'ARCHIEF
v.4PRTPARED FOR 14TH INTERNATIONAL TOWING TANK CONFERENCE 1975
C SEAKEEPING )
rASUR21ENT OF TORSIONAL AND BENDING MOINTS ACTING ON
A SHIP HULL IN REGULAR OBLIQUE WAVES*
by HITOSHI JJII, DR. ENG.
KUNIHIRO IiCAMI
OCTOBER 1974
Seakeeping Research Lat.oratory, Nagasaki Technical Institute,
Mitsubishi Heavy Indust;ries, Ltd.
* Summarized from the paper (in Japanese) published in
Journal of the Society of Naval Architects of Japan,
Vol. 136, December 1974.
Lab v Sciepsb
Technische Hogchoo1
DeIfL
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MEASURF.MENT OF TORSIONAL AND BENDING MOMENTS ACTING ON A SHIP HULL IN REGULAR OBLIQUE WAVES
BY H. JJ II AND K IKEGAMI
SUMMARY
The ship model tests were carried out in regular oblique waves to obtain the wave loads: the torsional moment, the vertical and lateral bending moments. The model consisted of four segments longitudinally jointed by three multi-component strain gauge balances. The wave loads were measu.red at the three longitudinal sections: S.S.3, midship and
S S.
7.
The measured values were compared wIth the computed ones by the strip method, and fairly good agreement was obtained for the vertical bending
mc.ment. However, discrepancies were found for the torsional moment and the lateral bending moment. In order to predict the wave loads more accurately, it is considered that the calculation method of wave exciting forces and moments should be improved.
1. INTRODUCTION
From the viewpoint of the economization in ship hull constructions, the transverse strength of ship has become one of the most important problems in ship design. And, therefore, it has been regarded as the matter of fundamental importance to be able to predict the lateral wave loads due to waves and, ship motions. For container ships or liquid gas carriers which have large deck operinirigs, the torsional strength,
especially, is the problem of the principal importance at the stage of the initial design of the ship hull constructions.
Attempts have been made to predict the wave loads by.theoretical approaches, and in recent years the calculation method of the wave loads was developed by the application of the strip method to the prediction of
ship motions in waves. (1) (2) (3) And from the results of the calculations, it has been confirmed that for vertical bending moment the computed value shows fairly good agreement with the meas'.ired one. However, such
confirmation has not yet been made for lateral wave loads owing to the, lack of suitable data and for the calculation method for lateral motions in
oblique waves.(4) (5) (6)
Present paper shows the results of the study on the torsional and the bending moments in regular oblique waves in reference to the model tests by use of a four-segmented ship model and the theoretical predictions.
2 MODEL EXPERIMENT 2.1 WAVE LOAD DETECTOR
A niulti-comporient strain gauge balance was designed as a wave load detector which i capable of connecting the segmented hulls and measuring
tne wave loads; vertical and lateral bending moments
and torsional moment.
Each of the three detectors used consists of four gauge springs on
which
the strain gauges are stuck and its construction is shown in
Pig.l.
Each
component of the wave loads is measured with very small mutual interference
by selecting the position of the gauges and their connection.
Thecalibration of detector was made separately for bending and torsional
moments and. their mutual interference was found to be less
than 1%.
2.2
TESTED MODEL AN])_TEST CONDITIONA wooden model, having 3m length, was divided into four longitudinal
segments at three cross sections: S.S.7', midship
and S.S.3, and they were
jointed with three wave load detectors.
The clearance between adjacent
segments is about 2m/m, and the interspace at each connecting part, was
kept watertight by flexible vynil membrance.
Model tests were conducted at the Seakeeping and ManoeuvringBasin of
Nagasaki Technical Institute, MEl.
Model was adjusted at full load and
even keel condition, and bilge keels and rudder were fitted.
Weight
distribution in the model was arranged so that each divided segment
keeps.
even keel condition and the height of the center
of gravity was made to be
equal to the designed value for the ship model as a whole.
The principal particulars and the test conditions are shown in
Table 1
and the test arrangement of model 'in Fig.2.
Ship motions in six degrees
of freedom: heave, pitch, surge, sway, yaw and roll, were
measured by use
of our six-component bala-ce, and wave loads in three components:
vertical and. lateral bending moments and torsional moment, were measured
at three sections by the wave load detectors.
Tested waves were regular and shorter length waves were chosen'
mainly
because in shorter wave length range the wave loads appear to be
coinpara-tively large.
