Nonlinear Finite Element Analysis of Concrete Structures

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insight into the physical behaviour of a structure. This was
demonstrated using figures of crack developments and stress
distributions. Figures showing contour lines of the nonlinearity
index proved to be very advantageous when evaluating failure
regions and failure modes. Using the standard version of the
program, the effect of using the two different failure criteria
was evaluated and, as expected, use of the writer's criterion
resulted in the closest agreement with experimental data. The
actual post-failure behaviour of concrete may be expected to
have a large influence on those stress redistributions that
take place, when the stresses are inhomogeneously distributed.
This was indeed confirmed by the finite element analysis, and
it was demonstrated that strain softening in the post-failure
region must be included in a realistic constitutive model.
Beams failing in shear represent problems of great theoretical
and practical importance. With the standard version of the program
using the writer's failure criterion and considering strain
softening in the post-failure region, a close agreement with
experimental data was demonstrated. This holds for the beam
without stirrups as well as for the beam with stirrups. For
both beams it was shown that the primary cause of failure is
strain softening in the region adjacent to the load point. This
strain softening causes a strain localization, which in turn
results in a tendency to diagonal cracking. For the beam without
shear reinforcement nothing prevents this tendency, and diagonal
tension failure follows both experimentally and theoretically.
For the beam with shear reinforcement, on the other hand, the
stirrups resist the tendency to diagonal cracking and a shearcompression
failure follows. Apart from the above mentioned,
there is no principle difference in the behaviour of the two
beams.However, it is important to note that modelling of strain
softening seems to be mandatory for the prediction of diagonal
cracking. Considering that shear is very dominant in the beams,
the influence of different shear retention factors was evaluated
to be relatively moderate. Variations, within realistic limits,
of the uniaxial tensile strength of the concrete was found to
influence the structural behaviour insignificantly. However,
the snalysis showed that modelling of secondary cracking, where