RotationShearCurve: Difference between revisions

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This command is used to construct a limit surface that defines the ultimate rotation of a plastic hinge that triggers lateral-strength degradation in PinchingLimitStateMaterial
This command is used to construct a limit surface that defines the ultimate deformation between two nodes and/or the ultimate force that trigger lateral-strength degradation in the [[Pinching Limit State Material]].
The curve can be used in two modes: 1) direct input mode where all parameters are input; and 2) calibrated mode where only key properties for a shear-critical reinforced concrete column are input for model to fully define parameters.
The curve can be used in two modes: 1) direct input mode, where all 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.
Note: when both strength and rotation limits are used. Lateral-strength degradation is triggered in the material model when the first limit is reached.
Note: when both strength and rotation limits are used. Lateral-strength degradation is triggered in the material model when the first limit is reached.
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.




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{|  
{|  
| style="background:yellow; color:black; width:800px" | '''uniaxialMaterial PinchingLimitStateMaterial $matTag $nodeT $nodeB $driftAxis $Kelas $crvTyp $crvTag '''
| style="background:yellow; color:black; width:800px" | '''limitCurve RotationShearCurve $crvTag $eleTag $ndI $ndJ $rotAxis $Vn $Vr $Kdeg $rotLim'''
'''$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'''
|}
|}


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{|
{|
|  style="width:150px" | '''$matTag ''' || unique material object integer tag
|  style="width:150px" | '''$crvTag ''' || unique limit curve object integer tag
|-
|-
|  '''$nodeT''' || integer node tag to define the first node at the extreme end of the associated flexural frame member (L3 or D5 in Figure)
|  '''$eleTag''' || integer element tag to define the associated beam-column element used to extract axial load
|-
|-
|  '''$nodeB''' || integer node tag to define the last node at the extreme end of the associated flexural frame member (L2 or D2 in Figure)
|  '''$ndI''' || integer node tag to define the node at the extreme end of the frame member bounding the plastic hinge (L1 or D1 for bottom spring and L4 or D6 for top spring 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 $rotAxis in Rotation Shear Curve definition)
|  '''$ndJ''' ||integer node tag to define the node bounding the plastic hinge (L2 or D3 for bottom spring and L3 or D4 for top spring in Figure)
driftAxis = 1 – Drift along the x-axis
driftAxis = 2 – Drift along the y-axis
driftAxis = 3 – Drift along the z-axis
|-
|-
|  '''$Kelas''' || floating point value to define the initial material elastic stiffness (Kelastic); Kelas > 0
|  '''$rotAxis''' || integer to indicate axis of measured rotation when triggering lateral-strength degradation
|-
|-
| '''$crvTyp''' || integer flag to indicate the type of limit curve associated with this material.
|   || rotAxis = 3 – Rotation about z-axis – 2D
crvTyp = 0 – No limit curve
 
crvTyp = 1 – axial limit curve
rotAxis = 4 – Rotation about x-axis – 3D
crvTyp = 2 – [[RotationShearCurve]]
 
rotAxis = 5 – Rotation about y-axis – 3D
 
rotAxis = 6 – Rotation about z-axis – 3D
|-
|-
|  '''$crvTag''' || integer tag for the unique limit curve object associated with this material
|  '''$Vn''' || floating point value to define the ultimate strength in material model
|-
|-
| '''$YpinchUPN''' || floating point unloading force pinching factor for loading in the negative direction
|   || Vn = -1 – strength limit is not used.
Note: This value must be between zero and unity
Vn > 0 – strength limit is the input value
|-
|-
|  '''$YpinchRPN''' || floating point reloading force pinching factor for loading in the negative direction
|  '''$Vr''' || floating point value to define the backbone residual strength
Note: This value must be between negative one and unity
|-
|-
| '''$XpinchRPN''' || floating point reloading displacement pinching factor for loading in the negative direction
|   || Vr = -1 – Residual strength = 0.2*(max. force in material model at initiation of degradation)
Note: This value must be between negative one and unity
-1 < Vr < 0 – Residual shear strength = Vr*(max. force in material model at initiation of degradation)
|-
 
