Limit State Material

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This command is used to construct a uniaxial hysteretic material object with pinching of force and deformation, damage due to ductility and energy, and degraded unloading stiffness based on ductility. Failure of the material is defined by the associated Limit Curve.

uniaxialMaterial LimitState $matTag $s1p $e1p $s2p $e2p $s3p $e3p $s1n $e1n $s2n $e2n $s3n $e3n $pinchX $pinchY $damage1 $damage2 $beta $curveTag $curveType.

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$matTag	integer tag identifying material
$s1p $e1p	stress and strain (or force & deformation) at first point of the envelope in the positive direction
$s2p $e2p	stress and strain (or force & deformation) at second point of the envelope in the positive direction
$s3p $e3p	stress and strain (or force & deformation) at third point of the envelope in the positive direction
$s1n $e1n	stress and strain (or force & deformation) at first point of the envelope in the negative direction*
$s2n $e2n	stress and strain (or force & deformation) at second point of the envelope in the negative direction*
$s3n $e3n	stress and strain (or force & deformation) at third point of the envelope in the negative direction*
$pinchX	pinching factor for strain (or deformation) during reloading
$pinchY	pinching factor for stress (or force) during reloading
$damage1	damage due to ductility: D1(m-1)
$damage2	damage due to energy: D2(Ei/Eult)
$beta	power used to determine the degraded unloading stiffness based on ductility, m-b (optional, default=0.0)
$curveTag	an integer tag for the LimitCurve defining the limit surface
$curveType	an integer defining the type of LimitCurve (0 = no curve, 1 = axial curve, all other curves can be any other integer)

NOTES:

• negative backbone points should be entered as negative numeric values

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EXAMPLE:

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DESCRIPTION:

Modeling Failures in Existing Reinforced Concrete Columns by Ken Elwood: File:ElwoodCJCE2004.pdf

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REFERENCES:

Elwood, K.J and Moehle, J.P., "Shake Table Tests and Analystical Studies on the Gravity Load Collapse of Reinforced Concrete Frames", Pacific Earthquake Engineering Research Center, University of California, Berkeley, CA. PEER 2003/01.

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Code Developed by: Ken Elwood, University of British Columbia