Nonlinear Finite Element Analysis of Concrete Structures

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sent values of total strains e, and e_ are obtained. The initial
stresses in question can then be determined through eq. (12).
For uniaxial reinforcement bars the approach is much simpler.
As perfect bond is assumed, the axial strain e is directly determined
in the finite element program. Through the uniaxial
stress-strain curve of fig. 3-1 a) the corresponding stress is
determined, i.e.,
a = a (e)
This constitutive equation is equivalent to
a = Ee + a_
where the initial stress is given by
o Q = a(e) - Ee (3-19)
No iteration sequence is involved here.
Summarizing, the constitutive equations for usual embedded reinforcement
corresponds to nonlinear elasticity. The numerical
considerations of plastic deformation are applied using the i-
nitiai stress method outlined in section 4.3.2. For a given
loading stage, the finite element program determines the total
strains in the reinforcement plane. For membrane reinforcement
the corresponding initial stresses are given by eq. (12) while
the initial stress for uniaxial reinforcement bars is given by
eq. (19).
4. FINITE ELEMENT MODELLING
In this section the finite element formulation of the AXIPLANEprogram
described by the writer (1980) is given.
This pro-