APPENDIX A 

 NUMERICAL EXAMPLE 



A numerical example is provided to illustrate the use of the curves presented herein. 

 A typical case has been chosen in which the dimensions could be those of a submarine pres- 

 sure hull with external frames. The pertinent scantlings are: 



R = 96 in. Af = 9.63 in.^ 



h = 0.768 in. 

 L( = 30 in. 



If = 80.48 in."* 



= 4.49 in. 



Lj = 384 in. 



The cylinder has 13 frames with one short bay at each end. First the value of the ef- 

 fective length Lg is found to be 13.48 in. Then 



—i- is 6.85 X 10-^ 



L.R^ 



and 



U-- (100 h/R - li-± is 4.26 



From Figure 3, p^^ is found to be approximately 1500 psi corresponding to the mode n =- 3, 

 Using the ratio L^^/R = 4 in Figure 1, p^ • R/lOOh is 150 psi. This is multiplied by 0.80, the 

 value of 100 h/R, to give p^ = 120 psi. From Figure 2, the value p, for n = 3 is 1370 psi. 

 Adding these two pressures, p is found to be 1490 psi as compared with 1500 psi found di- 

 rectly from Figure 3. 



Table 2 compares the values of p^^ for this example as determined by Kendrick Part I, 

 Kendrick Part III, Bryant, and this graphical method. While the pressure obtained from the 

 graphs agrees closely with Kendrick Part III, it is interesting to note that both the Kendrick 

 Part I and Bryant values are considerably higher and predict a different number of lobes. 



TABLE 2 

 Example of Results Given by Various Methods 





Bryant 



Kendrick 

 Parti 



Graphical 

 Method 



Kendrick 

 Part ill 



Per 



(psi) 



2045 



1855 



1490 



1409 



TV 



2 



2 



3 



3 



