ETL 1110-2-365
31 Aug 94
ANNEX 2: CRACKING CRITERION
A2-1. General
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, ti, is determined as:
σf,i εf E(ti)
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 t1, t2, and t3.
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.
A2-2. Failure Surface Generation
The failure surface is a function of the slow load
fracture stress, σs, the slow load fracture strain, εs,
and the aging modulus at the time of fracture, Es(t).
Figure A2-1. Cracking failure surface and ε
f
The strain axis intercept is determined as:
generation from the slow load fracture data
σs
εf εs
(A2-1)
Es(t)
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
Es(t)
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
Figure A2-2. Computer generated, time-dependent
the cracking criterion. Since the strain intercept
(aging modulus) cracking failure surfaces
A2-1