WAVE LOADS ON A T-2 TANKER

Transcription

1 Reprinted from «EUROPEAN SHIPBUILDINGD NO, 96, VOL X 96 Norwegian Ship Model Experiment Tank Publication No 62, February 96 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 M Letveit, Chr Miirer, B Vedeler and Hj Christensen

2 At - - THE TANKER MODEL RUNNING IN WAVES OF LENGTH EQUAL TO MODEL LENGTH AT A SPEED EQUIVALENT TO 6 KNOTS SHIP SPEED 3

3 WAVE LOADS ON A T-2 TANKER MODEL 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 ), Chr Miirer 2), B; Vedeler 2) and Hj Christensen 3) 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 investigations are sponsored by Det norske Veritas and backed economically by Norges Teknisk-Naturvitenskapelige Forskningsrad, and is being carried out in co-operation with the Davidson Laboratory, Stevens Institute of Technology in the USA 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 Accordingly, Det norske Veritas proposed in 958 a research programme at the Norwegian Ship Model Experiment Tank to investigate the influence 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 Davidson 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 models with block coefficients 068, 074 and 080 (see ref []), 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 measure not only the bending moments and shearing 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 Laboratory during the preceding years (see Appendix and ref [2] and [3]) A preliminary series of tests was undertaken in 958, mainly to test the new apparatus and instruments which had to be developed 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 introduce some minor alterations and improvements to the instrumentation employed in the following 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 investigations have been conducted One series involved a variation of still water bending moment while keeping the mass moment of inertia constant, the other series covered a variation 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 measurements, is given in the present report The basic load distribution of the model (Condition I) was approximately, that of a 4

4 30 Fr LIGHT MODEL CONDITION I CONDITION -CONDITIONDI SECTION AREAS 0 cv 20 _J CC LI 5 a_ r 0 cr o5 Li LU ) 0 EP M 482 WEIGHT DISTRIBUTIONS CONSTANT MASS MOMENT OF INERTIA loaded tanker and was very similar to the distribution applied at the Davidson Laboratory tests The still water bending moment corresponding 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 Further details concerning the weight distributions are given in Appendix A The model was made to scale : 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 recording the bending moments and shearing forces at the three sections A detailed description of the instrumentation for recording bending moments and shearing forces is given in Appendix B The towing arrangement is constructed to allow the model full freedom in pitch, heave and surge and continuous records of these 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 generator which is described in ref [4] Wave height and wave profile were recorded continuously during all the tests The tests were for all three loading conditions made in regular waves having wave lengths of X = 060 L, 075 L, 00 L, 25 L, 75 L and 225 L, where L is the length between 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 /40 The speed range covered for all wave lengths was : Model speed: v = 0 65 m/sek Corresp ship speed: V = knots Froude number: FR = 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

5 pendix C is given a description of the calibration procedure of the instrumentation for measuring bending moments and shearing forces Presentation of test results The aim has been to present all the test results in a dimensionless form which is convenient 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= C M 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 calculations, 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 question As there was practically no zero drift in the instrumentation for recording bending moments 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 negative 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 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 tendency 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 = 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 conditions 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 critical damping phenomena, as shown theoretically 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 moment and shearing force measurements 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 6

6 X4:4" PITCH DOUBLE AMPLITUDE _ PITCH DOUBLE AMPLITUDE, CONDITION I CONDITION II s CONDITION II I- 7 L CDNDITION I CONOITION II CONDITION II e x )k25, )7L k 45 e, L00! )7= 2/ e 2 r----, OS FR 8 5 P SPEED BM FR "I' B SHIP SPEED,KT5! Fig 2 Results of pitching motion measurements 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 comparison 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 moment 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 lengths A = 00 L and A = 25 L, but the variations 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 increases 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 = 075 L, A = 00 L and A = 25 L curves for the maximum bending moment occurring at any section are drawn on the figures The values for the maximum bending moment for each wave length, speed and loading condition have been read off the curves 7

