...
What
...
is
...
the
...
difference
...
between
...
a
...
Caltrans
...
hinge
...
and
...
a
...
fiber
...
hinge?
...
Extended
...
Question:
...
The
...
Caltrans
...
hinge
...
appears
...
to
...
be
...
conceptually
...
similar
...
to
...
the
...
fiber
...
hinge
...
in
...
that
...
both
...
are
...
based
...
on
...
strain
...
compatibility
...
and
...
equilibrium
...
of
...
forces.
...
As
...
shown
...
in
...
Figure
...
3.7
...
of
...
the
...
Caltrans
...
Seismic
...
Design
...
Criteria
...
v.
...
1.4
...
,
...
the
...
Caltrans
...
hinge
...
can
...
be
...
idealized
...
as
...
elastic-perfectly
...
plastic.
...
Does
...
the
...
software
...
use
...
this
...
idealized
...
model,
...
and
...
what
...
are
...
the
...
main
...
differences
...
between
...
the
...
Caltrans
...
and
...
fiber
...
hinge?
...
Answer:
...
A
...
comparison
...
between
...
these
...
two
...
...
options
...
is
...
given
...
as
...
follows:
...
Caltrans
...
hinge
...
The
...
Caltrans
...
hinge
...
is
...
a
...
...
...
based
...
on
...
the
...
3D
...
interaction
...
surface
...
which
...
defines
...
coupling
...
between
...
axial
...
and
...
biaxial-bending
...
behaviors.
...
Its
...
mathematical
...
formulation
...
and
...
elastic-perfectly
...
plastic
...
behavior
...
distinguishes
...
the
...
Caltrans
...
hinge
...
from
...
others.
...
Similar
...
to
...
other
...
P-M-M
...
hinges,
...
once
...
loading
...
conditions
...
combine
...
to
...
induce
...
yielding,
...
plastic
...
behavior
...
follows
...
an
...
energy-dependent
...
moment-rotation
...
curve
...
which
...
extends
...
along
...
the
...
angle
...
between
...
M2
...
and
...
M3,
...
normal
...
to
...
its
...
yield
...
point
...
on
...
the
...
interaction
...
surface.
...
Monotonic
...
loading
...
is
...
best
...
suited
...
for
...
this
...
phenomenological
...
approach.
...
Given
...
dynamic
...
application,
...
significant
...
...
should
...
be
...
avoided.
...
Fiber
...
hinge
...
The
...
fiber
...
hinge
...
is
...
also
...
useful
...
for
...
defining
...
coupled
...
axial
...
and
...
biaxial-bending
...
behavior
...
in
...
...
objects,
...
though
...
it
...
follows
...
a
...
different
...
approach.
...
The
...
cross
...
section
...
is
...
discretized
...
into
...
a
...
series
...
of
...
representative
...
axial
...
fibers
...
which
...
extend
...
longitudinally
...
along
...
hinge
...
length.
...
Depending
...
on
...
the
...
material
...
in
...
its
...
tributary
...
area,
...
each
...
fiber
...
has
...
a
...
stress-strain
...
relationship.
...
Integrating
...
behavior
...
over
...
the
...
cross
...
section,
...
then
...
multiplying
...
by
...
hinge
...
length,
...
provides
...
axial
...
force-deformation
...
and
...
biaxial
...
moment-rotation
...
relationships.
...
The
...
fiber-hinge
...
model
...
is
...
more
...
accurate
...
in
...
that
...
the
...
nonlinear
...
material
...
relationship
...
of
...
each
...
fiber
...
automatically
...
accounts
...
for
...
interaction,
...
changes
...
in
...
along
...
the
...
moment-rotation
...
curve,
...
and
...
plastic
...
axial
...
strain.
...
A
...
trade-off
...
is
...
that
...
fiber
...
application
...
is
...
more
...
computationally
...
intensive.
...
Fiber
...
hinges
...
are
...
ideal
...
for
...
dynamic
...
behavior
...
since
...
they
...
capture
...
nonlinear
...
hysteretic
...
effects.
...
How is I cr determined for Caltrans hinges?
Answer: I cr represents the cracked moment of inertia, calculated through basic principles as follows:
I cr = M p / (C p * E)
where:
C p = (C y * M p) / M y
and where:
M p = Plastic moment (idealized)
C p = Plastic curvature
E = Modulus of elasticity
C y = Yield curvature
M y = Yield moment
See Also
- P-M2-M3 hinges article