|  '''$YpinchUNP''' || floating point unloading force pinching factor for loading in the positive direction
Vr > 0 – Residual strength is the input value
Note: This value must be between zero and unity
|-
|  '''$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 $dmgSLim to zero if reloading strength damage is not required
|  '''$Kdeg''' || floating point value to define the backbone degrading slope of the material model.  
|-
|-
| '''$dmgE1 $dmgE2 $dmgE3 $dmgE4''' || floating point elastic stiffness damage factors ''α1,α2,α3,α4'' shown in Eq. 1
|   || Note: the degrading slope must be less than zero.
|-
|-
|  '''$dmgELim''' || floating point elastic stiffness damage limit ''Dlim'' shown in Eq. 1; Note: This value must be between zero and unity
|  '''$rotLim''' || floating point value to limit the rotational capacity across the plastic hinge (difference between $ndI and $ndJ in absolute value). When this value (radians) is exceeded during the analysis degrading behavior is triggered in the material model.  
|-
|  '''$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''' ==
== '''MODE 2: Calibrated Model for Shear-Critical Concrete Columns''' ==
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{|  
{|  
| 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="background:yellow; color:black; width:800px" | '''limitCurve RotationShearCurve $crvTag $eleTag $ndI $ndJ $rotAxis $Vn $Vr $Kdeg $defType $b $d $h $L $st $As $Acc $ld $db $rhot $f'c $fy $fyt $delta'''
|}
|}


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{|
{|
|  style="width:150px" | '''$matTag ''' || unique material object integer tag
|  style="width:150px" | '''$crvTag''' || unique limit curve object integer tag
|-
|-
|  '''$nodeT''' || integer node tag to define the first node at the extreme end of the associated flexural frame member (L3 or D5 in Figure)
|  '''$eleTag''' || integer element tag to define the associated beam-column element used to extract axial load
|-
|-
|  '''$nodeB''' || integer node tag to define the last node at the extreme end of the associated flexural frame member (L2 or D2 in Figure)
|  '''$ndI''' || integer node tag to define the node at one end of the region for which limiting rotations are defined (see $defType)  
|-
|-
|  '''$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 $rotAxis in Rotation Shear Curve definition)
|  '''$ndJ''' || integer node tag to define the node at the other end of the region for which limiting rotations are defined (see $defType)
driftAxis = 1 – Drift along the x-axis
driftAxis = 2 – Drift along the y-axis
driftAxis = 3 – Drift along the z-axis
|-
|-
|  '''$Kelas''' || floating point value to define the shear stiffness (Kelastic) of the shear spring prior to shear failure
|  '''$rotAxis''' || integer to indicate axis of measured rotation when triggering lateral-strength degradation.
|-
|  || rotAxis = 3 – Rotation about z-axis – 2D


Kelas = -4 – Shear stiffness calculated assuming double curvature and shear springs at both column element ends
rotAxis = 4 – Rotation about x-axis – 3D
 
rotAxis = 5 – Rotation about y-axis – 3D
 
rotAxis = 6 – Rotation about z-axis – 3D
|-
|  '''$Vn''' || floating point value to define the nominal shear strength
|-
|  || Vn = -1 – Shear strength limit is not used


Kelas = -3 – Shear stiffness calculated assuming double curvature and a shear spring at one column element end
Vn = 0 – Shear strength limit is calculated using ASCE 41-06 Eq. 6-4


Kelas = -2 – Shear stiffness calculated assuming single curvature and shear springs at both column element ends
Vn > 0 – Shear strength limit is the input value


Kelas = -1 – Shear stiffness calculated assuming single curvature and a shear spring at one column element end
Note: Shear capacity calculated according to ASCE 41 only gives the capacity with the k factor equal to 1 (i.e., shear capacity at small deformations)
|-
|  '''$Vr''' || floating point value to define the backbone residual shear strength
|-
|  || Vr = -1 – Residual shear strength = 0.2*( max. force in material model at initiation of degradation)


Kelas > 0 – Shear stiffness is the input value
-1 < Vr < 0 – Residual shear strength = Vr*( max. force in material model at initiation of degradation)


