Simplified bilinear Takeda curve - Takeda

This is the modified Takeda hysteresis loop described in Otani [1974], featuring however the unloading rules proposed by Emori and Schonobrich [1978]. Essentially, the model consists of a bilinear simplification of the original trilinear model proposed by Takeda et al. [1970], the inner cyclic rules of which were diverse from those proposed by Clough and Johnston [1966] in their original bilinear hysteresis model. This response curve has been initially programmed by Otani [1981] and five parameters need to be defined in order to fully characterise its behaviour:

Yielding strength (Fy)
The default value is 500

Initial stiffness (Ky)
The default value is 200000

Post-yielding to initial stiffness ratio ()
The default value is 0.1

Outer loop stiffness degradation factor (0)
The default value is 0.4

Inner loop stiffness degradation factor (1)
The default value is 0.9

Notes

1. The unloading stiffness from the post yielding curve in outer hysteresis loop is defined by:
   
   Ky: Initial stiffness
   Dy: Yielding displacement
   Dm: Previous maximum displacement
   0: Outer loop stiffness degradation factor (Krout), i.e. for unloading from the primary curve
2. The unloading stiffness in inner hysteresis loop is defined by:
   
   1: Inner loop stiffness degradation factor (Krin = 1 * Krout), i.e. for unloading and reloading in the inner cycles