Modified Ibarra-Medina-Krawinkler Deterioration Model with Bilinear Hysteretic Response (Bilin Material)

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This command is used to construct a bilin material. The bilin material simulates the modified Ibarra-Krawinkler deterioration model with bilinear hysteretic response. Note that the hysteretic response of this material has been calibrated with respect to more than 350 experimental data of steel beam-to-column connections and multivariate regression formulas are provided to estimate the deterioration parameters of the model for different connection types. These relationships were developed by Lignos and Krawinkler (2009, 2011) and have been adopted by PEER/ATC (2010). NOTE: before you use this material make sure that you have downloaded the latest OpenSees version.

uniaxialMaterial Bilin $matTag $K0 $as_Plus $as_Neg $My_Plus $My_Neg $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

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$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 (negative value)
$Lamda_S	Cyclic deterioration parameter for strength deterioration
$Lamda_C	Cyclic deterioration parameter for post-capping strength deterioration
$Lamda_A	Cyclic deterioration parameter for acceleration reloading stiffness deterioration (is not a deterioration mode for a component with Bilinear hysteretic response).
$Lamda_K	Cyclic deterioration parameter for unloading stiffness 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) (positive value)
$theta_pc_Plus	post-capping rotation for positive loading direction
$theta_pc_Neg	post-capping rotation for negative loading direction (positive value)
$Res_Pos	residual strength ratio for positive loading direction
$Res_Neg	residual strength ratio for negative loading direction (positive value)
$theta_u_Plus	ultimate rotation capacity for positive loading direction
$theta_u_Neg	ultimate rotation capacity for negative loading direction (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.

Image from: Lignos et al. (2011)

The deterioration model parameters can be calibrated based on actual experimental data of steel components. Instead, a user can determine the same parameters with predictive equations that have been developed by Lignos and Krawinkler (2009, 2011). These equations relate deterioration modelling parameters with geometric and material properties of steel components and have been developed with multivariate regression analysis after extensive calibration of a recently developed steel component database of more than 300 steel specimens (Lignos and Krawinkler 2007, 2009, 2011).

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References:

[1]	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.
[2]	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.
[3]	Karavasilis T.L., Ricles J.M., Sause R. (2009). "Implementation of deterioration elements in OpenSEES for collapse simulations" ATLSS Engineering Research Center, Rep. No. 09-11.
[4]	Lignos, D.G., and Krawinkler, H. (2007), “A database in support of modeling of component deterioration for collapse prediction of steel frame structures”, Proc. ASCE Structures Congress, Long Beach CA, SEI institute.
[5]	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]
[6]	Lignos, D. G., Krawinkler, H. and Whittaker, A.S. (2011). "Prediction and validation of sidesway collapse of two scale models of a 4-story steel moment frame", Earthquake Engineering and Structural Dynamics, EESD, Vol. 40 (7), 807-825.
[7]	Lignos, D.G., and Krawinkler, H. (2010). “A steel database for component deterioration of tubular hollow square steel columns under varying axial load for collapse assessment of steel structures under earthquakes”, Proc. 7th International Conference on Urban Earthquake Engineering (7CUEE), March 3-5, Tokyo, Japan.
[8]	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. File:BilinMaterialOpenSees.pdf
[9]	PEER/ATC (2010). “Modeling and acceptance criteria for seismic design and analysis of tall buildings”, PEER/ATC-72-1, prepared by the Applied Technology Council in cooperation with the Pacific Earthquake Engineering Research Center, Redwood City, CA..

Code Developed by : by Dr. Dimitrios G. Lignos, McGill University and was implemented by Dr. Theodore Karavasilis, Oxford University