User talk:Kkolozvari

Element MVLEM

The MVLEM element command is used to generate a two-dimensional Multiple-Vertical-Line-Element-Model (MVLEM; Vulcano et al., 1988; Orakcal et al., 2004) for simulation of flexure-dominated RC wall behavior. A single model element incorporates six global degrees of freedom, three of each located at the center of rigid top and bottom beams, as illustrated in Figure 1a. The axial/flexural response of the MVLEM is simulated by a series of uniaxial elements (or macro-fibers) connected to the rigid beams at the top and bottom (e.g., floor) levels, whereas the shear response is described by a shear spring located at height ch from the bottom of the wall element. Shear and flexural responses of the model element are uncoupled. The relative rotation between top and bottom faces of the wall element occurs about the point located on the central axis of the element at height ch (Figure 1b). Rotations and resulting transverse displacements are calculated based on the wall curvature, derived from section and material properties, corresponding to the bending moment at height ch of each element (Figure 1b). A value of c=0.4 was recommended by Vulcano et al. (1988) based on comparison of the model response with experimental results.

Source: /usr/local/cvs/OpenSees/SRC/element/MVLEM/

Figure 1. a) MVLEM Element, b) MVLEM Rotations and Displacements

---

Input Format:

Element MVLEM $eleTag $Dens $iNode $jNode $m $c -thick <Thicknesses> -width <Widths> -rho <Reinforcing_ratios> -matConcrete <Concrete_tags> -matSteel <Steel_tags> -matShear <Shear_tag>

$eleTag	Unique element object tag
$Dens	Wall density
$iNode $jNode	End node tags
$m	Number of element macro-fibers
$c	Location of center of rotation with from the iNode, c = 0.4 (recommended)
<Thicknesses>	Array of m macro-fiber thicknesses
<Widths>	Array of m macro-fiber widths
<Reinforcing_ratios>	Array of m reinforcing ratios corresponding to macro-fibers; for each fiber: rho,i = As,i/Agross,i (1 < i < m)
<Concrete _tags>	Array of m uniaxialMaterial tags for concrete
<Steel_tags>	Array of m uniaxialMaterial tags for steel
<Shear_tag>	Tag of uniaxialMaterial for shear material

---

Element Recorders:

The following recorders are available with the MVLEM element:

globalForce	Element global forces
Curvature	Element curvature
Shear_Force_Deformation	Element shear force-deformation relationship
Fiber_Strain	Vertical strain in m fibers along the cross-section
Fiber_Stress_Concrete	Vertical concrete stress in m fibers along the cross-section
Fiber_Stress_Steel	Vertical steel stress in m fibers along the cross-section

---

Examples:

Element MVLEM 1 0.0 1 2 8 0.4 -thick 4 4 4 4 4 4 4 4 -width 7.5 1.5 7.5 7.5 7.5 7.5 1.5 7.5 -rho 0.0293 0.0 0.0033 0.0033

0.0033 0.0033 0.0 0.0293 -matConcrete 3 4 4 4 4 4 4 3 -matSteel 1 2 2 2 2 2 2 1 -matShear 5

Recorder Element -file MVLEM_Fgl.out -time -ele 1 globalForce

Recorder Element -file MVLEM_FiberStrain.out -time -ele 1 Fiber_Strain

---

References:

Developed and Implemented by:

Kristijan Kolozvari, California State University Fullerton

Kutay Orakcal, Bogazici University, Istanbul

John Wallace, Univeristy of California, Los Angeles

1) Vulcano A., Bertero V.V., and Colotti V. (1988). “Analytical Modeling of RC Structural Walls”, Proceedings, 9th World Conference on Earthquake Engineering, V. 6, Tokyo-Kyoto, Japan, pp. 41-46.

2) Orakcal K., Conte J.P., and Wallace J.W. (2004). “Flexural Modeling of Reinforced Concrete Structural Walls - Model Attributes”, ACI Structural Journal, V. 101, No. 5, pp 688-698.

