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DO WE REALLY NEED INELASTIC DYNAMIC ANALYSIS?Amr S. Elnashaiaa
Mid-America Earthquake Center, Civil and Environmental Engineering
Department, University ofIllinois at Urbana-Champaign, USA
To cite this Article Elnashai, Amr S.(2002) 'DO WE REALLY NEED
INELASTIC DYNAMIC ANALYSIS?', Journal ofEarthquake Engineering, 6:
1, 123 130To link to this Article: DOI:
10.1080/13632460209350435URL:
http://dx.doi.org/10.1080/13632460209350435
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Journal of Earthquake Engineering, Vol. 6, Special Issue 1
(2002) 123-130 @ Imperial College Press
DO WE REALLY NEED INELASTIC DYNAMIC ANALYSIS?
AMR S. ELNASHAI Mid-Amerim Earthquake Center,
Civil and Environmental Enpneering Department, University of
Illinois at Urbana-Champaign, USA
The paper examines the requirements for inelastic static and
dynamic analysis applied to earthquake design and assessment.
Conventional pushover, with various load distribu- tions, as well
as advanced adaptive concepts are examined and compared to
incremental dynamic analysis. Regions of applicability of each are
discussed and suggestions on which method is better suited under a
given set of conditions are qualitatively made. I t is con- cluded
that there will always be a class of structure-input motion pairs
where inelastic dynamic analysis is necessary. Future developments
should aim a t reducing the regions where dynamic analysis is
needed, hence static analysis may be used with confidence in other
cases.
Keywords: Pushover analysis; adaptive techniques; inelastic
dynamic analysis.
1. Introduction
Whereas inelastic static analysis has become almost routine in
the design office en- vironment, its dynamic counterpart remains a
challenge. This may be attributed to the complexity of
time-integration algorithms, difficulties in damping representation
and the effect of both of the above on the results, especially in
terms of acceleration- and force-related quantities. If static
analysis is shown to give robust and reliable .results that are
representative of the dynamic response, with an acceptable level of
accuracy, more use of inelastic analysis will ensue, leading to
better failure mode control in seismic design. It would also lead
to more accurate assessments of ex- isting structures where
multi-level acceptance criteria are increasingly demanded. This has
been the driving force behind concerted efforts to develop advanced
static pushover methods [e-g. Freeman et al., 1975; Kunnath et d,
1992; Bracci et al., 1997; Krawinkler-and Seneviratna, 1998; Kim
and D'Amore, 1999; Papanikolaou, 2000; Antoniou, 2002; amongst many
others]. Notwithstanding its significance and increasing use,
pushover methods provide only a measure of "capacity" and have to
be combined with a "demand" measure to complete the "akssment"
picture. This limitation tends weight to the continuing use of
inelastic dynamic analysis, which indeed deals with both "demand"
and "supply". In the context of comparing methods of analysis using
the yardstick of "supply" and "demand", it is noteworthy that
response spectrum and linear elastic dynamic analysis are on
occasion used to estimate the demand, whilst static pushover or
even plastic limit analysis provide estimates of "capacity".
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In this paper, results from recent work on conventional and
adaptive pushover analysis are displayed and discussed. Comparisons
with dynamic analysis, applied incrementally to obtain a "dynamic
pushover curven are also presented from previ- ous work.
Outstanding hurdles to the further utilisation of static analysis
in earth- quake engineering are highlighted. Finally, a qualitative
assessment of the results is given, leading to suggestions for
application of advanced pushover methods and where to employ
dynamic analysis.
2. Pushover Analysis
Many researchers and practitioners have contributed to advancing
pushover anal- - ysis. The technique is more intuitive than
mathematical. If a set of actions or deformations can be found such
that a particular response mode, or a combina- tion of modes, is
represented statically, then the response of the structure under a
monotonically increasing vector of actions or deformations may
replace results from dynamic analysis. This is notwithstanding the
shortcoming of not knowing the demand deformation under the
earthquake motion record, but may be used in conjunction with a
demand spectrum [elastic, e.g. Freeman et d , 1975; or inelastic,
e.g. Fajfar, 1991 to assess the adequacy of the structure. The
capacity curve-demand spectrum comparison, referred to in the
literature as Capacity Spectrum Method, is powerful but is also not
devoid of pitfalls and defects. For example, the trans- formation
of the capacity curve from the force-displacement space to the
spectral acceleration-spectra1 displacement space is not trivial
since more than one mode may be contributing in the adaptive
techniques. Moreover, the level of equivalent damping for a given
level of displacement on the capacity curve is normally ignored in
selecting the demand spectrum. Indeed, it is argued herein that the
demand spectrum is a moving target and should be treated as
such.
