. As the recorded pitching motion is nearly sinusoidal it was found unnecessary to divide the pitching into positive and negative amplitudes.

For the three loading conditions of the model in question, the weight, trim and mass moment of inertia are kept constant.

As the deflections at the joints are so small that the model can be regarded as completely

stiff when the motions are considered, the

motions of the model in waves should be the

same for the three loading conditions. One

common curve for the pitching motion for the three conditions has therefore been drawn for each wave length in Fig. 2. As will be observed, the spots show some scatter, but no clear

ten-dency is evident ..to justify drawing separate

curves for each of the three loading conditions. The results of the measurements of pitching at a speed corresponding to 4 knots for the ship and in waves of length A = 1.25 L give spots which fall markedly above the faired curve for

all the loading conditions. As the model is

small in relation to the tank it is less likely that reflection of waves from the tank sides in this case would have disturbed the testing condi-tions more than in corresponding tests carried

out elsewhere. Despite this fact we feel that

wave reflection may possibly be the reason for

the observed irregularity. Another possible

explanation for the scatter of measured points at low speeds could be the influence of a criti-cal damping phenomena, as shown theoreti-cally by Havelock in ref. [5]. These matters will be investigated further.

If wave reflection has influenced the pitching it may also have influenced the bending mo-ment and shearing force measuremo-ments at law speeds. It is therefore considered to be correct

to make a reservation for all the test results

at the lowest speeds although the influences of wave reflections are believed to be small.

X4:4"

Bending moments and shearing forces as fu

tions of speed

The observed results are given as the mean amplitude value from the oscillograph record of each run. Figs. 3 and 4 show the bending moment coefficient and Figs. 5 and 6 show the shearing force coefficients plotted to a base of Froude number. The observations are indicated as marks and the curves are faired and drawn as mean curves. The three loading conditions are presented side by side for the sake of com-parison. Each diagram represents one wave

length, and as A/L is varied from 0-60 to

2-25, a total of six diagrams for bending

mo-ment and six for shearing force have been

drawn for each loading condition.

As will be seen, the bending moment changes somewhat with speed for all wave lengths. The most marked variations are found at the wave

Fig. 2. Results of pitching motion measurements.

lengths A = 1.00 L and A = 1.25 L, but the

va-riations are not the same for all the three

loading conditions.

For Conditions I and II it is found that the sagging moment at forward quarterlength in-creases most heavily with speed for these wave

lengths. These forward sagging moments at

the highest speeds here exceed those at the

midship section. However, Condition III does not show the same tendency. The variation of hogging moment with speed is not as marked as for the sagging moment, although it also in most cases shows a tendency to increase with

speed. For A = 0.75 L, A = 1.00 L and A = 1.25

L curves for the maximum bending moment occurring at any section are drawn on the fi-gures. The values for the maximum bending

moment for

each wave length, speed and

loading condition have been read off the curves 7

PITCH DOUBLE AMPLITUDE

.1 CONDITION I . CONDITION II s CONDITION II 1

I-

7 L . . e., )7L. 0.75 .. 9 9 L1.00 2 e , OS 005 00 810 015 2 020 4 16 025 FR. 8 5.11 P SPEED BM

_ PITCH DOUBLE AMPLITUDE, CDNDITIONI CONOITION II CONDITION II . )k.1.25 . . e x . . , 5

k.

145 . ° °! 2 1 0 )71.= 2/5 .r----° 2 065 0.10 015 4 6 8 10 12 010 14 16 6.23 FR. "I' 1B SHIP SPEED ,KT5!

OD

Fig. 3. Results of bending moment measurements.

MIDSHIP MAX. MOMENT LOADING CONDITION I .--- FORWARD IN ANY AFT SECTION OM A HOB 0034 2Y1.2(>6°

--.__

-=7--- ,-. 1.31 ---1 0024 0008 'i 0012 0012 o A/L. 075 _____ --.. -,../ -. °o d 2 002 0012 '1' OM )Y. 4 , 1.00 o _ -

...---_

.. ,... .... , 1-1

-. ____,-...

MI

o 0012

--

.rnimilimum '... .-. --IMOMWW1111aidli 2. 005 010 015 020 025 FR -2" 4 6 12 10is is SHIP SPEED KM . . . . . LOADING CONDITION ID MIDSHIP 0 ---FORWARD AFT MAX: MOMENT IN ANY SECTION

0012 FA. 0008 0004 )11:1)63 ...0 .c r=. -a .=7.--,-X1 - 7.- ----. .7-- :- -7-' . ele... ---.--...- -.--===-.. _ i ₀₀₁₂ 0012 6 I WOO 0004 1-/' 1/0 0.75 o-,-; . . ... _. _--. 0004 'd 0012 0012 .4 ... .." 0004 '..." *I-... oCO3 d NU

....

is

_ 2 OCT 010 4 6 8 045 0-20 10 12 14 16

"

FR. -21" II , SHIP'SPEED (ITS. MIDSHIP LOADING CONDITION 0 0--FORWARD AFT

MAX. MOMENT IN ANY SECTION

)/I.'06' ° 0011 1 0001 o 0001 0012 0012 6 0006 /12,075 1111. --

--. nilierWgi ...a. -A.- 4---. 00086 0012 ....---

-'..-',...

Dm lii_ 41-00 _...: ..04 ---_,....-. ---.=--.6.---,0--0001 .., ... .o.-... ',X, ...-0112

"=.---005 4 010 0.15 020 to T2 , CQ il SHIP SPEED K1S.

CO

Fig. 4: Results of bending moment measurements.

-MIDSHIP --7 MAX: MOMENT LOADING CONDITION II 0--- FORWARD IN AN -AF 7 OM Di 1 A /L. 1.25 .---

_

- _...5_,--. .... to... - ...,... ... ... MI'

-_--. HQ. . I me 000 di .--7---4"---1F7'...111".-- - --e. 00011 g 0012 00t2 g A' /02-25 LI -- ---- --X2---.--- ='-'.---$---'.---:::.---5 0 150t2 _

046

005 040 015 020 025 OM FR. 10 14 16 le SHIP SPEED PTS. LOADING CONDITION I

-MIDSHIP -- MAX. MOMENT ---FORWARD IN ANY SE C71.9/2 eI X 0 Ak 1.25 ....' NO -- - --.--:-.---". 44.---4'"_- -.-

-....---

di----.... --..----. ...-§ OHIO ..._ g ₀₀₁ 0042 7YL. 1.75 - ---.-._..._.,. . --- _.--- --°-7.-040 1 09 0012 A/L.225 1

- ,-..-.... ...-=2.. --. r.--- =--f 0012 _ 005 040 015' ! t 6 310. IT 020 025 1.6 16 IS ,_ 030 ER -... S01P SPEED TS. LOADING CONDITION IS

-MIDSNIP -- MAX MOMENT ---FORWARD IN ANY AFT SECTION 0012 woe A/ 1.25 _...---L ,.... er. ...0.-...-cr..." ...0 .-0.. . OM 00 -175 -.4t It -or -0-- -cr." ... ..,...! ,_ _....04. ----e. 0008 002 *.-0012 0008 102.25 00 ....-11-;..-...-e " 0004 .. ... ...AY. 00311 ----__.___________. 0012 005 040 4 . 6 015 020 0 FR.-ID 14 SFDP SPPED ET&

Fig. 5. Results of shearing force measurements. LOADING CONDITION In 006 hic060 00 ---- .-

--IPMII

Mal

. I 008 1. 002 _cf . 002 -... ... _..., --.00 . -. 010 015 10 12 020 HS 030 14 16 is SHIP SPEED MTS. LOADING CONDITION I ' ii. 040 013 006 00

-Mil

...- ... -la

lill''"=

II

11.1

1110.W.---..-..._... I o 002 ...'

