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Figure 1 Structural Idealized Response-Application Principle of Energy Conservation
(5)
According to Eqn. 5, the modification factor is a function of the ductility reduction factor and the
structural ductility factor Using different approaches, many investigators have attempted to estimate
the ductility reduction factor (R M ) and structural ductility factor (// 4 ) (Miranda and Bertero 1994). In
this study, the proposal of Newmark and Hall (1982) is used to estimate the ductility reduction factor
and the structural ductility factor.
The design input energy can be determined from the elastic design pseudo-acceleration spectra as
given in the building codes. In this study, the design is based on the UBC (1997) design spectrum
which, for elastic systems, is specified as:
A = ZlCg = ag (6)
where A is the design pseudo-acceleration, / is the importance factor, Z is the zone factor, C is the
elastic seismic coefficient, g is the acceleration due to gravity, and a = ZIC. The energy balance
. |W M.-2
- Wi ** 3
W\J n.= 4
\y *»s
Accln ; „ Velocity, **
Region "*["""* Displacement Regions
Period (sec)
Figure 2. Ductility reduction factors
proposed by Newmark and Hall (1982)
Figure 3. Modification factors for
energy equation versus period