Pinching Limit State Material: Difference between revisions

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This command is used to construct a uniaxial material that simulates a pinched load-deformation response and exhibits degradation under cyclic loading. Cyclic degradation can be introduced using deformation and energy damage algorithms. Cyclic degradation can be imposed on reloading stiffness and backbone strength. The material in association with a [[RotationShearCurve]] material can monitor key deformation and forces in an associated frame element and utilize those values during analyses to adjust the force-deformation response.
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 all pinching and damage parameters are 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.
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.




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{|  
{|  
| style="background:yellow; color:black; width:800px" | '''uniaxialMaterial PinchingLimitStateMaterial $matTag
| style="background:yellow; color:black; width:800px" | '''uniaxialMaterial PinchingLimitStateMaterial $matTag $nodeT $nodeB $driftAxis $Kelas $crvTyp $crvTag '''
$nodeT $nodeB $driftAxis $Kelas $crvTyp $crvTag
'''$YpinchUPN $YpinchRPN $XpinchRPN '''
$YpinchUPN $YpinchRPN $XpinchRPN
'''$YpinchUNP $YpinchRNP $XpinchRNP '''
$YpinchUNP $YpinchRNP $XpinchRNP
'''$dmgStrsLimE $dmgDispMax '''
$dmgStrsLimE $dmgDispMax
'''$dmgE1 $dmgE2 $dmgE3 $dmgE4 $dmgELim '''
$dmgE1 $dmgE2 $dmgE3 $dmgE4 $dmgELim
'''$dmgR1 $dmgR2 $dmgR3 $dmgR4 $dmgRLim '''
$dmgR1 $dmgR2 $dmgR3 $dmgR4 $dmgRLim $dmgRCyc
'''$dmgRCyc '''
$dmgS1 $dmgS2 $dmgS3 $dmgS4 $dmgSLim $dmgSCyc
'''$dmgS1 $dmgS2 $dmgS3 $dmgS4 $dmgSLim '''
'''
'''$dmgSCyc'''
|}
|}


