and B-8), fracture of concrete was assumed to occur. If the fracture 

 stress state lies in the tension-compression or tension-tension zone, a 

 crack was assumed to occur in a plane normal to the direction of the 

 offending principal tensile stress or strain . 



Finite Element Program . In the present work all the analyses were 

 performed using NFAP program (Ref 23) on computer system IBM model 

 370-158. NFAP is a modified and extended version of NONSAP-A pro- 

 gram (Ref 24), which is a modified version of the NONSAP program 

 originally developed by Bathe, Wilson, and Iding (Ref 25). The pre- 

 sent concrete constitutive model has been incorporated as a subroutine 

 in the NFAP program. The average computing time for the two- 

 dimensional (plane strain or axisymmetric) problems was about 5 minutes 

 for each case. The average computing time for each three-dimensional 

 analysis was about 62 minutes. 



Geometry of Analysis . The eight cases as listed in Table B-7 were 

 analyzed using isoparametric shell elements . 



(1) Cases 1 and 3 were modeled as axisymmetrical problems 

 with simple- support end -condition. 



(2) Cases 5 and 7 were modeled as plane strain, axisym- 

 metrical problems . 



(3) Cases 6 and 8 were modeled as plane strain, asymmet- 

 rical problems. Out-of-roundness in the form of n = 2 

 (see Table 2) was included in the analysis. 



(4) Cases 2 and 4 were treated as three-dimensional pro- 

 blems with large displacement. Out-of-roundness in 

 the form of n = 3 was included in the analysis . 



73 



