Nonlinear Finite Element Analysis of Concrete Structures

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Fig. 5.4-2: Punched-out piece of concrete. Cracks are
made visible using percil tracting.
Fig. 3 shows the analysed structure as well as the axisymmetric
finite element mesh consisting of 441 triangular elements. The
elements that represent the steel disc appear from this figure.
The pull-out force as well as the boundary conditions at the
location of the cylindrical counter-pressure are also indicated.
In the following, we will use the finite element program in its
standard form. Strain softening in the post-failure region will
be considered and in the first place the failure criterion of
the writer (1977) is utilized. To beain with, some important
aspects of the structural behaviour of the Lok-Test will be
illustrated. After that, the influence of some concrete material
data and of different failure criteria will be investigated
in detail.
To illustrate the structural behaviour we use concrete material
data that can be considered as quite representative and realistic.
For this purpose we approximate the behaviour of a specific
concrete tested by Kupfer (1973) . The constitutive model of
this relatively strong concrete is calibrated by the following
parameters all in accordance v.ith experimental data: E. = 3.24«
10 4 MPa, v ± = 0.2, o c = 31.8 MPa, o fc /o = 0.10, £ c = 2.17% and
D = 0.2. Using these data the normalized stress-strain curve is