Smooth curve - smooth
This is the smooth hysteresis loop, as described in Sivaselvan and Reinhorn [1999] and Sivaselvan and Reinhorn [2001]. The model is a variation of that originally proposed by Bouc [1967] and modified by several others (Wen [1976], Baber and Noori [1985], Casciati [1989] and Reinhorn et al. [1995]). It has been formulated with rules for stiffness and strength degradation, and pinching. Twenty-two parameters need to be defined in order to fully characterise this response curve. There are two groups of parameters: common parameters (the same as for the multilinear curve), related to the backbone curve, and then specific parameters for the hysteretic rules.
Common Envelope parameters
Initial flexural rigidity (EI)
The default value is 45400
Cracking Moment (positive) (PCP)
The default value is 10
Yield Moment (positive) (PYP)
The default value is 22
Yield Curvature (positive) (UYP)
The default value is 0.002
Ultimate Curvature (positive) (UUP)
The default value is 0.006
Post Yield Flexural Stiffness (positive) as % of elastic EI3P
The default value is 0.0088
Cracking Moment (negative) (PCN)
The default value is -10
Yield Moment (negative) (PYN)
The default value is -22
Yield Curvature (negative) (UYN)
The default value is -0.002
Ultimate Curvature (negative) (UUN)
The default value is -0.006
Post Yield Flexural Stiffness (negative) as % of elastic EI3N
The default value is 0.0088
Specific parameters
Stiffness degrading parameter (HC)
The default value is 200
Ductility-based strength decay parameter (HBD)
The default value is 0.001
Hysteretic energy-based strength decay parameter (HBE)
The default value is 0.001
Smoothness parameter for elastic-yield transition (NTRANS)
The default value is 10
Parameter for shape of unloading (ETA)
The default value is 0.5
Slip length parameter (HSR)
The default value is 0
Slip sharpness parameter (HSS)
The default value is 100
Parameter for mean moment level of slip (HSM)
The default value is 0
Exponent of gap closing spring (NGAP)
The default value is 10
Gap closing curvature parameter (PHIGAP)
The default value is 1000
Gap closing stiffness coefficient (STIFFGAP)
The default value is 1
Below, example applications are given, in order to illustrate the modelling capacities of this response curve (it is noted that the 'bordered' parameters have been changed with respect to the default values):