3. Dynamic Time-Marching
Whereas dynamic time-marching is the most natural approach
towards dynamic response analysis, its application has been
hampered until the past ten years or so due to its large
computational demands. The theoretical basis for accuracy and
stability analyses are also rather complex [Bathe, 19821, verging
on. the inexplicable for the case of inelastic response. Its
requirements, reviewed in Table 1, have also reduced its use in
design offices.
The selection of the integration scheme and the value of
integration operators have a profound effect on the results.
Manipulating algorithmic damping (inten- tionally) or falling
victim of it (inadvertently) could lead to 50% or more variation in
force response. The selection of damping parameters in the presence
of hysteretic damping is also a serious consideration that affects
the results obtained.
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Do We Really Need Inelastic Dynamic Analysis? 125
Table 1. Comparison of requirements for static and dynamic
analysis.
Static Analysis Dynamic Analysis
Detailed models needed Detailed models needed Stiffness and
strength represented Stiffness and strength represented No mass
representation required' Mass representation required No damping
representation required Damping required No additional operators
required Time integration operators required No input motion
required Input motion required Target displacement required Target
displacement is an output Action distribution fixed' Actions vary
in time Usually faster than dynamic analysis Usually slower than
static analysis
'This may not be the case for advanced adaptive pushover.
4. Fixed Distribution Pushover and Dynamic Analysis
Recent extensive work 1e.g. Mwafy, 2001; Mwafy and Elnashai,
20011 compared capacity curves obtained from fixed distribution
pushover analysis, using various combinations of modes, and
capacity curves obtained from running a large number of dynamic
analyses, under increasing earthquake intensity. A sample of
results is shown in Fig. 1. '
It is interesting to note that in this case, there is not a
single static curve that traces the entire dynamic curve
progression. The uniform distribution of actions (distribution C)
hits the target at very large deformations, an observation made
15000 h
s L 2 loo00 tj : a . 5000
0 0 200 400 600 800 1000
Top Disp. (mm) Fig. 1. Comparison of static and dynamic pushover
curves with different force distributions (Mwafy and Elnashai,
2001).
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126 A. S. Elnashai
0 200 400 60 0 800 1000 Top Disp. (mm)
Fig. 2. Comparisons of static analysis with multimodal
distribution and dynamic analysis [Mwafy and Elnashai, 20011.
in several other cases not reported herein. This is due to the
high 1eveI of damage at lower floors, leading to a distribution of
actions in the dynamic analysis close to uniform. It is instructive
at this stage to examine the individual dynamic anal- ysis points,
as opposed to the best-fit curve presented in Fig. 1, and to
introduce "spectrum scaling" and multimodal forces.
In Fig. 2, the response of an eight-storey RC structure to the
Kobe Univer- sity record, from the Hyogo-ken Nanbu earthquake of
1995, with different levels of ground motion scaling, is shown by
the black triangles. The left most distribution is for the design
storey forces, whilst (a) and (b) are for design spectrum-elastic
period and Kobe spectrum-inelastic period 'distributions. This
means that more than one mode is used (in this case the first two),
each scaled by the spectrum or- dinate corresponding to the period
of vibration. The proximity of the static results to the dynamic
points is rather reassuring. At large deformation levels the
uniform distribution gives better results though, as previously
noted. Spectrum scaling not only has no theoretical basis, but also
violates basic principles since it utilises su- perposition
concepts in conjunction with inelastic analysis. However, in many
cases it gives results superior to those obtained without due
consideration to the input motion frequency content, even when the
force distribution is fixed.
5. Adaptive Force Distribution and Dynamic Analysis
Several attempts at adapting the force distribution to the state
of inelasticity are described in the literature. These have
reported varying degrees of success. This adaptive approach is also
amenable to the application of spectrum scaling. In this case,
since the periods of vibration vary continuously, spectrum scaling
may lead to dramatic improvements in the static pushover curve. In
Fig. 3, the first three
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Do We Really Need Inelastic Dynamic Analysis? 127
Interstorey Drift Fig. 3. Variations of periods of vibration
during analysis [Antoniou, 20021.
Top Displacement (mm) Fig. 4. Fully adaptive analysis of a MDOF
idealised system.
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periods of an idealised multi-degree of freedom (!vmOF) system
are plotted, ver- sus interstorey drift [htoniou, 20021. It is
evident that period elongation is very si,pnificant for the
fundamental mode, and much less so for the Erst and second har-
monics. The spectral ordinates corresponding to the shown periods
will therefore vary continuously.