MIMI

--4--Mill. .

--.. --, , , 005 00 015 020 020 030 FR... 6 6 8 10 12 14 IS 18

SHIP SPEED ITS.

LOADING CONDITION 11

ooi Ix*

I

MIDSHIP

o-- FORWARD .-- AFT

Am040

1ii!I"i

... ----, ' 002 ..--:7-__. -,.-_=,....01 000

MN:.

. .../...' 002 --- --. -, ""....:::_ -006 --,0 030 005 OM 0-15 020 025 FR .--..-20 12 14 16 la SHIP SPEED NTS

Fig. 6. Results of shearing force measurements. LOADING CONDITION 0 005 ", MIDSHIP ---FORWARD . - - AFT Il l: 1'25

MEM=

002 _LP

mPli

i!ij

..-...-... -=-:-..-ooa ao 002 -==ete!.111.1...1=11 L,--LP

TiT

... 00 002 Lis -002 , -

MINIE"'--iMiniiiiidil

ilill1.1111/11.11

MEEEBEEMM=

-4-IgnimmiMplall

1006 405 095 010 015 020 025 Di° 2 6 6 0 22 14 g SHIP SPEED KM !LOADING CONDITION ,I . 000 , mirisHip 0 7-- FORWARD .' . --AFT . Ak.1-25.' ,.... ...f.e. ...,,,--o..,.... . !04. .. -....---. 1 --Y-04) . , ---.7-7 '. :74'; -.. -_ _- - - -__ __ ''' . _{-1..._._.} . __--_,, )12? 145 004 1-11 -1 -004 ---. ::-.4.-.:=--006 006 --)YL., 215 oo. _i./ ---..--___1...___________41 904 -0.C6 '003 005 040. 045 020 0 5 .-.1-14. 30 2 di 1 0 0 12 14 ,I6 -1I6 SHIP-SPEED SOS. . . . LOADING CONDITION DI. 0-00- GO2 MIDSHIP 0. , FORWARD i--7 AFT )1i. I-25 ,--0 , 002 00 _-ON -005 'YLa 1/5 004 __ o . 002

=1...111.11 SIN

.--0 --006 , 'YL =2-25 004 ;002

--004 406 2 005 GAO 4 i 6 10 045-020 12 14 6 .025 F.. o-3 a .6 SHIP SPEED .605.

Fig. 7. Variation of bending moment with wave length at constant speeds.

shown in Figs. 12 14 and similar curves.

The measured shearing forces are, as

ex-pected, in most cases found to be smaller at the rnidship section than at the quarterlengths. The most marked variation with speed is found

for the wave lengths A = 1.00 L and A =

1.25 L.

The results of the bending moment and

shearing force .measurements at these wave lengths clearly, indicate that the longitudinal

locations of maximum bending moments

change with speed.

Bending moment and shearing force as func-tion of wave length

The variation of bending moment with wave length is given in Figs. 7 and 8. The diagrams are plotted for constant speeds to a base of LA instead of the more common parameter A/L.

12

The main reason for choosing L/A as a base is that for constant wave height AIL = 0 has no physical meaning, whereas L/A = 0 means in-finitely long waves, which is the calm water condition. A presentation on a base of L/A is

therefore felt to give the clearest and most

correct picture.

The three loading conditions are presented in the same diagrams, thus showing the influ-ence of weight distribution. It will be seen that

the bending moments at zero speed have a

slight tendency to increase up to wave lengths

around 1.25 L and then fall

off with further

increase in wave length. Correspondingly, the maximum moments aft and amidships at 10 knots are found at a wave length between 0.9 L

and 1.25 L for all

three loading conditions,

although the magnitudes are not the same. At the forward section, however, Condition III is

SHIP SPEED . 0 KNOTS .

I II III CONDITION - - - -CONDITION ---CONDITION --FORWARD

IIIPIMats..._

7:---"' M IDS HI P 0.012 000 0004 ,4--- ,4--- ,4--- _ 6000 -./.1111111 4.4.... AFT 045 046 075 1/ 2.125- 175 1.125 tfo 100 125 1.50 o o op

SHIP SPEED=10 KNOTS

0012- 0.0011-I II III CONDITION -CONDITION - - -- -CONDITION ...- --.. ..., ... 4.,.. 44. 0000 -..., FORWARD 0412 0000 0404 0000 x 44... ... ..,sL. ...-._...--_. .,4 . --- - .--60/ 2 -M ID SHI P 6012 DON 12004 -,...111

MBIIL,-PgglTlgil-

---.. 0014 0003

IIIIIIiIllj-

__-.. ---r---AFT

.._

025XiL 2? 50551)75 07515 1-00 I./71/4 1130 1.25 I io 10 0)75

Fig. 8. Variation of bending moment with wave length at constarrt speeds.

completely different from the other two,

having its maximum values already at a wave length of 0.75 L and a minimum hogging at A

=-- 1.00 L. At 14 knots the situation forward and

aft is more or less the same as for 10 knots. Amidships the moments for Condition II are fairly constant for wave lengths shorter than 1.30 L with a maximum around A = 0.75 L. At 18 lmots' ship speed the maximum moments at the aft section are found to be around A = 1.25 L for all conditions. Conditions I and III have maximum moments at the midship section at

= 1.25 L as well,

Condition II, however,

shows a decrease with increasing wave length

above A. = 0.75 L. At the forward section,

Conditions I and II have maximum values at = 1.25 L whilst Condition III has its maxi-mum at about A = 0.90 L.

As a main conclusion we may say that the

highest values of bending moments for hogging as well as sagging were in most cases reached

in Waves of between 1.00 L and 1.25 L in length.

The variation of shearing force with wave length is plotted in Figs. 9 and 10. The shear-ing force Show little variation with wave length at zero speed for any loading condition over the

normal range of wave lengths. At 10 knots'

speed we find a Maximum value in shear at = 1.00 L for Condition I for all sections. The two other conditions have maximum values at wave lengths between 1.00 L and 1.25 L for the

section aft. Condition II shows maximum valties

at about 1.00 L for the niidship section, the forward section, however, displaying a general decrease with increasing, wave length. Condi-tion III has its maximum value in wave lengths between 1.00 L and 1.25 L at the forward sec-tion, showing a general decrease with increas-13

SHIP SPEED . 18 KNOTS

0012-o ul 0404 I III CONDITION ----CONDITION! ---CONDITION

WEE

4

El

Ira

"1111C.,

MIA

042 0008 d o_x 0012 48 ZA 0408 0.004 404 408 g S 0.012

4_1

6012 3 0.0.0 0.004

r

aill

arli.

