remains constant, the time dependency is related to

the time variation of the aging modulus for the region

The cracking criterion is a stress-strain interactive

of the structure being evaluated for cracking. This

criterion. It is made time dependent through the use

concept is illustrated in Figure A2-2. The stress axis

of a linear relationship between cracking stress and

intercept for a given age, *t*i, is determined as:

σf,*i * εf E(*t*i)

cracking strain which is dependent on the aging

(A2-3)

modulus. This criterion is illustrated in Figure A2-1.

Figure A2-2 shows three different failure surfaces for

If the principal stresses and their respective principal

the concrete ages of *t*1, t2, and *t*3.

strains, when plotted on Figure A2-1, are within the

triangle enclosed by the failure surface and the two

axes, no cracking occurs, and the cracking potential is

calculated. If the point of principal stress versus

principal strain lies outside the triangle, the concrete

has cracked. If the system is cracked, the constitutive

matrix, stress state, nodal forces, and stiffness matrix

are adjusted prior to continuation of the analysis.

The failure surface is a function of the slow load

The strain axis intercept is determined as:

σs

εf εs

(A2-1)

as shown in Figure A2-1. This intercept value

remains constant for the entire NISA and is a predic-

tion of the concrete cracking strain. ABAQUS input

data requires the user to input a cracking strain of:

σs

1

1

(A2-2)

ε

ε

εinput

2 s

2 f

All of these data should be obtained from the slow

load test. The factor of 1/2 is a function of the input

need by ANACAP-U to generate the correct strain

axis intercept within the subroutine used for checking

the cracking criterion. Since the strain intercept

A2-1

Integrated Publishing, Inc. |