LOADS ACTING ON A SHIP AND THE ELASTIC RESPONSE OF A SHIP 



301 



Mormacpenn on the eastward ciosisiii}>; of the fourth 

 voyage. This inchided February 8, 195G, on which the 

 second largest numbers of counts in the ranges 8-12,000 

 and 12-1(1,000 psi were recorded. Numerous observa- 

 tions chu'ing this crossing indicated that the ship had an 

 abnormally short rolling period. As the result of this, 

 it rolled violently with the amplitude of ±25 deg in head 

 seas at the time of maximum pitching. Since the strain 

 gage was installed on the port side only, it is possible 

 that high fretiuency of stress in. the foregoing ranges 

 resulted from the addition of the vertical and lateral 

 bending moments. Attention should be called to the 

 fact that terms vertical and lateral refer to ship co- 

 ordinates. A large lateral component may occur simul- 

 taneously with the vertical one when the ship's bow 

 plunges into a wave while the ship is at a large roll angle. 

 In the literature on ship stresses (for instance, SS 

 Ocean Vulcan) the impression is given that the addition 

 of the lateral moment is .seldom important. With ships 

 of reasonably long rolling period, significant rolling does 

 not occur in head or bow seas. With an abnormally short 

 rolling period, however, a severe rolling in head seas 

 may occur. In such a case there is a great probability 

 of the signihcant effect of the lateral moment. This 

 indicates that the information on rolling should be in- 

 cluded with other data describing ship conditions during 

 stress measurements. 



7 Statistical Data on Ship Bending Moments — 

 Unrelated to Sea Conditions 



Jasper (o-iySli) presented a large collection of statisti- 

 cal data on Ijending stresses measured on several ships. 

 These data were obtained from unmanned stress gages 

 and stress-cycle counters, and the ambient weather 

 conditions were not recorded. The nature of the data 

 permits, therefore, studies to be made of various statisti- 

 cal laws to which stress distributions are subjected. 

 It also indicates the stress levels which can be expected 

 on ships at sea. However, the relationship of these stress 

 levels to the conditions which caused them is not de- 

 terminable. 



Since the statistical stress-distribution laws were in- 

 vestigated separately on several ships, it would appear 

 to be possible to determine the effect of a ship form and 

 loading on stresses. However, the analysis of the rela- 

 tionshij) between the ship form and stre.ss le\'el was not 

 included in Jasper's paper. 



Additional data on Jasper's paper will be found in 

 Section 3-5.2. This section includes two quotations 

 defining the utility of the statistical information which 

 was collected and de\-elopecl by Jasper. 



7.1 Maximum Bending Moment Expected at Sea. 

 In his paper, Jasper (3-1956) included the discussion of 

 the maximum bending moment expected at sea. This is 

 based on the extrapolation of the freriuency distribution 

 of observed data using strictly statistical methods. 

 The author does not believe that this approach can be 

 fruitful. This opinion is based on the following: 



1 In a random distribution of mea.sured stres.ses, any 

 arbitrarily large stress can be indicated provided suffi- 

 ciently low probability of occurrence is specified. 



2 The extrapolation is based on the observational 

 data in which a very small numljer of occurrences of a 

 high stress is found. ^^ The starting point for the extrap- 

 olation is therefore uncertain. 



3 A statistical extrapolation necessarily assumes an 

 unchanged en\ironment. Howe\-er, the physical con- 

 ditions of a ship among waves change with excessi\e in- 

 crea.se of sea severity. The nonlinearities, which nor- 

 mally may not be important, grow in importance in waves 

 of extreme steepne.ss. 



It is the author's opinion that the evaluation of ex- 

 treme stresses shoukl be based on the consideration of 

 the physical conditions of ship operation. It has been 

 shown by calculations and by model tests that maximum 

 bending stresses are caused by waves of the length in the 

 range of 0.75 to 1.25 of a ship's length. Within this 

 length range, the stresses increase with wave steepness; 

 i.e., with the ratio of the wave height to wave length. 

 The wave steepness, however, cannot increase without 

 limits. In regular wa\'es the limiting steepness is V?. 

 Statistical methods, used in describing an irregular sea, 

 do not permit at pre.sent prediction of the steepness to be 

 expected in wa\'es of a specified length. The research 

 in formulating the necessary mathematical methods for 

 this purpose is recommended. 



Sea ob.servations on wave steepness as a function of 

 wave length had been made and were described in Chap- 

 ter 3.^' Relatively mild steepnesses were ob.served. 

 The extrapolation of these empirical observations to the 

 extreme conditions is, however, extremely uncertain. 

 Therefore, a theoretical research, mentioned previously, 

 is recommended. 



Ship stresses do not increase in proportion to wave 

 steepness. As the wa\'e steepness increases, the action 

 of the relieving dynamic effects rapidly increa.ses. An 

 effective limit to the maximum stress can therefore be 

 expected. 



It may be of interest to imagine a case of a small ship 

 carried on a crest of a regular wa\-e of the extreme V? 

 steepness. In appearance, the ship is in the hogging 

 condition as it is supported by the sharp crest of the wave. 

 In reality, the dynamic acceleration effects are such 

 that the ship and the water are essentially weightless, 

 being in the condition of a free falling body. The bend- 

 ing stresses are nil in this extreme condition. 



Theoretical and experimental model research are 

 recommended in order to evaluate the extreme bending 

 moment conditions on physical grounds. 



8 Concluding Remarks and General Research Suggestions 



Chapter 5 of the present monograph is concerned with 

 the methods of evaluating the loads on the basis of which 



™ This for instance is illustrated by Tables 12 and 1.3. 

 " See Figs. 3-37, 38 and 44. 



