FSAM - 2D RC Panel Constitutive Behavior

Developed and Implemented by:

Kristijan Kolozvari , California State University, Fullerton

Kutay Orakcal<span style=“color:black”>, Bogazici University, Istanbul, Turkey

Leonardo Massone<span style=“color:black”>, University of Chile, Santiago

John Wallace<span style=“color:black”>, Univeristy of California, Los Angeles

This command is used to construct a nDMaterial FSAM (Fixed-Strut-Angle-Model, Figure 1, Kolozvari et al., 2015), which is a plane-stress constitutive model for simulating the behavior of RC panel elements under generalized, in-plane, reversed-cyclic loading conditions (Ulugtekin, 2010; Orakcal et al., 2012). In the FSAM constitutive model, the strain fields acting on concrete and reinforcing steel components of a RC panel are assumed to be equal to each other, implying perfect bond assumption between concrete and reinforcing steel bars. While the reinforcing steel bars develop uniaxial stresses under strains in their longitudinal direction, the behavior of concrete is defined using stress-strain relationships in biaxial directions, the orientation of which is governed by the state of cracking in concrete. Although the concrete stress-strain relationship used in the FSAM is fundamentally uniaxial in nature, it also incorporates biaxial softening effects including compression softening and biaxial damage. For transfer of shear stresses across the cracks, a friction-based elasto-plastic shear aggregate interlock model is adopted, together with a linear elastic model for representing dowel action on the reinforcing steel bars (Kolozvari, 2013). Note that FSAM constitutive model is implemented to be used with Shear-Flexure Interaction model for RC walls (SFI_MVLEM), but it could be also used elsewhere.

Source: /usr/local/cvs/OpenSees/SRC/material/nD/reinforcedConcretePlaneStress/

Figure 1. FSAM for Converting In-Plane Strains to In-Plane Smeared Stresses on a RC Panel Element

Input Format:

nDMaterial FSAM $mattag $rho $sX $sY $conc $rouX $rouY
        $nu $alfadow
mattag

Unique nDMaterial tag

rho

Material density

sX

Tag of uniaxialMaterial simulating horizontal (x) reinforcement

sY

Tag of uniaxialMaterial simulating vertical (y) reinforcement

conc

Tag of uniaxialMaterial<sup class=“superscript”>1</sup> simulating concrete

rouX

Reinforcing ratio in horizontal (x) direction (rouX = A<sub class=“subscript”>s,x</sub>/A<sub class=“subscript”>gross,x</sub>)

rouY

Reinforcing ratio in vertical (y) direction (rouY = A<sub class=“subscript”>s,y</sub>/A<sub class=“subscript”>gross,y</sub>)

nu

Concrete friction coefficient (0.0 < nu < 1.5)

alfadow

Stiffness coefficient of reinforcement dowel action (0.0 < alfadow < 0.05)

<sup class=“superscript”>1</sup>nDMaterial FSAM shall be used with uniaxialMaterial ConcreteCM

Recommended values for parameter of a shear resisting mechanism (nu and alfadow, Figure 2) are provided above. Details about the sensitivity of analytical predictions using SFI_MVLEM element to changes in these parameters are presented by Kolozvari (2013).


Material Recorders:

The following output is available from the FSAM RC panel model:

panel_strain

Strains ε<sub class=“subscript”>x</sub>, ε<sub class=“subscript”>y</sub>, &gamma;<sub class=“subscript”>xy</sub> (Figure 1)

panel_stress

Resulting panel stresses σ<sub class=“subscript”>x</sub>, σ<sub class=“subscript”>y</sub>, &tau;<sub class=“subscript”>xy</sub> (concrete and steel, Figure 1)

panel_stress_concrete

Resulting panel concrete stresses σ<sub class=“subscript”>xc</sub>, σ<sub class=“subscript”>yc</sub>, &tau;<sub class=“subscript”>xyc</sub> (Figure 2b)

panel_stress_steel

Resulting panel steel stresses σ<sub class=“subscript”>xs</sub>, σ<sub class=“subscript”>ys</sub>, &tau;<sub class=“subscript”>xys</sub> (Figure 2e)

strain_stress_steelX

Uniaxial strain and stress of horizontal reinforcement ε<sub class=“subscript”>x</sub>, σ<sub class=“subscript”>xxs</sub> (Figure 2f)

strain_stress_steelY

Uniaxial strain and stress of vertical reinforcement ε<sub class=“subscript”>y</sub>, σ<sub class=“subscript”>yys</sub> (Figure 2f)

strain_stress_concrete1

Uniaxial strain and stress of concrete strut 1 ε<sub class=“subscript”>c1</sub>, σ<sub class=“subscript”>c1</sub> (Figure 2c)

strain_stress_concrete2

Uniaxial strain and stress of concrete strut 2 ε<sub class=“subscript”>c2</sub>, σ<sub class=“subscript”>c2</sub> (Figure 2c)

strain_stress_interlock1

Shear strain and stress in concrete along crack 1 ε<sub class=“subscript”>cr1</sub>, &tau;<sub class=“subscript”>cr1</sub> (Figure 2d)

strain_stress_interlock2

Shear strain and stress in concrete along crack 2 ε<sub class=“subscript”>cr2</sub>, &tau;<sub class=“subscript”>cr2</sub> (Figure 2d)

cracking_angles

Orientation of concrete cracks

Note that recorders for a RC panel (marco-fiber) are invoked as SFI_MVLEM element recorders using command RCPanel and one of the desired commands listed above. Currently, it is possible to output values only for one macro-fiber within one or multiple elements.


Example:

nDMaterial FSAM 1 0.0 1 2 4 0.0073 0.0606 0.1 0.01

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

Figure 2. Behavior and Input/Output Parameters of the FSAM Constitutive Model

References:

  1. Kolozvari K., Orakcal K., and Wallace J. W. (2015). “Shear-Flexure Interaction Modeling of reinforced Concrete Structural Walls and Columns under Reversed Cyclic Loading”, Pacific Earthquake Engineering Research Center, University of California, Berkeley, PEER Report No. 2015/12

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

      1. Orakcal K., Massone L.M., and Ulugtekin D. (2012). “Constitutive Modeling of Reinforced Concrete Panel Behavior under Cyclic Loading”, Proceedings, 15th World Conference on Earthquake Engineering, Lisbon, Portugal.

        1. Ulugtekin D. (2010). “Analytical Modeling of Reinforced Concrete Panel Elements under Reversed Cyclic Loadings”, M.S. Thesis, Bogazici University, Istanbul, Turkey.

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