P^b = critical buckling pressure, psi 



Pj,y = critical yielding pressure, psi 



Ri_o = local outside radius of a spherical shell, in. 



a = yield stress, psi 



The equations governing the collapse of cylinder shells are considerably 

 more complex than for spheres. A method developed by General Dynamics* 

 was used to analyze the collapse by yielding of a cylinder and hemispherical 

 cylinder heads. This method calculates outer fiber, midfiber, and inner fiber 

 stresses at frames and midbay as well as deflections and local stresses. 



Computations were made for two types of collapse of a cylinder by 

 buckling. Lobar buckling was approximated by 



2.42 E 



(1 - m") ^ 



Pk = 



Buckling by instability was approximated by 



,4 



Pk = 



Eh 

 a 



W 



1 + 



where P^, 



= lobar buckling, psi 



E 



= modulus of elasticity 



h 



= shell thickness, in. 



a 



= nominal outside shell radius, in. 



M 



= Poisson's ratio 



n 



= number of lobes 



m 



= a/L 



L 



= effective length of cylinder, in. 



1 



= moment of inertia of shell frame 



R 



= radius of frame-shell section, in. 



General Dynamics, Electrical Boat Division. "Circular Cylindrical Shell with Bulkheads 

 and Intermediate Stiffeners Subjected to Hydrostatic Pressure." 



22 