M

M004 6008 aa ----11111111111111111111MEE

ill

AFT 0-25 0-SO 075 1.00 __ , _I?! 1.-P° All. 2.p 7 I-25 1.50 0-60 i 0.75

SHIP SPEED . 14 KNOTS

6012- woe-I III CONDITION - CONDITION! --CONDITION

..iiiiiiim

P

.

111

0404 0., .._

mill.

0 008-FORWARD 0.012 0408 0 004 -".." ..--...\. .. \ \ ..." 0.012 ',... ...-MIDSHIP .12 3-... 0404 _ ' xi .4-4.4. --....--.4."'",---..._---... "--..."---- --`-'-'°--- - =-- .. 0404 0405 -", ----AFT .. . . . 025 050 075 100 225 1.75 1125 1.00, 125 150 Or L/A. 0175

14

Fig. 9. Variation of shearing force with wave length at constant speeds.

ing wave length at the midship section. At the speeds of 14 and 18 knots the curves also indi-cate that generally the maximum values of the shearing forces are reached in waves of lengths between 1.00 L and 1.25 L, although Condition II has maximum values in waves of A = 0.75 L in the forward section at the same speeds.

Variation of bending moment with time In Fig, 11 curves are given for the

instant-aneous longitudinal distribution of bending moment for the model at 8 different instants of time during one period of wave encounter, Te. The wave length in question is A = 1.00 L and

the longitudinal distribution of the bending

moment for the three loading conditions is

compared at ship speeds of 0 knots and 14 Icnots.

The time t = 0 refers to the condition when

the model's pitch angle is at -a maximum with

bow up. Both the instantaneous values of the recorded bending moments and of shearing

forces at the three joints were read off for

each instant of time. Thus the magnitude of the bending moment and the slope of the bending

moment curves at the three joints were

oh-taed and these very closely determined the

run of the curves for the instantaneous longitu-dinal distribution of the bending moment.

, The figure clearly shows how the bending

moment changes during one period from large sagging to large hogging moments. At zero speed there is very little difference between the three loading conditions. The distribution

along the length is not far from symmetric

about the middle length, and the maximum

moment occurs approximately at amidships.

At the speed of

14 knots, however, the

influence of differences In the longitudinal

SHIP SPEED =10 KNOTS

006 ' 406 .006 - --- CONDITION -- CONDITION CONDITION 1 0 0 j..0!".- ...---:;::::"' ...---:. ---FORWARD 006 002 -004 -..., .-- .-- .--... ... '--MIDSHIP 002 -002 404 -006 ...0....

....----..

----.7.-- ,_=.7.-...-.. .- :"...."---"1.--- ---. --- s,... ___.._ ___ AF 0-25 060 015 l'O 1-25 225 7 - 1-25 1.1 0.25 06 SHIP SPEED. 0 00 004 041 002 -004 406 406 - CONDITION - --- CONDITION -.- CONDITION 1 U 0 ..._-...-..._., . ...-- -,--... ... .

i

FORWARD . 096 004 002 -- ... -Olt -006 -0 06 - --- ----.

----

----MIDSHIP 002 ,...7 -006 008 _:: . ...,... .--....,...-:::. ----: ...

,

AFT I- ..--025 0-50 Ak 225 7. 075 0 125 075 LA 150 06

weight distribution is evident. The symmetry about amidships has been disturbed and the points of Maximum bending moments have been shifted towards the ends, for Condition III a little aft of amidships, for Condition I, and still more for Condition II, forward of amid-ships.

As the mass moment of inertia, the total

weight and trim are kept constant for the three loading conditions and as the natural pitching and heaving periods are the Same in the three

conditions, the instantaneous hydrodynamic

pressure distribution at corresponding times is independent of the loading condition in this case. The observed differences in the longitudi-nal distribution of wave-bending moment for the three loading conditions must therefore be due to differences in the longitudinal distri-bution of the inertia forces only. Thus, Fig. 11

Fig. 10. Variation of shearing force with wave length at constant speeds.

clearly indicates the importance' of the

accele-ration effects upon the wave-induced bending moments and their longitudinal distribution. The changes of moment distribution due to changes in weight distribution will, however, be further discussed in the following section on the maximum bending moment distribution. Distribution of maximum bending moments over the model length

The distribution of maximum bending

mo-ments for the three conditions is plotted in

Figs. 12, 13 and 14, for wave lengths A = 0.75 L, 1.00 L and 1.25 L respectively. Curves are given for four different speeds.'

The CM values amidships and at the

guar-terlengths are obtained from the curves in

Figs. 3 and 4. The slopes of the curves in Figs.

12-14 at the three measuring stations are

15

SHIP SPEED .18 KNOTS

092 -008 'CONDITION I coicitriorit -- coNdificin I

miim

11111

rAIMINIMIMIN

MI

-006 004 002 .002 -004 -006

I

INNEi%

EMIA-R=11111116.1M' .-.4,.... '...

s. MEI

MIDSHIP

EI

002

IlliffialliallirMMI

.002 -004

_kiiUW

....,

--DOB AFT 025 050 075 lb 2 75 1 1 25 ,0

0/1

650 4/A

--075 - - - -SHIP SPEED.14KNOTS p-os 094 642 di -D02 -004 -006 -00B I CONDITION I _ .,-- CONDITION 1 CONDITION I c..-...- ..."

--- :--... .7.---.-- .---.--FORWARD 006 004 0.02 -002 .00B .'`' . --. ...- ... -... ''. ... -4. --" --'MIDSHIP 006 004 002 SI -002 -004 006 ...---4. AFT 0.25 050 075 "--- ?./.1.. 2r ir ___ 025 10 125 F50 li,_44 or 06

-.010

WAVELENGTH A 2 Lpp SHIP SPEED 0,KNOTS

""...c.

t0

P

7/8,Te

A.F,

CONDITION I CONDITION CONDITION

F P

WAVELENGTH A= LPP SHIP SPEED 14 KNOTS

Fig. 11. Instantaneous longitudinal distributions of

bending moment during one period of encounter.

010 X

...'H

---010 .005 70 .00 5-0 .010 .015-F 0 .010 Ln _ M A.F.' .005 .0 -0 -I .010 .015-1

determined by reading off directly from the recording diagrams the shearing force at the instants of maximum bending moment values. As the maximum values of the bending mo-ments do not occur simultaneously at all sec-tions, the curves shown in Figs. 12-14 are not

instantaneous bending moment distributions fcir'

the model, but the envelope of such curves for one period of encounter.

When comparing the curves of Figs. 12-14 the following points may be emphasized (in this connection it is worth while recalling that

Condition I represents a small sagging still

Water moment, Condition II a small hogging moment and Condition III a large sagging

mo-ment):

1. For the Srnallest wave length (A/L 0.75)

there are fairly small differences between the loading conditions, though some difference is evident at 10 knots.

For wave lengths A = 1.00 L and L25 14, Figs. 13 and 14 show a general increase with speed in the influence of loading condition on moment distribution.

