THE
FOLLOWING IS A
DESCRIPTION OF
THE DIFFERENT
ANALYTICAL
PROCEDURES USED
BY STRUCTURAL
ENGINEERS IN
EARTHQUAKE
ENGINEERING
FROM:
FEMA 356: A
Prestandard and
Commentary for
the Seismic
Rehabilitation
of Buildings
(p28)
This
section
is
reproduced
from
FEMA
356
in
order
to
provide
an
introduction
to
the
types
of
analytical
procedures
used
for
seismic
risk
assessments
for
existing
buildings,
leading
upgrade
design.
It
is
provided
here
for
the
general
public
because
a
general
knowledge
of
these
procedures
and
terminology
can
better
equip
decision
makers
to
be
able
to
make
an
informed
decision
on
how
best
to
proceed
through
the
design
stage.
This
information
can
be
valuable
because
in
certain
situations
involving
complex
multistory
buildings
of
different
structural
systems,
the
more
more
elaborate
and
costly
analytical
procedure
can
sometimes
lead
to
much
greater
savings
in
construction
costs.
The
reason
for
this
is
that
the
simplified
procedures
are
not
only
less
precise,
but
also
potentially
overconservative,
and
thus
predictive
of
a
poorer
performance
in
earthquakes
than
is
actually
the
case.
NOTE
that
this
is
a
"prestandard,"
and
as
such,
the
language
is
in
the
form
of
demands
and
requirements,
so
that
it
can
be
incorporated
into
a
building
code
or
Citywide
ordinance.
It
is
not
published
here
with
the
intention
that
it
be
treated
as
more
than
a
source
of
information.
For
code
preparation,
please
refer
to
the
published
document
in
its
entirety,
as
the
materials
below
have
been
condensed
and
edited. 
C2.4
Analysis
Procedures:
Introduction
[The FEMA 356
"Prestandard"
specifies that]
an analysis of
the building,
including
rehabilitation
measures, shall
be conducted to
determine the
forces and
deformations
induced in
components of
the building by
ground motion
corresponding to
the selected
Earthquake
Hazard Level, or
by other seismic
geologic site
hazards
specified in
Section 4.2.2.
The analysis
procedure shall
comply with one
of the
following, and
comply with the
applicable
acceptance
criteria
selected in
accordance with
Section 2.4.4:
1.
Linear
analysis
subject to
limitations
specified
in Section
2.4.1, and
complying
with the Linear
Static
Procedure
(LSP)
in
accordance
with
Section
3.3.1, or
the Linear
Dynamic
Procedure
(LDP)
in
accordance
with
Section
3.3.2.
2.
Nonlinear
analysis
subject to
limitations
specified
in Section
2.4.2, and
complying
with the Nonlinear
Static
Procedure
(NSP)
in
accordance
with
Section
3.3.3, or
the Nonlinear
Dynamic
Procedure
(NDP)
in
accordance
with
Section
3.3.4.
3.
Alternative
rational
analysis
in
accordance
with
Section
2.4.3.
NOTE:
The
linear
analysis
procedures
maintain the
traditional use
of a linear
stressstrain
relationship,
but incorporate
adjustments to
overall building
deformations and
material
acceptance
criteria to
permit better
consideration of
the probable
nonlinear
characteristics
of seismic
response. The
Nonlinear Static
Procedure (NSP),
often called
"pushover
analysis,"
uses simplified
nonlinear
techniques to
estimate seismic
structural
deformations.
The Nonlinear
Dynamic
Procedure (NDP),
commonly known
as nonlinear
time history
analysis,
requires
considerable
judgment and
experience to
perform, and may
be used only
within the
limitations
described in
Section 2.4.2.2
of this
standard.
C2.4.1
Linear
Procedures
The
results of the
linear
procedures can
be very
inaccurate when
applied to
buildings with
highly irregular
structural
systems, unless
the building is
capable of
responding to
the design
earthquake(s) in
a nearly elastic
manner. The
procedures of
Section 2.4.1.1
are intended to
evaluate whether
the building is
capable of
nearly elastic
response.
C2.4.1.1
Method
to
Determine
Limitations
on
Use
of
Linear
Procedures:
The
magnitude
and
distribution
of
inelastic
demands
are
indicated
by
demandcapacity
ratios
(DCRs).
Note
that
these
DCRs
are
not
used
to
determine
the
acceptability
of
component
behavior.
The
adequacy
of
structural
components
and
elements
must
be
evaluated
using
the
procedures
contained
in
Chapter
3
along
with
the
acceptance
criteria
provided
in
Chapters
4
through
8.
