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equation can be re- written as:
288
l -rM(^ag (7)
Akiyama (1985) showed that the elastic vibrational energy can be calculated by assuming that the
entire structure is reduced into a single-degree-of-freedom system, i e.,
where Vis the yield base shear and Wis the total seismic weight of the structure (W=Mg). Substituting
Eqn. 8 into Eqn. 7 and rearranging terms gives:
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NEW LATERAL FORCE DISTRIBUTION FOR PROPOSED DESIGN PROCEDURE
Inelastic dynamic analyses were conducted to determine the distribution of maximum story shears. The
nonlinear analysis program SNAP-2DX [Rai et al., 1996] was used to perform the analyses. The study
frame was subjected to four selected earthquake records (Lee and Goel, 2000). Fig. 4 shows the
example 5-bay, 9 story steel frame. The relative distributions of maximum story shears due to four
selected earthquake records and the UBC static story shears are shown in Fig. 5. The ratio of the
earthquake induced story shear at level / to that at the top level, n, is assumed to be of the form:
where V t and V n , respectively, are the static story shears at level / and at the top level as computed
from the design forces given by the UBC lateral force equations. The value of exponent b = 0.5 was
derived from many analyses using different types of structures following the strong column- weak
beam mechanism (Lee and Goel, 2000).
Using the static story shears, V l and V n , at level i and the top story provided by UBC formulas, the
factor can be written as:
w,h, (i - o.or) + 0.077*2
(ID