FSAM - 2D RC Panel Constitutive Behavior

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Developed and Implemented by:

Kristijan Kolozvari, California State University, Fullerton

Kutay Orakcal, Bogazici University, Istanbul, Turkey

Leonardo Massone, University of Chile, Santiago

John Wallace, 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 uniaxialMaterial1 simulating concrete
$rouX Reinforcing ratio in horizontal (x) direction (rouX = As,x/Agross,x)
$rouY Reinforcing ratio in vertical (y) direction (rouY = As,y/Agross,y)
$nu Concrete friction coefficient (0.0 < nu < 1.5)
$alfadow Stiffness coefficient of reinforcement dowel action (0.0 < alfadow < 0.05)

1nDMaterial 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 εx, εy, γxy (Figure 1)
panel_stress Resulting panel stresses σx, σy, τxy (concrete and steel, Figure 1)
panel_stress_concrete Resulting panel concrete stresses σxc, σyc, τxyc (Figure 2b)
panel_stress_steel Resulting panel steel stresses σxs, σys, τxys (Figure 2e)
strain_stress_steelX Uniaxial strain and stress of horizontal reinforcement εx, σxxs (Figure 2f)
strain_stress_steelY Uniaxial strain and stress of vertical reinforcement εy, σyys (Figure 2f)
strain_stress_concrete1 Uniaxial strain and stress of concrete strut 1 εc1, σc1 (Figure 2c)
strain_stress_concrete2 Uniaxial strain and stress of concrete strut 2 εc2, σc2 (Figure 2c)
strain_stress_interlock1 Shear strain and stress in concrete along crack 1 εcr1, τcr1 (Figure 2d)
strain_stress_interlock2 Shear strain and stress in concrete along crack 2 εcr2, τcr2 (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.


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


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

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

3) 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.

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