LIST OF SYMBOLS 



Outside diameter 



Initial elastic modulus 



Secant elastic modulus 



Tangent elastic modulus 



Uniaxial concrete com- 

 pressive strength 



Material strength factor 

 for cylinder structures 



Material strength factor 

 for spherical structures 



Cylinder length 



Number of lobes 



External pressure 



Implosion pressure 



Analytical implosion pres- 

 sure controlled by strain 

 criteria 



Analytical implosion pres- 

 sure controlled by stress 

 criteria 



Average radius 



Outside radius 



Average wall thickness 



Minimum wall thickness 



Radial displacement from 

 initial to deflected shape 



Bending radial displace- 

 ments 



Membrane radial displace- 

 ments 



w„ Total radial displacement 



(see Figure B-17) 



AR 



Deviation in radius 



AR. Inside deviation from 



average radius 



AR Outside deviation from 



average radius 



At . t - t . 



mm mm 



£ Ultimate strain 



u 



£, Bending strain 



e Membrane strain 



m 



n Empirical plasticity reduc- 



tion factor 



Angular coordinate (see 



Figures B-26 and B-27) 



6^ , e„ Angular coordinates of 

 failure zone 



6„ Angular coordinate of 



center of failure zone 



V Pois son's ratio 



4 Nondimensional distance 



along cylinder length 

 (see Figure B-4) 



a Wall stress 



a. Wall stress at implosion 



(a. )t5 Wall stress at implosion 

 predicted by Bresse's 

 equation (Equation 5) 



(a. )j. Wall stress at implosion 

 predicted by Donnell's 

 equation (Equation 4) 



<|) Ratio of radial displace- 



ments between end and 

 middle of cylinder 



81 