Element SFI_MVLEM

The SFI_MVLEM command is used to construct a Shear-Flexure Interaction Multiple-Vertical-Line-Element Model (SFI-MVLEM, Kolozvari et al., 2014a, b), which captures interaction between axial/flexural and shear behavior of RC structural walls and columns under cyclic loading. The SFI_MVLEM element (Figure 1) incorporates 2-D RC panel behavior described by the Fixed-Strut-Angle-Model (nDMaterial FSAM; Ulugtekin, 2010; Orakcal et al., 2012), into a 2-D macroscopic fiber-based model (MVLEM). The interaction between axial and shear behavior is captured at each RC panel (macro-fiber) level, which further incorporates interaction between shear and flexural behavior at the SFI_MVLEM element level.

Source: /usr/local/cvs/OpenSees/SRC/element/SFI_MVLEM/

Figure 1. a) SFI_MVLEM Element, b) RC Panel Element (nDMaterial FSAM)

---

Input Format:

Element SFI_MVLEM $eleTag $iNode $jNode $m $c -thick <Thicknesses> -width <Widths> -mat <Material_tags>

$eleTag	Unique element object tag
$iNode $jNode	End node tags
$m	Number of element macro-fibers
$c	Location of center of rotation with from the iNode, c = 0.4 (recommended)
<Thicknesses>	Array of m macro-fiber thicknesses
<Widths>	Array of m macro-fiber widths
<Material_tags>	Array of m macro-fiber nDMaterial tags

---

Element Recorders:

The following recorders are available with the SFI_MVLEM element:

globalForce	Element global forces
Curvature	Element curvature
ShearDef	Element shear deformation
RCPanel $fibTag $Response	Returns RC panel (macro-fiber) $Response for a $fibTag-th panel (1 ≤ fibTag ≤ m). For available $Response-s refer to nDMaterial FSAM (LINK).

---

Examples:

Element SFI_MVLEM 1 1 2 5 0.4 -thick 6 6 6 6 6 -width 9 10 10 10 9 -mat 7 6 6 6 7

Recorder Element -file SFI_MVLEM_Fgl.out -time -ele 1 2 3 globalForce

Recorder Element -file SFI_MVLEM_panel_strain.out -time -ele 1 RCPanel 1 panel_strain

---

References:

Developed and Implemented by:

Kristijan Kolozvari, California State University Fullerton

Kutay Orakcal, Bogazici University, Istanbul

John Wallace, Univeristy of California, Los Angeles

1) Kolozvari K., Orakcal K., and Wallace J. W. (2015). ”Modeling of Cyclic Shear-Flexure Interaction in Reinforced Concrete Structural Walls. I: Theory”, ASCE Journal of Structural Engineering, 141(5), 04014135 doi

2) Kolozvari K., Tran T., Orakcal K., and Wallace, J.W. (2015). ”Modeling of Cyclic Shear-Flexure Interaction in Reinforced Concrete Structural Walls. II: Experimental Validation”, ASCE Journal of Structural Engineering, 141(5), 04014136 doi

3) Kolozvari K. (2013). “Analytical Modeling of Cyclic Shear-Flexure Interaction in Reinforced Concrete Structural Walls”, PhD Dissertation, University of California, Los Angeles.

uniaxialMaterial SteelMPF

This command is used to construct a uniaxialMaterial SteelMPF, which represents the well-known uniaxial constitutive nonlinear hysteretic material model for steel proposed by Menegotto and Pinto (1973), and extended by Filippou et al. (1983) to include isotropic strain hardening effects. The relationship is in the form of curved transitions (Figure 1), each from a straight-line asymptote with slope E0 (modulus of elasticity) to another straight-line asymptote with slope E1 = bE0 (yield modulus) where b is the strain hardening ratio. The curvature of the transition curve between the two asymptotes is governed by a cyclic curvature parameter R, which permits the Bauschinger effect to be represented, and is dependent on the absolute strain difference between the current asymptote intersection point and the previous maximum or minimum strain reversal point depending on whether the current strain is increasing or decreasing, respectively. The strain and stress pairs (<math>\epsilon</math>_r,<math>\sigma</math>_r) and (<math>\epsilon</math>₀,<math>\sigma</math>₀) shown on Figure 1 are updated after each strain reversal.