7 OD MIDSHIP LOADING CONDITION FORWARD AFT MAX MOMENT IN ANY SECTION )/I'06' o /2, nilierwgi - a -A ', Dm lii_ , _, = ,0-- _: "=--- -'- o- ',X, to T2, CQ il SHIP SPEED KS MIDSHIP MAX MOMENT LOADING CONDITION I --- FORWARD IN ANY AFT SECTION OM 2Y2(>6 A HOB = , 'i o A/L ,/ - o d 2 OM )Y 4, -_ 00 o _ -, - o -- rnimilimum,-mi - ' - -- IMOMWWaidli is is SHIP SPEED KM 025 FR -2" Fig 3 Results of bending moment measurements LOADING CONDITION ID MIDSHIP FORWARD AFT MAX: MOMENT IN ANY SECTION ):)63 FA =7--,- 0 c r= -a X :- -7-' -e---- -el ===- i 6 I /0 075 WOO 0004 o-,-; _-- _ -/' 0004 'd 4 " 0004 '" *I- oco3 d _ NU is " FR -2" OCT II, SHIP'SPEED (ITS , '' 2 _ 2

8 CO OM Di MI' HQ I me 000 di 000 g 00t2 g LI 0 50t2 - MIDSHIP --7 MAX: MOMENT AF 7 LOADING CONDITION II 0--- FORWARD - IN AN A /L _- - _5_,- - to -, -_ "---F7'" e A' / X ='-' $ '---::: _ FR le SHIP SPEED OM PTS LOADING CONDITION I --- FORWARD IN ANY - MIDSHIP -- MAX MOMENT SE C79/2 ei X Ak 25 ' di- NO :----" '" OHIO _ YL 75 g , _ A/L = ,- =-- r f _ '! t 6 30 IT IS,_ 030 ER - S0P SPEED TS Fig 4: Results of bending moment measurements - MIDSNIP -- MAX MOMENT LOADING CONDITION IS --- FORWARD IN ANY AFT SECTION A/ L 25 _---, woe er 0- -cr" 0-0 OM It -or cr" _04-4t,!,_ ----e e AY *- --;- FR- ID 4 SFDP SPPED ET& "

9 ooi Ix* LOADING CONDITION I MIDSHIP o-- FORWARD -- AFT Am040 ii!i"i ----, ' --:7- -,-_=,0 000 MN: /' , "":::_ --, OM FR la SHIP SPEED NTS LOADING CONDITION I ii 040 -la lill''"=ii 00 - Mil - 0W- ---_ o ' MIMI Mill -- --, FR IS 8 SHIP SPEED ITS Fig 5 Results of shearing force measurements cf 00 LOADING CONDITION In hic060 IPMII Mal _, HS is SHIP SPEED MTS,, ' I I

10 005 ", LP ooa LOADING CONDITION 0 MIDSHIP Il l: ' FORWARD MEM= - - AFT i!ij mpli -- -=-:-- ao LP TiT ==ete!= L,-- 00 Lis - - iminiiiiidil - MINIE"'-- ilill/ MEEEBEEMM= -4- IgnimmiMplall Di 6 g SHIP SPEED KM !LOADING CONDITION,I 000, miriship Ak-25' FORWARD,,,- -o, ' -- AFT, fe -!04 --Y ), ' :74'; ''' - --_,, )2? ::-4-:= )YL, oo i/ C6 ' di ,I6 - SHIP-SPEED SOS Fig 6 Results of shearing force measurements LOADING CONDITION DI MIDSHIP 0, FORWARD i--7 AFT )i I-25 GO2,-- 0, 00 -ON 005 'YLa /5 004 o = SIN 'YL = GAO F o-3 a 4 i SHIP SPEED 605, - I6, ; - 2

11 SHIP SPEED 0 KNOTS SHIP SPEED = 0 KNOTS CONDITION I CONDITION II III ---CONDITION CONDITION I II -CONDITION III CONDITION, , , FORWARD FORWARD 042 IIIPIMats_ 7:------"' , ,sl -_--_ M IDS HI P x 60/ 2 - M ID SHI P 000, DON / 44 _ , PgglTlgil- MBIIL,- 004 IIIIIIiIllj r AFT 0003 AFT / tfo op o o _ XiL 2? 5 ) I/7/4 25 I io 0)75 0 Fig 7 Variation of bending moment with wave length at constant speeds shown in Figs 2 4 and similar curves The measured shearing forces are, as expected, 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 = 00 L and A = 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 function 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 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 infinitely 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 influence 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 25 L and then fall off with further increase in wave length Correspondingly, the maximum moments aft and amidships at 0 knots are found at a wave length between 09 L and 25 L for all three loading conditions, although the magnitudes are not the same At the forward section, however, Condition III is 2