That is;
wave length:
wave height:
ware direôtions:
advance speed:
2'-/Lpp = 0.4, 0.5, 0.6, 0.8, 1.0, 1.5, 2.0
hw/Lpp = 1/60
:(constant)
.L4 =1500, 1200, 900, 60°, 300
(M= 1800 corresponds to head wave)
Fn = 0, 0.195
For the torsional moment, the positions of the wave load detectors were
changed vertically at two different points to investigate the effect of
position of torsional axis.
5.
TEST RESULTS ANI) COW3IDEHATIONSTo examine the applicability of prediction method on the wave loads,
ship motions and wave loads were computed by the method
presented in
reference (3) for the same condition in which the experiments were
carried out.
The measured values are compared with the computed ones.
3.1
REPRESENTATION OF REUL'PSnon-I4
-3-dimensional values, as follows.
For ship motions:
Heave amplitude : = ZA/hA . Sway amplitude :
7 =
yA/hAPitch amplitude : 8 = BA/khA, Yaw amplitude : = 9A/khA
Surge amplitude : Y = XA/hA , Roll amplitude : = 'PAIkhA
For wave loads:
Vertical bending moment : 1T = Mv/fgBL2h
Lateral bending moment : = M/fgBL2h
Torsional moment : = NT/fgBL2hA
3.2 SHIP MOTIONS
The measured and the computed response amplitude functions of six components of ship motions are shown in Fig.3, using the wave direction as a parameter in the case of Fn=O.l95 as an example. The measured values show fairly good agreement with the computed ones except for the case of beam wave, where the measured heave amplitudes are larger than the computed ones and for the case of quartering waves, where some discrepancies are found in roll and sway amplitudes.
The measured amplitude of heave is comparatively large. This may be due to the hull form with shallower draft; that is, the full form with larger beam-draft ratio as in the present case. The measured amplitude of roll is fairly small in the tested wave length range. This may have
resulted from the facts that the roll damping was larger and that the natural period of roll was very long. These may be due to the facts that the present ship has flat bottom and tha the vertical position of the center of gravity is rather high and, therefore, the lateral metacentric height is small.
3.3
WAVE LOADSThe measured and the computed response amplitude functions of wave loads at S.S.7, midship and
S.S.3
are shown in Fig.4, 5 and 6, usingthe wave direction as a parameter in the case of
=O.l95
as an example. (1) Vertical bending momentThe measured values of vertical bending moment at each seàtion show fairly good agreement with the computed ones. The response amplitude function of vertical bending moment resembles to that of pitch and the correlation is observed between them. Further, as for the pitch, there is fairly good agreement between measured values and the computed ones.
Therefore, the ordinary calculation method of vertical bending moment is considered to be useful for the prediction; however, the examination is
iecessary on the discrepancies with the test results in the shorter wave length range.
The measured values of vertical bending moment are large in the oases of wave direction A
1500
and 30° and its maximum value occurs nearO.80"l.O. The values at midship are larger than those of other sections, although the feature of the measured response amplitude function at each
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section shows similar tendency. Lateral bending moment
The measured values of lateral bending moment at each.section also show fairly good agreement as a whole with the computed ones. However, the degree of agreement is worse than that in the case of the vertical bending moment; some discrepancies are found in the shorter wave length
range.
The measured values of lateral bending moment are small at almost all wave directions tested in the longer wave length range, but they are large in the cases of ,L(=1200 and 60 in the shorter wave length range. 0Almost similar response is observed at the pair of cases: ,U=120 and 60 and )4-l500 and 30°. Clearer correlation
i8
observed between the lateral bending moment and the wave exciting force rather than ship motions;that is, the lateral bending moment is large in the shorter wave length range where ship motions are small and its response function resembles to that of the yaw moment.
Torsional moment
The measurcd values of torsional moment at each section are smaller than the computed ones, especially in the shorter wave length range, although the features of them show the similar tendency.
In every wave direction tested., the measured values are large in the shorter wave length range and remarkably large at ,U=l20 and 60 , and the effect of ady.nce speed on them seems to be small. The feature of response amplitude function of torsional moment resembles to that of lateral bending moment and also seems to be related to the wave exciting forces and
moments.
In the cases of Fn-0, Jl50° and 120°, the positions of wave load detectors were changed vertically at two different points to investigate the effect of position of torsional axis. The results are shown in Fig.7 and the tendency is observed that the torsional moment becomes small as
the torsional axis approarches to the water plane. This result may be due to the fact that the vertical center of wave exciting force is near
the water plane.