Source: /usr/local/cvs/OpenSees/SRC/material/uniaxial/

Figure 1. Constitutive Model for Steel (Menegotto and Pinto, 1973)

---

Input Format:

uniaxialMaterial SteelMPF $mattag $fyp $fyn $E0 $bp $bn $R0 $a1 $a2 <$a3 $a4>

$mattag	Unique nDMaterial tag
$fyp	Yield strength in tension (positive loading direction)
$$fyn	Yield strength in compression (negative loading direction)
$E0	Initial tangent modulus
$bp	Strain hardening ratio in tension (positive loading direction)
$bn	Strain hardening ratio in compression ( negative loading direction)
$R0	Initial value of the curvature parameter R (R0 = 20 recommended)
$a1	Curvature degradation parameter (a1 = 18.5 recommended)
$a2	Curvature degradation parameter (a2 = 0.15 or 0.0015 recommended)
$a3	Isotropic hardening parameter (optional, default = 0.01)
$a4	Isotropic hardening parameter (optional, default = 7.0)

---

Example:

uniaxialMaterial SteelMPF 1 60 60 29000 0.02 0.02 20.0 18.5 0.15

---

Discussion:

Although the Menegotto-Pinto model is already available in OpenSees (e.g., Steel02), the formulation of SteelMPF brings several distinctive features compared to existing models. For example, the model allows definition of different yield stress values and strain hardening ratios for tension and compression, and it considers degradation of cyclic curvature parameter R for strain reversals in both pre- and post- yielding regions, which could produce more accurate predictions of yield capacity for some RC wall specimens (see Example 1), whereas Steel02 considers the degradation in post-yielding region only. Strain-stress relationships obtained using SteelMPF and Steel02 are compared in Figure 2 for a strain history that includes strain reversals at strain values equal to one-half of the yield strain (e.i., <math>\epsilon</math>_r = ±0.001 = <math>\epsilon</math>_y/2). The model also allows calibration of isotropic hardening parameters through optional input variables a3 and a4, and uses default values of a3 = 0.01 and a4 = 7.0 as calibrated by Filippou et al. (1983) based on test results. To disregard isotropic strain hardening behavior in SteelMPF, parameter a3 needs to be assigned a zero value (a3 = 0.0).

Figure 2. Comparison of Steel02 and SteelMPF

---

References:

Developed and Implemented by:

Kristijan Kolozvari, California State University Fullerton

Kutay Orakcal, Bogazici University, Istanbul

John Wallace, Univeristy of California, Los Angeles

1) Menegotto, M., and Pinto, P.E. (1973). Method of analysis of cyclically loaded RC plane frames including changes in geometry and non-elastic behavior of elements under normal force and bending. Preliminary Report IABSE, vol 13.

2) Filippou F.C., Popov, E.P., and Bertero, V.V. (1983). "Effects of Bond Deterioration on Hysteretic Behavior of Reinforced Concrete Joints". Report EERC 83-19, Earthquake Engineering Research Center, University of California, Berkeley.

uniaxialMaterial ConcreteCM

This command is used to construct a uniaxialMaterial ConcreteCM, which is a uniaxial hysteretic constitutive model for concrete developed by Chang and Mander (1994). This model is a refined, rule-based, generalized, and non-dimensional constitutive model that allows calibration of the monotonic and hysteretic material modeling parameters, and can simulate the hysteretic behavior of confined and unconfined, ordinary and high-strength concrete, in both cyclic compression and tension (Figure 1). The model addresses important behavioral features, such as continuous hysteretic behavior under cyclic compression and tension, progressive stiffness degradation associated with smooth unloading and reloading curves at increasing strain values, and gradual crack closure effects. Details of the model are available in the report by Chang and Mander (1994). Note that ConcreteCM incorporates the unloading/reloading rules defined originally by Chang and Mander (1994), as opposed to Concrete07, which adopts simplified hysteretic rules.

Figure 1. Hysteretic Constitutive Model for Concrete by Chang and Mander (1994)

The Chang and Mander (1994) model successfully generates continuous hysteretic stress-strain relationships with slope continuity for confined and unconfined concrete in both compression and tension. The compression envelope curve of the model is defined by the initial tangent slope, (Ec), the peak coordinate (epcc, fpcc), a parameter (rc) from Tsai’s (1988) equation defining the shape of the envelope curve, and a parameter (xcrn) to define normalized (with respect to epcc) strain where the envelope curve starts following a straight line, until zero compressive stress is reached at the spalling strain, sp. These parameters can be controlled based on specific experimental results for a refined calibration of the compression envelope (Figure 2). Chang and Mander (1994) proposed empirical relationships for parameters Ec, epcc, and rc for unconfined concrete with compressive strength fpcc, based on review of previous research. Parameters fpcc, epcc, Ec, rc, and xcrn can also be calibrated to represent the stress-strain behavior of confined concrete in compression, to follow the constitutive relationships for confined concrete proposed by Mander et al (1988) or similar.