The above was taken into account in a parametric study on
idealised MDOF systems with stifhess and strength irregularity.
Sample results are shown in Fig. 4. Whereas most force
distributions result in good comparison with the dynamic analysis
points (solid circles), the curve corresponding to adaptive
analysis with spectrum scaling is spot-on. It is noted that this is
the best result obtained in the parametric study. There are cases
where the adaptive analysis fails completely to duplicate the
dynamic results.
In a recent study extending the work presented above
[Rovithakis, 20011 using complex 5-, 8- and 12-storey RC structures
[Mwafy and Elnashai, 20011, it was confirmed that whereas the fully
adaptive analysis using the newly developed pro- gram INDYAS
[Elnashai et aL, 2000) gives excellent results in many cases, this
is by no means guaranteed and is dependent on the interaction
between structure and strong-motion characteristics. In cases where
the response starts in a mode other than the fundamental, even the
initial stiffness is misrepresented by the adaptive pushover
[Antoniou, 20021. It is noteworthy that the additional complexity
required to perform fully adaptive pushover analysis is
considerable, in terms of accessing an efficient eignevalue solver,
scaling forces by spectral ordinates, updating applied force (or
displacement) vectors and switching to fixed-distribution
displacement control past the peak point on the load-displacement
curve. However, onus of these complications is on the programmer
and not the user. The only added complexity of fully adaptive
pushover is that a reasonable mass representation is required, as
indicated in Table 1 above.
6. The Model-Input Motion Application Domain
Experience gained by working on the developments previously
mentioned and taking stock of the experience reported in the
technical literature, indicates that there is a model-input motion
domain that is shared by static and dynamic in- elastic analysis.
This is schematically represented in Fig. 5. The boundaries of the
dynamic analysis region are receding on two fronts: model
complexity and strong- motion peculiarity. With regard to model
complexity, uniform distribution of mass, stiffness and strength
(with variations less than 10-15%) lead to static results in very
close agreement with dynamics. This is conditional on the
strong-motion be-
. ing "normal" or "usual", subject to the definition of the
latter two characteristics. On the other hand, if the strong-motion
record is of average duration (between about 10 and 30 s) and its
spectrum 'has high amplifications (in the normal range of 0.3-0.5
s) with no conspicuous near-source features (i.e. "normal" or
"usual"), the static results will be close to the dynamic analysis,
provided the model is not
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Do We Really Need inelastic Dynamic Analysis? 129
Fig. 5. Effect of' development of advanced static analysis on
model-input motion application domain.
highly irregular. Viewing the inelastic earthquake analysis
domain in the light of this framework:, aids in determining which
analysis is suited to which set of mo'del and strong-motion record
characteristics.
7 . The Answer
TO close, we do need dynamic analysis, but the "necessity
domain" is ever dimin- ishing. The boundaries of this domain are
receding under the attack of two distinct developments. The
horizontal boundary of "Structural Irregularity" in Fig. 5 is
receding due to the development of algorithms to update force
distributions, t ak- ing into account the level of irregularity of
mass, stiffness and most importantly strength. The vertical
boundary of "St rong-motion Peculiarity" is more difficult to push.
It is slo~vly receding under the at tack of spectrum scaling. This
is where new developments and ideas are most needed to take into
account strong-motion charac- teristics, especially duration,
frequency content and near-source features. Spectrum scaling is the
simplest approach, but it is unjustifiable and basically incorrect.
Application of "moving window discrete Fourier analysis" may
improve the static analysis, but by then there might not be a need
for static analysis. Knowing a prior2 if a higher mode .will
contribute from the start of the analysis would help, but inves-
tigating the structure a.ny further before analysis diminishes the
benefits of static analysis. Full:? adaptive pushover seems to have
entered a phase controlled by the "law of diminishing returns". A
breakthrough is needed, otherwise the "dynamic analysis necessity
domadinn will stand the test of time.
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Acknowledgement
T h e author would like to thank a number of exceptionally
talented researchers who worked with him on various aspects of
inelastic static and dynamic analysis over the past 15 years.
Special recognition is given to Drs. B. Izzuddin, P. Madas, B.
Broderick, A. Elghazouli, E. Martinez-Rueda, A. Mwafy, R. Pinho and
D. Lee. With regard to adaptive pushover, essential contributions
are due to Dr. R. Pinho, and Mr. V. Papanikolaou. However, the main
contribution is due to Mr. S. Antoniou.
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