Experimental determination of bending moments for T2-SE-A1 tanker model in regular wave

CONTENTS

Abstract

i

1. Foreword L 2. Description of Tests 1-2-1 Model

I

2-2 Test Program 2 3. Test Results 3 3-1 Motions 3 3-2 Bending Moments 4

4. Discussion and Conclusions 4

4-1 Trends of Bending Moments with Speed 4

4-2 Influence of Wave Length on Midship Bending Moments 5

4-3 Influence of Wave Height on Midship Bending Moments 5

4-4 Influence of Radius of Gyration on Midship Bending

Moments ₅

4-5 Maximum Longitudinal Bending Moment Distribution 5

4-6 Variation of Longitudinal Bending Moment Distribution

with Time ₅

Acknowledgement 6

EXPERIMENTAL DETERMINATION OF BENDING

MOMENTS FOR T2SE-A1 TANKER MODEL

IN REGULAR WAVES

Yoshio AKITA and Kunio GODA

Abstract

A T2-SE-A1 tanker model was tested in the T.T.R.I. Model Basin in order to determine longitudinal bending moments in regular waves. The hull of model was made of wood and cut at five sections. Each block of hull was connected by steel girder. Bending moments at five sections were obtained by measuring the bending stresses on steel girder at the sections by means of resistance wire strain gages. Hydrodynamical forces

acting on each part of hull were also measured.

Tests were made in regular head waves having heights of h/L=]/50 and 1/30, and lengths of A/L=0.75, 1.00, 1.25 and 1.50.

Foreword

In design of ships of reasonable strength, it is necessary to under-stand the details of longitudinal bending moments induced by waves.

As a subject at the Committee on Model Test, International Ship Structures Congress in September, 1961, in Glasgow, the model test results of benging moments obtained at several laboratories are intended to be compared and discussed.

Description of Tests

2-1 Mode'

The model of T2-SE-A1 tanker was made of wood.

Figs. i to 5

show the construction of the model.

The wooden hull was divided at

five sections. The individual blocks of hull were connected to a steel

girder by canti-levers and ball bearings. The electric motor, the propeller shaft, the ballast weights etc. were mounted on the steel girder.

The longitudinal bending moments were obtained by means of strain

gages on steel

girder, calibrated in terms of bending moment. The

positions of the strain gages are shown in Figs. 4 and 5.

For each section of the girder eight strain gages were used and connected as shown in Fig. 5. In this connection the influences of axial forces and lateral bending of steel girder are eliminated and the longitudinal bending moments are obtained. An example of the oscillograph record is given in Fig. 6. The strain gages on the canti-levers were used to obtain the resultants of hydrodynamical forces and inertia forces acting on each block of the model. This part of test results is not yet analysed.

The principal particulars of T2-SE-A1 tanker model are given in Table 2. The reason, why the natural frequency of vertical two-noded hull vibration of the model is rather low in comparison with the frequency corresponding to that of the actual ship,

is that rather small section

modulus of the steel girder was needed to obtain a measurable stress on the girder. Two weight curves are shown in Fig. 7. Table 5 shows the characteristics of the two weight distributions. For the requirement of the Committee on Model Test, the center of gravity and the mass moment of inertia of every block of model are given in Table 3. These values in Table 3 were not obtained by actual survey, but by calculation, because the steel girder was assembled by welding and then it was difficult to cut off. The model has neither bilge keel, nor additional bulwark to prevent the shippage of water.

2-2 Test Program

The model was free to pitch, heave and surge, but prevented in rolling and yawing. The tests were carried out by the self-propulsion

method. The measurements were made when the model synchronized

with the towing carriage.

In the experiments the following items were measured: Bending moments at five sections

Vertical hydrodynamical forces acting on each block of the

model

Pitching

-2-'Experimental Determination of Bending Moment for T2- SE- Al Tanker Model in Regular Wave

Heaving Surging

Vertical acceleration at midship, bow and stern Wave height

Wave profile at ship side (photograph)

The test program is shown in Table 4.

All tests except a test in wave of h = L/30, , = 1.25 L were carried out in

speed range up to

V/VLg = 0.3.

The tests in the wave having height of h=L/30, and

length of A=1.50L, at the speed over V/"../Lg =0.23 was impossible due to severe shippage of water and shortage of the power of the propelling

motor. Tests were carried out in the condition of the designed load draft

and of even keel. (The nomenclatures are explained in Table 1.)

