Page 172 - Dynamic Loading and Design of Structures

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quantifying Rµ and Rs can be found elsewhere (Fischinger and Fajfar, 1994; Kappos, 1999).

These and other studies have indicated significant values for the overstrength component Rs
(at least 1.5) for both R/C and steel structures. This is particularly important from the design
point of view, since ductile detailing requirements can be relaxed for structures possessing
substantial overstrength.
The concept expressed by eqn (4.22) is not explicitly recognized in Eurocode 8.
Nevertheless, if the ratio of the EC8 elastic spectra of eqns (4.13–4.17) to the inelastic
(design) spectra resulting from the aforementioned modifications is calculated, the resulting
R-factor (eqn 4.19) is period dependent (i.e. R<q for both short and long period structures, and
R=q only for the intermediate period (from T to T ) structures).
B
C
Contrary to the EC8 approach, the American codes specify essentially period independent
values of the R factors, something that has been criticized in the past (Miranda and Bertero,
1994). Although a proposal has been made by SEAOC (1996) to include a two component
(R R ) reduction factor in the UBC, this has not been done in the 1997 edition, which,
µ s
however, does include a redundancy factor (ρ≤1.5), intended as a lower bound, below which a
penalty (an increase of up to 50 per cent) is applied with regard to seismic force levels in
structures lacking redundancy. Some other national codes have adopted expressions for R that
explicitly differentiate between the ductility and the overstrength component of R (Fischinger
and Fajfar, 1994).

Design displacements
In addition to the determination of the ‘inelastic’ forces expected in a structure, it is also
necessary to have an estimate of the inelastic displacements under the design and/or the
serviceability earthquake; these are typically required for checking that the code-specified
drift limits are not exceeded. Based on the previous discussion, it is reasonable to assume that
elastic and inelastic displacements are about the same (except for short period structures), and
calculate the latter by simply amplify-ing the (elastic) displacements, calculated for the
factored seismic loading (corresponding to Fel/R), by the reduction factor (R) used for forces.
This is indeed the recommended procedure in Eurocode 8: Under the serviceability
earthquake (inelastic) drifts are calculated as , where is the drift calculated on the
basis of the design seismic forces and v is a factor intended to account for the lower intensity
of the serviceability earthquake (for buildings v=2.0 to 2.5).
The corresponding procedure in the UBC (ICBO, 1997) is to estimate drifts under the
design earthquake as (i.e. the amplification factor for inelastic displacements is 30 per
cent lower than the reduction factor (R) for forces). Although the UBC background document
(SEAOC, 1996) claims that this is a better ‘average’ value of the inelastic drift, this is a point
of rather considerable controversy.