Materials

Once the nodes have been defined, the next step towards defining elements is the material (nDMaterial Command, uniaxialMaterial Command) definition. This step may not be necessary when using elastic element or sections, as the materials are defined with the element or section.

There are two types of materials currently available in OpenSees, uniaxial materials and nDmaterials. The different types of concrete and steel materials are among the uniaxial materials. There are three types of concrete available:

1. Concrete01: uniaxial Kent-Scott-Park concrete material object with degraded linear unloading/reloading stiffness according to the work of Karsan-Jirsa and no tensile strength
2. Concrete02: uniaxial concrete material object with tensile strength and linear tension softening
3. Concrete03: uniaxial concrete material object with tensile strength and nonlinear tension softening.

Concrete02 will be used for the structure under consideration, as the tensile strength of the concrete is of interest in the elastic range, and modeling nonlinear tension softening is not considered necessary for the purpose of the example. The cover and core concrete will be modeled as different materials, using the same material type, but different stress and strain characteristics and different material tags. Steel01 will be used for the reinforcing steel.

Because some material characteristics are dependent on others, it is recommended that the user define the material properties using variables.

# Confined concrete:

set fc [expr -5.5*$ksi]; # CONCRETE Compressive Strength, ksi (+Tension, -Compression)

set Ec [expr 57*$ksi*sqrt(-$fc/$psi)]; # Concrete Elastic Modulus

set fc1C [expr 1.26394*$fc]; # CONFINED concrete (mander model), maximum stress

set eps1C [expr 2.*$fc1C/$Ec]; # strain at maximum stress

set fc2C $fc; # ultimate stress

set eps2C [expr 5*$eps1C]; # strain at ultimate stress

# Unconfined concrete:

set fc1U $fc; # UNCONFINED concrete (todeschini parabolic model), maximum stress

set eps1U -0.003; # strain at maximum stress

set fc2U [expr 0.1*$fc]; # ultimate stress

set eps2U -0.006; # strain at ultimate stress

# Concrete02 variables:

set lambda 0.1 ; # ratio between unloading slope at $epscu and initial slope

set ftC [expr -$fc1C/10.]; # tensile strength +tension

set ftU [expr -$fc1U/10.]; # tensile strength +tension

set Ets [expr $Ec/10.]; # tension softening stiffness

# reinforcing steel

set Fy [expr 68.*$ksi]; # STEEL yield stress

set Es [expr 29000.*$ksi]; # modulus of steel

set epsY [expr $Fy/$Es]; # steel yield strain

set Fu [expr 95.2*$ksi]; # ultimate stress of steel

set epsU 0.1; # ultimate strain of steel

set E2 [expr ($Fu-$Fy)/($epsU-$epsY)]; # post-yield tangent stiffness

set Bs [expr $E2/$Es]; # post-yield stiffness ratio of steel

To facilitate referencing the different material types, the user should set up material tags as variables:

# set up parameters for column section and element definition

set IDcore 1; # ID tag for core concrete

set IDcover 2; # ID tag for cover concrete

set IDsteel 3; # ID tag for steel

The materials are defined using the uniaxialMaterial command:

uniaxialMaterial Concrete02 $IDcore $fc1C $eps1C $fc2C $eps2C $lambda $ftC $Ets; # CORE CONCRETE

uniaxialMaterial Concrete02 $IDcover $fc1U $eps1U $fc2U $eps2U $lambda $ftU $Ets; # COVER CONCRETE

uniaxialMaterial Steel01 $IDsteel $Fy $Es $Bs; # REINFORCING STEEL