12 ' i SHIP WEE SPEED 8 KNOTS - I o CONDITION ----CONDITION! ul ---CONDITION III 4 El "C, 602- CONDITION I - CONDITION! --CONDITION III woe , _ SHIP SPEED 4 KNOTS iiiiiiimp mill FORWARD highest values of bending moments for hogging as well as sagging were in most cases reached in Waves of between 00 L and 25 L in length The variation of shearing force with wave length is plotted in Figs 9 and 0 The shearing force Show little variation with wave length at zero speed for any loading condition over the normal range of wave lengths At 0 knots' speed we find a Maximum value in shear at = 00 L for Condition I for all sections The two other conditions have maximum values at wave lengths between 00 L and 25 L for the section aft Condition II shows maximum valties at about 00 L for the niidship section, the forward section, however, displaying a general decrease with increasing, wave length Condition III has its maximum value in wave lengths between 00 L and 25 L at the forward section, showing a general decrease with increas d o x MIA Ira "" ZA \ \ \ ', _ xi "'",-----_--- "--"---- -", L/A , MIDSHIP --`-'-' =-- " AFT Or Fig 8 Variation of bending moment with wave length at constarrt speeds g S 4_ r aill arliṁ M a ----MEE ill SO All 2p 7, _I?! -P AFT I completely different from the other two, having its maximum values already at a wave length of 075 L and a minimum hogging at A =-- 00 L At 4 knots the situation forward and aft is more or less the same as for 0 knots Amidships the moments for Condition II are fairly constant for wave lengths shorter than 30 L with a maximum around A = 075 L At 8 lmots' ship speed the maximum moments at the aft section are found to be around A = 25 L for all conditions Conditions I and III have maximum moments at the midship section at = 25 L as well, Condition II, however, shows a decrease with increasing wave length above A = 075 L At the forward section, Conditions I and II have maximum values at = 25 L whilst Condition III has its maximum at about A = 090 L As a main conclusion we may say that the 3

13 SHIP SPEED 0 SHIP SPEED = 0 KNOTS CONDITION CONDITION -- CONDITION U ' CONDITION CONDITION 0 -- CONDITION 0 04 j0!"- ---:;::::"' - _-- _, -- -,- - i --: FORWARD FORWARD , -Olt ' MIDSHIP MIDSHIP : _::, --,-:::,_= :""------" , s,7, Ak AFT I- LA Fig 9 Variation of shearing force with wave length at constant speeds l'o -25 AF ing wave length at the midship section At the speeds of 4 and 8 knots the curves also indicate that generally the maximum values of the shearing forces are reached in waves of lengths between 00 L and 25 L, although Condition II has maximum values in waves of A = 075 L in the forward section at the same speeds Variation of bending moment with time In Fig, curves are given for the instantaneous 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 = 00 L and the longitudinal distribution of the bending moment for the three loading conditions is compared at ship speeds of 0 knots and 4 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 ohtaed and these very closely determined the run of the curves for the instantaneous longitudinal 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 4 knots, however, the influence of differences In the longitudinal 4

14 of p-os di -D B CONDITION I _,-- CONDITION CONDITION I I SHIP SPEED4KNOTS ---- : " FORWARD c SHIP SPEED 8 KNOTS 'CONDITION I coicitriori t miim -- condificin I raiminimimin I INNEi% MI B SI '' '`' " 'MIDSHIP EI -4, ' -004 EMIA-R=6M' s MEI -006 MIDSHIP -004_kiiUW IlliffialliallirMMI, Fig 0 Variation of shearing force with wave length at constant speeds -DOB 0/ "---?/ 2r ir 025 AFT 0 25 F50 li, _44 or lb ,0 075 AFT 4/A -- 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 amidships 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 longitudinal distribution of wave-bending moment for the three loading conditions must therefore be due to differences in the longitudinal distribution of the inertia forces only Thus, Fig clearly indicates the importance' the acceleration 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 moments for the three conditions is plotted in Figs 2, 3 and 4, for wave lengths A = 075 L, 00 L and 25 L respectively Curves are given for four different speeds' The CM values amidships and at the guarterlengths are obtained from the curves in Figs 3 and 4 The slopes of the curves in Figs 2-4 at the three measuring stations are 5

