290 



THEORY OF SEAKEEPING 



Fig. 4 1 Typical form of measured stress on ship deck at slam- 

 ming speeds (from Ochi, 1956<?) 



On the USCGC Unimak, Greenspoii (3-195G) and Green- 

 spon, Jasper and Birmingham (3-1956) found the peak 

 pressure readings of inch vidua! gages up to 295 psi, 

 but (juote the pressure of 86 psi as the highest mean over 

 a plate at an instant of maximum strain. AUhough the 

 figure of 86 psi is of the same order of magnitude as was 

 given by Ochi and Watanabe, it is recorded here on a 

 ship of finer hues. The explanation lies in the fact that 

 this is a sturdily built small ship and apparently it was 

 operated more daringly than would be practical in a 

 cargo ship. 



Warnsinck and St. Denis stated that in most slams 

 during destroyer tests the peak liytirod.ynamic pressure 

 did not exceed 25 psi. Only about 15 per cent of slams 

 exceeded a pressure of 50 psi. During one slam a peak 

 pressure in excess of 100 psi was recorded. 



Ochi's papers (19566 and 1957) contain a number of 

 diagrams indicating the slamming forces and ship areas 

 affected at different speeds. Most slamming is shown to 

 occur at a speed slightly above the synchronous one. 

 Watanatie (1957) made an extensive theoretical analysis 

 of a ship's slamming conditions. This analysis is rather 

 difficult to follow because of the large number of ap- 

 proximations introduced in the process. Watanabe 

 demonstrated, however, a good correlation of his ap- 

 proximate theoretical results with the data on ship- 

 bottom damages. Various criteria for evaluating the 

 effect of a ship's form on slamming were introduced by 

 Iving (3-1934/35), Han.sen (1935), Lehman (1936), 

 Watanabe (1957), and Ochi. Ochi used as a criterion 

 the .section coefficient at 10 per cent of a ship's length at 

 50 per cent of the design draft. 



5.5 Relationship Between Slamming Load and Bend- 

 ing Moment. In the process of heaving and pitching in 

 \va\'cs, a ship is subjected to bending moments which 

 vary approximately harmonically with time. In such a 

 case the true bending moment is related to the moment 

 calculated statically by the factor 



r,- 



rp^, _ y,.. 



(5) 



where 7'i is the period of the wave encounter and T is 

 the natural period of vibration. With the average 

 period of the wa\'c encounter of 6 sec and the natural 

 period of the two-node ship vibration of 0.6 sec, this 

 factor is so near miity that it can be neglected. The 

 bending stress is related to the imposed loading es.sen- 



Fig. 



G 7 

 Impact Force - 



42 Comparison between computed and measured stress 

 (from Ochi, 1956a) 



tially by the rules of statics. This condition is often 

 referred to as the "quasi-static." 



Different conditions exist when a ship is subjected to a 

 local impact as in a slam. The deflection of a loaded 

 ship's part is permitted by the elasticity of the adjacent 

 structure and the impulse of the impact force is first 

 absorbed by the momentum of the masses in its immedi- 

 ate vicinity. After the impact impulse is expended, the 

 structure is left in a strained state and the interplay 

 of elastic and inertial forces produces a state of vibration. 

 Immetliately at the end of an impulse, the maximimi 

 bending moment (hogging) apparently is foiaid at the 

 point of the load application. The bending-moment 

 diagram has essentiall.v the form labelled "from theory" 

 in Fig. 42. This is a transient state of short duration 

 and there appears to be little probability that it can be 

 spotted in model experiments. Experience shows that 

 a two-node vibration is established so quickly that it is 

 the only one commented upon in sea observations. 

 There is no doubt, however, that a transient state exists 

 and could be recorded by suitable instrumentation. 

 Investigation of this transient state is important in order 

 to establish the redistribution of stresses from the maxi- 

 mum hogging at the point of slamming-load application 

 to the maximum hogging-sagging at approximately 

 amidship in the final two-node vibration. Ochi (1956a) 

 shows in Fig. 42 ("from Experiment") that the effect of 

 the slamming is to cause the maximum bending moment 

 to occur somewhat forward of the midship section. In 

 his report Ochi neglected, however, to represent the im- 

 pact stresses as functions of time and the stress distri- 

 bution labelled "from Experiment" apparently refers 

 to an undetermined instant of a transient process. 



A theoretical analysis of the response of a typical ship 

 structure to an impact load apparently has not been at- 

 tempted. A simplified analysis, treating a ship as a 

 beam of uniform section, was made by Lockwood Taylor 

 (1946), Ormondroyd, et al (1948, 1951), and Ochi (1956a, 

 1958rf and e) Papers on the response of a beam to an 

 impact also were published by Arnold (1937), Frank- 

 land (1942, 1948) and Salvadori (1947). The paper by 



