(1) Stress Criterion 



f(a..) = J_ +4a I, + a I,^ = t ^ (B-6) 



ij 23ullu 



where A and t are material constants and where a is equal to zero 

 when the principal stresses are in the compression state and equal to 

 -1/6 when in the tension-compression or tension-tension state. The 

 first invariant, I , corresponds to the mean stress component of the 

 stress state. The term J„ is the second invariant of deviatoric 

 stresses. 



(2) Strain Criterion 



A/e\ r, / e \2 



u / u \ .^ , 2 



;(^j) = J2"y^l^)i^ = ^- iT^l (B-7) 



Maximum of the Principal Strains = e (B-8) 



in which I' corresponds to volumetric strain and J' is the second invari- 

 ant of deviatoric strains . The terms £ and e specify the maximum 

 ductilities of concrete under uniaxial compressive and tensile loading 

 conditions, respectively. Herein, the compressive cylinder strength 

 was assumed as 7,000 and 8,000 psi (48 and 55 MPa); and maximum 

 compressive strain, e , was 3,500 pin. /in. The tensile strength, f, 



was assumed to be 0.09 f; and maximum tensile strain, e^, was 800 



c ' t 



|jin./in. When the stress state in the concrete satisfied either the 

 stress criterion (Equation B-6) or the strain criteria (Equations B-7 



72 



