Page 170 - Dynamic Loading and Design of Structures

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other hand, the differences are much smaller when a mechanism involving primarily beam
hinging forms. Moreover, the increase in the ductility demands in the MDOF system is larger
for increased target ductility factors and for longer fundamental periods (i.e. for taller
buildings). The need therefore arises for modifying the (inelastic) design spectrum in the long
period range to remedy the previous situation. Newmark and Hall (1982) have suggested
lowering the exponent (k1 in eqns 4.16, 4.17) of the period dependent term giving spectral
accelerations in the long period range (T>1 sec) from 1 to ; this has been adopted by several
seismic codes but Krawinkler and Nassar (1992) have found that it is only valid for well-
designed structures (i.e. those forming beam mechanisms).

Code spectra
The design spectrum in Eurocode 8 is defined by eqns (4.13–4.17), with the following
modifications:

●the term is substituted by , where the so-called behaviour factor q is analogous to
the R-factor of eqn (4.19).
●the exponents k =1.0 and k =2.0 are replaced by and respectively;
1
2
●a cut-off value of for the design acceleration is introduced.
The introduction of the reduced kd exponents in combination with the cut-off of 0.2α g, results
in a substantial increase in the design forces for long period structures, such as tall buildings
or long span bridges. This is generally in line with the remarks made previously for such
structures, although no particular justification appears to exist for specifying a constant
minimum seismic force (the cut-off value).
Design spectra in the American codes are similarly derived from the corresponding elastic
spectra (i.e. factors similar to q are specified for reducing the elastic spectrum ordinates
and/or the elastic base shear). They are called response modification factors (R) in the
NEHRP [National Earthquake Hazard Reduction Program] Provisions (FEMA 1995, 1997a),
whereas they are referred to simply as the R coefficients in UBC. It is deemed that the term
response reduction factor (or force reduction factor) offers a clearer indication of the nature of
this factor, which plays a paramount role in seismic design, and is discussed in more detail in
the next section. Unlike EC8, the American UBC specifies a lower bound to the design base
shear equal to 90 per cent of the value used in the equivalent (static) lateral force procedure
(Section 4.3.5); this appears to be mainly due to historical reasons, as lateral force design has
long prevailed, whereas modal analysis was traditionally restricted to ‘special’ structures.
Similarly to EC8, the UBC specifies a minimum base shear (see Section 4.3.5), lower than the
EC8 one.

Force reduction factors
The force reduction factor can be defined as the ratio of the elastic strength demand (i.e. the
strength that would be required in the structure if it were to respond elasti-