15 -00 t0 ""c P WAVELENGTH A 2 Lpp SHIP SPEED 0,KNOTS F P 7/8,Te AF, CONDITION I CONDITION CONDITION WAVELENGTH A= LPP SHIP SPEED 4 KNOTS Fig Instantaneous longitudinal distributions of bending moment during one period of encounter 'H 00 X

16 F 0 00 Ln _ 2/L = -75 CONDITION I CONDITION 2 M AF' I Fig 2 Longitudinal distribution of maximum bending moment at constant speeds 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 moments do not occur simultaneously at all sections, the curves shown in Figs 2-4 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 2-4 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 moment): For the Srnallest wave length (A/L 075) there are fairly small differences between the loading conditions, though some difference is evident at 0 knots For wave lengths A = 00 L and L25 4, Figs 3 and 4 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 different loading conditions are directly proportional to the acceleration at each section in question, we should expect that at low frequencies 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 = 075 L there is a reduction of pitching at increasing speed above about 8 knots' ship speed, and from Fig 2 we find that the curves for the three loading conditions become more similar at increasing speed above 0 knots for this wave length For A = 00 L we find that there is a small reduction in pitch amplitude from 4 knots to 8 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 3 we find about the same differences between the curves for the three loading conditions at 4 knots and at 8 knots For A = 25 L there is a general increase in the pitching amplitude with increase in speed up to the highest speeds covered In Fig 4 we find increasing differences in the curves for the three loading conditions at increasing speed up to 8 knots 2 The difference between the loading,conditons stated under Point is characterized by -7

17 05: CONDITION I CONDITION CONDITION ICE Fig 3 Longitudinal distribution of maximum bending moment at constant speeds CONDITION CONDITION I -005: -00- Fig 4 Longitudinal distribution of maximum bending moment at constant speeds 8

18 -, al- i a quite different trend in the shift of position of maximum bending moments In Fig 5 this position of maximum moments has been plotted as a function of speed for three wave lengths A = 075 L,A = 00 L and A = 25 L The letter x is the distance from amidships to the section where the maximum bending moment occurs and separate curves are given of x/l for sagging and hogging As will be seen, the shorter wave length (A = 075 L) shows only a small shift forward for Conditions I and II up to about 0 knots (FR = 03) With further increase in speed the maximum point moves back towards the midship position For Condition III the maximum moment occurs amidships almost independently of speed At the other two wave lengths (A = 00 L and A = 25 L) the position of maximum moment shows a large shift forward for Condition II and a smaller one for Condition I, for both conditions in the speed range 4 to 0 knots (FR = ) at AIL = 00 and in the range 9 to 6 knots (FR -= 02 02) at AIL = 25 For Condition III the maximum point Is fairly constant a little aft of amidships for the practical speed range up to 6 knots, but Shows tendencies to shift forwards at higher speed also for this condition An exception may be the sagging moment at A = 25 L, but it is impossible to draw any definite conclusion because of the upper speed limit of the tests From Figs 2, 3, 4 and 5 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 moment is rather smaller for the hogging moments Special attention is paid to the opposite trend of the maximum moment curves of Conditions II and III with increasing speed at A/L = 00 and 25 Condition II shows the forming 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 2 4, 03 - CONDITION I _ CONDITION II I ---CONDITION III SAGGING 0, WI 3, - ct LA: 0 c , - HOGGING 0 g 02 o SAGGING CONDITION CCiNDITIDti -----CONDITION ;csdi- : x ---r HOGGING CONDITION g -----CONDITION ct PI 2 0 / - In _ - SAGGING ' Fig 5 Position of maximum bending moment x -- distance from rnidship section model (Condition III) are largest for the hogging wave moments Comparing these trends of the wave bending moment curves with the weight curves of Fig 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 - I I speeds above 4 knots (FR 08) and wave lengths A =- 00 L and 25 L- The peak moments in hogging are smaller and situated nearer the midship section --_ k075 I II III - 0 ID III III I,, 0-5 0;20-0 / / /-- -J I -- " "--- DOD ' r_ FR --- L A/c i FR I I ] HOGGING! A/L 2 5 I 9