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|-
|-
|  '''$driftAxis''' || 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''' || 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 $rotAxis in Rotation Shear Curve definition)
driftAxis = 1 – Drift along the x-axis
|-
|  || driftAxis = 1 – Drift along the x-axis
driftAxis = 2 – Drift along the y-axis
driftAxis = 2 – Drift along the y-axis
driftAxis = 3 – Drift along the z-axis
driftAxis = 3 – Drift along the z-axis
Line 37: Line 38:
|-
|-
|  '''$crvTyp''' || integer flag to indicate the type of limit curve associated with this material.
|  '''$crvTyp''' || integer flag to indicate the type of limit curve associated with this material.
crvTyp = 0 – No limit curve
|-
|  || crvTyp = 0 – No limit curve
crvTyp = 1 – axial limit curve
crvTyp = 1 – axial limit curve
crvTyp = 2 – [[RotationShearCurve]]
crvTyp = 2 – [[RotationShearCurve]]
Line 44: Line 46:
|-
|-
|  '''$YpinchUPN''' || floating point unloading force pinching factor for loading in the negative direction
|  '''$YpinchUPN''' || floating point unloading force pinching factor for loading in the negative direction
Note: This value must be between zero and unity
|-
|  || Note: This value must be between zero and unity
|-
|-
|  '''$YpinchRPN''' || floating point reloading force pinching factor for loading in the negative direction
|  '''$YpinchRPN''' || floating point reloading force pinching factor for loading in the negative direction
Note: This value must be between negative one and unity
|-
|  || Note: This value must be between negative one and unity
|-
|-
|  '''$XpinchRPN''' || floating point reloading displacement pinching factor for loading in the negative direction
|  '''$XpinchRPN''' || floating point reloading displacement pinching factor for loading in the negative direction
Note: This value must be between negative one and unity
|-
|  || Note: This value must be between negative one and unity
|-
|-
|  '''$YpinchUNP''' || floating point unloading force pinching factor for loading in the positive direction  
|  '''$YpinchUNP''' || floating point unloading force pinching factor for loading in the positive direction  
Note: This value must be between zero and unity  
|-
|  || Note: This value must be between zero and unity  
|-
|-
|  '''$YpinchRNP''' || floating point reloading force pinching factor for loading in the positive direction  
|  '''$YpinchRNP''' || floating point reloading force pinching factor for loading in the positive direction  
Note: This value must be between negative one and unity
|-
|  || Note: This value must be between negative one and unity
|-
|-
|  '''$XpinchRNP''' || floating point reloading displacement pinching factor for loading in the positive direction
|  '''$XpinchRNP''' || floating point reloading displacement pinching factor for loading in the positive direction
Note: This value must be between negative one and unity
|-
|-
|  '''$dmgStrsLimE''' || 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 $dmgELim to zero
|  || Note: This value must be between negative one and unity
|-
|-
|  '''$dmgDispMax''' || 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 $dmgSLim to zero if reloading strength damage is not required
|  '''$dmgStrsLimE''' || floating point force limit for elastic stiffness damage (typically defined as the lowest of shear strength or shear at flexrual yielding).  
|-
|-
|  '''$dmgE1 $dmgE2 $dmgE3 $dmgE4''' || floating point elastic damage factors ''α1,α2,α3,α4'' shown in Eq. 1
|  || 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 $dmgELim to zero
|-
|-
|  '''$dmgELim''' || floating point elastic damage limit ''Dlim'' shown in Eq. 1; Note: This value must be between zero and unity
|  '''$dmgDispMax''' || 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 $dmgE3 $dmgE4''' || floating point elastic stiffness damage factors ''α1,α2,α3,α4'' shown in Eq. 1
|-
|  '''$dmgELim''' || floating point elastic stiffness damage limit ''Dlim'' shown in Eq. 1; Note: This value must be between zero and unity
|-
|-
|  '''$dmgR1 $dmgR2 $dmgR3 $dmgR4''' || floating point reloading stiffness damage factors ''α1,α2,α3,α4'' shown in Eq. 1
|  '''$dmgR1 $dmgR2 $dmgR3 $dmgR4''' || floating point reloading stiffness damage factors ''α1,α2,α3,α4'' shown in Eq. 1
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|  '''$dmgRCyc''' || floating point cyclic reloading stiffness damage index; Note: This value must be between zero and unity
|  '''$dmgRCyc''' || floating point cyclic reloading stiffness damage index; Note: This value must be between zero and unity
|-
|-
|  '''$dmgS1 $dmgS2 $dmgS3 $dmgS4''' || floating point strength damage factors ''α1,α2,α3,α4'' shown in Eq. 1
|  '''$dmgS1 $dmgS2 $dmgS3 $dmgS4''' || floating point backbone strength damage factors ''α1,α2,α3,α4'' shown in Eq. 1
|-
|-
|  '''$dmgSLim''' || floating point strength damage limit ''Dlim'' shown in Eq. 1; Note: This value must be between zero and unity
|  '''$dmgSLim''' || floating point backbone strength damage limit ''Dlim'' shown in Eq. 1; Note: This value must be between zero and unity
|-
|-
|  '''$dmgSCyc''' || floating point cyclic strength damage index; Note: This value must be between zero and unity
|  '''$dmgSCyc''' || floating point cyclic backbone strength damage index; Note: This value must be between zero and unity
|-
|-
|}
|}




NOTES:
== '''MODE 2: Calibrated Model for Shear-Critical Concrete Columns''' ==


[[Image:PinchingLimitStateMaterial2.png|550px]]


[[Image:PinchingLimitStateMaterial1-2.jpg]]
{|
| style="background:yellow; color:black; width:800px" | '''uniaxialMaterial PinchingLimitStateMaterial $matTag $nodeT $nodeB $driftAxis $Kelas $crvTyp $crvTag $eleTag $b $d $h $a $st $As $Acc $ld $db $rhot $f'c $fy $fyt'''
|}


----


{|
|  style="width:150px" | '''$matTag ''' || unique material object integer tag
|-
|  '''$nodeT''' || integer node tag to define the first node at the extreme end of the associated flexural frame member (L3 or D5 in Figure)
|-
|  '''$nodeB''' || integer node tag to define the last node at the extreme end of the associated flexural frame member (L2 or D2 in Figure)
|-
|  '''$driftAxis''' || 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''' || 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


Damage Model Equations:
Kelas = -3 – Shear  stiffness calculated assuming double curvature and a shear spring at one column element end


Elastic stiffness, reloading stiffness, and strength can be adjusted using the following energy and displacement damage model (from Mitra and Lowes (2007)):
Kelas = -2 – Shear stiffness calculated assuming single curvature and shear springs at both column element ends


[[Image:PinchingLimitStateMaterialEq1.png]]
Kelas = -1 – Shear stiffness calculated assuming single curvature and a shear spring at one column element end


