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IBRACON Structures and Materials Journal • 2012 • vol. 5 • nº 6
S. H. C. Santos | S. S. Lima | A. Arai
Chilean and Argentinean standards). Only for the sake of exempli-
fication, in the Brazilian standard the seismic forces for the design
of structures with a “weak story” irregularity shall be multiplied by
an overstrength factor Ω
0
.
For regular and simple structures, all the standards allow for a
lateral force (static equivalent) method of analysis, in the cases
that the contribution of the fundamental mode in each horizontal
direction is preponderant in the dynamic response. All the stan-
dards provide also formulas for the approximate evaluation of the
fundamental periods of a structure. The use of two planar mod-
els, one for each horizontal direction, is typically allowed only for
regular structures.
All the standards allow also for the use of the modal response
spectrum analysis. In all the analyzed standards, the required
number of considered modes shall assure that at least 90% of the
total mass of the structure should be captured in each orthogonal
horizontal direction (except in the Argentinean code, that defines
that all modes with a contribution superior to 5% of the one cor-
responding the fundamental period should be considered). The
Venezuelan standard presents also a formula for explicitly define
the required number of modes. For the combination of the modal
components, the Complete Quadratic Combination (CQC) rule
is considered as the preferable one in almost all the standards
(excepting the Peruvian and Argentinean codes that define other
combination formulas). ASCE/SEI 7/10 indicates a limitation in the
structural periods obtained analytically, by comparing them with
periods obtained with approximate empirical evaluation formulas.
All the standards (excepting the Chilean code) allows also for lin-
ear time-history analysis, using some (at least three in all stan-
dards, excepting the Venezuelan and Brazilian codes, which don’t
define this point and the Peruvian code, that requires five) record-
ed or artificial time-histories matching the design response spec-
tra, applied simultaneously at least in the two horizontal directions.
ASCE/SEI 7/10 and Brazilian standards require the comparison
between the results obtained with the time history analysis with the
ones obtained with a spectral analysis.
Some codes (e.g. Eurocode 8) admit non-linear analysis in the
time domain, but as long as substantiated with respect to more
conventional methods, or even subjected to a review from an inde-
pendent team of experts (Ecuadorian code).
Some codes (e.g. Eurocode 8 and Venezuelan code) allow also for
non-linear static (pushover) analyses.
4. Numerical example
4.1 Considered numerical data
A simple and symmetrical building structure has been chosen as
an example for illustrating the comparison among the seismic stan-
dards. The building is rectangular in plan, with dimensions roughly
of 10.00m x 18.00m, as shown in Fig.3. The columns have trans-
versal section of 40cm x 100cm. A schematic view of the build-
ing, presented in Fig.4, shows the ten floors of the structure that
is 30m high. The total permanent weight to be considered in the
seismic analyses, for each of the ten floors is 1268.7 kN, which cor-
responds to a distributed area mass of roughly 0.7 t/m
2
.
In order to possibilitate the comparison among the several
standards, a particular location has been carefully chosen. It
The factor
I
can vary, for instance, between
I
= 0.6 (Chilean stan-
dard, provisory constructions) to
I
= 1.5 (Peruvian and other stan-
dards, essential constructions).
It is outside the scope of this paper to present and discuss the
design dimensioning rules defined by the several standards for the
different structural materials. It can be said that, generally, the par-
tial safety factors used in the standards for defining design load-
ing combinations from characteristic or nominal loads are taken
all equal to 1.0, applied to permanent, live and seismic loads. An
exception to this almost general rule is the Brazilian standard that
defines a design loading combination with a partial safety factor
1.2 for permanent loads combined with factors 1.0 applied to ac-
cidental and seismic load.
3.6 Seismic force-resisting systems and respective
response modification coefficients
All the analyzed standards recognize the impossibility of requiring
that the structures should behave in a purely elastic way. Under
seismic excitation, the structures are expected to behave in the
non-linear range, developing large deformations and dissipating a
large amount of energy. For this, the structures shall be designed
and detailed in order to assure the necessary capacity of energy
dissipation. As long as the necessary degree of ductility is assured,
it is possible to consider the transformation of the elastic spectra in
design spectra, in which the considered ductility is implied.
A consistent criterion for obtaining the response modification fac-
tors (reduction factors), as a function of the available ductility, is
only found in the Argentinean standard. The other standards define
the reduction factors as a function of the structural systems and of
the structural materials. The reduction factors are also expressed
as a function of the ductility classes (e.g., medium and high ductility
in the Eurocode 8 or ordinary, intermediate and special detailing in
the ASCE/SEI 7/10). The numerical value of these coefficients is
often empirically defined in the standards with basis in past experi-
ence and/or good engineering judgement.
It is outside of the scope of this paper to present a comprehen-
sive comparative analysis of the several modification coefficients
defined in the standards. Only for the sake of exemplification, in
the Brazilian standard, a response modification coefficient R=3 is
defined for concrete frames with usual detailing, for reducing the
elastic seismic forces to the design seismic forces that considers
the non-linear behaviour.
3.7 Structural irregularities and allowed
procedures for the seismic analysis
All the analyzed standards are strict in recommending, as stated
in item 4.2.1 of Eurocode 8, the following basic principles in the
conceptual design of a construction: structural simplicity, uniformity
and regularity in plan and in elevation, bi-directional and torsional
resistance and stiffness, diaphragmatic behaviour in the floor plans
and adequate foundation.
Irregularity in plan or elevation are punished by the standards,
that accordingly require more elaborated methods of analysis,
more stringent criteria for the consideration of design forces, etc.
Structural irregularity is more or less quantitatively defined in the
standards (e.g., no specific guidance in this point is given in the