19 C) - _ V- 0 KNOTS CONDITION --- CONDITION CONDITION Ill V-0 KNOTS FP AP Fig 6 Longitudinal distribution of maximum shearing force at constant speeds b) Concentration of weights in the vicinity of the midship section (Condition III) results in large hogging moments in the same vicinity at speeds above 0 knots for A= 00 L and at all speeds for A = 25 L The sagging moments show the same trend, although the peak values are somewhat smaller The test results show that there is clearly some relationship between the weight distribution and the distribution 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 variation 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 moments 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 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 -= 075 L, A= 00 L and A-= 25 L and four different speeds are shown in Figs 6 8 These curves are the counterparts to the curves for maximum bending moments at the different sections shown in Figs 2-4 The run of the maximum bending moment curves is determined by the end conditions, the recorded bending moments at three sections and the slope of the curves at those sections, thus being fixed within close limits The curves for maximum shearing force, however, are determined by the end conditions and the recorded t hearing forces at three sections only, thus leaving 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 6l8 show that the largest shearing forces occur in the vicinity of the quarterlengths For A = 00 L and = 25L and at the higher speeds, however, loading Condition II is an exception as the largest 20

20 006, _ AP _ CONDITION I --- CONDITION CONDITION M Fig 7 Longitudinal distribution of maximum shearing- force at constant speeds AP V- 0 KNOTS CONDITION I -- CONDITION II -- CONDITION III /L= P AP -004 V-0 KNOTS V-8 KNOTS :r -006 Fig 8 Longitudinal distribution of maximum shearing force at constant speeds shearing forces are in some cases found quite near amidships When comparing Figs 2-4 with Figs 6 8 it may be noted that in cases where the curves - for maximum bending moments run - smoothly and show one maximum value, the curves for maximum shearing forces show two pronounced maxima In cases where- a tendendy towards two maxima in the bending mo, ment curves are found, however, only one 2

21 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 construction 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 Veritas employ the following expression for both the sagging and hogging wave bending moment (ref [6], eq (22) ): ME = L 2B (C + 08) h or in dimensionless form: MB -2 Cm = 2 = 09 0 (CE + 08) 7 L B h For a T-2 tanker with C B= 074 we thus have: Cm --= 0039 Comparing this Civi value with the observed test results of Figs 3 and 4 we find that it is exceeded only in one case, namely by a hogging moment in loading Condition III at AIL = 25 and ship speed 8 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 = (CE + 08) y LBh or in dimensionless form: QB Co = (CB + 08) 7 LB h For the T-2 tanker we have CQ = Comparing this CQ value with the observed test results of Figs 7 and 8 we find that it is exceeded in loading Conditions I and III for A/L = 00 at speeds above 0 knots and for AIL = 25 at 8 knots In Condition II the shearing force exceeds the rule value in the midship range at 8 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 waveinduced 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 obviously be found as a result of the present and future work of the oceanographers Conclusions This experimental study represents an extension of earlier model tests in regular waves: to cover the longitudinal distribution of waveinduced 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 bending moments and shearing forces occur simultaneously with heavy pitching and heaving of the model and are recorded at wave lengths A = 00 L and A = 25 L The instantaneous longitudinal bending moment distribution and the distribution of maximum bending moments and shearing forces are greatly influenced by wave length, speed and weight distribution The observed large differences in bending 22

