3.1.5.18. IMKBilin Material

This command is used to construct a material with a hysteretic bilinear response based on the modified Ibarra-Medina-Krawinkler deterioration model.

uniaxialMaterial IMKBilin $matTag $Ke $dp_pos $dpc_pos $du_pos $Fy_pos $FmaxFy_pos $FresFy_pos $dp_neg $dpc_neg $du_neg $Fy_neg $FmaxFy_neg $FresFy_neg $Lamda_S $Lamda_C $Lamda_K $c_S $c_C $c_K $D_pos $D_neg

Argument	Type	Description
$matTag	integer	integer tag identifying material
$Ke	float	Elastic stiffness
$dp_pos	float	Pre-capping deformation in positive loading direction
$dpc_pos	float	Post-capping deformation in positive loading direction
$du_pos	float	Ultimate deformation in positive loading direction
$Fy_pos	float	Yield strength in positive loading direction
$FmaxFy_pos	float	Maximum-to-yield strength ratio in positive loading direction
$FresFy_pos	float	Residual-to-yield strength ratio in positive loading direction
$dp_neg	float	Pre-capping deformation in negative loading direction
$dpc_neg	float	Post-capping deformation in negative loading direction
$du_neg	float	Ultimate deformation in negative loading direction
$Fy_neg	float	Yield strength in negative loading direction
$FmaxFy_neg	float	Maximum-to-yield strength ratio in negative loading direction
$FresFy_neg	float	Residual-to-yield strength ratio in negative loading direction
$Lamda_S	float	Cyclic deterioration parameter for yield strength deterioration
$Lamda_C	float	Cyclic deterioration parameter for post-capping stiffness deterioration
$Lamda_K	float	Cyclic deterioration parameter for unloading stiffness deterioration
$c_S	float	Rate of yield strength deterioration
$c_C	float	Rate of post-capping stiffness deterioration
$c_K	float	Rate of unloading stiffness deterioration
$D_pos	float	rate of cyclic deterioration in the positive loading direction. This parameter is used to create asymmetric hysteretic behavior as in the case of a composite beam (0< D_pos <1). For symmetric hysteretic response use 1.0.
$D_neg	float	rate of cyclic deterioration in the negative loading direction. This parameter is used to create asymmetric hysteretic behavior as in the case of a composite beam (0< D_pos <1). For symmetric hysteretic response use 1.0.

Note

All material model parameters (in both the positive and negative direction) shall be specified as positive values.

Lamda is used to compute the reference energy based on the following equation Ref_Energy = Lamda * Fy

Fig. 3.1.5.9 IMKBilin backbone curve

Fig. 3.1.5.10 IMKBilin sample response

Example

The following is used to construct a IMKBilin material with symmetric hysteretic response.

set Ke      10000.;
set dp      0.01;
set dpc     0.05;
set du      0.08;
set My      100.;
set Mc_My   1.10;
set Mres_My 0.10;
set lambda  0.50;
set c_S     1.00;
set c_C     1.00;
set c_K     1.00;
set c_A     1.00;
set D_pos   1.00;
set D_neg   1.00;

uniaxialMaterial IMKBilin  1 $Ke $dp $dpc $du $My $Mc_My $Mres_My $dp $dpc $du $My $Mc_My $Mres_My $lambda $lambda $lambda $c_S $c_S $c_K $D_pos $D_neg;

3.1.5.18.1. References:

• Model rules:

Ibarra, L. F., Medina, R. A., and Krawinkler, H. (2005). “Hysteretic models that incorporate strength and stiffness deterioration.” Earthquake Engineering & Structural Dynamics, 34(12), 1489-1511, DOI: https://doi.org/10.1002/eqe.495.

• Model parameters for steel beams as part of rigid beam-to-column connections:

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, 137(11), 1291-1302, DOI: https://doi.org/10.1061/(ASCE)ST.1943-541X.0000376.

• Model parameters for steel beam-columns:

Lignos, D. G., Hartloper, A., Elkady, A., Deierlein, G. G., and Hamburger, R. (2019). “Proposed updates to the asce 41 nonlinear modeling parameters for wide-flange steel columns in support of performance-based seismic engineering.” Journal of Structural Engineering, 145(9), 04019083, DOI: https://doi.org/10.1061/(ASCE)ST.1943-541X.0002353.

3.1.5.18.2. Code inquiry or bug reporting

• Kazuki Ichinohe, University of Tokyo, e-mail: z-ichinohe@g.ecc.u-tokyo.ac.jp

• Ahmed Elkady, University of Southampton, e-mail: a.elkady@soton.ac.uk