This is the steel model of Menegotto and
Pinto, which was modified by Filippou et al.
fy:
Yield strength of reinforcing steel
E:
Modulus of elasticity
b:
Stiffness reduction factor after yielding
Ro, a1,
a2: Coefficients for shape index (R) for steel fiber constitutive
model
This Stress-Strain hysteresis model is outlined
as follows:
The above formula represents a curved transition
from the elastic range to the yielding range.
and are
normalized values and are calculated as follows:
The above formula represents a curved transition
from the elastic range to the yielding range.
and
are normalized values and are calculated as follows:
This
model has two asymptotes as shown below. One asymptote has a slope of
elastic stiffness and the other has a slope of yielding stiffness.
is a point intersected by two asymptotes.
is the point where the last unloading occurred.
While unloading and reloading, these points are updated, so that the transition
curve is affected.
R is the value that
can affect the shape of the transition curve and represents the Bauschinger
effect. The value of R is determined
as follows:
Coefficients
are determined from experimental hysteresis results. MIDAS uses 18.5,
0.15 and 20, respectively, as default values. These default values are
suggested in the original reference (Menegotto and Pinto,1973).
is a shape coefficient
and updated at every unloading.