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)
Vr > 0 – Residual shear strength is the input value
|-
|  '''$Kdeg''' || floating point value to define the backbone degrading slope.
|-
|  || Kdeg = 0 – Degrading slope calculated by calibrated regression model.
Kdeg < 0 – Degrading slope is the input value
|-
|-
|  '''$crvTag''' || integer tag for the unique limit curve object associated with this material
|  '''$defType''' || integer flag to define which rotation-based shear failure model is used
|-
|-
|  '''$eleTag''' || integer element tag to define the associated beam-column element used to extract axial load
|   ||
 
1 – Flexure-Shear capacity based on θ_f rotation capacity (Eq. 4.4; Leborgne 2012)
For this case select $ndI=D1 or L1 and $ndJ=D3 or L2 for the bottom spring in Fig. 1
 
2 – Flexure-Shear capacity based on θ_total rotation capacity (Ghannoum and Moehle 2012)
For this case select $ndI=D1 or L1 and $ndJ=D3 or L2 for the bottom spring in Fig. 1
 
3 – Flexure-Shear capacity based on θflexural rotation capacity (Ghannoum and Moehle 2012)
For this case select $ndI=D2 and $ndJ=D3 for the bottom spring in Fig. 1
 
4 – Flexure-Shear capacity based on θ_total-plastic rotation capacity (Ghannoum and Moehle 2012)
For this case select $ndI=L1 and $ndJ=L2 for the bottom spring in Fig. 1
 
5 – Flexure-Shear capacity based on θ_flexural-plastic rotation capacity (Ghannoum and Moehle 2012)
This is a special case not shown in Fig. 1 where column flexural plastic deformations are simulated separately from bar-slip induced plastic rotations in a lumped-plasticity model
|-
|-
|  '''$b''' || floating point column width (inches)
|  '''$b''' || floating point column width (inches)
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|  '''$h''' || floating point column height (inches)
|  '''$h''' || floating point column height (inches)
|-
|-
|  '''$a''' || floating point shear span length (inches)
|  '''$L''' || floating point column clear span length (inches)
|-
|-
|  '''$st''' || floating point transverse reinforcement spacing (inches) along column height
|  '''$st''' || floating point transverse reinforcement spacing (inches) along column height
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|-
|-
|  '''$fyt''' || floating point transverse steel yield strength (ksi)
|  '''$fyt''' || floating point transverse steel yield strength (ksi)
|-
|  '''$delta''' || floating point offset (radians) added to shear failure models to adjust shear failure location.
|-
|  || Note: This value should remain at zero to use the model as per calibration
|}
|}


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[[Image:PinchingLimitStateMaterial1-2.jpg]]
[[Image:PinchingLimitStateMaterial1-2.jpg]]
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)):
[[Image:PinchingLimitStateMaterialEq1.png|350px]]




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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.


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: <span style="color:blue"> Matthew Leborgne and Wassim M. Ghannoum, University of Texas at Austin</span>
 

Latest revision as of 20:59, 23 April 2014




This command is used to construct a limit surface that defines the ultimate deformation between two nodes and/or the ultimate force that trigger lateral-strength degradation in the Pinching Limit State Material. The curve can be used in two modes: 1) direct input mode, where all 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. Note: when both strength and rotation limits are used. Lateral-strength degradation is triggered in the material model when the first limit is reached.


MODE 1: Direct Input

limitCurve RotationShearCurve $crvTag $eleTag $ndI $ndJ $rotAxis $Vn $Vr $Kdeg $rotLim
$crvTag unique limit curve object integer tag
$eleTag integer element tag to define the associated beam-column element used to extract axial load
$ndI integer node tag to define the node at the extreme end of the frame member bounding the plastic hinge (L1 or D1 for bottom spring and L4 or D6 for top spring in Figure)
$ndJ integer node tag to define the node bounding the plastic hinge (L2 or D3 for bottom spring and L3 or D4 for top spring in Figure)
$rotAxis integer to indicate axis of measured rotation when triggering lateral-strength degradation
rotAxis = 3 – Rotation about z-axis – 2D

rotAxis = 4 – Rotation about x-axis – 3D

rotAxis = 5 – Rotation about y-axis – 3D

rotAxis = 6 – Rotation about z-axis – 3D

$Vn floating point value to define the ultimate strength in material model
Vn = -1 – strength limit is not used.