3. Test Results

3-1 Motions

The measured values of motions are presented in Figs. 10 and 11. The test results of the motions are presented in the form of non-dimensional parameter Z/h and /(h/L),

where

Z= double amplitudes of heaving çS = double amplitudes of pitching h = wave height

L= length between perpendiculars

In these figures, the phase angle of motions is given with respect to the wave motion at the center of gravity of the model.

Assuming the motion to be given by a=ae"t ; a=z or a=çb and the

wave motion at the place of the center of gravity of the model by

r =

het, then

represents the phase angle in this report. The wave

elevation is defined to be positive for surface rising, further the heave and pitch elevation are defined to be positive for model rising and bow descending, respectively. The wave motion has not been measured during

the tests at the center of gravity of the model, but measured with a wave

height transducer fixed to the towing carriage in front of the model.

3-The distance between this transducer and the model was not constant due to the surging motion of the model. The measured mean position has been used for calculating the phase difference.

In lower speed range, the tank wall interference effects on the motions of the model. In this range the assumed curves are indicated by dotted line in these figures.

3-2 Bending Moments

The test results of bending moments are plotted in Figs. 12 to 14. Figs. 12 and 13 give the midship bending moments in various test conditions, and Fig. 14 give the bending moments at fore and after sections in one wave condition, i. e. h = L/50, = 1.00 L. The bending moments are

ex-pressed in the form of dimensionless parameter C,

where

c

M

pgL2Bh

M= bending moment p=density of water g= acceleration of gravity

L = length between perpendiculars B=breadth of the model

h = wave height

The base line of the bending moment was refered to the reading at standstill state in still water. The superimposed vibratory bending moment was faired out and is not included in the bending moments shown in these

figures. As mentioned previously the results in lower speed range are not

reliable due to the tank wall effect. Therefore the results in such a range were indicated by the dotted lines or thinner lines in the various figures. The coefficients of the bending moment in still water were calculated as h = L/50 or L/30.

4. Discussion and Conclusions

4-1 Trends of Bending Moments with Speed

As can be seen from Figs. 12 to 14, the trend of the midship bending moments with speed varies with the test conditions i.e. wave lengths,

-4-Experimental Determination of Bending Moments for T2- SE- Al Tanker Model in Regular Wave

wave heights, and weight distributions. However, the trends of total bend-ing moments at every sections in the same test condition with speed are

similar. (Fig. 14)

In most cases there is no large difference between the hogging and the sagging moments at the midship section.

4-2 Influence of Wave Length on Midship Bending Momen4s

Fig. _{15 shows the comparison of the midship bending moments in}

waves of various lengths. As found in Fig. 15 the wave length in which the maximum midship bending moment occurs varies with model speed.

4-3 IfIuence of Wave Height on Midship Bending Moments

A linear relation between the wave height and the midship bending moments is found in the test results in waves of A = 1.00 L. This relation, however, does not hDld good in waves of A = 1.25 L at speed range over about V/L-. = 0.17. At zero speed the linear relation hold sufficiently for both cases. (Top and middle figures in Fig. 13)

4-4 Influence of Weight Distribution on Midship Bending Moments The bottom figure in Fig. 13 shows the comparison of test results of midship bending moments at two different weight distributions. As found in this figrure variation of the weight distribution to this extent does not bring on large change in the midship bending moments.

4-5 Maximum Longitudinal Bending Moment Distribution

The maximum hogging and sagging moments at every sections at different speeds are shown in Fig. 16. Consequently, these curves

re-present the envelop of bending moment curves occuring over one period. A feature of Fig. 16 is that the section at which the maximum sagging moment occurs shifts forward at high speed.

4-6 Variation of Longitudinal Bending Moment Distribution with

Time

Fig. 17 shows the variation of longitudinal bending moment distribution over one period at speeds of Vh/E=0 and 0.30.

