3. Laws of behavior#

3.1. For reinforcements and sheets#

The behavior for steels is of the elasto-plastic type with linear kinematic work hardening. This vmis_cine_gc [Code_aster] behavior corresponds to the recommendations of the various regulations: BAEL91 (§A.2.2), Eurocode2 (§3.2, §3.2.7), eurocode3 (§3.2) and eurocode4 (§3.2, §3.3).

The same behavior is used for all steels: reinforcement of beams and columns, reinforcement sheets, steel plates. The parameters of the law (elastic limit, plastic slope) are adapted according to the grades of the steels and their use. For post-treatment, the criteria [DEFI_MATER_GC] ELS and ELU are available in addition to conventional quantities (stress, deformation).

The necessary characteristics are: Young’s modulus” E “, the elastic limit “SY”.

ARMA_GCNL = DEFI_MATER_GC (

RHO = 7800.0, ACIER =_F (E= 2.0E+11, SY= 400.0E+06, ,) ),

)

3.2. For concrete#

The behavior for concrete is elastic-damaging in tension and compression. The mazars_gc [Code_aster] behavior, available in code_aster, is similar to the recommendations (they are not obligations) of the various regulations: bael91 (§A.2.1, §A.4.3.3, §A.4.3.3, §A.4.3.4, §A.4.3.4, §A.4.3.4, §A.4.4.32), eurocode2 (§A.4.4.32), eurocode2 (§3.1, §3.1.5), eurocode4 (§3.1). The defi_mater_gc [DEFI_MATER_GC] command makes it very easy to define the parameters of the law according to these two regulations.

The same behavior is used for all concrete models for walls and floors. For post-treatment, criteria ELS and ELU are available in addition to conventional quantities (stress, deformation). By modifying the parameters of the law, it is possible to represent various behaviors of concrete both in tension and in compression: elasticity, zero tensile strength, rectangular parabola in compression. It is currently, in code_aster, the only concrete behavior law written in plane stress for use with multilayer DKT, which makes it possible to avoid a De Borst algorithm.

The required characteristics are [DEFI_MATER_GC]:

  • if CODIFICATION =” BAEL “, the characteristic compression strength FCJ.

  • if CODIFICATION =” EUROCODE “, the concrete class.

  • the stress units used during the study.

BETO_GCNL = DEFI_MATER_GC (

RHO = 2500.0,

MAZARS =_F (CODIFICATION = “BAEL91”, UNITE_CONTRAINTE “, =**” Pa “,** FCJ =**50.0E+06**) ),

)

Note: The eurocode2 allows the use of a simpler modeling of the behavior of concrete (rectangular or bilinear parabola diagram for compressed concrete) but the question arises of a representativeness when the stress is no longer one-dimensional, as in walls and floors. Modeling the behavior of concrete with the la*mazars_gc [Code_aster]* makes it possible to account, to a certain extent,*of these multi-axial loads.

3.3. Criteria ELS and ELU#

The laws of behavior defined with DEFI_MATER_GC [DEFI_MATER_GC] include the calculation of the criteria ELS and ELU. These criteria are standardized by limit values derived either from regulations or from data provided by the user.

The internal variables for criteria ELS and ELU are respectively V1 and V2 or “CRITSIG”, “CRITEPS”.

3.4. Choice of behaviors according to the analysis#

Depending on the analyses, it may be necessary to change the behavior of the materials. For example, if one wishes to carry out a dynamic analysis on a modal basis, the behavior of the materials will be elastic, while for a transitory dynamic study, if necessary, they can be non-linear. The realization of a study with ultimate limit states, and therefore non-linear, is very simply carried out by changing the behavior of the materials.

The law of behavior of steel is based on a Von Mises plasticization criterion, but this law is capable of representing elastic behavior.

The law of behavior of concrete is based on a damaging law. By adjusting these material parameters, this law can have:

  • elastic behavior during traction and/or compression

  • zero residual tensile strength, corresponding to cracked concrete.

  • in compression, a behavior similar to the « parabola-rectangle ».

Note: The use of non-linear behavior requires some precautions for use that can be found in the documentation «  [U2.03.07]: Overview of the tools available to perform concrete Civil Engineering structural calculations [U2.03.07] » .