We have mentioned that the differences in the distribution of maximum bending moment for the three loading conditions must be due to

differences in the distribution of the inertia

forces. As the magnitude of the inertia forces and the differences between inertia forces for

CONDITION I

CONDITION 121

2/L = -75

Fig. 12. Longitudinal distribution of maximum bending moment at constant speeds.

different loading conditions are directly pro-portional to the acceleration at each section in

question, we should expect that at low

fre-quencies of encounter and in cases where the amplitude of the motions are small there would be small differences in the curves for the three loading conditions. If the curves of pitch angles (Fig. 2) are recalled, we find that for A = 0.75 L there is a reduction of pitching at increasing

speed above about 8 knots' ship speed, and

from Fig. 12 we find that the curves for the three loading conditions become more similar

at increasing speed above 10 knots for this

wave length. For A = 1.00 L we find that there is a small reduction in pitch amplitude from 14 knots to 18 knots' ship speed. HoWeVer, as

the frequency of encounter increases at the

same time, there will be no reduction in the

pitch accelerations, and in Fig.

13 we find

about the same differences between the curves for the three loading conditions at 14 knots and at 18 knots.

For A = 1.25 L there is a general increase in the pitching amplitude with increase in speed up to the highest speeds covered. In Fig. 14 we find increasing differences in the curves for the three loading conditions at increasing speed up to 18 knots.

2. The difference between the loading.,condi-tons stated under Point 1 is characterized by -17

.015: .005 0 -010- -015--005: -0 1. -010-18 CONDITION I CONDITION 11 CONDITION ICE CONDITION I CONDITION

Fig. 13. Longitudinal distribution of maximum bending moment at constant speeds.

a quite different trend in the shift of position of maximum bending moments.

In Fig. 15 this position of maximum

mo-ments has been plotted as a function of speed for three wave lengths A = 0.75 L,A. = 1.00 L

and A = 1.25 L. The letter x is the distance

from amidships to the section where the

maxi-mum bending moment occurs and separate

curves are given of x/L for sagging and

hogging.

As will be seen, the shorter wave length

(A = 0.75 L) shows only a small shift forward for Conditions I and II up to about 10 knots (FR = 0.13). With further increase in speed the maximum point moves back towards the mid-ship position. For Condition III the maximum

moment occurs amidships almost

indepen-dently of speed.

At the other two wave lengths (A. = 1.00 L and A = 1.25 L) the position of maximum mo-ment shows a large shift forward for Condition II and a smaller one for Condition I, for both

conditions in the speed range 4 to 10 knots

(FR = 0.05 -- 0.15) at AIL = 1.00 and in the

range 9 to 16 knots (FR -= 0.12 0.21) at AIL

= 1.25. For Condition III the maximum point Is fairly constant a little aft of amidships for the practical speed range up to 16 knots, but Shows tendencies to shift forwards at higher speed also for this condition. An exception may be the sagging moment at A = 1.25 L, but it is

impossible to draw any definite

conclusion

because of the upper speed limit of the tests. From Figs. 12, 13, 14 and 15 it will be seen that the trend is very similar for sagging and hogging moments. It may be stated, however,

that the variation in position of maximum

ment is rather smaller for the hogging

mo-ments.

Special attention is paid to the opposite

trend of the maximum moment curves of Con-ditions II and III with increasing speed at A/L = 1.00 and 1.25. Condition II shows the form-ing of a peak value on each side of amidships with lower values in the rnidship range, whilst

in Condition III the moment curve forms

a

larger peak near amidships. In sagging, the

peak moment values of Condition II moves as

far as to the quarterlengths at the higher

speeds.

It is also worth while noting that the special

trend of the moment curves of the hogging

loaded model (Condition II) is most pronounced for the sagging wave moments, Whilst the peaks

amidships of the curves of the sagging loaded

Fig. 15. Position of maximum bending moment. x

--distance from rnidship section.

model (Condition III) are largest for the hog-ging wave moments.

Comparing these trends of the wave bending moment curves with the weight curves of Fig. 1 one may draw the following conclusions:

a) _{Concentration of weights in the vicinity of}

the quarterlengths (Condition II) results in large sagging moments in the same vicinity (especially at the forward quarterlength) at

speeds above 14 knots (FR 0.18) and

wave lengths A =- 1.00 L and 1.25 L.- The

peak moments in hogging are smaller and situated nearer the midship section.

19 2 4 ,0.3 _ 0.2 1 0 1 - CONDITION I1 CONDITION II I III ----CONDITION -SAGGING . -__ I I -r_ . ,0-3 WI 31 LA:

-

0-05 c.-7---- . --, - HOGGING 0-10 ... 015 020 0 25 0.30 --_ . k.0.75 , -ct 0-3-0.1 I II III ----CONDITION - ----CCiNDITIDti ---CONDITION --... 01 I ..,.., 1 I. SAGGING g o ;cs-di- :-. 0.05 02 0 ID ---0-15 0;20 - 0 1"---51-"--..-'--- 4 25 0 30 FR

---L A/c i.00 , 0 1 x

---r

HOGGING ---- ... -g ct 2 -041 PI 1 0 / .-In III III ----CONDITION ---CONDITION _

/

/

/.. -SAGGING 01 ' 0.3- 0-05 al...-. 010 015 -J ....1. DOD i - 1 ... _..-] 025 I__.. 0.30 FR ---___ .. . -..- -.-. I . ... ... .A/L. 1.25 HOGGING ! I

0-06 0041 0.02. C.) -002_ 0 04. 006 006 004 0.02 -002 0.04 -0 06. 20

b) Concentration of weights in the vicinity of the midship section (Condition III) results in large hogging moments in the same vici-nity at speeds above 10 knots for A= 1.00 L and at all speeds for A = 1.25 L. The

sag-ging moments show the same trend,

al-though the peak values are somewhat smaller.

The test results show that there is clearly

some relationship between the weight distribu-tion and the distribudistribu-tion of maximum bending

moment.

The magnitude of

the maximum

bending moment and the position of the section where this moment occurs are to a large extent dependent on the weight distribution. As a va-riation in the still water bending moment in most practical cases also involves a change in the mass moment of inertia, it is considered inadvisable to -'-draw any general conclusion about the influence of the still water bending moment upon the wave-induced bending mo-ments until some further tests have been fully analysed. So far, however, the results clearly indicate that such a dependence exists, although the still water bending moment alone may not be the most suitable parameter in this case.

V- 0 KNOTS CONDITION 1 --- CONDITION 11 CONDITION Ill 075 FP AP V-10 KNOTS

Fig. 16. Longitudinal distribution of maximum shearing force at constant speeds.

Distribution of maximum shearing force over the model length

Curves giving the maximum shearing force at each section along the length of the model for the three loading conditions and for wave length A -= 0.75 L, A= 1.00 L and A-= 1.25 L and four different speeds are shown in Figs. 16 18. These curves are the counterparts to the curves for maximum bending moments at the different sections shown in Figs. 12-14. The run of the maximum bending moment curves is determined by the end conditions, the recor-ded bending moments at three sections and the slope of the curves at those sections, thus being fixed within close limits The curves for maxi-mum shearing force, however, are determined by the end conditions and the recorded t hear-ing forces at three sections only, thus leavhear-ing considerably more freedom when drawing the

curves than was the case with the bending

moment curves. Too great attention should not

therefore be paid to minor details in these

curves, although the overall tendency should be well established from the test results.