While the section at

5-which the maximum bending moment occures travels lengthwise at zero speed as found in the static calculation, this feature is not found at speed of Vh/Eg= 0.3. In these figures, T means a period of encounter, and OT indicates the instant when sagging moment reaches the maximum value. Ackno viedgement

The authors wish to acknowledge the contributions of members of the Transportation Technical Research Institute staff for this report. Special

thanks are extended to Mr. K. Tsuchida, and Mr. R. Tazaki, members of the Ship Propulsion Division, and to Mr. M. Azuma and Mr. M. Tani, members of Ship Construction Division.

Tables and Figures

Length between perpendiculars, L Breadth moulded, B

Depth moulded, D

Draft for desgin, moulded, d Displacement, 4

Londitudinal center of buoyancy

Block coefficient, Cb

Radii of gyration in air, K

Natural frequency of vertical two-noded hull vibration, in calm water, for K=O.250L Scale ratio

6-500 m 0. 608 m 0. 351 m 0. 268 m 0. 530 m3 0.017 m. forward of midship 0.74 0. 250L & 0. 272L 0 c. p. s. 1/34. 07 Table i Nomenclature

L Length between perpendiculars C Bending moment coefficient

B Breadth f) Density of water

K Radius of gyration g Acceleration of gravity

V Model speed T Period of encounter

2 Wave length 4A Displacement of after body

h Wave height 4F Displacement of fore body

z Double amplitudes of heaving Double amplitudes of pitching

1A Longitudinal center of gravity of after body from midship

Phase angle between wave and heaving Phase angle between wave and pitching

Lingitudinal center of gravity of fore body from midship

M Bending moment

Experimental Determination of Bending Moments for T2- SE- Al Tanker Model in Regular Wave

Table 3 Center of buoyancy, center of gravity and mass moment of inertia of individual block CaIculated)

* Values in upper columns are for Case i (K=0. 250 L) and in lower columns are for Case 2

(K=0. 272 L).

Table 4 Test Program

Wave length, A Still water ; Case i (K=0. 250L) A; Case 2 (K= 0. 272L) 0.75 L 1.00 L 1.25 L 1.50 L L/50

.

-7-Wave height, h L/30

.

Block 1 Block 2 Block 3 Block 4 Block 5 Block 6 Total

Calcu-lated sured Mea-Displacement of block, _0.0600

mm3 0. 1100 0.0958 0.0958 0. 1129

990

0. 0594 0.5339 0. 530 Longitudinal center of

buoyancy of block from

midship, in mm 1665 956 300 300 1686

Vertical center of buoy-ancy of block from base

line of model, in mm 158.4 137. 0 136. 5 70. 5 136. 5 137. 2 142. 0 Weight of block, in kg 85.6 100.9 85.4 114. 1 73.5 530 13. 5 fore 100. 2 126. 1 30.5 35. 4 146. 2 91.5 Longitudinal center of gravity of block from midship, in mm

1637 950 280 294 1025 1643

1641 977 306 271 993 1626 12.5_fore

Vertical center of

gravity of block from base line of model, in

mm 257 226 118 158 158 249 194 190 263 246 127 220 177 4. 23 257 2. 64 223 680. 5 231

Mass moment of inertia

of block about

trans-verse axis through

center of gravity of block, in kg-m2 6. 87 -6. 75 7. 70 1. 88 4. 50 670.8 7. 75 1.49 3. 50 5. 95 3. 03 Speed range _{V/./Lg r0'0.3}

Table 5 Characteristics for two cases of the weight distribution

Fig. 1 Model

BLOCK H BLOCK 2 BLOCKS BLOCK ¿7 BLOCK S BLOCK

R / ACCELEROMETER HCCELERON005I

/SCTION I SECTION? SECTION? 500)004 SUCTION 5 /

I i i

-uI

IN

Fig. 3 Steel girder and canti-levers in Model

00CL

UIOLL

UNTAEROAL JOINT I STEEL SAbER 1)35 mm) STRAIN 0500 )W000EN HULL

/ MOTOR \sBALL BRAISING

THRUST BEARING \\ \ 5TEEL CANT-LOVER

Fig. 4 Model setup for determining bending moments in waves

ROXO1U'N

Fig. 2 Inside of Model

E150L GIALLO STRUT

ERS LS1! ATtC1 &AUC,

SAGTo solD. 05101

WOODEN HULL /

As ROL BESOINS

aHI COATI-LIVOR

Fig. 5 Midship section and connection of strain gages SILT K 4A 4 'A L 'F IA4A 1F4F 4 L U L4 Case 1 0. 250L 0.485 0. 515 0.220 0. 214 0. 107 0. 110 Case 2 0. 272L 0.485 0. 515 0. 257 0. 247 0. 125 0. 127 OTC EL AT OR OUT PUT ODCILL010R

Experimental Determination of Bending Moments for T2- SE. Al Tanker Model in Regular Wave

Fig. 7-A Weight curve in Case i

KO.2OL *-/5o, V4.

