Civil Engineering Reference
In-Depth Information
the presence of this type of response in the analysis model usually indicates
that the tension stiffening is unreasonably low.
As the concrete cracks, its shear stiffness is diminished. This effect is
defined by specifying the reduction in the shear modulus as a function of
the opening strain across the crack. You can also specify a reduced shear
modulus for closed cracks. This reduced shear modulus will also have an
effect when the normal stress across a crack becomes compressive. The
new shear stiffness will have been degraded by the presence of the crack.
When the principal stress components are dominantly compressive, the
response of the concrete is modeled by an elastic-plastic theory using a
simple form of yield surface written in terms of the equivalent pressure stress,
p
, and the Mises equivalent deviatoric stress,
q
; this surface is illustrated in
Figure 5.21
. Associated flow and isotropic hardening are used. This model
significantly simplifies the actual behavior. The associated flow assumption
generally overpredicts the inelastic volume strain. The yield surface cannot
be matched accurately to data in triaxial tension and triaxial compression
tests because of the omission of third stress invariant dependence. When
the concrete is strained beyond the ultimate stress point, the assumption that
the elastic response is not affected by the inelastic deformation is not realistic.
In addition, when concrete is subjected to very high pressure stress, it
exhibits inelastic response: no attempt has been made to build this behavior
into the model. Modelers can define the stress-strain behavior of plain con-
crete in uniaxial compression outside the elastic range. Compressive stress
data are provided as a tabular function of plastic strain and, if desired, tem-
perature and field variables. Positive (absolute) values should be given for the
compressive stress and strain. The stress-strain curve can be defined beyond
the ultimate stress, into the strain-softening regime.
The cracking and compressive responses of concrete that are incorpo-
rated in the concrete model are illustrated by the uniaxial response of a spec-
imen shown in
Figure 5.19
.
When concrete is loaded in compression, it
initially exhibits elastic response. As the stress is increased, some nonrecov-
erable (inelastic) straining occurs and the response of the material softens. An
ultimate stress is reached, after which the material loses strength until it can
no longer carry any stress. If the load is removed at some point after inelastic
straining has occurred, the unloading response is softer than the initial elastic
response: the elasticity has been damaged. This effect is ignored in the
model, since we assume that the applications involve primarily monotonic
straining, with only occasional, minor unloadings. When a uniaxial concrete
specimen is loaded in tension, it responds elastically until, at a stress that is
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