Analysis and modelling of the seismic behaviour of high ... - Ingegneria

3. SEISMIC BEHAVIOUR OF BOLTED END PLATE BEAM-TO-COLUMN STEEL JOINTS
conducted for monotonic loading conditions only. As in prior analytical studies on
welded moment connections performed by El-Tawil et al. (1998), it is assumed that
the conclusions drawn from this study are qualitatively applicable to cyclic
conditions.
In order to reduce the computational effort, the onset of cracking method is
considered in the models. Hence, the J-integral is adopted to characterize the
energy release associated with the crack growth. As sharp cracks are considered,
see Figure 3.29b, an accurate evaluation of the contour integral is obtained.
Toughness demands are quantified in the analyses by means of the CTOD index,
that represents the tearing at the crack tip. In detail, the CTOD is determined in the
analyses evaluating the J-integral and converting it into the CTOD value by means
of Eq. (3.1).
To evaluate and compare the different analyzed connection configurations for
ductile fracture potential, a rupture index is computed at different locations of the
connection. Others [6] have used the same approach in analytical connection
studies. The rupture index (RI) is defined as:
86
εp
εy
RI =
σ
exp −1.5
σ
m
eff
( 3.16 )
where εp, εy σm and σeff are, respectively, the equivalent plastic strain, yield strain,
hydrostatic stress, and equivalent stress (also known as von Mises stress). The
rupture index was motivated by the research of Hancock and MacKenzie (1976) on
the equivalent plastic rupture strain of steel for different conditions of stress
triaxiality. The process of ductile fracture initiation is caused by high tensile triaxial
stresses (i.e., high tensile hydrostatic stress) that result in damage accumulation
through microvoid nucleation and coalescence. The ratio of hydrostatic stress-to-
von Mises stress ( m/ eff) that appears in the denominator of (16) is called the
triaxiality ratio (TR). High triaxiality can cause a large reduction in the rupture strain
of a material, thereby limiting its ductility (Lemaitre, 1996). For instance, a value of
triaxiality ratio in the range 0.75 < σm/σeff < 1.5 may cause a large reduction of the
ultimate strength in metals, whereas a triaxiality ratio σm/σeff > 1.5 entails fragile
behaviour Thus, locations in a connection with higher values for RI have a greater
potential for fracture. The ratio of equivalent plastic strain-to-yield strain that
appears in the numerator of (1) is called the plastic equivalent strain (PEEQ) index.
This index is a measure of the local inelastic strain demand, and is also useful in
comparing the different analyzed configurations. The PEEQ index is computed by: