# 4.14.5.32. Pinching Limit State Material¶

This command is used to construct a uniaxial material that simulates a pinched load-deformation response and exhibits degradation under cyclic loading. This material works with the RotationShearCurve limit surface that can monitor a key deformation and/or a key force in an associated frame element and trigger a degrading behavior in this material when a limiting value of the deformation and/or force are reached. The material can be used in two modes: 1) direct input mode, where pinching and damage parameters are directly input; and 2) calibrated mode for shear-critical concrete columns, where only key column properties are input for model to fully define pinching and damage parameters.

uniaxialMaterial('PinchingLimitStateMaterial', matTag, nodeT, nodeB, driftAxis, Kelas, crvTyp, crvTag, YpinchUPN, YpinchRPN, XpinchRPN, YpinchUNP, YpinchRNP, XpinchRNP, dmgStrsLimE, dmgDispMax, dmgE1, dmgE2, dmgE3, dmgE4, dmgELim, dmgR1, dmgR2, dmgR3, dmgR4, dmgRLim, dmgRCyc, dmgS1, dmgS2, dmgS3, dmgS4, dmgSLim, dmgSCyc)

MODE 1: Direct Input

 matTag (int) integer tag identifying material nodeT (int) integer node tag to define the first node at the extreme end of the associated flexural frame member (L3 or D5 in Figure) nodeB (int) integer node tag to define the last node at the extreme end of the associated flexural frame member (L2 or D2 in Figure) driftAxis (int) integer to indicate the drift axis in which lateral-strength degradation will occur. This axis should be orthogonal to the axis of measured rotation (see rotAxis in Rotation Shear Curve definition) driftAxis = 1 - Drift along the x-axis driftAxis = 2 - Drift along the y-axis driftAxis = 3 - Drift along the z-axis Kelas (float) floating point value to define the initial material elastic stiffness (Kelastic); Kelas > 0 crvTyp (int) integer flag to indicate the type of limit curve associated with this material. crvTyp = 0 - No limit curve crvTyp = 1 - axial limit curve crvTyp = 2 - RotationShearCurve crvTag (int) integer tag for the unique limit curve object associated with this material YpinchUPN (float) floating point unloading force pinching factor for loading in the negative direction. Note: This value must be between zero and unity YpinchRPN (float) floating point reloading force pinching factor for loading in the negative direction. Note: This value must be between negative one and unity XpinchRPN (float) floating point reloading displacement pinching factor for loading in the negative direction. Note: This value must be between negative one and unity YpinchUNP (float) floating point unloading force pinching factor for loading in the positive direction. Note: This value must be between zero and unity YpinchRNP (float) floating point reloading force pinching factor for loading in the positive direction. Note: This value must be between negative one and unity XpinchRNP (float) floating point reloading displacement pinching factor for loading in the positive direction. Note: This value must be between negative one and unity dmgStrsLimE (float) floating point force limit for elastic stiffness damage (typically defined as the lowest of shear strength or shear at flexrual yielding). This value is used to compute the maximum deformation at flexural yield (δmax Eq. 1) and using the initial elastic stiffness (Kelastic) the monotonic energy (Emono Eq. 1) to yield. Input 1 if this type of damage is not required and set dmgE1, dmgE2, dmgE3, dmgE4, and dmgELim to zero dmgDispMax (float) floating point for ultimate drift at failure (δmax Eq. 1) and is used for strength and stiffness damage. This value is used to compute the monotonic energy at axial failure (Emono Eq. 2) by computing the area under the backbone in the positive loading direction up to δmax. Input 1 if this type of damage is not required and set dmgR1, dmgR2, dmgR3, dmgR4, and dmgRLim to zero for reloading stiffness damage. Similarly set dmgS1, dmgS2, dmgS3, dmgS4, and dmgSLim to zero if reloading strength damage is not required dmgE1 dmgE2 (float) floating point elastic stiffness damage factors α1,α2,α3,α4 shown in Eq. 1 dmgE3 dmgE4 (float) floating point elastic stiffness damage factors α1,α2,α3,α4 shown in Eq. 1 dmgELim (float) floating point elastic stiffness damage limit Dlim shown in Eq. 1; Note: This value must be between zero and unity dmgR1 dmgR2 (float) floating point reloading stiffness damage factors α1,α2,α3,α4 shown in Eq. 1 dmgR3 dmgR4 (float) floating point reloading stiffness damage factors α1,α2,α3,α4 shown in Eq. 1 dmgRLim (float) floating point reloading stiffness damage limit Dlim shown in Eq. 1; Note: This value must be between zero and unity dmgRCyc (float) floating point cyclic reloading stiffness damage index; Note: This value must be between zero and unity dmgS1 dmgS2 (float) floating point backbone strength damage factors α1,α2,α3,α4 shown in Eq. 1 dmgS3 dmgS4 (float) floating point backbone strength damage factors α1,α2,α3,α4 shown in Eq. 1 dmgSLim (float) floating point backbone strength damage limit Dlim shown in Eq. 1; Note: This value must be between zero and unity dmgSCyc (float) floating point cyclic backbone strength damage index; Note: This value must be between zero and unity
uniaxialMaterial('PinchingLimitStateMaterial', matTag, dnodeT, nodeB, driftAxis, Kelas, crvTyp, crvTag, eleTag, b, d, h, a, st, As, Acc, ld, db, rhot, fc, fy, fyt)