DCRs
are
used
only
to
determine
a
structure's
regularity.
It
should
be
noted
that
for
complex
structures,
such
as
buildings
with
perforated
shear
walls,
it
may
be
easier
to
use
one
of
the
nonlinear
procedures
than
to
ensure
that
the
building
has
sufficient
regularity
to
permit
use
of
linear
procedures.
If
all
of
the
computed
controlling
DCRs
for
a
component
are
less
than
or
equal
to
1.0,
then
the
component
is
expected
to
respond
elastically
to
the
earthquake
ground
shaking
being
evaluated.
If
one
or
more
of
the
computed
DCRs
for
a
component
are
greater
than
1.0,
then
the
component
is
expected
to
respond
elastically
to
the
earthquake
ground
shaking
being
evaluated.
If
one
or
more
of
the
computed
DCRs
for
the
component
are
greater
than
1.0,
then
the
component
is
expected
to
respond
inelastically
to
the
earthquake
ground
shaking.
2.4.1.2
Limitations
on
Use
of
the
Linear
Static
Procedure:
The
Linear
Static
Procedure
shall
not
be
used
for
a
building
with
one
or
more
of
the
following
characteristics:
1.
The
fundamental
period
of
the
building,
T,
is
greater
than
or
equal
to
3.5
times
Ts.
2.
The
ratio
of
the
horizontal
dimension
at
any
story
to
the
corresponding
dimension
at
an
adjacent
story
exceeds
1.4
(excluding
penthouses).
see:
Irregularities
3.
The
building
has
a
severe
torsional
stiffness
irregularity
in
any
story.
A
severe
torsional
stiffness
irregularity
exists
in
a
story
if
the
diaphragm
above
the
story
under
consideration
is
not
flexible
and
the
results
of
the
analysis
indicate
that
the
drift
along
any
side
of
the
structure
is
more
than
150%
of
the
average
story
drift.
see:
Irregularities
4.
The
building
has
a
severe
vertical
mass
or
stiffness
irregularity.
A
severe
vertical
mass
or
stiffness
irregularity
exists
when
the
average
drift
in
any
story
(except
penthouses)
exceeds
that
of
the
story
above
or
below
by
more
than
150%.
see:
Irregularities
5.
The
building
has
a
nonorthogonal
lateralforce
resisting
system.
For
buildings
in
which
linear
procedures
are
applicable,
but
the
Linear
Static
Procedure
is
not
permitted,
use
of
the
Linear
Dynamic
Procedure
shall
be
permitted.
NOTE:
For
buildings
that
have
irregular
distributions
of
mass
or
stiffness,
irregular
geometries,
or
nonorthogonal
lateralforceresisting
systems,
the
distribution
of
demands
predicted
by
an
LDP
analysis
will
be
more
accurate
than
those
predicted
by
the
LSP.
Either
the
response
spectrum
method
or
time
history
method
may
be
used
for
evaluation
of
such
structures.

2.4.2
Nonlinear
Procedures
Nonlinear
procedures shall
be permitted for
any of the
rehabilitation
strategies
contained in
Section 2.5.
Nonlinear
procedures shall
be used for
analysis of
buildings when
linear
procedures are
not permitted.
Data collection
for use with
nonlinear
procedures shall
be in accordance
with Section
2.2.6.
2.4.2.1
Nonlinear Static
Procedure
The
NSP shall be
permitted for
structures in
which higher
mode effects are
not significant,
as defined in
this section. To
determine if
higher modes are
significant, a
modal response
spectrum
analysis shall
be performed for
the structure
using sufficient
modes to capture
90% mass
participation. A
second response
spectrum
analysis shall
also be
performed,
considering only
the first mode
participation.
Higher mode
effects shall be
considered
significant if
the shear in any
story resulting
from the modal
analysis
considering
modes required
to obtain 90%
mass
participation
exceeds 130% of
the
corresponding
story shear
considering only
the first mode
response.
If
higher mode
effects are
significant, the
NSP shall be
permitted if an
LDP analysis is
also performed
to supplement
the NSP.
Buildings with
significant
higher mode
effects must
meet the
acceptance
criteria of this
standard for
both analysis
procedures,
except that an
increase by a
factor of 1.33
shall be
permitted in the
LDP acceptance
criteria for
deformationcontrolled
actions
(mfactors)
provided in
Chapters 5
through 9. A
building
analyzed using
the NSP, with or
without a
supplementary
LDP evaluation,
shall meet the
acceptance
criteria for
nonlinear
procedures
specified in
Section 3.4.3.
