Models for Simulating the Seismic Response of Concrete Structures - Dynamic Behavior of Concrete and Seismic Engineering - page 247

to zero, provided the strain is higher than a specific threshold: 3*H tm . Path 5 follows
the non-linear law of concrete in simple compression to a new inversion of loading,
which involves a discharge along the E2 slope straight line (path 6) passing a focal
point (f c ; H 0 ), with

H f c / E

, as suggested by Mander et al. [MAN 88] and Park 0 0

[PAR 90].

A concept similar to the damage concept affecting the modulus can also be found
with stress intensity. When the stress exceeds -f t (path 7), the E 1 modulus
corresponding to the crack closing up is still found. Paths 8 and 9 obey the same
rules as paths 3 and 4. The behavior of an initially compressed point (or a spot that
has not completely cracked due to a reversed loading) is described by similar laws,
presented in detail elsewhere [ILE 00].

7.3.4. Cyclic models for steel

Because of its geometry, the reinforcement can only be modeled with uniaxial
laws, even for calculations involving 2D or 3D problems.

As a rule, the laws used are elasto-plastic, with or without hardening. The most
exhaustive laws [MEN 73] successfully reproduce phenomena including non-linear
strain hardening (Figure 7.11a), Bauschinger's effect with cyclic loading (Figure
7.11b) and compression bar buckling when frames are not close enough (Figure
7.11c).

a) Behavior with monotonous loading