:<math>k_i = k_0(1 -\delta k_i)</math>
Kelas > 0 – Shear stiffness is the input value


where <math>k_i</math> is the unloading stiffness at time <math>t_i</math>, <math>k_0</math>  is the initial unloading stiffness (for the case of no damage), and <math>\delta k_i</math>(defined below) is the value of the stiffness damage index at time <math>t_i</math>.
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)
|-
|  '''$crvTag''' || integer tag for the unique limit curve object associated with this material
|-
|  '''$eleTag''' || integer element tag to define the associated beam-column element used to extract axial load
|-
|  '''$b''' || floating point column width (inches)
|-
|  '''$d''' || floating point column depth (inches)
|-
|  '''$h''' || floating point column height (inches)
|-
|  '''$a''' || floating point shear span length (inches)
|-
|  '''$st''' || floating point transverse reinforcement spacing (inches) along column height
|-
|  '''$As''' || floating point total area (inches squared) of longitudinal steel bars in section
|-
|  '''$Acc''' || floating point gross confined concrete area (inches squared) bounded by the transverse reinforcement in column section
|-
|  '''$ld''' || floating point development length (inches) of longitudinal bars using ACI 318-11 Eq. 12-1 and Eq. 12-2
|-
|  '''$db''' || floating point diameter (inches) of longitudinal bars in column section
|-
|  '''$rhot''' || floating point transverse reinforcement ratio (Ast/st.db)
|-
|  '''$f'c''' || floating point concrete compressive strength (ksi)
|-
|  '''$fy''' || floating point longitudinal steel yield strength (ksi)
|-
|  '''$fyt''' || floating point transverse steel yield strength (ksi)
|}


:<math>d_{\text{max i}} = d_{\text{max 0}}(1 -\delta d_i)</math>
----


where <math>d_{\text{max i}}</math> is the deformation demand that defines the end of the reload cycle for increasing deformation demand, <math>d_{\text{max 0}} </math> is the maximum historic deformation demand (which would be the deformation demand defining the end of the reload cycle if degradation of reloading stiffness is ignored), and  <math>\delta d_i</math> (defined below) is the value of reloading stiffness damage index at time <math>t_i</math>.
DESCRIPTION:


:<math>f_{\text{max i}} = f_{\text{max 0}}(1 -\delta f_i)</math>
[[Image:PinchingLimitStateMaterial2.png|550px]]


where <math>f_{\text{max i}}</math>  is the current envelope maximum strength at time <math>t_i</math>, <math>f_{\text{max 0}} </math> is the initial envelope maximum strength for the case of no damage, and <math>\delta f_i</math> (defined below) is the value of strength value index at time <math>t_i</math>.
[[Image:PinchingLimitStateMaterial1-2.jpg]]


The damage indices <math>\delta k_i</math>, <math>\delta d_i</math>,  and <math>\delta f_i</math>, may be defined to be a function of displacement history only ($dmgType = "cycle") or displacement history and energy accumulation ($dmgType = "energy"). For either case, all of the damage indices are computed using the same basic equation.


If the damage indices are assumed to be a function of displacement history and energy accumulation, the unloading stiffness damage index, <math>\delta k_i</math> is computed as follows:
The material model coupled with the [[RotationShearCurve]] limit surface: 1) has the ability to continually monitor forces and deformations in the flexural elements for conditions that trigger lateral-strength degradation, 2) has a built-in function that compensates for flexural deformation offsets that arise from the degrading behavior of the material in shear springs, and 3) is able to trigger lateral-strength degradation through either a limiting lateral force or element deformations (whichever is reached first).  The material introduces several functionalities that give users a high degree of control over the triggering of strength degradation and the ensuing cyclic degrading behavior. Damage algorithms are implemented to control the degrading behavior through elastic stiffness, reloading stiffness, and backbone strength degradation (Fig. 2). The rate of damage accumulation can be controlled by energy-, displacement-, and cycle-based damage computation algorithms.


During the degrading behavior, the model automatically adjusts reloading stiffness to achieve a symmetric global-element lateral load-vs lateral displacement behavior. The model does so by automatically adjusting the reloading stiffness and backbone curve of the material model to compensate for dissymmetry introduced by the unloading of the flexural elements in series with shear springs governed by the model.


