Nonlinear Finite Element Analysis of Concrete Structures

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here at 82% loading. At the failure load, the region adjacent to
the load point is stressed far into the post-failure region and
this is considered to be the primary cause of the beam collapse.
This underlines the importance of realistic constitutive modelling
in the pre- as well as post-failure region for stress states
where tensile stresses are present but no cracking occurs. Moreover,
the arch-action of the beam is apparent from fig. 5. No
plastic deformation of the reinforcement occurs even at failure.
The predicted crack development of the OA-2 beam with increasing
loading is shown in fig. 6. Cracking initiates in the middle of
the beam as flexural cracks already at 9% loading. Fig. 6a)
shows these type of cracks. At increased loading the cracks develop
towards the support and a slight inclination of the cracks
becomes present, cf. fig. 6b). Secondary cracks where cracks
v/ith different inclinations exist at the same location are initiated
at 62% loading. The crack pattern just before failure is
shown in fig. 6c). The inclination of the cracks as well as the
secondary cracks appear from this figure. Fig. 6d) shows the
cracking at the failure load at the last iteration before the
calculations were terminated. It is of interest to notice the
clearly developed diagonal cracks running towards the load point.
This is in accordance with the experimentally observed diagonal
tension failure. However, it is important to recall that the concrete
near the load point is stressed far into the post-failure
region and that the primary failure takes place here. This causes
a strain localization which in turn results in diagonal cracking.
Therefore, the increase of the diagonal cracks is considered
more as a consequence of this failure than as its cause.
Fig..7 shows the experimentally observed cracking after failure
of the OA-2 beam. Apart from the horizontal splitting along the
reinforcement the predicted cracking is in good agreement with
the observed cracking, cf. fig. 6d). However, it is important
to note that this horizontal splitting occurs when the beam collapses.
Obviously, at failure the concrete has lost its shear
capacity and a considerable increase of the dowel forces can
therefore be expected resulting in splitting along the rein-