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For simplicity, a linear distribution of the lateral design forces has been generally used in the codes
However, many studies have shown that this distribution may not be applicable in the inelastic stage
and may underestimate the story shears. It can also be too conservative for the design of columns in the
performance based plastic design procedure. Moreover, this distribution does not satisfactorily
recognize the higher mode effects for high-rise building structures. In this study, a new distribution of
the lateral forces is presented and applied to a new performance based plastic design procedure. The
results of nonlinear static and nonlinear dynamic analyses of an example steel moment frame designed
by the new method are also presented and discussed.
MODIFIED ENERGY BALANCE EQUATION
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In the earlier study (Leelataviwat, 1998), the energy balance equation was written as:
E = E.+E p (1)
where E(= l/2MS^ is the elastic input energy, and E d and E p are the elastic and plastic components
of work required to push the structure monotonically up to the target drift. Based on studies by
Newmark and Hall (1982) and Uang (1994), Eqn. 5 can be modifies as:
7E = (E e + E p ) (2)
where 7 is a modification factor, which depends on the structural ductility factor ( ju & ) and the ductility
reduction factor ( R^),
Fig. 1 shows the relationship between the base shear ratio (C) and the drift ( A ), and Eqn. 2 can be
written as:
(3)
Using the expression for drifts ( A ), Eqn. 3 can be rewritten as:
where A tf and A inax from Fig. 1 are equal to R^ A v and // 4 A y , respectively. Substituting these terms in
Equation 8, the energy modification factor y can be determined as: