CHAPTER 5 



Loads Acting on a Ship and 

 the Elastic Response of a Ship 



1 Introduction 



A most important factor in the design of a ship's 

 structure is the bending moment acting on the midship 

 section. In the design process, this is obtained by 

 drawing a curve of load distribution along the length of a 

 ship and integrating it twice. The details of this pro- 

 cedure can be found in a number of existing textbooks 

 and will not be discussed further in this monograph. 

 Bending moments also have been measured by means of 

 suitable dispositions of strain gages on models in towing 

 tanks and on ships at sea. Results of such measure- 

 ments indicate a wide range of possible stresses which 

 depend on a wave size and form, properties of a ship's 

 sections and a ship's form, speed, and weight distribu- 

 tion. These data can be systematized and better under- 

 stood if considered in the light of a suitable theory. 

 Therefore, a theory of bending moments acting on a 

 ship will, be presented first and will be followed by 

 model-test and sea-observation data. A complete 

 separation of these three domains of activity is, however, 

 not practical and frequent cross references will be made. 



1.1 Conventional Static Method of Bending Moment 

 Calculation. The method of evaluation of the load- 

 distribution curve, which is in general use at present, 

 was introduced by Reed (1872). It consists of placing 

 a ship on an imaginary wave equal in length to the ship's 

 length and V20 of this length in height. The wave is 

 imagined as stationary and all effects of orbital water 

 velocities and of wave celerity are neglected. A ship 

 poised on such a wave is also considered as stationary. 

 In fact, the entire complex system of a moving ship 

 among moving waves is replaced by a static model. 

 The loading curve is then calculated considering the 

 difference between the weight and buoyancy at each 

 section of a ship. Two critical conditions are evaluated. 

 These are known as "hogging" and "sagging." In the 

 first, the wave crest is located at the midship section 

 and the resultant bending moment causes tensile stresses 

 in the deck structure and compressive stresses in a ship's 

 bottom structure. In the second condition, the wave 

 trough is placed at the midship section so that the deck 

 is under compression and the bottom is in tension. 



The inadequacy of the foregoing static model to rep- 

 resent true ship stresses is subsequently compensated 



by supplementary empirical rules. If the computed 

 bending moment were a true moment, it would be suffi- 

 cient to equate it to the product of the section modulus 

 and the allowable strength of the material used. In- 

 stead, the choice of the section modulus is based on 

 various supplementary rules which have been developed 

 empirically by classification societies and various govern- 

 ment agencies. 



1.2 Attempts at Improvement of the Static Method. 

 Several attempts were made to supplement the fic- 

 titious static-wave method by introducing certain con- 

 cepts based on the true laws of nature. The most 

 important of these was due to W. E. Smith (3-1883). * 

 Smith called attention to the fact that orbital velocities 

 of water in waves modify the hydrostatic-pressure gradi- 

 ent. As a result of accelerations of water particle^, the 

 water appears to be lighter than normal at wave crests 

 and heavier than normal at wave troughs. When these 

 properties are taken into account in otherwise conven- 

 tional computations, a decrease of the bending moment 

 is found to occur. Conversely, neglect of the "Smith 

 effect" will result in overestimation of the bending 

 moment. 



Smith calculated the relative values for three sample 

 ships as shown in Table 1. 



The modification of the pressure gradient with depth 

 (the Smith correction) follows an exponential law^ 



Table 1 Range of Stress From Maximum Hogging to 

 Maximum Sagging Calculated on the Basis of: 



Buoyancy Buoyancy simply 



with Smith's proportioned to 



correction, volume displaced, 



per cent per cent 



Ship 1 100 170 



Ship 2 100 165 



Ship 3 100 155 



and depends on a ship's draft and section coefficients. 

 Use of this correction has become a universal practice 



' An Arabic number preceding the .year indicates the chapter at 

 the end of which the complete reference will be found. References 

 without such preceding numbers will be found in the Bibliography 

 at the end of this chapter. 



'^ See Table 1 of Appendix A. 



256 