NOTE:
The NSP is
generally a more
reliable
approach to
characterizing
the performance
of a structure
than are linear
procedures.
However, it is
not exact, and
cannot
accurately
account for
changes in
dynamic response
as the structure
degrades in
stiffness or
account for
higher mode
effects. When
the NSP is
utilized on a
structure that
has significant
higher mode
response, the
LDP is also
employed to
verify the
adequacy of the
design. When
this approach is
taken, less
restrictive
criteria are
permitted for
the LDP,
recognizing the
significantly
improved
knowledge that
is obtained by
performing both
analysis
procedures.
2.4.2.2
Nonlinear
Dynamic
Procedure
The
NDP shall be
permitted for
all structures.
An analysis
performed using
the NDP shall be
reviewed and
approved by an
independent
thirdparty
engineer with
experience in
seismic design
and nonlinear
procedures.
2.4.3
Alternative
Rational
Analysis
Nothing
in this standard
shall be
interpreted as
preventing the
use of any
approved
alternative
analysis
procedure that
is rational and
based on
fundamental
principles of
engineering
mechanics and
dynamics. Such
alternative
analyses shall
not adopt the
acceptance
criteria
contained in
this standard
without first
determining
their
applicability.
All projects
using
alternative
rational
analysis
procedures shall
be reviewed and
approved by an
independent
thirdparty
engineer with
experience in
seismic design.
2.4.4
Acceptance
Criteria
2.4.4.1
General
The
acceptability of
force and
deformation
actions shall be
evaluated for
each component
in accordance
with the
requirements of
Section 3.4.
Prior to
selecting
component
acceptance
criteria for use
in Section 3.4,
each component
shall be
classified as
primary or
secondary in
accordance with
Section 2.4.4.2,
and each action
shall be
classified as
deformationcontrolled
(ductile) or
forcecontrolled
(nonductile) in
accordance with
Section 2.4.4.3.
Component
strengths,
material
properties, and
component
capacities shall
be determined in
accordance with
Sections
2.4.4.4,
2.4.4.5, and
2.4.4.6,
respectively.
Component
acceptance
criteria not
presented in
this standard
shall be
determined by
qualification
testing in
accordance with
Section 2.8.
The
rehabilitated
building shall
be provided with
at least one
continuous load
path to transfer
seismic forces,
induced by
ground motion in
any direction,
from the point
of application
to the final
point of
resistance. All
primary and
secondary
components shall
be capable of
resisting force
and deformation
actions within
the applicable
acceptance
criteria of the
selected
performance
level.
C2.4.4.2
Primary and
Secondary
Elements and
Components
In
a typical
building, nearly
all elements,
including many
nonstructural
components, will
contribute to
the building's
overall
stiffness, mass,
and damping, and
consequently its
response to
earthquake
ground motion.
However, not all
of these
elements are
critical to the
ability of the
structure to
resist collapse
when subjected
to strong ground
shaking. The
secondary
designation
typically will
be used when a
component or
element does not
contribute
significantly or
reliably in
resisting
earthquake
effects because
of low lateral
stiffness,
strength, or
deformation
capacity.
For
example,
exterior
cladding and
interior
partitions can
add substantial
initial
stiffness to a
structure, yet
this stiffness
is not typically
considered in
the design of
new buildings
because the
lateral strength
of these
elements is
often small.
Similarly, the
interaction of
floor framing
systems and
columns in shear
wall buildings
can add some
stiffness,
although
designers
typically
neglect such
stiffness when
proportioning
the building's
shear walls.
The
concept of
primary and
secondary
elements permits
the engineer to
differentiate
between the
performance
required of
elements that
are critical to
the building's
ability to
resist collapse
and of those
that are not.
For a given
performance
level,
acceptance
criteria for
primary elements
and components
will typically
be more
restrictive than
those for
secondary
elements and
components.
Use
of the secondary
classification
will allow
certain
components to
experience
greater damage
and larger
displacements
than would
otherwise be
permitted for
primary
elements, as
explained
below.
1.
Although
damage to
the
primary
elements
and some
degradation
of their
stiffness
may be
permitted
to occur,
the
overall
function
of these
elements
in
resisting
structural
collapse
should not
be
compromised.
2.
For some
structural
performance
levels,
substantial
degradation
of the
lateralforceresisting
stiffness
and
strength
of
secondary
elements
and
components
is
permissible.
However,
the
ability of
these
secondary
elements
and
components
to support
gravity
loads
under the
maximum
induced
deformations
must be
preserved.