Generally, Figs. 16l8 show that the largest

shearing forces occur in the vicinity of the

quarterlengths. For A = 1.00 L and = 1.25.L

and at the higher speeds, however, loading

0.06, 002. 0 A.P -0-02_ 006. 0.06_ 004 0-02. --002. 004. 0.06 0.06 0-04 02 A.P -002 0.04 0.06 0.06 0-04 0-02 -0.04 -0.06 V-10 KNOTS

shearing forces are in some cases found quite

near amidships.

When comparing Figs. 12-14 with Figs. 16

18 it may be noted that in cases where the

curves for maximum bending moments run

-V- 0 KNOTS CONDITION I -- CONDITION II --. CONDITION III /L= 1.25 . .P AP CONDITION I --- CONDITION 1 CONDITION M

Fig. 17. Longitudinal distribution of maximum shearing- force at constant speeds.

Fig. 18. Longitudinal distribution of maximum shearing force at constant speeds.

V-18 KNOTS :r

smoothly and show one maximum value, the.. curves for maximum shearing forces show two pronounced maxima. In cases where- a ten-dendy towards two maxima in the bending mo,

ment curves are found, however, only one

maximum value in the shearing force curves is evident. It will also be observed that in cases where smaller bending moments are observed amidships than elsewhere along the hull girder, the shearing forces in the vicinity of amidships show relatively high values. However, it may

be pointed out that the maximum shearing

force and the maximum bending moment at a

section do not necessarily occur simultaneously,

as a phase difference between them may exist. The phase angles will, however, be dealt with

more closely in a later report.

Comparison of observed moments and shearing forces with those from static calculations

It may be of interest to compare the observed wave bending moments and shearing forces with the formulae which now constitute the basis of Det norske Veritas' rules for the con-struction of steel ships.

The formulae employed by this classification society for the determination of wave bending moments and shearing forces were developed from static calculations, the results of which are given in ref. [6]. Trochoidal waves were used and -the Smith's correction was included. In their latest tanker rules Det norske Veri-tas employ the following expression for both the sagging and hogging wave bending moment

(ref. [6], eq. (22) ): ME = 0.9 10-2 7 L2B (C + 0.8) h or in dimensionless form: MB -2 Cm = 2 = 0.9 10 (CE + 0.8) 7 L B h

For a T-2 tanker with C B= 0.74 we thus have:

Cm --= 0.0139.

Comparing this Civi value with the observed test results of Figs. 13 and 14 we find that it is

exceeded only in one case, namely by a hogging

moment in loading Condition III at AIL = 1.25 and ship speed 18 knots. This speed is rather high for the block coefficient in question, and for the practical speed range the rule value of the wave bending moment may be said to cover the test results quite well.

The rule forniulae for the shearing forces at

the quarterlengths are according to ref. [6],

eq. (26): QB = 3.12 10 2(CE + 0.8) y LBh 22 or in dimensionless form: QB Co =-3.12 -107 (CB + 0.8) 7 LB h

For the T-2 tanker we have

CQ =-- 0.048.

Comparing this CQ value with the observed test results of Figs. 17 and 18 we find that it is exceeded in loading Conditions I and III for A./L = 1.00 at speeds above 10 knots and for

AIL = 1.25 at 18 knots. In Condition II the

shearing force exceeds the rule value in the

midship range at 18 knots' speed. Consequently, the rule formula for the wave shearing force may be said to give rather low values at the

forward quarterlength. Furthermore, special

attention should be paid to the fact that certain weight distributions rhay result in large wave shearing forces in the midship range.

In connection with this comparison it should be pointed out that the choice of appropriate CQ and Cm values does not provide the whole solution to the problem of estimating wave-induced loads on the hull girder. There is also the question of choosing the right wave height to be used in the shearing force and bending moment formulae. The answer to this will ob-viously be found as a result of the present and future work of the oceanographers.

Conclusions

This experimental study represents an exten-sion of earlier model tests in regular waves: to cover the longitudinal distribution of wave-induced shearing forces and bending moments -along the hull girder as influenced by changes in weight distribution. A number of important conclusions may be drawn already from the analysis of this first series of experiments.

From the test results it is evident that the magnitude of bending moments and shearing forces is to a great extent dependent on wave length, speed and weight distribution in the model. The highest recorded values for bend-ing moments and shearbend-ing forces occur simul-taneously with heavy pitching and heaving of the model and are recorded at wave lengths A. = 1.00 L and A. = 1.25 L.

The instantaneous longitudinal bending mo-ment distribution and the distribution of maxi-mum bending moments and shearing forces are greatly influenced by wave length, speed and weight distribution.

moment and shearing force magnitude and

dis-tributionfor the three loading conditions at

constant speed and wave length are due to

differences in the longitudinal distribution of the inertia forces only. The acceleration effects thus play an important role for the

wave-indu-ced

bending moments and shearing

forces

alang the hull girder. Static calculation of wave bending moments and wave shearing forces may therefore give quite misleading results, especially for high-speed ships.

The results of these tests clearly confirm the conclusions drawn by Jacobs [7] on the basis of analytical calculations of the wave bending moments. She finds that the bending moment is a second order effect dependent on small

va-riations in the longitudinal distribution of loads. The weight distribution is very

impor-tant nd the bending moment is found to be

sensitive to any small changes in weight distri-bution because of the mass-acceleration effects. 4. The longitudinal location of the maximum bending moment and shearing force is depen-dent on wave length, speed and weight distri-bution. In the cases where the highest bending moments are recorded the maximum bending

Dalzell, J. F.: «Effect of Speed and Fullness on Hull Bending Moments in Waves)), DL Report 707, Febr. 1959.

Lewis, E. V.: «Ship Model Tests to Determine Bending Moments in Waves». Trans. SNAME 62

(1954), pp. 426-490.

Lewis, E. V., and Dalzell, J. F.: «Motion, Bending Moment and Shear Measurements on a Destroyer Model in Waves", DL Report 656, Apr. 1958. Christensen, Hj., Letveit, M., and Niiirer, Chr. : ((Mode/ Tests to Determine Shearing Forces and Bending Moments on a Ship in Regular Waves»

(In Norwegian), Scandinavian Ship Technical

Conference, Gothenburg, October 1958. (Publica-tion No. 53 of the Norwegian Ship Model Experi-ment Tank, Trondheim).

Havelock, T. IL The Effect of Speed of Advance

REFERENCES

LIST OF SYMBOLS

moment does not usually occur amidships. If the midship wave bending moment. is used as an indication of the maximum wave bending moment, this may give quite erroneous results. In one special case (Condition II, A = 1.25 L and FR = 0.29) the maximum sagging bending moment was more than three times the midship sagging wave bending moment.

Consequent on the above-mentioned

conclu-sions it is recommended that further investiga-tion to determine the magnitude of wave bend-ing moments and shearbend-ing forces should be

planned and carried out in such a way that

their longitudinal distribution can be

deter-mined.