Figure 2. Compression and Tension Envelope Curves

The shape of the tension envelope curve in the model is the same as that of the compression envelope; however, the tension envelope curve is shifted to a new origin that is based on the unloading strain from the compression envelope (Figure 2). As well, the strain ductility experienced previously on the compression envelope is also reflected on the tension envelope. The parameters associated with the tension envelope curve include the tensile strength of concrete (ft), the monotonic strain at tensile strength (et), a parameter (rt) from Tsai’s (1988) equation defining the shape of the tension envelope curve, and a parameter (xcrp) to define normalized (with respect to et) strain where the tension envelope curve starts following a straight line, until zero tensile stress is reached at a strain of crk. These parameters can also be controlled and calibrated based on specific experimental results or empirical relations proposed by other researchers (e.g., Belarbi and Hsu, 1994) to model the behavior of concrete in tension and the tension stiffening phenomenon. Concrete experiencing tension stiffening can be considered not to crack completely; that is, a large value for parameter xcrp (e.g., 10000) can be defined.

Source: /usr/local/cvs/OpenSees/SRC/material/uniaxial/

---

Input Format:

uniaxialMaterial ConcreteCM $mattag $fpcc $epcc $Ec $rc $xcrn $ft $et $rt $xcrp <-GapClose $gap>

$mattag	Unique uniaxialMaterial tag
$fpcc	Compressive strength
$epcc	Strain at compressive strength
$Ec	Initial tangent modulus
$rc	Shape parameter in Tsai’s equation defined for compression
$xcrn	Non-dimensional critical strain on compression envelope (where the envelope curve starts following a straight line)
$ft	Tensile strength
$rt	Shape parameter in Tsai’s equation defined for tension
$xcrp	Non-dimensional critical strain on tension envelope (where the envelope curve starts following a straight line – large value [e.g., 10000] recommended when tension stiffening is considered)
<-GapClose $gap>	gap = 0, less gradual gap closure (default); gap = 1, more gradual gap closure

---

Example:

uniaxialMaterial ConcreteCM 1 -6.2 -0.0021 4500 7 1.035 0.30 0.00008 1.2 10000

Example of hysteretic stress–strain history generated by the model code is illustrated in Figure 2.

Figure 2. Concrete Stress-Strain Behavior

---

Discussion:

An optional input parameter gap is introduced in the ConcreteCM model implemented in OpenSees for providing the users with the opportunity to control the intensity of gap closure in the stress-strain behavior of concrete, which in-turn influences the level of pinching in the lateral load-displacement behavior of a RC wall. The original Chang and Mander (1994) model adopts a non-zero tangent stiffness at zero stress level upon unloading from the tension envelope, which is represented by gap = 1 in ConcreteCM. Using gap = 0 (default) produces less gradual gap closure, since it assumes zero tangent stiffness at zero stress level upon unloading from the tension envelope, and is suitable for most analyses. Example 1 compares flexural response predictions of a slender wall obtained using more gradual (gap = 1) and less gradual (gap = 0) gap closure behavior, to illustrate the impact of this parameter on the analytical results.

File:ConcreteCM 2.png

Figure 3. Comparison of Steel02 and SteelMPF

---

References:

Developed and Implemented by:

Kristijan Kolozvari, California State University Fullerton

Kutay Orakcal, Bogazici University, Istanbul

John Wallace, Univeristy of California, Los Angeles

1) Menegotto, M., and Pinto, P.E. (1973). Method of analysis of cyclically loaded RC plane frames including changes in geometry and non-elastic behavior of elements under normal force and bending. Preliminary Report IABSE, vol 13.

2) Filippou F.C., Popov, E.P., and Bertero, V.V. (1983). "Effects of Bond Deterioration on Hysteretic Behavior of Reinforced Concrete Joints". Report EERC 83-19, Earthquake Engineering Research Center, University of California, Berkeley.