Models for Simulating the Seismic Response of Concrete Structures - Dynamic Behavior of Concrete and Seismic Engineering - page 249

7.3.5.1. Influence of the transverse reinforcement (stirrups)
Due to the formalism of multi-layer and multi-fiber models, some building
arrangements can directly influence material laws. In this way, stirrups increase the
ductility of an element and act on its strength. They are taken into account by
increasing, in the behavior law of concrete, stress at the peak and/or by raising the
post-peak phase to improve the failure strain when the volume ratio of the stirrups
increases. As far as column-type or beam-type elements are concerned, stirrups
delay the buckling of steel under alternating loading.
7.3.5.2. Anchoring and overlapping of the reinforcements
The phenomena linked to the steel/concrete bond (lack of overlapping or lack of
anchoring) that tend to soften the structure and increase displacements can be
modeled by specific non-linear and non-dissipative laws. Taking these phenomena
into account can become really important in old reinforced concrete structures that
do not respect the latest construction layouts (generally having inadequate
overlapping or anchoring length). A modeling example ([CON 01], [MON 00] and
[XIA 97]) involves drawing a parallel between a steel model and a steel-concrete
interface model using an adapted law that splits the total strain into two parts: one
related to the behavior of steel and the other describing sliding between steel and
concrete [ELI 93].
7.3.5.3. Taking transverse load non-linearity into account
In Timoshenko beam elements, cross-sections do not stay orthogonal to the
longitudinal axis. This can be taken into account by additional stresses linked to the
shear diagonal cracking and enables verification of the transverse load collapse
modes. The law describing layer behavior is no longer uniaxial, but should take the
shear component forces into account [GHA 98]. As far as spatial problems (multi-
fiber element) are concerned, the problem is somewhat more complex, but
introducing a warping function is a good way to proceed [CAZ 03].
7.3.5.4. P-Delta effects
For very slender elements supporting an important axial load - a bridge pier for
instance - a second-order bending effect due to the displacement at the top is added
to the front-mass inertia effect. The digital implementation of this phenomenon for
seismic conditions can be found in [GHA 98].
7.3.5.5. Structure-support interaction
This effect can be decisive. The support - typically the soil - has its own
behavior and, at the interface, generates rotation and/or uplift effects. The main
phenomena can be taken into account either using a 2D or 3D representation of the