Acknowledgement

The authors wish to express their gratitude to the administration of Det norske Veritas and

of

the Norwegian Ship Model Experiment

Tank, Trondheim, for being given permission

to publish the results of these model tests.

Further thanks are extended to those members

of the tank staff who worked out the test

equipment and performed all the test runs.

upon the Damping of Heave and Pitch, Trans.

INA 100 (1958), pp. 131-135.

Abraharnsen, E., and Vedeler, G.: The Strength of Large Tankers», Det norske Veritas, Publica-tion No. 6, March 1958 (Also European Shipbuild-ing, No. 6, 1957 and No. 1, 1958).

Jacobs, W. F.: The Analytical Calculation of

Ship Bending Moments in Regular Waves.

Journ. of Ship Research 2 (1958) No. 1, pp. 20 29.

Lockwood Taylor, J.: «Vibration of Ships», Trans.

INA 72 (1930) p. 173.

Kjaer, V. A.: a Vertical Vibrations in Cargo and Passenger Ships, Acta Polytechnica Scandirra-vica, Mech. Eng. Ser. No. 2, 1958.

Christensen, Hj. and Funder, J. E.: «Pressure Gauge for Ship-Model Huils>, Electronics, Jan. 1955, pp. 197-207.

,

23

B breadth moulded _{FR vil/gL Froude number}

C _{= VgA/ 27r} velocity of trochoidal wave acceleration due to gravity

CB block coefficient wave height (from drest to

Cm = M/7L2Bh bending moment coefficient trough)

CQ = Q/71,Bh shearing force coefficient length betWeen perpendulars

draught _Liwl length of load Waterline

24

APPENDIX A

The mode/ .

The model M 482 is a wooden model of a

T-2-SE-Al tanker and the model scale is 1:50. The

model is

specially built for the purpose of

measuring vertical bending moments and

shearing forces in waves. To avoid, the model shipping water and thereby disturbing some

parts of the instrumentation, it is equipped

with an extra high bulwark. The deck and the bulwark are made of 1.0 mm aluminium plate.

The model is cut into four parts and joined

together by means of specially designed flexure beams which also serve as important parts of the bending moment and shearing force dyna-mometers. (See Fig. 22 and Fig. 24.)

At the joints there are gaps of about 3.0 mm between the wooden parts of the model. These gaps were sealed by means of very elastic and thin rubber tape. The rubber seals were formed as small bellows penetrating about 2.0 mm in between the wooden parts of the model. Thus the rubber sealing yields practically no resi-stance to the bending deflections and a very small resistance to the shearing deflections of

the model. The rubber sealings maintained

complete watertightness during all the tests.

The joints are situated at L/2 and at L/4

forward and aft of L/2, see Fig. 19. The four parts of the model can be regarded as

comple-tely stiff in relation to the stiffness of the

wave shearing force wetted surface

period of wave encounter model speed (in m/sec) ship speed (in knots)

induced voltages in dynamo-meter windings

distance from amidships of position of maximum

bend-joints. The bending deflections of the model may therefore be assumed to be due to rotation of the joints only. The shearing deflections of the model are very small compared with the bending deflections and may also be regarded

as taking place at the joints only.

The breadth of the flexure beams joining the model at the quaterlengths is 80 per cent of the breadth of the beam joining the model amid-ships. Thus, with the same thickness the ness of the end joints is 80 per cent of the stiff-ness at the joint amidships. The stiffstiff-ness of the joints was adjusted in such a way that the

natural frequency of the two-node vertical

vibration of the model corresponds to the fre-quency of two-node vibration of the ship.

In Condition I the natural frequency of the two-node vertical vibration of the model was 8.29 cycles/second which corresponds to 70.3 cycles/minute for the ship. By forced excitation of vertical vibrations in the model and by gra-dually increasing the frequency of excitation it was found possible to excite two, three and four-node vertical vibrations in the model. The

ratio of the natural frequencies for two and

three nodal vibrations was 1:2.5. No accurate registration of the natural frequency of four-node vibrations was made. When the model is struck at the bow or stern, a two-node vertical vibration is excited, giving a gradually damped

out vibration record. Some tests of this type

1

Fig. 19. The four parts of the model before joining them together.

jag moment (positiv for-ward)

specific gravity of water displacement

wave length

pitch amplitude (single) (in radians).

1.4

Te = A./(v+c)

V

kept constant for the three conditions, but the weight distribution was varied in such a way that the variations in the still water bending

moment amidships were quite near to the

Maximum possible variations limited by the c6nstant mass moment of inertia and the actual ratio between fixed and movable weights in the model. Two of the weight distributions (Condi-tion II and Condi(Condi-tion III) may be characterized as extreme. The intermediate weight

distribu-tion '(Cohdidistribu-tion I) may be characterized as a

«normal» weight distribution. This weight

distribution is very similar to the one used by Lewis and others ([1] and [2]).

Some characteristic data for the three weight

distributions are given in Table II. The data

have been made dimensionless by dividing all weights by the displacement of the model and all lengths by the length of the Model. The four

parts of the model have been numbered as

shown in Fig. 29, and complete weight distri-butions for the three conditions are shown in Fig. 1, together with the sectional area curve which gives the distribution of the displaced Water.

The terms afterbody and forebody are used for the aft and fore halves of the model.

The tow point is located 0.121 L aft of L/2

and 0.875 d above the base line. The neutral

axis of the beams connecting the four parts of the model are situated 0.50 D above the base line. Thus, the position of the neutral axis of the model, which coincides with the neutral axis of the beams, corresponds closely to the position of the neutral axis of a full-scale ship. 25 Fig. 20. The body plan and bow and stern contours for M 482.

were carried out and the vibrations were re-corded by means of an accelerometer mounted on deck at the fore perpendicular of the model. Based upon these records it was found that the damping of the two-nodal vertical vibrations in the model expressed as logarithmic decre-ment was 0.0104, which is about five times the value to be expected for the ship, [8] and [9]. The natural frequency for two-node vertical vibrations determined by forced and free

vibra-tions showed complete agreement. .,

The main particulars of the model are given in Table I and the body plan is shown in Fig. 20.

TABLE I.

Main particulars of M 482

Length between perpendiculars L 3.066 in

Length of waterline Liwi 3.128 m

Breadth moulded B 0.415 in

Depth D 0.239 m

Draught loaded d 0.183 m

Displacement in fresh water 172.5 kg

Wetted surface S 1.900m2

Block coefficient CB 0.741

Centre of buoyancy forward of L/2 0.3% of L

The weight distribution

Machined, circular iron weights were used to give the model the desired weight and weight distribution. Two rows of screws were arranged in the model to keep the weights fixed in their desired position during the tests. The longitu-dinal distance between two adjacent screws was L/20. The model was loaded down to the load waterline and floating on even keel in all of the three loading conditions referred to in this report. The mass moment of inertia WIS.

