Ramberg-Osgood curve - Ramberg_Osgood

This is the Ramberg-Osgood hysteresis loop [Ramberg and Osgood, 1943], as described in the work of Kaldjian [1967]. It has been initially programmed by Otani [1981] and requires four parameters to be defined in order to fully characterise its behaviour:

Yield strength (Fy)
The default value is 500

Yield displacement (Dy)
The default value is 0.0025

Ramberg-Osgood Parameter ()
The default value is 1.5

Convergence limit for the Newton-Raphson procedure ()
The default value is 0.001

Notes

1. The loading curve is defined by:
   
2. The curve passes at (Fy, (1+Dy)) for any value of , which controls the shape of the primary curve. As shown below, the loading curve may vary from a linear elastic line for = 1.0, to an elasto-plastic bilinear segment, for = infinity.
   
3. The unloading curve from the maximum point (Do, Fo) follows the equation:
   
4. The force is computed by an iterative procedure using the Newton–Raphson method.
5. As pointed out by Otani [1981] this hysteretic model dissipates energy even if the ductility factor is less than one. The dissipated energy is sensitive to , increasing with the increasing of this parameter.