5ECflO'

2 /

9-S3CT1ON 3

TIPlE

Fig. 6 Sample oscillograph record of bending moments

'J-Fig. 7-B Weight curve in Case 2

Fig. 8 Two attitudes of Model in regular wavesofA=1. 001, h=L/30, at speed of V/VLg r0.24

JJLL

SECTION 4 SECTION 5 F.P AP. SECTION I SECTION 2 SECTION 4 SECTION S Pp.

PI-J K-0272L J. L K= O 050L L E ¡

t

OAPI SECTION SECTION 2

Fig. lo Pitching motions

.

L k

Fig. 9 Model in still water at speed of

= 0.28

lo

-Fig. 11 Heaving motions

IDO 1.0

I0j_.

RÇ

O.250L X=I.50L S.. À lOOL 0.5 _7À=0.15L LS LO

io____

Zî.r_.

K=0250L

I

X=I.25L. Àl.25L. ESL,íO L,0 05:1_S

.'

SS .L0OL.h5L,t,

____-_.

ASIDO L

-

.

i°0 :: LO

ui.jiii

KS

/

K 0.200L O.272L

-

RÍI1!

MODEL SPEED -Ioc -20c 300 S_O

K=O.250L -5s L,'50 - /À=I.50L

-.t.

A5i.00L -iOO -OOo 300 OS S_O

--

-hSL/50 h5L/30

-

=-=

K-0250L

___

AI.25L. sI25L À=LOOL, 0=L,'50

2.51

.o-3OO 7.5 S_D iOOL L,,5 /K-ozlzL KO25OL 0 S.l 02 0.3 MODEL SPEED

Experimental Determination of Bending Moments for T2- SE- Al Tanker Model in Regular Wave

Fig. 12 Bending moments at midship section

Fig. 13 Bending moments at

midship section SECTION 3 0= 0.250 L h= L/50

o

C N STILL WATER 0.010 10.010 0.00 A= 1.00 L

---= 0005_U_i

::U.!Ii

1;.°

t.

U1

0.0 III 0.005 00.005 O X=.25 L

j

__-u..

1111111 osos 0.305

o-=---::!p!!.

.

0.210 0 si 02 03

MODEL SPEED

V//U-SECTION 3 --- IN C M f5LBh STILL WATER K=0.25DL h= L/30 )sIOOL /

0.OIOU_

UU.

₁

;

0.005 K= 0.255 h=

LhL4DI

A= 1.25 L 0.01 0 O 5

U

Ui

0.01 O MODEL SPEED V/J[_

Fig. 14 Bending moments at different sections

12

-Fig. 15 Comparison of midship bending moments in waves of different wave

lengths 0.015 0.010 0.005 0.00 5 0.0 IO , 0.005 0.010 0.0 IO 0.010 0.0 00 0.0 15 K0.250L X= .00 L 1 0.010 COIS

Fig. 16 Maximum longitudinal bending

moment distribution in wave of 2=100L at different speeds

7 PP.

Fig. 17 Change in longitudinal bending moment distribution over one period

SECTION 3 =O250L b.L/50

ip5OL

SPEED MODEL K=0250L )I.00L hL/5Q _---IN M WATER p0L25h STILL 0.010 0.005 0.010 SECTION I

-

020L AP. ER ¡0.010 =0005 o D O.005 10.010 SECTI0 2 -. 1-0.13L ALF. 2

_j=___./"

W S 0.010 = 0.005 o.00s 10.010 StTIOSo 4 r-.P. 00 4 FR

O..-.--.

-r OCIO 0.005 o C 0.0O5 0.010 0 SECTION 5 AP. 5FF -0 0.1 0.2 03 MODEL SPEED 0.010 0.005 ' 5/0T

AP__

Fe 0.015 0.01 0 i: 0.005 1= 0.005 0.0 0 0.015