26 Picture number TABLE II APPENDIX B Instrumentation

During the test runs 11 dynamic quantities in all were measured and recorded by electrical and electronic means. These were: bending

moments and shearing forces at

the three

joints, the wave position with respect to the hull, the acceleration at the bow in the vertical

plane, surging, pitching and heaving. At the

same time static (average) quantities such as the wave height, hull average speed and tow-ing force were measured. In addition, a num-ber of photographs, usually 3-5 for each test run, were taken. The photography was

electri-Bending moments 8. shearing forces

Fore Midship Alt

0

p

Pc2 let.5

ban Dor n - channel

recorder

Sanborn 2-channel

recorder

cally synchronized with the dynamic quantities recording. The block diagram in Fig. 21 gives the overall picture of the instrumentation

eniployed.

The quantities of pitching, heaving and

surging were measured by precision electrical potentiometers. The wave profile and the wave position with respect to the hull were deter-mined by a conductive probe consisting of two thin vertical wires iimnersed in the tank water.

The bow acceleration was measured by an

electrical accelerometer (Lan-Elec, Type ITI-22F-31) which was calibrated in advance on an oscillating table by mechanical oscillation of known amplitude and frequency.

We shall limit ourselves below to describing

in detail the arrangement for measuring the

bending moments and the shearing forces only.

As mentioned earlier, the four parts of the

model are joined by means of three flexure

beams. Each beam, with its associated two in-ductive pick-ups, forms the bending moment and the shearing force dynamometer. The prin-ciple of design, which follows closely the one established by E. V. Lewis and J. F. Dalzell

[3], is shown in Fig. 22.

The design of the inductive pick-ups, see

Fig. 23, is based on the one used earlier-at the Norwegian Ship Model Experiment Tank M. a

hydrodynamic pressure measuring cell [10].

The pick-up, which is really a variable coupling transformer, consists of an E-shaped core and

five windings on the niidleg: two pick-up

windings P, two compensating windings C, and one driving winding D. In order to obtain as much symmetry as possible, the pick-up wind-ings and the compensating windwind-ings are

subdi-Pc6

Kelvin P. Hughes h- charnel recorder

Fig. 21. The instrumentation block diagram.

\./

Sanborn 1 - channel recorder

0

Brush 2-channel recorder Timinti mark Loading Conditions I H III

RaditiS of gyration of the

model (per cent of L) 23 23 23 Weights in per cent

Afterbody 49.0 53.5 52.2 Forebody 51.0 46.5 47.8 Part (1) 15.8 11.0 13.7 Part (2) 33.2 42.5 38.5 Part (3) 34.4 22.9 32.1 Part (4) 16.6 23.6 15.7 Distances of centre of

gravity from L/2 in per

cent of L Afterbody 19.4 18.7 15.9 Forebody 19.2 22.2 18.0 Part (1) 34.3 33.6 36.3 Part (2) 12.3 14.8 8.7 Part (3) 12.3 14.2 8.7 Part (4) 33.5 30.0 38.2

az.

Ktv _{k__I}

A:\

Fig. 22.

The bending moment and shearing force dynamometer.

a - supporting beam (steel) b - hull (wood)

c - flexure beam (steel) d - pick-up arm (aluminium)

- pick-up coil

f - compensating -I- driving coils - laminated core (murnetal)

vided and interlaced. A higher degree of

sub-division than used was advisable but not

physically possible owing to the small size of

the coils.

A pair of pick-ups, one on each side of a

flexure beam, is interconnected in the manner

shown in Fig. 23. The working principle of

the dynamometer is as follows. The driVing windings D are connected in parallell and sup-plied with AC voltage (7 volts, 1,000 c/s). For zero conditions of mechanical load the voltages which are then induced in the various windings are cancelled against the voltages induced in the corresponding windings C. This is achieved by balancing the voltage Vp over the winding P1 against the voltage Vc1 over the winding C1 and so on for other pairs of C and P

wind-ings. This balancing is achieved by suitable

choice of the respective turn-numbers and by relative coil positions in the AC flux. In order to make it possible to cope with various static

load conditions there is a zero setting screw

adjustment of the position of the coil P relative to the core.

Let us now assume, starting from the zero

conditions, that the dynamometer is loaded by a pure positive bending moment + M (as

posi-tive direction in this connection we may

spe-cify the clock-wise direction). Under this load condition, as will be inferred from Fig. 22, the flexure beam will bend symmetrically so as to

r

a

,

_2...Bending rnorr.tent

1!

Inductive pick-up (sectiOn)

Shearing forte

Summative and differential connection of

twee inductive pick-upa

Fig. 23. The pick-up design and connection.

advance the pick-up coils P on both sides of the beam some small equal distances towards the driving coils D. This movement of the pick-up coils P is followed by changes in the induced voltages in the pick-up windings so as to give:

AVp2 AVp.2 Vm = Km M

as an output on the + terminal, which is pro-portional to the bending moment M.

At the same time we get an output:

AVpi AVp' = VQ'

at the terminal. For full mechanical and

electrical symmetry of the dynamometerwe

have:

AVp = AVp'/ and thus VQ' = 0.

Next, we remove the bending moment + M

and load the dynamometer with a

pure

po-sitive shearing force '+ Q (as a popo-sitive shear-ing force direction we choose the one which

distorts the flexure beam in such a way as to

lift its left-hand side and to lower the

right-hand side.) This loading will be followed by

changes in the induced voltages in the P wind-ings so as to give:

AVE, ( AVp' AVp AVp' VQ = KQ Q

as an output at the terminal, which is

pro-portional to the shearing force Q. Simultaneously we have:

AVp2 AVp '2 = Vm'

at the + terminal.

Again, for full mechanical and electrical

symmetry we would have:

AVp2 AVp'2 and thus Vm' = 0

However, in practice, it Was not possible to realize perfect symmetry, thus the system

dis-played a certain amount of qcross-talko, i.e.

the quantities VQ' and Vm' were not zero.

6

1011"."*-7PJZ

1E

Fig. 24.

Bending moment and shearing force dynamometer.

This cross-talk from the M channel to the Q channel and vice versa was investigated expe-rimentally by subjecting the dynamometer to pure bending moments and pure shearing for-ces in a manner described in Appendix C. It then turned out, since the shearing deflections were small compared with the bending deflec-tions for the range of bending moments and shearing forces to be covered, that quantity

0 whereas the quantity VQ' K' M,

where K' is

the «cross-tallv> constant from

the M channel to the Q channel. Correction had to be *lade for this effect.

Fig. 24 shows one of the three dynamometers mounted on the supporting beams detached from the hull sections.

Fig. 25 shows the diagram for the amplifier

employed to amplify the Q-channel output

through to the recorder. The amplifier is phase-sensitive, the necessary reference voltage being

the one supplied to the driving

coils. The

amplifier showed good zero and gain stability.

10 28 n 6S L7 680K 6H6 0 ₀ 1112,4pF 12,6pF 12,6 pF

Fig. 25. The Q-channel amplifier diagram.

Fig. 26. The filter diagram.

A calibration signal for each channel was

built in.

The amplifier employed for the M-channel output is of similar design to the one for the Q channel but of less gain.