:<math>\delta k_i =  \left( \text{gK1} (d_{max})^\text{gK3} + \text{gK2} \left (\frac{E_i}{E_\text{monotonic}} \right )^\text{gK3} \right ) <= \text{gKLim}</math>


where
DAMAGE:


:<math>(d_{max} = \text{max} \left[ \frac{d_\text{max i}}{\text{def}_\text{max}}, \frac{d_\text{min i}}{\text{def}_\text{min}} \right ]</math>
Damage accumulations effects based on numbers of cycles can be introduced to reloading stiffness and backbone strength through the simple parameters $dmgRCyc and $dmgSCyc with values ranging from 0 to 1.
----


EXAMPLE:
Elastic stiffness, reloading stiffness, and strength can be adjusted using the following energy and displacement damage model (from Mitra and Lowes (2007)):


[[PinchingLimitStateMaterial Example]]  
[[Image:PinchingLimitStateMaterialEq1.png|350px]]


----




DESCRIPTION:
----


EXAMPLE:


[[PinchingLimitStateMaterial Example]]




Line 140: Line 201:
1. LeBorgne M. R., 2012, "Modeling the Post Shear Failure Behavior of Reinforced Concrete Columns." Austin, Texas: University of Texas at Austin, PhD, 301.
1. LeBorgne M. R., 2012, "Modeling the Post Shear Failure Behavior of Reinforced Concrete Columns." Austin, Texas: University of Texas at Austin, PhD, 301.


2. LeBorgne M. R. , Ghannoum W. M., 2013, "Analytical Element for Simulating Lateral-Strength Degradation in Reinforced Concrete Columns and Other Frame Members," Journal of Structural Engineering, V. doi: 10.1061/(ASCE)ST.1943-541X.0000925
2. LeBorgne, M.R., Ghannoum, W.M., 2014, "Analytical Element for Simulating Lateral-Strength Degradation in Reinforced Concrete Columns and Other Frame Members," Journal of Structural Engineering, V. 140, No. 7, pp. 04014038 1-12.
 
3.      LeBorgne, M.R., Ghannoum, W.M., 2014, "Calibrated Analytical Element for Lateral-Strength Degradation of Reinforced Concrete Columns," Engineering Structures, V. 81, pp. 35-48.


3. Ghannoum W. M., Moehle J. P., 2012, "Rotation-Based Shear Failure Model for Lightly Confined Reinforced Concrete Columns," Journal of Structural Engineering, V. 138, No. 10, 1267-78.
3. Ghannoum W. M., Moehle J. P., 2012, "Rotation-Based Shear Failure Model for Lightly Confined Reinforced Concrete Columns," Journal of Structural Engineering, V. 138, No. 10, 1267-78.

Latest revision as of 14:49, 10 July 2015



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.


MODE 1: Direct Input

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

$matTag unique material object integer tag
$nodeT integer node tag to define the first node at the extreme end of the associated flexural frame member (L3 or D5 in Figure)
$nodeB integer node tag to define the last node at the extreme end of the associated flexural frame member (L2 or D2 in Figure)
$driftAxis 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 floating point value to define the initial material elastic stiffness (Kelastic); Kelas > 0
$crvTyp 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 integer tag for the unique limit curve object associated with this material
$YpinchUPN floating point unloading force pinching factor for loading in the negative direction
Note: This value must be between zero and unity
$YpinchRPN floating point reloading force pinching factor for loading in the negative direction
Note: This value must be between negative one and unity
$XpinchRPN floating point reloading displacement pinching factor for loading in the negative direction
Note: This value must be between negative one and unity
$YpinchUNP floating point unloading force pinching factor for loading in the positive direction
Note: This value must be between zero and unity
$YpinchRNP floating point reloading force pinching factor for loading in the positive direction
Note: This value must be between negative one and unity
$XpinchRNP floating point reloading displacement pinching factor for loading in the positive direction
Note: This value must be between negative one and unity
$dmgStrsLimE 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 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 $dmgE3 $dmgE4 floating point elastic stiffness damage factors α1,α2,α3,α4 shown in Eq. 1
$dmgELim floating point elastic stiffness damage limit Dlim shown in Eq. 1; Note: This value must be between zero and unity
$dmgR1 $dmgR2 $dmgR3 $dmgR4 floating point reloading stiffness damage factors α1,α2,α3,α4 shown in Eq. 1
$dmgRLim floating point reloading stiffness damage limit Dlim shown in Eq. 1; Note: This value must be between zero and unity
$dmgRCyc floating point cyclic reloading stiffness damage index; Note: This value must be between zero and unity
$dmgS1 $dmgS2 $dmgS3 $dmgS4 floating point backbone strength damage factors α1,α2,α3,α4 shown in Eq. 1
$dmgSLim floating point backbone strength damage limit Dlim shown in Eq. 1; Note: This value must be between zero and unity
$dmgSCyc floating point cyclic backbone strength damage index; Note: This value must be between zero and unity