Vn > 0 – strength limit is the input value

$Vr floating point value to define the backbone residual strength
Vr = -1 – Residual strength = 0.2*(max. force in material model at initiation of degradation)

-1 < Vr < 0 – Residual shear strength = Vr*(max. force in material model at initiation of degradation)

Vr > 0 – Residual strength is the input value

$Kdeg floating point value to define the backbone degrading slope of the material model.
Note: the degrading slope must be less than zero.
$rotLim floating point value to limit the rotational capacity across the plastic hinge (difference between $ndI and $ndJ in absolute value). When this value (radians) is exceeded during the analysis degrading behavior is triggered in the material model.

MODE 2: Calibrated Model for Shear-Critical Concrete Columns

limitCurve RotationShearCurve $crvTag $eleTag $ndI $ndJ $rotAxis $Vn $Vr $Kdeg $defType $b $d $h $L $st $As $Acc $ld $db $rhot $f'c $fy $fyt $delta
$crvTag unique limit curve object integer tag
$eleTag integer element tag to define the associated beam-column element used to extract axial load
$ndI integer node tag to define the node at one end of the region for which limiting rotations are defined (see $defType)
$ndJ integer node tag to define the node at the other end of the region for which limiting rotations are defined (see $defType)
$rotAxis integer to indicate axis of measured rotation when triggering lateral-strength degradation.
rotAxis = 3 – Rotation about z-axis – 2D

rotAxis = 4 – Rotation about x-axis – 3D

rotAxis = 5 – Rotation about y-axis – 3D

rotAxis = 6 – Rotation about z-axis – 3D

$Vn floating point value to define the nominal shear strength
Vn = -1 – Shear strength limit is not used

Vn = 0 – Shear strength limit is calculated using ASCE 41-06 Eq. 6-4

Vn > 0 – Shear strength limit is the input value

Note: Shear capacity calculated according to ASCE 41 only gives the capacity with the k factor equal to 1 (i.e., shear capacity at small deformations)

$Vr floating point value to define the backbone residual shear strength
Vr = -1 – Residual shear strength = 0.2*( max. force in material model at initiation of degradation)

-1 < Vr < 0 – Residual shear strength = Vr*( max. force in material model at initiation of degradation)

Vr > 0 – Residual shear strength is the input value

$Kdeg floating point value to define the backbone degrading slope.
Kdeg = 0 – Degrading slope calculated by calibrated regression model.

Kdeg < 0 – Degrading slope is the input value

$defType integer flag to define which rotation-based shear failure model is used

1 – Flexure-Shear capacity based on θ_f rotation capacity (Eq. 4.4; Leborgne 2012) 

	For this case select $ndI=D1 or L1 and $ndJ=D3 or L2 for the bottom spring in Fig. 1

2 – Flexure-Shear capacity based on θ_total rotation capacity (Ghannoum and Moehle 2012) 

	For this case select $ndI=D1 or L1 and $ndJ=D3 or L2 for the bottom spring in Fig. 1

3 – Flexure-Shear capacity based on θflexural rotation capacity (Ghannoum and Moehle 2012) 

	For this case select $ndI=D2 and $ndJ=D3 for the bottom spring in Fig. 1

4 – Flexure-Shear capacity based on θ_total-plastic rotation capacity (Ghannoum and Moehle 2012) 

	For this case select $ndI=L1 and $ndJ=L2 for the bottom spring in Fig. 1

5 – Flexure-Shear capacity based on θ_flexural-plastic rotation capacity (Ghannoum and Moehle 2012) 

	This is a special case not shown in Fig. 1 where column flexural plastic deformations are simulated separately from bar-slip induced plastic rotations in a lumped-plasticity model
$b floating point column width (inches)
$d floating point column depth (inches)
$h floating point column height (inches)
$L floating point column clear 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)
$delta floating point offset (radians) added to shear failure models to adjust shear failure location.
Note: This value should remain at zero to use the model as per calibration

DESCRIPTION:


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., 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

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.


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

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