22 moment and shearing force magnitude and distributionfor 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-induced 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 variations in the longitudinal distribution of loads The weight distribution is very important nd the bending moment is found to be sensitive to any small changes in weight distribution because of the mass-acceleration effects 4 The longitudinal location of the maximum bending moment and shearing force is dependent on wave length, speed and weight distribution In the cases where the highest bending moments are recorded the maximum bending 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 = 25 L and FR = 029) the maximum sagging bending moment was more than three times the midship sagging wave bending moment Consequent on the above-mentioned conclusions it is recommended that further investigation to determine the magnitude of wave bending moments and shearing forces should be planned and carried out in such a way that their longitudinal distribution can be determined 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 Dalzell, J F: «Effect of Speed and Fullness on Hull Bending Moments in Waves)), DL Report 707, Febr 959 Lewis, E V: «Ship Model Tests to Determine Bending Moments in Waves» Trans SNAME 62 (954), pp Lewis, E V, and Dalzell, J F: «Motion, Bending Moment and Shear Measurements on a Destroyer Model in Waves", DL Report 656, Apr 958 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 958 (Publication No 53 of the Norwegian Ship Model Experiment Tank, Trondheim) Havelock, T IL The Effect of Speed of Advance REFERENCES LIST OF SYMBOLS upon the Damping of Heave and Pitch, Trans INA 00 (958), pp 3-35 Abraharnsen, E, and Vedeler, G: The Strength of Large Tankers», Det norske Veritas, Publication No 6, March 958 (Also European Shipbuilding, No 6, 957 and No, 958) Jacobs, W F: The Analytical Calculation of Ship Bending Moments in Regular Waves Journ of Ship Research 2 (958) No, pp Lockwood Taylor, J: «Vibration of Ships», Trans INA 72 (930) p 73 Kjaer, V A: a Vertical Vibrations in Cargo and Passenger Ships, Acta Polytechnica Scandirravica, Mech Eng Ser No 2, 958 Christensen, Hj and Funder, J E: «Pressure Gauge for Ship-Model Huils>, Electronics, Jan 955, pp 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/7,Bh shearing force coefficient length between perpendulars draught Liwl length of load Waterline depth wave bending moment, 23

23 Te = A/(v+c) V VC, VP, Vm and VQ jag moment (positiv forward) specific gravity of water displacement wave length pitch amplitude (single) (in radians) APPENDIX A The mode/ The model M 482 is a wooden model of a T-2- SE-Al tanker and the model scale is :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 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 dynamometers (See Fig 22 and Fig 24) At the joints there are gaps of about 30 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 20 mm in between the wooden parts of the model Thus the rubber sealing yields practically no resistance 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 9 The four parts of the model can be regarded as completely 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 dynamometer windings distance from amidships of position of maximum bendjoints 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 amidships Thus, with the same thickness the stiffness of the end joints is 80 per cent of the stiffness at the joint amidships The stiffness 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 frequency of two-node vibration of the ship In Condition I the natural frequency of the two-node vertical vibration of the model was 829 cycles/second which corresponds to 703 cycles/minute for the ship By forced excitation of vertical vibrations in the model and by gradually 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 :25 No accurate registration of the natural frequency of fournode 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 4 Fig 9 The four parts of the model before joining them together 24

24 Fig 20 The body plan and bow and stern contours for M 482 were carried out and the vibrations were recorded 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 decrement was 0004, 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 vibrations 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 3066 in Length of waterline Liwi 328 m Breadth moulded B 045 in Depth D 0239 m Draught loaded d 083 m Displacement in fresh water 725 kg Wetted surface S 900m2 Block coefficient CB 074 Centre of buoyancy forward of L/2 03% 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 longitudinal 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, 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 (Condition II and Condition III) may be characterized as extreme The intermediate weight distribution '(Cohdition I) may be characterized as a «normal» weight distribution This weight distribution is very similar to the one used by Lewis and others ([] 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 distributions for the three conditions are shown in Fig, 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 02 L aft of L/2 and 0875 d above the base line The neutral axis of the beams connecting the four parts of the model are situated 050 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

25 TABLE II APPENDIX B Loading Conditions I H III RaditiS of gyration of the model (per cent of L) Weights in per cent Afterbody Forebody Part () Part (2) Part (3) Part (4) Distances of centre of gravity from L/2 in per cent of L Afterbody Forebody Part () Part (2) Part (3) Part (4) Instrumentation During the test runs 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 towing force were measured In addition, a number of photographs, usually 3-5 for each test run, were taken The photography was electri- cally synchronized with the dynamic quantities recording The block diagram in Fig 2 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 determined 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-3) 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 inductive pick-ups, forms the bending moment and the shearing force dynamometer The principle 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 [0] 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 windings and the compensating windings are subdi- Bending moments 8 shearing forces Fore Midship Alt Pc2 let5 0 p Pc6 0 Picture number \/ ban Dor n recorder - channel Sanborn 2-channel recorder Kelvin P Hughes h- charnel recorder Sanborn - channel recorder Brush 2-channel recorder Timinti mark Fig 2 The instrumentation block diagram 26

