ModIMKPinching

This command is used to construct a ModIMKPinching material. This material simulates the modified Ibarra-Medina-Krawinkler deterioration model with pinching hysteretic response. NOTE: before you use this material make sure that you have downloaded the latest OpenSees version. A youtube video presents a summary of this model including the way to be used within openSees (http://youtu.be/YHBHQ-xuybE).

uniaxialMaterial ModIMKPinching $matTag $K0 $as_Plus
        $as_Neg $My_Plus $My_Neg $FprPos $FprNeg $A_pinch $Lamda_S $Lamda_C
        $Lamda_A $Lamda_K $c_S $c_C $c_A $c_K $theta_p_Plus $theta_p_Neg
        $theta_pc_Plus $theta_pc_Neg $Res_Pos $Res_Neg $theta_u_Plus
        $theta_u_Neg $D_Plus $D_Neg

matTag

integer tag identifying material

K0

elastic stiffness

as_Plus

strain hardening ratio for positive loading direction

as_Neg

strain hardening ratio for negative loading direction

My_Plus

effective yield strength for positive loading direction

My_Neg

effective yield strength for negative loading direction (Must be defined as a negative value)

FprPos

Ratio of the force at which reloading begins to force corresponding to the maximum historic deformation demand (positive loading direction)

FprNeg

Ratio of the force at which reloading begins to force corresponding to the absolute maximum historic deformation demand (negative loading direction)

A_Pinch

Ratio of reloading stiffness

Lamda_S

Cyclic deterioration parameter for strength deterioration [E_t=Lamda_S*M_y, see Lignos and Krawinkler (2011); set Lamda_S = 0 to disable this mode of deterioration]

Lamda_C

Cyclic deterioration parameter for post-capping strength deterioration [E_t=Lamda_C*M_y, see Lignos and Krawinkler (2011); set Lamda_C = 0 to disable this mode of deterioration]

Lamda_A

Cyclic deterioration parameter for accelerated reloading stiffness deterioration [E_t=Lamda_A*M_y, see Lignos and Krawinkler (2011); set Lamda_A = 0 to disable this mode of deterioration]

Lamda_K

Cyclic deterioration parameter for unloading stiffness deterioration [E_t=Lamda_K*M_y, see Lignos and Krawinkler (2011); set Lamda_K = 0 to disable this mode of deterioration]

c_S

rate of strength deterioration. The default value is 1.0.

c_C

rate of post-capping strength deterioration. The default value is 1.0.

c_A

rate of accelerated reloading deterioration. The default value is 1.0.

c_K

rate of unloading stiffness deterioration. The default value is 1.0.

theta_p_Plus

pre-capping rotation for positive loading direction (often noted as plastic rotation capacity)

theta_p_Neg

pre-capping rotation for negative loading direction (often noted as plastic rotation capacity) (must be defined as a positive value)

theta_pc_Plus

post-capping rotation for positive loading direction

theta_pc_Neg

post-capping rotation for negative loading direction (must be defined as a positive value)

Res_Pos

residual strength ratio for positive loading direction

Res_Neg

residual strength ratio for negative loading direction (must be defined as a positive value)

theta_u_Plus

ultimate rotation capacity for positive loading direction

theta_u_Neg

ultimate rotation capacity for negative loading direction (must be defined as a positive value)

D_Plus

rate of cyclic deterioration in the positive loading direction (this parameter is used to create assymetric hysteretic behavior for the case of a composite beam). For symmetric hysteretic response use 1.0.

D_Neg

rate of cyclic deterioration in the negative loading direction (this parameter is used to create assymetric hysteretic behavior for the case of a composite beam). For symmetric hysteretic response use 1.0.

ModIMKDefinitionFigure.png

Image from: Lignos and Krawinkler (2012)

The deterioration model parameters can be calibrated based on actual experimental data of RC beams in terms of load - displacement or moment - rotation. Examples of such calibrations can be found in Lignos (2008) and Lignos and Krawinkler (2012).


References:

[1]

Lignos, D.G., Krawinkler, H. (2012). “Development and Utilization of Structural Component Databases for Performance-Based Earthquake Engineering”, Journal of Structural Engineering, ASCE, doi: 10.1061/(ASCE)ST.1943-541X.0000646.

[2]

Lignos, D.G., and Krawinkler, H. (2011). “Deterioration modeling of steel components in support of collapse prediction of steel moment frames under earthquake loading”, Journal of Structural Engineering, ASCE, Vol. 137 (11), 1291-1302.

[3]

Lignos, D.G. and Krawinkler, H. (2012). “Sidesway collapse of deteriorating structural systems under seismic excitations,” Rep.No.TB 177, The John A. Blume Earthquake Engineering Research Center, Stanford University, Stanford, CA. [electronic version: https://blume.stanford.edu/tech_reports]

[4]

Lignos, D.G. (2008). “Sidesway collapse of deteriorating structural systems under seismic excitations,” Ph.D. Dissertation, Department of Civil and Environmental Engineering, Stanford University, Stanford, CA.

[5]

Ibarra L.F., and Krawinkler, H. (2005). “Global collapse of frame structures under seismic excitations”, Rep. No. TB 152, The John A. Blume Earthquake Engineering Center, Stanford University, Stanford, CA. [electronic version: https://blume.stanford.edu/tech_reports]

[6]

Ibarra L.F., Medina R. A., and Krawinkler H. (2005). “Hysteretic models that incorporate strength and stiffness deterioration”, Earthquake Engineering and Structural Dynamics, 34(12), 1489-1511.

Code Developed by : by Dr. Dimitrios G. Lignos, McGill University

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