MODE 2: Calibrated Model for Shear-Critical Concrete Columns

 matTag (int) integer tag identifying material nodeT (int) integer node tag to define the first node at the extreme end of the associated flexural frame member (L3 or D5 in Figure) nodeB (int) integer node tag to define the last node at the extreme end of the associated flexural frame member (L2 or D2 in Figure) driftAxis (int) integer to indicate the drift axis in which lateral-strength degradation will occur. This axis should be orthogonal to the axis of measured rotation (see rotAxis in Rotation Shear Curve definition) driftAxis = 1 - Drift along the x-axis driftAxis = 2 - Drift along the y-axis driftAxis = 3 - Drift along the z-axis Kelas (float) floating point value to define the shear stiffness (Kelastic) of the shear spring prior to shear failure Kelas = -4 - Shear stiffness calculated assuming double curvature and shear springs at both column element ends Kelas = -3 - Shear stiffness calculated assuming double curvature and a shear spring at one column element end Kelas = -2 - Shear stiffness calculated assuming single curvature and shear springs at both column element ends Kelas = -1 - Shear stiffness calculated assuming single curvature and a shear spring at one column element end Kelas > 0 - Shear stiffness is the input value Note: integer inputs allow the model to know whether column height equals the shear span (cantelever) or twice the shear span (double curvature). For columns in frames, input the value for the case that best approximates column end conditions or manually input shear stiffness (typically double curvature better estimates framed column behavior) crvTag (int) integer tag for the unique limit curve object associated with this material eleTag (int) integer element tag to define the associated beam-column element used to extract axial load b (float) floating point column width (inches) d (float) floating point column depth (inches) h (float) floating point column height (inches) a (float) floating point shear span length (inches) st (float) floating point transverse reinforcement spacing (inches) along column height As (float) floating point total area (inches squared) of longitudinal steel bars in section Acc (float) floating point gross confined concrete area (inches squared) bounded by the transverse reinforcement in column section ld (float) floating point development length (inches) of longitudinal bars using ACI 318-11 Eq. 12-1 and Eq. 12-2 db (float) floating point diameter (inches) of longitudinal bars in column section rhot (float) floating point transverse reinforcement ratio (Ast/st.db) f'c (float) floating point concrete compressive strength (ksi) fy (float) floating point longitudinal steel yield strength (ksi) fyt` (float) floating point transverse steel yield strength (ksi)