3.1.7.4. ASDCoupledHinge3D

This command is used to construct an ASDCoupledHinge3D section object.

It is a phenomenological section for lumped-plasticity modeling of RC beam-column elements that considers P-M-M interaction.

Internally it uses the Pinching4 material object for the moment-rotation responses in the My and Mz DOFs.

Using a P-M-M interaction domain, it internally updates the backbone curves of the My/Mz materials to account for P-M-M interaction.

section ASDCoupledHinge3D $tag $Ktor $Kvy $Kvz? $Kax

-initialFlexuralStiffness $Ky $Kz

-thetaP $thetaPy $thetaPz

-thetaPC $thetaPCy $thetaPCz

<-simpleStrengthDomain $Nmin $Nmax $MyMax $MzMax $NMMax>

<-strengthDomainByPoints $nN $nTheta $listN $listMy $listMz>

<-hardening $as>

<-hystereticParams $rDispP $rForceP $uForceP $rDispN $rForceN $uForceN>

<-damageUnloadStiffness $gk1 $gk2 $gk3 $gk4 $gklim>

<-damageReloadStiffness $gd1 $gd2 $gd3 $gd4 $gdlim>

<-damageForce $gf1 $gf2 $gf3 $gf4 $gflim>

<-damageType $type $ge>

Argument	Type	Description
$tag	integer	Unique tag identifying this section.
$Ktor $Kvy $Kvz? $Kax	4 float	Mandatory. Penalty stiffnesses for torsional, shear-y, shear-z and axial responses respectively.
-initialFlexuralStiffness $Ky $Kz	string + 2 string	Mandatory. -initialFlexuralStiffness: A keyword preceding the 2 strings. $Ky and $Kz: Strings representing (currently Tcl only) expressions for the initial rotational stiffnesses.
-thetaP $thetaPy $thetaPz	string + 2 string	Mandatory. -thetaP: A keyword preceding the 2 strings. $thetaPy and $thetaPz: Strings representing (currently Tcl only) expressions for the pre-cap rotations.
-thetaPC $thetaPCy $thetaPCz	string + 2 string	Mandatory. -thetaPC: A keyword preceding the 2 strings. $thetaPCy and $thetaPCz: Strings representing (currently Tcl only) expressions for the post-cap rotations.
<-simpleStrengthDomain $Nmin $Nmax $MyMax $MzMax $NMMax>	string + 5 float	Optional. -simpleStrengthDomain: A keyword activating the use of the simplified interaction domain. $Nmin $Nmax $MyMax $MzMax $NMMax: Values for the simplified interaction domain representing the minimum axial strength, maximum axial strength, maximum My, maximum Mz and the value of axial coordinate of MyMax and MzMax.
<-strengthDomainByPoints $nN $nTheta $listN $listMy $listMz>	string + 2 integer + 3 list	Optional. -strengthDomainByPoints: A keyword activating the use of the interaction domain as a structured list of triplets (N, My, Mz). $nN $nTheta: 2 integers defining the number of points along the axial direction and the number of points along each My-Mz section. $listN $listMy $listMz: Lists of floats (size = nN * nTheta) for the N, My and Mz (respectively) coordinates of each point. Points are expected going from Nmin to Nmax. For each N coordinate, nTheta values (at constant N) of N My and Mz are expected going in ccw direction from the point N(i), My(max), Mz(zero).
<-hardening $as>	string + 1 float	Optional. -hardening: A keyword defining the hardening ratio. $as: Hardening ratio of Mu (ultimate moment) to My (yield moment).
<-hystereticParams $rDispP $rForceP $uForceP $rDispN $rForceN $uForceN>	string + 6 float	Optional. Same as those defined for Pinching4 material here: https://opensees.berkeley.edu/wiki/index.php/Pinching4_Material.
<-damageUnloadStiffness $gk1 $gk2 $gk3 $gk4 $gklim>	string + 5 float	Optional. Same as those defined for Pinching4 material here: https://opensees.berkeley.edu/wiki/index.php/Pinching4_Material.
<-damageReloadStiffness $gd1 $gd2 $gd3 $gd4 $gdlim>	string + 5 float	Optional. Same as those defined for Pinching4 material here: https://opensees.berkeley.edu/wiki/index.php/Pinching4_Material.
<-damageForce $gf1 $gf2 $gf3 $gf4 $gflim>	string + 5 float	Optional. Same as those defined for Pinching4 material here: https://opensees.berkeley.edu/wiki/index.php/Pinching4_Material.
<-damageType $type $ge>	string + string + float	Optional. Same as those defined for Pinching4 material here: https://opensees.berkeley.edu/wiki/index.php/Pinching4_Material.

Notes

• In the current implementation this section works only for the Tcl interpreter. The Python counterpart will be available soon.

Example 1 - Link to the live webinar

Webinar page: https://asdea.eu/software/webinars/

Link to youtube video: https://www.youtube.com/live/C1iwsf7-mbU

Example 2 - Simple Tcl example

ASDCoupledHinge3D_Example.tcl

Code Developed by: Diego A. Talledo at IUAV, Italy. Massimo Petracca at ASDEA Software, Italy.