The analysis of the preliminary test results in regular waves showed that at certain fre-quencies of encounter the two-node vertical vibrations of the hull were considerably

ex-cited. These oscillations added to the wave

induced forces and moments so as to make the recorded wave forms complex and difficult to

analyse. This

difficulty was overcome by

designing a special low-pass filter (M-derived type) which could be switched in or out of the circuit at the amplifier end-stage. Fig. 26 shows the filter diagram with the switching arrange-ment. All the six filters, one for each amplifier,

could be switched in or out by one master

switch. All the test runs were recorded partly

300 V 1K 0

410

Recorder coils .-105 V --o 6V6 6V6 Vp Col 1 5K 6SN7

20

0

9 TO 11 12

Fig. 27. The frequency response of the low-pass filter.

a 4

filtered and partly unfiltered, as the latter con-ditions were thought to be of interest in them-selves. Fig. 27 shows the filter frequency res-ponse (average of six), experimentally deter-mined. With nominal attention peak at 8.25 c/s the filter gives an attenuation of the hull/dy-namometer system recorded oscillations by a factor of about 10 (without noticeably influ-encing the bending moment or the shearing force time functions). The highest frequency of encounter for the model was 1.8 c/s and in the cases where the highest values of bending mo-ments and shearing forces were recorded the frequency of encounter was about 1.0 c/s, and

in this frequency range it was found

unneces-sary to apply any frequency-dependent

correc-tion of. the bending moment and shearing force

recordings due to the filter (see Fig. 27.)

The filters and amplifiers, with some

asso-ciated equipment, are shown in Fig. 28. APPENDIX C

The calibration of the instrumentation for

mea-suring bending moments and shearing forces The total bending moments and shearing for-ces acting upon a hull girder in a seaway are

usually divided into a still water part and

a

wave part. As no major difficulties are

invol-ved in calculating the still water bending

mo-ments and shearing forces, there is no need for any experimental determination of the magni-tude of these. The experimental investigations described have therefore been concentrated

purely on the wave-induced parts

of the

bending moments and shearing forces. The

instrumentation has been set to «zero» when

the model is floating at rest in calm

water,

trimmed and ready for tests, and this condition has throughout been used as a basis of

refer-to-of

41111ftn..1100i

Fig. 28. The amplifier and filter rack.

ence for the measured bending moments and

shearing forces.

The calibration of the instrumentation for

measuring bending moments and

shearing

forces has been carried out with the model

floating in calm water in «ready for test»

con-dition. The principle of the calibration is to introduce changes of known magnitude in the static bending moment and shearing force and to record the outcome of the instrumentation. Thus, the calibration of the instrumentation was carried out as static calibration only. A simple way of introducing changes of known magnitude in the bending moments and

shear-ing forces is to add weights or move weights

onboard. By this method both the bending

moments and the shearing forces are usually

changed simultaneously. _{This is no}

disadvan-tage when the registration of bending moments

and shearing forces is quite independent. Due

to the cross-talk effect in the instrumentation, however, the registration of shearing forces

will to a small degree depend

_{on the actual}

magnitude of the bending moment. For this reason it was found advisable to apply methods

by which mutually independent changes could

be made in the bending moments and _shearing

forces.

t

29 -; _[ -, , i 1 ; 1 1 i 1 _i .

J

I

i

-1 1 1 ' . _i_ I --F army Low Pass _I 1 I Response nib.-1 I ' I for 8,25 _I cTs1 - --1i , 1 , j_ -IT1 ,!---I

IT

_ H 1 I -1- ...411MENI -40111 !

jI

I J ---1 10 a 6

Fig. 29. The introduction of pure bending moment.

The methods used to introduce a «pureD

bending moment are outlined in Fig. 29. By

loading the thin ropes, which are fixed to the

aluminium tube rods, and which run

com-pletely horizontally between the tubes and the pulleys, with equal weights P, a pure bending moment of P. a is simultaneously introduced in all sections of the model between the rods. No change in the shearing forces has been

in-troduced and the axial force inin-troduced

be-tween the rods does not influence the record-ing of bendrecord-ing moments and shearrecord-ing forces.

The principles of introducing pure shearing forces is illustrated in Fig. 30. Three wooden

pieces are fixed to the deck of the model at

each joint. Fig. 30 shows the joint between

Part 3 and Part 4 of the model.

The centre

wooden piece is fixed to Part 4 and extends

over the gap without coming into contact with

Part 3 of the model. Similarly the side pieces

are fixed to Part 3, extending over

the gap

Without coming into contact with Part 4 of

the model. If two weights of equal size P origi-nally placed on the outer wooden pieces are shifted athwartships to the centre position, a change in the shearing force at the joint of 2P will be introduced without any change in the bending moment.

For the calibration of the instrumentation for measuring dynamic bending moments and shearing forces, bending moments and shearing forces of known magnitudes were introduced, both by shifting weights in the longitudinal direction and by the methods described for the

introduction of pure bending moments and

shearing forces. A double control of the cali-bration was thus obtained both for the

instru-mentation for measuring bending moments

and the instrumentation for measuring shear-ing forces. There was always good agreement

between the two types of calibration of the

bending moment instrumentation, and the

re-cording of bending moments proved to be

completely independent of the magnitude of

shearing forces within the actual range of

30

Fig. 30. The introduction of pure shearing force.

shearing forces.

When pure bending moments were introdu-ced, apparent shearing forces of small magni-tude were usually recorded due to the earlier mentioned cross-talk from M channel to the Q

channel. Hence, the recorded shearing forces

had to be corrected for the influence of the

bending moments. Based upon the calibrations with pure bending moments, correction curves for the influence of the bending moments upon the recording of shearing forces were plotted. When the actual shearing force records had been corrected for the influence of the bending moments, the agreement for the two types of calibration was goad. Typical calibration curves for shearing force and bending moment record-ing are shown in Fig. 31.

Complete calibrations of the instrumentation were carried out every morning before the tests

- started and every night when the tests for the

day were finished. Apart from the correction curves for the influence of the magnitude of bending moment upon the shearing force re-cording, all the calibration curves remained constant during all the tests reported. The

cor-rection curves for shearing force recording

were somewhat influenced by changes

in

weight distribution or by taking the model out of the water, but remained constant for each

loading condition.

Apart from the mechanical calibration, all the channels for recording bending moments and shearing forces were equipped with built-in electrical calibration signals. These electri-cal check-points were used continuously be-tween the test runs to check the electrical

in-strumentation and to

check that the gain

PURE SHEARING FORCE

COM BINED SHEAR AND BENDING (CORRECTED) 10 SHEARING FORCE kg -6.0 -5.0 -4.0 73.0 -2.0 -1.0 1.0 .2.0 .3.0 .4.0 .5.0 .6.0 SHEARING FORCE kg 3 g FORE JOINT CALIBRATION 22.6.59 UI ce UI cc 5 g ; 6 CE HOGGING 18 16 14 E 12 PURE BENDING 010 COMBINED BENDING cc AND SHEAR _cc 8 cc 6 0 .w cc 4 BENDING MOMENT kgm 6.0 5.0 4.0 3.0 2.0 10 _SAGGING 1.0 2.0 3.0 4.0 5.0 6.0 2 BENDING MOMENT kgm cci, 0 12IC`jc 14 6 10 20

Fig. 31. Typical calibration curves for shearing force and bending moment recording.

FORE JOINT