MODE 2: Calibrated Model for Shear-Critical Concrete Columns

uniaxialMaterial PinchingLimitStateMaterial $matTag $nodeT $nodeB $driftAxis $Kelas $crvTyp $crvTag $eleTag $b $d $h $a $st $As $Acc $ld $db $rhot $f'c $fy $fyt
$matTag unique material object integer tag
$nodeT integer node tag to define the first node at the extreme end of the associated flexural frame member (L3 or D5 in Figure)
$nodeB integer node tag to define the last node at the extreme end of the associated flexural frame member (L2 or D2 in Figure)
$driftAxis 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 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 integer tag for the unique limit curve object associated with this material
$eleTag integer element tag to define the associated beam-column element used to extract axial load
$b floating point column width (inches)
$d floating point column depth (inches)
$h floating point column height (inches)
$a floating point shear span length (inches)
$st floating point transverse reinforcement spacing (inches) along column height
$As floating point total area (inches squared) of longitudinal steel bars in section
$Acc floating point gross confined concrete area (inches squared) bounded by the transverse reinforcement in column section
$ld floating point development length (inches) of longitudinal bars using ACI 318-11 Eq. 12-1 and Eq. 12-2
$db floating point diameter (inches) of longitudinal bars in column section
$rhot floating point transverse reinforcement ratio (Ast/st.db)
$f'c floating point concrete compressive strength (ksi)
$fy floating point longitudinal steel yield strength (ksi)
$fyt floating point transverse steel yield strength (ksi)

DESCRIPTION:


The material model coupled with the RotationShearCurve limit surface: 1) has the ability to continually monitor forces and deformations in the flexural elements for conditions that trigger lateral-strength degradation, 2) has a built-in function that compensates for flexural deformation offsets that arise from the degrading behavior of the material in shear springs, and 3) is able to trigger lateral-strength degradation through either a limiting lateral force or element deformations (whichever is reached first). The material introduces several functionalities that give users a high degree of control over the triggering of strength degradation and the ensuing cyclic degrading behavior. Damage algorithms are implemented to control the degrading behavior through elastic stiffness, reloading stiffness, and backbone strength degradation (Fig. 2). The rate of damage accumulation can be controlled by energy-, displacement-, and cycle-based damage computation algorithms.

During the degrading behavior, the model automatically adjusts reloading stiffness to achieve a symmetric global-element lateral load-vs lateral displacement behavior. The model does so by automatically adjusting the reloading stiffness and backbone curve of the material model to compensate for dissymmetry introduced by the unloading of the flexural elements in series with shear springs governed by the model.


DAMAGE:

Damage accumulations effects based on numbers of cycles can be introduced to reloading stiffness and backbone strength through the simple parameters $dmgRCyc and $dmgSCyc with values ranging from 0 to 1.

Elastic stiffness, reloading stiffness, and strength can be adjusted using the following energy and displacement damage model (from Mitra and Lowes (2007)):


EXAMPLE:

PinchingLimitStateMaterial Example


REFERENCES:

1. LeBorgne M. R., 2012, "Modeling the Post Shear Failure Behavior of Reinforced Concrete Columns." Austin, Texas: University of Texas at Austin, PhD, 301.

2. LeBorgne, M.R., Ghannoum, W.M., 2014, "Analytical Element for Simulating Lateral-Strength Degradation in Reinforced Concrete Columns and Other Frame Members," Journal of Structural Engineering, V. 140, No. 7, pp. 04014038 1-12.

3. LeBorgne, M.R., Ghannoum, W.M., 2014, "Calibrated Analytical Element for Lateral-Strength Degradation of Reinforced Concrete Columns," Engineering Structures, V. 81, pp. 35-48.

3. Ghannoum W. M., Moehle J. P., 2012, "Rotation-Based Shear Failure Model for Lightly Confined Reinforced Concrete Columns," Journal of Structural Engineering, V. 138, No. 10, 1267-78.

4. Mitra Nilanjan, Lowes Laura N., 2007, "Evaluation, Calibration, and Verification of a Reinforced Concrete Beam--Column Joint Model," Journal of Structural Engineering, V. 133, No. 1, 105-20.



Code Developed by: Matthew Leborgne and Wassim M. Ghannoum, University of Texas at Austin

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