where St = meridional membrane stress (psi) 



5 2 = equatorial membrane stress (psi) 



5 3 = radial wall stress (psi) 



p = external hydrostatic pressure (psi) 



R = external radius of sphere (in.) 



Rj = internal radius of sphere (in.) 



r = radius to point where stress is to be found (in.) 



Solving Equations 5 and 6 for S, and S 3 when p = 450 psi ( 1 , 000-foot 

 operational depth), the following stress values were determined for internal 

 and external shell surfaces: 



at R St = S 2 = -3,330 psi and S 3 = -450 psi 



at Rj St = S 2 = 3,550 psi and S 3 = 



From consideration of the calculated stresses, it appeared that the selection 

 of the t/R = 0.685 wall thickness for the sphere on the basis of the elasto- 

 plastic instability Equation 4 is probably satisfactory from the stress 

 magnitude viewpoint also, as the general stress level in acrylic plastic at 

 the operational depth of 1 ,000 feet appears to be less than 4,000 psi. If 

 the stress magnitude level turned out subsequently to be too high because 

 of the local stress raiser effect of metal plates in the polar penetrations, the 

 reduction in operational depth from 1,000 to 600 feet (minimum continental 

 shelf depth requirement) would probably lower the overall stress level suffi- 

 ciently to bring the peak stress at the hatch penetration below ultimate failure 

 stress level for acrylic plastic. 



Selection of the hatch plate thickness presented a more complicated 

 problem than the selection of acrylic plastic hull thickness. From the view- 

 point of stresses in the hatch plate, it was desirable to make the plates as 

 thick as possible, while from the viewpoint of stresses in the acrylic plastic 

 bearing surface, it was mandatory to keep the thickness to the absolute 

 minimum so that the mismatch in wall rigidity was minimized. Since 

 neither the effect of hatch plate thickness on the stress concentration in 

 acrylic plastic, nor the effect of acrylic plastic hull on the magnitude of 

 stresses in the metallic hatch was known for sustained loading during a 

 typical dive, either one of the viewpoints taken would result in an unknown 

 quantity. Ultimately the viewpoint was taken that minimization of stress 

 raiser effect in acrylic plastic was more important than minimizing the stress 



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