26 ! Inductive pick-up (section) az Ktv A:\ k I 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 subdivision 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 supplied with AC voltage (7 volts,,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 P against the voltage Vc over the winding C and so on for other pairs of C and P windings 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 positive direction in this connection we may specify 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 _2Bending rnorrtent 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 AVp2 Vm = Km M as an output on the + terminal, which is proportional to the bending moment M At the same time we get an output: AVp' = VQ' AVpi at the terminal For full mechanical and electrical symmetry of the dynamometer we have: AVp = AVp' / and thus VQ' = 0 Next, we remove the bending moment + M and load the dynamometer with a pure positive shearing force '+ Q (as a positive shearing 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 righthand side) This loading will be followed by changes in the induced voltages in the P windings so as to give: AVE, ( AVp' AVp AVp' VQ = KQ Q as an output at the terminal, which is proportional 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 displayed a certain amount of qcross-talko, ie the quantities VQ' and Vm' were not zero 27

27 6 2,4pF 2,6pF 0""*-7PJZ E 2,6 pf Fig 24 Bending moment and shearing force dynamometer This cross-talk from the M channel to the Q channel and vice versa was investigated experimentally by subjecting the dynamometer to pure bending moments and pure shearing forces in a manner described in Appendix C It then turned out, since the shearing deflections were small compared with the bending deflections 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 phasesensitive, the necessary reference voltage being the one supplied to the driving coils The amplifier showed good zero and gain stability 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 frequencies of encounter the two-node vertical vibrations of the hull were considerably excited 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 arrangement 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 n V Vp Col 6S L7 6H6 6SN7 5K 40 6V6 6V6 K K Fig 25 The Q-channel amplifier diagram Recorder coils -05 V --o 28

28 ;, ', _i I 0 a 20 0, - ; _[ 6,!-- I I - i I! ji I J a 4 i J i - --i - -, j_ --- IT F army Response Low Pass nib- 9 TO 2 Fig 27 The frequency response of the low-pass filter _I H ' I _i_ I for 8,25 cts _I MENI -IT _ -I -- The calibration of the instrumentation for measuring bending moments and shearing forces The total bending moments and shearing forces 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 involved in calculating the still water bending moments and shearing forces, there is no need for any experimental determination of the magnitude 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 referto-of t filtered and partly unfiltered, as the latter conditions were thought to be of interest in themselves Fig 27 shows the filter frequency response (average of six), experimentally determined With nominal attention peak at 825 c/s the filter gives an attenuation of the hull/dynamometer system recorded oscillations by a factor of about 0 (without noticeably influencing the bending moment or the shearing force time functions) The highest frequency of encounter for the model was 8 c/s and in the cases where the highest values of bending moments and shearing forces were recorded the frequency of encounter was about 0 c/s, and in this frequency range it was found unnecessary to apply any frequency-dependent correction of the bending moment and shearing force recordings due to the filter (see Fig 27) The filters and amplifiers, with some associated equipment, are shown in Fig 28 APPENDIX C 4ftn00i 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» condition 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 shearing 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 disadvantage 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 29

29 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 completely 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 introduced and the axial force introduced between the rods does not influence the recording of bending moments and shearing 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 originally 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 calibration was thus obtained both for the instrumentation for measuring bending moments and the instrumentation for measuring shearing forces There was always good agreement between the two types of calibration of the bending moment instrumentation, and the recording of bending moments proved to be completely independent of the magnitude of shearing forces within the actual range of Fig 30 The introduction of pure shearing force shearing forces When pure bending moments were introduced, apparent shearing forces of small magnitude 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 recording are shown in Fig 3 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 recording, all the calibration curves remained constant during all the tests reported The correction 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 builtin electrical calibration signals These electrical check-points were used continuously between the test runs to check the electrical instrumentation and to check that the gain remained unchanged 30

30 PURE SHEARING FORCE COM BINED SHEAR AND BENDING (CORRECTED) E 2 PURE BENDING 00 COMBINED BENDING cc AND SHEAR cc 8 cc 6 0 w cc 4 SHEARING FORCE kg BENDING MOMENT kgm SAGGING SHEARING FORCE kg HOGGING BENDING MOMENT kgm 3 g FORE JOINT UI CALIBRATION ce cc UI 5 g ; 6 CE cci, 0 2 IC`jc FORE JOINT CALIBRATION 22 6: Fig 3 Typical calibration curves for shearing force and bending moment recording