Considerations
The wave loads become large in the shorter wave length range and the measured and the computed values do not agree in that range. These facts are the same with the feature of the hydrodynamic pressure arid it is considered that a key of improvement of calculation method will be found in this point. In research on the hydrodynaniic pressure, total pressure is divided into the components: radiation.prsure, diffraction pressure and pressure due to Froude-Kriloff hypothesis, and the computed values of each terms have been examined by the corresponding experiments. It is pointed out from the results of these researches that the calculation method of diffraction pressure should be improved.
In order tc be able to predict lateral bending moment and torsional moment more accurately, it is considered that the calculation method of the wave exciting forces and mcients should be improved.
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4. CONCLUSIONS
In order to examine the applicability of the calculation method on wave loads, modcl experiments were carried out in regular oblique waves using the four-segmented model. The results can be sunmarized as follows:
Wave loads are larger in shorter wave length range where ship motions are comparatively small.
The response amplitude functions of wave. loads at each section show similar tendency.
Remarkable effect of advance speed is found in the vertical bending moment, whereas for the lateral bending and the torsional moments, there is little effect.
Pairly good agreement is obtained between the measured vertical bending moment and the theoretical predictions by use of the strip method.
However, discrepancies are found for lateral bending moment and torsional. moment in shorter wave length range.
To improve accuracy of theoretical predictions of the wave loads, it would be necessary first to improve the calculation method of the wave exciting forces and moments in shorter wave length range.
REFERENCES
1. Fukuda, J., "Strip Method and Its Application", Bulletin of the Society of Naval Architects of Japan,
No.435, 1969.
2.Sa].vesen, N., Tuck, E.O, and Faltinsen, 0., "Ship Notions and Sea Loads", TSNANE, Vol.781 1970.
Nagamoto, R., Konuma, M., Iizuka, L, Aoki, N. and Ta.kahashi,
T.,
"Theoretical Calculation of Lateral Shear Force, Lateral Bending Moment and Torsional Moment Acting on the Ship Hull among Waves", J.S.N.A. of Japan, Vol.132,
1972.
Coda, K. and Ogawa, A.,
"Bending and Torsional Moments and Motions of a T2-SE-A]. Tanker Model in Oblique
Regular Waver", Proceeding of 2nd ISSC,
1964.
Wahab, R., "Amidships Forces and Moments on a Cb = 0.80 "Series 60" Model in Waves from Various
Directions", TNO, Report No. 100S,
1967.
Pakaishi, Y. and Yoshirio,
T., "Midship Bending and Torsional Moments of a Container Ship in Oblique Waves", Journal of the Kansai Society of Naval Architects,Japan,
.FleAi shaft
.Lth-tEt.rirg 'ci P-7-Fig. 1
Wave load detector
A'paratus
for muring
SIL
J?fflL.QLJfltiPQ....
Vn'l film
Fij. 2
Teat arrangement
L.W.L
Length (1..,,) 3.000m Metacentric radius (GM)
0.021 m
Breadth (B) 0.514 m Transverse gyradius
(KfB)
0. 3965 Draught
(d)
0. 127 m Longitudinal gyradius(K/J..,,) 0. 2373
Displacement (4) 137.27kg C. C. from midship
(zC) 0.014 m
Block coefficient (Cb) 0. 6994 C. C. below waterline (ZG) 0. 082 rn
1.0 9 0.5 Pitching amplitude 1.0 Surging amplitude
-8-L. 2.0 2.0 1Fig. 3
Ship motiona
I Swayinc amplitude
:-7'
/1
£-005
1.0 2 Rolling amplitude/
I,, .
/4
0 i5
.o 1s F,, I L1 M.
Comp -0.155 I 150' 0l20J
--I(
60' L__.* 30' I.
1.01 Yawing amplitude 0.5. At midshD
-
.9
-Fn 0.195 150° 120°. Meat. Como0
a 90° 60° A I 300 S i----0.5 1.0 1.5 . 20 aol MN s.s.3 0.5 1.0!L._
2.0p
-10-Fn19
A I 30' S Comp 0002tS7+1
'L\_
L
0001 0 L&t s.s.3 aooi S Fn 4._LLJ
-I S £---Fig. 7 Effect of torsional moment axis
t
-.
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